Carbon nanotube length measurement system

Abstract

Provided is a carbon nanotube length measurement system including an image data acquisition unit for acquiring image data of a carbon nanotube, a physical property data acquisition unit for acquiring a plurality of physical property data of the carbon nanotube, at least one processor for executing a command for measuring a length of the carbon nanotube using data acquired by the acquisition unit, and a memory for storing at least one command executed by the at least one processor, wherein the at least one command includes a command for directly extracting a length from the image data of the carbon nanotube, a command for generating an indirect length by combining the plurality of physical property data of the carbon nanotube to correct an error occurring in the direct length, a command for generating a correction model for correcting a length measurement error based on the direct length and the indirect length, and a command for determining a length of the carbon nanotube whose length measurement error has been corrected by using the correction model. Through the carbon nanotube length measurement system including the above configuration and command, representativeness and reliability of a measurement result can be improved.

Description

Technical Field

[0001] This application claims the benefit of priority based on Korean Patent Application No. 10-2025-0021384, filed on February 19, 2025, and Korean Patent Application No. 10-2026-0021436, filed on February 3, 2026, the entire contents of which are incorporated herein by reference.

[0002] This invention relates to a system for measuring the length of carbon nanotubes. Specifically, it relates to a system for measuring the length of carbon nanotubes using a calibration model. More specifically, a system for measuring the length of carbon nanotubes is provided, comprising: an image data acquisition unit for acquiring image data of carbon nanotubes; a physical property data acquisition unit for acquiring multiple physical property data of the carbon nanotubes; at least one processor for executing commands for measuring the length of the carbon nanotubes using the data acquired by the acquisition unit; and a memory for storing at least one command executed by the at least one processor, wherein the at least one command includes: a command for extracting a direct length from the image data of the carbon nanotubes; a command for generating an indirect length by combining multiple physical property data of the carbon nanotubes to correct errors occurring in the direct length; a command for generating a calibration model for correcting length measurement errors based on the direct and indirect lengths; and a command for determining the length of the carbon nanotubes whose length measurement errors have been corrected using the calibration model. Background Technology

[0003] Carbon nanotubes (CNTs) are tubular carbon allotropes with diameters ranging from a few nanometers to tens of nanometers and lengths ranging from tens of micrometers to tens of centimeters. Based on the number of graphene layers, carbon nanotubes can be broadly classified into single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). These carbon nanotubes are well-known for their unique structure and excellent properties, such as mechanical strength, electrical conductivity, thermal conductivity, and chemical resistance.

[0004] Due to their excellent properties, carbon nanotubes, as described above, have been extensively studied in various fields, such as reinforcing composite materials and fabricating transparent conductive films. In particular, there is increasing interest in energy storage technologies. Among various electrochemical devices, lithium-ion batteries, which are rechargeable, operate at high voltages, and possess extremely high energy density, have attracted considerable attention. Therefore, carbon nanotubes are actively used as conductive materials with excellent conductivity and mechanical strength in electrode fabrication.

[0005] Carbon nanotubes are used as additives in various fields, and the main purpose of using carbon nanotubes is to improve properties such as mechanical strength and electrical conductivity. The use and content of carbon nanotubes as additives are determined by numerical values ​​of the physical properties (such as mechanical strength and electrical conductivity) possessed by the material.

[0006] However, since there are physical limitations to determining whether to utilize all available carbon nanotubes by individually measuring their physical properties (such as mechanical strength and electrical conductivity), the length of carbon nanotubes, which is closely related to these physical properties, plays a crucial role in the selection of carbon nanotubes. Accordingly, to measure the length of carbon nanotubes, the main methods used are: measuring the aspect ratio using atomic force microscopy (AFM) or scanning electron microscopy (SEM), or indirectly deriving the length by measuring the viscosity in the liquid state. However, while measuring the aspect ratio using microscopy allows for accurate measurement of observed carbon nanotubes, it has the following problems: it is difficult to apply to carbon nanotubes with long lengths and is limited to measurements of local areas. Furthermore, the method of indirectly deriving the length of carbon nanotubes by viscosity has the following problems: the dynamic characteristics of the dispersion can vary depending on various factors such as temperature, and significant measurement errors may occur when the carbon nanotubes are not completely dispersed.

[0007] Therefore, there is a need to develop a method for measuring the length of carbon nanotubes, which enables accurate measurement of carbon nanotubes present in a sample to be measured, while also allowing for an overall length assessment of the sample.

[0008] [Existing Technical Documents]

[0009] [Non-patent literature]

[0010] (Non-patent literature 1) Macromolecules 2016, 49, 2, 681-689 Summary of the Invention

[0011] [Technical Issues]

[0012] The purpose of this invention is to provide a system for measuring the length of carbon nanotubes. The system includes: an image data acquisition unit for acquiring image data of carbon nanotubes; a physical property data acquisition unit for acquiring multiple physical property data of the carbon nanotubes; at least one processor for executing commands for measuring the length of the carbon nanotubes using the data acquired by the acquisition unit; and a memory for storing at least one command executed by the at least one processor, wherein the at least one command includes: a command for extracting a direct length from the image data of the carbon nanotubes; a command for generating an indirect length by combining multiple physical property data of the carbon nanotubes to correct errors occurring in the direct length; a command for generating a correction model for correcting length measurement errors based on the direct and indirect lengths; and a command for determining the length of the carbon nanotubes whose length measurement errors have been corrected using the correction model.

[0013] [Technical Solutions]

[0014] According to a first aspect of the present invention, a method for measuring the length of carbon nanotubes is provided, the method comprising: a generation step of generating a correction model for correcting length measurement errors by inputting an indirect length and a direct length of the carbon nanotube; and a determination step of using the correction model to determine the length of the carbon nanotube whose length measurement error has been corrected, wherein the indirect length is generated by combining multiple different physical property data of the carbon nanotube, and the direct length is extracted from image data of the carbon nanotube.

[0015] In one specific embodiment of the present invention, the correction model is a Bayesian learning model.

[0016] In one specific embodiment of the present invention, the calibration model is a model that can use input data as random variables to learn the probability distribution between random variables.

[0017] In one specific embodiment of the present invention, the generation step includes a process of learning the probability distribution of the indirect length using the input indirect length data as a random variable.

[0018] In one specific embodiment of the invention, the generation step includes learning the probability distribution of the indirect length using the input indirect length data as a random variable, and the determination step includes a process of adjusting the probability distribution of the indirect length by reflecting the direct length.

[0019] In one specific embodiment of the invention, the determining step includes deriving a posterior probability of the carbon nanotube length using a prior probability and a likelihood, wherein the prior probability is generated based on the indirect length and the likelihood is generated based on the direct length.

[0020] In one specific embodiment of the present invention, the multiple physical property data include physical properties selected from the group consisting of thickness, aspect ratio, tensile viscosity and combinations thereof.

[0021] In one specific embodiment of the invention, the indirect length is generated based on a combination of the thickness and aspect ratio of the carbon nanotube, and the aspect ratio is generated based on the tensile viscosity of the carbon nanotube.

[0022] In one specific embodiment of the invention, the thickness of the carbon nanotubes is measured by atomic force microscopy (AFM).

[0023] In one specific embodiment of the invention, the extraction of direct length includes the step of extracting each carbon nanotube framework from image data.

[0024] In one specific embodiment of the present invention, the extraction of direct length includes the step of calculating the perimeter of each skeleton based on the extracted carbon nanotube skeleton.

[0025] In one specific embodiment of the present invention, the perimeter of the skeleton is calculated using polygon approximation.

[0026] In one specific embodiment of the invention, image data of carbon nanotubes is captured by scanning electron microscopy (SEM).

[0027] In one specific embodiment of the present invention, carbon nanotubes include single-walled carbon nanotubes (SWCNTs).

[0028] According to a second aspect of the present invention, a system for measuring the length of carbon nanotubes is provided. The system includes: an image data acquisition unit for acquiring image data of carbon nanotubes; a physical property data acquisition unit for acquiring multiple physical property data of the carbon nanotubes; at least one processor for executing a command for measuring the length of the carbon nanotubes using the data acquired by the acquisition unit; and a memory for storing at least one command executed by the at least one processor, wherein the at least one command includes: a command for extracting a direct length from the image data of the carbon nanotubes; a command for generating an indirect length by combining multiple physical property data of the carbon nanotubes to correct errors occurring in the direct length; a command for generating a correction model for correcting length measurement errors based on the direct length and the indirect length; and a command for determining the length of the carbon nanotubes whose length measurement errors have been corrected using the correction model.

[0029] In one specific embodiment of the invention, the command for generating the calibration model includes a command for learning the probability distribution of the indirect length using the input indirect length data as a random variable.

[0030] In one specific embodiment of the invention, the command for generating the calibration model includes a command for learning the probability distribution of the indirect length using the input indirect length data as a random variable, and the command for determining the length of the carbon nanotube includes a command for adjusting the probability distribution of the indirect length by reflecting the direct length.

[0031] In one specific embodiment of the invention, the command for determining the length of the carbon nanotube includes a command for deriving a posterior probability of the length of the carbon nanotube using a prior probability and a likelihood, wherein the prior probability is generated based on the indirect length and the likelihood is generated based on the direct length.

[0032] In one specific embodiment of the present invention, the physical property data acquisition unit includes an atomic force microscope, and the thickness of the carbon nanotubes is acquired from the atomic force microscope.

[0033] In one specific embodiment of the invention, the command for extracting direct length includes a command for extracting each carbon nanotube framework from image data.

[0034] In one specific embodiment of the invention, the command for extracting the direct length includes a command for calculating the perimeter of each skeleton based on the extracted carbon nanotube skeleton.

[0035] In one specific embodiment of the present invention, the image data acquisition unit includes a scanning electron microscope, and the image data of the carbon nanotubes is acquired from the scanning electron microscope.

[0036] [Beneficial Effects]

[0037] The carbon nanotube length measurement system according to the present invention is a system for measuring the length of carbon nanotubes. The system includes: an image data acquisition unit for acquiring image data of carbon nanotubes; a physical property data acquisition unit for acquiring multiple physical property data of carbon nanotubes; at least one processor for executing commands for measuring the length of carbon nanotubes using the data acquired by the acquisition unit; and a memory for storing at least one command executed by the at least one processor, wherein the at least one command includes: a command for extracting a direct length from the image data of the carbon nanotubes; a command for generating an indirect length by combining multiple physical property data of the carbon nanotubes to correct errors occurring in the direct length; a command for generating a correction model for correcting length measurement errors based on the direct and indirect lengths; and a command for determining the length of the carbon nanotubes whose length measurement errors have been corrected using the correction model, thereby combining information about the overall length of carbon nanotubes contained in the sample to be measured with information about the length of specific carbon nanotubes within the sample to improve the representativeness and reliability of the measurement results.

[0038] Furthermore, when the measurement system of the present invention is applied to processes in which carbon nanotubes are used, the predictability of physical properties directly or indirectly altered by the length of carbon nanotubes can be improved, thereby enabling the establishment of optimal process conditions. In particular, when the measurement system of the present invention is used in battery manufacturing processes, the predictability of conductivity affected by the length of carbon nanotubes can be improved, thereby enabling the manufacture of batteries with improved electrochemical properties. Attached Figure Description

[0039] Figure 1 The image is obtained after extracting the carbon nanotube skeleton using a skeletonization algorithm according to an embodiment of the present invention.

[0040] Figure 2 This is an operational flowchart of a system for measuring the length of carbon nanotubes according to an embodiment of the present invention.

[0041] Figure 3 This is an operation flowchart of the command for extracting the direct length of carbon nanotubes according to an embodiment of the present invention.

[0042] Figure 4 This is a block diagram of a system for measuring the length of carbon nanotubes according to an embodiment of the present invention. Detailed Implementation

[0043] The invention will be described in more detail below.

[0044] The terms and words used in this specification and claims should not be construed as limited to their typical or dictionary meanings, but rather should be interpreted as having meanings and concepts consistent with the technical concept of the invention, based on the principle that the inventor may appropriately define the concepts of the terms in order to best describe his or her own invention. Therefore, since the configurations described in the embodiments of this specification are only the most preferred embodiments and do not represent the entire technical concept of the invention, it should be understood that various equivalents and modifications that may replace these configurations may exist at the time of filing this application.

[0045] Throughout this specification, when a part is referred to as "comprising" a component, unless otherwise specified, this does not mean that it excludes other components, but rather that it may include other components.

[0046] The invention is described in detail below.

[0047] Methods for measuring the length of carbon nanotubes

[0048] This invention provides a method for measuring the length of carbon nanotubes.

[0049] Carbon nanotubes are secondary structures formed by assembling all or part of carbon nanotube units into bundles. These units consist of graphite sheets rolled into cylinders with nanometer-scale diameters and include sp² bonding structures. Due to this unique structure, carbon nanotubes exhibit unique mechanical, electrical, and thermal properties, and these unique physical properties enable their application in various fields, such as electrochemistry, biomedicine, and mechanical engineering.

[0050] Carbon nanotubes are primarily used in these fields to supplement mechanical, electrical, or thermal properties. To achieve this, it is necessary to first identify the physical properties of the carbon nanotubes to be used and then appropriately adjust their content. However, due to physical limitations in measuring all the physical properties to be supplemented with all existing carbon nanotubes and then selecting the most suitable ones, the currently used method is to first select the carbon nanotubes to be used by measuring inherent physical properties such as the length of the carbon nanotubes that affect conductivity.

[0051] Conventionally, to measure the length of these carbon nanotubes, atomic force microscopy (AFM) is used to capture images, and the thickness of the carbon nanotubes is calculated from these images to derive the length. However, this method suffers from the following problems: self-aggregation caused by van der Waals interactions of the carbon nanotubes and impurities in the sample of carbon nanotubes being measured introduce errors in the measurement results, which reduces accuracy and reliability.

[0052] To compensate for these problems, methods utilizing dynamic light scattering or multi-angle light scattering are used; however, these methods have the limitation of only being able to measure the average length of carbon nanotubes in liquid samples. Furthermore, issues such as reduced accuracy due to self-aggregation and impurities persist.

[0053] Therefore, the present invention provides a method for measuring the length of carbon nanotubes, wherein the indirect and direct lengths of the carbon nanotubes are input into a calibration model to determine the carbon nanotube length after correcting for measurement errors, thereby improving the representativeness and reliability of the obtained carbon nanotube length.

[0054] In one specific embodiment of the present invention, a method for measuring the length of carbon nanotubes includes: a generation step of generating a correction model for correcting length measurement errors by inputting the indirect length and direct length of the carbon nanotubes; and a determination step of using the correction model to determine the length of the carbon nanotubes whose length measurement errors have been corrected.

[0055] The following sections will describe in detail each configuration of the method used to measure the length of carbon nanotubes.

[0056] Indirect length

[0057] Indirect length is the measurement of the overall length of carbon nanotubes within the sample to be measured, and is generated by combining multiple different physical property data of carbon nanotubes.

[0058] Multiple physical property data for carbon nanotubes refer to multiple data obtained by measuring different types of physical properties, and specifically to data that, while not directly measuring the length of the carbon nanotubes, can be used in combination with other physical properties, such as mathematical relationships, to generate the length of the carbon nanotubes. For example, crystallinity, Raman spectroscopy IL, etc., may be directly or indirectly related to the length of the carbon nanotubes. G / I D Ratios, tensile viscosity, thickness, and aspect ratio can be considered as such physical property data, but are not limited to them, as long as these data can be combined with other physical property data to generate carbon nanotube lengths. Multiple different data points refer to data obtained by measuring different physical properties among these physical properties.

[0059] In one specific embodiment of the invention, the physical property data of the carbon nanotubes include physical properties selected from the group consisting of thickness, aspect ratio, tensile viscosity, and combinations thereof. By combining physical properties selected from this group to generate an indirect length, a length with a small error compared to the actual length of the carbon nanotube can be generated.

[0060] The thickness, aspect ratio, and tensile viscosity of carbon nanotubes can be measured and generated using physical property measurement methods commonly known in the relevant technical fields. For example, measurements can be performed using atomic force microscopy (AFM), rheometers, transmission electron microscopy (TEM), etc., but are not limited to these.

[0061] In one specific embodiment of the present invention, the indirect length can be generated based on a combination of the thickness and aspect ratio of the carbon nanotube, and the aspect ratio can be derived from the tensile viscosity of the carbon nanotube. Specifically, the indirect length is derived by the following steps: measuring the tensile viscosity of the carbon nanotube, calculating the aspect ratio of the carbon nanotube based on the tensile viscosity, and generating the indirect length by combining the aspect ratio with the thickness of the carbon nanotube.

[0062] In one specific embodiment of the invention, the thickness of the carbon nanotubes can be measured by atomic force microscopy (AFM). Using AFM to measure the thickness of carbon nanotubes can minimize the occurrence of errors in the measurement results.

[0063] In one specific embodiment of the present invention, the tensile viscosity of carbon nanotubes is measured using a rheometer. Using a rheometer to measure the tensile viscosity of carbon nanotubes can improve the speed and accuracy of the measurement.

[0064] The aspect ratio derived from the tensile viscosity of carbon nanotubes can be achieved using mathematical formulas or theoretical models that express the relationship between tensile viscosity and aspect ratio. Specifically, the aspect ratio can be derived from theoretical equations expressing the tensile viscosity and aspect ratio in a rigid rod solution, but is not limited to this, as long as a reliable aspect ratio can be obtained, and this derivation can be performed by hardware, software, or a combination thereof.

[0065] Combinations of multiple different physical property data for carbon nanotubes can be achieved through simple mathematical relationships or theoretical modeling, but are not limited to these, and such combinations can be performed through hardware, software, or a combination thereof. For example, the length of carbon nanotubes can be determined by measuring the crystallinity of the carbon nanotubes or the Ig of their Raman spectra. G / I D The ratio is then used to calculate the length of the carbon nanotubes through mathematical calculations or theoretical modeling using other physical properties. The length of the carbon nanotubes can also be generated by measuring the thickness and aspect ratio of the carbon nanotubes and multiplying these values.

[0066] In one specific embodiment of the invention, the indirect length derived from the combination of the thickness and aspect ratio of the carbon nanotube is generated by multiplying the thickness and aspect ratio of the carbon nanotube.

[0067] direct length

[0068] Direct length refers to the length of a specific carbon nanotube selected and directly measured within the sample to be measured, and extracted from the captured image data of the carbon nanotube.

[0069] Image data captured from carbon nanotubes refers to image data captured at a scale sufficient to confirm the presence of a carbon nanotube framework in a measured sample. Image data can be captured using methods commonly known in the relevant art. For example, image data can be captured using atomic force microscopy (AFM), transmission electron microscopy (TEM), scanning electron microscopy (SEM), etc., but is not limited to these methods.

[0070] In one specific embodiment of the invention, image data of carbon nanotubes can be captured by scanning electron microscopy (SEM). When images of carbon nanotubes are captured using a scanning electron microscope (SEM), images suitable for measuring the length of carbon nanotubes can be obtained, demonstrating the convenience of measurement and applicability to practical applications.

[0071] Extracting direct length from image data of carbon nanotubes may involve manually identifying the carbon nanotube skeleton based on the image data and comparing it with the scale of the image data to directly extract the length of the carbon nanotubes, and undergoing separate processing to isolate the carbon nanotube skeleton to be identified and extract its length, but is not limited to this, and the extraction may be performed using hardware, software or a combination thereof.

[0072] In one specific embodiment of the invention, the extraction of direct length includes the step of extracting each carbon nanotube framework from image data. The extraction of the carbon nanotube framework can be performed manually or through a separate image processing procedure, but is not limited to these methods, and the extraction can be performed using hardware, software, or a combination thereof.

[0073] In one specific embodiment of the invention, the extraction of the carbon nanotube framework is performed through image data processing. Processing image data for framework extraction means extracting the framework of a specific object through relationships such as shadow differences and tonal variations between each pixel in the image. This process can be performed using relevant programs or methods generally known in the relevant art. For example, algorithm libraries that can be used for image analysis, such as OpenCV and Scikit-Image, or algorithms within these libraries, such as skeletonization algorithms, can be implemented using programs such as Python, but are not limited thereto.

[0074] In one specific embodiment of the present invention, the extraction of the carbon nanotube framework is performed using a framework-based algorithm.

[0075] In one specific embodiment of the invention, the direct length derivation includes the step of calculating the perimeter of each skeleton based on the extracted carbon nanotube skeleton. By including the step of calculating the skeleton perimeter in the direct length derivation, the accuracy of length measurement can be improved by compensating for problems such as reference point selection or uneven skeleton travel paths that may occur when attempting to directly extract length from the extracted carbon nanotube skeleton. The extraction of the carbon nanotube skeleton can be performed manually or through a separate data processing procedure, but is not limited thereto, and the extraction can be performed using hardware, software, or a combination thereof.

[0076] In one specific embodiment of the invention, the perimeter of the skeleton is calculated through image data processing. Processing image data to perform perimeter calculation refers to predicting the three-dimensional structure of the carbon nanotubes based on the extracted skeleton. This process can be performed using relevant programs or methods generally known in the relevant art. For example, algorithm libraries that can be used for image analysis, such as OpenCV and Scikit-Image, or algorithms within these libraries, such as polygon approximation, can be implemented using programs such as Python, but are not limited thereto.

[0077] In one specific embodiment of the present invention, the perimeter of the skeleton is calculated using polygon approximation.

[0078] In one specific embodiment of the invention, the direct length is calculated as half the perimeter of the skeleton as calculated as described above.

[0079] In one specific embodiment of the present invention, the extraction of direct length includes a step of identifying each carbon nanotube from the image data prior to the step of extracting the carbon nanotube framework. The step of identifying carbon nanotubes involves separating background information from carbon nanotube information within the image data and individually identifying multiple carbon nanotubes included in the image data. The identification of carbon nanotubes can be performed manually or through a separate image data processing procedure, but is not limited thereto, and the identification can be performed using hardware, software, or a combination thereof. Specifically, the determination of direct length includes the following steps: (1) identifying each carbon nanotube from the image data, and (2) extracting each carbon nanotube framework from the image data.

[0080] In one specific embodiment of the invention, carbon nanotube identification is performed through image data processing. Processing image data for carbon nanotube identification means distinguishing similar objects and separating each object individually based on relationships between pixels within the image data, such as shadow differences, tonal variations, and the presence or absence of patterns. This process can be performed using relevant programs or methods generally known in the relevant art. For example, algorithm libraries that can be used for image analysis, such as the Segment Anything model, OpenCV, and Scikit-Image, and especially segmentation algorithms within these libraries, can be executed through programs such as Python, but are not limited thereto.

[0081] In one specific embodiment of the invention, the identification of carbon nanotubes is performed using a segmented-all model.

[0082] Generation steps and determination steps

[0083] The generation steps are as follows: the indirect and direct lengths of the carbon nanotubes are used as input variables (parameters) in the calibration model used to correct for length measurement errors, and the calibration model is generated based on the theory on which the model is based. Furthermore, the determination steps are as follows: based on the generation results, the input variables are used to obtain the carbon nanotube lengths corrected for measurement errors, and the corresponding determined values ​​are output.

[0084] While the aforementioned indirect and direct lengths offer improved accuracy during their derivation, indirect lengths are not directly measured for carbon nanotubes within the sample. Instead, they correspond to values ​​generated by combining multiple data points related to different physical properties of the carbon nanotubes. Therefore, while indirect lengths represent the overall length of carbon nanotubes within the sample and are thus representative to some extent, their reliability is slightly insufficient due to potential errors arising from variations in aggregation and impurities within the sample. In contrast, direct lengths correspond to values ​​obtained by directly measuring the length from captured image data of the carbon nanotubes. Accordingly, while direct lengths offer very high reliability, they are insufficiently representative of the overall carbon nanotube count within the sample, as they represent only a small fraction of the numerous carbon nanotubes contained within it.

[0085] Therefore, the method of the present invention for measuring the length of carbon nanotubes includes the above-described generation and determination steps, thereby deriving a carbon nanotube length that has been corrected for length measurement errors based on both indirect and direct lengths to compensate for the inherent representativeness and reliability issues of each variable, and determining the length of carbon nanotubes in the sample to closely approximate the actual value.

[0086] The calibration model can learn the input variables and derive a corrected length measurement error value based on the theory upon which the model is based. In other words, the calibration model is based on a theory that can improve the mutual representativeness and reliability of indirect and direct lengths, and learns the input indirect and direct lengths as variables according to the theory on which the model is based, thereby determining the carbon nanotube length corrected for the length measurement error.

[0087] The correction model can be a generative model commonly known in the relevant technical field, and can be, for example, a Bayesian learning model, a nonlinear regression model, and a decision tree model, but is not limited thereto.

[0088] In one specific embodiment of the invention, the number of indirect lengths of the carbon nanotubes input to the calibration model is between 10 and 500. Specifically, the number of indirect lengths can be 10 or more, 20 or more, 30 or more, 40 or more, 50 or more, 60 or more, or 70 or more, and 500 or less, 450 or less, 400 or less, 350 or less, 300 or less, 250 or less, 200 or less, 150 or less, 100 or less, 90 or less, or 80 or less, as well as 10 to 500, 20 to 400, or 50 to 200. When the number of indirect lengths meets the above ranges, a reliable calibration model can be generated, while ensuring the economic feasibility and efficiency of measuring carbon nanotube lengths suitable for practical use.

[0089] In one specific embodiment of the invention, the calibration model is a model capable of learning the probability distribution among random variables using input data as random variables. Learning the probability distribution refers to deriving the overall probability distribution of related variables based on homogeneous input variables. For example, when the calibration model uses indirect length as a random variable, multiple indirect lengths are input into the calibration model, and the calibration model derives the probability distribution of the indirect length for a single measurement sample based on the multiple indirect lengths.

[0090] By using a model that can learn the probability distribution between random variables as a calibration model, the length of the entire population can be considered without biasing the results of the input sample group, and the impact of errors present in the input variables on the results can also be reduced to some extent.

[0091] In one specific embodiment of the present invention, the probability distribution represents a Gaussian distribution.

[0092] In one specific embodiment of the invention, the generation step includes a process of learning a probability distribution of the indirect length using input indirect length data as a random variable. The learning of the probability distribution has the same content as the method described above, and multiple indirect measurement data are input to utilize the indirect length data as random variables. As mentioned above, the indirect length is somewhat unreliable, but it is a variable representing the overall length of the carbon nanotube and has a predetermined representativeness. When using this indirect length as a random variable to learn the probability distribution, a probability distribution of carbon nanotube lengths with predetermined representativeness can be obtained.

[0093] In one specific embodiment of the invention, the generation step includes a process of learning the probability distribution of the indirect length using input indirect length data as a random variable, and the determination step includes a process of adjusting the probability distribution of the indirect length by reflecting the direct length. This adjustment by reflecting the direct length is intended to correct errors in the learned probability distribution by inputting reliable data, thereby supplementing the probability distribution. In other words, the probability distribution of the indirect length generated in the generation step has a predetermined representativeness but lacks reliability. In the determination step, a process of supplementing the probability distribution by using reliable direct lengths input into the calibration model to closely approximate the probability distribution possessed by the length of carbon nanotubes in actual samples is performed.

[0094] In other words, the measurement method according to a specific embodiment of the present invention ensures the representativeness of the carbon nanotube length by including the above-described generation step, and at the same time ensures reliability by including the above-described determination step, thereby determining the carbon nanotube length after correcting for measurement errors.

[0095] In one specific embodiment of the present invention, the correction model is a Bayesian learning model.

[0096] Bayesian learning models are learning models that perform probabilistic inference by updating the probability of hypotheses using new information, based on Bayes' theorem. When using a Bayesian learning model, heterogeneous variables input into the model can be linked to derive complementary results. Bayesian learning models can be applied in a form that can be used across related technical fields to derive the length of carbon nanotubes after correcting for length measurement errors.

[0097] In one embodiment of the invention, a Bayesian learning model uses the prior probability of the target in probabilistic inference and additional information associated with the prior probability to derive the posterior probability of the relevant target. The prior probability is derived from the learning result based on minimal data input to the learning model, and the additional information refers to the likelihood. The Bayesian learning model can update the prior probability by combining the likelihood with the prior probability, thereby deriving an error-corrected posterior probability. When using this Bayesian learning model, since the final decision is made in a manner that supplements the overall probability of the inferred target, the final decision result does not change significantly even if outliers exist in the input data. Furthermore, because the Bayesian learning model is based on prior probability, the uncertainty that occurs when using other machine learning models can be quantified, thereby improving the accuracy of the decision result.

[0098] In one specific embodiment of the invention, the determining step includes deriving a posterior probability of the carbon nanotube length using a prior probability and a likelihood, wherein the prior probability is generated based on the indirect length and the likelihood is generated based on the direct length. As described above, when the prior probability is derived from data about an indirect length with predetermined representativeness and adjusted by reflecting a likelihood generated based on a reliable direct length, both the representativeness and reliability of the finally determined carbon nanotube length can be improved.

[0099] carbon nanotubes

[0100] Carbon nanotube units can be classified into single-walled carbon nanotubes (SWCNTs), double-walled carbon nanotubes (DWCNTs), and multi-walled carbon nanotubes (MWCNTs) based on the number of bonds forming the walls.

[0101] In one specific embodiment of the present invention, carbon nanotubes include at least one of single-walled carbon nanotubes, double-walled carbon nanotubes, and multi-walled carbon nanotubes.

[0102] In one specific embodiment of the present invention, carbon nanotubes include single-walled carbon nanotubes (SWCNTs).

[0103] Since single-walled carbon nanotubes have only one wall forming unit, the length of the carbon nanotube has a more direct impact on its thickness, diameter, and other properties. Therefore, the accuracy of measuring the length of carbon nanotubes is considered more important.

[0104] System for measuring the length of carbon nanotubes

[0105] The present invention also provides a system (100) for measuring the length of carbon nanotubes.

[0106] In one specific embodiment of the present invention, a system (100) for measuring the length of carbon nanotubes includes: an image data acquisition unit (110) for acquiring image data of carbon nanotubes; a physical property data acquisition unit (120) for acquiring multiple physical property data of carbon nanotubes; at least one processor (130) for executing a command for measuring the length of carbon nanotubes using the data acquired by the acquisition units (110) and (120); and a memory (140) for storing at least one command executed by the at least one processor (130).

[0107] The image data acquisition unit (110) is capable of acquiring image data of carbon nanotubes (S111), which can directly capture images of carbon nanotubes or provide captured images of carbon nanotubes. Specifically, the image data of carbon nanotubes (S111) refers to image data captured at a scale sufficient to confirm the carbon nanotube framework included in the measured sample (S111). The image data (S111) can be acquired using methods generally known in the relevant art, including but not limited to atomic force microscopy, transmission electron microscopy, scanning electron microscopy, etc.

[0108] In one specific embodiment of the present invention, the image data acquisition unit (110) includes a scanning electron microscope.

[0109] In one specific embodiment of the present invention, image data (S111) of carbon nanotubes is acquired from a scanning electron microscope.

[0110] The physical property data acquisition unit (120) is capable of acquiring physical property data of carbon nanotubes (S121), which can directly measure the physical properties of carbon nanotubes or provide measured physical property data of carbon nanotubes (S121). Specifically, the physical property data of carbon nanotubes (S121) does not directly measure the length of carbon nanotubes, but refers to data that can be generated by combining with other types of physical properties using mathematical relationships, etc. The physical property data (S121) can be acquired using methods commonly known in the relevant technical field, including but not limited to atomic force microscopy, rheometer, transmission electron microscopy, etc. When multiple physical property data (S121) can be acquired from a single configuration, the physical property data acquisition unit (120) may include only one configuration.

[0111] In one specific embodiment of the invention, the multiple data include data selected from the group consisting of thickness, aspect ratio, tensile viscosity, and combinations thereof.

[0112] In one specific embodiment of the present invention, the physical property data acquisition unit (120) includes an atomic force microscope.

[0113] In one specific embodiment of the invention, the thickness of the carbon nanotubes is obtained from an atomic force microscope.

[0114] In one specific embodiment of the present invention, the physical property data acquisition unit (120) includes a rheometer.

[0115] In one specific embodiment of the invention, the tensile viscosity of carbon nanotubes is measured using a rheometer.

[0116] In one specific embodiment of the present invention, the system includes a memory (140), a processor (130), a transmitting and receiving system (150), an input interface system (160), an output interface system (170), and a storage system.

[0117] The components within the system are interconnected and can communicate with each other. Specifically, each component is connected via a bus (190) and can communicate with each other.

[0118] The memory (140) and the storage system may be composed of at least one of volatile storage media and non-volatile storage media. For example, the memory (140) and the storage device (180) may be composed of at least one of read-only memory (ROM) and random access memory (RAM).

[0119] The memory (140) includes at least one command executed by the processor (130).

[0120] The processor (130) may refer to a central processing unit (CPU), a graphics processing unit (GPU), or a dedicated processor (130) on which the methods according to embodiments of the present invention are executed.

[0121] As described above, the processor (130) can execute at least one program command stored in the memory (140).

[0122] In one specific embodiment of the present invention, at least one command includes: a command for extracting the direct length from image data of carbon nanotubes (S110); a command for generating an indirect length by combining multiple physical property data of carbon nanotubes to correct errors occurring in the direct length (S120); a command for generating a correction model for correcting length measurement errors based on the direct length and the indirect length (S130); and a command for determining the length of the carbon nanotube whose length measurement error has been corrected using the correction model (S140).

[0123] The correction model is the same as the correction model described above, and the command (S110) for extracting the direct length is the same as the direct length extraction command described above.

[0124] In one specific embodiment of the invention, the command for extracting direct length (S110) includes a command (S113) for extracting each skeleton of carbon nanotubes from image data (S111).

[0125] In one specific embodiment of the present invention, the extraction of the carbon nanotube framework (S113) is performed by image data processing (S111).

[0126] In one specific embodiment of the present invention, the extraction of the carbon nanotube framework (S113) is performed using a framework algorithm.

[0127] Specifically, the command for extracting the direct length (S110) includes a command (S113) for extracting each carbon nanotube skeleton from the image data of carbon nanotubes (S111), and the extraction of the carbon nanotube skeleton (S113) can be performed using a skeletonization algorithm.

[0128] In one specific embodiment of the invention, the command for extracting the direct length (S110) includes a command for calculating the perimeter of each skeleton based on the extracted carbon nanotube skeleton (S114).

[0129] In one specific embodiment of the present invention, the perimeter of the skeleton is calculated through image data processing (S111).

[0130] In one specific embodiment of the invention, the calculation of the perimeter of the skeleton (S114) is performed using polygon approximation.

[0131] Specifically, the command for extracting the direct length (S110) includes a command for calculating the perimeter of each skeleton based on the extracted carbon nanotube skeleton (S114), and the calculation of the skeleton perimeter (S114) can be performed by polygon approximation.

[0132] In one specific embodiment of the invention, the command for extracting the direct length (S110) includes a command (S112) for identifying each carbon nanotube from the image data of carbon nanotubes (S111).

[0133] In one specific embodiment of the present invention, the identification of carbon nanotubes (S112) is performed through image data (S111) processing.

[0134] In one specific embodiment of the invention, the identification of carbon nanotubes (S112) is performed using a segmented-all model.

[0135] Specifically, the command for extracting the direct length (S110) includes a command (S112) for identifying each carbon nanotube from the image data (S111), and the identification of carbon nanotubes (S112) can be performed using the segmentation model.

[0136] The command (S120) for generating the indirect length is the same as the one used for generating the indirect length described above.

[0137] In one specific embodiment of the invention, the command for generating the indirect length (S120) includes a command for generating the indirect length by combining the thickness and aspect ratio of the carbon nanotubes.

[0138] In one specific embodiment of the invention, the command for generating the indirect length (S120) includes a command for deriving the aspect ratio based on the tensile viscosity of the carbon nanotubes. The aspect ratio can be derived using a mathematical expression or theoretical model representing the relationship between tensile viscosity and aspect ratio. Specifically, deriving the aspect ratio based on the tensile viscosity of the carbon nanotubes can be performed using a relational equation representing the theoretical relationship between tensile viscosity and aspect ratio in a rigid rod solution.

[0139] The command for extracting the direct length (S110) and the command for generating the indirect length (S120) can be executed in parallel.

[0140] The command (S130) for generating the calibration model is the same as the generation step described above, and the command (S140) for determining the length of the carbon nanotube is the same as the determination step described above.

[0141] In one specific embodiment of the invention, the command (S130) for generating the calibration model may include a command for learning the probability distribution of the indirect length using the input indirect length data as a random variable.

[0142] In one specific embodiment of the invention, the command (S130) for generating the calibration model includes a command for learning the probability distribution of the indirect length using the input indirect length data as a random variable.

[0143] In one specific embodiment of the invention, the command (S140) for determining the length of the carbon nanotube includes a command for adjusting the probability distribution of the indirect length by reflecting the direct length.

[0144] In one specific embodiment of the invention, the command (S140) for determining the length of the carbon nanotube includes a command for deriving a posterior probability of the length of the carbon nanotube using a prior probability and a likelihood, wherein the prior probability is generated based on the indirect length and the likelihood is generated based on the direct length.

[0145] Specific examples of the invention are presented below. However, the examples described below are intended to illustrate or describe the invention only and are not intended to limit the invention. Furthermore, any details not described herein will be fully inferred technically by those skilled in the art, and therefore their description will be omitted.

[0146] Example

[0147] Example 1: Indirect length of carbon nanotubes

[0148] (1) Aspect ratio of carbon nanotubes

[0149] After preparing dispersions of single-walled carbon nanotubes for samples A to C, the dispersions were subjected to a Hengyi strain of 0.76 at 25°C using a capillary fracture tensile rheometer (CaBER1, manufactured by Thermo Fisher Scientific). The decrease in diameter over time was then observed to measure the tensile viscosity, from which the aspect ratio of the carbon nanotubes was calculated. The aspect ratio of the carbon nanotubes was calculated according to the method described in Non-Patent Literature 1 (Macromolecules 2016, 49, 2, 681-689).

[0150] (2) Indirect length of carbon nanotubes

[0151] A few drops of carbon nanotube dispersion were placed on a silicon wafer (Si wafer) and dried to prepare the carbon nanotube dispersion for measurement. The thickness of the carbon nanotubes was measured using an atomic force microscope (AFM; NX10, manufactured by Park System), and the indirect length of the carbon nanotubes was obtained by multiplying the calculated aspect ratio of the carbon nanotubes by their thickness.

[0152] Example 2: Direct length of carbon nanotubes

[0153] Images of the carbon nanotube dispersion sample were captured using a scanning electron microscope (SEM; FESEM-09-JSM7610F, manufactured by JEOL Corporation). Each skeleton of the carbon nanotubes was extracted from the images, and the perimeter of each skeleton was calculated based on the extracted carbon nanotube skeletons. Subsequently, the direct length of the carbon nanotubes was determined to be half of the perimeter.

[0154] The extraction of the carbon nanotube framework was performed using a framework optimization algorithm, and the extraction results were... Figure 1 As shown in the image. Figure 1 The numbers 0 to 13 shown indicate the number of each carbon nanotube extracted within the image. The perimeter of the extracted framework was calculated using polygon approximation.

[0155] Example 3: Determining the Length of Carbon Nanotubes

[0156] For each carbon nanotube sample, 16 aspect ratios and 5 thicknesses were measured, from which 80 indirect lengths were derived. These indirect length values ​​were then fed into a Bayesian learning model to learn the probability distribution of the indirect lengths. Subsequently, in the learning model, the probability distribution of the indirect lengths was adjusted to reflect the direct lengths, where the prior probability is given by the indirect length distribution and the likelihood is given by the direct length for each sample. This allows for the calculation of the posterior probability of the carbon nanotube length, based on which the length corrected for measurement errors is determined.

[0157] The average indirect length, the direct length set as the likelihood value, and the carbon nanotube length corresponding to the median of the posterior probability, which is corrected for the length measurement error, are shown in Table 1 below.

[0158] [Table 1]

[0159]

[0160] Although the preferred embodiments of the present invention have been described in detail above, the scope of the present invention is not limited thereto, but may include various modifications and alterations made by those skilled in the art using the basic concept of the present invention as defined in the claims.

[0161] [Explanation of reference numerals in the attached figures]

[0162] 100: A system for measuring the length of carbon nanotubes

[0163] 110: Image Data Acquisition Unit

[0164] 120: Physical property data acquisition unit

[0165] 130: Processor

[0166] 140: Memory

[0167] 150: Transmitting and Receiving Systems

[0168] 160: Input Interface System

[0169] 170: Output Interface System

[0170] 180: Storage device

[0171] 190: Bus

[0172] S100: Command executed by the system's processor for measuring the length of carbon nanotubes.

[0173] S110: Command for extracting the direct length from image data of carbon nanotubes.

[0174] S111: Image data of carbon nanotubes

[0175] S112: Command used to identify each carbon nanotube from image data of carbon nanotubes.

[0176] S113: Command used to extract each carbon nanotube framework from image data of carbon nanotubes.

[0177] S114: Command used to calculate the perimeter of each skeleton based on the extracted carbon nanotube skeleton.

[0178] S120: A command used to generate indirect lengths by combining multiple physical property data of carbon nanotubes to correct for errors in the direct length.

[0179] S121: Multiple physical property data of carbon nanotubes

[0180] S130: Command for generating a correction model based on direct and indirect lengths to correct for length measurement errors.

[0181] S140: Command used to determine the length of carbon nanotubes whose length measurement error has been corrected using a calibration model.

Claims

1. A system for measuring the length of carbon nanotubes, comprising: An image data acquisition unit is used to acquire image data of carbon nanotubes; A physical property data acquisition unit is used to acquire multiple physical property data of the carbon nanotube; At least one processor, the at least one processor being configured to execute a command for measuring the length of the carbon nanotube using data acquired by the acquisition unit; as well as A memory for storing at least one command executed by the at least one processor. Wherein, the at least one command includes: Commands for extracting the direct length from the image data of the carbon nanotubes; A command for generating an indirect length by combining the multiple physical property data of the carbon nanotubes to correct for errors occurring in the direct length; Commands for generating a correction model for correcting length measurement errors based on the direct length and the indirect length; and A command used to determine the length of the carbon nanotube whose length measurement error has been corrected using the correction model.

2. The system according to claim 1, wherein, The correction model is a Bayesian learning model.

3. The system according to claim 1, wherein, The calibration model is a model that can use input data as random variables to learn the probability distribution between the random variables.

4. The system according to claim 1, wherein, The commands used to generate the calibration model include commands for learning the probability distribution of the indirect length using the input indirect length data as random variables.

5. The system according to claim 1, wherein, The commands for generating the calibration model include commands for learning the probability distribution of the indirect length using the input indirect length data as random variables, and... Commands for determining the length of the carbon nanotube include commands for adjusting the probability distribution of the indirect length by reflecting the direct length.

6. The system according to claim 1, wherein, The commands for determining the length of the carbon nanotubes include commands for deriving the posterior probability of the length of the carbon nanotubes using prior probability and likelihood. Wherein, the prior probability is generated based on the indirection length, and The likelihood is generated based on the direct length.

7. The system according to claim 1, wherein, The multiple physical property data include physical properties selected from the group consisting of thickness, aspect ratio, tensile viscosity, and combinations thereof.

8. The system according to claim 1, wherein, The indirect length is generated based on a combination of the thickness and aspect ratio of the carbon nanotubes, and The aspect ratio is determined based on the tensile viscosity of the carbon nanotubes.

9. The system according to claim 8, wherein, The physical property data acquisition unit includes an atomic force microscope (AFM), and The thickness of the carbon nanotubes was obtained from the atomic force microscope.

10. The system according to claim 1, wherein, Commands for extracting the direct length include commands for extracting each carbon nanotube framework from the image data.

11. The system according to claim 10, wherein, The commands for extracting the direct length include commands for calculating the perimeter of each skeleton based on the extracted carbon nanotube skeleton.

12. The system according to claim 11, wherein, The perimeter of the skeleton is calculated using polygon approximation.

13. The system according to claim 1, wherein, The image data acquisition unit includes a scanning electron microscope (SEM), and The image data of the carbon nanotubes were acquired from the scanning electron microscope.

14. The system according to claim 1, wherein, The carbon nanotubes include single-walled carbon nanotubes (SWCNTs).

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