Methods and systems of producing 2d nanosheets by polymer-assisted ball-mill exfoliation

Abstract

The present invention provides methods of producing an exfoliated two- dimensional (2D) material, wherein the method comprises: providing a mixture comprising a 2D material and a polymer additive; and processing the mixture in a ball-mill apparatus, thereby producing an exfoliated 2D material, and the machine-learning guided production of said 2D materials.

Description

[0001] TITLE OF THE INVENTION

[0002] METHODS AND SYSTEMS OF PRODUCING 2D NANOSHEETS BY POLYMER-

[0003] ASSISTED BALL-MILL EXFOLIATION

[0004] CROSS-REFERENCE TO RELATED APPLICATIONS

[0005] This application claims priority to U.S. Provisional App. No. 63 / 573,111, filed on April 2, 2024, incorporated herein by reference in its entirety.

[0006] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0007] This invention was made with government support under Grant Nos. 1539999 and 2113882, awarded by the National Science Foundation. The United States government has certain rights in the invention.

[0008] BACKGROUND OF THE INVENTION

[0009] 2D materials are well-known for their unique properties in physics and chemistry, as their thickness decreases from bulk to a few layers and eventually monolayers (Novoselov et al., 2004, Science, 306, 666; Splendiani et al., 2010, Nano Lett., 10, 1271). To make practical use of the desirable characteristics found in laboratory-scale 2D materials, it is highly necessary to develop techniques that can produce ultra-thin 2D flakes on a larger scale. The reduced graphene oxide ink made from Hummer’s method provides a great example of facilitating the real -world application of 2D materials by developing a reproducible, controllable, and low-cost exfoliation process (Hummers, 2002, J. Am. Chem. Soc., 180, 1339; Abdolhosseinzadeh et al., 2015, Sci. Rep. 5). Unfortunately, Hummer’s method does not work well with 2D materials such as hexagonal boron nitride (hBN) that are chemically inert and therefore hard to intercalate with an exfoliation medium (Lin et al., 2009, J. Phys. Chem. Lett., 1, 277; Hung et al, 2014, NASA / TM-2014-218125; Shen et al., 1999, J. Solid State Chem., 147, 74). In fact, the availability of chemical methods to effectively exfoliate hBN is much more limited compared with other 2D materials. The extremely high chemical stability of hBN means harsher conditions are needed to chemically exfoliate it, e.g. high- temperature oxidation (Cui et al., 2014, Small, 10, 2353; Han et al., 2022, Chemical Engineering Journal, 437, 135482; Xue et al., 2023, Chemical Engineering Journal, 474, 145791), aggressive chemical treatment (Yu et al., 2021, Nanotechnology, 32, 405601; Wang et al., 2011, J. Mater. Chem., 21, 11371; Kovtyukhova et al., 2017, ACS Nano, 11, 6746; Zhu et al., 2024, Precision Chemistry, 2, 398; Zuo et al., 2022, Nat. Commun. 13, 32193), and high-pressure reaction (Wang et al., 2019, Materials Today, 27, 33; Li et al., 2013, Advanced Materials, 2200). Furthermore, harsh chemical treatment and reaction towards bulk hBN are highly likely to lead to the formation of defects on the exfoliated hBN and undesired degradation of the hBN flake quality (Hua Li et al., 2014, ACS Nano,

[0010] 8, 1457; Lee et al., 2019, Compos. B. Eng., 156, 276). This issue becomes a critical challenge in applications where a defect-free barrier layer made of hBN is preferred (Strand et al., 2020, Journal of Physics Condensed Matter, 32, 055706).

[0011] When it comes to high-quality hBN flakes that are frequently used for demanding applications, such as ultra-thin hBN dielectric layer and corrosion-inhibition layer (Zhang et al., 2016, Nanotechnology, 27, 364004; Hattori et al., 2015, ACS Nano,

[0012] 9, 916; Knoblock et al., 2021, Nature Electronics, 4, 98), the tape exfoliation method is still the most popular, successful, and universal approach to producing high-quality, ultrathin 2D flakes (Huang et al., 2015, ACS Nano, 9, 10612; Huang et al., 2020, Nat. Commun., 11, 2453). This method was developed at the very beginning of 2D material research for graphene preparation and has proven to be highly effective. Although tape exfoliation guarantees an exceptionally high crystalline quality by eliminating defects that are unavoidable in chemical exfoliation, it has equally obvious drawbacks. On one hand, the thickness of the exfoliated flakes largely depends on the number of the ‘presstear’ exfoliation cycles applied to the bulk material. Therefore, a considerable amount of time and labor work is required to produce ultra-thin 2D flakes (Mag-isa et al., 2015, 2D Mater., 2, 34017; Jia et al., 2021, Mater. Today Nano, 16, 100135). On the other hand, tape exfoliation is essentially a manually operated process that heavily relies on the skills of the scientist, and key parameters such as the pressure applied to tapes are difficult to quantify. Therefore, the lack of reproducibility becomes a major issue when the same procedure is repeated by others (Yuan et al., 2016, AIP Adv., 6, 125201). Lastly, tape exfoliation method has limited capacity to handle large-scale material production, even when manual operation is upgraded with automated design (Dicamillo et al., 2019, IEEE Trans. Nanotechnol., 18, 144).

[0013] Current ways to produce ultra-thin two-dimensional flakes from bulk precursors, i.e., exfoliation of layered materials, include tape (mechanical) exfoliation, solvent exfoliation, chemical exfoliation and conventional ball-mill. Current ways of exfoliation cannot meet the requirement of universality, low-cost, scalability, high-yield and controllability at the same time. For example, tape exfoliation has very low repeatability and huge challenge in scaling up; solvent and chemical exfoliation does not apply to materials with high stability such as hexagonal boron nitride and depending on the type of materials, the cost of solvents and chemicals varies in a wide range, which makes the process very expensive sometimes, e.g., chemical exfoliation of molybdenum disulfide with butyllithium; and conventional ball-mill has very low-yield in producing ultra-thin flakes with fairly high aspect-ratio. As a result, current ways of exfoliation are not able to solve the problem of translating lab knowledge into practical technology, while this invention is able to address all the points and facilitate the real applications.

[0014] Thus, there is a need in the art for improved methods and systems for producing ultra-thin two-dimensional nanosheets. This invention satisfies this unmet need.

[0015] This invention was funded in part by the Robert A. Welch Foundation under Welch Grant No. C-1716.

[0016] SUMMARY OF THE INVENTION

[0017] The present invention provides in part a method of producing an exfoliated two-dimensional (2D) material, wherein the method comprises: providing a mixture comprising a 2D material and a polymer additive; and processing the mixture in a ball-mill apparatus, thereby producing an exfoliated 2D material.

[0018] In some embodiments, the 2D material is a van der Waals layered material. In some embodiments, the 2D material is chemically inert. In some embodiments, the 2D material is selected from the group consisting of nitrides, graphene, transition metal dichalcogenides, layered metal oxides, layered metal hydroxides, and combinations thereof. In some embodiments, the 2D material is selected from the group consisting of hexagonal boron nitride (hBN), graphite, molybdenum disulfide (M0S2), tin selenide (SnSe), tungsten diselenide (WSe?), gallium selenide (Ga2Sea), lead iodide (Pbb), black phosphorus, and combinations thereof.

[0019] In some embodiments, the polymer additive comprises a polysaccharide. In some embodiments, the polymer additive comprises a synthetic polymer. In some embodiments, the polymer additive comprises a polymer selected from the group consisting of wax, starch, polyvinyl alcohol (PVA), polyvinyl chloride (PVC), polyvinylidene fluoride (PVDF), polytetrafluoroethylene (PTFE), polyacrylamide (PAM), polyacrylic acid (PAA), polyvinylpyrrolidone (PVP), polymethyl methacrylate (PMMA), polyethylene glycol (PEG), ethyl cellulose (EC), chitin, sodium carboxymethyl cellulose (CMC), agar, gelatin, gum arabic, and combinations thereof. In some embodiments, the polymer additive comprises a polymer having a covalent organic framework. In some embodiments, the polymer additive comprises com starch.

[0020] In some embodiments, the mixture comprises the 2D material and the polymer additive at a weight proportion of 1 to at least 5. In some embodiments, the step of processing the mixture in a ball-mill apparatus comprises ball-milling the mixture for at least 1 hour.

[0021] In some embodiments, the method further comprises the step of selecting the polymer additive based on a desired characteristic of the exfoliated 2D material. In some embodiments, the desired characteristic of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size. In some embodiments, a machine learning model is configured to select the polymer additive. In some embodiments, characteristics of the exfoliated 2D material are used to retrain the machine learning model.

[0022] In some embodiments, the method further comprises the step of determining ball-milling parameters for producing the exfoliated 2D material based on the selected polymer additive. In some embodiments, the ball-milling parameters comprise at least one of milling time, milling speed, milling temperature, and grinding media size. In some embodiments, a machine learning model is configured to determine the ball-milling parameters. In some embodiments, the machine learning model incorporates data from real-time monitoring of ball-milling to adjust ball-milling conditions dynamically.

[0023] The present invention further provides in part an exfoliated 2D material produced using the method described herein. In some embodiments, the exfoliated 2D material has an average aspect ratio of at least 1.

[0024] The present invention further provides an exfoliated two-dimensional (2D) material, comprising a 2D material selected from the group consisting of hBN, graphite, molybdenum disulfide (M0S2), tin selenide (SnSe), tungsten diselenide (WSe2), gallium selenide (Ga2Se3), lead iodide (Pbh), black phosphorus, and combinations thereof, wherein the exfoliated 2D material has an average aspect ratio of at least 1.

[0025] In some embodiments, the exfoliated 2D nanosheet has an average thickness of less than 100 nm. In some embodiments, the invention relates to a semiconductor material comprising the exfoliated 2D material described herein. In some embodiments, the invention relates to a thermal interface material comprising the exfoliated 2D material described herein.

[0026] The present invention further provides a system for producing an exfoliated 2D material comprising: a ball-milling apparatus; and a computing device operatively connected to the ball-milling apparatus comprising a processor and a non- transitory computer-readable medium with instructions stored thereon, which when executed by the processor perform the steps of: selecting a polymer additive based on a desired characteristic of an exfoliated 2D material; providing a mixture comprising a 2D material and the polymer additive; and processing the mixture in the ball-mill apparatus, thereby producing an exfoliated 2D material.

[0027] In some embodiments, the desired characteristic of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size. In some embodiments, a machine learning model is configured to select the polymer additive. In some embodiments, the processing step further comprises adding a functional group to the exfoliated 2D material. In some embodiments, the processing step further comprises introducing defects to the exfoliated 2D material.

[0028] BRIEF DESCRIPTION OF THE DRAWINGS The following detailed description of embodiments of the invention will be better understood when read in conjunction with the appended drawings. It should be understood that the invention is not limited to the precise arrangements and instrumentalities of the embodiments shown in the drawings.

[0029] Fig. 1, comprising Fig. 1A through Fig. 1J, depicts a schematic illustration of tape exfoliation. Fig. 1A depicts a diagram of scotch tape with a piece of layered material flake to mechanically exfoliate. Fig. IB depicts a diagram of a second tape to contact the flake. Fig. 1C depicts how pressure is applied to ensure the contact is good. Fig. ID depicts how exfoliated flakes remain at both tapes. Fig. IE through Fig. 1J depicts a schematic illustration of the proposed mechanism of polymer-assisted dry ball mill process. Fig. IE depicts a pair of mill balls mixed with polymer powder before dry ball-mill. Fig. IF and Fig. 1G depict the motion of ball collision and resulting deformed polymer attached to the balls. Fig. 1H, Fig. II, and Fig. 1 J depict how polymer-attached balls act as ‘tapes’ to form good contact with an hBN flake during a collision with another ball and subsequently exfoliate it into thinner flakes as the balls rebound and separate.

[0030] Fig. 2, comprising Fig. 2A through Fig. 2E, depicts representative AFM height images of hBN nanoflakes produced from starch-assisted dry ball-mill (Fig. 2A) and dry ball-mill without any polymer additives (Fig. 2B), with nanosheet thicknesses labeled and indicated by the color intensity bars. Fig. 2C and Fig. 2D depict histogram plots of thickness and aspect ratio of hBN without any polymer additives (grey) and with starch as additive (blue). Fig. 2E depicts a comparison of average area, thickness, average aspect ratio and fractioned thickness of hBN nanoflakes without and with seventeen polymer additives. Abbreviations: PVA - polyvinyl alcohol, PVC - polyvinyl chloride, PVDF - polyvinylidene fluoride, PTFE - polytetrafluoroethylene, PAM - polyacrylamide, PAA - polyacrylic acid, PVP - polyvinylpyrrolidone, PMMA - polymethyl methacrylate, PEG - polyethylene glycol, EC - ethyl cellulose, CMC - carboxymethyl cellulose.

[0031] Fig. 3, comprising Fig. 3A and Fig. 3B, depicts scanning electron microscopy (SEM) images of hBN nanoflakes produced from a plain dry ball-mill process (Fig. 3A) and a PVDF-assisted dry ball-mill process (Fig. 3B). Fig. 4 depicts a correlation matrix of all the polymer features (physical properties) obtained from parallel experimental methods including AFM force-distance measurement, nanoindentation, thermogravimetric analysis-differential scanning calorimetry (TGA-DSC) and contact angle measurement.

[0032] Fig. 5 depicts rankings of the most relevant features of the polymer additives to the morphology parameters including lateral size, thickness, and aspect ratio of the hBN nanoflakes produced by polymer-assisted dry ball-mill determined by linear regression.

[0033] Fig. 6 depicts rankings of unselected features for each of the morphology parameters.

[0034] Fig. 7 depicts a schematic illustration shows how polymer deformation facilitates the mechanical gripping from polymer to hBN in polymer-assisted dry ballmill exfoliation. The deformation of the polymer is caused by the conversion of kinetic energy and heat from the motion of the mill ball into mechanical deformation.

[0035] Fig. 8, comprising Fig. 8A and Fig. 8B, depict SEM images on com starch without (Fig. 8A) and with hBN (Fig. 8B) after ball-mill.

[0036] Fig. 9, comprising Fig. 9A through Fig. 9G, depict polymer-assisted dry ball-mill of layered materials beyond hBN. SEM images of graphite (Fig. 9A), M0S2 (Fig. 9B), and Pb I2 (Fig. 9C) before and after ball-mill (Fig. 9D, Fig. 9E, and Fig. 9F, respectively). Fig. 9G depicts statistics on lateral size, thickness and aspect ratio values of ball-milled nanoflakes obtained from AFM images. PVDF was used as the assisting polymer for graphite, M0S2, SnSe and Ga2Sea, while PVP was used for Pbh.

[0037] Fig. 10 depicts Raman spectra of bulk layered powder (blue lines) and 2D nanoflakes from polymer-assisted ball-milled (gray lines) for different materials. Insets are the atomic structures of the corresponding materials. All Raman measurements were done in a Renishaw inVia Raman microscope using 532 nm laser excitation.

[0038] Fig. 11 depicts SEM and AFM analysis of pristine hBN flakes (Alfa Aesar, 11078) prior to ball-mill. The thickness of the original flakes ranges from 100.0 nm to 300.0 nm, scale bar 5pm. Fig. 12 depicts AFM analysis of polymer-assisted ball-milled 2D nanosheets (a-c) Ga2Se3, (d-f) SnSe, (g-i) PbI2, (j-1) MoS2 and (m-o) Graphite. Scale bar: 2pm.

[0039] Fig. 13 is a diagram of an exemplary computing environment.

[0040] DETAILED DESCRIPTION

[0041] The present invention relates in part to methods and systems for preparing, fabricating, and manufacturing ultra-thin two-dimensional (2D) materials having tailored geometric parameters uniquely suited for versatile applications. In some embodiments, the present invention provides methods and systems of producing 2D nanosheets by polymer-assisted ball-mill exfoliation. In some embodiments, the present invention provides methods and systems for the machine-learning guided production of 2D nanosheets by polymer-assisted ball-mill exfoliation, including modeling the effect of polymer additives in ball-milling to produce exfoliated 2D materials having tailored geometric parameters. In some embodiments, the present invention can be applied to the preparation, fabrication, and manufacture of exfoliated 2D materials from various layered materials including van der Waals layered materials. The methods of the present invention provide materials with unexpectedly enhanced geometric parameters, such as high aspect ratios and low thicknesses, when compared to materials generated using current methods in the art.

[0042] The present invention further relates to the machine-learning guided production of 2D materials. Thus, in some embodiments, the present invention provides methods of preparing 2D nanosheets by polymer-assisted ball-mill exfoliation of layered materials, and methods of modeling the effect of polymer additives in ball-mill exfoliation in machine learning. The present invention further provides 2D materials produced by the methods described herein, such as 2D nanosheets having geometric parameters for use in diverse applications including but not limited to semiconductor devices and thermal interface materials. Definitions

[0043] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0044] As used herein, each of the following terms has the meaning associated with it in this section.

[0045] The articles “a” and “an” are used herein to refer to one or to more than one (i.e., to at least one) of the grammatical object of the article. By way of example, “an element” means one element or more than one element.

[0046] “About” as used herein when referring to a measurable value such as an amount, a temporal duration, and the like, is meant to encompass variations of ±20%, ±10%, ±5%, ±1%, or ±0.1% from the specified value, as such variations are appropriate to perform the disclosed methods.

[0047] A “2D material”, as used herein, is a material that comprises at least one sub-layer that, within each sub-layer, tends to form strong bonds such as covalent bonds, whereas sub-layers are held together via weaker interactions such as Van der Waals interactions. Electrons in each sub-layer of these materials are free to move in the two- dimensional plane, but their motion in the third dimension can be restricted and is governed by quantum mechanics. Graphene is an example of a “2D material” in which each sub-layer has a thickness of only a single atom. Molybdenum disulfide (M0S2) is an example of a “2D material” in which each sub-layer has three internal monolayers: a middle monolayer of Mo, sandwiched between upper and lower monolayers of S. The bonds between the Mo atoms and the S atoms are covalent, whereas interactions between the lower S monolayers of one layer and the upper S monolayers of the layer below it are Van der Waals interactions.

[0048] The terms “2D nanosheet” and “2D flake” may be used interchangeably herein and are used to describe a structure having dimensions on the order of approximately 0.1 to 100 nm comprising between 1 to several atomic or molecular monolayers, wherein “2D” can be defined as having a lateral dimension and a width dimension (or thickness) wherein the lateral dimensions may be greater than the width or thickness. The 2D nanosheets of the present invention may be derived from 2D materials. The dimensions of a 2D nanosheet of the present invention can be further characterized by an “aspect ratio”, which is defined herein as the area (or length of the lateral major axis) divided by or the average thickness (or width of the minor axis). For example, a 2D nanosheet having an average edge length of 100 nm and an average thickness of 100 nm has an aspect ratio of 1.

[0049] Ranges: throughout this disclosure, various aspects of the invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 2.7, 3, 4, 5, 5.3, and 6. This applies regardless of the breadth of the range.

[0050] Methods of Preparing Two-Dimensional Nanosheets

[0051] The present invention provides in part a method for the production of ultra-thin exfoliated two-dimensional (2D) materials and nanosheets by exfoliating a 2D material with a polymer additive using a ball-mill apparatus. In some embodiments, exfoliated 2D materials are regarded as 2D nanosheets. Thus, in some embodiments, the present invention provides a method of producing an exfoliated two-dimensional (2D) material, wherein the method comprises: providing a mixture comprising a 2D material and a polymer additive; and processing the mixture in a ball-mill apparatus, thereby producing an exfoliated 2D material, or a 2D nanosheet. A representative schematic of the method described herein is shown in Fig. 1.

[0052] The present method grants uniquely tailored control over geometric parameters of the produced exfoliated 2D material, including but not limited to, thickness of the 2D material and aspect ratio of the 2D material.

[0053] The methods described herein can be readily applied to a diverse set of 2D materials including, but not limited to, those that are chemically inert and van der Waals layered materials. Exemplary materials include, without limitation, nitrides, such as hexagonal boron nitride (hBN), graphene, graphite, graphene oxide, reduced graphene oxide, transition metal dichalcogenides, for example, WO2, WS2, WSe2, WTe2, MnCh, MoO2, M0S2, MoSe2, MoTe2, NiCh, NiTe2, NiSe2, VO2, VS2, VSe2, TaS2, TaSe2, RuO2, RhTe2, PdTe2, HfS2, NbS2, NbSe2, NbTe2, FeS2, TiO2, TiS2, TiSe2, and ZrS2, transition metal trichalcogenides such as, for example, TaO.3, MnCh, WO3, ZrSa, ZrSea, HfSi, and HfSea, sulfides, selenides, and tellurides of Group 13-16 elements, oxides, for example, LaVCh, LaMnCh, TiCh, MnCh, V2O5, TaCh, RuCh, MnO.i, WO3, LaNbO?, Ca2Nb30io, Ni(0H)2, and Eu(0H)2, layered copper oxides, micas, bismuth strontium calcium copper oxide (BSCCO), phosphides, for example, Li?MnP4, and MnP4, silicene, germanene, stanene, metal iodides, for example PbE, black phosphorus, and combinations thereof.

[0054] The polymer additives which may be employed in the methods described herein are unrestricted and encompass natural and synthetic polymers that are commonly available and / or are readily synthesized. In some embodiments, the polymer additive comprises a natural polymer, including, but not limited to, polysaccharides, such as starch derived from corn, potato, rice, tapioca, wheat, barley, cassava, or arrowroot, modified starches, cellulose, chitin, glycogen, galactogen, amylose, amylopectin, agar, gelatin, gum arabic, derivatives thereof, plasticized variants thereof, and combinations thereof. In some embodiments, the polymer additive comprises a synthetic polymer, including, but not limited to, petroleum derived polymers, such as polyolefins, polyesters, polyamides, polyurethanes, and polyvinyl chloride. In some embodiments, the polymer additive comprises a polymer selected from the group consisting of wax, starch, polyvinyl alcohol (PVA), polyvinyl chloride (PVC), polyvinylidene fluoride (PVDF), polytetrafluoroethylene (PTFE), polyacrylamide (PAM), polyacrylic acid (PAA), polyvinylpyrrolidone (PVP), polymethyl methacrylate (PMMA), polyethylene glycol (PEG), ethyl cellulose (EC), chitin, sodium carboxymethyl cellulose (CMC), agar, gelatin, gum arabic, and combinations thereof. In some embodiments, the polymer additive comprises corn starch. In some embodiments, the polymer additive comprises PVDF. In some embodiments, the polymer additive comprises gelatin. In some embodiments, the polymer additive comprises a polymer having a covalent organic framework (COF), including, but not limited to, TpPA-1 and crystalline COFs.

[0055] The polymer additives that are used herein may be of any molecular weight and may be at least about 1 kDA, 5 kDA, 10 kDA, 25 kDA, 50 kDA, 100 kDA, 150 kDa, 200 kDa, 500 kDa, or greater than 100 kDa.

[0056] In some embodiments, the mixture comprises the 2D material and the polymer additive at a weight proportion wherein the polymer additive is in large excess. For example, the weight proportion of the 2D material to polymer additive in the mixture may be between about 1 : 1 (one to one) and about 1: 10, about 1 : 1 and about 1 :9, about 1 : 1 and about 1 :8, about 1 : 1 and about 1:7, about 1 : 1 and about 1 :6, about 1 : 1 and about 1 :5, about 1 : 1 and about 1 :4, about 1 : 1 and about 1 :3, about 1 : 1 and about 1 :2, or about 1 : at least about 1 (i.e.: 1 :2, 1:3, 1 :4, etc.), about 1 : at least about 2, about 1 : at least about 3, about 1 : at least about 4, about 1 : at least about 5, about 1 : at least about 6, about 1 : at least about 7, about 1 : at least about 8, about 1 : at least about 9, or about 1 : at least about 10. In some embodiments, the mixture comprises the 2D material and the polymer additive at a weight proportion that is 1 : 1. In some embodiments, the mixture comprises the 2D material and the polymer additive at a weight proportion that is 1 to at least 5. For example, the mixture comprises 100 g of the 2D material and at least 500 g of the polymer additive. In some embodiments, the mixture comprises the 2D material and the polymer additive at a weight proportion that is 1 :5. For example, the mixture comprises 100 g of the 2D material and 500 g of the polymer additive.

[0057] In some embodiments, the step of processing the mixture in a ball-mill apparatus comprises ball-milling the mixture for any period of time required to observe formation of the exfoliated 2D material. For example, the step of processing the mixture in a ball-mill apparatus may comprise ball-milling the mixture for any period of time lasting between about 1 minute and about 5 hours, about 30 minutes and about 5 hours, about 1 hour and about 5 hours, about 1 hour and about 4 hours, about 1 hour and about 3 hours, about 1 hour and about 2 hours, or about 2 hours and about 3 hours, or at least about 1 minute, 5 minutes, 30 minutes, 1 hour, 2 hours, 3 hours, 4 hours, or 5 hours. In some embodiments, the step of processing the mixture in a ball-mill apparatus comprises ball-milling the mixture for at least about 1 hour. In some embodiments, the step of processing the mixture in a ball-mill apparatus comprises ball-milling the mixture for at least about 2 hours.

[0058] The ball-mill apparatus employed in the present invention can be any ballmill apparatus comprising a hollow shell which rotates about an axis and a grinding media, i.e. balls. In some embodiments, the ball-mill apparatus is selected from a dry ball-mill apparatus, a vertical ball-mill apparatus, a planetary ball-mill apparatus, a batch ball-mill apparatus, a continuous ball-mill apparatus, a horizontal ball-mill apparatus, a rotary ball-mill apparatus, a tumbling ball-mill apparatus, a conical ball-mill apparatus, or a ball-mill apparatus having the combined properties of any of the ball-mill apparatus thereof. A ball-mill apparatus having the combined properties of any of the ball-mill apparatus thereof can be otherwise defined as a ball-mill apparatus which logically combines several properties of existing ball-mill apparatus. For example, a ball-mill apparatus having the combined properties of any of the ball-mill apparatus thereof could be a dry, vertical, planetary ball-mill apparatus. The method described herein can further be expanded to industrial variants of ball-mill apparatus.

[0059] The ball-mill apparatus may comprise beads of any diameter appropriate to induce exfoliation of the mixture, or to induce adhesion of the 2D material to the polymer additive on the beads, and are not limited to circular beads as grinding media and may include other grinding media such as rods or pebbles. In some embodiments, the ball-mill apparatus comprises beads made from a material selected from zirconia, yttria stabilized zirconia (YSZ), zirconium silicate, zirconia toughened alumina, agate, alumina, tungsten carbide, steel, chrome steel, stainless steel, glass, polymer resins, or combinations thereof. The beads that may be used in the present invention may have a diameter of at least about 1 mm, 3 mm, 5 mm, 10 mm, 100 mm, 500 mm, or combinations thereof. In some embodiments, the ball-mill apparatus comprises a combination of beads having diameters of 1 mm and 3 mm. The size of the beads are not limited to the values recited thereof and include beads having diameters on the order of centimeters and meters depending on the size of the ball-mill apparatus.

[0060] In some embodiments, the method may further comprise the step of isolating the exfoliated 2D material. This step may be performed using any method of material / nanosheet isolation known in the art, including but not limited to, drop-casting, precipitating, and centrifuging. In some embodiments, the exfoliated 2D material is dispersed in a solvent where the polymer additive is fully soluble. For example, the exfoliated 2D material is dispersed in a solvent selected from water, polar organic solvents, such as acetone, acetonitrile, methanol, dichloromethane, dimethylformamide, dimethylsulfoxide, ethyl acetate, ethanol, tetrahydrofuran, and chloroform, nonpolar organic solvents, such as benzene, toluene, and xylenes, ionic liquids, and combinations thereof. In some embodiments, the solvent is heated to increase solubility of the polymer additive. In some embodiments, the exfoliated 2D material can then be isolated from the solution comprising the dissolved polymer additive.

[0061] In some embodiments, the method may further comprise the step of depositing the exfoliated 2D material onto a substrate using any deposition method known in the art, including but not limited to, drop-casting, spray coating, inkjet printing, dip coating, gravure coating, extrusion coating, brush coating, roll coating, flow coating, heat press molding and combinations thereof.

[0062] Two-Dimensional Nanosheets

[0063] The present invention further provides exfoliated two-dimensional (2D) nanosheets produced by the methods described herein. Thus, the present invention relates to an exfoliated two-dimensional (2D) nanosheet, wherein the exfoliated 2D nanosheet comprises a 2D material described elsewhere herein and has an average aspect ratio of at least 1. In some embodiments, the exfoliated 2D nanosheet is a flake of a 2D material described herein.

[0064] The exfoliated 2D nanosheets of the invention are characterized by unexpectedly improved aspect ratios. In some embodiments, the aspect ratios of the exfoliated 2D nanosheets between about 0.1 to about 20, about 0.1 to about 15, about 0.1 to about 10, about 0.1 to about 9, about 0.1 to about 8, about 0.1 to about 7, about 0.1 to about 6, about 0.1 to about 5, about 0.1 to about 4, about 0.1 to about 3, about 0.1 to about 2, about 0.1 to about 1, about 1 to about 2, about 1 to about 3, about 1 to about 4, about 1 to about 5, about 1 to about 6, about 1 to about 7, about 1 to about 8, about 1 to about 9, about 1 to about 10, about 1 to about 11, about 1 to about 12, about 1 to about 13, about 1 to about 14, about 1 to about 15, about 1 to about 16, about 1 to about 17, about 1 to about 18, about 1 to about 19, about 1 to about 20, or at least about 0.1, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20.

[0065] In some embodiments, the exfoliated 2D nanosheets of the invention can have a range of aspect ratios and can thus be characterized by an average aspect ratio. The term “average aspect ratio” is defined herein as the arithmetic mean value of aspect ratios obtained for at least two 2D material and / or nanosheet flakes observed using means such as AFM. In some embodiments, the 2D nanosheets have an average aspect ratio of at least about 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 2, 3, 4, or 5.

[0066] In some embodiments, the exfoliated 2D nanosheets have a range of areas and can thus be characterized by an average area. In some embodiments, the exfoliated 2D nanosheets have an area or average area of between about 5 nm2and about 2 x 105nm2, about 100 nm2and about 2 x 105nm2, about 1 x 103nm2and about 2 x 105nm2, about 1 x 104nm2and about 2 x 105nm2, about 5 x 104nm2and about 2 x 105nm2, about 1 x 105nm2and about 2 x 105nm2, 5 nm2and about 1 x 105nm2, about 100 nm2and about 1 x 105nm2, about 1 x 103nm2and about 1 x 105nm2, about 1 x 104nm2and about 1 x 105nm2, about 5 x 104nm2and about 1 x 105nm2, or at least about 5 nm2, 100 nm2, 1 x 103nm2, 1 x 104nm2, 5 x 104nm2, 1 x 105nm2, or 2 x 105nm2.

[0067] In some embodiments, the exfoliated 2D nanosheets have a range of thicknesses and can thus be characterized by an average thickness. In some embodiments, the exfoliated 2D nanosheets have a thickness or average thickness of between about 1 nm and about 150 nm, about 5 nm and about 150 nm, about 20 nm and about 150 nm, about 30 nm and about 150 nm, about 40 nm and about 150 nm, about 50 nm and about 150 nm, about 60 nm and about 150 nm, about 70 nm and about 150 nm, about 80 nm and about 150 nm, about 90 nm and about 150 nm, about 100 nm and about 150 nm, about 110 nm and about 150 nm, about 120 nm and about 150 nm, about 130 nm and about 150 nm, about 140 nm and about 150 nm, 1 nm and about 100 nm, about 5 nm and about 100 nm, about 20 nm and about 100 nm, about 30 nm and about 100 nm, about 40 nm and about 100 nm, about 50 nm and about 100 nm, about 60 nm and about 100 nm, about 70 nm and about 100 nm, about 80 nm and about 100 nm, about 90 nm and about 100 nm, 1 nm and about 50 nm, about 5 nm and about 50 nm, about 20 nm and about 50 nm, about 30 nm and about 50 nm, about 40 nm and about 50 nm, 1 nm and about 40 nm, about 5 nm and about 40 nm, about 20 nm and about 40 nm, about 30 nm and about 40 nm, 1 nm and about 30 nm, about 5 nm and about 30 nm, about 20 nm and about 30 nm, or less than about 150 nm, 140 nm, 130 nm, 120 nm, 110 nm, 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50 nm, 40 nm, 30 nm, 20 nm, 10 nm, or 1 nm.

[0068] In some embodiments, the exfoliated 2D nanosheets are further functionalized with a functional group. The functionalization of the exfoliated 2D nanosheets can be performed using any technique known in the art of materials science, organic synthesis, and nanoengineering. Exemplary functional groups include, but are not limited to, reactive functional groups such as hydroxyl groups, thiol groups, carbonyls, amino groups, and carboxyls, functional groups comprising moieties such as alkenes and alkynes, and cross-linkable functionalities such as primary amines, thiols, and acrylates.

[0069] System for Exfoliated 2D Material

[0070] Various systems are disclosed herein that are capable of receiving desired characteristics of an exfoliated 2D material and providing starting materials (e.g., a polymer additive) based on the desired characteristics. In some embodiments, a software is disclosed that will select polymer additive, polymer types and / or characteristics of the polymers based on a desired exfoliated 2D material. In some embodiments, machine learning and / or artificial intelligence guide the selection of the starting material and / or characteristics of the starting material based on the desired characteristics of the final product (e.g., an exfoliated 2D material). In general, the described systems may be utilized with any of the devices, equipment and methods disclosed herein.

[0071] In some embodiments, any of the methods described herein may include systems that promote machine-learning guided production of 2D nanosheets by polymer- assisted ball-mill exfoliation. In some embodiments, the systems can include machinelearning guided production of nanosheets by polymer-assisted ball-mill exfoliation of van der Waals layered materials. In general, in another embodiment, the invention features a system for exfoliating a two-dimensional (2D) material. In some embodiments, the system is configured to produce ultra-thin 2D flakes. In some embodiments, the system includes a dry ball-mill apparatus. For example, in addition to any equipment and component parts described herein for performing the inventive methods, the system may further include a first source that includes one or more 2D materials. In some embodiments, the one or more 2D materials is not graphene. In some embodiments, the system further includes a machine learning model configured to select milling conditions and / or a polymer additive to mix with the 2D material. In some embodiments, the system further includes a second source comprising the polymer additive selected by the machine learning model. The dry -ball mill apparatus, the first source, and the second source are operatively connected such that (i) the 2D materials can be mixed with the polymer additive to form a mixture, (ii) the mixture can be processed by the dry ball-mill apparatus, and (iii) the system can produce the ultra-thin 2D flakes from the mixture after processing.

[0072] The dry ball-mill apparatus can be operated under conditions selected based on a machine learning model. The machine learning model can incorporate data from real-time monitoring of the ball-mill apparatus to adjust milling conditions dynamically. The machine learning model can receive inputs comprising polymer additive properties, two-dimensional material type, and desired geometric parameters of the ultra-thin 2D flakes. The system can further include a feedback loop wherein the characteristics of the ultra-thin 2D flakes are used to retrain the machine learning model.

[0073] The machine learning model can output optimal milling conditions for the ultra-thin 2D flakes. The method can further include introducing defects into the ultrathin 2D flakes under controlled milling conditions as determined by the machine learning model. The defects a can be selected from the group consisting of vacancies, interstitials, and substitutional atoms.

[0074] Accordingly in certain embodiments, the present invention is process that first can build the machine-learning model of polymer-assisted ball-mill with experimental data. A series of polymers such as PTFE, PVDF, PVA and starch with different physical properties such as elastic modulus, hardness, adhesion energy, friction coefficient, surface energy and melting point that cover a wide range of values are used to ball- mill with van der Waals layered materials such as graphite, hexagonal boron nitride and molybdenum disulfide. The geometric parameters including thickness, lateral size and aspect ratio of the ball-milled product are determined by AFM. The values of the physical properties and geometric parameters are used as training data to build machinelearning models that describe selected features and ranking of importance of physical properties on geometric parameters.

[0075] The process thereinafter can predict the geometric parameters of ultra-thin two-dimensional flakes from polymer properties or guide polymer design with targeted geometric parameters of ultra-thin two-dimensional flakes. The model can predict the geometric parameters of ultra-thin flakes made from ball-mill assisted by a polymer with all the featured physical parameters identified. The model can also provide the values of physical properties for an ideal polymer candidate to produce the desired ultra-thin flakes using a polymer-assisted ball-mill, as well as defects engineering to introduce catalytic properties. The precision of the model can be varied depending on the size and data of distribution of the training group, and the parameters of the model can be varied depending on the type of van der Waals materials that is ball-milled as well as the specification of the ball-mill equipment.

[0076] Accordingly, a system for producing exfoliated 2D materials utilizing machine learning is disclosed herein. In some embodiments, a system for producing an exfoliated 2D material comprises a processor and a non-transitory computer-readable medium with instructions stored thereon, which when executed by the processor perform the steps of: receiving input data corresponding to at least one desired characteristic (e.g., a target geometric parameter) of an exfoliated 2D material, or input data corresponding to at least one selected polymer additive for an exfoliated 2D material. When at least one target geometric parameter is received, the processor performs the step of determining at least one recommended polymer additive based on the at least one target geometric parameter and physical properties of at least one candidate polymer additive, or when at least one selected polymer additive is received, the processor performs the step of determining at least one geometric parameter based on the at least one selected polymer additive and physical properties of at least one candidate polymer additive. In some embodiments, the processor performs the step of outputting data indicative of the at least one recommended polymer additive or the at least one determined geometric parameter.

[0077] In some embodiments, determining the at least one recommended polymer additive comprises accessing a database of candidate polymer additives, candidate polymer physical properties, and geometric parameters of exfoliated 2D materials produced from the candidate polymer additives, applying a machine learning model trained on historical data comprising relationships between candidate polymer additives, candidate polymer physical properties and geometric parameters of exfoliated 2D materials produced from the candidate polymer additives, and determining the at least one recommended polymer additive based on a predicted correlation between the target geometric parameter, the at least one candidate polymer additive and geometric parameters of exfoliated 2D materials produced from the at least one candidate polymer additive. In some embodiments, the processor performs the step of determining the at least one geometric parameter based on a predicted correlation between the at least one selected polymer additive and the geometric parameters of exfoliated 2D materials produced from the at least one selected polymer additive.

[0078] In some embodiments, the at least one target geometric parameter of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size.

[0079] In some embodiments, the physical properties of candidate polymer additives comprise at least one of mechanical properties, thermal properties, surface properties, adhesion energy, friction coefficient, hardness, elastic modulus, softening point, melting point, decomposition point, water contact angle, surface energy, hydrophobicity and hydrophilicity.

[0080] In some embodiments, the processor further performs the steps of determining ball-milling parameters for producing an exfoliated 2D material based on the at least one recommended polymer additive or the at least one determined geometric parameter; and outputting data indicative of the determined ball-milling parameters.

[0081] In some embodiments, determining ball-milling parameters comprises accessing a database of candidate polymer additives, candidate polymer physical properties, ball-milling parameters, and geometric parameters of exfoliated 2D materials produced from the candidate polymer additives by way of ball-milling; applying a machine learning model trained on historical data comprising relationships between candidate polymer additives, candidate polymer physical properties, ball milling parameters, and geometric parameters of exfoliated 2D materials produced from the candidate polymer additives by way of the ball milling; and determining the ball milling parameters based on a predicted correlation between the at least one recommended polymer additive or at least one determined geometric parameter and the ball-milling parameters of a produced exfoliated 2D material.

[0082] In some embodiments, the ball-milling parameters comprise at least one of milling time, milling speed, milling temperature, and combination of grinding media with different sizes. In some embodiments, the system receives real-time data of ball-milling of the production of an exfoliated 2D material.

[0083] Accordingly the aforementioned systems may include computing devices communicatively and / or operatively connected to the systems for performing one or more steps of any of the disclosed methods. For example, in some embodiments, the computing devices enable machine learning and / or artificial intelligence with neural networks for aiding in the selection of polymer additives based on the desired characteristics of the exfoliated 2D material. In some aspects of the present invention, software executing the instructions provided herein may be stored on a non-transitory computer-readable medium (e.g., code or model), wherein the software performs some or all of the steps of the present invention when executed on a processor.

[0084] Aspects of the invention relate to algorithms executed in computer software. Though certain embodiments may be described as written in particular programming languages, or executed on particular operating systems or computing platforms, it is understood that the system and method of the present invention is not limited to any particular computing language, platform, or combination thereof. Software executing the algorithms described herein may be written in any programming language known in the art, compiled, or interpreted, including but not limited to C, C++, C#, Objective-C, Java, JavaScript, MATLAB, Python, PHP, Perl, Ruby, or Visual Basic. It is further understood that elements of the present invention may be executed on any acceptable computing platform, including but not limited to a server, a cloud instance, a workstation, a thin client, a mobile device, an embedded microcontroller, a television, or any other suitable computing device known in the art.

[0085] Parts of this invention are described as software running on a computing device. Though software described herein may be disclosed as operating on one particular computing device (e.g. a dedicated server or a workstation), it is understood in the art that software is intrinsically portable and that most software running on a dedicated server may also be run, for the purposes of the present invention, on any of a wide range of devices including desktop or mobile devices, laptops, tablets, smartphones, watches, wearable electronics or other wireless digital / cellular phones, televisions, cloud instances, embedded microcontrollers, thin client devices, or any other suitable computing device known in the art.

[0086] Similarly, parts of this invention are described as communicating over a variety of wireless or wired computer networks. For the purposes of this invention, the words “network”, “networked”, and “networking” are understood to encompass wired Ethernet, fiber optic connections, wireless connections including any of the various 802.11 standards, cellular WAN infrastructures such as 3G, 4G / LTE, or 5G networks, Bluetooth®, Bluetooth® Low Energy (BLE) or Zigbee® communication links, or any other method by which one electronic device is capable of communicating with another. In some embodiments, elements of the networked portion of the invention may be implemented over a Virtual Private Network (VPN).

[0087] Fig. 13 and the following discussion are intended to provide a brief, general description of a suitable computing environment in which the invention may be implemented. While the invention is described above in the general context of program modules that execute in conjunction with an application program that runs on an operating system on a computer, those skilled in the art will recognize that the invention may also be implemented in combination with other program modules.

[0088] Generally, program modules include routines, programs, components, data structures, and other types of structures that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced with other computer system configurations, including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, and the like. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices. Fig. 13 depicts an illustrative computer architecture for a computer 3000 for practicing the various embodiments of the invention. The computer architecture shown in Fig. 13 illustrates a conventional personal computer, including a central processing unit 3050 (“CPU”), a system memory 3005, including a random access memory 3010 (“RAM”) and a read-only memory (“ROM”) 3015, and a system bus 3035 that couples the system memory 3005 to the CPU 3050. A basic input / output system containing the basic routines that help to transfer information between elements within the computer, such as during startup, is stored in the ROM 3015. The computer 3000 further includes a storage device 3020 for storing an operating system 3025, application / program 3030, and data.

[0089] The storage device 3020 is connected to the CPU 3050 through a storage controller (not shown) connected to the bus 3035. The storage device 3020 and its associated computer-readable media provide non-volatile storage for the computer 3000. Although the description of computer-readable media contained herein refers to a storage device, such as a hard disk or CD-ROM drive, it should be appreciated by those skilled in the art that computer-readable media can be any available media that can be accessed by the computer 3000.

[0090] By way of example, and not to be limiting, computer-readable media may comprise computer storage media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer.

[0091] According to various embodiments of the invention, the computer 3000 may operate in a networked environment using logical connections to remote computers through a network 3040, such as TCP / IP network such as the Internet or an intranet. The computer 3000 may connect to the network 3040 through a network interface unit 3045 connected to the bus 3035. It should be appreciated that the network interface unit 3045 may also be utilized to connect to other types of networks and remote computer systems.

[0092] The computer 3000 may also include an input / output controller 3055 for receiving and processing input from a number of input / output devices 3060, including a keyboard, a mouse, a touchscreen, a camera, a microphone, a controller, a joystick, or other type of input device. Similarly, the input / output controller 3055 may provide output to a display screen, a printer, a speaker, or other type of output device. The computer 3000 can connect to the input / output device 3060 via a wired connection including, but not limited to, fiber optic, Ethernet, or copper wire or wireless means including, but not limited to, Wi-Fi, Bluetooth, Near-Field Communication (NFC), infrared, or other suitable wired or wireless connections.

[0093] As mentioned briefly above, a number of program modules and data files may be stored in the storage device 3020 and / or RAM 3010 of the computer 3000, including an operating system 3025 suitable for controlling the operation of a networked computer. The storage device 3020 and RAM 3010 may also store one or more applications / programs 3030. In particular, the storage device 3020 and RAM 3010 may store an application / program 3030 for providing a variety of functionalities to a user. For instance, the application / program 3030 may comprise many types of programs such as a word processing application, a spreadsheet application, a desktop publishing application, a database application, a gaming application, internet browsing application, electronic mail application, messaging application, and the like. According to an embodiment of the present invention, the application / program 3030 comprises a multiple functionality software application for providing word processing functionality, slide presentation functionality, spreadsheet functionality, database functionality and the like. In some embodiments, computer 3000 operates a software that produces a user interface (UI) or graphical user interface (GUI), incorporating and / or visualizing any disclosed methods, steps and results.

[0094] The computer 3000 in some embodiments can include a variety of sensors 3065 for monitoring the environment surrounding and the environment internal to the computer 3000. These sensors 3065 can include a Global Positioning System (GPS) sensor, a photosensitive sensor, a gyroscope, a magnetometer, thermometer, a proximity sensor, an accelerometer, a microphone, biometric sensor, barometer, humidity sensor, radiation sensor, or any other suitable sensor.

[0095] Aspects of the invention relate to machine learning executed on a computing device, wherein the computing device may be computer 3000. In some embodiments, the disclosed system and method utilize machine learning algorithms and models, including one or more neural networks, that may operate on at least one computing device (e.g., computer 3000). The disclosed system may employ various types of neural networks known in the art, including but not limited to feedforward neural networks (FNNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), transformer networks, autoencoders, generative adversarial networks (GANs), Radial Basis Function Networks (RBFNs), extreme learning machines (ELMs), quantum neural networks (QNNs), and deep neural networks (DNNs).

[0096] Machine learning is a branch of artificial intelligence (Al) that enables systems to learn and improve from experience without being explicitly programmed. Machine learning models analyze data sets to identify patterns and correlations, and then use those patterns to make predictions or decisions. Machine learning models can generally be categorized into three primary types: supervised learning, unsupervised learning, and semi-supervised learning.

[0097] Supervised learning involves training a model using labeled datasets to classify data or predict outcomes accurately. As input data is fed into the model, the model adjusts its internal parameters (e.g., weights) to minimize prediction errors. Common methods used in supervised learning include neural networks, naive Bayes classifiers, linear regression, logistic regression, random forests, and support vector machines (SVMs).

[0098] Classification is a common task in supervised learning, where data inputs are categorized into distinct classes. Classification models may include binary classifiers (e.g., spam vs. non-spam) and multi-class classifiers (e.g., identifying different species of animals). A decision tree is a widely used classification method that applies a sequence of "if-then" conditions to narrow down possible outcomes.

[0099] Regression is another form of supervised learning where the output is a continuous variable rather than a discrete category. Linear regression predicts a continuous value based on a linear relationship between inputs and outputs, while logistic regression predicts categorical outcomes based on defined inputs.

[0100] Unsupervised learning involves analyzing unlabeled datasets to identify hidden patterns or groupings without human intervention. Principal component analysis (PCA) and singular value decomposition (SVD) are common techniques used to reduce data dimensionality and reveal underlying structures.

[0101] Clustering is a key unsupervised learning technique where data points are grouped based on shared features or proximity. K-means clustering is a widely used method where the number of clusters is defined by a variable "k," and the algorithm iteratively adjusts cluster centroids to minimize variance within each cluster. Other clustering methods include hierarchical clustering and probabilistic clustering.

[0102] Semi-supervised learning combines elements of both supervised and unsupervised learning. A model is initially trained using a smaller labeled dataset, which then guides the classification and feature extraction from a larger unlabeled dataset. Semi-supervised learning is particularly useful when acquiring large amounts of labeled data is costly or impractical.

[0103] Deep learning is a subfield of machine learning that uses neural networks with multiple hidden layers to process and analyze complex data. Neural networks mimic the structure and function of the human brain, comprising layers of interconnected nodes (neurons). Each neuron receives input data, applies a transformation based on assigned weights, and passes the result to the next layer.

[0104] A typical neural network consists of: input layer - receives raw data inputs; hidden layer(s) - applies mathematical transformations using weighted connections; and output layer - generates the final prediction or classification.

[0105] Convolutional neural networks (CNNs) are a type of neural network particularly well-suited for processing image and spatial data. CNNs use convolutional layers to extract spatial features from input data, pooling layers to reduce dimensionality, and fully connected layers to generate output predictions.

[0106] Deep neural networks (DNNs) are composed of multiple hidden layers and are capable of learning complex patterns in large datasets. Recurrent neural networks (RNNs) are a type of deep learning network designed for sequential data, such as time series or natural language, where previous inputs influence future outputs. Long shortterm memory (LSTM) networks are a specialized form of RNN that mitigates issues with long-term dependencies.

[0107] In some embodiments, the disclosed system may include an Al model trained using reinforcement learning, where an agent learns to make decisions through trial and error by interacting with an environment and receiving feedback in the form of rewards or penalties.

[0108] Devices of the Invention

[0109] The exfoliated 2D nanosheets provided herein may be found in any form conducive to incorporation of the exfoliated 2D nanosheets into any suitable device, such as a layer, thin film or a coating comprising the 2D nanosheets of the invention. Exemplary devices which may include the exfoliated 2D nanosheets of the present invention may include, but are not limited to, semiconductor devices, fillers and thermal interface materials (TIMs).

[0110] In some embodiments, the exfoliated 2D nanosheets can be used in semiconductor device packaging. In some embodiments, the present invention provides methods for producing ultra-thin two-dimensional flakes as functional centers for nextgeneration electronics, valleytronics, spintronics, catalysts, and multi-functional coatings. The versatility and adaptability of the present invention make it a valuable contribution to advancing diverse technological fields.

[0111] EMBODIMENTS

[0112] 1. A method of producing an exfoliated two-dimensional (2D) material, wherein the method comprises: providing a mixture comprising a 2D material and a polymer additive; and processing the mixture in a ball-mill apparatus, thereby producing an exfoliated 2D material.

[0113] 2. The method of embodiment 1, wherein the 2D material is a van der Waals layered material. 3. The method of embodiments 1 or 2, wherein the 2D material is chemically inert.

[0114] 4. The method of any one of embodiments 1-3, wherein the 2D material is selected from the group consisting of nitrides, graphene, transition metal dichalcogenides, layered metal oxides, layered metal hydroxides, and combinations thereof.

[0115] 5. The method of any one of embodiments 1-4, wherein the 2D material is selected from the group consisting of hexagonal boron nitride (hBN), graphite, molybdenum disulfide (M0S2), tin selenide (SnSe), tungsten diselenide (WSe2), gallium selenide (Ga2Sea), lead iodide (Pbh), black phosphorus, and combinations thereof.

[0116] 6. The method of any one of embodiments 1-5, wherein the polymer additive comprises a polysaccharide.

[0117] 7. The method of any one of embodiments 1-6, wherein the polymer additive comprises a synthetic polymer.

[0118] 8. The method of any one of embodiments 1-7, wherein the polymer additive comprises a polymer selected from the group consisting of wax, starch, polyvinyl alcohol (PVA), polyvinyl chloride (PVC), polyvinylidene fluoride (PVDF), polytetrafluoroethylene (PTFE), polyacrylamide (PAM), polyacrylic acid (PAA), polyvinylpyrrolidone (PVP), polymethyl methacrylate (PMMA), polyethylene glycol (PEG), ethyl cellulose (EC), chitin, sodium carboxymethyl cellulose (CMC), agar, gelatin, gum arabic, and combinations thereof.

[0119] 9. The method of any one of embodiments 1-8, wherein the polymer additive comprises a polymer having a covalent organic framework.

[0120] 10. The method of any one of embodiments 1-9, wherein the polymer additive comprises com starch. 11. The method of any one of embodiments 1-10, wherein the mixture comprises the 2D material and the polymer additive at a weight proportion of 1 to at least 5.

[0121] 12. The method of any one of embodiments 1-11, wherein the step of processing the mixture in a ball-mill apparatus comprises ball-milling the mixture for at least 1 hour.

[0122] 13. The method of any one of embodiments 1-12, further comprising the step of selecting the polymer additive based on a desired characteristic of the exfoliated 2D material.

[0123] 14. The method of embodiment 13, wherein the desired characteristic of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size.

[0124] 15. The method of embodiment 13 or 14, wherein a machine learning model is configured to select the polymer additive.

[0125] 16. The method of embodiment 15, wherein characteristics of the exfoliated 2D material are used to retrain the machine learning model.

[0126] 17. The method of embodiment 13, further comprising the step of determining ballmilling parameters for producing the exfoliated 2D material based on the selected polymer additive.

[0127] 18. The method of embodiment 17, wherein the ball-milling parameters comprise at least one of milling time, milling speed, milling temperature, and grinding media size

[0128] 19. The method of embodiment 17 or 18, wherein a machine learning model is configured to determine the ball-milling parameters. 20. The method of embodiment 19, wherein the machine learning model incorporates data from real-time monitoring of ball-milling to adjust ball-milling conditions dynamically.

[0129] 21. An exfoliated 2D material produced using the method of any one of embodiments 1-20.

[0130] 22. The exfoliated 2D material of embodiment 21, wherein the exfoliated 2D material has an average aspect ratio of at least 1.

[0131] 23. An exfoliated two-dimensional (2D) material, comprising a 2D material selected from the group consisting of hBN, graphite, molybdenum disulfide (M0S2), tin selenide (SnSe), tungsten diselenide (WSe?), gallium selenide (Ga2Se.3), lead iodide (Pbh), black phosphorus, and combinations thereof, wherein the exfoliated 2D material has an average aspect ratio of at least 1.

[0132] 24. The exfoliated 2D material of embodiment 23, wherein the exfoliated 2D nanosheet has an average thickness of less than 100 nm.

[0133] 25. A semiconductor material comprising the exfoliated 2D material of any one of embodiments 21-24.

[0134] 26. A thermal interface material comprising the exfoliated 2D material of any one of embodiments 21-24.

[0135] 27. A system for producing an exfoliated 2D material comprising: a ball-milling apparatus; and a computing device operatively connected to the ball-milling apparatus comprising a processor and a non-transitory computer-readable medium with instructions stored thereon, which when executed by the processor perform the steps of: selecting a polymer additive based on a desired characteristic of an exfoliated 2D material; providing a mixture comprising a 2D material and the polymer additive; and processing the mixture in the ball-mill apparatus, thereby producing an exfoliated 2D material.

[0136] 28. The system of embodiment 27, wherein the desired characteristic of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size

[0137] 29. The system of embodiment 27 or 28, wherein a machine learning model is configured to select the polymer additive.

[0138] 30. The system of any one of embodiments 27-29, wherein the step of processing the mixture in the ball-mill apparatus further comprises adding a functional group to the exfoliated 2D material.

[0139] 31. The system of any one of embodiments 27-30, wherein the step of processing the mixture in the ball-mill apparatus further comprises introducing defects to the exfoliated 2D material.

[0140] EXPERIMENTAL EXAMPLES

[0141] The invention is further described in detail by reference to the following experimental examples. These examples are provided for purposes of illustration only, and are not intended to be limiting unless otherwise specified. Thus, the invention should in no way be construed as being limited to the following examples, but rather, should be construed to encompass any and all variations which become evident as a result of the teaching provided herein.

[0142] Without further description, it is believed that one of ordinary skill in the art can, using the preceding description and the following illustrative examples, make and utilize the present invention and practice the claimed methods. The following working examples therefore are not to be construed as limiting in any way the remainder of the disclosure.

[0143] Example 1 : Machine-learning guided scalable production of 2D nanosheets by polymer-assisted ball-mill exfoliation of van der Waals layered materials

[0144] This invention is a new process to prepare / fabricate / manufacture ultra-thin two-dimensional materials with tailored geometric parameters to meet the requirements of versatile applications. The process includes modeling the effect of assistive polymers in ball-mill with machine-learning and using the model to provide guidance and prediction on polymer-assisted ball-mill to produce exfoliated materials with desired geometric parameters. The process can be applied to prepare / fabricate / manufacture ultrathin flakes of all types of van der Waals layered materials.

[0145] In a representative process, the first section is to build the machinelearning model of polymer-assisted ballmill with experimental data. A series of polymers such as PTFE, PVDF, PVA and starch with different physical properties such as elastic modulus, hardness, adhesion energy, friction coefficient, surface energy and melting point that cover a wide range of values are used to ballmill with van der Waals layered materials such as graphite, hexagonal boron nitride and molybdenum disulfide. The geometric parameters including thickness, lateral size and aspect ratio of the ball-milled product are determined by AFM. The values of the physical properties and geometric parameters are used as training data to build machine-learning models that describe selected features and ranking of importance of physical properties on geometric parameters. The second section is to predict the geometric parameters of ultra-thin two- dimensional flakes from polymer properties or guide polymer design with targeted geometric parameters of ultra-thin two-dimensional flakes. The model can predict the geometric parameters of ultra-thin flakes made from ball-mill assisted by a polymer with all the featured physical parameters identified. The model can also provide the values of physical properties for an ideal polymer candidate to produce the desired ultra-thin flakes using a polymer-assisted ball-mill, as well as defects engineering to introduce catalytic properties. The precision of the model can be varied depending on the size and data of distribution of the training group, and the parameters of the model can be varied depending on the type of van der Waals material that is ball-milled as well as the specification of the ball-mill equipment.

[0146] The invention disclosed herein facilitates the production of ultra-thin two- dimensional flakes, catering to a diverse range of applications. These applications include serving as a solid phase in inks for inkjet printing or 3D printing in electronics, a solid phase in slurry / paste for painting and coating, a filler in composites, lubricants, and raw materials for research purposes. The innovation effectively addresses the challenge of translating knowledge pertaining to ultra-thin two-dimensional materials into practical technologies.

[0147] In particular, as the demands for hardware advancements continue to escalate, thermal management stands out as a critical factor in semiconductor device packaging. It plays a pivotal role in ensuring the performance, reliability, and longevity of semiconductor devices. Traditional thermal interface materials (TIM), such as silicone and alumina, exhibit insufficient thermal conductivity. Furthermore, with the emergence of technologies like 2.5D / 3D advanced packaging, there is a growing need for innovative solutions. This invention expedites the integration of 2D materials as next-generation TIMs by offering a universal, low-cost, scalable, reproducible, high yield, and controllable process for producing ultra-thin two-dimensional flakes with enhanced and customizable properties.

[0148] Moreover, the invention extends its applicability to producing ultra-thin two-dimensional flakes as functional centers for next-generation electronics, valleytronics, spintronics, catalysts, and multifunctional coatings. The versatility and adaptability of the disclosed process make it a valuable contribution to advancing diverse technological fields.

[0149] Example 2: Scalable Mechanical Exfoliation of Two-Dimensional Nanosheets by Polymer- Assisted Dry Ball-mill of Layered Materials and Insights from Machine Learning

[0150] To fully capitalize on the unique properties of 2D materials, cost-effective techniques for producing high-quality 2D flakes at scale are crucial. The present example demonstrates that dry ball-milling, a commonly used powder-processing technique, can be effectively and efficiently upgraded into an automated exfoliation technique. It is done by adding polymer as adhesives into a ball mill to mimic the well-known tape exfoliation process, which is known to produce 2D flakes with the highest quality but is limited by its extremely low efficiency on large-scale production. Seventeen types of commonly seen polymers, including both artificial and natural ones, have been examined as additives to dry ball-mill hexagonal boron nitride. A parallel comparison between different additives identifies low-cost natural polymers such as starch as promising dry ball-mill additives to produce ultrathin flakes with the largest aspect ratio. The mechanical, thermal, and surface properties of the polymers are proposed as key features that simultaneously determine the exfoliation efficiency, and their ranking of importance in the mechanical exfoliation process is revealed using a machine learning model. Finally, the potential of the polymer-assisted ball-mill exfoliation method as a universal way to produce ultra-thin 2D nanosheets is also demonstrated (Zhang et al., 2025, Materials Today Nano, 30, 100604).

[0151] The limitations of tape exfoliation can be fully addressed with the dry ballmill technique presented herein. The dry ball -mill method is a well-established process that has been widely used in the industry for powder processing. The advantage of the dry ball-mill method is reflected in its controllability towards the size of the milled powder by adjusting the ball parameters and mill conditions (Bond, 1958, Mining Eng., 10, 592; Austin et al., 1973, Industrial & Engineering Chemistry Process Design and Development, 12, 121). High-frequency ball collision (impact) is the main interaction between mill balls and the material to realize size reduction, accompanied by some inevitable frictional interactions (Monov et al., 2013, Grinding in Ball Mills: Modeling and Process Control, Cybernetics and Information Technologies, 12, 51). The frictional interaction has been proposed to be the main contributor to the exfoliation process in previous reports, showing that the dry ball-mill process with small molecule additives can exfoliate hBN and produce ultra-thin flakes (Li et al., 2011, J. Mater. Chem., 21, 11872; Lei et al., 2015, Nat. Commun., 6; Lee et al., 2015, Nano Lett., 15, 1238; Ding et al., 2018, 2D Mater., 5, 45015). The collision between balls and the material is closer to a point contact scenario, where the concentrated stress at the contact point breaks the material into smaller particles. In this sense, the ‘collide-rebound’ cycle, despite its importance during ball collision, is nowhere like the ‘press-tear’ cycle during tape exfoliation. However, if by some means the effective contact area of ball collision could be significantly increased, the dry ball-mill can become a controllable, automated, high- frequency and large-scale tape exfoliation process that is able to produce high-quality ultra-thin hBN flakes at scale. This example demonstrates that such modifications of the conventional dry ball-mill process can be realized by simply adding polymers as co-mill medium to the plain dry ball-mill process. The polymer serves as the deformable adhesive medium to increase the collision contact area and facilitate the tape-exfoliationlike behaviors in the modified dry ball-mill process.

[0152] Results and Discussion

[0153] The proposed physical model and experimental design.

[0154] The conventional tape exfoliation method can be summarized in several steps (Fig. 1). Stepwise, the adhesive on the tape binds with one side of a 2D flake (Fig. 1A). A second tape forms good contact with the other side of the 2D flake by applying pressure (Fig. IB, Fig. 1C). Due to the stronger binding forces between the 2D flake and the tape adhesive compared with the Van der Waals interactions between layers of the 2D flake, tearing apart the two tapes will leave a thinner 2D flake on each tape (Fig. ID). Note that in practical operation, the tape exfoliation process will simultaneously break hBN flakes into fractured pieces with smaller lateral sizes.

[0155] Inspired by the tape exfoliation process, a physical model is proposed for the polymer-assisted dry ball-mill process (Fig. IE through Fig. 1J). Specifically, polymer additives will deform and attach to the mill balls as the balls collide with each other (Fig. IE - Fig. 1G). The deformed and attached polymer works in the same way as the adhesive in tape exfoliation, binding 2D flakes and tearing them into thinner (and potentially smaller) pieces during the ‘collide - rebound’ cycles of the dry ball-mill process (Fig. 1H - Fig. 1 J). Mill ball collision is the dominant physical process during dry ball-mill. Therefore, the transformation of the conventional ball collision into a mechanical exfoliation cycle, to the largest extent, expands the dry ball-mill's ability to exfoliate the layered material. Several properties of polymer are taken into account in this model, including adhesion energy and friction, which describe how ‘sticky’ the polymers are when a slab and the polymer are moving perpendicularly to and along their interface, respectively; hardness, which describes how easy for the polymers to deform under stress; polymer softening point and decomposition point, which describe how resistant the polymers are towards heat-induced phase transition and degradation; and finally water contact angle, which describes the surface energy and hydrophilicity of the polymers. These properties of polymer potentially correlate with the proposed working mechanism for the polymer-assisted dry ball-mill process, which includes deformation of the polymer due to mechanical motion, softening of the polymer due to the heat generated from dissipated mechanical energy, degree of expansion of polymer on mill balls and hBN, as well as binding strength between the polymer and the layered material such as hBN. Although all these factors can contribute to the exfoliation of hBN, however, their ranking of importance is unknown at this moment.

[0156] To verify the proposed physical model and assess the relative importance of different polymer properties on the polymer-assisted dry ball-mill process, seventeen types of commonly seen polymers are tested as assistive polymers during dry ball-mill of hBN. Those polymers cover a wide range of mechanical, thermal, and surface properties such as adhesion, hardness, elasticity, and hydrophobicity. For instance, among the polymers are those known to be good adhesives, such as polyvinyl alcohol (PVA) and sodium carboxymethyl cellulose (CMC), as well as non-sticky material such as polytetrafluoroethylene (PTFE). Apart from synthetic polymers, there are also several types of natural polymers, such as corn starch, chitin, and gum Arabic. It is expected that the diversity in the physical properties of those polymers correlates with different exfoliation effects so we can understand the process better and further improve the physical model of polymer-assisted dry ball-mill exfoliation of layered materials.

[0157] Morphology of hBN flakes produced by polymer-assisted dry ballmill.

[0158] Many previous reports on chemical and mechanical exfoliation of layered 2D materials, including hBN, take advantage of high-speed centrifugation to remove large particles in their exfoliated materials. This is the so-called fraction of the product and makes it easier to find ultra-thin layers by minimizing the interruption from thicker layers (Kang et al., 2014, Nat. Commun., 5; Green et al., 2010, J. Phys. Chem. Lett., 1, 544). However, the fraction process at the same time will make it impossible to record the complete product information, including the thickness and lateral size distribution of the exfoliated flakes. In order to obtain full product profiles of the exfoliated hBN produced by the polymer-assisted dry ball mill, throughout our sample preparation, no fraction method was used. Freshly stirred suspensions of exfoliated hBN were used to spread hBN nanoflakes onto silicon wafers for subsequent AFM characterizations.

[0159] AFM scans on hBN nanoflake samples made from the dry ball-mill process assisted by seventeen polymers were carried out. To derive accurate area and thickness information of the hBN flakes from the AFM height images, image processing algorithms were used to identify individual hBN flakes first (segmentation), followed by adding the original AFM data into the segmentations to obtain their equivalent lateral size and average thickness, as well as the ratio between them which is defined as the aspect ratio. The exfoliation effect of hBN varies depending on the type of polymer, and some of the polymers exhibit highly promising exfoliation results. For instance, with the assistance of com starch, the thickness of the majority of the dry ball-milled hBN in one typical AFM height image ranges between 10 to 20 nm, while the low and high bounds reach 6 and 65 nm (Fig. 2A). In comparison, the dry ball-mill without any polymer additive produces hBN flakes with a much wider thickness range down to 10 nm thin and up to 200 nm thick (Fig. 2B). At the same time, for the nanoflakes with similar thickness, those produced from the starch-assisted dry ball-mill process have significantly larger lateral size compared with those from plain the dry ball-mill process, leading to a huge increase in the aspect ratio of the hBN flakes by adding starch to the dry ball-mill. With the complete information on the thickness and lateral size of hBN nanoflakes, a more comprehensive comparison between the dry ball-mill exfoliation process with and without starch can be made. For instance, the histogram for flake thickness (Fig. 2C) shows that the peak position of the histogram, which means the most frequently appeared thickness, has decreased from around 25 nm to 7 nm with starch in dry ball-mill. The width of the histogram, which means the distribution of the thickness, has significantly narrowed after adding starch in the dry ball-mill. It is worth noting that a wide distribution of flake size from plain dry ball mill matches best with the scenario of material fracture, where intense breaking stresses resulting from impact or ball collision are the dominant factor during the interaction between balls and the material to be milled. The histogram of the flake aspect ratio further reveals that starch helps improve the aspect ratio of the product, which is considered a highly important parameter when ultrathin 2D flakes are desired. The difference in their histogram clearly indicates that starch as an additive can drastically change the way dry ball-mill of hBN works and makes the process closer to the conventional tape exfoliation process.

[0160] Finally, the collection of information on the average lateral size, thickness, and average aspect ratio of hBN nanoflakes produced from the dry ball-mill process assisted by seventeen polymers (Fig. 2E) . Most polymers can reduce hBN nanoflakes with thicknesses down to sub-hundred nanometers, and the lateral size down to less than 200 nm (Fig. 3). Trends of the lateral size and the thickness of hBN nanoflakes produced by using different polymer additives follow a similar pattern, while such a trend for the aspect ratio displays an opposite pattern (Fig. 2E). Considering low thickness and high aspect ratio as the most critical parameters for hBN nanoflakes for many applications such as hBN ink for printing and coating, it was observed that among the polymers that have been investigated, PVDF, corn starch and gelatin make the highest quality hBN - they yield lowest ratio of thick hBN flakes (> 50 nm), and highest ratio of ultra-thin hBN flakes (< 20 nm) . It is believed that corn starch and gelatin as additives for the dry ballmill process are especially promising candidates for large-scale production of ultra-thin hBN nanoflakes with the additional benefits of low-cost, being environmentally friendly, and bio-degradable.

[0161] Machine-learning analysis of the polymer-assisted dry ball-mill process.

[0162] To better understand and, more importantly, to control the polymer- assisted dry ball-mill process better, machine-learning tools (Erps et al., 2021, Sci. Adv., 7, eabf7435; Abueidda et al., 2019, Compos. Struct., 227, 111264; Hannan et al., 2020, Sci. Rep., 10; Wang et al., 2021, NPJ 2D Mater. Appl., 5; Zou et al., 2021, Energy Environ. Sci., 14, 3965; Tao et al., 2021 , NPJ Comput. Mater., 7) are employed for more detailed sample analyses. To understand the origin of the differences in hBN nanoflakes produced with the addition of different polymers, the polymers’ mechanical, thermal, and interface properties are collected (see method section) and used as the features (X) to determine the morphology parameters (Y) using a machine-learning approach (Table 1). Measured and predicted morphology parameters of TpPa-1 are depicted in Table 2.

[0163] Table 1. Summary of measured physical properties and morphology parameters of hBN nanoflake samples produced by dry ball-mill with seventeen polymer additives, plus TpPa-1 and without any polymer additive.

[0164] PVDF 0.72 0.83 1.02 3.65 186.13 157.09 394.23 91.40 1.31E+04 35.29 0.88

[0165] PVA 1.34 1.13 1.13 3.60 127.98 194.49 237.96 67.00 2.71E+04 50.97 0.57

[0166] PEG 0.74 0.91 0.98 3.40 186.00 60.92 352.01 16.90 6.00E+04 77.39 0.40

[0167] PVP 0.87 1.07 1.64 5.86 326.63 162.29 375.81 18.20 3.63E+04 70.11 0.50

[0168] PAM 0.46 0.69 0.39 10.91 136.88 200.66 353.99 180.00 4.13E+04 161.64 0.18

[0169] PTFE 1.23 0.86 0.61 1.49 54.73 250.25 474.12 126.65 2.57E+04 60.57 0.61

[0170] Wax 2.04 1.37 0.29 3.83 18.16 51.21 177.86 103.40 1.08E+05 90.84 0.30

[0171] PVC 0.32 0.52 0.71 4.60 235.04 162.85 249.52 97.75 2.00E+04 78.77 0.40

[0172] PAA 0.54 0.74 0.71 23.48 623.45 201.10 263.40 99.90 1.11E+05 103.13 0.25

[0173] PMMA 0.85 0.94 0.59 5.50 358.25 158.94 313.83 106.10 3.98E+04 77.37 0.38

[0174] CMC 5.01 2.50 1.92 0.33 24.96 244.20 250.82 29.85 5.31E+04 80.28 0.39

[0175] EC300 0.57 0.77 1.90 3.22 178.15 243.30 289.97 96.65 2.16E+04 61.43 0.52

[0176] Gum 1.23 1.07 1.15 6.71 245.78 159.78 234.43 74.40 4.02E+04 71.04 0.40

[0177] Starch 4.26 2.16 1.57 4.81 262.78 266.10 275.61 54.45 9.39E+03 26.67 1.22

[0178] Gelatin 1.18 1.10 0.81 5.86 279.21 219.08 248.46 64.55 3.25E+04 34.90 0.76

[0179] Agar 1.05 1.05 0.90 9.64 418.44 220.61 228.58 49.50 3.32E+04 53.53 0.52

[0180] Chitin 1.54 1.24 1.24 5.76 405.11 234.01 280.58 14.65 1.24E+05 113.68 0.25

[0181] Plain 1.63E+05 160.22 0.16

[0182] TpPa-1 1.61 1.21 0.49 0.57 43.66 321.12 468.46 6.10 7.41E+04 89.60 0.39 Table 2. Measured and predicted morphology parameters of TpPa-1.

[0183] Lateral Size Thickness Aspect ratio

[0184] Measured 0.56501 0.46623 0.19713

[0185] Predicted (Ts=321.121) -0.0167 -0.0164 0.66811

[0186] Predicted (Ts=25) 0.56329 0.26602 0.21076

[0187] Ts: softening point

[0188] To get started, the independence of the features, i.e., mechanical properties including the hardness and the reduced elastic modulus, thermal properties including the softening point and decomposition point, and interface properties including the adhesion energy, the detachment force, the friction, and the contact angle are checked in a correlation matrix (Fig. 4). The adhesion energy and the detachment force, which are simultaneously obtained from AFM force-distance spectroscopy, show the highest correlation index (0.98). Hardness and reduced elastic modulus, which are simultaneously obtained from nanoindentation measurements, show the second-highest correlation index (0.77). Therefore, the detachment force and the reduced elastic modulus are excluded as adhesion energy / detachment force and hardness / reduced elastic modulus are the only two pairs of features that have a significantly high correlation (> 0.7). The rest of the features all show moderate or low correlation. Therefore, we consider them all contribute independently to the morphology parameters.

[0189] However, it is quite possible that not necessarily all mechanical, thermal, and interface properties have a significant impact on the morphology of the dry ball- milled hBN nanoflakes. In other words, it makes sense to select those features that are most relevant in a rational physical model. In order to determine which features are most relevant to the morphology parameters, recursive feature addition (RFA), recursive feature elimination (RFE), and exhaustive search methods are used to select corresponding feature sets for each morphology parameter. For each morphology parameter, the feature selection is done by finding the sets of features with the smallest mean absolute error (MAE). Both RFA and RFE methods provide the identical selection for the most relevant features as exhaustive search method does. Once the most relevant features are determined, their ranking of importance in affecting the morphology parameters is determined by linear regression analysis (Fig. 5). The bar plots of the selected features with different scale and direction reflect how they contribute to the objective morphology parameters. For instance, when getting larger lateral size flakes is the primary objective, hardness, adhesion energy, softening point and friction are most relevant features following a descending order. Meanwhile, hardness and adhesion energy show positive correlation on the lateral size while friction and softening point show negative correlation, meaning higher hardness and adhesion energy, and lower friction and softening point help increase the lateral size of hBN nanoflakes.

[0190] Refining the dry ball-mill physical model.

[0191] The trained machine-learning model provides useful feedback to refine the original model proposed for polymer-assisted dry ball-mill process. Among all physical properties that were originally included as contributing factors to the dry ball-mill exfoliation of hBN, the machine-learned model suggests that for each morphology parameter only selected properties are considered essential. For example, adhesion energy to a large extent affects lateral size, but not as much affects thickness, and can be neglected in aspect ratio of hBN nanoflakes. Contact angle plays important roles in affecting both thickness and aspect ratio of hBN nanoflakes. Hardness and softening point are the only properties that have a significant impact on all three morphology parameters. Based on our assumption for the physical model of polymer-assisted dry ballmill process, decomposition of polymers is not likely to happen during the process. Therefore, decomposition point of polymers is expected to be excluded in the trained model. In the models with feature selection (RFA, RFE, and exhaustive search), decomposition only appears in the thickness model, and its ranking is at a minimum level (close to zero in terms of bar height). Without feature selection, there is a high chance that inappropriate models are trained, e.g., a model where decomposition point is determined as a high-ranking feature (Fig. 6).

[0192] The fact that physical properties of polymers such as hardness and softening point, which reflect how easily polymer deforms due to mechanical load and heat, respectively, are significant to all morphology parameters of produced hBN nanoflakes, implies that mechanical gripping dominants the dry ball-mill exfoliation process instead of adhesion. Meanwhile, polymer with low water contact angle produces hBN nanoflakes with low thickness and high aspect ratio. This agrees with the mechanical gripping model because such polymers due to the low surface energy, can spread well on hBN flakes when deformed (Fig. 7, Fig. 8), and facilitate the gripping effect by increasing the hBN / polymer contact area. Note that the present model indicates that ‘sticky’ polymers does not necessarily lead to efficient exfoliation by making high aspect ratio nanoflakes, which is different from the observation that ‘glue’ will facilitate hBN exfoliation in a hand mill process (grinding) (Yang et al., 2021, Materials Today, 51, 145) and the conventional thinking that the same principle applies to other milling methods. Additionally, unlike dry ball-mill exfoliation with urea, sodium hydroxide, and other small molecule additives where friction is believed to be the primary physical process that drives the exfoliation (Yao et al., 2012, J. Mater. Chem., 22, 13494), in the present model friction has limited impact on exfoliation, implying that mill ball collision is the primary physical process in polymer-assisted dry ball-mill. This, in turn, supports our initial motivation to utilize ball collision in a dry ball-mill to the largest extent for hBN exfoliation.

[0193] Polymer-assisted dry ball-mill exfoliation of 2D materials beyond hBN.

[0194] The polymer-assisted dry ball mill, which is identified as an automated mechanical exfoliation process from the above discussion, can be adapted to produce other 2D materials beyond hBN. Several types of layered materials in their bulk form, including graphite, M0S2, SnSe, and Pbh are used as starting materials in such process. Ga2Se3 is also included here, as an example of nonlayered materials that were reported to exhibit 2D form (Puthirath Balan et al., 2018, Nat. Nanotechnol., 13, 602; Zhou et al., 2019, ACS Nano, 13, 6297; Xue et al., 2022, Small, 18) All materials here have poor stability towards flame-torching removal of polymer. As a result, PVDF is selected as the assisting polymer for graphite, M0S2, SnSe and Ga2Se3 so that dimethylformamide (DMF) can be used to remove PVDF for the clean AFM sample preparation. PVP is selected as the assisting polymer for Pbh, as Pbh dissolves in DMF but not in cold water. SEM images reveal that both the lateral size and thickness of the 2D powders are significantly reduced after ball-mill (Fig. 9). All materials dimensions are effectively reduced to monolayer or few layer with optimized aspect ratios after ball-mill based on their Raman spectra (Fig. 10). (Zhou et al., 2019, ACS Nano, 13, 6297; Xue et al., 2022, Small, 18; Island et al., 2015, Science Letters Journal, 4, 1; Qiu et al., 2019, RSC Adv., 9, 3232; Kaushik et al., 2018, Nanomaterials, 8, 587; Afrin et al., 2018, IEEE 13thNanotechnology Materials and Devices Conference, 1; Liu et al., 2017, Nanoscale Res. Lett., 12; Brenner et al., 2016, Chemistry of Materials, 28, 6501; Zheng et al., 2019, Advanced Sciences, 6; Wangyang et al., 2016, Mater. Lett., 168, 68; Yamada et al., 1992, Jpn. J. Appl. Phys., 31, L186). Quantitative data obtained from AFM analysis shows that the average thicknesses of the various type of nanosheets produced by polymer-assisted ball-mill are generally below 22 nm. Meanwhile, the average aspect ratios are above 1 (Fig. 9G). SnSe has a similar puckered structure as black phosphorous but a much stronger interlayer coupling strength (Li et al., 2019, J. Mater. Chem. A Mater., 7, 23958). The latter makes SnSe a more challenging layered material to exfoliate (Shi et al., 2018, Semicond. Sci. Technol., 33; Hu et al., 2016, Physical Chemistry Chemical Physics, 18, 20256), yet polymer-assisted ball-mill is able to thin down the material efficiently and still keep it at large aspect ratio. Pbh, which is a relatively unstable layered material, is also successfully exfoliated by polymer-assisted ball-mill and can be further chemically converted into lead-based perovskite materials. Our results demonstrate that polymer-assisted ball-mill is a universal method to exfoliate layered materials and produce high-quality 2D nanosheets.

[0195] In summary, the present example demonstrates the transformation of ball collision in a conventional ball-mill process into the scaled-up ‘tape’ exfoliation of hBN by adding polymers into the dry ball mill in this work. Among the polymers tested, natural com starch has been identified as a low-cost and highly efficient additive. Dry ball-mill of hBN with starch produces ultra-thin hBN flakes with average thickness below 30 nm and the highest aspect ratio among all polymers. Machine-learning was subsequently applied to build a more accurate physical model for the polymer-assisted dry ball-mill process. Physical properties of seventeen polymers and morphology parameters of correspondingly exfoliated hBN nanoflakes were used as features and objectives to refine a physical model in a feature selection approach. The machine- learned model indicates that deformation-enabled mechanical gripping of hBN from polymer additive is critical in facilitating the exfoliation of hBN with low thickness and high aspect ratio. Finally, various types of layered bulk material, including graphite, M0S2, Ga2Se3, SnSe, and Pbh, were successfully exfoliated into ultra-thin 2D nanoflakes via the polymer-assisted dry ball-mill process.

[0196] Materials and methods:

[0197] Materials. Hexagonal boron nitride powder (Alfa Aesar, 11078), M0S2 (Alfa Aesar,41827), graphite (Alfa Aesar, 46304), , gum Arabic from acacia tree (Millipore Sigma, G9752), ethyl cellulose (Millipore Sigma, 200654), gelatin from bovine skin (Millipore Sigma, G9391), agar (Millipore Sigma, A1296), starch from com (Millipore Sigma, S4180), polyethylene glycol 10000 (Millipore Sigma 8.21881), paraffin wax (327204), polyvinyl chloride (Millipore Sigma, 189588), polytetrafluoroethylene (Millipore Sigma, 182478), polyacrylamide (Millipore Sigma, 92560), polymethyl methacrylate (Alfa Aesar, 43982), chitin (Alfa Aesar, J61206), sodium carboxymethyl cellulose (Millipore Sigma, 419303), polyvinyl alcohol (Millipore Sigma, 363170), polyacrylic acid (Millipore Sigma, 181285), polyvinylpyrrolidone (Millipore Sigma, PVP40), polyacrylonitrile (Millipore Sigma, 181315) and poly vinylidene fluoride (Millipore Sigma, 182702) were used as received without further treatment. Pbb single crystals were prepared by cooling saturated hot Pbh (Millipore Sigma, 211168) aqueous solution and separating the precipitation by centrifuge and vacuum drying. SnSe (Alfa Aesar, 18781), Ga2Se.3 (Alfa Aesar, 45572) and Pbh single crystals were first ball-milled into micro-sized fine powders before further exfoliation by polymer-assisted ball-mill.

[0198] Dry ball-mill. The polymer-assisted dry ball-mill was done using a vertical lab planetary dry ball-mill (Hanshen Instrument, DECO-PBM-V-0.4L). 4.55 g zirconia beads with a diameter of 3 mm and 8.4 g zirconia beads (MSE Supplies LLC, US) with a diameter of 1mm were used for all ball-mill processes. In a typical mill, 100 mg of commercially available hBN powder and 500 mg of polymer powder were mixed and placed together with alumina balls in an agate mill jar. The hBN / polymer mixture was dry ball-milled at 800 rpm for 2 hours. After the dry ball-mill, the sample and balls were separated with a mesh No. 325 siege. The polymer in the hBN / polymer mixture was then sonicated and fully dispersed in solvents where the polymer was soluble (water if the polymer is not soluble otherwise). The dispersion was immediately drop-casted onto a bare silicon wafer before it started to settle down. The silicon wafer was dried naturally and heated with a butane torch to remove the polymer residue.

[0199] AFM morphology. The morphology of the hBN flakes was examined using PARK NX20 AFM tapping mode. AFM tip (NANO WORLD, NCHR-10) was used for all tapping mode scans. AFM tip (APPNANO, HYDRA6R-200NG-10) was used for all the contact scans. Multiple images with pixel resolution of 256 x 256 and scan size of 5 x 5 mm2were collected for each sample.

[0200] Dimensional parameters. Statistic information including the area and average thickness of the dry ball-mill samples were extracted from AFM morphology images by standard image processing methods. OpenCV and scikit-image were used to apply grayscale conversion, contrast enhancement, and thresholding operation to the AFM images. Individual nanoflakes were identified using OpenCV contour tools. The area of an individual flake was determined by counting the number of pixels inside the flake contour and multiply it by the actual area of a pixel. The equivalent lateral size of a flake was calculated from the square root of the flake area. The average thickness was determined by adding up the thickness of each pixel inside all flake contours and averaging it with the total number of pixels. The aspect ratio of an individual was calculated by dividing its area with its average thickness. The average aspect ratio was determined by adding up the value of area divided by thickness of each pixel inside all flake contours and averaging it with the total number of pixels.

[0201] Hardness and reduced elastic modulus (Er). The hardness of the polymers was measured using Hysitron TI 980 TriboIndenter. Before the test, polymer powders were casted into continuous films by a hot-press method. Specifically, a small amount of as-purchased polymer in the form of powder was spread on a silicon wafer. The wafer was heated on a hot plate to soften the polymer powder and a glass slide was used to press the powder into a continuous film. The softening point differs depending on the polymer selected. Load control with a peak force of 500 mN and 15 s of loading and unloading periods were applied during the nanoindentation test (Fig. 10). The hardness and Erwere obtained using the TriboIndenter software.

[0202] Friction. The friction of the polymer was measured using Park NX20 AFM under contact mode. AppNano AFM tip (HYDRA-6R-200N) was used for all AFM measurements. The friction was determined by the median value of the difference between the lateral voltage of trace and retrace scans, assuming the tortuosity of the tip induced by friction was at the same degree in trace and retrace scans. The lateral voltage values obtained were not further converted into the exact friction force, as they are proportional to the force values and eventually were normalized for the machine-learning model. Considering the fact that the polymer residue will make the tip dirtier after each scan on the polymer sample, a scan on a clean region of the silicon wafer was carried out to get rid of such residues each time before the scanning on polymer samples took place. The friction values of polymers were corrected by dividing corresponding reference values.

[0203] Detachment force and adhesion energy. The detachment force and adhesion energy were measured using Park NX 20 AFM under contact mode. After the scanned friction image was obtained, multiple points on the image were selected and force-distance (FD) curve measurements were carried out at those positions. The detachment force and adhesion energy were derived from the FD curves using XEI software. Like the friction value, the detachment force and adhesion energy of polymers were corrected using scans on bare silicon wafers as references.

[0204] Softening and decomposition point. The softening point and decomposition of polymers were derived from TGA-DSC measurements. Q600 SDT (TA Instruments) was used to conduct all the tests. During the TGA tests, the ramping rate was set to 2 °C per minute. The samples were heated up to 500 °C in argon atmosphere. TA Universal Analysis was used to analyze the data. The softening point is defined as the lower value of the glassy transition point and / or the melting point extracted from the DSC curve. The decomposition point is defined as the onset point on the TGA curve where the weight of the sample starts to decrease. Contact angle. The water contact angles of the polymers were measured using a surface tension meter CAM 101 (KSV Instruments Ltd., Finland). The polymers were hot pressed into films that were large enough to accommodate water droplets using glass slides as substrates. ImageJ with a contact angle analysis plugin was used to process the images and measure the contact angles.

[0205] Machine-learning. All codes were compiled under a Python environment. Pandas package was used to calculate the correlation matrix. Scikit-learn package was used to conduct the regression analysis.

[0206] TpPA-1 synthesis. A Pyrex tube was charged with 42 mg Triformylphloroglucinol (Tp), 32 mg p-Phenylenediamine (PDA), 2 mL of the mixture of mesitylene and 1-4 dioxane (v:v=l:l), 0.2 mL of 3 M aqueous acetic acid. This mixture was sonicated for 10 minutes and then flash frozen at 77 K and degassed by three freeze- pump-thaw cycles. The tube was sealed and then heated at 120 °C for 3 days. The resulting dark red precipitates were isolated by vacuum fdtration, washed with 1,4- dioxane and dry acetone, and then dried under vacuum at 120 °C.

[0207] Additional Experimental Data

[0208] Pristine hBN flakes were also analyzed through SEM and AFM in order to determine the original thickness of the flakes (Fig. 11).

[0209] Various types of layered bulk material, including graphite, M0S2, GazSe?, SnSe, and Pbh, were successfully exfoliated into ultra-thin 2D nanoflakes via the polymer-assisted dry ball-mill process. The resulting nanoflakes were analyzed using AFM (Fig. 12).

[0210] The disclosures of each and every patent, patent application, and publication cited herein are hereby incorporated herein by reference in their entirety. While this invention has been disclosed with reference to specific embodiments, it is apparent that other embodiments and variations of this invention may be devised by others skilled in the art without departing from the true spirit and scope of the invention. The appended claims are intended to be construed to include all such embodiments and equivalent variations.

Claims

CLAIMSWhat is claimed is:

1. A method of producing an exfoliated two-dimensional (2D) material, wherein the method comprises: providing a mixture comprising a 2D material and a polymer additive; and processing the mixture in a ball-mill apparatus, thereby producing an exfoliated 2D material.

2. The method of claim 1, wherein the 2D material is selected from the group consisting of nitrides, graphene, transition metal dichalcogenides, layered metal oxides, layered metal hydroxides, and combinations thereof.

3. The method of claim 1, wherein the 2D material is selected from the group consisting of hexagonal boron nitride (hBN), graphite, molybdenum disulfide (M0S2), tin selenide (SnSe), tungsten diselenide (WSe?), gallium selenide (Ga2Se3), lead iodide (Pbh), black phosphorus, and combinations thereof.

4. The method of claim 1, wherein the polymer additive comprises a polymer selected from the group consisting of wax, starch, polyvinyl alcohol (PVA), polyvinyl chloride (PVC), polyvinylidene fluoride (PVDF), polytetrafluoroethylene (PTFE), polyacrylamide (PAM), polyacrylic acid (PAA), polyvinylpyrrolidone (PVP), polymethyl methacrylate (PMMA), polyethylene glycol (PEG), ethyl cellulose (EC), chitin, sodium carboxymethyl cellulose (CMC), agar, gelatin, gum arabic, and combinations thereof.

5. The method of claim 1, wherein the polymer additive comprises a polymer having a covalent organic framework.

6. The method of claim 1, wherein the polymer additive comprises com starch.

7. The method of claim 1, wherein the mixture comprises the 2D material and the polymer additive at a weight proportion of 1 to at least 5.

8. The method of claim 1, wherein the step of processing the mixture in a ball-mill apparatus comprises ball-milling the mixture for at least 1 hour.

9. The method of any one of claims 1-8, further comprising the step of selecting the polymer additive based on a desired characteristic of the exfoliated 2D material.

10. The method of claim 9, wherein the desired characteristic of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size.

11. The method of claim 9, wherein a machine learning model is configured to select the polymer additive.

12. The method of claim 9, further comprising the step of determining ball-milling parameters for producing the exfoliated 2D material based on the selected polymer additive.

13. The method of claim 12, wherein the ball-milling parameters comprise at least one of milling time, milling speed, milling temperature, and combination of grinding media with different sizes.

14. The method of claim 12, wherein a machine learning model is configured to determine the ball-milling parameters.

15. An exfoliated 2D material produced using the method of claim 1.

16. The exfoliated 2D material of claim 15, wherein the exfoliated 2D material has an average aspect ratio of at least 1.

17. An exfoliated two-dimensional (2D) material, comprising a 2D material selected from the group consisting of hBN, graphite, molybdenum disulfide (M0S2), tin selenide (SnSe), tungsten diselenide (WSe?), gallium selenide (Ga2Se3), lead iodide (Pbh), black phosphorus, and combinations thereof, wherein the exfoliated 2D material has an average aspect ratio of at least 1.

18. A system for producing an exfoliated 2D material comprising: a ball-milling apparatus; and a computing device operatively connected to the ball-milling apparatus comprising a processor and a non-transitory computer-readable medium with instructions stored thereon, which when executed by the processor perform the steps of: selecting a polymer additive based on a desired characteristic of an exfoliated 2D material; providing a mixture comprising a 2D material and the polymer additive; and processing the mixture in the ball-mill apparatus, thereby producing an exfoliated 2D material.

19. The system of claim 18, wherein the desired characteristic of the exfoliated 2D material comprises at least one aspect ratio, thickness, and lateral size.

20. The system of claim 18, wherein a machine learning model is configured to select the polymer additive.

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