Clothlike cell arrangements and belts for producing

Abstract

Papermaking belts and masks for papermaking belts having a pattern of cells that impart a clothlike appearance to a fibrous structure. Fibrous structures having a pattern of cells that impart a clothlike appearance.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 713,185, filed Oct. 29, 2024, and U.S. Provisional Application No. 63 / 700,114, filed Sep. 27, 2024, the entire disclosures of which are hereby incorporated by reference.FIELD

[0002] The present disclosure generally relates to fibrous structures comprising discrete elements situated in patterns, and more specifically to fibrous structures comprising discrete elements situated in patterns that emulate the organic, non-engineering, and irregular qualities of cloth. The present disclosure also generally relates to papermaking belts that are used in creating such fibrous structures.BACKGROUND

[0003] Fibrous structures, such as sanitary tissue products, are useful in everyday life in various ways. These products may be used as wiping implements for post-urinary and post-bowel movement cleaning (toilet tissue and wet wipes), for otorhinolaryngological discharges (facial tissue), and multi-functional absorbent and cleaning uses (paper towels). Retail consumers of such fibrous structures look for products with certain performance properties, for example softness, smoothness, strength, and absorbency. For fibrous structures provided in roll form (e.g., toilet tissue and paper towels), retail consumers also look for products with roll properties that indicate value and quality, such as higher roll bulk, greater roll firmness, and lower roll compressibility. Of further importance in today's retail environment are the consumer-desired aesthetics of the fibrous structures and the expectation they set for what the product may achieve in use. However, many times the independent goals of superior product performance (e.g., performance properties and / or roll properties) and consumer desired aesthetics are in contradiction to one another. Moreover, consumers limit the tasks they use fibrous tissue products for based on look, especially relative to the expectation that a durable woven textile such as a kitchen towel, dish cloth or bath towel sets even though a premium fibrous tissue may be capable of these tasks. For instance, the smoothness of a paper towel may depend on the wet-laid structure provided by the papermaking belt utilized during paper production and / or the emboss pattern applied during the paper converting process. But such papermaking-belt-provided structure and / or emboss may make the product visually unappealing and look too simple to have qualities of a durable woven textile to the consumer. Or a paper towel may be visually appealing and have more rugged features like durable woven textiles to the consumer through the papermaking-belt-provided structure and / or emboss but have an undesired level of smoothness, be thin, not flexible or not absorbent. Accordingly, manufacturers continually seek to make new fibrous structures with a combination of good performance and consumer-desired aesthetics through selection of material components, as well as selection of equipment and processes used in manufacturing the fibrous structures. Various knuckle and pillow patterns have been disclosed and marketed to achieve these desired properties. Applicants, however, have discovered knuckle and pillow patterns that create improved properties by using discrete knuckle (or discrete pillow) structures that distill the 3-dimensional aspects of woven textiles into 2-dimensional patterns for application to wet forming discrete fibers into substrates that mimic textiles in look and have premium function. The patterns comprise elements of irregularity in the cell shape, size, orientation, with regularity in the placement. The patterns comprise greater distance between isotropy surface autocorrelation peaks leaving it more difficult to perceive pattern repetition. Additionally, the patterns may induce in the fibrous substrates three dimensional surfaces with high periodicity that drives a consistent premium surface feel. These inventive cell perimeters, knuckles, pillows, cell clusters, and cell patterns result in fibrous structures that have desired and improved properties, including: improved cloth-like feel (Emtec TS7, TS750) with visual aspects of cloth (isotropy, period, and periodicity measures) while performing with premium level strength (Total Dry Tensile Strength), absorbency (CRT rate and SST rate), flexibility (plate stiffness, GM Flexural Rigidity) and thickness (caliper, Resilient Bulk).

[0004] The discussion of shortcomings and needs existing in the field prior to the present disclosure is in no way an admission that such shortcomings and needs were recognized by those skilled in the art prior to the present disclosure.SUMMARY

[0005] Various embodiments solve the above-mentioned problems and provide fibrous substrates that have desired aesthetics and properties, as well as methods and devices useful for producing such fibrous substrates themselves.

[0006] One embodiment relates to a fibrous substrate comprising a plurality of cells. The fibrous substrate may define a major coordinate plane. The plurality of cells may comprise at least a first cell and a second cell. The first cell may comprise a first perimeter defining a first shape and a first size, a first position relative to the major coordinate plane, and a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane. Similarly, the second cell may comprise a second perimeter defining a second shape and a second size, a second position relative to the major coordinate plane, and a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane. The first position and the second position may be substantially within a first row. The first row may comprise a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis. The longitudinal row axis may be oriented at a row angle relative to an axis of the major coordinate plane. The plurality of cells may define a fibrous substrate having a Fibrous Structure Texture Isotropy of less than about 84% and a Fibrous Structure Period (first Secondary Peak) of greater than about 4 mm. The plurality of cells may define a fibrous substrate having a Fibrous Structure Period (first Secondary Peak) of greater than about 12 mm. The plurality of cells may define a towel fibrous structure having a Fibrous Structure Period (first Secondary Peak) greater than about 7 mm. The plurality of cells may define a fibrous substrate having a Fibrous Structure Periodicity (first Secondary Peak) of greater than about 53% and a Fibrous Structure Period (first Secondary Peak) of greater than about 7 mm. The first shape and the second shape may be substantially the same. The first shape and the second shape may be substantially different. The first shape may be irregular. The second shape may be irregular. The first size and the second size may be substantially the same or may be substantially different. The first angle and the second angle may be substantially the same or may be substantially different. The first cell may abut the second cell, or the first cell may not abut the second cell. The row angle may be in a range of from about 0 to about 90 degrees. An axis of the major coordinate plane may be substantially aligned with a machine direction in which the fibrous substrate is produced or may be substantially aligned with a cross direction that is perpendicular to the machine direction. The plurality of cells may comprise a third cell. The third cell may comprise a third perimeter defining a third shape and a third size, a third position relative to the major coordinate plane, and a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane. The first position and the third position may be substantially within a second row. The first row and the second row may intersect or may not intersect. The first row and the second row may be continuous or discontinuous. The first cell may have from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary. The first cell may have from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.

[0007] One embodiment relates to a mask for a papermaking belt comprising a plurality of cells.

[0008] The mask may define a major coordinate plane. The plurality of cells may comprise at least a first cell and a second cell. The first cell may comprise a first perimeter defining a first shape and a first size, a first position relative to the major coordinate plane, and a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane. Similarly, the second cell may comprise a second perimeter defining a second shape and a second size, a second position relative to the major coordinate plane, and a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane. The first position and the second position may be substantially within a first row. The first row may comprise a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis. The longitudinal row axis may be oriented at a row angle relative to an axis of the major coordinate plane. The plurality of cells may define a tissue pattern having a Mask / Belt Period (first secondary peak) greater than about 7 mm and a Mask / Belt Percent Texture Isotropy greater than about 67%. The plurality of cells may define a fibrous structure pattern having a Mask / Belt Period (first secondary peak) greater than about 4 mm and a Mask / Belt Percent Texture Isotropy less than about 62%. The plurality of cells may define a fibrous structure pattern having a Mask / Belt Period (first secondary peak) greater than about 40 mm. The plurality of cells may define a tissue pattern having a Mask / Belt Period (first secondary peak) greater than about 13 mm. The plurality of cells may define a tissue pattern having a Mask / Belt period (third secondary peak) greater than about 13 mm. The first shape and the second shape may be substantially the same. The first shape and the second shape may be substantially different. The first shape may be irregular. The second shape may be irregular. The first size and the second size may be substantially the same or may be substantially different. The first angle and the second angle may be substantially the same or may be substantially different. The first cell may abut the second cell, or the first cell may not abut the second cell. The row angle may be in a range of from about 0 to about 90 degrees. An axis of the major coordinate plane may be substantially aligned with a machine direction in which the fibrous substrate is produced or may be substantially aligned with a cross direction that is perpendicular to the machine direction. The plurality of cells may comprise a third cell. The third cell may comprise a third perimeter defining a third shape and a third size, a third position relative to the major coordinate plane, and a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane. The first position and the third position may be substantially within a second row. The first row and the second row may intersect or may not intersect. The first row and the second row may be continuous or discontinuous. The first cell may have from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary. The first cell may have from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.

[0009] One embodiment relates to a papermaking belt comprising a plurality of cells. The papermaking belt may define a major coordinate plane. The plurality of cells may comprise at least a first cell and a second cell. The first cell may comprise a first perimeter defining a first shape and a first size, a first position relative to the major coordinate plane, and a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane. Similarly, the second cell may comprise a second perimeter defining a second shape and a second size, a second position relative to the major coordinate plane, and a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane. The first position and the second position may be substantially within a first row. The first row may comprise a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis. The longitudinal row axis may be oriented at a row angle relative to an axis of the major coordinate plane. The plurality of cells may define a tissue pattern having a Mask / Belt Period (first secondary peak) greater than about 7 mm and a Mask / Belt Percent Texture Isotropy greater than about 67%. The plurality of cells may define a fibrous structure pattern having a Mask / Belt Period greater than about 4 mm and a Mask / Belt Percent Texture Isotropy less than about 62%. The plurality of cells may define a fibrous structure pattern having a Mask / Belt Period greater than about 40 mm. The plurality of cells may define a tissue pattern having a Mask / Belt Period greater than about 13 mm. The plurality of cells may define a tissue pattern having a Mask / Belt Period (third secondary peak) greater than about 13 mm. The first shape and the second shape may be substantially the same. The first shape and the second shape may be substantially different. The first shape may be irregular. The second shape may be irregular. The first size and the second size may be substantially the same or may be substantially different. The first angle and the second angle may be substantially the same or may be substantially different. The first cell may abut the second cell, or the first cell may not abut the second cell. The row angle may be in a range of from about 0 to about 90 degrees. An axis of the major coordinate plane may be substantially aligned with a machine direction in which the fibrous substrate is produced or may be substantially aligned with a cross direction that is perpendicular to the machine direction. The plurality of cells may comprise a third cell. The third cell may comprise a third perimeter defining a third shape and a third size, a third position relative to the major coordinate plane, and a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane. The first position and the third position may be substantially within a second row. The first row and the second row may intersect or may not intersect. The first row and the second row may be continuous or discontinuous. The first cell may have from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary. The first cell may have from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.

[0010] These and other features, aspects, and advantages of various embodiments will become better understood with reference to the following description, figures, and claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The above-mentioned and other features and advantages of this disclosure, and the manner of attaining them, will become more apparent and the disclosure itself will be better understood by reference to the following description of non-limiting examples of the disclosure taken in conjunction with the accompanying drawings.

[0012] FIG. 1 is a representative papermaking belt of the kind useful to make the fibrous structures of the present disclosure.

[0013] FIG. 2 is a photograph of a portion of a paper towel product previously marketed by The Procter & Gamble Co.

[0014] FIG. 3 is a plan view of a portion of a mask pattern used to make the papermaking belt that may produce a paper towel like the one shown in FIG. 2.

[0015] FIG. 4 is a plan view of a conceptual cell that may represent a knuckle or a pillow of a fibrous structure or a knuckle-forming element or a pillow-forming region of a structuring layer of a papermaking belt or a mask that may be used to produce the structuring layer.

[0016] FIG. 5 is a plan view of a conceptual cell that may represent a knuckle or a pillow of a fibrous structure or a knuckle-forming element or a pillow-forming region of a structuring layer of a papermaking belt or a mask that may be used to produce the structuring layer.

[0017] FIG. 6A is a top view of a mask that may be used to produce a structuring layer on a papermaking belt like the one shown in FIG. 6B.

[0018] FIG. 6B is an isometric view of a structuring layer on a papermaking belt that includes a plurality of conceptual cells in the form of knuckle-forming elements as well as pillow-forming regions therebetween.

[0019] FIG. 7 is an isometric view of a fibrous structure that may be produced with the papermaking belt shown in FIG. 6, the fibrous structure comprising conceptual cells in the form of higher-density knuckles as well as lower-density pillows therebetween.

[0020] FIG. 8A is a top view of a mask that may be used to produce a structuring layer on a papermaking belt like the one shown in FIG. 8B.

[0021] FIG. 8B is an isometric view of a structuring layer on a papermaking belt that includes a plurality of conceptual cells in the form of pillow-forming regions as well as knuckle-forming elements therebetween.

[0022] FIG. 9 is an isometric view of a fibrous structure that may be produced with the structuring layer shown in FIG. 8, the fibrous structure comprising conceptual cells in the form of lower-density pillows as well as higher-density knuckles therebetween.

[0023] FIG. 10 is a plan view of a plurality of conceptual cells having different positions and rotations relative to a major coordinate plane.

[0024] FIG. 11 is a plan view showing positions of conceptual cells disposed substantially within intersecting rows.

[0025] FIG. 12 is a plan view showing positions of conceptual cells disposed substantially within continuous rows.

[0026] FIG. 13 is a plan view showing positions of conceptual cells disposed substantially within discontinuous rows.

[0027] FIG. 14 is a plan view showing positions of conceptual cells disposed substantially within discontinuous, non-aligned rows.

[0028] FIG. 15 is a plan view showing positions of conceptual cells disposed substantially within a variety of rows.

[0029] FIG. 16 is a plan view of a cell cluster comprising a plurality of conceptual cells.

[0030] FIG. 17 is a plan view of a clothlike pattern of cells.

[0031] FIG. 18 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 17.

[0032] FIG. 19 is a plan view of a clothlike pattern of cells.

[0033] FIG. 20 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 19.

[0034] FIG. 21 is a plan view of a clothlike pattern of cells.

[0035] FIG. 22 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 21.

[0036] FIG. 23 is a plan view of a clothlike pattern of cells.

[0037] FIG. 24 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 23.

[0038] FIG. 25 is a plan view of a clothlike pattern of cells.

[0039] FIG. 26 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 25.

[0040] FIG. 27 is a plan view of a clothlike pattern of cells.

[0041] FIG. 28 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 27.

[0042] FIG. 29 is a plan view of a clothlike pattern of cells.

[0043] FIG. 30 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 29.

[0044] FIG. 31 is a plan view of a clothlike pattern of cells.

[0045] FIG. 32 is a schematic representation of portion of the clothlike pattern of cells shown in FIG. 31.

[0046] FIG. 32 is a schematic representation of portion of the clothlike pattern of cells.

[0047] FIG. 33 is a schematic representation of portion of the clothlike pattern of cells.

[0048] FIG. 34 is a schematic representation of portion of the clothlike pattern of cells.

[0049] FIG. 35 is a schematic representation of portion of the clothlike pattern of cells.

[0050] FIG. 36 is a schematic representation of portion of the clothlike pattern of cells.

[0051] FIG. 37A is a schematic representation of method for achieving a clothlike pattern of cells.

[0052] FIG. 37 B is a schematic representation of method for achieving a clothlike pattern of cells.

[0053] FIG. 38 is a schematic representation of cells substantially within rows.

[0054] FIG. 39 is a schematic representation a repeat unit of cells.

[0055] FIG. 40 is a schematic representation of cell neighbors.

[0056] FIG. 41 is a schematic representation of cell neighbors.

[0057] FIG. 42 is a schematic representation of cell neighbors.

[0058] FIG. 43A is a plan view of a comparative pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 1.

[0059] FIG. 43B is a plan view of a comparative pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 2.

[0060] FIG. 43C is a plan view of a comparative pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 3.

[0061] FIG. 43D is a plan view of a comparative pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 4.

[0062] FIG. 43E is a plan view of a comparative pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 5.

[0063] FIG. 43F is a plan view of a comparative pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 6.

[0064] FIG. 43G is a plan view of an inventive pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 7.

[0065] FIG. 43H is a plan view of an inventive pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 8.

[0066] FIG. 43I is a plan view of an inventive pattern of cells examined using the Mask / Belt Isotropy Test Method in Example 9.

[0067] FIG. 44A is a plan view of a comparative pattern of cells examined according to the Total Pillow Perimeter Test Method, the Surface Void Volume Test Method, and the Emtec Test Method in Example 10.

[0068] FIG. 44B is a plan view of a comparative pattern of cells examined according to the Total Pillow Perimeter Test Method, the Surface Void Volume Test Method, and the Emtec Test Method in Example 11.

[0069] FIG. 44C is a plan view of an inventive pattern of cells examined according to the Total Pillow Perimeter Test Method, the Surface Void Volume Test Method, and the Emtec Test Method in Example 12.

[0070] FIG. 45A is a plan view of a pattern of cells.

[0071] FIG. 45B is a plan view of a pattern of cells.

[0072] FIG. 45C is a plan view of a pattern of cells.

[0073] FIG. 45D is a plan view of a pattern of cells.

[0074] FIG. 45E is a plan view of a pattern of cells.

[0075] FIG. 45F is a plan view of a pattern of cells.

[0076] FIG. 45G is a plan view of a pattern of cells.

[0077] FIG. 45H is a plan view of a pattern of cells.

[0078] FIG. 45I is a plan view of a pattern of cells.

[0079] FIG. 45J is a plan view of a pattern of cells.

[0080] FIG. 45K is a plan view of a pattern of cells.

[0081] FIG. 45L is a plan view of a pattern of cells.

[0082] FIG. 45M is a plan view of a pattern of cells.

[0083] FIG. 45N is a plan view of a pattern of cells.

[0084] FIG. 45O is a plan view of a pattern of cells.

[0085] FIG. 45P is a plan view of a pattern of cells.

[0086] FIG. 45Q is a plan view of a pattern of cells.

[0087] FIG. 45R is a plan view of a pattern of cells.

[0088] FIG. 45S is a plan view of a pattern of cells.

[0089] FIG. 45T is a plan view of a pattern of cells.

[0090] FIG. 45U is a plan view of a pattern of cells.

[0091] FIG. 45V is a plan view of a pattern of cells.

[0092] FIG. 45W is a plan view of a pattern of cells.

[0093] FIG. 45X is a plan view of a pattern of cells.

[0094] FIG. 45Y is a plan view of a pattern of cells.

[0095] FIG. 45Z is a plan view of a pattern of cells.

[0096] FIG. 45AA is a plan view of a pattern of cells.

[0097] FIG. 45AB is a plan view of a pattern of cells.

[0098] FIG. 45AC is a plan view of a pattern of cells.

[0099] FIG. 46 is a binary image for use in the Micro-CT Intensive Property Measurement Method.

[0100] FIG. 47A is a schematic representation of a pressure box and its components used in the Surface Void Volume Test Method.

[0101] FIG. 47B is a schematic representation of a pressure box and its components used in the Surface Void Volume Test Method.

[0102] FIG. 48 is a table showing test results obtained for masks or belts having the patterns associated the indicated figures.

[0103] FIG. 49 is a chart illustrating data from the table shown in FIG. 48, particularly the Mask / Belt percent isotropy vs period (first secondary peak).

[0104] FIG. 50 is a chart illustrating data from the table shown in FIG. 48, particularly the Mask / Belt percent isotropy vs period (third secondary peak).

[0105] FIG. 51 is a table showing test results obtained for fibrous structures having the patterns associated the indicated figures and commercially available comparative fibrous structures.

[0106] FIG. 52 is a chart illustrating data from the table shown in FIG. 51, particularly the Fibrous Structure percent isotropy vs period (first secondary peak).

[0107] FIG. 53 is a chart illustrating data from the table shown in FIG. 51, particularly the Fibrous Structure period (first secondary peak) vs periodicity (first secondary peak).

[0108] It should be understood that the various embodiments are not limited to the examples illustrated in the figures.DETAILED DESCRIPTIONIntroduction and Definitions

[0109] This disclosure is written to describe the invention to a person having ordinary skill in the art, who will understand that this disclosure is not limited to the specific examples or embodiments described. The examples and embodiments are single instances of the invention which will make a much larger scope apparent to the person having ordinary skill in the art. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by the person having ordinary skill in the art. It is also to be understood that the terminology used herein is for the purpose of describing examples and embodiments only, and is not intended to be limiting, since the scope of the present disclosure will be limited only by the appended claims.

[0110] All the features disclosed in this specification (including any accompanying claims, abstract, and drawings) may be replaced by alternative features serving the same, equivalent, or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. The examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to the person having ordinary skill in the art and are to be included within the spirit and purview of this application. Many variations and modifications may be made to the embodiments of the disclosure without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure. For example, unless otherwise indicated, the present disclosure is not limited to particular materials, reagents, reaction materials, manufacturing processes, or the like, as such may vary. It is also to be understood that the terminology used herein is for purposes of describing particular embodiments only and is not intended to be limiting. It is also possible in the present disclosure that steps may be executed in different sequence where this is logically possible.

[0111] All numeric values are herein assumed to be modified by the term “about,” whether or not explicitly indicated. The term “about” generally refers to a range of numbers that one of skill in the art would consider equivalent to the recited value (for example, having the same function or result). In many instances, the term “about” may include numbers that are rounded to the nearest significant figure.

[0112] In everyday usage, indefinite articles (like “a” or “an”) precede countable nouns and noncountable nouns almost never take indefinite articles. It must be noted, therefore, that, as used in this specification and in the claims that follow, the singular forms “a,”“an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a support” includes a plurality of supports. Particularly when a single countable noun is listed as an element in a claim, this specification will generally use a phrase such as “a single.” For example, “a single support.”

[0113] Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit (unless the context clearly dictates otherwise), between the upper and lower limit of that range, and any other stated or intervening value in that stated range, is encompassed within the disclosure. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the disclosure, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the disclosure.

[0114] Fibrous structures such as sanitary tissue products, including paper towels, bath tissues and facial tissues are typically made in “wet-laid” papermaking processes. In such papermaking processes, a fiber slurry, usually wood pulp fibers, is deposited onto a forming wire and / or one or more papermaking belts such that a nascent fibrous structure is formed. After drying and / or bonding the fibers of the nascent fibrous structure together, a fibrous structure is formed. Further processing of the fibrous structure may then be carried out after the papermaking process. For example, the fibrous structure may be wound on the reel and / or ply-bonded and / or embossed. As further discussed herein, visually distinct features may be imparted to the fibrous structures in different ways. In a first method, the fibrous structures may have visually distinct features added during the papermaking process. In a second method, the fibrous structures may have visually distinct features added during the converting process (i.e., after the papermaking process). Some fibrous structure examples disclosed herein may have visually distinct features added only during the papermaking process, and some fibrous structure examples may have visually distinct features added both during the papermaking process and the converting process.

[0115] Regarding the first method, a wet-laid papermaking process may be designed such that the fibrous structure has visually distinct features “wet-formed” during the papermaking process. Any of the various forming wires and papermaking belts utilized may be designed to leave physical, three-dimensional features within the fibrous structure. Such three-dimensional features are well known in the art, particularly in the art of “through air drying” (TAD) papermaking processes, with such features often being referred to in terms of “knuckles” and “pillows.”

[0116] “Knuckles,” or “knuckle regions,” are typically relatively high-density regions that are wet-formed within the fibrous structure (extending from a pillow surface of the fibrous structure) and correspond to the knuckles of a papermaking belt, i.e., the filaments or resinous structures that are raised at a higher elevation than other portions of the belt. The knuckles of a papermaking belt may also be referred to as knuckle-forming elements.

[0117] “Relatively high density” as used herein means a portion of a fibrous structure having a density that is higher than a relatively low-density portion of the fibrous structure. Relatively high density may be about 0.5 g / cm3 or greater, whereas a relatively low density may be less than about 0.4 g / cm3. Likewise, “pillows,” or “pillow regions,” are typically relatively low-density regions that are wet-formed within the fibrous structure and correspond to the relatively open regions between or around the knuckles of the papermaking belt. These relatively open regions between or around the knuckle-forming elements of a paper-making belt may also be referred to as pillow-forming regions, pillow regions, or deflection conduit. The pillow regions may form a pillow surface of the fibrous structure from which the knuckle regions extend.

[0118] “Relatively low density” as used herein means a portion of a fibrous structure having a density that is lower than a relatively high-density portion of the fibrous structure.

[0119] Further, the knuckles and pillows wet-formed within a fibrous structure may exhibit a range of basis weights and / or densities relative to one another, as varying the size of the knuckles or pillows on a papermaking belt may alter such basis weights and / or densities. A fibrous structure (e.g., sanitary tissue products) made through a TAD papermaking process as detailed herein is known in the art as “TAD paper.”

[0120] In the description herein, the terms “knuckles” or “knuckle regions,” or the like may be used to reference either the raised portions of a papermaking belt or the densified, raised portions wet-formed within the fibrous structure made on the papermaking belt (i.e., the raised portions that extend from a surface of the fibrous structure), and the meaning should be clear from the context of the description herein. Likewise, “pillows” or “pillow regions” or the like may be used to reference either the portion of the papermaking belt between or around knuckles (also referred to herein and in the art as “deflection conduits” or “pockets”), or the relatively uncompressed regions wet-formed between or around the knuckles within the fibrous structure made on the papermaking belt, and the meaning should be clear from the context of the description herein. Knuckles or pillows may each be either continuous or discrete, as described herein.

[0121] A “structuring layer” refers to a patterned structure that may be integral with or affixed to a papermaking belt. The structuring layer may provide knuckle-forming elements that are elevated relative to a supporting layer upon which the structuring layer is affixed. The structuring layer may also provide pillow-forming regions in the spaces between the knuckle-forming elements.

[0122] A “mask” refers to a material, precisely patterned or shaped to selectively block or allow the passage of specific wavelengths or types of radiation. It enables the controlled exposure of radiation-sensitive materials or processes, resulting in the formation of desired patterns, structures, or features on the underlying substrate. The mask may comprise a plurality printed portions that may be spaced apart. The mask may be used in producing structuring layers on papermaking belts that would create fibrous structures that have discrete knuckles and continuous / substantially continuous pillows or continuous / substantially continuous knuckles and discrete pillows.

[0123] The term “discrete” as used herein with respect to knuckles and / or pillows means a portion of a papermaking belt or fibrous structure that is defined or surrounded by, or at least mostly defined or surrounded by, a continuous / substantially continuous knuckle or pillow. The term “continuous / substantially continuous” as used herein with respect to knuckles and / or pillows means a portion of a papermaking belt or fibrous structure network that fully, or at least mostly, defines or surrounds a discrete knuckle or pillow. Further, the substantially continuous member may be interrupted by macro patterns formed in the papermaking belt, as disclosed in U.S. Pat. No. 5,820,730 issued to Phan et al. on Oct. 13, 1998.

[0124] Knuckles and pillows in paper towels and bath tissue may be visible to the retail consumer of such products. The knuckles and pillows may be imparted to a fibrous structure from a papermaking belt at various stages of the papermaking process (i.e., at various consistencies and at various unit operations during the drying process) and the visual pattern generated by the pattern of knuckles and pillows may be designed for functional performance enhancement as well as to be visually appealing. Such patterns of knuckles and pillows may be made according to the methods and processes described in U.S. Pat. No. 6,610,173, issued to Lindsay et al. on Aug. 26, 2003, or U.S. Pat. No. 4,514,345 issued to Trokhan on Apr. 30, 1985, or U.S. Pat. No. 6,398,910 issued to Burazin et al. on Jun. 4, 2002, or US Pub. No. 2013 / 0199741; published in the name of Stage et al. on Aug. 8, 2013. The Lindsay, Trokhan, Burazin and Stage disclosures describe belts that are representative of papermaking belts made with cured resin on a woven reinforcing member, of which aspects of the present disclosure are an improvement. But in addition, the improvements detailed herein may be utilized as a fabric crepe belt as disclosed in U.S. Pat. No. 7,494,563, issued to Edwards et al. on Feb. 24, 2009, or U.S. Pat. No. 8,152,958, issued to Super et al. on Apr. 10, 2012, as well as belt crepe belts, as described in U.S. Pat. No. 8,293,072, issued to Super et al on Oct. 23, 2012. When utilized as a fabric crepe belt, a papermaking belt of the present disclosure may provide the relatively large, recessed pockets and sufficient knuckle dimensions to redistribute the fiber upon high impact creping in a creping nip between a backing roll and the fabric to form additional bulk in conventional wet-laid press processes. Likewise, when utilized as a belt in a belt crepe method, a papermaking belt of the present disclosure may provide the fiber enriched dome regions arranged in a repeating pattern corresponding to the pattern of the papermaking belt, as well as the interconnected plurality of surrounding areas to form additional bulk and local basis weight distribution in a conventional wet-laid process. In addition, the improvements detailed herein, including the formation of discrete cells comprising irregular cells arranged in substantially aligned rows, may be utilized as an uncreped through air dried (UCTAD) belt. UCTAD (un-creped through air drying) is a variation of the TAD process in which the sheet is not creped but rather dried up to 99% solids using thermal drying, removed from the structured fabric, and then optionally calendered and reeled. U.S. Pat. No. 6,808,599 describes an uncreped through air dried process. U.S. Pat. No. 10,610,063 describes an uncreped through air dried product made using a belt. In addition, the improvements herein may be utilized as an ATMOS belt. The ATMOS process has been developed by the Voith company and marketed under the name ATMOS. The process / method and paper machine system has several variations, but all involve the use of a structured fabric in conjunction with a belt press. This process is described in numerous patent publications including U.S. Pat. Nos. 7,510,631, 7,686,923, 7,931,781, 8,075,739, and 8,092,652. In addition, the improvements herein may be utilized as an NTT belt. The NTT process has been developed by the Metso company and marketed under the name NTT. The NTT process includes an extended press nip where the sheet is transferred from a press felt onto a texturing belt. Examples of texturing belts used in the NTT process may be viewed in International Publication Number WO 2009 / 067079 A1 and US Patent Application Publication No. 2010 / 0065234 A1. As said, all such processes of this paragraph may be utilized to form the discrete cells of the present disclosure.

[0125] “Cell” may refer to an element on a papermaking belt or to an element of a fibrous structure. For example, “cell” may refer to a knuckle-forming element or a pillow-forming region of a mask on a papermaking belt. Additionally, “cell” may also refer to a knuckle or a pillow of a fibrous structure. Since the shape and orientation of elements on the papermaking belt are transferred to the fibrous structure, it is convenient to provide simplified illustrations of “cells” with the understanding that the cells shown may represent knuckle-forming elements, pillow-forming regions, knuckles, or pillows.

[0126] “Irregular” may refer to a characteristic of a feature or a pattern of features, such as a single cell or a group of cells. In this context, “irregular” indicates that cells are not uniform in shape, size, and / or arrangement. “Irregular” may mean that the individual cell or pattern of cells may lack symmetry, having no axis about which the cell or the pattern is mirrored.

[0127] Aspects of this disclosure involve “clothlike patterns.” These patterns may be incorporated into fibrous materials. Papermaking belts, and the masks used to create them, may utilize clothlike patterns to transfer those patterns onto fibrous materials during the papermaking process. In simpler terms, the patterns on belts used to make products like tissue, towels, and napkins may have and impart clothlike textures. A “clothlike pattern” might resemble the randomness found in woven textiles, showing little to no repetition of shapes or predictable symmetry at different levels of scale. While terms like “limited repetition”, “limited symmetry”, “lacking an axis of mirroring” are used, this doesn't exclude patterns with large-scale repetition or symmetry, like woven or braided designs. These patterns may still exhibit limited repetition and symmetry when viewed at a smaller, more localized level. For example, at a localized-level clothlike pattern may appear to be organic, non-engineered, and irregular, but might have an overall pattern that is repetitive and / or symmetrical. Especially at a local level, a clothlike pattern may appear to flow in a way that feels spontaneous, featuring uneven or asymmetrical forms and spacing and may avoid mirrored or repetitive unit cells. The cells that make up a clothlike pattern may vary in size, shape, texture, or rotation, creating an overall impression of imperfection and fluidity, akin to the irregularities found in a textile towel. Thus, particularly at a local level, a clothlike pattern exudes an unstructured, handcrafted quality rather than precise, calculated order.

[0128] “Isotropy” refers to the uniformity or consistency of a pattern in all directions. The opposite of isotropy is “anisotropy,” where a pattern varies depending on the direction. Isotropy for a surface texture may be quantified by measuring and comparing its properties in different directions across the surface. The degree of isotropy may be given as a “texture isotropy percentage” as measured according to the Mask / Belt Isotropy Test Method and the Fibrous Structure Isotropy Test Method described herein. Isotropic surfaces have a texture isotropy percentage of 100%. Anisotropic surfaces have a texture isotropy percentage of 0%.

[0129] The Mask / Belt Isotropy Test Method and the Fibrous Structure Isotropy Test Method may also be used to measure the Isotropy, Periodicity, Period, and Angle of a pattern using image analysis, between the central peak and the four highest secondary autocorrelation peaks. To provide a general overview, the periodicity is the ratio between the height of the highest point of the secondary lobe and the height of the highest point of the central lobe and may be expressed as percentage. The nearer the periodicity value is to 100%, the more periodic the surface. The period is the horizontal distance between the highest point of the central lobe and the highest point of a secondary lobe and may be expressed as a linear dimension such as mm. The angle is the direction of the straight line going through the XY-coordinates of the highest point of the central lobe and the XY-coordinates of the highest point of the secondary lobe and may be expressed in degrees. The Mask / Belt Isotropy Test Method may be used to calculate these values for any mask or belt pattern. The Fibrous Structure Isotropy Test Method may be used to calculate these values for any fibrous structure. For some fibrous structures, like those that are wet formed, creped at a high impact angle and positive draw between Yankee and reel, and / or dry converted without emboss the Mask / Belt and Fibrous Structure isotropy measures will be similar. For substrates that are less formed to the structuring belt by low molding, are creped with a low impact angle and / or run at negative Yankee to reel draw, and / or dry converted with emboss the measures may be different Thus, each pattern referenced herein may have a percent isotropy (%) as well as a periodicity (%), a period (mm), an angle (deg) relative to the central node and subsequent first, second, third or fourth secondary autocorrelation peak for the mask / belt pattern and the fibrous substrate.

[0130] Based on these definitions, it would appear that achieving a clothlike pattern would require a low degree of isotropy or a low texture isotropy percentage or a short period as measured by the Mask / Belt Isotropy Test Method and / or the Fibrous Structure Isotropy Test Method. As will be discussed, however, it has been unexpectedly discovered that a “clothlike” pattern and premium level functional product may be achieved with a pattern having a relatively high texture isotropy percentage, if that pattern also exhibits a relatively high period and optionally high periodicity.Papermaking Belt

[0131] An example of a papermaking belt structure of the general type useful in the present disclosure and made according to the disclosure of U.S. Pat. No. 4,514,345 is shown in FIG. 1. As shown, the papermaking belt 10 may comprise a woven reinforcing member 11 formed by one or more woven filaments 12, as is known in the art of papermaking belts, for example resin coated papermaking belts. A structuring layer 20 may be affixed to or integral with the papermaking belt 10. The structuring layer 20 may comprise one or more knuckles or knuckle-forming elements 21. The knuckles 21 may comprise cured resin elements 21a. The knuckles 21 may be disposed on the woven reinforcing member 11. The knuckles 21 may be spaced apart to define one or more pillow-forming regions 22. The specific papermaking belt 10 shown in FIG. 1 includes discrete knuckles 21d and a continuous deflection conduit, or pillow region 22c. The discrete knuckles 20d may be wet-form densified knuckles within the fibrous structure made thereon; and, likewise, the continuous deflection conduit, i.e. pillow region 22c, may be wet-form a continuous pillow region within the fibrous structure made thereon. The knuckles 21 may be arranged in a pattern described with reference to an X-Y coordinate plane 60, having an x-axis 60x and a y-axis 60y, which may be defined relative to the papermaking belt 10, relative to the structuring layer 20, or relative to a fibrous structure 30 produced thereon. A distance between knuckles 21 in at least one of the X or Y directions may vary according to the examples disclosed herein. For clarity, a fibrous structure's visually distinct knuckle(s) and pillow(s) that are wet-formed in a wet-laid papermaking process are different from, and independent of, any further structure added to the fibrous structure during later, optional, converting processes (e.g., one or more embossing processes).Fibrous Structures

[0132] The fibrous structures of the present disclosure may be single-ply or multi-ply and may comprise cellulosic pulp fibers. Other naturally-occurring and / or non-naturally occurring fibers may also be present in the fibrous structures. In some examples, the fibrous structures may be wet-formed and through-air dried in a TAD process, thus producing TAD paper. The fibrous structures may be marketed as single- or multi-ply sanitary tissue products.

[0133] The fibrous structures detailed herein will be described in the context of paper towels and bath tissue, and in the context of a papermaking belt comprising cured resin on a woven reinforcing member. However, the scope of disclosure is not limited to paper towels (scope also includes, for example, other sanitary tissues such as napkins and facial tissue) and includes other known processes that impart the knuckles and pillow patterns described herein, including, for example, the fabric crepe and belt crepe processes described above, and modified as described herein to produce the papermaking belts and paper as detailed herein.

[0134] In general, examples of the fibrous structures may be made in a process utilizing a papermaking belt that has a pattern of cured resin knuckles on a woven reinforcing member of the type described in reference to FIG. 1. The resin pattern may be dictated by a patterned mask having opaque regions and transparent regions. The transparent regions may permit curing radiation to penetrate and to cure the resin, while the opaque regions may prevent the radiation from curing portions of the resin. Once curing is achieved and the patterned mask is removed, the uncured resin may be washed away to leave a pattern of cured resin that may be substantially identical to the mask pattern. The cured resin portions may be the knuckles of the papermaking belt, and the areas between / around the cured resin portions may be the pillows or deflection conduits of the belt. Thus, the mask pattern is replicated in the cured resin pattern of the papermaking belt, which may be essentially replicated again in the fibrous structure made on the papermaking belt. Therefore, in describing the fibrous structures' patterns of knuckles and pillows herein, a description of the patterned mask may serve as a proxy. One skilled in the art will understand that the dimensions and appearance of the patterned mask are essentially identical to the dimensions and appearance of the papermaking belt made through utilization of the mask. One skilled in the art will further understand that the dimensions and appearance of the wet-laid fibrous structure made on the papermaking belt may also be essentially identical to the dimensions and appearance of the patterned mask. Further, in processes that use a papermaking belt that are not made from a mask, the dimensions and appearance of the papermaking belt may also be imparted to the fibrous structure, such that the dimensions of features of such papermaking belt may also be measured and characterized as a proxy for the dimensions and characteristics of the fibrous structure produced thereon. Intensity of molding and creping on the paper machine may shrink or expand certain aspects of the dimensions, and dry converting transformations like embossing may add another dimension of texture however the overall plurality of cells pattern will be substantially similar.

[0135] After completion of the papermaking process, a second way to provide visually distinct features to a fibrous structure is through embossing. Embossing is a well-known converting process in which at least one embossing roll having a plurality of discrete embossing elements extending radially outwardly from a surface thereof may be mated with a backing, or anvil, roll to form a nip in which the fibrous structure may pass such that the discrete embossing elements compress the fibrous structure to form relatively high density discrete elements (“embossed regions”) in the fibrous structure while leaving an uncompressed, or substantially uncompressed, relatively low density continuous, or substantially continuous, network (“non-embossed regions”) at least partially defining or surrounding the relatively high density discrete elements.

[0136] Embossed features in paper towels and bath tissues may be visible to the retail consumer of such products. Such patterns are well known in the art and may be made according to the methods and processes described in US Pub. No. US 2010-0028621 A1 in the name of Byrne et al. or US 2010-0297395 A1 in the name of Mellin, or U.S. Pat. No. 8,753,737 issued to McNeil et al. on Jun. 17, 2014. For clarity, such embossed features may originate during the converting process, and are different from, and independent of, the pillow and knuckle features that are wet-formed on a papermaking belt during a wet-laid papermaking process as described herein.

[0137] FIG. 2 illustrates a portion of a sheet on a roll 1 of fibrous substrate 30, such as a sanitary tissue or a paper towel, previously marketed by The Procter & Gamble Co. as BOUNTY® paper towels. While the actual papermaking belt and mask used to make the fibrous substrate 30 shown in FIG. 2 are not shown, it is to be appreciated that a papermaking belt of the general type shown in FIG. 1 was employed. As shown, fibrous substrate 30 exhibits a pattern of knuckles 31 which were formed by discrete cured resin knuckles 21d on a papermaking belt 10.

[0138] The pattern of knuckles 31 and pillows 32 is considered the “wet-formed” background pattern, and the pattern of embossments 33 overlaid thereon is considered “dry-formed”. Thus, the pattern of knuckles and pillows and the embossments together give the paper towel its visual appearance. The previously marketed sanitary tissue products, an example of which is shown in FIG. 2, will be used to contrast the newly disclosed examples of fibrous structures detailed herein. Thus, the newly disclosed examples of fibrous structures detailed herein are an improvement over such previously marketed sanitary tissue products, with some of the improvements described below.Conceptual Cells and Cell Patterns

[0139] Again, as used herein, the term “cell” may be used to represent a discrete element of a mask, a papermaking belt, a structuring layer on a papermaking belt, or a fibrous structure such as a sanitary tissue or a paper towel. Thus, FIG. 3 may be viewed as a representation of a structuring layer 20, a fibrous substrate 30, or mask 100 that may be used to produce a structuring layer 20. When viewed as a representation of a structuring layer 20 used to produce a fibrous substrate 30, the cells 40 may represent knuckle-forming regions or pillow-forming regions. When viewed as a representation of a fibrous substrate 30, the cells 40 may represent knuckles or pillows. When viewed as a mask, the cells may represent transparent portions or opaque portions.

[0140] The method of identifying one or more cells from a fibrous sample may be determined according to the Micro-CT Intensive Property Method herein. In FIG. 3, the schematic representation of cells 40 may be considered representations of a discrete element of one or more transparent portions of a mask, one or more knuckles on a papermaking belt, or one or more knuckles in a fibrous structure. But the examples detailed herein are not limited to one method of making, so the term “cell” may refer to a discrete feature such as a raised element, a dome-shaped element or knuckle formed by belt or fabric creping on a fibrous structure, for example. The term “cell” may also represent discrete transparent or opaque portions of a mask, a discrete deflection conduit in a papermaking belt, or a discrete relatively low density / basis weight portion of a fibrous structure.

[0141] Referring again to FIG. 2, a fibrous substrate 30 may exhibit a pattern of knuckles 31 which were formed by discrete cured resin knuckles 21d on a papermaking belt 10. These knuckles may correspond to the black areas, referred to as cells 40 of the mask 100 shown in FIG. 3. As more clearly seen in the mask of FIG. 3, the cell 40 shape and orientation are both constant and the cells are ordered in straight rows 51x, 51y. One set of rows 51x is oriented in a direction that is parallel to an X-axis of the mask 100 (i.e., in an X-direction) and one set of rows 51y is oriented in a direction that is parallel to an Y-axis of the mask 100 (i.e., in a Y-direction). In other words, all cells 40 of the mask / fibrous structure will be a member of a row 51x that is oriented in an X-direction and will also be a member of a row 51y that is oriented in a Y-direction.

[0142] Any portion of the pattern of FIG. 3 that is black may represent a transparent region of the mask, which permits radiative curing (such as via UV-light) of curable resin to form a knuckle on the papermaking belt. The inverse is also possible, in which black portions may represent opaque regions of the mask, which do not permit curing of a curable resin. This convention avoids unnecessary duplication of figures. After the mask is removed, the uncured resin is ultimately washed away to form a deflection conduit or a pillow-forming region on the papermaking belt. When a fibrous structure is made on the papermaking belt, the fibers will wet-form into the deflection conduit or pillow-forming region to form a relatively low-density pillow 22 within the fibrous structure. Again, it is to be appreciated, however, that FIG. 3 may also represent the inverse.

[0143] Generally, the fibrous structures illustrated herein either exhibit a structure of discrete pillows and a continuous / substantially continuous knuckle region, or a structure of discrete knuckles and a continuous / substantially continuous pillow region. However, for every example described or illustrated herein, the inverse of such structure is also contemplated. In other words, if a structure of discrete knuckles and a continuous / substantially continuous pillow region is shown, an inverse similar structure of continuous / substantially continuous knuckles and discrete pillows is also contemplated. Moreover, in regard to the papermaking belts, as may be understood by the description herein, the inverse relationship may be achieved by inverting the black and white (or, more generally, the opaque and transparent) portions of the mask used to make the belt that is used to make the fibrous structure. This inverse relation (black / white) may apply to all patterns of the present disclosure, although all fibrous structures / patterns of each category are not illustrated for brevity. Some specific papermaking belts and the process of making them are described in further detail below.Fibrous Structure Properties

[0144] In one example, a fibrous structure of the present disclosure has a pattern of knuckles and pillows imparted to it by a papermaking belt having a corresponding pattern of knuckle-forming elements and pillow-forming regions that provides for superior product performance over known fibrous structures and is visually appealing to a retail consumer.

[0145] In another example, a fibrous structure of the present disclosure has a pattern of knuckles and pillows imparted to it by a papermaking belt having a corresponding pattern of knuckle-forming elements and pillow-forming regions, as well as an emboss pattern, which together provide for an overall visual appearance that is appealing to a retail consumer.

[0146] In another example, a fibrous structure of the present disclosure has a pattern of knuckles and pillows imparted to it by a papermaking belt having a corresponding pattern of knuckle-forming elements and pillow-forming regions, as well as an emboss pattern, which together provide for an overall visual appearance that is appealing to a retail consumer and exhibit superior product performance over known fibrous structures.Clothlike Cell Patterns

[0147] There is a substantial opportunity in the market to develop paper towels and other fibrous substrates that possess heightened cloth-like attributes. This opportunity arises from the observation that while consumers appreciate the convenience and disposability of paper products, they often underestimate their full potential for performance and versatility. By enhancing the softness, absorbency, visual appearance and resilience of paper towels and bath tissue to more closely resemble cloth, manufacturers may showcase the untapped capabilities of these products and elevate their perceived value, so that tasks traditionally reserved for cloth towels, such as cleaning up large spills and scrubbing are attempted or less sheets of textured bath tissue are formed into an implement because the consumer trusts that the soft, strong, flexible and visually reassuring implement may hold up to wiping. To improve the product performance properties and / or aesthetics of the previously and currently marketed sanitary tissue products new patterns were created for the shape of pillows, knuckles, cells, perimeters, cell clusters, and cell neighborsCells Useful for Clothlike Cell Patterns

[0148] FIGS. 4 and 5 are plan views of a conceptual cell 40. The conceptual cell 40 may represent a portion of a papermaking belt 10 such as a knuckle-forming element 21 or a pillow-forming region 22 of a structuring layer 20. The conceptual cell 40 may represent a knuckle 31 or a pillow 32 of a fibrous structure 30. The conceptual cell 40 may also represent a transparent portion 102 or an opaque portion 104 of a mask 100 that may be used to produce a structuring layer 20 on a papermaking belt 10. A major coordinate plane 60 may be defined relative to the papermaking belt 10, the structuring layer 20, the mask 100, or the fibrous structure 30, as appropriate for the context. The major coordinate plane 60 may comprise an x-axis 60x and a y-axis 60y. The cell 40 may have a position 42 on the papermaking belt 10, the structuring layer 20, the mask 100, or the fibrous structure 30. The position 42 of the cell 40 may define its location on the major coordinate plane 60. The position 42 of the cell 40 may be at a centroid C of a shape 45 defined by a perimeter 44 of the cell. The “centroid” of an irregularly shaped object is the point that represents the center of mass of the object. It is the point at which a cutout of the object would balance on a pin. The cell 40 may also have a size 46 that may be defined by the area 44a within the perimeter 44.

[0149] A minor coordinate system 41 may be centered on the position 42 of the cell 40 and, as will be discussed hereinafter with respect to FIG. 10, may be useful to compare the relative rotation of cells 40 relative to the major coordinate system 60. The minor coordinate system 41 may comprise an x-axis 41x and a y-axis 41y. The cell 40 may be oriented at an angle 43 relative to the major coordinate system. The angle 43 may be measured between an axis of the minor coordinate system 41, such as y-axis 41y and an axis of the major coordinate system 60, such as y-axis 60y. The angle 43 may be about 0 degrees to about 180 degrees, 10 degrees to about 170 degrees, or about 15 degrees to about 165 degrees, or about 30 degrees to about 150 degrees, or about 45 degrees to about 135 degrees, or about 60 degrees to about 120 degrees, or about 75 degrees to about 105 degrees, or about 90 degrees. The rows 51 may optionally intersect at an intersection region 53.

[0150] A boundary 47 may be defined at a radius 48 from the position 42 of the cell 40. In order to qualify as a “neighboring cell” or “cell neighbor” another cell 40 must have a perimeter 44 that at least partially extends across the boundary 47 toward the position 42 of the cell 40. The radius 48 may be dimensioned such that the area 47a within the boundary 47 is from about 100% to about 500%, or about 125% to about 475%, or about 150% to about 450%, or about 175% to about 425%, or about 200% to about 400%, or about 225% to about 375%, or about 250% to about 350%, or about 225% to about 325%, or about 300% of the area 44a within the perimeter 44 of the cell 40. Referring to FIG. 5, each cell 40 may have maximum dimension 49 extending from a first point 49a on the perimeter 44 to a second point 49b on the perimeter 44 along a line extending through the centroid C of the cell 40 and thereby intersecting the position 42. The maximum dimension 49 is defined as the longest such line that may be drawn from points on the perimeter 44 of the cell 40 through the centroid of the cell 40. A cell 40 may have any number of neighboring cells. For example, a cell 40 may have from 0 to 4, or 0 to 6, or 0 to 12, or 1 to 11, or 2 to 10, or 3 to 9, or 4 to 8, or 5 to 7, or 6 neighboring cells.

[0151] The cell may have a uniform (solid) or nonuniform (not solid) structure. For example, as shown in FIG. 4, the perimeter 44 of the cell 40 may surround a uniform structure. The uniform structure may be a knuckle-forming element 21 or a pillow-forming region 22 of a structuring layer 20 or a papermaking belt 10 or may be a transparent portion 102 or an opaque portion 104 of a mask 100 used to make a structuring layer 20. The uniform structure may be a knuckle 31 or a pillow 32 of a fibrous structure 30. On the other hand, as shown in FIG. 5, the perimeter 44 of the cell 40 may surround a nonuniform structure. The nonuniform structure may comprise a knuckle-forming element 21 and a pillow-forming region 22 of a structuring layer 20 or papermaking belt 10 or may be a transparent portion 102 or an opaque portion 104 of a mask 100 used to make a structuring layer 104. The nonuniform structure may comprise a knuckle 31 and a pillow 32 of a fibrous structure 30. These variations are difficult to convey in a 2-D image, thus FIG. 6-9 are also provided.

[0152] FIG. 6A is a top view of a mask 100 that may be used to produce a structuring layer 20 on a papermaking belt 10. The mask 100 may comprise conceptual cells 40 in the form of transparent portions 102 and / or in the form of opaque portions 104.

[0153] FIG. 6B is an isometric view of a structuring layer 20 on a papermaking belt 10 that includes a plurality of conceptual cells 40 in the form of knuckle-forming elements 21 as well as pillow-forming regions 22 therebetween. The knuckle-forming elements 21 correspond to the transparent portions 102 of the mask 100 shown in FIG. 6A, indicating that these knuckle-forming elements 21 may have been formed by passing radiation through the transparent portions 102 to cure a resin on the papermaking belt 10. Uncured portions of the resin that were beneath the opaque portions 104 of the mask 100 may have been washed away to leave the pillow-forming regions 22.

[0154] FIG. 7 is an isometric view of a fibrous structure 30 that may be produced with the structuring layer 20 shown in FIG. 6, the fibrous structure 30 comprising conceptual cells 40 in the form of higher-density knuckles 31 as well as lower-density pillows 32 therebetween. It is to be understood that FIG. 7 is only a conceptual, schematic representation; the crisp edges and corners shown in FIG. 7 would typically be more rounded providing a smoother transition between the knuckles 31 and the pillows 32.

[0155] FIG. 8A is a top view of a mask 100 that may be used to produce a structuring layer 20 on a papermaking belt 10. The mask 100 may comprise conceptual cells 40 in the form of transparent portions 102 and / or in the form of opaque portions 104.

[0156] FIG. 8B is an isometric view of a structuring layer 20 on a papermaking belt 10 that includes a plurality of conceptual cells 40 in the form of pillow-forming regions 22 as well as knuckle-forming elements 21 therebetween. The knuckle-forming elements 21 correspond to the transparent portions 102 of the mask 100 shown in FIG. 8A, indicating that these knuckle-forming elements 21 may have been formed by passing radiation through the transparent portions 102 to cure a resin on the papermaking belt 10. Uncured portions of the resin that were beneath the opaque portions 104 of the mask 100 may have been washed away to leave the pillow-forming regions 22.

[0157] FIG. 9 is an isometric view of a fibrous structure 30 that may be produced with the structuring layer 20 shown in FIG. 8, the fibrous structure 30 comprising conceptual cells 40 in the form of higher-density knuckles 31 as well as lower-density pillows 32 therebetween. It is to be understood that FIG. 9 is only a conceptual, schematic representation; the crisp edges and corners shown in FIG. 9 would typically be more rounded providing a smoother transition between the knuckles 31 and the pillows 32.

[0158] FIG. 10 is a plan view of a plurality 400 of conceptual cells 40a, 40b, 40c having different positions and rotations relative to a major coordinate plane 60 that may be defined by a papermaking belt 10, a structuring layer 20, a mask 100, or a fibrous structure 30. The major coordinate plane 60 may comprise an x-axis 60x and a y-axis 60y. The first cell 40a may have a first minor coordinate system 41a comprising a first x-axis 411x and a first y-axis 411y, centered on a first position 42a of the first cell 40a. The first cell 40a may comprise a first perimeter 44a having a first shape 45a and a first size 46a. The first cell 40a may be oriented at a first angle 43a relative to the major coordinate plane 60. The first angle 43a may be measured between an axis, such as the first y-axis 411y, of the first minor coordinate system 41a of the first cell 40a and an axis, such as the y-axis 60y, of the major coordinate plane 60. Similarly, the second cell 40b may have a second minor coordinate system 41b comprising a second x-axis 421x and a second y-axis 421y, centered on a second position 42b of the second cell 40b. The second cell 40b may comprise a second perimeter 44b having a second shape 45b and a second size 46b. The second cell 40b may be oriented at a second angle 43b relative to the major coordinate plane 60. The second angle 43b may be measured between an axis, such as the second y-axis 421y, of the second minor coordinate system 41b of the second cell 40b and an axis, such as the y-axis 60y, of the major coordinate plane 60. The second perimeter 44b of the second cell 40b may abut the first perimeter 44a of the first cell 40a at an abutment region 52. Finally, the third cell 40c may have a third minor coordinate system 41c comprising a third x-axis 431x and a third y-axis 431y, centered on a third position 42c of the third cell 40c. The third cell 40c may comprise a third perimeter 44c having a third shape 45c and a third size 46c. The third cell 40c may be oriented at a third angle 43c relative to the major coordinate plane 60. The third angle 43c may be measured between an axis, such as the third y-axis 431y, of the third minor coordinate system 41c of the third cell 40c and an axis, such as the y-axis 60y, of the major coordinate plane 60. As shown the cells 40a, 40b, 40c have the same shapes 45a, 45b, 45c and the same sizes 46a, 46b, 46c, but different angles 43a, 43b, 43c relative to the major coordinate plane 60. It is to be appreciated that other variations are possible, such as different shapes, different sizes or same angles and combinations therein.Groupings of Cells Useful for Clothlike Cell Patterns

[0159] FIG. 11 is a plan view showing positions 42a, 42b, 42c, 42d, 42e, 42f, 42g of conceptual cells 40 disposed substantially within one or more rows 51. Each row 51 may have a longitudinal row dimension 56 and a lateral row dimension 57 perpendicular to the longitudinal row dimension 56. The longitudinal row dimension 56 may be longer than the lateral row dimension 57. Each row 51 may have a longitudinal row axis 54 substantially parallel to the longitudinal row dimensions 56 and a lateral row axis 55 substantially parallel to the lateral row dimension 57. The longitudinal row axis 54 may be disposed at a row angle 58 relative to a major coordinate plane 60. The major coordinate plane 60 may comprise an x-axis 60x and a y-axis 60y and may be defined by a papermaking belt 10, a structuring layer 20, a mask 100, or a fibrous substrate 30. An axis of the major coordinate plane 60 may, but need not, align with a machine direction MD corresponding to a direction in which a fibrous substrate 30 is formed. Additionally, or alternatively, an axis of the major coordinate plane 60 may, but need not, align with a cross direction CD that is perpendicular to the machine direction MD. For example, the longitudinal row axis 54 may be disposed at a row angle 58 relative to a y-axis of the major coordinate plane 60, which may be substantially aligned with a machine direction MD. The row angle 58 may be about 0 degrees to about 180 degrees, 0 degrees to about 180 degrees, or about 15 degrees to about 165 degrees, or about 30 degrees to about 150 degrees, or about 45 degrees to about 135 degrees, or about 60 degrees to about 120 degrees, or about 75 degrees to about 105 degrees, or about 90 degrees. The rows 51 may optionally intersect at an intersection region 53.

[0160] The longitudinal row dimension 56 may be any dimension or length. The lateral row dimension 57 may also be any dimension or alternatively may be limited based on the maximum dimension 49 of cells 40 within the row 51. For example, the lateral row dimension 57 may be in a range of from about 25% to about 500% 50% to about 475%, or about 75% to about 450%, or about 100% to about 425%, or about 125% to about 400%, or about 150% to about 375%, or about 175% to about 350%, or about 200% to about 325%, or about 225% to about 300%, or about 250% to about 275% of the maximum dimension 49 of any cell 40 with a position 42 substantially within the row 51. It is to be appreciated that a row 51 may contain cells of varying sizes and shapes, in which case the maximum dimension 49 refers to the largest cell 40.

[0161] FIG. 12 is a plan view showing positions 42a, 42b, 42c of conceptual cells 40a, 40b, 40c disposed substantially within continuous rows 51a, 51b. “Continuous rows” abut each other and have at least one axis substantially aligned. For example, continuous rows may abut each other along their longitudinal row dimensions or along the lateral row dimensions and may substantially align with each other along their longitudinal row axes or along their lateral row axes. The lateral row dimensions and / or the longitudinal row dimensions of continuous rows may be the same or different. As shown in FIG. 12, each of the continuous rows 51a, 51b may comprise a longitudinal row axis 54a, 54b, which may be substantially aligned. The continuous rows 51a and 51b also abut at a continuous row abutment region 59 along their respective lateral row dimensions 57a, 57b. FIG. 13 is a plan view showing positions 42a, 42b, 42c of conceptual cells 40a, 40b, 40c disposed substantially within discontinuous rows 51a, 51b. FIG. 14 is a plan view showing positions 42a, 42b, 42c of conceptual cells 40a, 40b, 40c disposed substantially within discontinuous, non-aligned rows 51a, 51b. FIG. 15 is a plan view showing positions 42a, 42b, 42c of conceptual cells disposed substantially within a variety of rows 51a, 51b, 51c, 51d, 51e, 51f, 51g.

[0162] FIG. 16 is a plan view of a cell cluster 70 comprising a plurality of conceptual cells 40. As used herein, the term “cell cluster” may refer to a group of cells. At least some of the cells 40 that make up the cluster may abut each other at one or more abutment regions 52. Like an individual cell 40, a cell cluster 70 may have a perimeter 74, having a shape 75 and a size 76. The shape 75 may be any shape and may be regular or irregular. The size 76 may be defined as the area encompassed by the perimeter. The cell cluster 70 may have a centroid C and a minor coordinate system 71 centered on the centroid C. The cell cluster 70 may also have a position 72 corresponding with the centroid C and defining a location of the cell cluster 70 with respect to a major coordinate system 60 defined relative to a papermaking belt, a mask, or a fibrous structure 30. The major coordinate system 60 may comprise an x-axis 60x and a y-axis 60y. The minor coordinate system 71 may be positioned at an angle 73 relative to the major coordinate system 60. The angle 73 may be measured between an axis of the minor coordinate system 71, such as y-axis 71y and an axis of the major coordinate system 60, such as y-axis 60y. The angle 73 may be about 0 degrees to about 180 degrees, 0 degrees to about 180 degrees, or about 15 degrees to about 165 degrees, or about 30 degrees to about 150 degrees, or about 45 degrees to about 135 degrees, or about 60 degrees to about 120 degrees, or about 75 degrees to about 105 degrees, or about 90 degrees.Exemplary Clothlike Cell Patterns

[0163] FIGS. 17, 19, 21, 23, 25, 27, 29, 31, 33, 34, 35, and 36 are a plan views of various clothlike patterns 50 of cells 40. Typically, such illustrations represent a mask, but it is to be appreciated that each of these patterns 50 may represent the structure of a mask for a paper making belt or the structure of a fibrous structure formed by such a mask. Each of FIGS. 17, 19, 21, 23, 25, 27, 29, 31, 33, 34, 35, and 36 may represent a mask in which case it is to be appreciated the shaded portions may represent pillow-forming regions and the unshaded portions may represent knuckle-forming elements, or the shaded portions may represent knuckle-forming elements, and the unshaded portions may represent pillow-forming regions. When such a figure represents a mask, it is more common for the shaded portions to represent pillow-forming regions and the unshaded portions to represent knuckle-forming elements, but it is to be appreciated that the inverse is also intended to be represented. FIGS. 17, 19, 21, 23, 25, 27, 29, 31, 33, 34, 35, and 36 may also represent a fibrous structure in which case it is to be appreciated the shaded portions may represent pillows and the unshaded portions may represent knuckles, or the shaded portions may represent knuckles, and the unshaded portions may represent pillows. When such a figure represents a fibrous structure, it is more common for the shaded portions to represent pillows and the unshaded portions to represent knuckle, but it is to be appreciated that the inverse is also intended to be represented.

[0164] FIG. 18 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 17. This pattern 50 may include a plurality of conceptual cells 40. As already explained above with respect to FIGS. 17, 19, 21, 23, 25, 27, and 29, each conceptual cell may represent a knuckle, a pillow, a knuckle-forming region, or a pillow forming region. The cells 40 may have an irregular perimeter 44 and lack an axis of symmetry. Some of the cells 40 may abut other cells 40 at an abutment region 52. The perimeters 44 of some cell neighbors may merge. One or more cell clusters 70 may be present. As illustrated previously in FIG. 15, the cells 40 may also be aligned in rows.

[0165] FIG. 20 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 19. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. Each of cells 40 may have a position 42. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51.

[0166] FIG. 22 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 21. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. The perimeters 44 of the cells 40 may have a variety of shapes 45 and sizes 46. For example, cell 40a has a first perimeter 44a having a first size 45a and a first shape 46a, while cell 40b has a second perimeter 44b having a second size 45b and a second shape 46b. The first size 45a may be larger than the second size 45b. The first shape 46a may be different than the second shape 46b. Although a specific example is illustrated, it is to be appreciated that a first size 45a of a first cell 40a may be the same as, substantially the same as, larger than, or smaller than the second size 45b of a second cell 40b. Similarly, it is to be appreciated that the first shape 46a of a first cell 40a may be the same as, substantially the same as, or different than the second shape 46b of a second cell 40b. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51.

[0167] FIG. 24 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 23. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. The perimeters 44 of the cells 40 may have a variety of shapes 45 and sizes 46. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51.

[0168] FIG. 26 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 25. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. The perimeters 44 of the cells 40 may have a variety of shapes 45 and sizes 46. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51.

[0169] FIG. 28 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 27. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. The perimeters 44 of the cells 40 may have a variety of shapes 45 and sizes 46. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51. Some of the cells 40 may be grouped into cell clusters 70. Each cell cluster 70 may have a position 72. The positions 72 of at least some of the cell clusters 70 may be substantially aligned in one or more rows 51.

[0170] FIG. 30 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 29. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. The perimeters 44 of the cells 40 may have a variety of shapes 45 and sizes 46. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51. Some of the cells 40 may be grouped into cell clusters 70. Each cell cluster 70 may have a position 72. The positions 72 of at least some of the cell clusters 70 may be substantially aligned in one or more rows 51.

[0171] FIG. 32 is a schematic representation of portion of the clothlike pattern 50 of cells 40 shown in FIG. 31. The cells 40 may have an irregular perimeter 44 and the cells 40 may abut other cells 40 at one or more abutment regions 52. The perimeters 44 of the cells 40 may have a variety of shapes 45 and sizes 46. The positions 42 of at least some of the cells 40 may be substantially aligned in one or more rows 51.Achieving Clothlike Patterns with a Combination of High Isotropy and High Period Length

[0172] Without wishing to be bound by theory, it is believed that a woven textile may have an overall texture that is relatively uniform, but that the textile may have a clothlike appearance if the individual features that make up the texture are non-uniform. Various embodiments may attempt to mimic such a configuration.

[0173] As already explained, “isotropy” refers to the uniformity or consistency of a pattern in all directions and a “clothlike pattern” requires a certain degree of randomness, showing little to no repetition of shapes or predictable symmetry. It might appear, therefore, that achieving a clothlike pattern would require a low degree of isotropy or a low texture isotropy percentage as measured by the Mask / Belt Isotropy Test Method or the Fibrous Structure Isotropy Test Method. This is generally true, but it has been unexpectedly discovered, however, that a “clothlike” pattern may also be achieved with a pattern having a relatively high degree of isotropy as measured by the Mask / Belt Isotropy Test Method or the Fibrous Structure Isotropy Test Method, if that pattern also exhibits a relatively high period as measured by the Mask / Belt Isotropy Test Method or the Fibrous Structure Isotropy Test Method. The “relatively high texture isotropy percentage” as measured by the Mask / Belt Isotropy Test Method or the Fibrous Structure Isotropy Test Method may be in a range of about 50% to about 100%, or about 55% to about 95%, or about 60% to about 90%, or about 65% to about 85%, or about 70% to about 80%, or about 75% or greater than 60% or greater than 70%. The “relatively high period” as measured by the Mask / Belt Isotropy Test Method or the Fibrous Structure Isotropy Test Method may be in a range of from about 5 mm to about 100 mm, or about 10 mm to about 95 mm, or about 15 mm to about 90 mm, or about 20 mm to about 85 mm, or about 25 mm to about 80 mm, or about 30 mm to about 75 mm, or about 35 mm to about 70 mm, or about 40 mm to about 65 mm, or about 45 mm to about 60 mm, or about 50 mm to about 55 mm, or greater than about 7 mm or greater than about 13 mm. It is to be appreciated that a “clothlike” pattern may be achieved with a pattern having a combination of any of these relatively high degrees of isotropy and any of these relatively high periods.

[0174] More generally, various aspects contemplate fibrous structures having a clothlike appearance, wherein the fibrous structures have a degree of isotropy, a periodicity, and / or a period, as measured by the Fibrous Structure Isotropy Test Method, and as specified herein.

[0175] A fibrous structure according to various aspects may have a percentage of isotropy (%), as measured by the Fibrous Structure Isotropy Test Method, in a range of 10% to 100%, or 2% to 95%, or 3% to 90%, or 4% to 85%, or 5% to 84%, or 6% to 83%, or 7% to 82%, or 8% to 81%, or 9% to 80%, or 10% to 79%, or 11% to 78%, or 12% to 77%, or 13% to 76%, or 14% to 75%, or 15% to 74%, or 16% to 73%, or 17% to 72%, or 18% to 71%, or 19% to 70%, or 20% to 69%, or 21% to 68%, or 22% to 67%, or 23% to 66%, or 24% to 65%, or 25% to 64%, or 26% to 63%, or 27% to 62%, or 28% to 61%, or 29% to 60%, or 30% to 59%, or 31% to 58%, or 32% to 57%, or 33% to 56%, or 34% to 55%, or 35% to 54%, or 36% to 53%, or 37% to 52%, or 38% to 51%, or 39% to 50%, or 40% to 49%, or 41% to 48%, or 42% to 47%, or 43% to 46%, or 44% to 45%, or less than 84%, or less than 82%, or less than 80%.

[0176] A fibrous structure according to various aspects may have a periodicity (%), as measured by the Fibrous Structure Isotropy Test Method, in a range of 50% to 100%, or 51% to 99%, or 52% to 98%, or 53% to 97%, or 54% to 96%, or 55% to 95%, or 56% to 94%, or 57% to 93%, or 58% to 92%, or 59% to 91%, or 60% to 90%, or 61% to 89%, or 62% to 88%, or 63% to 87%, or 64% to 86%, or 65% to 85%, or 66% to 84%, or 67% to 83%, or 68% to 82%, or 69% to 81%, or 70% to 80%, or 71% to 79%, or 72% to 78%, or 73% to 77%, or 74% to 76%, or greater than 53%, or greater than 56, or greater than 58%.

[0177] A fibrous structure according to various aspects may have a period (mm), as measured by the Fibrous Structure Isotropy Test Method, in a range of greater than 4 mm, or greater than 6 mm, or greater than 8 mm, or greater than 10 mm, or greater than 12 mm, or from 4 mm to 60 mm, or 5 mm to 59 mm, or 6 mm to 58 mm, or 7 mm to 57 mm, or 8 mm to 56 mm, or 9 mm to 55 mm, or 10 mm to 54 mm, or 11 mm to 53 mm, or 12 mm to 52 mm, or 13 mm to 51 mm, or 14 mm to 50 mm, or 15 mm to 49 mm, or 16 mm to 48 mm, or 17 mm to 47 mm, or 18 mm to 46 mm, or 19 mm to 45 mm, or 20 mm to 44 mm, or 21 mm to 43 mm, or 22 mm to 42 mm, or 23 mm to 41 mm, or 24 mm to 40 mm, or 25 mm to 39 mm, or 26 mm to 38 mm, or 27 mm to 37 mm, or 28 mm to 36 mm, or 29 mm to 35 mm, or 30 mm to 34 mm, or 31 mm to 33 mm.

[0178] Similarly, various aspects contemplate belts or masks for producing fibrous structures having a clothlike appearance, where the belts or masks have a degree of isotropy, a periodicity, and / or a period, as measured by the Mask / Belt Isotropy Test Method, and as specified herein.

[0179] A mask or a belt according to various aspects may have a percentage of isotropy (%), as measured by the Mask / Belt Isotropy Test Method, in a range of 66% to 100%, or 67% to 99%, or 68% to 98%, or 69% to 97%, or 70% to 96%, or 71% to 95%, or 72% to 94%, or 73% to 93%, or 74% to 92%, or 75% to 91%, or 76% to 90%, or 77% to 89%, or 78% to 88%, or 79% to 87%, or 80% to 86%, or 81% to 85%, or 82% to 84%, or greater than 66%, or greater than 68%, or greater 70%

[0180] A mask or a belt according to various aspects may have a periodicity (%), as measured by the Mask / Belt Isotropy Test Method, in a range of 5% to 99%, or 10% to 98%, or 15% to 97% or greater than 40%, or greater than 50%, or greater than 60%.

[0181] A mask or a belt according to various aspects may have a period (mm), as measured by the Mask / Belt Isotropy Test Method, in a range of greater than 4 mm, or greater than 6 mm, or greater than 8 mm, or greater than 10 mm, or greater than 13 mm, or from 4 mm to 60 mm, or 5 mm to 59 mm, or 6 mm to 58 mm, or 7 mm to 57 mm, or 8 mm to 56 mm, or 9 mm to 55 mm, or 10 mm to 54 mm, or 11 mm to 53 mm, or 12 mm to 52 mm, or 13 mm to 51 mm, or 14 mm to 50 mm, or 15 mm to 49 mm, or 16 mm to 48 mm, or 17 mm to 47 mm, or 18 mm to 46 mm, or 19 mm to 45 mm, or 20 mm to 44 mm, or 21 mm to 43 mm, or 22 mm to 42 mm, or 23 mm to 41 mm, or 24 mm to 40 mm, or 25 mm to 39 mm, or 26 mm to 38 mm, or 27 mm to 37 mm, or 28 mm to 36 mm, or 29 mm to 35 mm, or 30 mm to 34 mm, or 31 mm to 33 mm.

[0182] It has been unexpectedly discovered that increasing the isotropy increased the identical features in all directions but simultaneously increasing the period length expanded the distance between isotropy nodes. The term “isotropy node” refers to a specific, autocorrelation region within a larger pattern. This means that the properties and characteristics of this region appear largely the same regardless of the direction from which they are observed or measured. There will be a primarily autocorrelation node and subsequent nodes and these nodes may be arranged in a periodic or repeating manner. Thus, various embodiments provide a unique combination of overall uniformity created by repeating clusters of non-uniform cells. In other words, the overall texture is uniform as is expected in a woven textile, yet the elements making up the texture (cells, orientation, rotation, placement) are non-uniform, as is generated in woven textiles because of the mobility of the tufts or flexibility of the fabric. Additionally, it was unexpectedly discovered that in a molded discrete fiber substrate such patterns do not compromise strength, absorbency, or thickness in a soft and visually appealing substrate. Usually uniformity increases homogeneity of molding, which decreases the driving force for water to move between small pores and large, which ultimately results in lesser absorbency. In contrast non-uniformity usually compromises the bonding network of discrete fibers thus result in less strength, inconsistent molding for thickness and a topically and visually heterogenous surface which is less soft (due to the inconsistencies) and looks messy. According to various embodiments, increasing isotropy and period length between nodes (all indicators of similar-ness) with non-uniform (non-similar) elements may result in a non-engineered clothlike visual with a substrate that functions, feels good, and looks like a woven textile.

[0183] Additionally, it was surprisingly discovered that in the wet formed and optionally dry converted fibrous substrate the varied 3-dimensional surface topology enhanced by molding and creping becomes more clothlike without sacrificing strength, absorbency or softness when periodicity and period length increase. The similarity in node height indicated by increasing periodicity drives homogeneity while the increasing period drive heterogeneity. Without being bound by theory, this contrast captures the organized spontaneity of woven textiles and drive premium product characteristics of strength, absorbency and softness.Method for Producing Clothlike Patterns

[0184] An additional need exists to convert existing structuring belt designs into designs that will have and will produce a clothlike pattern. The current landscape includes structuring belts with a woven grid pattern or topically applied designed patterns that are engineered and regular. The cells and patterns are generally homogenous. Some heterogeneity may be achieved by modulating spacing, size or orientation of cells, by creating intricate many layered weaves, by tiling variously sized or shaped cells, or by applying a large widely spaced badge over a regular pattern. These techniques for introducing heterogeneity all rely on regular repeats, mirroring and / or straight walled elements. The resulting patterns are easy to produce, but generally result in homogenous, engineered looking product. Importantly, they do not look like textiles that, while having a woven grid structure at the 2-D level (X-Y), have an organic variability and movement in the 3rd dimension (Z) and a 4th (time). For example, a terry towel loop may bend and flex in 360 degrees to add an irregular aspect to the regular grid. Thus, various aspects of the present invention provide methods for converting such patterns into clothlike patterns that visually convey the “regular irregularity” that is inherent with textiles or produce the function that comes with the 3-dimensional variability ability to respond to consumer implement needs (wiping, conforming, scrubbing). These methods translate the 3-Dimensional capability of a woven textile—a base grid, with z-direction irregularity from threads & loops that is macroscopically polyplanar—to a 2-dimension macroscopically monoplanar wet formed non-woven made with discrete fibers. The non-woven substrate takes on 3-dimensional aspects that are responsive to consumer use and look and function more like a woven textile.

[0185] It has been discovered that one solution for translating 3-dimensional qualities that change with the 4th dimension of time and use into a 2-dimensional forming pattern was to capture the different 3-dimensional states across the 4-dimensional dimensions and to distill the constrained non-regularity into a 2-dimensional pattern that could then be formed to create a macroscopically mono-planar 3-dimensional surface. Distilling poly-planar textile shapes into wet molded monoplanes may comprise adding a third dimension within the x-y plane of the structuring belt pattern.

[0186] It was surprisingly discovered that inducing a lack of mirror axis into the cells provides this 3rd vector in the X-Y dimensions—the unexpected irregularity of the non-engineered shape provides a dynamic visual that suggests movement and depth and creates auxiliary molding regions to enhance function.

[0187] It was also surprisingly discovered that combining 5 aspects of patterning (shape, irregularity within shape, rotation, size, and spacing) may induce a 3rd vector in the X-Y dimensions—the unexpected irregularity of the non-engineered pattern provides a dynamic visual that suggests movement and depth and creates auxiliary molding regions to enhance function.

[0188] Further, it was surprisingly discovered that providing irregular perimeters having texture and roughness into the cells provides this 3rd vector in the X-Y dimensions—the unexpected irregularity of the non-engineered shape provides a dynamic visual that suggests movement and depth and creates auxiliary molding regions to enhance function. For example, FIGS. 31, 33, 34, and 35, are schematic representations of exemplary portions of various clothlike patterns 50 of cells 40 having irregular perimeters 44 comprising protrusions and recesses.

[0189] Additionally, it was surprisingly discovered that placing the augmented cells within rows tends to constrain the irregularity so that the resulting pattern is not a pile of shapes without meaning and undirected wet formed molding. Rather, the constraint may provide a network of familiarity for visual cues and allow for fiber alignment during formation that drive premium strength, softness and thickness even though it is composed of nonuniform cells.

[0190] FIG. 37A is a schematic representation of a method 80 of making a structuring belt pattern may comprise a step 81 of providing a first cell 801 having a perimeter 802, having an original shape 803, the original shape 803 having an axis of symmetry 804. The method 80 may comprise a step 82 of imparting at least one or more imperfections 805 to a perimeter 802 of the first cell 801 to modify the original shape 803 and to give the first cell 801 a modified shape 806a. The method 80 may comprise a step 83 of placing the first cell 801 next to a second cell 807 having the original shape 803 to form a structuring belt pattern 808. The first cell 801 and the second cell 802 may have substantially the same orientations. The method 80 may further comprise a step 84 of reorienting the first cell 801 to cause the first cell 801 and the second cell 802 to have different orientations. The method 80 may comprise a step 85 of imparting at least one or more imperfections 805 to a perimeter 802 of the second cell 807 to modify the original shape 803 and to give the second cell 807 a modified shape 806b, which may be the same or different as the modified shape 806a of the first cell 801. The method 80 may further comprise a step 86 of placing additional cells 809 in a regular arrangement 810. Additionally, or alternatively, the method 80 may further comprise a step 87 of placing additional cells 809 in a regular arrangement 811. Additionally, or alternatively any combination of steps 82, 83, 84, 85, 86 and 87 may be employed.

[0191] FIG. 37B is a schematic representation of method 80 for achieving a clothlike pattern of cells. A first pattern of cells 50a comprising a first plurality of cells 400a may be a starting point in the method 90. Alternatively, the method 90 may comprise creating a pattern of cells. The pattern of cells may comprise cells having an axis of symmetry. The first plurality of cells 400a may comprise cells having a blocky, highly-engineered, highly-uniform shape, resembling, for example linked dominos. A first step 91 of the method 90 may comprise rounding the corners of all or some of the first plurality of cells 400a to produce a second pattern of cells 50b comprising a second plurality of cells 400b. The second plurality of cells 400b may have asymmetric cells shown. A second step 92 of the method 90 may comprise rotating all or some of the second plurality of cells 400b to produce a third pattern of cells 50c comprising a third plurality of cells 400c. The third plurality of cells 400c may exhibit an irregular orientation, such that an axis of their minor coordinate system (as shown, for example, in FIG. 5) is at an angle relative to an axis of a major coordinate system defined by a papermaking belt, a structuring layer of a papermaking belt, a mask, or a fibrous substrate. One or more of the cells in the third plurality of cells 400c may be oriented at the same or different angles. A third step 93 of the method 90 may comprise placing cells with cell neighbors all or some of the third plurality of cells 400c to produce a fourth pattern of cells 50d comprising a fourth plurality of cells 400d. The fourth plurality of cells 400d may exhibit irregular cell clusters (as shown, by way of non-limiting example, in FIG. 16, 18, 26, 28, or 30). The fourth plurality of cells 400d may still exhibit uniform links 95. Thus, a fourth step 94 of the method 90 may comprise replacing at least some of the uniform links 95 with additional cell neighbor to produce a fifth pattern of cells 50d comprising a fifth plurality of cells 400e. The second through the fifth pattern of cells 50d exhibit clothlike appearance, strength, softness and flexibility. For example, fifth pattern of cells 50d may exhibit a period greater than 7 mm and a texture isotropy percentage greater than 50.0%.Other Properties

[0192] Any of the fibrous structures described herein may have any or all of a variety of additional properties. These additional properties may make the fibrous structures more commercially desirable to consumers. It is to be appreciated that the values given for these properties are only exemplary and are not intended to be limiting; other values are possible.

[0193] The fibrous structures in the form of bath tissue may exhibit a Total Dry Tensile Strength as measured according to the Dry Elongation, Tensile Strength, TEA and Modulus Test Methods for Bath tissue of from 150 g / in to 1700 g / in, or from 200 to 1500 g / in, or from 250 to 1350 g / in or greater than 150 g / in or greater than 200 g / in or greater than 250 g / in or greater than 300 g / in or greater than 350 g / in. The fibrous structures in the form of paper towels may exhibit a a Total Dry Tensile Strength as measured according to the Dry Elongation, Tensile Strength, TEA and Modulus Test Methods for Paper Towels of from 1200 g / in to 3200 g / in, or from 1600 g / in to 2800 g / in or greater than 1200 g / in, or greater than 1400 g / in or greater than 1600 g / in.

[0194] The fibrous structures in the form of paper towels may exhibit a CRT Rate, as measured according to the CRT Rate and Capacity Test Method of from 0.30 g / s to 0.95 g / s, or from 0.40 to 0.90 g / s or greater than 0.30 g / s or greater than 0.40 g / s or greater than about 0.50 g / s or greater than about 0.60 g / s or greater than about 0.70 g / s. The fibrous structures in the form of bath tissue may exhibit a CRT Rate, as measured according to the CRT Rate and Capacity Test Method of from 0.10 g / s to 0.6 g / s or greater than 0.10 g / s or greater than about 0.15 g / s or greater than about 0.20 g / s or greater than about 0.25 g / s or greater than about 0.30 g / s.

[0195] The fibrous structures in the form of paper towels may exhibit a SST Rate, as measured according to the SST Absorbency Rate Test Method of from 1.0 to 3.0 g / sec0.5, or from 1.2 to 2.8 g / sec0.5, or from 1.4 to 2.6 g / sec0.5 or greater than about 1.0 g / sec0.5, or greater than about 1.2 g / sec0.5, or greater than about 1.4 g / sec0.5, or greater than about 1.6 g / sec0.5. The fibrous structures in the form of bath tissue may exhibit a SST Rate, as measured according to the SST Absorbency Rate Test Method of from 0.2 to 1.5 g / sec0.5 or greater than about 0.2 g / sec0.5, or greater than about 0.25 g / sec0.5, or greater than about 0.30 g / sec0.5.

[0196] The fibrous structures may exhibit various properties associated with flexibility. The fibrous structures in the form of paper towels may exhibit a Plate Stiffness, as measured according to the Plate Stiffness Test Method of from 6 to 30 N*mm, or from 7 to 28 N*mm, or greater than 6 N*mm, or greater than 7 N*mm or greater than about 8 N*mm or greater than about 9 N*mm or greater than about 10 N*mm or greater than about 11 N*mm. The fibrous structures in the form of bath tissues may exhibit a Plate Stiffness, as measured according to the Plate Stiffness Test Method of from 2 to 8 N*mm or greater that about 2 N*mm or greater than about 3 N*mm or greater than about 4 N*mm or less than about 15 N*mm or less than about 13 N*mm or less than about 10 N*mm. The fibrous structures in the form of paper towels may exhibit a GM Flexural Rigidity, as measured according to the Flexural Rigidity Test Method of from 300 to 2000 mg-cm, or from 400 to 1800 mg-cm or greater than about 300 mg-cm or greater than about 400 mg-cm or greater than about 500 mg-cm or greater than about 600 mg-cm or greater than about 700 mg-cm or greater than about 800 mg-cm or less than about 2000 mg-cm or less than about 1900 mg-cm or less than about 1800 mg-cm or less than about 1700 mg-cm. The fibrous structures in the form of bath tissues may exhibit a GM Flexural Rigidity, as measured according to the Flexural Rigidity Test Method of from 20 to 700 mg-cm, or from 30 to 500 mg-cm or greater than about 20 mg-cm or greater than about 30 mg-cm or greater than about 40 mg-cm or greater than about 50 mg-cm or less than about 700 mg-cm or less than about 600 mg-cm or less than about 500 mg-cm.

[0197] The fibrous structures in the form of paper towels may exhibit various properties associated with thickness. The fibrous structures in the form of paper towels may exhibit a caliper, as measured according to the Dry Caliper Test Method of from 25 mils to 60 mils, or from 25 mils to 70 mils, or from 25 to 80 mils or greater than about 25 mils or greater than about 30 mils or greater than about 35 mils. The fibrous structures in the form of bath tissue may exhibit a caliper, as measured according to the Dry Caliper Test Method of from 15 mils to 30 mils, or from 15 mils to 40 mils, or from 15 mils to 50 mils.

[0198] The fibrous structures in the form of paper towels may exhibit a Resilient Bulk, as measured according to the Stack Compressibility and Resilient Bulk Method of from 50 to 150 cm3 / g, or from 60 to 130 cm3 / g or greater than 50 cm3 / g or greater than about 60 cm3 / g or greater than about 70 cm3 / g. The fibrous structures in the form of bath tissue may exhibit a Resilient Bulk, as measured according to the Stack Compressibility and Resilient Bulk Method of from 15 to 100 cm3 / g, or from 20 to 90 cm3 / g, or greater than about 15 cm3 / g or greater than about 20 cm3 / g or greater than about 25 cm3 / g or greater than about 30 cm3 / g.

[0199] The fibrous structures may exhibit various other properties determined according to the Micro-CT Intensive Property Measurement Method, such as an Average pillow Basis Weight of 15.00 to 60.00 gsm or greater than about 15 gsm or greater than about 20 gsm or greater than about 25 gsm; an Average pillow Thickness of 90.0 to 500.0 microns or greater than about 90 microns or greater than about 95 microns or greater than about 100 microns; and / or an Average pillow Density of 0.1000 to 0.4000 g / cc or greater than about 0.1000 g / cc or greater than about 0.1500 g / cc or greater than about 0.2000 g / cc.EXAMPLES

[0200] The following examples are put forth to provide those of ordinary skill in the art with a complete disclosure and description of how to perform the methods, how to make, and how to use the compositions and compounds disclosed and claimed herein. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.), but some errors and deviations should be accounted for. The purpose of the following examples is not to limit the scope of the various embodiments, but merely to provide examples illustrating specific embodiments.Example 1

[0201] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the comparative pattern shown in FIG. 43A. The results are summarized in Table 1.TABLE 1PropertyValuePeriodicity (%) [First Secondary Peak]79Period (mm) [First Secondary Peak]2.0Angle (deg) [First Secondary Peak]−60Texture Isotropy (%)49Example 2

[0202] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the comparative pattern shown in FIG. 43B. The results are summarized in Table 2.TABLE 2PropertyValuePeriodicity (%) [First Secondary Peak]96Period (mm) [First Secondary Peak]0.5Angle (deg) [First Secondary Peak]−95Texture Isotropy (%)9Example 3

[0203] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the comparative pattern shown in FIG. 43C. The results are summarized in Table 3.TABLE 3PropertyValuePeriodicity (%) [First Secondary Peak]29Period (mm) [First Secondary Peak]2.8Angle (deg) [First Secondary Peak]134Texture Isotropy (%)98Example 4

[0204] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the comparative pattern shown in FIG. 43D. The results are summarized in Table 4.TABLE 4PropertyValuePeriodicity (%) [First Secondary Peak]83Period (mm) [First Secondary Peak]11.5Angle (deg) [First Secondary Peak]141Texture Isotropy (%)91Example 5

[0205] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the comparative pattern shown in FIG. 43E. The results are summarized in Table 5.TABLE 5PropertyValuePeriodicity (%) [First Secondary Peak]81Period (mm) [First Secondary Peak]22.8Angle (deg) [First Secondary Peak]180Texture Isotropy (%)83Example 6

[0206] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the comparative pattern shown in FIG. 43F. The results are summarized in Table 6.TABLE 6PropertyValuePeriodicity (%) [First Secondary Peak]89Period (mm) [First Secondary Peak]10.9Angle (deg) [First Secondary Peak]−97Texture Isotropy (%)93Example 7

[0207] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the inventive pattern shown in FIG. 43G. The results are summarized in Table 7.TABLE 7PropertyValuePeriodicity (%) [First Secondary Peak]83Period (mm) [First Secondary Peak]19.1Angle (deg) [First Secondary Peak]−94Texture Isotropy (%)87Example 8

[0208] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the inventive pattern shown in FIG. 43H. The results are summarized in Table 8.TABLE 8PropertyValuePeriodicity (%) [First Secondary Peak]85Period (mm) [First Secondary Peak]12.8Angle (deg) [First Secondary Peak]−5Texture Isotropy (%)75Example 9

[0209] A purpose of this example is to demonstrate the application of the Fibrous Structure Isotropy Test Method to the inventive pattern shown in FIG. 43I. The results are summarized in Table 9.TABLE 9PropertyValuePeriodicity (%) [First Secondary Peak]96Period (mm) [First Secondary Peak]3.3Angle (deg) [First Secondary Peak]−95Texture Isotropy (%)70Examples 10-12

[0210] For each of Examples 10, 11, and 12, a fibrous structure was prepared using the pattern identified. For each fibrous structure, a knuckle perimeter was determined by the Total Pillow Perimeter Test Method. For each fibrous structure, a surface void volume was determined at 1.7 psi and at 0.88 psi according to the Surface Void Volume Test Method. For each fibrous structure, a TS7 value and TS750 value was determined according to the Emtec Test Method. The Total Pillow Perimeter Test Method and Surface Void Volume Test Method are measures for texture while Emtec TS7 and TS750 are measures for softness and smoothness. A ratio of Total Pillow Perimeter to Surface Void Volume at 0.88 psi is shown to demonstrate the relationship between texture and volume. This is calculated by dividing Total Pillow Perimeter by Surface Void Volume at 0.88 psi. The results of Examples 10, 11, 12, and 13 are summarized in Table 10.Example 10

[0211] A purpose of this example is to demonstrate properties of a comparative fibrous structure made using the pattern shown in FIG. 44A. The structure is formed by adding fiber and chemicals to water to form a dilute solution. The composition without water is approximately 45% northern softwood kraft and 54% eucalyptus fiber, and less than 1% of wet strength additive and dry strength additives by weight. The dilute solution is jetted onto a wire and after draining is subsequently wet transferred to the belt to wet form knuckles and pillows as shown in FIG. 44A, where the black indicates pillow structures and white indicates knuckle structures. The substrate is adhered to the Yankee drying surface, creped and calendered to the desired thickness. The substrate is embossed and ply-bonded to a second web, where it is perforated, wound and cut into roll form.

[0212] This comparative fibrous substrate has a total pillow perimeter of 28.2 in / in2 and 259 [in / in2 / mm3 / m2] perimeter / volume at 0.88 psi. The Emtec TS7 is 10.2 dB V2 rms and Emtec TS750 26.6 dB V2 rms.Example 11

[0213] A purpose of this example is to demonstrate properties of a comparative fibrous structure made using the pattern shown in FIG. 44B. The structure is formed by adding fiber and chemicals to water to form a dilute solution. The composition without water is approximately 45% northern softwood kraft and 54% eucalyptus fiber, and less than 1% of wet strength additives and dry strength additives by weight. The dilute solution is jetted onto a wire and after draining is subsequently wet transferred to the belt to wet form knuckles and pillows as shown in FIG. 44B, where the black indicates pillow structures and white indicates knuckle structures. The substrate is adhered to the Yankee drying surface, creped and calendered to the desired thickness. The substrate is embossed and ply-bonded to a second web, where it is perforated, wound and cut into roll form.

[0214] This comparative fibrous substrate has a total pillow perimeter of 28.8 in / in2 and 288 259 [in / in2 / mm3 / m2] perimeter / volume at 0.88 psi. The Emtec TS7 is 9.5 dB V2rms and Emtec TS750 31.3 dB V2 rms.Example 12

[0215] A purpose of this example is to demonstrate properties of an inventive fibrous structure made using the pattern shown in FIG. 44C. The structure is formed by adding fiber and chemicals to water to form a dilute solution. The composition without water is approximately 45% northern softwood kraft and 54% eucalyptus fiber, and less than 1% of wet and dry strength additives by weight. The dilute solution is jetted onto a wire and after draining is subsequently wet transferred to the belt to wet form knuckles and pillows as shown in FIG. 44C, where the black indicates pillow structures and white indicates knuckle structures. The substrate is adhered to the Yankee drying surface, creped and calendered to the desired thickness. The substrate is embossed and ply-bonded to a second web, where it is perforated, wound and cut into roll form.

[0216] This inventive fibrous substrate has a total pillow perimeter of 34.9 in / in2 and 306 [in / in2 / mm3 / m2] perimeter / volume at 0.88 psi, higher than the prior two comparative examples. This indicates clothlike texture that holds up under pressure. Additionally, it has improved softness with lower Emtec TS7 at 8.9 dB V2rms and Emtec TS750 at 26.4 dB V2rmsExample 13

[0217] A purpose of this example is to demonstrate properties of an inventive fibrous structure made using the pattern shown in FIG. 45T. The structure is formed by adding fiber and chemicals to water to form a dilute solution. The composition without water is approximately 45% northern softwood kraft and 54% eucalyptus fiber, and less than 1% of wet and dry strength additives by weight. The dilute solution is jetted onto a wire and after draining is subsequently wet transferred to the belt to wet form knuckles and pillows as shown in FIG. 44C, where the black indicates pillow structures and white indicates knuckle structures. The substrate is adhered to the Yankee drying surface, creped and calendered to the desired thickness. The substrate is embossed and ply-bonded to a second web, where it is perforated, wound and cut into roll form.

[0218] This fibrous substrate has a total pillow perimeter of 30.7 in / in2 and 330 [in / in2 / mm3 / m2] perimeter / volume at 0.88 psi, much higher than the prior two comparative examples. This indicates clothlike texture that holds up under pressure. It has similar softness Emtec TS7 at 10.5 dB V2rms despite all the additional texture.TABLE 10SurfaceSurfaceTotal PillowVoidVoidPerimeter / SurfaceTotal PillowVolume atVolume atVoid Volume (atPerimeter / area,1.7 psi,0.88 psi,0.88 psi),Emtec TS7,Emtec TS750,Examplein / in2mm3 / m2mm3 / m2[in / in2 / mm3 / m2]dB V2 rmsdB V2 rms1028.2.0930.10925910.226.61128.80.0820.1002889.531.31234.90.1080.1143068.926.41330.70.0790.09338933010.5Example 14—Isotropy Results for Various Masks and Belts

[0219] A purpose of this example is to compare the texture isotropy percentage and period for a variety of masks and belts that may be used to prepare towels and tissues. The Mask / Belt Isotropy Test Method was applied to the figures referenced. The results are summarized in the table shown in FIG. 48 and in the charts shown in FIGS. 49 and 50. Isotropy, period, angle and periodicity may be used to describe the distillation of 3-dimensional aspects of woven textiles into 2-dimensional patterns for application to wet forming fibrous substrates. Mask and structuring belt patterns that comprise greater distance between isotropy surface autocorrelation peaks, i.e. period, make it difficult to perceive pattern repetition, unlike in current engineered tissue and towel masks, belts and fibrous substates. Combining the larger period with higher isotropy and / or other dimensions of organic pattern shapes (cell shape, perimeter texture, size, orientation, placement regularity) may further drive the visual perception of organic irregularity within an engineered design as exemplified for example by data on FIG. 45K, 45Q, 45L. Less isotropic patterns benefit from increased period to drive visual complexity that ladders to textile impression, as exemplified by data on FIGS. 45V, 45X and 45AC. Tissue mask and belt patterns particularly benefit from increased period without impacting super premium product quality.Example 15—Isotropy Results for Various Fibrous Structures

[0220] A purpose of this example is to compare the texture isotropy percentage and period for a variety of fibrous substrates, including patterns of comparative towel and tissue and inventive towel and tissue. The Fibrous Substrate Fibrous Structure Isotropy Test Method was applied to the figures referenced. The results are summarized in the table shown in FIG. 51 and in the charts shown in FIGS. 52 and 53. Isotropy, period, angle and periodicity may be used to describe the distillation of 3-dimensional aspects of woven textiles into masks or structuring belts that are then used to form fibrous substrates. Through the wet forming and dry converting process, some of the pattern characteristics captured in the mask and / or belt pattern are enhanced while others are reduced. Fibrous substrates have premium function while delivering visual reassurance that the products will perform when they are not completely isotropic, have a high period and high periodicity. The 3-dimensional fibrous substrates drive more woven textile appearance that may counteract their underlying engineered nature when the pattern repeat is spaced farther apart (period) with some directionality (not 100% isotropic) and / or has greater than 40%, 45% or 50% periodicity as exemplified by fibrous substrate data for FIGS. 45T, 45Q and 45R.Aspects of the Present Disclosure

[0221] The following aspects of the disclosure are exemplary only and not intended to limit the scope of the disclosure:Fibrous Substrate1. A fibrous substrate comprising a plurality of cells;

[0223] wherein the fibrous substrate defines a major coordinate plane;

[0224] wherein the plurality of cells comprises at least a first cell and a second cell;

[0225] wherein the first cell comprises

[0226] a first perimeter defining a first shape and a first size,

[0227] a first position relative to the major coordinate plane,

[0228] a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane

[0229] wherein the second cell comprises

[0230] a second perimeter defining a second shape and a second size,

[0231] a second position relative to the major coordinate plane,

[0232] a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane;

[0233] wherein the first position and the second position are substantially within a first row;

[0234] wherein the first row comprises a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis; and

[0235] wherein the longitudinal row axis is oriented at a row angle relative to an axis of the major coordinate plane.

[0236] 2. The fibrous substrate of aspect 1, wherein the plurality of cells defines a pattern having a Fibrous Structure Period (first secondary peak) greater than 4 mm and a Fibrous Structure Percent Texture Isotropy less than 84%.

[0237] 3. The fibrous substrate of any one of aspects 1-2, wherein the first shape and the second shape are substantially the same.

[0238] 4. The fibrous substrate of any one of aspects 1-3, wherein the first shape and the second shape are substantially different.

[0239] 5. The fibrous substrate of any one of aspects 1-4, wherein the first shape is irregular.

[0240] 6. The fibrous substrate of any one of aspects 1-5, wherein the second shape is irregular.

[0241] 7. The fibrous substrate of any one of aspects 1-6, wherein the first size and the second size are substantially the same.

[0242] 8. The fibrous substrate of any one of aspects 1-7, wherein the first size and the second size are substantially different

[0243] 9. The fibrous substrate of any one of aspects 1-8, wherein the first angle and the second angle are substantially the same.

[0244] 10. The fibrous substrate of any one of aspects 1-9, wherein the first angle and the second angle are substantially different.

[0245] 11. The fibrous substrate of any one of aspects 1-10, wherein the first cell abuts the second cell.

[0246] 12. The fibrous substrate of any one of aspects 1-11, wherein the first cell does not abut the second cell.

[0247] 13. The fibrous substrate of any one of aspects 1-12, the row angle is in a range of from about 0 to about 90 degrees.

[0248] 14. The fibrous substrate of any one of aspects 1-13, wherein an axis of the major coordinate plane is substantially aligned with a machine direction.

[0249] 15. The fibrous substrate of any one of aspects 1-14, wherein an axis of the major coordinate plane is substantially aligned with a cross direction.

[0250] 16. The fibrous substrate of any one of aspects 1-15, wherein the plurality of cells comprises a third cell,

[0251] wherein the third cell comprises

[0252] a third perimeter defining a third shape and a third size,

[0253] a third position relative to the major coordinate plane,

[0254] a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane;

[0255] wherein the first position and the third position are substantially within a second row.

[0256] 17. The fibrous substrate of aspect 16, wherein the first row and the second row intersect.

[0257] 18. The fibrous substrate of aspects 16 or 17, wherein the first row and the second row are continuous.

[0258] 19. The fibrous substrate of any one of aspects 16-18, wherein the first row and the second row are discontinuous.

[0259] 20. The fibrous substrate of any one of aspects 1-19, wherein the first cell has from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary.

[0260] 21. The fibrous substrate of aspect 20, wherein the first cell has from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.Mask22. A mask for producing a structuring layer of a papermaking belt comprising a plurality of cells;

[0262] wherein the mask defines a major coordinate plane;

[0263] wherein the plurality of cells comprises at least a first cell and a second cell;

[0264] wherein the first cell comprises

[0265] a first perimeter defining a first shape and a first size,

[0266] a first position relative to the major coordinate plane,

[0267] a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane

[0268] wherein the second cell comprises

[0269] a second perimeter defining a second shape and a second size,

[0270] a second position relative to the major coordinate plane,

[0271] a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane;

[0272] wherein the first position and the second position are substantially within a first row;

[0273] wherein the first row comprises a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis; and

[0274] wherein the longitudinal row axis is oriented at a row angle relative to an axis of the major coordinate plane.

[0275] 23. The mask of aspect 22, wherein the plurality of cells defines a pattern having a Mask / Belt period greater than 4 mm and a Percent Texture Isotropy less than 63.0%.

[0276] 24. The mask of any one of aspects 22-23, wherein the first shape and the second shape are substantially the same.

[0277] 25. The mask of any one of aspects 22-24, wherein the first shape and the second shape are substantially different.

[0278] 26. The mask of any one of aspects 22-25, wherein the first shape is irregular.

[0279] 27. The mask of any one of aspects 22-26, wherein the second shape is irregular.

[0280] 28. The mask of any one of aspects 22-27, wherein the first size and the second size are substantially the same.

[0281] 29. The mask of any one of aspects 22-28, wherein the first size and the second size are substantially different

[0282] 30. The mask of any one of aspects 22-29, wherein the first angle and the second angle are substantially the same.

[0283] 31. The mask of any one of aspects 22-30, wherein the first angle and the second angle are substantially different.

[0284] 32. The mask of any one of aspects 22-31, wherein the first cell abuts the second cell.

[0285] 33. The mask of any one of aspects 22-32, wherein the first cell does not abut the second cell.

[0286] 34. The mask of any one of aspects 22-33, the row angle is in a range of from about 0 to about 90 degrees.

[0287] 35. The mask of any one of aspects 22-34, wherein an axis of the major coordinate plane is substantially aligned with a machine direction.

[0288] 36. The mask of any one of aspects 22-35, wherein an axis of the major coordinate plane is substantially aligned with a cross direction.

[0289] 37. The mask of any one of aspects 22-36, wherein the plurality of cells comprises a third cell,

[0290] wherein the third cell comprises

[0291] a third perimeter defining a third shape and a third size,

[0292] a third position relative to the major coordinate plane,

[0293] a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane;

[0294] wherein the first position and the third position are substantially within a second row.

[0295] 38. The mask of aspect 37, wherein the first row and the second row intersect.

[0296] 39. The mask of aspects 37 or 38, wherein the first row and the second row are continuous.

[0297] 40. The mask of any one of aspects 37-39, wherein the first row and the second row are discontinuous.

[0298] 41. The mask of any one of aspects 22-40, wherein the first cell has from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary.

[0299] 42. The mask of aspect 41, wherein the first cell has from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.Papermaking Belt43. A papermaking belt comprising a plurality of cells;

[0301] wherein the papermaking belt defines a major coordinate plane;

[0302] wherein the plurality of cells comprises at least a first cell and a second cell;

[0303] wherein the first cell comprises

[0304] a first perimeter defining a first shape and a first size,

[0305] a first position relative to the major coordinate plane,

[0306] a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane

[0307] wherein the second cell comprises

[0308] a second perimeter defining a second shape and a second size,

[0309] a second position relative to the major coordinate plane,

[0310] a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane;

[0311] wherein the first position and the second position are substantially within a first row; wherein the first row comprises a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis; and

[0312] wherein the longitudinal row axis is oriented at a row angle relative to an axis of the major coordinate plane.

[0313] 44. The papermaking belt of aspect 43, wherein the plurality of cells defines a pattern having a Mask / Belt period greater than 4 mm and a Percent Texture Isotropy less than 63.0%.

[0314] 45. The papermaking belt of any one of aspects 43-44, wherein the first shape and the second shape are substantially the same.

[0315] 46. The papermaking belt of any one of aspects 43-45, wherein the first shape and the second shape are substantially different.

[0316] 47. The papermaking belt of any one of aspects 43-46, wherein the first shape is irregular.

[0317] 48. The papermaking belt of any one of aspects 43-47, wherein the second shape is irregular.

[0318] 49. The papermaking belt of any one of aspects 43-48, wherein the first size and the second size are substantially the same.

[0319] 50. The papermaking belt of any one of aspects 43-49, wherein the first size and the second size are substantially different

[0320] 51. The papermaking belt of any one of aspects 43-50, wherein the first angle and the second angle are substantially the same.

[0321] 52. The papermaking belt of any one of aspects 43-51, wherein the first angle and the second angle are substantially different.

[0322] 53. The papermaking belt of any one of aspects 43-52, wherein the first cell abuts the second cell.

[0323] 54. The papermaking belt of any one of aspects 43-53, wherein the first cell does not abut the second cell.

[0324] 55. The papermaking belt of any one of aspects 43-54, the row angle is in a range of from about 0 to about 90 degrees.

[0325] 56. The papermaking belt of any one of aspects 43-55, wherein an axis of the major coordinate plane is substantially aligned with a machine direction.

[0326] 57. The papermaking belt of any one of aspects 43-56, wherein an axis of the major coordinate plane is substantially aligned with a cross direction.

[0327] 58. The papermaking belt of any one of aspects 43-57, wherein the plurality of cells comprises a third cell,

[0328] wherein the third cell comprises

[0329] a third perimeter defining a third shape and a third size,

[0330] a third position relative to the major coordinate plane,

[0331] a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane;

[0332] wherein the first position and the third position are substantially within a second row.

[0333] 59. The papermaking belt of aspect 58, wherein the first row and the second row intersect.

[0334] 60. The papermaking belt of aspects 58 or 59, wherein the first row and the second row are continuous.

[0335] 61. The papermaking belt of any one of aspects 58-60, wherein the first row and the second row are discontinuous.

[0336] 62. The papermaking belt of any one of aspects 43-61, wherein the first cell has from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary.

[0337] 63. The papermaking belt of aspect 62, wherein the first cell has from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.Additional Aspects64. A structuring belt pattern with a Mask / Belt period (first secondary peak) greater than 40 mm

[0339] Or

[0340] A tissue structuring belt pattern with a Mask / Belt period (first secondary peak) greater than 13 mm

[0341] Or

[0342] A fibrous structure with a fibrous structure period (first secondary peak) greater than 4 mm and a fibrous structure texture isotropy less than 84%.

[0343] Or

[0344] A fibrous structure with a fibrous structure period (first secondary peak) greater than 7 mm and a fibrous structure periodicity (first secondary peak) greater than 53%.

[0345] 65. A fibrous substrate comprising a pattern of cells,

[0346] wherein the cells are arranged in rows,

[0347] wherein none of the cells comprise an axis about which a perimeter of the cell is mirrored.

[0348] 66. The fibrous structure of 65, wherein at least some of the rows are regular.

[0349] 67. The fibrous structure of 65, wherein at least some of the irregular.

[0350] 68. The fibrous structure of 65, wherein at least some of the rows are substantially aligned with a machine direction in which the fibrous substrate is produced.

[0351] 69. The fibrous structure of 65, wherein at least some of the rows are substantially aligned with a cross direction perpendicular to a machine direction in which the fibrous substrate is produced.

[0352] 70. The fibrous structure of 65, wherein at least some of the rows are aligned at an angle of from about 0 to about 180 degrees with a machine direction in which the fibrous substrate is produced.

[0353] 71. The fibrous structure of 65, wherein at least some of the rows are continuous.

[0354] 72. The fibrous structure of 65, wherein at least some of the rows are discontinuous.

[0355] 73. The fibrous structure of 65, wherein at least some of the rows intersect.

[0356] 74. The fibrous structure of 65, wherein at least some of the cells have the same shape.

[0357] 75. The fibrous structure of 65, wherein at least some of the cells have the same shape but are oriented at a different angles.

[0358] 76. The fibrous structure of 65, wherein at least some of the cells have different sizes.

[0359] 77. The fibrous structure of 65, wherein at least some of the cells have no more than 4 neighboring cells.

[0360] 78. A structured tissue comprising a plurality of cells that are aligned generally linearly, and wherein the plurality of cells exhibit two or more characteristics selected from the group consisting of.

[0361] at least one of the plurality of cells has no axis about which it can mirror,

[0362] at least two of the plurality of cells are different shapes,

[0363] at least two of the plurality of cells have different angles of orientation,

[0364] at least two of the plurality of cells are different sizes, and

[0365] at least a first pair of the plurality of cells have a first centroid-to-centroid distance that is different from a second centroid-to-centroid distance of a second pair of the plurality of cells.

[0366] 79. The fibrous substrate of 78, wherein the fibrous substrate comprises a semi-irregular pattern of cells.

[0367] 80. A fibrous substrate comprising perimeters defining protrusions and recesses where the perimeter is irregular.

[0368] 81. A structured tissue with cells located on a grid with at least one cell having a 1-30 degree orientation difference.

[0369] 82. A method of making a structuring belt pattern, the method comprising:

[0370] providing a first cell having an original shape, the original shape having an axis of symmetry,

[0371] imparting at least one or more imperfections to a perimeter of the first cell to modify the original shape and to give the first cell a modified shape, and

[0372] placing the first cell next to a second cell having the original shape to form a structuring belt pattern.

[0373] 83. The method of 82, further comprising reorienting the first cell to cause the first cell and the second cell to have different orientations.

[0374] 84. The method of 82, wherein the first cell and the second cell have substantially the same orientations.

[0375] 85. The method of 82, further comprising imparting at least one or more imperfections to a perimeter of the second cell to modify the original shape and to give the second cell a modified shape.

[0376] 86. The method of 82, further comprising placing additional cells in a regular arrangement.

[0377] 87. The method of 82, further comprising placing additional cells in an irregular arrangement.

[0378] 88. A cell pattern comprising one or more repeating patterns.

[0379] 89. A cell pattern having a length to volume ratio or length perimeter of the perimeter.

[0380] 90. A cell cluster comprising at least 3 neighboring cells, wherein the cell cluster does not comprise an axis of symmetry about which its shape is mirrored.

[0381] 91. A fibrous structure comprising a pattern of knuckles,

[0382] wherein a circle of 0.036″ diameter or larger cannot be inscribed within any of the knuckles,

[0383] wherein knuckles forming any angular elements cannot be less than 180-degrees

[0384] wherein the fibrous structure has a TS750 value less than or equal to 28 as measured by an Emtec Test Method.

[0385] 92. The fibrous structure according to aspect 91, wherein the pattern exhibits a minimum 30 in / in2 of pillow perimeter, determined by the Total Pillow Perimeter Test Method.

[0386] 93. The fibrous structure according to aspect 91, wherein the pattern exhibits a minimum surface volume of 0.090 mm3 / mm2 at 1.7 psi, according to a Surface Void Volume Test Method.

[0387] 94. The fibrous structure according to aspect 91, wherein the pattern exhibits a minimum surface volume of 0.108 mm3 / mm2 at 0.88 psi, according to a Surface Void Volume Test Method.

[0388] 95. A structure selected from the group consisting of a fibrous structure, a papermaking belt, a structuring layer, and a mask, the structure comprising a plurality of cells;

[0389] wherein the structure defines a major coordinate plane;

[0390] wherein the plurality of cells comprises at least a first cell and a second cell;

[0391] wherein the first cell comprises

[0392] a first perimeter defining a first shape and a first size,

[0393] a first position relative to the major coordinate plane,

[0394] a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate plane

[0395] wherein the second cell comprises

[0396] a second perimeter defining a second shape and a second size,

[0397] a second position relative to the major coordinate plane,

[0398] a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane;

[0399] wherein the first position and the second position are substantially within a first row;

[0400] wherein the first row comprises a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis; and

[0401] wherein the longitudinal row axis is oriented at a row angle relative to an axis of the major coordinate plane.

[0402] 96. The structure of aspect 95, wherein the structure is selected from the group consisting of a papermaking belt, a structuring layer, and a mask, wherein the plurality of cells defines a pattern having first secondary peak period greater than 40 mm.

[0403] 97. The structure of aspect 95, wherein the structure is selected from the group consisting of a papermaking belt, a structuring layer, and a mask, wherein the plurality of cells defines a pattern having a Mask / Belt period (first secondary peak) greater than 4 mm and a Mask / Belt Percent Texture Isotropy less than 62%.

[0404] 98. The structure of aspect 95, wherein the structure is selected from the group consisting of a papermaking belt, a structuring layer, and a mask, wherein the plurality of cells defines a pattern having a Mask / Belt period (first secondary peak) greater than 13 mm.

[0405] 99. The structure of aspect 95, wherein the structure is selected from the group consisting of a papermaking belt, a structuring layer, and a mask, wherein the plurality of cells defines a pattern having a Mask / Belt period (first secondary peek) greater than 7 mm and a Mask / Belt Percent Texture Isotropy greater than 66%Test Methods

[0406] Unless otherwise specified, all tests described herein including those described under the Definitions section and the following Test Methods are conducted on samples that have been conditioned in a conditioned room at a temperature of 23° C.±1.0° C. and a relative humidity of 50%±2% for a minimum of 2 hours prior to the test. The samples tested are “usable units.”“Usable units” as used herein means sheets, flats from roll stock, pre-converted flats, and / or single or multi-ply products. All tests are conducted in such conditioned room. Do not test samples that have defects such as wrinkles, tears, holes, and like. All instruments are calibrated according to manufacturer's specifications.Micro-CT Intensive Property Measurement Method

[0407] The micro-CT intensive property measurement method measures the basis weight, thickness and density values within visually discernable zones or regions of a substrate sample. It is based on analysis of a 3D x-ray sample image obtained on a micro-CT instrument (a suitable instrument is the Scanco μCT 50 available from Scanco Medical AG, Switzerland, or equivalent). The micro-CT instrument is a cone beam microtomograph with a shielded cabinet. A maintenance free x-ray tube is used as the source with an adjustable diameter focal spot. The x-ray beam passes through the sample, where some of the x-rays are attenuated by the sample. The extent of attenuation correlates to the mass of material the x-rays have to pass through. The transmitted x-rays continue on to the digital detector array and generate a 2D projection image of the sample. A 3D image of the sample is generated by collecting several individual projection images of the sample as it is rotated, which are then reconstructed into a single 3D image. The instrument is interfaced with a computer running software to control the image acquisition and save the raw data. The 3D image is then analyzed using image analysis software (a suitable image analysis software is MATLAB available from The Mathworks, Inc., Natick, MA, or equivalent) to measure the basis weight, thickness and density intensive properties of regions within the sample.Sample Preparation

[0408] To obtain a sample for measurement, lay a single layer of the dry substrate material out flat and die cut a circular piece with a diameter of 16 mm. If the sample being measured is a 2 (or more) ply finished product, carefully separate an individual ply of the finished product prior to die cutting. The sample weight is recorded. A sample may be cut from any location containing the region or cells to be analyzed. Regions, zones, or cells within different samples taken from the same substrate material can be analyzed and compared to each other. Care should be taken to avoid embossed regions, folds, wrinkles, or tears when selecting a location for sampling.Image Acquisition

[0409] Set up and calibrate the micro-CT instrument according to the manufacturer's specifications. Place the sample into the appropriate holder, between two rings of low-density material, which have an inner diameter of 12 mm. This will allow the central portion of the sample to lay horizontal and be scanned without having any other materials directly adjacent to its upper and lower surfaces. Measurements should be taken in this region. The 3D image field of view is approximately 20 mm on each side in the xy-plane with a resolution of approximately 3400 by 3400 pixels, and with a sufficient number of 6 micron thick slices collected to fully include the z-direction of the sample. The reconstructed 3D image contains isotropic voxels of 6 microns. Images were acquired with the source at 45 kVp and 133 μA with no additional low energy filter. These current and voltage settings should be optimized to produce the maximum contrast in the projection data with sufficient x-ray penetration through the sample, but once optimized held constant for all substantially similar samples. A total of 1700 projections images are obtained with an integration time of 500 ms and 4 averages. The projection images are reconstructed into the 3D image and saved in 16-bit format to preserve the full detector output signal for analysis.Image Processing

[0410] Load the 3D image into the image analysis software. The largest cross-sectional area of the sample should be nearly parallel with the x-y plane, with the z-axis being perpendicular. Threshold the 3D image at a value which separates, and removes, the background signal due to air, but maintains the signal from the sample fibers within the substrate.

[0411] Five 2D intensive property images are generated from the thresholded 3D image. The first is the Basis Weight Image, which is a projection image. Each x-y pixel in this image represents the summation of the intensity values along voxels in the z-direction. This results in a 2D image where each pixel now has a value equal to the cumulative signal through the entire sample.

[0412] The weight of the sample divided by the z-direction projected area of the punched sample provides the actual average basis weight of the sample. This correlates with the average signal intensity from the Basis Weight image described above, allowing it to be represented in units of g / m2 (gsm).

[0413] The second intensive property 2D image is the Thickness Image. To generate this image the upper and lower surfaces of the sample are identified, and the distance between these surfaces is calculated giving the sample thickness. The upper surface of the sample is identified by starting at the uppermost z-direction slice and evaluating each slice going through the sample to locate the z-direction voxel for all pixel positions in the xy-plane where sample signal was first detected. The same procedure is followed for identifying the lower surface of the sample, except the z-direction voxels located are all the positions in the xy-plane where sample signal was last detected. Once the upper and lower surfaces have been identified they are smoothed with a 15×15 median filter to remove signal from stray fibers. The 2D Thickness Image is then generated by counting the number of voxels that exist between the upper and lower surfaces for each of the pixel positions in the xy-plane. This raw thickness value is then converted to actual distance, in microns, by multiplying the voxel count by the 6 μm slice thickness resolution.

[0414] The third intensive property 2D image is the Density Image (see for example FIG. 12). To generate this image, divide each xy-plane pixel value in the Basis Weight Image, in units of gsm, by the corresponding pixel in the Thickness Image, in units of microns. The units of the Density Image are grams per cubic centimeter (g / cc).

[0415] For each x-y location, the first and last occurrence of a thresholded voxel position in the z-direction is recorded. This provides two sets of points representing the Top Layer and Bottom Layer of the sample. Each set of points are fit to a second-order polynomial to provide smooth top and bottom surfaces. These surfaces define fourth and fifth 2D intensive property images, the top-layer and bottom-layer of the sample. These surfaces are saved as images with the gray values of each pixel representing the z-value of the surface point.Micro-CT Basis Weight, Thickness and Density Intensive Properties

[0416] This sub-section of the method may be used to measure zones or regions generally. Begin by identifying the zone or region to be analyzed. Next, identify the boundary of the identified region to be analyzed. The boundary of a region is identified by visual discernment of differences in intensive properties when compared to other regions within the sample. For example, a region boundary can be identified based by visually discerning a thickness difference when compared to another region in the sample. Any of the intensive properties can be used to discern region boundaries on either on the physical sample itself or any of the micro-CT intensive property images. Once the boundary of a zone or region has been identified draw the largest circular region of interest that can be inscribed within the region. From each of the first three intensive property images calculate the average basis weight, thickness, and density within the region of interest. Record these values as the region's micro-CT basis weight to the nearest 0.01 gsm, micro-CT thickness to the nearest 0.1 micron and micro-CT density to the nearest 0.0001 g / cc.

[0417] To calculate the percent difference between zones or regions may be calculated according to the “Percent (%) difference” definition above.Concavity Ratio and Packing Fraction Measurements

[0418] As outlined above, five different types of 2D intensive property images are created. These images include: (1) a basis weight image, (2) a thickness image, (3) a density image, (4) a top-layer image, and (5) a bottom-layer image.

[0419] To measure discrete pillow and knuckle Concavity Ratio and Packing Fraction, begin by identifying the boundary of the selected discrete pillow or knuckle cells. The boundary of a cell is identified by visual discernment of differences in intensive properties when compared to other cells within the sample. For example, a cell boundary can be identified based by visually discerning a density difference when compared to another cell in the sample. Any of the intensive properties (basis weight, thickness, density, top-layer, and bottom-layer) can be used to discern cell boundaries on either the physical sample itself or any of the micro-CT 2D intensive property images.

[0420] Using the image analysis software, manually draw a line tracing the identified boundary of each individual whole and partial discrete knuckle or discrete pillow cell 1000 visible within the sample boundary 2400, and generate anew binary image containing only the closed filled in shapes of all the identified discrete cells (see for example FIG. 46). Analyze all the individual discrete cell shapes in the binary image and record the following measurements for each: 1) Area and 2) Convex Hull Area.

[0421] The Concavity Ratio is a measure of the presence and extent of concavity within the shapes of the discrete knuckle or pillow cells. Using the recorded measurements calculate the Concavity Ratio for each of the analyzed discrete cells as the ratio of the shape area to its convex hull area. Identify ten substantially similar replicate discrete knuckle or pillow cells and average together their individual Concavity Ratio values and report the average Concavity Ratio as a unitless value to the nearest 0.01. If ten replicate cells cannot be identified in a single sample, then a sufficient number of replicate samples are to be analyzed according to the described procedure. If the sample contains discrete knuckle or pillow cells of differing size or shape, identify ten substantially similar replicates of each of the different shapes and sizes, calculate an average Concavity Ratio for each and report the minimum average Concavity Ratio value.

[0422] The Packing Fraction is the fraction of the sample area filled by the discrete knuckle and pillow shapes. The Packing Fraction value for the sample is calculated by summing all the recorded whole and partial identified shape areas, regardless of shape or size, and dividing that total by the sample area within the sample boundary 1000. The Packing Fraction is reported as a unitless value to the nearest 0.01.Emtec Test Method

[0423] TS7 and TS750 values are measured using an EMTEC Tissue Softness Analyzer (“Emtec TSA”) (Emtec Electronic GmbH, Leipzig, Germany) interfaced with a computer running Emtec TSA software (version 3.19 or equivalent). According to Emtec, the TS7 value correlates with the real material softness, while the TS750value correlates with the felt smoothness / roughness of the material. The Emtec TSA comprises a rotor with vertical blades which rotate on the test sample at a defined and calibrated rotational speed (set by manufacturer) and contact force of 100 mN. Contact between the vertical blades and the test piece creates vibrations, which create sound that is recorded by a microphone within the instrument. The recorded sound file is then analyzed by the Emtec TSA software. The sample preparation, instrument operation and testing procedures are performed according to the instrument manufacture's specifications.Sample Preparation

[0424] Test samples are prepared by cutting square or circular samples from a finished product. Test samples are cut to a length and width (or diameter if circular) of no less than about 90 mm, and no greater than about 120 mm, in any of these dimensions, to ensure the sample can be clamped into the TSA instrument properly. Test samples are selected to avoid perforations, creases or folds within the testing region. Prepare 8 substantially similar replicate samples for testing. Equilibrate all samples at TAPPI standard temperature and relative humidity conditions (23° C.±2° C. and 50%±2%) for at least 1 hour prior to conducting the TSA testing, which is also conducted under TAPPI conditions.Testing Procedure

[0425] Calibrate the instrument according to the manufacturer's instructions using the 1-point calibration method with Emtec reference standards (“ref.2 samples”). If these reference samples are no longer available, use the appropriate reference samples provided by the manufacturer. Calibrate the instrument according to the manufacturer's recommendation and instruction, so that the results will be comparable to those obtained when using the 1-point calibration method with Emtec reference standards (“ref2 samples”).

[0426] Mount the test sample into the instrument and perform the test according to the manufacturer's instructions. When complete, the software displays values for TS7 and TS750. Record each of these values to the nearest 0.01 dB V2rms. The test piece is then removed from the instrument and discarded. This testing is performed individually on the top surface (outer facing surface of a rolled product) of four of the replicate samples, and on the bottom surface (inner facing surface of a rolled product) of the other four replicate samples.

[0427] The four test result values for TS7 and TS750 from the top surface are averaged (using a simple numerical average); the same is done for the four test result values for TS7 and TS750 from the bottom surface. Report the individual average values of TS7 and TS750 for both the top and bottom surfaces on a particular test sample to the nearest 0.01 dB V2rms. Additionally, average together all eight test value results for TS7 and TS750, and report the overall average values for TS7 and TS750 on a particular test sample to the nearest 0.01 dB V2 rms.Total Pillow Perimeter Test Method

[0428] The Total Pillow Perimeter value of a fibrous structure can be determined from a molding member upon which the fibrous structure is made and / or from the fibrous structure itself as follows:

[0429] a. Molding Member

[0430] If one has access to the molding member upon which the fibrous structure was made,

[0431] i. the discrete pillow perimeter (for example a circle pillow perimeter) is the total measured length of the line (edge of resin) forming the boundary between the knuckles and the discrete pillows. For example, if the molding member's pattern has a repeat unit, then the discrete pillow perimeter of a repeat unit is the line forming the boundary between the knuckles and the discrete pillows of the repeat unit.

[0432] ii. the semi-continuous pillow perimeter (for example a line pillow perimeter) is the total measured length of the line (edge of resin) forming the boundary between the knuckles and the semi-continuous pillows. For example, if the molding member's pattern has a repeat unit, then the semi-continuous pillow perimeter of a repeat unit is the line forming the boundary between the knuckles and the semi-continuous pillows of the repeat unit.

[0433] iii. the continuous pillow perimeter is the total measured length of the line (edge of resin) forming the boundary between the knuckles and the continuous pillows. For example, if the molding member's pattern has a repeat unit, then the continuous pillow perimeter of a repeat unit is the line forming the boundary between the knuckles and the continuous pillows of the repeat unit.

[0434] iv. Total Pillow Perimeter value is the total measured length of the line (edge of resin) forming the boundary between all of the knuckles and all of the pillows, for example the discrete pillow perimeter value+semi-continuous pillow perimeter value+continuous pillow perimeter value. For example, if the molding member's pattern has a repeat unit, then the total pillow perimeter of a repeat unit is the line forming the boundary between the knuckles and the pillows of the repeat unit.

[0435] v. Area is the entire area of the knuckles and pillows. For example, if the molding member's pattern has a repeat unit, then the area is the entire area of the repeat unit including the knuckles and the pillows.

[0436] vi. Discrete Pillow Perimeter / Area can be calculated.

[0437] vii. Semi-Continuous Pillow Perimeter / Area can be calculated.

[0438] viii. Total Pillow Perimeter / Area can be calculated.

[0439] b. Fibrous Structure

[0440] To determine the Total Pillow Perimeter value from a fibrous structure:

[0441] i. Obtain clean, unaltered, undamaged, new sample of fibrous structure to be measured.

[0442] ii. the discrete pillow perimeter (for example a circle pillow perimeter) is the total measured length of the line (transition zone) forming the boundary between the non-pillow regions and adjacent discrete pillow regions, if any.

[0443] iii. the semi-continuous pillow perimeter (for example a line pillow perimeter) is the total measured length of the line (transition zone) forming the boundary between the non-pillow regions and adjacent semi-continuous pillow regions.

[0444] iv. the continuous pillow perimeter is the total measured length of the line (transition zone) forming the boundary between the non-pillow regions and adjacent continuous pillow regions.

[0445] v. Total Pillow Perimeter value is the total measured length of the line (transition zone) forming the boundary between all of the non-pillow regions and all of the adjacent pillow regions, for example the discrete pillow perimeter value+semi-continuous pillow perimeter value+continuous pillow perimeter value.

[0446] vi. For example, some fibrous structures comprise 3D patterned ripples. In order to measure the semi-continuous pillow perimeter of a fibrous structure comprising ripples, one measures the length of the boundary of a ripple (straight or curvilinear) in a sheet along the ripple's transition zone between the ripple pillow region and the adjacent non-pillow region. Once the semi-continuous pillow perimeter has been measured for one ripple, since it is a repeating pattern, one can count the number of ripples per sheet and then multiply the number of ripples per sheet by the perimeter of a ripple to arrive at the Total Ripple (Pillow) Perimeter value.

[0447] vii. Area of a sheet is the sheet width×sheet length.

[0448] viii. Discrete Pillow Perimeter / Area is calculated.

[0449] ix. Semi-Continuous Pillow Perimeter / Area is calculated.

[0450] x. Total Pillow Perimeter / Area is calculated.Surface Void Volume Test Method

[0451] The Surface Void Volume measurement is obtained from analysis of a 3D surface topography image of a fibrous structure sample while under a uniform compressive pressure. The image is obtained using an optical 3D surface topography measurement system (a suitable optical 3D surface topography measurement system is the MikroCAD Premium instrument commercially available from LMI Technologies Inc., Vancouver, Canada, or equivalent). The system includes the following main components: a) a Digital Light Processing (DLP) projector with direct digital controlled micro-mirrors; b) a CCD camera with at least a 1600×1200 pixel resolution; c) projection optics adapted to a measuring area of at least 60 mm×45 mm; d) recording optics adapted to a measuring area of 60 mm×45 mm; e) a table tripod based on a small hard stone plate; f) a blue LED light source; g) a measuring, control, and evaluation computer running surface texture analysis software (a suitable software is MikroCAD software with MountainsMap technology, or equivalent); and h) calibration plates for lateral (x-y) and vertical (z) calibration available from the vendor. The uniform compressive pressure is applied to the sample by a pressure box containing a flexible bladder beneath the sample, which is pressurized by air, and a transparent window above, through which the sample surface is visible to the camera.

[0452] The optical 3D surface topography measurement system measures the surface height of a sample using the digital micro-mirror pattern fringe projection technique. The result of the measurement is a map of surface height (z-directional or z-axis) versus displacement in the x-y plane. The system has a field of view of 60×45 mm with an x-y pixel resolution of approximately 40 microns. The height resolution is set at 0.5 micron / count, with a height range of + / −15 mm. All testing is performed in a conditioned room maintained at about 23±2° C. and about 50±2% relative humidity.

[0453] The instrument is calibrated according to manufacturer's specifications using the calibration plates for lateral (x-y axis) and vertical (z axis) available from the vendor.

[0454] Referring to FIGS. 47A and 47B, the pressure box consists of a Delrin base 2001 a silicone bladder 2002, an aluminum frame 2003 to attach the bladder (e.g. Bisco HT-6220, solid silicone elastomer, 0.20 in. thickness with a durometer Shore A of 20 pts; (available from Marian Chicago Inc., Chicago Ill., or equivalent) to the Base 2001, an acrylic window 2004 and an aluminum lid 2005. The base 2001 is 24.0 in. long by 7.0 in. wide and 1.0 in. thick. It has a rectangular well 2006 routed into the base that is 4.0 in. wide by 14.5 in. long by 0.7 in. deep and is centered within the base. The well has a rectangular counter sink 2007 that is 0.5 in. deep and extends 0.75 in. from the edges of the well. The frame 2003 is 0.5 in. wide by 0.25 in. thick and fits within the lip of the well. The frame is used to attach the bladder 2002 to the base using 12 screws. The base has two thru holes 2008 and 2009 that are used to introduce and regulate pressurized air from underneath the bladder 2002. A back pressure regulator 2012 is used to adjust the pressure within the system. The lid 2005 is 24.0 in. long by 7.0 in. wide and 0.25 in. thick. It has four cutouts panes; the two center panes 2013 are 6.0 in. wide by 4.75 in. long and the two outbound 2014 panes are 6 in. wide by 3.0 in. long. There are three 0.25 in. bridges 2015 between the panes. The window 2004 is made of transparent acrylic that is 24.0 in. long by 7.0 in. wide and 0.125 in. thick. The window 2004 is attached to the lid 2005 using six screws. The lid and window assembly are attached to the base with a hinge 2011 along its side that aligns the two parts and secures them along the edge. When closed, the window rest flush with the top of the base. Three clamps 2010, which are attached to the base with hinges, are closed to secure the lid 2005 with the base 2001.

[0455] Test samples are prepared by cutting square samples of a fibrous structure. Test samples are cut to a length and width of about 90 mm to ensure the sample fills the camera's field of view. Test samples are selected to avoid perforations, creases or folds within the testing region. Prepare five (5) substantially similar replicate samples for testing. Equilibrate all samples at TAPPI standard temperature and relative humidity conditions (23° C.±2 C.° and 50%±2%) for at least 1 hour prior to conducting the measurement, which is also conducted under TAPPI conditions. The fibrous structure sample is laid flat on the bladder 2002 surface and is sealed inside the pressure box so that the entire region of the sample surface to be measured is visible through a center pane 2013 in the lid 2005. The pressure box is then placed on the table with the center pane directly beneath the camera so that the sample surface fills the entire field of view. The pressure is steadily raised to 0.88 psi within approximately 60 seconds.

[0456] Without delay a height image (z-direction) of the sample is collected by following the instrument manufacturer's recommended measurement procedures, which may include, focusing the measurement system and performing a brightness adjustment. No pre-filtering options should be utilized. The collected height image file is saved to the evaluation computer running the surface texture analysis software.

[0457] Immediately following the image collection at the lower pressure, the pressure in the box is steadily raised to 1.7 psi within approximately 60 seconds, and the image collection procedure is repeated.

[0458] Analysis of a surface height image is initiated by opening the image in the surface texture analysis software. A recommended filtration process is described in ISO 25178-2:2012. Accordingly, the following filtering procedure is performed on each image: 1) a Gaussian low pass S-filter with a nesting index (cut-off) of 2.5 μm; 2) an F-operation of removing the least squares plane; and 3) a Gaussian high pass L-filter with a nesting index (cut-off) of 25 mm (ISO 16610-61). Both Gaussian filters are run utilizing end effect correction. This filtering procedure produces the S-L surface from which the areal surface texture parameters will be calculated.

[0459] Select the entire field of view for measurement and calculate the areal surface void volume parameter on the S-L Surface.

[0460] The Surface Void Volume measurement is based on the Core Void Volume (Vvc) parameter which is described in ISO 25178-2:2012. The parameter Vvc is derived from the Areal Material Ratio (Abbott-Firestone) curve described in the ISO 13565-2:1996 standard extrapolated to surfaces, it is the cumulative curve of the surface height distribution histogram versus the range of surface heights. A material ratio is the ratio, given as a %, of the intersecting area of a plane passing through the surface at a given height to the cross sectional area of the evaluation region. Vvc is the difference in void volume between p and q material ratios. The Surface Void Volume is the volume of void space above the surface of the sample between the height corresponding to a material ratio value of 2% to the material ratio of 98%, which is the Vvc parameter calculated with a p value of 2% and q value of 98%. The units of Surface Void Volume are mm3 / mm2.

[0461] The Surface Void Volume of the five replicate fibrous structure samples are measured at both the 0.88 psi and 1.7 psi. The five Surface Void Volume values at each pressure are averaged together, and each is reported to the nearest 0.001 mm3 / m2.Mask / Belt Isotropy Test Method

[0462] The Mask / Belt Isotropy Test Method measures the Isotropy, Periodicity, Period, and Angle of a pattern using image analysis. The input pattern for analysis is a binary image (I) representing an area of 127 mm by 127 mm having 3000 by 3000 pixels leading to a resolution of 0.0423 mm / pixel.

[0463] Using an image analysis software (a suitable image analysis software is MATLAB available from The Mathworks, Inc., Natick, MA, or equivalent) generate the autocorrelation image of I. Generally, the autocorrelation is the inverse fast Fourier transform (FFT) of the FFT of an image, multiplied by the complex conjugate of the FFT of the image. Following is an exemplary MATLAB script used to generate a normalized autocorrelation image. One skilled in the art will appreciate that this code can be translated and used in equivalent image analysis software packages.[x,y]=size(I);⁢m=2^nextpow⁢2⁢(2⋆x);⁢n=2^nextpow⁢2⁢(2⋆y);⁢t=ifft⁢ 2⁢ (fft⁢ 2⁢ (I,m,n ) .* conj⁢(fft⁢2⁢(I,m,n)));⁢u=(abs⁢(fftshift⁢(t)));⁢v=max⁢(max⁡(u));⁢w=u. / ⁢v;

[0464] An explanation of each line in the script is provided below for clarity.

[0465] [x,y]=size(I): This line determines the size of the input matrix I and assigns the number of rows to x and the number of columns to y.

[0466] m=2{circumflex over ( )}nextpow2(2*x): This line calculates the smallest power of 2 that is greater than or equal to twice the number of rows (2*x). It assigns this value to m, which will be used to determine the size of the transformed matrix in the next step.

[0467] n=2{circumflex over ( )}nextpow2(2*y): Similar to the previous step, this line calculates the smallest power of 2 that is greater than or equal to twice the number of columns (2*y). It assigns this value to n, which will be used to determine the size of the transformed matrix in the next step.

[0468] t=ifft2(fft2(I,m,n).*conj(fft2(I,m,n))) This line performs a series of operations on matrix I. First, it computes the 2D fast Fourier transform (FFT) of I using the fft2 function, extending I to size (m, n) using zero-padding if necessary. Then, it calculates the complex conjugate of the FFT result using the conj function. Finally, it performs an element-wise multiplication of the original FFT result and its complex conjugate. The ifft2 function is then used to compute the inverse FFT, resulting in the variable t.

[0469] u=(abs(fftshift(t))): In this line, the fftshift function is used to shift the zero-frequency component of the Fourier-transformed correlation matrix t to the center. Then, the abs function is applied to obtain the magnitude of each element in the shifted matrix, which is assigned to u. This matrix u is the autocorrelation image.

[0470] v=max(max(u)): This line finds the maximum value in the autocorrelation image u by applying the max function twice. The result is assigned to v, which represents the maximum value in the autocorrelation image. This maximum value is the amplitude of the primary central peak.

[0471] w=u. / v: Finally, this line normalizes the autocorrelation image u by dividing each element by the maximum value v. This normalization step scales the values in u to the range between 0 and 1, and the normalized autocorrelation image is assigned to the variable w.

[0472] Using the normalized autocorrelation image, identify the coordinates (x,y) and amplitudes of the four highest secondary peaks. Secondary autocorrelation peaks are peaks in the autocorrelation image excluding the primary central peak.

[0473] Record the ratio of the amplitude of each of the secondary peaks to the primary central peak as its Periodicity value. Report this value individually for each of the secondary peaks as a percentage to the nearest whole percent.

[0474] Calculate the Euclidian distance between the central peak and the secondary peaks. Report this distance individually for each of the secondary peaks as the Period to the nearest 0.1 mm.

[0475] Calculate the angle of the line segment connecting the secondary peaks to the central peak. This angle is measured relative to the positive x-axis with the central peak being the origin. Report the Angle individually for each of the secondary peaks to the nearest whole degree.

[0476] Select a rectangular region of interest containing the central peak and create a new matrix containing this data. Increase the resolution of this sub-sampled image by five times using nearest neighbor interpolation. Threshold this image at a value of 0.6 to generate a binary image of the cut central peak with the region of the peak above the threshold value in the foreground. Evaluate the shape of the cut central peak region by measuring its maximum Feret diameter and minimum Feret diameter. Maximum Feret diameter is defined as the maximum distance between any two boundary points on the antipodal vertices of a convex hull that enclose the object. Minimum Feret diameter is defined as the minimum distance between any two boundary points on the antipodal vertices of a convex hull that enclose the object.

[0477] Calculate the Isotropy value by dividing the Minimum Feret Diameter value by the Maximum Feret Diameter value. Report the Isotropy value as a percentage to the nearest whole percent.Fibrous Structure Isotropy Test Method

[0478] The Fibrous Structure Isotropy Test Method measures the Isotropy, Periodicity, Period, and Angle of an aerial surface topography image of a fibrous structure sample surface obtained via optical profilometry.Sample Preparation

[0479] Test samples are prepared by carefully removing a fibrous structure sheet from a roll, box, or package of finished product, such that no permanent distortions are made to the sample sheet testing surface. Test samples are selected to avoid perforations, creases or folds within the testing region. Prepare five (5) substantially similar replicate samples for testing. Equilibrate all samples at TAPPI standard temperature and relative humidity conditions (23° C.±2 C.° and 50%±2%) for at least 1 hour prior to conducting the measurement, which is also conducted under TAPPI conditions.3D Surface Image Acquisition

[0480] A three-dimensional (3D) surface topography image of the non-embossed inner facing surface of the sample (relative to its orientation on the roll) is obtained using a structured-light 3D surface topography measurement system (a suitable surface topography measurement system is the Gocator 3210 commercially available from LMI Technologies Inc., Vancouver, Canada, or equivalent). These measurement systems are 3D snapshot sensors, meaning they capture an entire surface in 3D in a single snapshot. These sensors project several structured light patterns in a rapid sequence onto the target. The reflection of the pattern off the target is captured by two cameras. The sample target must remain stationary during the camera exposure of the light patterns. A Structured Light Modulator (SLM) produces a sequence of high resolution / high contrast light patterns using a blue LED. Two cameras capture the reflected light pattern from different viewing angles. The sensor can then use either stereo correlation or independent triangulation to generate 3D points from the light pattern. The result of the measurement is a 3D data set of surface height (defined as the Z-axis) versus displacement in the horizontal (XY) plane. This 3D data set can also be thought of as an image in which every pixel in the image has an associated XY displacement, and the value of the pixel is the recorded Z-axis height value. The sensor is mounted above the base table (clearance distance) to produce a height image with a field of view of approximately 100×154 mm with an XY pixel resolution of approximately 75 microns.

[0481] The instrument is calibrated, installed, and operated according to the manufacturer's specifications.

[0482] The sample is placed flat on the table beneath the camera with the sample centered within the field of view. The sample should be oriented such that the CD is aligned parallel to the short side of the image field of view which is along the X-axis, and the MD is aligned parallel to the long side of the image field of view which is along the Y-axis. A transparent glass plate (Gorilla Glass, 10×7 inches, 1 mm thick; supplied by Cat-I Glass, South Elgin, IL, or equivalent) is carefully placed on top of the sample. Using the instrument's control and acquisition software, a 3D surface topography image of the sample surface is collected by following the instrument manufacturer's recommended measurement procedures, including the setting of an appropriate exposure time. The collected height image file is saved to an evaluation computer running a surface texture processing software (a suitable texture processing software is Mountains Map version 9.2, Digital Surf, Besangon, France, or equivalent).3D Surface Image Processing

[0483] Processing of a surface height image is initiated by opening the image in the surface texture analysis software. The following post processing and filtering procedure is performed on each height image: 1) If the sample area is smaller than the image field of view, select the largest rectangular region of interest that can fit within the sample area and crop the image to that size; 2) fill in non-measured points; 3) remove by subtraction the least squares plane to level the surface 4) apply a 3×3 pixel median smoothing filter; and 5) apply a zero-order robust Gaussian filter with an 8 mm cut-off wavelength. Finally, export this processed surface for further analysis by saving it as an ASCII text file containing the XYZ coordinates for all pixels in the image.3D Surface Angle Analysis

[0484] The XYZ text file is saved to an evaluation computer running 3D data analysis software (a suitable analysis software is MATLAB R2023a available from The Mathworks, Inc., Natick, MA, or equivalent). Analysis of the 3D height data is initiated by opening the XYZ surface data in the 3D data analysis software and designating it as I. Using the image analysis software generate the autocorrelation image of I. Generally, the autocorrelation is the inverse fast Fourier transform (FFT) of the FFT of an image, multiplied by the complex conjugate of the FFT of the image. Following is an exemplary MATLAB script used to generate a normalized autocorrelation image. One skilled in the art will appreciate that this code can be translated and used in equivalent image analysis software packages.[x,y]=size⁢ (I);⁢m=2^nextpow⁢2⁢(2⋆x);⁢n=2^nextpow⁢2⁢(2⋆y);⁢t=ifft⁢ 2⁢ (fft⁢ 2⁢ (I,m,n ) .* conj⁢(fft⁢2⁢(I,m,n)));⁢u=(abs⁢(fftshift⁢(t)));⁢v=max⁢(max⁢(u));⁢w=u. / ⁢v;

[0485] An explanation of each line in the script is provided below for clarity.

[0486] [x,y]=size(I): This line determines the size of the input matrix I and assigns the number of rows to x and the number of columns to y.

[0487] m=2{circumflex over ( )}nextpow2(2*x): This line calculates the smallest power of 2 that is greater than or equal to twice the number of rows (2*x). It assigns this value to m, which will be used to determine the size of the transformed matrix in the next step.

[0488] n=2{circumflex over ( )}nextpow2(2*y): Like the previous step, this line calculates the smallest power of 2 that is greater than or equal to twice the number of columns (2*y). It assigns this value to n, which will be used to determine the size of the transformed matrix in the next step.

[0489] t=ifft2(fft2(I,m,n).*conj(fft2(I,m,n))) This line performs a series of operations on matrix I. First, it computes the 2D fast Fourier transform (FFT) of I using the fft2 function, extending I to size (m, n) using zero-padding if necessary. Then, it calculates the complex conjugate of the FFT result using the conj function. Finally, it performs an element-wise multiplication of the original FFT result and its complex conjugate. The ifft2 function is then used to compute the inverse FFT, resulting in the variable t.

[0490] u=(abs(fftshift(t))): In this line, the fftshift function is used to shift the zero-frequency component of the Fourier-transformed correlation matrix t to the center. Then, the abs function is applied to obtain the magnitude of each element in the shifted matrix, which is assigned to u. This matrix u is the autocorrelation image.

[0491] v=max(max(u)): This line finds the maximum value in the autocorrelation image u by applying the max function twice. The result is assigned to v, which represents the maximum value in the autocorrelation image. This maximum value is the amplitude of the primary central peak.

[0492] w=u. / v: Finally, this line normalizes the autocorrelation image u by dividing each element by the maximum value v. This normalization step scales the values in u to the range between 0 and 1, and the normalized autocorrelation image is assigned to the variable w.

[0493] Using the normalized autocorrelation image, identify the coordinates (x,y) and amplitudes of the four highest secondary peaks. Secondary autocorrelation peaks are peaks in the autocorrelation image excluding the primary central peak.

[0494] Record the amplitude of each of the secondary peaks as its Periodicity value. Record this value individually for each of the secondary peaks as a percentage to the nearest whole percent.

[0495] Calculate the Euclidian distance between the central peak and the secondary peaks. Record this distance individually for each of the secondary peaks as the Period to the nearest 0.1 mm.

[0496] Calculate the angle of the line segment connecting the secondary peaks to the central peak. This angle is measured relative to the positive x-axis with the central peak being the origin. Record the Angle individually for each of the secondary peaks to the nearest whole degree.

[0497] Select a rectangular region of interest containing the central peak and create a new matrix containing this data. Increase the resolution of this sub-sampled image by five times using nearest neighbor interpolation. Threshold this image at a value of 0.6 to generate a binary image of the cut central peak with the region of the peak above the threshold value in the foreground. Evaluate the shape of the cut central peak region by measuring its maximum Feret diameter and minimum Feret diameter. Maximum Feret diameter is defined as the maximum distance between any two boundary points on the antipodal vertices of a convex hull that enclose the object. Minimum Feret diameter is defined as the minimum distance between any two boundary points on the antipodal vertices of a convex hull that enclose the object.

[0498] Calculate the Isotropy value by dividing the Minimum Feret Diameter value by the Maximum Feret Diameter value. Record the Isotropy value as a percentage to the nearest whole percent.

[0499] This procedure is repeated for all five replicate test samples and the reported values for each of the parameters is the arithmetic mean of the five individual measurements.Dry Elongation, Tensile Strength, TEA and Modulus Test Methods for Bath Tissue

[0500] Please note that a method is provided for Paper Towels, i.e., “Dry Elongation, Tensile Strength, TEA and Modulus Test Methods for Paper Towels”.

[0501] Elongation, Tensile Strength, TEA and Tangent Modulus are measured on a constant rate of extension tensile tester with computer interface (a suitable instrument is the EJA Vantage from the Thwing-Albert Instrument Co. Wet Berlin, NJ) using a load cell for which the forces measured are within 10% to 90% of the limit of the load cell. Both the movable (upper) and stationary (lower) pneumatic jaws are fitted with smooth stainless steel faced grips, with a design suitable for testing 1 inch wide sheet material (Thwing-Albert item #733GC). An air pressure of about 60 psi is supplied to the jaws.

[0502] Twenty usable units of fibrous structures are divided into four stacks of five usable units each. The usable units in each stack are consistently oriented with respect to machine direction (MD) and cross direction (CD). Two of the stacks are designated for testing in the MD and two for CD. Using a one inch precision cutter (Thwing Albert) take a CD stack and cut two, 1.00 in±0.01 in wide by at least 3.0 in long strips from each CD stack (long dimension in CD). Each strip is five usable unit layers thick and will be treated as a unitary specimen for testing. In like fashion cut the remaining CD stack and the two MD stacks (long dimension in MD) to give a total of 8 specimens (five layers each), four CD and four MD.

[0503] Program the tensile tester to perform an extension test, collecting force and extension data at an acquisition rate of 20 Hz as the crosshead raises at a rate of 4.00 in / min (10.16 cm / min) until the specimen breaks. The break sensitivity is set to 50%, i.e., the test is terminated when the measured force drops to 50% of the maximum peak force, after which the crosshead is returned to its original position.

[0504] Set the gage length to 2.00 inches. Zero the crosshead and load cell. Insert the specimen into the upper and lower open grips such that at least 0.5 inches of specimen length is contained each grip. Align specimen vertically within the upper and lower jaws, then close the upper grip. Verify specimen is aligned, then close lower grip. The specimen should be under enough tension to eliminate any slack, but less than 0.05 N of force measured on the load cell. Start the tensile tester and data collection. Repeat testing in like fashion for all four CD and four MD specimens.

[0505] Program the software to calculate the following from the constructed force (g) verses extension (in) curve:

[0506] Tensile Strength is the maximum peak force (g) divided by the product of the specimen width (1 in) and the number of usable units in the specimen (5), and then reported as g / in to the nearest 1 g / in.

[0507] Adjusted Gage Length is calculated as the extension measured at 11.12 g of force (in) added to the original gage length (in).

[0508] Elongation is calculated as the extension at maximum peak force (in) divided by the Adjusted Gage Length (in) multiplied by 100 and reported as % to the nearest 0.1%.

[0509] Tensile Energy Absorption (TEA) is calculated as the area under the force curve integrated from zero extension to the extension at the maximum peak force (g*in), divided by the product of the adjusted Gage Length (in), specimen width (in), and number of usable units in the specimen (5). This is reported as g*in / in2 to the nearest 1 g*in / in2.

[0510] Replot the force (g) verses extension (in) curve as a force (g) verses strain curve. Strain is herein defined as the extension (in) divided by the Adjusted Gage Length (in).

[0511] Program the software to calculate the following from the constructed force (g) verses strain curve:

[0512] Tangent Modulus is calculated as the least squares linear regression using the first data point from the force (g) verses strain curve recorded after 190.5 g (38.1 g×5 layers) force and the 5 data points immediately preceding and the 5 data points immediately following it. This slope is then divided by the product of the specimen width (2.54 cm) and the number of usable units in the specimen (5), and then reported to the nearest 1 g / cm.

[0513] The Tensile Strength (g / in), Elongation (%), TEA (g*in / in2) and Tangent Modulus (g / cm) are calculated for the four CD specimens and the four MD specimens. Calculate an average for each parameter separately for the CD and MD specimens.Calculations:Geometric⁢ Mean⁢ Tensile=Square⁢ Root⁢ of [MD⁢ Tensile⁢ Strength⁢ ⁢(g / in)×
CD⁢ Tensile⁢ Strength⁢ (g / in)]⁢Geometric⁢ Mean⁢ Peak⁢ Elongation=Square⁢ Root⁢ of [MD⁢ ⁢Elongation⁢ (%)×CD⁢ ⁢Elongation⁢ (%)]⁢Geometric⁢ Mean⁢ TEA=Square⁢ Root⁢ of [MD⁢ TEA⁢ (g*in / in2)×CD⁢ TEA⁢ (g*in / in2)]⁢Geometric⁢ Mean⁢ Modulus=Square⁢ Root⁢ of [MD⁢ Modulus⁢ (g / cm)×CD⁢ Modulus⁢ (g / cm)]⁢Total⁢ Dry⁢ Tensile⁢ Strength⁢ (TDT)=MD⁢ Tensile⁢ Strength⁢ (g / in)×CD⁢ Tensile⁢ Strength⁢ (g / in)⁢Total⁢ TEA=MD⁢ TEA⁢ (g*in / in2)+CD⁢ TEA⁢ (g*in / in2)⁢Total⁢ Modulus=MD⁢ Modulus⁢ (g / cm) / CD⁢ Modulus⁢ (g / cm)⁢Tensile⁢ Ratio=MD⁢ Tensile⁢ Strength⁢ (g / in) / CD⁢ Tensile⁢ Strength⁢ (g / in)Dry Elongation, Tensile Strength, TEA and Modulus Test Methods for Paper Towels

[0514] Please note that a method is provided for Bath Tissues, i.e., “Dry Elongation, Tensile Strength, TEA and Modulus Test Methods for Bath Tissue”.

[0515] Elongation, Tensile Strength, TEA and Tangent Modulus are measured on a constant rate of extension tensile tester with computer interface (a suitable instrument is the EJA Vantage from the Thwing-Albert Instrument Co. Wet Berlin, NJ) using a load cell for which the forces measured are within 10% to 90% of the limit of the load cell. Both the movable (upper) and stationary (lower) pneumatic jaws are fitted with smooth stainless steel faced grips, with a design suitable for testing 1 inch wide sheet material (Thwing-Albert item #733GC). An air pressure of about 60 psi is supplied to the jaws.

[0516] Eight usable units of fibrous structures are divided into two stacks of four usable units each. The usable units in each stack are consistently oriented with respect to machine direction (MD) and cross direction (CD). One of the stacks is designated for testing in the MD and the other for CD. Using a one inch precision cutter (Thwing Albert) take a CD stack and cut one, 1.00 in±0.01 in wide by at least 5.0 in long stack of strips (long dimension in CD). In like fashion cut the remaining stack in the MD (strip long dimension in MD), to give a total of 8 specimens, four CD and four MD strips. Each strip to be tested is one usable unit thick and will be treated as a unitary specimen for testing.

[0517] Program the tensile tester to perform an extension test, collecting force and extension data at an acquisition rate of 20 Hz as the crosshead raises at a rate of 4.00 in / min (10.16 cm / min) until the specimen breaks. The break sensitivity is set to 50%, i.e., the test is terminated when the measured force drops to 50% of the maximum peak force, after which the crosshead is returned to its original position.

[0518] Set the gage length to 4.00 inches. Zero the crosshead and load cell. Insert the specimen into the upper and lower open grips such that at least 0.5 inches of specimen length is contained each grip. Align specimen vertically within the upper and lower jaws, then close the upper grip. Verify specimen is aligned, then close lower grip. The specimen should be under enough tension to eliminate any slack, but less than 0.05 N of force measured on the load cell. Start the tensile tester and data collection. Repeat testing in like fashion for all four CD and four MD specimens.

[0519] Program the software to calculate the following from the constructed force (g) verses extension (in) curve:

[0520] Tensile Strength is the maximum peak force (g) divided by the specimen width (1 in), and reported as g / in to the nearest 1 g / in.

[0521] Adjusted Gage Length is calculated as the extension measured at 11.12 g of force (in) added to the original gage length (in).

[0522] Elongation is calculated as the extension at maximum peak force (in) divided by the Adjusted Gage Length (in) multiplied by 100 and reported as % to the nearest 0.1%.

[0523] Tensile Energy Absorption (TEA) is calculated as the area under the force curve integrated from zero extension to the extension at the maximum peak force (g*in), divided by the product of the adjusted Gage Length (in) and specimen width (in). This is reported as g*in / in2 to the nearest 1 g*in / in2.

[0524] Replot the force (g) verses extension (in) curve as a force (g) verses strain curve. Strain is herein defined as the extension (in) divided by the Adjusted Gage Length (in).

[0525] Program the software to calculate the following from the constructed force (g) verses strain curve:

[0526] Tangent Modulus is calculated as the least squares linear regression using the first data point from the force (g) verses strain curve recorded after 38.1 g force and the 5 data points immediately preceding and the 5 data points immediately following it. This slope is then divided by the specimen width (2.54 cm), and then reported to the nearest 1 g / cm.

[0527] The Tensile Strength (g / in), Elongation (%), TEA (g*in / in2) and Tangent Modulus (g / cm) are calculated for the four CD specimens and the four MD specimens. Calculate an average for each parameter separately for the CD and MD specimens.Calculations:Geometric⁢ Mean⁢ Tensile=Square⁢ Root⁢ of [MD⁢ Tensile⁢ Strength⁢ ⁢(g / in)×
CD⁢ Tensile⁢ Strength⁢ ⁢(g / in)]⁢Geometric⁢ Mean⁢ Peak⁢ Elongation=Square⁢ Root⁢ of [MD⁢ ⁢Elongation⁢ (%)×CD⁢ ⁢Elongation⁢ (%)]⁢Geometric⁢ Mean⁢ TEA=Square⁢ Root⁢ of [MD⁢ TEA⁢ (g*in / in2)×CD⁢ TEA⁢ (g*in / in2)]⁢Geometric⁢ Mean⁢ Modulus=Square⁢ Root⁢ of [MD⁢ Modulus⁢ (g / cm)×CD⁢ Modulus⁢ (g / cm)]⁢Total⁢ Dry⁢ Tensile⁢ Strength⁢ (TDT)=MD⁢ Tensile⁢ Strength⁢ (g / in)×CD⁢ Tensile⁢ Strength⁢ (g / in)⁢Total⁢ TEA=MD⁢ TEA⁢ (g*in / in2)+CD⁢ TEA⁢ (g*in / in2)⁢Total⁢ Modulus=MD⁢ Modulus⁢ (g / cm) / CD⁢ Modulus⁢ (g / cm)⁢Tensile⁢ Ratio=MD⁢ Tensile⁢ Strength⁢ (g / in) / CD⁢ Tensile⁢ Strength⁢ (g / in)Flexural Rigidity Test Method

[0528] This test is performed on 1 inch×6 inch (2.54 cm×15.24 cm) strips of a fibrous structure sample. A Cantilever Bending Tester such as described in ASTM Standard D 1388 (Model 5010, Instrument Marketing Services, Fairfield, NJ) is used and operated at a ramp angle of 41.5±0.5° and a sample slide speed of 0.5±0.2 in / second (1.3±0.5 cm / second). A minimum of n=16 tests are performed on each sample from n=8 sample strips.

[0529] No fibrous structure sample which is creased, bent, folded, perforated, or in any other way weakened should ever be tested using this test. A non-creased, non-bent, non-folded, non-perforated, and non-weakened in any other way fibrous structure sample should be used for testing under this test.

[0530] From one fibrous structure sample of about 4 inch×6 inch (10.16 cm×15.24 cm), carefully cut using a 1 inch (2.54 cm) JDC Cutter (available from Thwing-Albert Instrument Company, Philadelphia, PA) four (4) 1 inch (2.54 cm) wide by 6 inch (15.24 cm) long strips of the fibrous structure in the MD direction. From a second fibrous structure sample from the same sample set, carefully cut four (4) 1 inch (2.54 cm) wide by 6 inch (15.24 cm) long strips of the fibrous structure in the CD direction. It is important that the cut be exactly perpendicular to the long dimension of the strip. In cutting non-laminated two-ply fibrous structure strips, the strips should be cut individually. The strip should also be free of wrinkles or excessive mechanical manipulation which can impact flexibility. Mark the direction very lightly on one end of the strip, keeping the same surface of the sample up for all strips. Later, the strips will be turned over for testing, thus it is important that one surface of the strip be clearly identified, however, it makes no difference which surface of the sample is designated as the upper surface. Equilibrate all samples at TAPPI standard temperature and relative humidity conditions (23° C.±2° C. and 50%±2%) for at least 1 hour prior to conducting the TSA testing, which is also conducted under TAPPI conditions.

[0531] Using other portions of the fibrous structure (not the cut strips), determine the basis weight of the fibrous structure sample in lbs / 3000 ft2 and the caliper of the fibrous structure in mils (thousandths of an inch) using the standard procedures disclosed herein. Place the Cantilever Bending Tester level on a bench or table that is relatively free of vibration, excessive heat and most importantly air drafts. Adjust the platform of the Tester to horizontal as indicated by the leveling bubble and verify that the ramp angle is at 41.5±0.5°. Remove the sample slide bar from the top of the platform of the Tester. Place one of the strips on the horizontal platform using care to align the strip parallel with the movable sample slide. Align the strip exactly even with the vertical edge of the Tester wherein the angular ramp is attached or where the zero mark line is scribed on the Tester. Carefully place the sample slide bar back on top of the sample strip in the Tester. The sample slide bar must be carefully placed so that the strip is not wrinkled or moved from its initial position.

[0532] Move the strip and movable sample slide at a rate of approximately 0.5±0.2 in / second (1.3±0.5 cm / second) toward the end of the Tester to which the angular ramp is attached. This can be accomplished with either a manual or automatic Tester. Ensure that no slippage between the strip and movable sample slide occurs. As the sample slide bar and strip project over the edge of the Tester, the strip will begin to bend, or drape downward. Stop moving the sample slide bar the instant the leading edge of the strip falls level with the ramp edge. Read and record the overhang length from the linear scale to the nearest 0.5 mm. Record the distance the sample slide bar has moved in cm as overhang length. This test sequence is performed a total of eight (8) times for each fibrous structure in each direction (MD and CD). The first four strips are tested with the upper surface as the fibrous structure was cut facing up. The last four strips are inverted so that the upper surface as the fibrous structure was cut is facing down as the strip is placed on the horizontal platform of the Tester.

[0533] The average overhang length is determined by averaging the sixteen (16) readings obtained on a fibrous structure.Overhang⁢ Length⁢ MD=Sum⁢ of⁢ 8⁢ MD⁢ readings8⁢Overhang⁢ Length⁢ CD=Sum⁢ of⁢ 8⁢ CD⁢ readings8⁢Overhang⁢ Length⁢ Total=Sum⁢ of⁢ all⁢ 16⁢ readings16⁢Bend⁢ Length⁢ MD=Overhang⁢ Length⁢ MD2⁢Bend⁢ Length⁢ CD=Overhang⁢ Length⁢ CD2⁢Bend⁢ Length⁢ Total=Overhang⁢ Length⁢ Total2⁢Flexural⁢ Rigidity=0.1629×W×C3wherein W is the basis weight of the fibrous structure in lbs / 3000 ft2; C is the bending length (MD or CD or Total) in cm; and the constant 0.1629 is used to convert the basis weight from English to metric units. The results are expressed in mg-cm.GM⁢ Flexural⁢ Rigidity=Square⁢ Root⁢ of⁢ (MD⁢ ⁢Flexural⁢ Rigidity×CD⁢ Flexural⁢ Rigidity)Plate Stiffness Test MethodAs used herein, the “Plate Stiffness” test is a measure of stiffness of a flat sample as it is deformed downward into a hole beneath the sample. For the test, the sample is modeled as an infinite plate with thickness “t” that resides on a flat surface where it is centered over a hole with radius “R”. A central force “F” applied to the tissue directly over the center of the hole deflects the tissue down into the hole by a distance “w”. For a linear elastic material, the deflection can be predicted by:w=3⁢F4⁢π⁢Et3⁢(1-v)⁢(3+v)⁢ R2where “E” is the effective linear elastic modulus, “v” is the Poisson's ratio, “R” is the radius of the hole, and “t” is the thickness of the tissue, taken as the caliper in millimeters measured on a stack of 5 tissues under a load of about 0.29 psi. Taking Poisson's ratio as 0.1 (the solution is not highly sensitive to this parameter, so the inaccuracy due to the assumed value is likely to be minor), the previous equation can be rewritten for “w” to estimate the effective modulus as a function of the flexibility test results:E≈3⁢R24⁢t3⁢FwThe test results are carried out using an MTS Alliance RT / 1, Insight Renew, or similar model testing machine (MTS Systems Corp., Eden Prairie, Minn.), with a 50 newton load cell, and data acquisition rate of at least 25 force points per second. As a stack of five tissue sheets (created without any bending, pressing, or straining) at least 2.5-inches by 2.5 inches, but no more than 5.0 inches by 5.0 inches, oriented in the same direction, sits centered over a hole of radius 15.75 mm on a support plate, a blunt probe of 3.15 mm radius descends at a speed of 20 mm / min. For typical perforated rolled bath tissue, sample preparation consists of removing five (5) connected usable units, and carefully forming a 5 sheet stack, accordion style, by bending only at the perforation lines. When the probe tip descends to 1 mm below the plane of the support plate, the test is terminated. The maximum slope (using least squares regression) in grams of force / mm over any 0.5 mm span during the test is recorded (this maximum slope generally occurs at the end of the stroke). The load cell monitors the applied force and the position of the probe tip relative to the plane of the support plate is also monitored. The peak load is recorded, and “E” is estimated using the above equation.The Plate Stiffness “S” per unit width can then be calculated as:S=Et312and is expressed in units of Newtons*millimeters. The Testworks program uses the following formula to calculate stiffness (or can be calculated manually from the raw data output):S=(Fw)[(3+v)⁢R2 1⁢6⁢π]wherein “F / w” is max slope (force divided by deflection), “v” is Poisson's ratio taken as 0.1, and “R” is the ring radius.The same sample stack (as used above) is then flipped upside down and retested in the same manner as previously described. This test is run three more times (with different sample stacks). Thus, eight S values are calculated from four 5-sheet stacks of the same sample. The numerical average of these eight S values is reported as Plate Stiffness for the sample.CRT Rate and Capacity Test MethodCRT Rate and Capacity values are generated by running the test procedure as defined in U.S. Patent Application No. US 2017-0183824.SST Absorbency Rate Test MethodThis test incorporates the Slope of the Square Root of Time (SST) Test Method. The SST method measures rate over a wide spectrum of time to capture a view of the product pick-up rate over the useful lifetime. In particular, the method measures the absorbency rate via the slope of the mass versus the square root of time from 2-15 seconds.OverviewThe absorption (wicking) of water by a fibrous sample is measured over time. A sample is placed horizontally in the instrument and is supported with minimal contact during testing (without allowing the sample to droop) by an open weave net structure that rests on a balance. The test is initiated when a tube connected to a water reservoir is raised and the meniscus makes contact with the center of the sample from beneath, at a small negative pressure. Absorption is controlled by the ability of the sample to pull the water from the instrument for approximately 20 seconds. Rate is determined as the slope of the regression line of the outputted weight vs sqrt(time) from 2 to 15 seconds.ApparatusConditioned Room—Temperature is controlled from 73° F.±2° F. (23° C.±1° C.). Relative Humidity is controlled from 50%±2%Sample Preparation—Product samples are cut using hydraulic / pneumatic precision cutter into 3.375 inch diameter circles.

[0543] Capacity Rate Tester (CRT)—The CRT is an absorbency tester capable of measuring capacity and rate. The CRT consists of a balance (0.001 g), on which rests on a woven grid (using nylon monofilament line having a 0.014″ diameter) placed over a small reservoir with a delivery tube in the center. This reservoir is filled by the action of solenoid valves, which help to connect the sample supply reservoir to an intermediate reservoir, the water level of which is monitored by an optical sensor. The CRT is run with a −2 mm water column, controlled by adjusting the height of water in the supply reservoir.

[0544] A diagram of the testing apparatus set up is shown in FIG. 9.

[0545] Software—LabView based custom software specific to CRT Version 4.2 or later.

[0546] Water—Distilled water with conductivity <10 μS / cm (target <5 μS / cm) @ 25° C.Sample Preparation

[0547] For this method, a usable unit is described as one finished product unit regardless of the number of plies. Condition all samples with packaging materials removed for a minimum of 2 hours prior to testing. Discard at least the first ten usable units from the roll. Remove two usable units and cut one 3.375-inch circular sample from the center of each usable unit for a total of 2 replicates for each test result. Do not test samples with defects such as wrinkles, tears, holes, etc. Replace with another usable unit which is free of such defectsSample TestingPre-Test Set-Up1. The water height in the reservoir tank is set −2.0 mm below the top of the support rack (where the towel sample will be placed).

[0549] 2. The supply tube (8 mm I.D.) is centered with respect to the support net.

[0550] 3. Test samples are cut into circles of 3⅜″ diameter and equilibrated at Tappi environment conditions for a minimum of 2 hours.Test Description1. After pressing the start button on the software application, the supply tube moves to 0.33 mm below the water height in the reserve tank. This creates a small meniscus of water above the supply tube to ensure test initiation. A valve between the tank and the supply tube closes, and the scale is zeroed.

[0552] 2. The software prompts you to “load a sample”. A sample is placed on the support net, centering it over the supply tube, and with the side facing the outside of the roll placed downward.

[0553] 3. Close the balance windows and press the “OK” button—the software records the dry weight of the circle.

[0554] 4. The software prompts you to “place cover on sample”. The plastic cover is placed on top of the sample, on top of the support net. The plastic cover has a center pin (which is flush with the outside rim) to ensure that the sample is in the proper position to establish hydraulic connection. Four other pins, 1 mm shorter in depth, are positioned 1.25-1.5 inches radially away from the center pin to ensure the sample is flat during the test. The sample cover rim should not contact the sheet. Close the top balance window and click “OK”.

[0555] 5. The software re-zeroes the scale and then moves the supply tube towards the sample. When the supply tube reaches its destination, which is 0.33 mm below the support net, the valve opens (i.e., the valve between the reserve tank and the supply tube), and hydraulic connection is established between the supply tube and the sample. Data acquisition occurs at a rate of 5 Hz and is started about 0.4 seconds before water contacts the sample.

[0556] 6. The test runs for at least 20 seconds. After this, the supply tube pulls away from the sample to break the hydraulic connection.

[0557] 7. The wet sample is removed from the support net. Residual water on the support net and cover is dried with a paper towel.

[0558] 8. Repeat until all samples are tested.

[0559] 9. After each test is run, a *.txt file is created (typically stored in the CRT / data / rate directory) with a file name as typed at the start of the test. The file contains all the test set-up parameters, dry sample weight, and cumulative water absorbed (g) vs. time (sec) data collected from the test.Calculation of Rate of Uptake

[0560] Take the raw data file that includes time and weight data.

[0561] First, create a new time column that subtracts 0.4 seconds from the raw time data to adjust the raw time data to correspond to when initiation actually occurs (about 0.4 seconds after data collection begins).

[0562] Second, create a column of data that converts the adjusted time data to square root of time data (e.g., using a formula such as SQRT( ) within Excel).

[0563] Third, calculate the slope of the weight data vs the square root of time data (e.g., using the SLOPE( ) function within Excel, using the weight data as the y-data and the sqrt(time) data as the x-data, etc.). The slope should be calculated for the data points from 2 to 15 seconds, inclusive (or 1.41 to 3.87 in the sqrt(time) data column).Calculation of Slope of the Square Root of Time (SST)

[0564] The start time of water contact with the sample is estimated to be 0.4 seconds after the start of hydraulic connection is established between the supply tube and the sample (CRT Time). This is because data acquisition begins while the tube is still moving towards the sample and incorporates the small delay in scale response. Thus, “time zero” is actually at 0.4 seconds in CRT Time as recorded in the *.txt file.

[0565] The slope of the square root of time (SST) from 2-15 seconds is calculated from the slope of a linear regression line from the square root of time between (and including) 2 to 15 seconds (x-axis) versus the cumulative grams of water absorbed. The units are g / sec5.Dry and Wet Caliper Test Methods

[0566] Dry and Wet Caliper values are generated by running the test procedure as defined in U.S. Pat. No. 7,744,723 and states, in relevant part:Dry Caliper Test Method

[0567] Samples are conditioned at 23+ / −1° C. and 50%+ / −2% relative humidity for two hours prior to testing.

[0568] Dry Caliper of a sample of fibrous structure product is determined by cutting a sample of the fibrous structure product such that it is larger in size than a load foot loading surface where the load foot loading surface has a circular surface area of about 3.14 in 2. The sample is confined between a horizontal flat surface and the load foot loading surface. The load foot loading surface applies a confining pressure to the sample of 14.7 g / cm2 (about 0.21 psi). The caliper is the resulting gap between the flat surface and the load foot loading surface. Such measurements can be obtained on a VIR Electronic Thickness Tester Model II available from Thwing-Albert Instrument Company, Philadelphia, Pa. The caliper measurement is repeated and recorded at least five (5) times so that an average caliper can be calculated. The result is reported in mils.Stack Compressibility and Resilient Bulk Test Method

[0569] Stack thickness (measured in mils, 0.001 inch) is measured as a function of confining pressure (g / in2) using a Thwing-Albert (14 W. Collings Ave., West Berlin, NJ) Vantage Compression / Softness Tester (model 1750-2005 or similar) or equivalent instrument, equipped with a 2500 g load cell (force accuracy is + / −0.25% when measuring value is between 10%-100% of load cell capacity, and 0.025% when measuring value is less than 10% of load cell capacity), a 1.128 inch diameter steel pressure foot (one square inch cross sectional area) which is aligned parallel to the steel anvil (2.5 inch diameter). The pressure foot and anvil surfaces must be clean and dust free, particularly when performing the steel-to-steel test. Thwing-Albert software (MAP) controls the motion and data acquisition of the instrument.

[0570] The instrument and software are set-up to acquire crosshead position and force data at a rate of 50 points / sec. The crosshead speed (which moves the pressure foot) for testing samples is set to 0.20 inches / min (the steel-to-steel test speed is set to 0.05 inches / min). Crosshead position and force data are recorded between the load cell range of approximately 5 and 1500 grams during compression. The crosshead is programmed to stop immediately after surpassing 1500 grams, record the thickness at this pressure (termed Tmax), and immediately reverse direction at the same speed as performed in compression. Data is collected during this decompression portion of the test (also termed recovery) between approximately 1500 and 5 grams. Since the foot area is one square inch, the force data recorded corresponds to pressure in units of g / in2. The MAP software is programmed to the select 15 crosshead position values (for both compression and recovery) at specific pressure trap points of 10, 25, 50, 75, 100, 125, 150, 200, 300, 400, 500, 600, 750, 1000, and 1250 g / in2 (i.e., recording the crosshead position of very next acquired data point after the each pressure point trap is surpassed). In addition to these 30 collected trap points, Tmax is also recorded, which is the thickness at the maximum pressure applied during the test (approximately 1500 g / in2).

[0571] Since the overall test system, including the load cell, is not perfectly rigid, a steel-to-steel test is performed (i.e., nothing in between the pressure foot and anvil) at least twice for each batch of testing, to obtain an average set of steel-to-steel crosshead positions at each of the 31 trap points described above. This steel-to-steel crosshead position data is subtracted from the corresponding crosshead position data at each trap point for each tested stacked sample, thereby resulting in the stack thickness (mils) at each pressure trap point during the compression, maximum pressure, and recovery portions of the test.StackT⁢ (trap)=StackCP⁢ (trap)-SteelCP⁢ (trap)⁢Where:⁢trap=trap⁢ point⁢ pressure⁢ at⁢ either⁢ compression,recovery,or⁢ max⁢StackT=Thickness⁢ of⁢ Stack⁢ (at⁢ trap⁢ pressure)⁢StackCP=Crosshead⁢ position⁢ of⁢ Stack⁢ in⁢ test⁢ (at⁢ trap⁢ pressure)⁢SteelCP=Crosshead⁢ position⁢ of⁢ steel-to-steel⁢ test⁢ (at⁢ trap⁢ pressure)

[0572] A stack of five (5) usable units thick is prepared for testing as follows. The minimum usable unit size is 2.5 inch by 2.5 inch; however, a larger sheet size is preferable for testing, since it allows for easier handling without touching the central region where compression testing takes place. For typical perforated rolled bath tissue, this consists of removing five (5) sets of 3 connected usable units. In this case, testing is performed on the middle usable unit, and the outer 2 usable units are used for handling while removing from the roll and stacking. For other product formats, it is advisable, when possible, to create a test sheet size (each one usable unit thick) that is large enough such that the inner testing region of the created 5 usable unit thick stack is never physically touched, stretched, or strained, but with dimensions that do not exceed 14 inches by 6 inches.

[0573] The 5 sheets (one usable unit thick each) of the same approximate dimensions are placed one on top the other, with their MD aligned in the same direction, their outer face all pointing in the same direction, and their edges aligned+ / −3 mm of each other. The central portion of the stack, where compression testing will take place, is never to be physically touched, stretched, and / or strained (this includes never to ‘smooth out’ the surface with a hand or other apparatus prior to testing).

[0574] The 5 sheet stack is placed on the anvil, positioning it such that the pressure foot will contact the central region of the stack (for the first compression test) in a physically untouched spot, leaving space for a subsequent (second) compression test, also in the central region of the stack, but separated by ¼ inch or more from the first compression test, such that both tests are in untouched, and separated spots in the central region of the stack. From these two tests, an average crosshead position of the stack at each trap pressure (i.e., StackCP(trap)) is calculated for compression, maximum pressure, and recovery portions of the tests. Then, using the average steel-to-steel crosshead trap points (i.e., SteelCP(trap)), the average stack thickness at each trap (i.e., StackT(trap) is calculated (mils).

[0575] Stack Compressibility is defined here as the absolute value of the linear slope of the stack thickness (mils) as a function of the log(10) of the confining pressure (grams / in2), by using the 15 compression trap points discussed previously (i.e., compression from 10 to 1250 g / in2), in a least squares regression. The units for Stack Compressibility are [mils / (log(g / in2))] and is reported to the nearest 0.1 [mils / (log(g / in2))].

[0576] Resilient Bulk is calculated from the stack weight per unit area and the sum of 8 StackT(trap) thickness values from the maximum pressure and recovery portion of the tests: i.e., at maximum pressure (Tmax) and recovery trap points at R1250, R1000, R750, R500, R300, R100, and R10 g / in2 (a prefix of “R” denotes these traps come from recovery portion of the test). Stack weight per unit area is measured from the same region of the stack contacted by the compression foot, after the compression testing is complete, by cutting a 3.50 inch square (typically) with a precision die cutter, and weighing on a calibrated 3-place balance, to the nearest 0.001 gram. The weight of the precisely cut stack, along with the StackT(trap) data at each required trap pressure (each point being an average from the two compression / recovery tests discussed previously), are used in the following equation to calculate Resilient Bulk, reported in units of cm3 / g, to the nearest 0.1 cm3 / g.Resilient⁢ Bulk=SUM⁢(StackT⁢(Tmax,R⁢1250,R⁢1000,R⁢750,R⁢500,R⁢300,R⁢100,R⁢10))*0.00254M / A⁢Where:⁢StackT=Thickness⁢ of⁢ Stack⁢ (at⁢ trap⁢ pressures⁢ of⁢ Tmax⁢ and⁢
 recovery⁢ pressures⁢ listed⁢ above),(mils)⁢M=weight⁢ ⁢of⁢ precisely⁢ cut⁢ stack,(grams)⁢A=area⁢ of⁢ the⁢ precisely⁢ cut⁢ stack,(cm2)Further Definitions and Cross-References

[0577] The dimensions and values disclosed herein are not to be understood as being strictly limited to the exact numerical values recited. Instead, unless otherwise specified, each such dimension is intended to mean both the recited value and a functionally equivalent range surrounding that value. For example, a dimension disclosed as “40 mm” is intended to mean “about 40 mm.”

[0578] Every document cited herein, including any cross referenced or related patent or application and any patent application or patent to which this application claims priority or benefit thereof, is hereby incorporated herein by reference in its entirety unless expressly excluded or otherwise limited. The citation of any document is not an admission that it is prior art with respect to any invention disclosed or claimed herein or that it alone, or in any combination with any other reference or references, teaches, suggests or discloses any such invention. Further, to the extent that any meaning or definition of a term in this document conflicts with any meaning or definition of the same term in a document incorporated by reference, the meaning or definition assigned to that term in this document shall govern.

[0579] While particular embodiments of the present disclosure have been illustrated and described, it would be obvious to those skilled in the art that various other changes and modifications may be made without departing from the spirit and scope of the invention. It is therefore intended to cover in the appended claims all such changes and modifications that are within the scope of this invention.

Claims

1. A structure selected from the group consisting of a fibrous structure, a papermaking belt, a structuring layer, and a mask, the structure comprising a plurality of cells;wherein the structure defines a major coordinate plane;wherein the plurality of cells comprises at least a first cell and a second cell;wherein the first cell comprisesa first perimeter defining a first shape and a first size,a first position relative to the major coordinate plane,a first minor coordinate system centered on the first position and oriented at a first angle relative to the major coordinate planewherein the second cell comprisesa second perimeter defining a second shape and a second size,a second position relative to the major coordinate plane,a second minor coordinate system centered on the second position and oriented at a second angle relative to the major coordinate plane;wherein the first position and the second position are substantially within a first row;wherein the first row comprises a longitudinal row axis, a lateral row axis, a longitudinal row dimension substantially along the longitudinal row axis, and a lateral row dimension substantially along the lateral row axis; andwherein the longitudinal row axis is oriented at a row angle relative to an axis of the major coordinate plane.

2. The fibrous substrate of claim 1, wherein the plurality of cells defines a pattern having a Fibrous Structure Period (first secondary peak) greater than 4 mm and a Fibrous Structure Percent Texture Isotropy less than 84%.

3. The structure of claim 1, wherein the first shape and the second shape are substantially the same.

4. The structure of claim 1, wherein the first shape and the second shape are substantially different.

5. The structure of claim 1, wherein the first shape is irregular.

6. The structure of claim 1, wherein the second shape is irregular.

7. The structure of claim 1, wherein the first size and the second size are substantially the same.

8. The structure of claim 1, wherein the first size and the second size are substantially different.

9. The structure of claim 1, wherein the first angle and the second angle are substantially the same.

10. The structure of claim 1, wherein the first angle and the second angle are substantially different.

11. The structure of claim 1, wherein the first cell abuts the second cell.

12. The structure of claim 1, wherein the first cell does not abut the second cell.

13. The structure of claim 1, the row angle is in a range of from about 0 to about 90 degrees.

14. The structure of claim 1, wherein an axis of the major coordinate plane is substantially aligned with a machine direction.

15. The structure of claim 1, wherein an axis of the major coordinate plane is substantially aligned with a cross direction.

16. The structure of claim 1, wherein the plurality of cells comprises a third cell,wherein the third cell comprisesa third perimeter defining a third shape and a third size,a third position relative to the major coordinate plane,a third minor coordinate system centered on the third position and oriented at a third angle relative to the major coordinate plane; andwherein the first position and the third position are substantially within a second row.

17. The structure of claim 16, wherein the first row and the second row intersect.

18. The structure of claim 16, wherein the first row and the second row are continuous.

19. The structure of claim 16, wherein the first row and the second row are discontinuous.

20. The structure of claim 1, wherein the first cell has from 0 to 12 cell neighbors, each having a perimeter disposed at least partially within a neighboring cell boundary.

21. The structure of claim 20, wherein the first cell has from 0 to 4 neighboring cells, each having a perimeter disposed at least partially within the neighboring cell boundary.

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