THEREOF

Technical Field

The present invention relates, in general terms, to 2D materials having hierarchical topography and methods of fabricating the 2D materials thereof. The present invention also relates to a method using the 2D material for authentication in anti-counterfeiting applications.

Background

Physical unclonable function (PUF), possessing unique physical manifestations with sufficient complexity, is one of the cornerstones of highly secure anti-counterfeiting technologies. PUF refers to the physical object with inherent, distinct, and fingerprint-like features, which is fundamentally secure. In principle, unique PUF patterns are generated in a stochastic and nondeterministic fashion and can provide huge encoding capacity (i.e., theoretical maximum number of distinct PUF patterns), making them nearly impossible to be repeated or reproduced. Conventional approaches to achieving PUF secure keys for anti- counterfeiting usually involve solution chemistry affording large parameter space and high randomness or construction of complex electronic systems with diverse disorders and inherent defects. Most of these approaches require additional taggants for readout purposes (e.g., stimulated luminescence, surface-enhanced Raman scattering) and/or delicate device fabrication (e.g., micro-transistors). In addition, a long-lasting challenge exists in current PUF systems, where the readout and authentication processes (e.g., spectrum verification, current profile measurement, minutiae extraction and comparison) are inevitably time- consuming, due to the necessity of conducting one-by-one search-and-compare algorithms within huge databases. Another challenge of current PUF tags is their limited environmental stability (e.g., light, heat, physical stress), restricting the long-term uses for anti- counterfeiting. In this regard, conventional PUF systems encounter several bottlenecks, such as complicated manufacturing, insufficient environmental stability, tedious readout, and authentication processes, all of which restrict their practical anti-counterfeiting applications.

There is a constant need to develop new technology in the field of anti-counterfeiting as pirates will, over time, work out means to overcome current technologies. In this regard, one of the goal in the field of anti-counterfeiting is to come up with alternative and new technologies as they present extra hurdles that pirates need to overcome and can thus combat counterfeit.

It would be desirable to overcome or ameliorate at least one of the above-described problems, or at least to provide a useful alternative.

Summary

The present invention provides a method of fabricating a two dimensional material (2DM) with a hierarchical topography, comprising: a) preparing a substrate in an expanded state; b) adhering the 2DM to the substrate in the expanded state; c) contracting the substrate from the expanded state to a first contracted state in order to form a first structure on the 2DM; d) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the first contracted state; and e) contracting the substrate from the first contracted state to a second contracted state in order to form a second structure below the first structure; wherein the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN) and montmorillonite (MMT) nanosheets.

Advantageously, sequential contraction steps allow for a sequential contraction of the 2DM, and different morphologies to form on the 2DM, and thus allows for a hierarchical topography. Further, by altering the inter-plane bonding of the 2DM and/or interfacial bonding between the 2DM and the substrate, the type and formation of the morphology can be controlled. This allows a random and unique but yet characterisable pattern to form, which is advantageous for use in authentication.

In some embodiments, the step of altering an inter-planar bond within the 2DM comprises altering the Young's modulus of the 2DM.

In some embodiments, the Young's modulus is altered by intercalating the 2DM with a cation.

In other embodiments, the intercalation of the 2DM with a cation comprises contacting the 2DM and substrate in a cation solution.

In other embodiments, the cation is selected from Al ³⁺ , Mg ²⁺ and Ca ²⁺ .

In some embodiments, the step of altering an interfacial bond between the 2DM and the substrate in the first contracted state comprises altering the interfacial adhesion between the 2DM and the substrate in the first contracted state.

In other embodiments, the interfacial adhesion is altered by condensing water molecules between the 2DM and the substrate.

In other embodiments, the condensation of water molecules between the 2DM and the substrate comprises storing the 2DM on the substrate under low temperature and subsequently subjecting the 2DM on the substrate to a relative humidity of at least 60%.

In other embodiments, the low temperature is from about -80 °C to about 4 °C.

In some embodiments, the contraction steps (step c and e) are independently selected from an isotropic contraction or an anisotropic contraction. In some embodiments, the substrate preparation step (step a) comprises treating the substrate with plasma.

In some embodiments, the substrate in the expanded state has a shape selected from sphere or tube.

In some embodiments, the substrate is an elastomeric substrate.

In some embodiments, the substrate is a latex balloon or a polystyrene film.

Advantageously, an elastomeric substrate having elastic properties allows both ID wrinkle and 2D crumple morphologies on 2DMs to be generated.

In some embodiments, the step of contacting the 2DM on the substrate (step b) comprises applying the 2DM as a dispersion onto the substrate and allowing the dispersion to dry.

In some embodiments, the method further comprises a step prior to the contracting step in order to form the first structure on the 2DM (step c)) of: altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the expanded state.

Advantageously, an additional altering step allows for a substantial increase in the number of unique patterns, and accordingly, allows for a larger number of PUFs.

In some embodiments, the method further comprises the steps after the contracting step from the first contracted state to a second contracted state (step e)) of: altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the second contracted state; and contracting the substrate from the second contracted state to a third contracted state in order to form a third structure on or below the first and second structures. In some embodiments, the method further comprises a step of delaminating the 2DM from the substrate.

The present invention also provides a two dimensional material (2DM) with a hierarchical topography, comprising a first structure superimposed on a second structure; wherein the first structure is of about 5 pm x 5 pm to about 20 pm x 20 pm; and wherein the second structure is of about 20 pm x 20 pm to about 100 pm x 100 pm; and wherein the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN) and montmorillonite (MMT) nanosheets.

In some embodiments, the first structure and second structure are independently selected from wrinkle, crumble and/or buckle.

In some embodiments, the first structure and second structure are independently anisotropically or isotropically disordered.

In some embodiments, the 2DM further comprises a third structure, wherein the first structure and second structure are superimposed on the third structure.

In some embodiments, the third structure is at least about 100 pm x 100 pm.

In some embodiments, the 2DM is stable at a temperature of about -50 °C to about 200 °C.

In some embodiments, the 2DM is stable at a humidity of about 0% to about 90%.

In some embodiments, the 2DM is stable to organic solvents and/or UV radiation.

The present invention also provides a physical unclonable function (PUF) comprising the 2DM as disclosed herein, for use in authenticating a product. The present invention also provides a product encoded with a 2DM as disclosed herein.

The present invention also provides a method of authenticating a product comprising a 2DM as disclosed herein, the method comprising: a) classifying an image of the 2DM using a trained model that is configured to classify images into a category of a plurality of categories of hierarchical structure, to thereby obtain a class label; b) determining respective similarity scores of the image to respective stored images labelled with the class label; and c) outputting a positive authentication result if at least one of the respective similarity scores is greater than a threshold.

In some embodiments, the method further comprises reading the 2DM using a scanning electron microscope or a 3D laser microscope.

Brief description of the drawings

Embodiments of the present invention will now be described, by way of non-limiting example, with reference to the drawings in which:

Figure 1 illustrates a schematics of the transfer-free and scalable fabrication of hierarchical two-dimensional material (2DM) topographies with classifiable physical unclonable function (PUF) patterns for the development of efficient anti-counterfeiting technology accompanied with deep learning (DF)-facilitated authentication;

Figure 2 illustrates cation intercalation (Cl) treatment for creation of hierarchical graphene oxide (GO) topographies via adjusting interfacial mechanical mismatch;

Figure 3 shows the definition and quantification of crumple size formed using the Cl step; Figure 4 illustrates moisture induced lubrication (MIF) treatment for creation of hierarchical MXene topographies through transitioning deformation mechanism from conformal wrinkling to delaminated buckling;

Figure 5 illustrates the definition and measurement of MXene crumple sizes with and without MIL treatment;

Figure 6 illustrates MIL treatment applied for creation of hierarchical GO topographies through transitioning deformation mechanism from conformal wrinkling to delaminated buckling; Figure 7 illustrates engineering ID wrinkles using tube-shaped substrates (balloons);

Figure 8 illustrates programmable architecturing of multigenerational two-dimensional material (2DM) topographies;

Figure 9 illustrates environmental stability, PUF nature, and classifiable characteristics of multigenerational 2DM topographies enabled their applications as anticounterfeiting tags coupled with DL-accelerated classification & validation;

Figure 10 shows the classification and validation precision of a two-step DL-accelerated authentication for each category;

Figure 11 illustrates the synergy between classifiable 2DM PUF patterns and DL-accelerated authentication mechanism enabled the development of DeepKey anticounterfeiting technology;

Figure 12 illustrates a schematic of the structure and components of DeepKey technology; and

Figure 13 illustrates sequential deflations of 2DM-coated latex balloon without any in situ treatments (Cl and/or MIL).

Detailed description

The present invention is predicated on the understanding that complex out-of-plane topographies can emerge in the ultrathin two-dimensional material (2DM) layers attached to elastomeric substrates under in-plane contractions. The inventors believe that owing to the unpredictable interfacial deformations at micro-/nano-scale, the resulting 2DM topographies (e.g., crumples, wrinkles) exhibit random and unclonable physical micro-patterns, which can serve as the PUF secure keys. Further, the excellent physical stability of 2DMs makes them advantageous for the fabrication of stable PUF key-based tags. Furthermore, the higher dimensional characteristics of 2DM micro-structures can be programmably designed across multiple length scales, producing various hierarchical topographies with unique PUF features. The orientation and combination of multiscale features serve as unique identifiers to classify and categorize the resulting 2DM tags into specific subgroups. As such, a pre categorization step can be implemented to accelerate the overall authentication process of 2DM tags. However, the majority of methods for creating sophisticated design of hierarchical 2DM topographies involved repeated substrate dissolution and/or delicate 2DM film transfer, severely limiting the scalability of tag fabrication and the capability of topographic tuning. To this end, it is desirable to develop a facile and scalable approach to fabricating 2DM anti-counterfeiting tags with classifiable features, which are essential for the concept of accelerated authentication.

In this regard, the inventors have found that various structures and thus various hierarchical topographies can be fabricated on various 2DMs by altering the contact of the 2DM and the substrate. Such alteration can be introduced as a result from the change in physical properties of the 2DM and/or a change in the interfacial adhesion between the 2DM and the substrate. For example, the step of altering a mechanical mismatch (step c) can be cation intercalation (Cl) step. Alternatively, a moisture-induced lubrication (MIL) step can be applied between the 2DM and the substrate. When the substrate is subsequently contracted, due to the mechanical mismatch, hierarchical topographies can be fabricated on the 2DMs.

Figure 1 shows a schematic of the present invention. In particular, Figure la shows an exemplary schematic illustration of transfer-free fabrication of multigenerational 2DM topographies, which included the following steps: (i) transfer of planar 2DM thin film (Go) onto a substrate being in an expanded state (inflated latex balloon), (ii) first stage balloon deflation, (iii) altering the contact such as intermediate cation intercalation (Cl) treatment to adjust mechanical mismatch or intermediate moisture induced lubrication (MIL) treatment to tune interfacial adhesion energy, and (iv) second stage deflation. Steps (iii) and (iv) could be repeated n times to achieve (v) multigenerational (G„ _+i ) 2DM topographies. Diverse micro- to nano-scale features (i.e., 2D crumples and ID wrinkles) could be encoded.

As examples, graphene oxide (GO) and titanium carbide (T13C2T _X ) MXene can be adopted as building block units (Figure la). With both Cl and MIL treatments, multigenerational GO and MXene structures (11 types for each 2DM) were produced by the pre-determined deflation programs without the need of substrate removal or film transfer. Advantageously, the classifiable 2DM hierarchies can be utilized as PUF key-based tags for anti counterfeiting applications (Figure lb). By training a deep-learning (DL) model to pre categorize the 2DM tags, a two-step authentication mechanism was built to increase the authentication speed. With the synergy of 2DM PUF tags and DL authentication software, an economic, highly reliable, and stable anticounterfeiting technology, is demonstrated, which can perform superior encoding capacity (>10 ^144,494 ) and accelerated processing (~3.5 minutes for readout plus authentication).

Accordingly, the present invention provides a method of fabricating a two dimensional material (2DM) with a hierarchical topography, comprising: a) preparing a substrate in the expanded state; b) adhering the 2DM to the substrate in the expanded state; c) altering the contact between the 2DM and the substrate in the expanded state; and d) contracting the substrate from the expanded state to a first contracted state in order to form a structure on the 2DM.

Advantageously, the step of altering the contact (step (c)) is an in situ intermediate treatment step, thus avoiding the need for repeated substrate dissolution and/or delicate 2DM film transfer. This allows for a facile and scalable approach to fabricating 2DM.

Depending on the desired structure and hierarchical topography, step c and step d can be performed interchangeably. For example, the contracting step can be performed before the altering step and vis versa. Step c and step d can also be independently performed more than one time, in order to include the number of hierarchical structures. For example, the method can comprise a step of partially contracting the substrate, altering the inter-planar bond and/or the interfacial bond, and subsequently contracting the substrate.

In some embodiments, the substrate in the expanded state is a substrate which is inflated. In this regard, the substrate can comprise a closed vessel, which when in an expanded state, the closed vessel has an increased volume and/or increased surface area. In some embodiments, the substrate comprises a flexible material. In some embodiments, the substrate is an elastomeric substrate. An elastomeric substrate is a natural or synthetic polymer having elastic properties; displaying rubber-like elasticity. It is generally a polymer with viscoelasticity (i.e., both viscosity and elasticity) and has very weak intermolecular forces, generally low Young's modulus and high failure strain compared with other materials. Examples of elastomeric substrates are, but is not limited to, polystyrene film, natural rubbers, styrene-butadiene block copolymers, polyisoprene, polybutadiene, ethylene propylene rubber, ethylene propylene diene rubber, silicone elastomers, fluoroelastomers, polyurethane elastomers, and nitrile rubbers. In some embodiments, the substrate is a latex substrate, for example, a latex balloon.

The subsequent step of contraction acts to reduce the substrate in the expanded state to a smaller size, area, number, range or volume. For example, an inflated substrate can be deflated. In other embodiments, when the substrate comprise a closed vessel, the closed vessel decreases in volume. In other embodiments, the substrate decreases in surface area.

When the step of altering the contact between the 2DM and the substrate in the expanded state is a Cl step, it can be implemented to tune the mechanical mismatch between 2DM layer and elastomeric substrate during sequential deformations. For example, when the contraction occurs in one dimension, the classic equation for wrinkles (ID) generated in a thin film compliantly bonded to an elastomeric substrate is shown in Equation 1, l = 2nh(E _f /3E _s y/ ³ (1) where L is the characteristic wavelength of wrinkle, h is the thickness of film, E _f and E _s stand for the Young’s moduli of top-layer film (f) and bottom-layer substrate (s), respectively; E = E/ 1 — v ² ) , v is the Poisson’s ratio. A way to tune the wrinkle wavelength can be through adjusting the Young’s modulus of top 2DM layer (e.g., GO) via the intercalation of metal ions into 2DM multilayers. It is noted that the Young’s modulus of a GO film, for example, after overnight immersion in A1(N0 ₃ ) ₃ solution, increased from 0.99 (neat GO) to 3.39 GPa (Al ³⁺ -intercalated GO, 1.26 at.% (atomic ratio), abbreviated as Al-GO), while the modulus of latex substrate remained unchanged at -0.6 MPa (Figure 2a, b). To visualize the Cl effect on the GO topographies under large deformation, a 500- nm-thick, planar GO film (generation 0, Go) was first transferred onto an inflated latex balloon. The conformal adhesion of GO nanocoating was enabled by the pre-treatment of oxygen plasma of latex balloon, which generated hydroxyl groups on the elastomeric surface and induced hydrogen bonding with top GO layer. The GO-coated inflated balloon then underwent overnight Al ³⁺ intercalation followed by one-step isotropic (2D) deflation to produce Gi I2D Al-GO crumple structures. For comparison, Gi I2D GO crumple structures were also fabricated for comparison. Both Al-GO/latex and GO/latex structures exhibited extended and interlocked interfaces (Figure 2c), indicating that they followed the same deformation mode of conformal wrinkling. Because of the rigidification of top GO layer via Al ³⁺ intercalation (larger mismatch with latex), the sizes of Gi I2D Al-GO crumples were much larger than the Gi I2D GO ones under the same degree of contraction (Figure 2d).

As used herein, 'wrinkle' refers to a line or fold in the 2DM. In this regard, a wrinkle can be considered to have a directionality, and can, for example, be formed from to a change in the 2DM in a single dimension; i.e. anisotropic change in the 2DM, structures formed from ID contraction.

As used herein, 'crumple' refers to a crease or a crushed fold in the 2DM. In this regard, a crumple can be considered to be directionless or have a random orientation. It can, for example, be formed from a change in the 2DM in multiple dimensions; i.e. isotropic change in the 2DM, structures formed from 2D contraction.

In particular, Figure 2 illustrates cation intercalation (Cl) treatment for creation of hierarchical graphene oxide (GO) topographies via adjusting interfacial mechanical mismatch (a, b) Stress-strain curves of latex substrates and GO thin films before and after overnight immersion in 0.1 M A1(N0 ₃ ) ₃ solution (c) Schematic illustration and corresponding cross-sectional SEM images of GO/latex and Al ³⁺ -intercalated GO (Al- GO)/latex bilayer structures after the areal strain ( _< -;. _\) released, where the conformal and interlocked interfaces were observed for both structures. Scale bar, 5 mpi. (d) Top-view SEM images of generation 1 isotropic (Gi/2 ) GO and Gi 12D Al-GO crumples generated under the ;-;A of 100%, 200%, 400%, and 600%, exhibiting the GO crumple sizes decreasing from ~15 x 15, 10 x 10, 6 x 6, to 4 x 4 pm, which were respectively smaller than the Al-GO crumple sizes varying from ~30 x30, 20 x 20, 10 x 10, to 6 x 6 pm. Scale bar, 10 pm. (e) Top-view SEM images of hierarchical Gi/2D-2D topographies fabricated by sequential deflations of GO-coated balloon with intermediate Cl treatment. The feature sizes of both Gi and G2 crumples were finely tuned by controlling the areal strain released ( \ _< v, _\) at each deflation stage. As representatives, for two-stage deflations of 100%-300%, 200%-200%, and 300%-100% (denoted as at first stage- \ _< v. _\ at second stage), the Gi crumple size varied from ~3 x 3, 6 x 6, to 10 x 10 pm and the G2 crumple size varied from ~20 x 20, 30 x 30, to 40 x 40 pm, respectively. Scale bars, 20 (top row) and 10 pm (bottom row).

As used herein, 'areal strain released' or ’ \ _< v _\ ’ refers to a change in a superficial area of a thin film before and after substrate shrinkage. D _A = DA/A _f x 100% where DA is the change (A _f - Ao) of superficial area of a thin film before (Ao as the planar film is deposited) and after the substrate shrinkage (A _f as the film is fully compressed). For example, D _A = 300% corresponds to uniaxial strains in each direction of s _x = 100% and s _y = 100%.

In some embodiments, the step of adhering the 2DM on the substrate (step b) comprises applying the 2DM as a dispersion onto the substrate and allowing the dispersion to dry. The 2DM is thus physically and/or chemically adhered to the substrate. The dispersion can comprise the 2DM in a solvent. The solvent can be an aqueous solvent. In some embodiments, the dispersion has a 2DM concentration of about 0.02 mg mlr ¹ to about 1 mg mlr ¹ . In other embodiments, the dispersion has a 2DM concentration of about 0.03 mg ml ¹ to about 1 mg mL ¹ , about 0.03 mg mlr ¹ to about 0.9 mg mL ¹ , about 0.03 mg mlr ¹ to about 0.8 mg mL ^-1 , about 0.03 mg mlr ¹ to about 0.7 mg mL ^-1 , about 0.04 mg mlr ¹ to about 0.7 mg mL ^-1 , about 0.05 mg mlr ¹ to about 0.7 mg mL ^-1 , or about 0.06 mg mL ^-1 to about 0.66 mg mL ^-1 . Depending on the concentration, the thickness of 2DM on the substrate can be controlled. In some embodiments, the thickness of 2DM on the substrate is about 100 nm to about 1000 nm. In other embodiments, the thickness of 2DM on the substrate is about 200 nm to about 1000 nm, about 300 nm to about 1000 nm, about 400 nm to about 1000 nm, about 400 nm to about 900 nm, about 400 nm to about 800 nm, about 400 nm to about 700 nm, or about 400 nm to about 600 nm.

In some embodiments, the step of altering the contact between the 2DM and the substrate in the expanded state comprises altering the Young's modulus of the 2DM. In other embodiments, the stress strain relationship is altered. For example, the Young's modulus can be altered from about 1 GPa to about 3.4 GPa. Alternatively, the Young's modulus can be altered from about 1 GPa to about 2 GPa, about 1 GPa to about 2.5 GPa, about 1 GPa to about 3 GPa, about 1 GPa to about 4 GPa, or about 1 GPa to about 4.5 GPa.

Young's modulus, is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation.

In some embodiments, the Young's modulus is altered by intercalating the 2DM with a cation. In other embodiments, the intercalation of the 2DM with a cation comprises contacting the 2DM and substrate in a cation solution. The cation solution can be selected from A1(N0 ₃ ) ₃ , Mg(N0 ₃ ) ₂ or Ca(N0 ₃ ) ₂ - The cation can be any cation with a +2 or +3 charge. In other embodiments, the cation is selected from Al ³⁺ , Mg ²⁺ and Ca ²⁺ .

In some embodiments, the cation is provided at a concentration of about 0.01 M to about 1 M. In other embodiments, the concentration is about 0.05 M to about 1 M, about 0.1 M to about 1 M, about 0.1 M to about 0.9 M, about 0.1 M to about 0.8 M, about 0.1 M to about 0.7 M, about 0.1 M to about 0.6 M, or about 0.1 M to about 0.5 M.

In some embodiments, the altering step is performed for at least about 1 h, about 2 h, about 3 h, about 4 h, about 5 h, about 6 h, about 7 h, about 8 h, about 9 h, about 10 h, about 11 h, about 12 h, or about 24 h. In some embodiments, the substrate preparation step (step a) comprises treating the substrate with plasma. Plasma treatment is a surface modification technique that readily primes any surface for better acceptance of secondary manufacturing applications. Plasma is a reactive treatment process where positive and negative ions, electrons, and radicals react and collide as long as an electric potential difference exists.

Figure 3 shows the definition and quantification of crumple size. The crumples shown were formed using the Cl step. The crumple size is defined as the wavelength of a whole crumple. (a) Under the pre-applied areal strains (¾ _\ ) of 100%, 200%, 400%, and 600%, the sizes of

Gi I2D GO crumples were extracted to vary from ~15 x 15, 10 x 10, 6 x 6, to 4 x 4 pm, while the sizes of Gi I2D Al-GO crumples were extracted to vary from ~30 x30, 20 x 20, 10 x 10, to 6 x 6 pm. Scale bar, 10 pm. (b) For the hierarchical G2 /2D-2D GO topographies derived from the two-stage deflation programs with of 100%-300%, 200%-200%, and 300%- 100%, the Gi crumple sizes were extracted to vary from ~3 x 3, 6 x6, to 10 x 10 pm, and the G2 crumple sizes were extracted to vary from ~20 x 20, 30 x 30, to 40 x 40 pm, respectively. Scale bars, 20 (top row) and 10 pm (bottom row).

To generate additional hierarchical GO topographies, sequential deflations of GO-coated balloon and with intermediate Cl treatment can be performed. For instance, a Go GO film was transferred onto an inflated latex balloon followed by first-stage deflation. The partially deflated GO-coated balloon then underwent the Cl treatment to increase the Young’s modulus of top 2DM layer. After second-stage (full) deflation, hierarchical Al-GO structures (G212D-2D) composed of small Gi crumples (from first-stage deflation) on top of large G2 crumples (from second-stage deflation) were observed (Figure 2e). Without intermediate Cl treatment, no hierarchical characteristic was obtained after multi-stage deflations (Figure 13). In addition, by modulating the areal strain ( _<- :. _\) released at each deflation stage, the characteristic features can be precisely tuned at different length scales. By programming the areal strains of sequential deflations (( \ _< v, _\ at first stage)-! \ _< v. _\ at second stage)), the Gi/2D- 2D GO hierarchies that followed the deflation programs of 300%-100%, 200%-200%, and 100%-300% exhibited the Gi crumples sizing from ~3 x 3, 6 x 6, to 10 x 10 pm and the G2 crumples from ~20 x 20, 30 x 30, to 40 x 40 pm, respectively (Figure 3b). Both Gi and G2 feature sizes can be further tuned upon specific requests by simply adjusting the at each deflation stage, demonstrating dominant advantages over conventional multi-step methods with fixed pre-strain for each deformation. Moreover, the intercalated Al ³⁺ ions within as- deformed Al-GO topographies were able to be completely rinsed out by dilute HC1 solution. This demonstrates that the intermediate Cl treatment is suitable for 2DM that can crosslink with metal ions, such as GO.

Accordingly, in some embodiments, feature sizes of the structure is tunable by modulating the contraction of the substrate. In other embodiments, the feature sizes of the structure is tunable by altering the inter-planar bond within the 2DM. In other embodiments, the feature sizes of the structure is tunable by modulating the contraction of the substrate and by altering the inter-planar bond within the 2DM. For example, the feature size of the structure is tunable from about 2 x 2 pm to about 50 x 50 pm.

In some embodiments, features of different sizes on a 2DM are provided by varying the number of altering steps and/or contracting steps. In other embodiments, sequential contraction of the substrate and with an intermediate altering step is performed in order to provide a hierarchical topography with structures of two different sizes. In this regard, the hierarchical topography can have a first structure with a feature size of about l x l pm to about 20 x 20 pm and a second structure with a feature size of about 20 x 20 pm to about 50 x 50 pm. The first structure is formed on the second structure and thus provides for the hierarchical topography.

To expand the selection of available 2DM candidates and/or hierarchical topographies which can endow add-on functions to the anticounterfeiting tags, another way to alter the contact between the 2DM and the substrate was explored.

The inventors have found that another factor that can be tuned is the interfacial adhesion energy ( G ) between top 2DM layer and bottom latex substrate. When the G of 2DM layer on latex is lower than the critical adhesion energy (Gc) calculated by Equation 2, G _c = s ² E _f h (2) where e is the uniaxial strain, the formation of delaminated large buckles is energetically preferred over conformal wrinkling upon the strain release. Inspired by this, an intermediate MIL treatment was implemented between consecutive deflation stage by introducing moisture as a benign lubricant, which attenuates the G of 2DM/latex interface to be lower than Gc- After the MIL treatment, the deformation mode can be intentionally transitioned from conformal wrinkling to delaminated buckling. MXene was chosen as the representative 2DM for the MIL treatment. Similarly, a 500-nm-thick MXene film was first transferred onto an inflated latex balloon, where the adhesion between MXene film and latex was enhanced by the pre-treatment of oxygen plasma on latex. To introduce the moisture lubricant, the MXene-coated inflated balloon was kept at 4 °C overnight and then taken out to room temperature (25 °C, at the relative humidity (RH) of 68%) to condense the moisture layer at MXene/latex interface. The mechanical properties of MXene and latex were well retained after the MIL treatment. On the other hand, the G of MXene/latex interface (under ;-;A of 100%) before and after the introduction of moisture lubricant was characterized by the delamination tests using a Universal Testing System (Instron 5567, Instron, Canton, MA). The MXene/latex bilayer structure (with pre-applied ;-;A of 100%) were prepared with dimension of 0.5 x 0.5 cm ² . Afterwards, the square-shaped MXene/latex devices were adhered by super glue in between two pieces of plastic strips (Figure 4a), where the G dramatically decreased from 200.8 to 90.4 J nr ² (corresponding Gc was 142.9 J nr ² ), demonstrating the successful transition of deformation mechanism to delaminated buckling (Figure 4b).

As used herein, 'buckle' refers to a portion of the 2DM which separates from the substrate.

In particular, Figure 4 illustrates moisture induced lubrication (MIL) treatment for creation of hierarchical MXene topographies through transitioning deformation mechanism from conformal wrinkling to delaminated buckling (a) Delamination tests of MXene/latex interface before and after MIL treatment (b) Adhesion energy decreased from 200.8 to 90.4 J nr ² after MIL treatment, resulting in the transition of deformation mechanism from conformal wrinkling to delaminated buckling (c) Schematic illustration and cross-section SEM images of MIL-treated MXene/latex structures confirmed the transition of deformation mechanism, where much larger delaminated buckles were observed after MIL treatment. Scale bars, 5 (top) and 50 pm (bottom) (d) Top-view SEM images of as-transferred Gi 12D MXene crumples and Gi I2D MIL-induced MXene buckles generated under the ;-;A of 100%, 200%, 400%, and 600%, exhibiting the MXene crumple sizes decreasing from ~30 x 30, 20 x 20, 12 x 12, to 6 x 6 pm, which were respectively smaller than the sizes of MIL-induced MXene buckles varying from -150 x 150, 120 x 120, 80 x 80, to 50 x 50 pm. Scale bars, 10 (top row) and 100 pm (bottom row) (e) Top-view SEM images of hierarchical G2 I2D- 2D topographies fabricated by sequential deflations of MXene-coated balloon with intermediate MIL treatment. The sizes of both Gi and G ₂ crumples were finely tuned by controlling at each deflation stage. As representatives, for two-stage deflations with of 100%-300%, 200%-200%, and 300%-100%, the Gi crumple sizes varied from -5 x 5, 8 x 8, to 10 x 10 pm, and the G ₂ crumple sizes varied from -40 x 40, 55 x 55, to 75 x75 pm, respectively. Scale bars, 20 (top row) and 10 pm (bottom row).

To visualize the MIL effect on the MXene topographies under deformation, the MIL-treated MXene-coated balloon was fully deflated to produce a Gi 12D MXene/latex structure. After the MIL treatment, the attenuated adhesion energy resulted in the partial delamination of MXene film accompanied with isotropic buckling during latex contraction, as indicated by the cross-sectional SEM image (Figure 4c). Figure 4d shows that the delaminated MXene buckles (treated by MIL) exhibited much larger topographic features than the conformal MXene crumples (without MIL). Similarly, hierarchical MXene topographies were produced by conducting sequential deflations of MXene-coated balloon with intermediate MIL treatment implemented. A Go planar MXene film was first transferred onto an inflated latex balloon followed by first-stage deflation. The partially deflated MXene-coated balloon subsequently underwent the MIL treatment to transition the deformation mode to delaminated buckling. After second-stage (full) deflation, hierarchical MXene structures (G ₂ 12D-2D) with combinative structural characteristics were obtained, where smaller Gi crumples (from first-stage deflation) was on top of large G ₂ buckles (from second-stage deflation). The details regarding quantification of buckle and crumple size are in Figure 5a, b. Without the MIL treatment, no hierarchical characteristic was obtained after multi stage deflations (Figure 13). Still, by adjusting the at each deflation step, the sizes of primary buckles and secondary crumples in G2 /2D-2D GO hierarchies were able to be programmably controlled (Figure 4e). This MIL approach can be as versatile, if not more, than the Cl treatment, and can be also applicable to other 2DMs (e.g., GO, as shown in Figure 6a, b). The intermediate Cl and MIL treatments can be applied sequentially during the multi-stage balloon deflations to create multigenerational 2DM hierarchies.

Figure 5 illustrates the definition and measurement of MXene crumple sizes with and without MIL treatment. The crumple size is defined as the wavelength of a whole crumple (a) Under the pre-applied of 100%, 200%, 400% and 600%, the sizes of G _\ /2D MXene crumples without MIL treatment were extracted to vary from ~30 x 30, 20 x 20, 12 x 12, to 6 x 6 pm, while the sizes of Gi I2D MXene crumples generated after MIL treatment were extracted to vary from -150 x 150, 120 x 120, 80 x 80, to 50 x 50 pm. Scale bars, 10 (top row) and 100 pm (bottom row) (b) For the hierarchical G2 /2D-2D MXene topographies derived from the two-step deflations of 100%-300%, 200%-200%, and 300%- 100%, the Gi crumple sizes were extracted to vary from -5 x 5, 8 x 8, to 10 x 10 pm, and the G2 crumple sizes were extracted to vary from -40 x 40, 55 x 55, to 75 x75 pm, respectively. Scale bars, 20 (top row) and 10 pm (bottom row).

Accordingly, in some embodiments, the step of altering the contact between the 2DM and the substrate in the expanded state comprises altering the interfacial adhesion between the 2DM and the substrate in the expanded state. In other embodiments, the interfacial adhesion is altered by condensing water molecules between the 2DM and the substrate. In other embodiments, the condensation of water molecules between the 2DM and the substrate comprises storing the 2DM on the substrate under low temperature and subsequently subjecting the 2DM on the substrate to a relative humidity of at least 60%. In other embodiments, the relative humidity is at least about 70%, or about 80%. In other embodiments, the low temperature is from about 4 °C to about -80 °C, from about 4 °C to about -60 °C, from about 4 °C to about -40 °C, from about 4 °C to about -20 °C, from about 4 °C to about -10 °C, or from about 4 °C to about 0 °C. When the 2DM is held at a relative humidity of at least 60%, the temperature can be at room temperature. In other embodiments, the temperature is an ambient temperature. In other embodiments, the temperature is from 15 °C to about 35 °C, from 15 °C to about 30 °C, or from 15 °C to about 25 °C.

As described herein, the deformation by the MIL step is a result of the change the adhesion energy G. In some embodiments, the resultant adhesion energy G after the step of altering the contact (step c) is about 60 J nr ² , about 70 J nr ² , about 80 J nr ² , about 90 J nr ² , about 100 J nr ² , about 110 J nr ² , about 120 J nr ² , about 130 J nr ² , about 140 J nr ² , about 150 J nr ² , about 160 J nr ² , about 170 J nr ² , about 180 J nr ² , or about 190 J nr ² .

In some embodiments, feature sizes of the structure is tunable by modulating the contraction of the substrate. In other embodiments, the feature sizes of the structure is tunable by altering interfacial bond between the 2DM and the substrate. In other embodiments, the feature sizes of the structure is tunable by modulating the contraction of the substrate and by altering interfacial bond between the 2DM and the substrate. For example, the feature size of the structure is tunable from about 40 x 40 pm to about 200 x 200 pm.

In some embodiments, features of different sizes on a 2DM are provided by varying the number of altering steps and/or contracting steps. In other embodiments, sequential contraction of the substrate and with an intermediate altering step is performed in order to provide a hierarchical topography with features of two different sizes. In this regard, the hierarchical topography can have a first structure with a feature size of about l x l pm to about 10 x 10 pm and a second structure with a feature size of about 20 x 20 pm to about 80 x 80 pm. The first structure is formed on the second structure and thus provides for the hierarchical topography.

Figure 6 illustrates MIL treatment applied for creation of hierarchical GO topographies through transitioning deformation mechanism from conformal wrinkling to delaminated buckling (a) Schematic illustration and cross-section SEM images of MIL treated GO/latex structures confirmed the transition of deformation mechanism, where large delaminated buckles were observed after MIL treatment. Scale bars, 50 (top) and 20 pm (bottom) (b) Top-view SEM images of hierarchical CL/2D-2D topographies fabricated by sequential deflations of GO-coated balloon with intermediate MIL treatment. The sizes of both Gi and G2 crumples were finely tuned by controlling at each deflation stage. As representatives, for two-stage deflations with of 100%-300%, 200%-200%, and 300%-100%, the Gi crumple sizes varied from ~3 x 3, 5 x 5, to 8 x 8 pm, and the G2 crumple sizes varied from ~30 x 30, 50 x 50, to 60 x 60 pm, respectively. Scale bars, 20 (top row) and 10 pm (bottom row).

Figure 13 illustrates sequential deflations of 2DM-coated latex balloon without any in situ treatments (i.e., Cl and/or MIL) did not lead to hierarchical structures (a, b) SEM images of GO “G2 /2D-2D” and GO “G3 /2D-2D-2D” structures prepared by following the multi-stage deflation programs with no Cl treatment applied in between. Only GO crumple topographies similar with those prepared by one-stage deflation were observed, while no hierarchical structures were seen. Scale bars, 20 (top row) and 10 pm (bottom row) (c, d) SEM images of MXene “G212D-2D” and MXene “G3 /2D-2D-2D” structures prepared by following the multi-stage deflation programs with no MIL treatment applied in between. Only MXene crumple morphologies similar with those prepared by the one-stage deflation were observed, while no hierarchical structures were seen. Scale bars, 20 (top row) and 10 pm (bottom row).

As used herein, 2D materials (2DM) refer 2D layered materials and includes single-layer materials, which are materials consisting of a single layer of atoms. Such materials can also be crystalline. They can either be 2D allotropes of various elements or compounds (consisting of two or more covalently bonding elements). The elemental 2D materials generally carry the -ene suffix in their names while the compounds have -ane or -ide suffixes. Layered structures and layered combinations of different 2D materials (van der Waals heterostructures) are also included within the scope of this invention. In some embodiments, the 2DM is selected from graphene, graphene oxide, borophene, germanene, silicene, stanine, plumbene, phosphorene, antimonene and bismuthene. The 2DM can be a compound selected from graphane, hexagonal boron nitride, borocarbonitride, germanane and transition metal dichalcogenides such as molybdenum disulphide, tungsten diselenide and hafnium disulphide. The 2DM can also be a MXene. MXenes are layered transition metal carbides and carbonitrides with general formula of M _n+i X _n T _x , where M stands for early transition metal, X stands for carbon and/or nitrogen and T _x stands for surface terminations (mostly =0, -OH or -F), and n=l-4. MXenes have high electric conductivity (10000-1500 Scm ^-1 ) combined with hydrophilic surfaces that can be tuned with solvents. They can be synthesized from ceramic precursor MAX phases by removing the single atomic layer "A" where M stands for Ti, Mo, W, Nb, Zr, Hf, V, Cr, Ta, Sc, A stands for Al, Si, and X stands for C, N. More than 30 MXenes have been synthesized and these are known to the skilled person in the art. In some embodiments, the MXene is titanium carbide.

The 2DM can comprise graphene oxide. Graphite oxide is a compound of carbon, oxygen, and hydrogen in variable ratios, obtained by treating graphite with strong oxidizers. The maximally oxidized bulk product is a yellow solid with C:0 ratio between 2.1 and 2.9, that retains the layer structure of graphite but with a much larger and irregular spacing. Graphene oxide layers are about 1.1 + 0.2 nm thick, the layers can be buckled and the interlayer spacing is about two times larger (-0.7 nm) than that of graphite.

The 2DM can comprise molybdenum disulphide (M0S2). It is commonly classified as a transition metal dichalcogenide.

The 2DM can comprise hexagonal boron nitride (h-BN). Hexagonal BN is also called h-BN, a-BN, g-BN, and graphitic boron nitride. Hexagonal boron nitride (point group = D6h; space group = P63/mmc) has a layered structure similar to graphite. Within each layer, boron and nitrogen atoms are bound by strong covalent bonds, whereas the layers are held together by weak van der Waals forces. The interlayer "registry" of these sheets differs, however, from the pattern seen for graphite, because the atoms are eclipsed, with boron atoms lying over and above nitrogen atoms. This registry reflects the polarity of the B-N bonds.

The 2DM can comprise montmorillonite (MMT) nanosheets. Montmorillonite is a very soft phyllosilicate group of minerals that form when they precipitate from water solution as microscopic crystals, known as clay. Montmorillonite, a member of the smectite group, is a 2:1 clay, meaning that it has two tetrahedral sheets of silica sandwiching a central octahedral sheet of alumina. The particles are plate-shaped with an average diameter around 1 pm and a thickness of 0.96 nm. Member of the smectite group can be characterized as having greater than 50% octahedral charge; its cation exchange capacity is due to isomorphous substitution of Mg for A1 in the central alumina plane. The substitution of lower valence cations in such instances leaves the nearby oxygen atoms with a net negative charge that can attract cations. The individual crystals of montmorillonite clay are not tightly bound hence water can intervene, causing the clay to swell. The water content of montmorillonite is variable and it increases greatly in volume when it absorbs water. Chemically, it is hydrated sodium calcium aluminium magnesium silicate hydroxide (Na,Ca)o _.33 (Al,Mg) ₂ (Si ₄ 0io)(OH) ₂ -nH ₂ 0. Potassium, iron, and other cations are common substitutes, and the exact ratio of cations varies with source. It often occurs intermixed with chlorite, muscovite, illite, cookeite, and kaolinite.

In some embodiments, the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN), montmorillonite (MMT) nanosheets or a mixture thereof. In this regard, the 2DM can be a composition that comprises doped or mixtures of the above mentioned materials. For example, the 2DM can be doped graphene oxide.

In some embodiments, the 2DM comprises less than 20 layers of 2DM. In other embodiments, the 2DM comprises less than 18 layers, 16 layers, 14 layers, 12 layers, 10 layers, 8 layers, 6 layers or 4 layers. In other embodiments, the 2DM is a monolayer 2DM.

Besides the isotropic 2DM crumples fabricated by the deflation of a sphere-shaped balloon, periodic wrinkle textures with certain orientation were created by deflating a tube-shaped balloon (see Figure 7a-c for details of orientation and wavelength controls). Through the sequential deflations of sphere- or tube-shaped balloons together with the intermediate modification step(s) (Cl and/or MIL), both wrinkle (ID) and crumple (2D) features were programmed into hierarchical 2DM structures with desired combinations at different length scales. The programmable architecturing of upper 2DM layers enabled the fabrication of multigenerational 2DM structures, starting from planar Go nanocoatings to multiscale G3 topographies. The genealogies of GO and MXene are shown in Figure 8 (12 members for each family tree), and the detailed fabrication processes of each 2DM micro-structure can be found in Experimental Section (see Supporting information).

Figure 7 illustrates engineering ID wrinkles using tube-shaped substrates (balloons) (a-c) Illustration of fabrication processes and SEM images of Gi/ID GO topographies generated by deflation of tube-shaped balloon with Ae (along tube axis direction) of 50%, 100%, and 200%, showing wrinkle wavelengths varying from —35, 24, to 12 pm, respectively. Scale bar, 20 pm.

In some embodiments, the contraction step (step d) is selected from an isotropic contraction or an anisotropic contraction. In this regard, the isotropic contraction occurs along a single dimension while the anisotropic contraction occurs concurrently in 2 dimensions. In other embodiments, the contraction from one state to a contracted state is about 10% of the expanded state. In other embodiments, the contraction is about 20%, 30%, 50%, 100%, 150%, 200%, 250%, 300%, 350%, 400%, 450%, or 500% of the expanded state.

In other embodiments, the expanded state is measured with respect to an internal volume of a vessel. For example, starting from a fully contracted state, the volume can be increased by about 800% to provide an expanded state. In other embodiments, the volume is increased by about 700%, 600%, 500%, 400%, 350%, 300%, 250%, 200%, 150%, 100%, 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20% or 10%. The expanded state can accordingly deflate by the same volume (or a proportion of the volume) to get to a contracted state. For example, the inflation/deflation of the balloon is controlled by varying the volume of liquid injected into/vented from the balloon.

In other embodiments, the contraction controlled by varying the areal strain. In other embodiments, the areal strain is varied about 100%, about 200%, about 300%, about 400%, about 500% or about 600%. In some embodiments, the substrate being in the expanded state has a shape selected from sphere or tube. An anisotropic contraction can be performed on a sphere or a tube. An isotropic contraction can, for example, be performed on a tube. The isotropic contraction can occur along the longitudinal axis of the tube, or perpendicular to the longitudinal axis of the tube.

As mentioned herein, a step of contracting the substrate with the 2DM allows for the formation of a topography on the 2DM. By repeating and/or varying the contracting step, a hierarchical topography on the 2DM can be formed.

Accordingly, in an aspect, the method comprises: a) preparing a substrate in an expanded state; b) adhering the 2DM to the substrate in the expanded state; c) contracting the substrate from the expanded state to a first contracted state in order to form a first structure on the 2DM; d) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the first contracted state; and e) contracting the substrate from the first contracted state to a second contracted state in order to form a second structure below or under the first structure; wherein the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN) and montmorillonite (MMT) nanosheets.

In these embodiments, the contracting step (step (c)) creates a partially deformed 2DM. The subsequent altering of the contact between the 2DM and the substrate further adds hierarchy topography to the 2DM. In this way, more information can be incorporated within the 2DM.

A hierarchy is an arrangement of items in which the items are represented as being "above", "below", or "at the same level as" one another. For example, the first contracting step (step (c)) can create a first hierarchical structure and the second contracting step (step (e)) can create a second hierarchical structure. The first hierarchical structure can be above (superimposed on) or below the second hierarchical structure.

Figure 8 illustrates programmable architecturing of multigenerational two-dimensional material (2DM) topographies. Genealogies of GO and MXene structures from planar Go nanocoating to multiscale G3 hierarchies, where ID wrinkle or 2D crumple features are programmably encoded at each generation. Colored connection lines represent the deformation types applied, where simple black line stands for the typical 2D deflation of a sphere-shaped balloon, double lines with black, red, and green colors stand for 2D, parallel ID {ID (II)), and vertical ID {ID (1)) deflations of a tube-shaped balloon, respectively. Golden arrow and parallel lines stand for features of 2D crumples and ID wrinkles, respectively. Scale bars for GO genealogy from top to bottom, 1 (Go), 10 (Gi), 20 and 10 (G2), 50 and 10 pm (G3). Scale bars for MXene genealogy from top to bottom, 1 (Go), 10 (Gi), 50 and 20 (G ), 100 and 50 pm (G ).

The multigenerational, multidirectional, multiscale texturing techniques involved the combination of various fabrication strategies, including (i) the use of sphere- or tube-shaped latex balloons, (ii) the programmable deflation sequences, (iii) the intermediate Cl and/or MIL treatment(s) implemented between consecutive stages of deflations. This programmable architecturing of upper GO and MXene layers rendered rich libraries containing diverse surface textures with disordered yet classifiable topographic characteristics varying from Go, Gi HD, Gi I2D, G i!2D-2D, Cn/2D-I D. Cn/I D-2D, G 2/IDIID, G ₃ /2D-2D-2D, G 2D-ID-2D, G 2D-1D11D, G 1D\\1D-2D, G 1D-2D-1D, G3 /2D-2D-1D, to G3 HD-2D-2D, etc., which were named after the certain deflation programs applied. The connection line between two topographies in different generations represents one of four deformation orientations, including ID (||) deflation of a tube balloon parallel to its axis, ID (1) deflation of a tube balloon perpendicular to its axis, and 2D deflation of a sphere- or a tube-shaped balloon. In the family tree of GO topographies, either Cl or MIL treatment can be implemented between two 2D deflations to fabricate G2 structure. To achieve multiscale G3 GO structures, either two sequential MIL treatments (at 4 °C and -80 °C subsequently) or sequential CI-MIL treatments were applied during the three-stage deflations. For the genealogy of MXene topographies, the MXene-coated balloons underwent one MIL treatment (at 4 °C) and two sequential MIL treatments (at 4 °C and -80 °C subsequently) to obtain G2 and G3 architectures, respectively.

Based on the genealogies of 2DM topographies and the corresponding fabrication procedures, several general trends can be elucidated. First, the characteristic feature and orientational (dis)order are dependent on the sequence of balloon deflations, that is, the deflation steps do not provide commutative results due to the plastic deformations of 2DM layer. Second, the largest topographic feature is determined by the final deformation mode, where the previous series of deformations generated smaller features decorated on top of the largest feature. Third, the characteristic feature size increased with the increasing deflation stages applied, which could be due to that the 2DM nanocoating underwent effective increases in thickness and stiffness while generated the out-of-plane topographies, leading to the formation of features with larger sizes in the following generation. For example, the crumple sizes of G312D-2D-2D GO architecture generated at Gi, G2, and G3 increased from ~10 x 10, 30 x 30, to 100 x 100 pm, respectively. Finally, both MXene and GO families could be further expanded by either increasing the generation numbers or adjusting the \;-; _A / \;; at each deflation step, where the hierarchical structures were able to be finely tuned at different length scales, promising excellent capability of constructing diverse topographies with theoretically unlimited complexity.

In this regard, there can be several contracted states. The isotropic contraction and anisotropic contraction can also be used alone or in combination. For example, the substrate being in the expanded state can be contracted to a first contracted state, and subsequently contracted to a second contracted state. In this regard, the substrate in the first contracted state is partially deflated. The contraction can occur either anisotropically or isotropically.

In some embodiments, the method of fabricating a two dimensional material (2DM) with a hierarchical topography, comprises: a) preparing a substrate in an expanded state; b) adhering the 2DM to the substrate in the expanded state; c) contracting the substrate from the expanded state to a first contracted state in order to form a first structure on the 2DM; d) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the first contracted state; and e) optionally repeating the contracting step (step c) and/or altering step (step d) in order to form a further structure below the first structure; wherein the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN) and montmorillonite (MMT) nanosheets.

The optional step can be repeated a desired number of times to create additional features in order to form the hierarchical structures. For example, the optional contracting step can be performed 1 time, 2 times, 3 times or 4 times. For example, the optional altering step can be performed 1 time, 2 times, 3 times or 4 times.

In some embodiments, the method comprises: a) preparing a substrate in an expanded state; b) adhering the 2DM to the substrate in the expanded state; c) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the expanded state; d) contracting the substrate from the expanded state to a first contracted state in order to form a first structure on the 2DM; e) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the first contracted state; and f) contracting the substrate from the first contracted state to a second contracted state in order to form a second structure below the first structure.

Advantageously, the inclusion of an additional altering step allows for further fine-tuning and control of the hierarchical structures. This can allow for a more reproducible PUF.

In some embodiments, the method comprises: a) preparing a substrate in an expanded state; b) adhering the 2DM to the substrate in the expanded state; c) contracting the substrate from the expanded state to a first contracted state in order to form a first structure on the 2DM; d) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the first contracted state; e) contracting the substrate from the first contracted state to a second contracted state in order to form a second structure below the first structure; e) altering an inter-planar bond within the 2DM and/or an interfacial bond between the 2DM and the substrate in the second contracted state; and d) contracting the substrate from the second contracted state to a third contracted state in order to form a third structure below the second structure.

In this embodiment, due to the 3 contracting steps, more hierarchical structures can be incorporated into the 2DM.

In some embodiments, if Cl is used in combination with MIL, the Cl step can be conducted prior to the MIL. For example, Cl is used at the before the substrate is contracted to the first contracted state (step c) and MIL is used after the substrate is contracted to the first contracted state and before the substrate is contracted to the second contracted state (step e). Advantageously, this ensures conformal attachment of upper 2DM layer; otherwise, irreversible detachment of 2DM layer may appear.

The advantage of altering the bonding several times in sequential contraction steps is that greater variations can be introduced, which allows for a larger number of unique PUFs.

In some embodiments, the method further comprises a step of delaminating or removing the 2DM from the substrate. This separates the 2DM from the substrate such that it can be applied to a product for use in applications such as authentication. In this regard, the substrate is not used for authentication. By harnessing the surface instability of balloon deflations, the multigenerational GO and MXene topographies were intrinsically disordered, which were then applied as the PUF keys for anticounterfeiting applications. As the tag stability is a continual challenge for current PUF systems, we examined the environmental stability of Gi 12D GO and MXene micro structures under multiple simulated conditions. As shown in Figure 9a, the crumple-like GO topographies remained intact upon exposure to low (-20 °C) and high temperatures (150 °C), 0% and 90% RH conditions, organic solvent (dichlorome thane), UV light, and long term daylight. The Gi I2D MXene patterns (Figure 9b) exhibited higher stability in acidic and alkaline solutions, where the microstructures were preserved after the immersion in 6.0 M HC1 and NaOH. Also, the material costs of 2 X 2 mm ² -sized MXene and GO tags were estimated to be 0.0020 and 0.0016 USD/each, respectively, showing their economic feasibility and the readiness to be integrated into various products without largely increasing the final costs. In the meantime, the superior structure complexity of the 2DM topographies rendered high difficulties in copying their fine details using typical molding method. For example, the details cannot be replicated using a PDMS mold. These specialties of 2DM hierarchies make them competitive candidates as PUF key-based tags for anticounterfeiting.

The present invention provides a two dimensional material (2DM) with a hierarchical topography prepared by the method as disclosed herein.

The present invention also provides a two dimensional material (2DM) with a hierarchical topography, comprising: a) a first hierarchical structure of about 5 pm x 5 pm to about 20 pm x 20 pm; and b) a second hierarchical structure of about 30 pm x 30 pm to about 100 pm x 100 pm; wherein the first hierarchical structure is supported on the second hierarchical structure; wherein the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN) and montmorillonite (MMT) nanosheets.

The present invention also provides a two dimensional material (2DM) with a hierarchical topography, comprising a first structure superimposed on a second structure; wherein the first structure is of about 5 mpi x 5 mpi to about 20 mpi x 20 mpi; and wherein the second structure is of about 20 mpi x 20 mpi to about 100 mpi x 100 mpi; and wherein the 2DM comprises graphene oxide, MXene (such as titanium carbide), molybdenum disulphide (M0S2), hexagonal boron nitride (h-BN) and montmorillonite (MMT) nanosheets.

In some embodiments, the first structure is about 5 pm x 5 pm to about 15 pm x 15 pm, or about 5 pm x 5 pm to about 10 pm x 10 pm.

In some embodiments, the second structure of about 35 pm x 35 pm to about 100 pm x 100 pm, 40 pm x 40 pm to about 100 pm x 400 pm, 45 pm x 45 pm to about 100 pm x 100 pm, 50 pm x 50 pm to about 100 pm x 100 pm, 60 pm x 60 pm to about 100 pm x 100 pm, or 70 pm x 70 pm to about 100 pm x 100 pm.

In some embodiments, the first structure and second structure are independently selected from wrinkle, crumble and/or buckle. In other embodiments, the first structure is a wrinkle. In other embodiments, the second structure is a crumble and/or buckle.

In some embodiments, the first structure and second structure are independently anisotropically or isotropically disordered. In other embodiments, the first structure is isotropically disordered. In other embodiments, the second structure is anisotropically disordered.

In some embodiments, the 2DM further comprises a third structure. The first structure and second structure can be superimposed on the third structure. In other embodiments, the third structure is at least about 100 pm x 100 pm.

In other embodiments, the 2DM is stable at a temperature of about -50 °C to about 200 °C. In other embodiments, the 2DM is stable at a humidity of about 0% to about 90%. In other embodiments, the 2DM is stable to organic solvents such as dichloromethane. In other embodiments, the 2DM is stable to UV irradiation. In other embodiments, the 2DM is stable in acid and/or alkaline. In these regard, the micro-structures on the 2DM are not changed as a result of these conditions; i.e. the micro- structures remain intact.

The present invention also provides a physical unclonable function (PUF) comprising the 2DM as disclosed herein, for use in authenticating a product.

The present invention also provides a product encoded with a 2DM as disclosed herein.

The 2DM can be applied to a high end product by, for example, using glue or stitching. The high end product can be, for example, a high value product such as electronics, drugs, jewellery, wine, and chips.

To examine the topographic uniqueness of multigenerational 2DM topographies, SEM images of various 2DM were compared and the structural similarity index (SSIM) for each comparison calculated. SSIM is a weighted measurement between two 2DM topographies in the aspects of structure, brightness, and contrast. By continuously comparing the corresponding areas within the sliding window (7 x 7 pixels) traversing a pair of SEM images (300 x 200 pixels), the calculated SSIM value was between -1 and +1 , where a higher index indicates higher structural similarity. Figure 9c presents the similarity map of randomly selected 296 SEM images (across Gi to G3), where a sharply bright diagonal line (SSIM = 1.0) trespassing the dark region (SSIM < 0.1) demonstrates that each 2DM micro- structure possesses unique PUF pattern. As the SSIM algorithm involves every pixel of SEM image as a variable, an ultrahigh encoding capacity of ~10 ^144,494 (256 ⁶⁰ ’ ⁰⁰⁰ ) was achieved for the 2DM anticounterfeiting tag with a pattern resolution of 60,000 pixels at 256 greyscale intensities.

Figure 9 illustrates environmental stability, PUF nature, and classifiable characteristics of multigenerational 2DM topographies enabled their applications as anticounterfeiting tags coupled with DL-accelerated classification & validation. Physical stability of (a) Gi I2D GO and (b) Gi I2D MXene topographies upon exposure to various harsh environments. Scale bar, 10 pm. (c) Similarity map for 296 randomly selected SEM images of 2DM topographies, indicating that their PUF nature with high structural uniqueness and randomness. High structural similarity (with structure similarity index SSIM = 1.0 for the bright diagonal line) was observed for self-comparison, while very low structural similarity (SSIM < 0.1 for the rest dark region) was obtained when comparing with others (d) t-SNE plot of 2DM PUF patterns from five representative categories demonstrates high inter-category heterogeneity yet high intra-category homogeneity (e) 2DM PUF patterns from five representative categories were input to train a CNN DF model. Both high quality (HQ) and low quality (FQ) images (with variations induced by algorithm or practical image taking scenarios) were fed into the DF model to obtain high-precision classification capabilities. CNN model consisted of one input layer (2DM PUF pattern), three convolutional layers, three max pooling (MP) layers, one fully connected (FC) layer, and one output layer (classification model) (f) Box plot representing the SSIM distributions for REAF and FAKE PUF patterns, which were calculated based on the practical application scenarios. To avoid any “false positive” validation, the threshold SSIM values were set to be at 0.37, 0.06, 0.08, 0.07, and 0.23 for G _\ l ID, G _\ !2D, Gi/lDllD, G212D-2D, and G72D-2D-2D categories, respectively, to differentiate REAF and FAKE cases.

The 2DM when formed as a PUF presents a unique code, which can be used to uniquely identify a source or authenticity of a product. The unique code can be provided by the different combinations and numbers of contracting and altering steps as well as by the randomness of the fabrication method. When compared to a database of 2DM surface morphologies, a match will indicate that the 2DM is an original 2DM and hence the PUF and the product is authentic. Because of the large variations in the number and combination of steps and its innate randomness, it is also difficult to recreate an exact replica of the 2DM or PUF.

In some embodiments, a PUF can be distinguished from another PUF. This is based on a weighted measurement between the two 2DM topographies in the aspects of structure, brightness, and contrast. In this regard, every PUF is unique; i.e. dissimilar from another PUF. Similar with other PUF systems, a continual tradeoff existed in our high-encoding-capacity 2DM tags, where the long decoding and authentication time was inevitably required if conventional search-and compare algorithm was still adopted. To address this challenge, the advantage of the classifiable characteristics of the 2DM tags can be utilized (e.g., level of structural complexity, type/sequence of deformations, size of topographic features) and a two-step authentication mechanism developed composed of classification and validation. Figure 9d presents the t-distributed Stochastic Neighbor Embedding (t-SNE) scatterplot of five representative 2DM PUF patterns (i.e., Gi/ ID, Gi I2D, Gi/lDllD, Gi/2D-2D, and G3 /2D-2D-2D), where their structural characteristics underwent dimension reduction and were converted into two dimensionless parameters (i.e., t-SNE dimension 1 and 2). All the data points scattering throughout the t-SNE data space indicate the high structural heterogeneity of 2962DM PUF patterns examined. On the other hand, the data points from the same category were prone to form cluster(s) (as highlighted in different colors), showing high structural homogeneity within the micro-structures fabricated from the same deflation program. With high intra-category homogeneity yet high inter-category heterogeneity, these 2DM PUF patterns were classifiable by the rapidly evolving DL algorithms, which increased the authentication speed by conducting a pre-classification step prior to one-by-one search- and-compare validation.

To train a DL model for the tag classification, 296 representative SEM images in high quality (HQ) from five different categories (Gi HD, Gi I2D, G2/ID-ID, Gi/2D-2D, and G3 /2D-2D- 2D) were input into Convolutional Neural Network (CNN, see details in Experimental Section), as shown in Figure 9e. Next, additional 296 SEM images in low quality (LQ) with the algorithm-induced variations in brightness, contrast, angle, and focus were also fed to improve the classification precision of DL model. To further improve the adaptability of DL model for practical applications, additional 1,168 SEM images from these five categories that were taken under various practical scenarios (e.g., auto mode, varying focus, brightness and contrast) were further used to cultivate the high-precision classification capabilities. After the CNN DL model was systematically trained with the input of 1,760 randomly chosen PUF patterns (80% for training and 20% for testing), the classification precision reached 100%, 100%, 93%, 97%, and 96% for classifying the Gi HD, G _\ !2D, Gi/ 1 Dll D, Gi/2D-2D, and G72D-2D-2D PUF patterns (Figure 10), respectively, which were regarded as high precision values based on current data input and training progress.

Figure 10 shows the classification and validation precision of a two-step DL-accelerated authentication for each category. The classification precision reached 100%, 100%, 93%, 97%, and 96% for classifying the Gi /ID, G,/2D, G i/lDllD, G i/2D-2D, and GJ2D-2D-2O PUF patterns, respectively. For the second step of validating within the specific category, the validation precision all reached 100% for Gi/1D, Gi I2D, Gi/lDllD, G2 /2D-2D, and G72D-2D-2D categories, with the SSIM thresholds set at 0.37, 0.06, 0.08, 0.07, and 0.23, respectively.

After the classification step, the search-and-compare algorithm was subsequently carried out only within the database of a selected subgroup, and the SSIM index was taken as a criterion to finally validate the test PUF pattern. To determine the proper SSIM thresholds for differentiating REAL and FAKE patterns, 1,168 SEM images of PUF patterns from five categories taken under diverse practical scenarios were used for SSIM calculations. In each subgroup, the threshold SSIM for REAL was determined by calculating SSIM between HQ SEM images and their corresponding LQ SEM images for the same PUF patterns (i.e., under practical scenarios such as, out of focus, inappropriate brightness & contrast). On the other hand, the threshold SSIM of FAKE was determined by calculating SSIM between SEM images of different PUF patterns. Similar calculations were conducted for all five categories. The resulting SSIM distributions of REAL and FAKE were presented in Figure 9f, based on which the SSIM thresholds were set at 0.37, 0.06, 0.08, 0.07, and 0.23 for Gi HD, Gi I2D, G2/IDIID, G2 /2D-2D, and G72D-2D-2D categories, respectively, leading to 100% validation precision for all categories (Figure 10).

As such, to increase the authentication speed, a two-step authentication mechanism involving classification (Step I) and validation (Step II) was developed (Figure 11a). At Step I, the structural features of test PUF pattern were first checked by the DL model to determine whether it was classified into any category within the database. If the classification result is a FALSE (not matched to any), the test pattern will be considered as FAKE directly. On the other hand, if the result is a TRUE (matched to one of the categories within the database), the test pattern will be sent for subsequent pattern validation. At Step II, a direct search-and-compare algorithm based on SSIM comparison is carried out only within the database of a specific subgroup to validate the PUF pattern. If the validation result is a FALSE (not matched to any), the PUF pattern will be concluded as FAKE; if the result is a TRUE (matched to one of the PUF patterns within the subgroup), the test pattern will be finally confirmed to be REAL. Figure lib demonstrates several typical scenarios for the two-step authentication mechanism consisting of DL-accelerated classification and SSIM validation. With the trained DL model and the preset SSIM thresholds, the two-step authentication ensured zero “false -positive” case (i.e., FAKE pattern is mis-authenticated) in the database of 1,760 PUF patterns. Still, 2.9% “false-negative” cases (i.e., TURE pattern fails the authentication) were observed due to low image quality, which can be resolved by taking multiple images for practical authentication situations.

Figure 11 illustrates the synergy between classifiable 2DM PUF patterns and DL-accelerated authentication mechanism enabled the development of DeepKey anticounterfeiting technology (a) A two-step authentication mechanism, involving classification (Step I) and validation (Step II), was developed to accelerate the overall authentication process. Step I was used to classify the input PUF pattern {via DL model), and Step II was to conduct the pattern validation within a narrowed, specific database {via search-and-compare algorithm) (b) Typical scenarios for the two-step authentication mechanism consisting of DL- accelerated classification and validation: (i) HQ PUF pattern that was not in any categories (FAKE), (ii) HQ PUF pattern that was classified into one category yet failed pattern validation (FAKE), (iii) HQ PUF pattern that passed both classification and validation (REAL, with SSIM of 1.00), and (iv) LQ PUF pattern (out of focus) that passed both classification and validation (REAL, with SSIM of 0.43). (c) The DL-accelerated authentication significantly shortened the process time in comparison with direct search- and-compare approach {m times faster, where m is the number of categories) (d) The anticounterfeiting technology demonstrated far higher encoding capacity and shorter processing time compared to state-of-art systems (e) Two layers of information security in a DeepKey anticounterfeiting tag consisting of a 2DM PUF pattern attached to a QR code (both were encoded with product information). Only when the PUF pattern was verified to be REAL by the DeepKey authentication software as well as the revealed product information matched that from the QR code, this product was confirmed as AUTHENTIC, preventing the case of reusing old anticounterfeiting tag.

With the synergy between classifiable 2DM tags and two-step authentication mechanism, a stable anticounterfeiting technology, DeepKey, was developed and featured with ultrahigh encoding capacity (>10 ^144,494 ) and fast authentication time (<3.5 minutes). The structure and components of DeepKey technology are shown in Figure 12; the complete readout and authentication processes are demonstrated in Video SI. Benefited from the DL-enabled classification model, the database for search-and-compare validation was narrowed down, thus the authentication speed was largely increased, leading to a shorter time consumed than the conventional method (by m times, where m is the number of PUF categories in the database, Figure 11c). Based on our current database size (1,760) and CPU model (AMD Ryzen 52600 Six-Core Processor 3.40 GHz), an average authentication time of 1.69 seconds was obtained by our two-step authentication mechanism, which was at least ~5-time faster than that of the conventional search-and-compare validation (11.61 seconds). Meanwhile, because the SSIM algorithm involves every pixel in SEM image as a variable, an ultrahigh encoding capacity >10 ¹⁴⁴ ’ ⁴⁹⁴ was achieved for our 2DM tag, which was higher than those of the state-of-art PUF systems (up to 3xl0 ^{15 051} , Figure lid). Furthermore, without using specialized equipment or complicated characterization setup, the PUF patterns of our 2DM tags were obtained by simply using a benchtop SEM within 3 minutes. As shown in Video SI, the overall processing time (SEM readout + data sync + authentication) was verified to be 3.5 minutes, rather than 2 to 40 minutes estimated for other PUF systems without real showcases.

The high-capacity 2DM tags can be further integrated with other information encoding technologies, such as QR code, to serve as an additional security layer and address the counterfeiting cases of reusing old tags onto forged products. As shown in Figure lie, a QR code (blue box) was used as the first security layer to store the product information, which was read by an optical camera and retrieved by our self-developed DeepKey software. A MXene tag (2 x 2 mm ² , yellow box) was attached onto the bottom right corner of a QR code and served as a covert security layer to further authenticate the product information. The MXene PUF pattern was then captured by a benchtop SEM within 3 minutes, which was then synced and examined by the DeepKey software (based on two-step classification/validation mechanism). Only when the MXene PUF pattern is confirmed to be REAL (passes both classification and validation steps), the product information will be revealed by the DeepKey software. On top of that, only when the information retrieved from QR code and PUF pattern are identical, the product will be confirmed as AUTHENTIC. Any other case will be suspected as COUNTERFEIT.

The present invention also provides a method of authenticating a product comprising a 2DM as disclosed herein, the method comprising: a) classifying the 2DM by comparing with a database; and b) validating the 2DM against the database.

In some embodiments, the method comprises: a) classifying an image of the 2DM using a trained model that is configured to classify images into a category of a plurality of categories of hierarchical structure; and b) determining a similarity of the image to stored images of the same category.

In some embodiments, the method comprises: a) classifying an image of the 2DM using a trained model that is configured to classify images into a category of a plurality of categories of hierarchical structure, to thereby obtain a class label; b) determining respective similarity scores of the image to respective stored images labelled with the class label; and c) outputting a positive authentication result if at least one of the respective similarity scores is greater than a threshold.

In some embodiments, the classification step comprises matching the 2DM with a category in the database. In some embodiments, the category is selected from Gi/1D, Gi I2D, Gi/lDllD, Cn/2D-2D, and G V2D-2D-2D. In other embodiments, the category established based a convolutional neural network with one input layer (PUF patterns), three convolutional layers, three max-pooling (MP) layers, one fully connected (FC) layer, and one output layer. In this regard, if an image of the 2DM falls within a category in the trained model, the image proceeds to the second validation step. If the image does not fall within any category in the trained model, the 2DM and the corresponding product is deemed to be not authentic.

In some embodiments, the validation step comprises searching and comparing the 2DM with the database. In other embodiments, the validation step comprises matching the 2DM with the database by performing weighted measurement between the 2DM and a sample 2DM in the database. In other embodiments, the weighted measurement is based on the structure of the 2DM, and the brightness and contrast of an image of the 2DM. In this regard, by cross- referencing the image of the 2DM to the images in the database, the 2DM and the corresponding product is deemed to be authentic if the image of the 2DM matches with that in the database. If a match is not found, the product is deemed to be not authentic.

In some embodiments, the method can be completed in less than 5 min. In other embodiments, the method is completed in less than 4.5 min, 4 min, 3.5 min or 3 min.

In some embodiments, the method further comprises reading the 2DM using a scanning electron microscope or a 3D laser microscope. The skilled person would understand that the 2DM can be read with any instrument that is able to observe a surface of a material.

To conclude, a scalable, programmable, and generalized fabrication approaches for creation of multigenerational topographies of GO and MXene was developed, which were achieved by applying intermediate in situ treatments between sequential substrate contractions. For example, the intermediate Cl and MIL treatments were developed to adjust the mechanical mismatch and weaken the adhesion energy at 2DM/latex interface, respectively, enabling programmable topographic control in a transfer-free fashion. The Cl treatment was specifically designed for the 2DM units with rich surface functional groups (e.g., GO), while the MIL treatment was more versatile for various 2DM candidates (e.g., GO, MXene). Together with the utilization of both sphere- and tube-shaped balloons, libraries of 2DM topographies were constructed by following pre-programmed deflation sequences with intermediate Cl and/or MIL treatments implemented. In addition, by simply varying the strain release at each deflation step, the feature size (-3-100 pm) of the resulting 2DM hierarchies was able to be further tuned, rendering nearly unlimited freedom in engineering their characteristic features at multiscale.

Benefited from their intrinsic topographic uniqueness, the multigenerational 2DM topographies with high-level characteristics (e.g., structural complexity, deformation type/sequence, feature size) were applied as the PUF secure keys with high encoding capacity (>10 ^144,494 ) for anticounterfeiting. The classifiable features of 2DM topographies were captured by a commercially available benchtop SEM and further recognized by a well- trained DL model, enabling the development of a two-step authentication mechanism composed of classification and validation. Benefited from the fast SEM image capture (readout) and the DL-assisted authentication, the total processing time was significantly shortened (<3.5 minutes) without sacrificing its anticounterfeiting reliability (i.e., zero “false-positive” case). Our 2DM anticounterfeiting tag was further used as an add-on covert layer for conventional information security techniques (e.g., QR code). The DeepKey anticounterfeiting technology demonstrates high practical applicability and well addressed the technological challenge of insufficient environmental stability as well as long processing time required for authenticating complex PUF key-based tags.

Examples

Preparation of TbC2Tx MXene nanosheets

Ti C T _x MXene nanosheets were prepared according to the literature with some modifications. Briefly, 3.0 g of LiF was added to 9.0 M HC1 aqueous solution (40 mL) under vigorous stirring. After the dissolution of LiF, 1.0 g of TLA1C ₂ MAX powders was slowly added into the solution. The mixture was then kept at 36 °C for 24 hours. Afterwards, the solid residue was washed with 2.0 M HC1 solution (3 times) and DI water (5 times) until the pH value reached 7.0. Subsequently, the washed residue was added into 30 mL of DI water, ultrasonicated for 30 minutes, and centrifuged at 3,000 r.p.m. for 20 minutes. The supernatant was finally collected as the final suspension of T1 ₃ C ₂ T _X MXene nanosheets, and the concentration of MXene suspension was about 20 mg mlr ¹ . Further dilution was applied as required.

Cation intercalation (Cl) treatment

Taking graphene oxide (GO) as an example, a 500-nm-thick GO thin film with a diameter of 35 mm was first prepared by filtering 1 mL of 0.5 mg ml ¹ GO aqueous dispersion through a hydrophobic polyvinylidene fluoride (PVDF) membrane (PVDF, 0.22 pm pore size, Merck Millipore). Then, the air-dried GO thin film was cut into certain dimensions, detached from PVDF membrane in ethanol, and transferred onto the plasma-treated latex balloon with certain inflation volume. After evaporation of ethanol, the GO-coated latex balloon was immersed in 0.1 M A1(N0 ₃ ) ₃ aqueous solution overnight. Upon further drying, the Al ³⁺ -intercalated GO (Al-GO) film on latex balloon underwent the specific sequence of deflation(s) to achieve the Al-GO crumples with larger feature sizes as compared to those of the neat GO crumples achieved under the same deflation conditions.

Moisture induced lubrication (MIL) treatment

Taking MXene as an example, a 500-nm-thick MXene thin film with a diameter of 35 mm was first prepared by filtering 1 mL of 1.6 mg ml ¹ MXene aqueous dispersion through the PVDF membrane. Then, the dried MXene thin film was cut into certain dimensions, detached from PVDF membrane in ethanol, and transferred onto the plasma-treated latex balloon with certain inflation volume. After evaporation of ethanol, the MXene-coated latex balloon was kept at low temperature overnight, which was then taken out into the room temperature environment with a relative humidity of 68% to condense moisture layer between the top MXene layer and bottom latex substrate. The MXene-coated latex balloon after the MIL treatment finally underwent the specific sequence of deflation(s) to achieve the MXene buckles with larger feature size as compared to those of the MXene crumples generated from the fabrication processes without MIL treatment. The temperature of MIL treatment could be varied to control the degree of delaminated buckling for tuning the resulting feature size. For example, temperatures of 4 °C and -80 °C can be chosen for the intermediate MIL treatments for the generation of G2 and G3 topographies, respectively, where the latter resulted in larger feature size.

Programmable architecturing of multigenerational 2D-material (2DM) topographies

For the fabrication of multigenerational GO topographies, both Cl and MIL treatments can be used. For example, sphere- and tube-shaped balloons can be adopted, while the tube shaped balloon was specifically required to encode ID wrinkle feature. To obtain Gi topographies, Cl, MIL, or no additional treatment was applied up to the requirement of ultimate patterns. To achieve G2 topographies, either Cl or MIL (at 4 °C) treatment could be applied between the first-second deflations. To fabricate G3 topographies, two routes were applicable: (i) apply Cl and MIL (at -80 °C) treatments between the first-second and second-third deflations, respectively, (ii) apply MIL treatments (at 4 °C and at -80 °C) between the first-second and second- third deflations, respectively.

For fabrication of the MXene multigenerational topographies, MIL treatment was adopted during the sequential deflations of a MXene -coated inflated balloon. Both sphere- and tube shaped balloons can be adopted, while the tube-shaped balloon was specifically required to encode ID wrinkle feature. To obtain Gi topographies, MIL or no additional treatment was applied up to the requirement of ultimate patterns. To achieve G2 topographies, MIL (at 4 °C) treatment was applied between the first-second deflations. To fabricate G3 topographies, MIL treatments (at 4 °C and at -80 °C) were applied in between the first-second and second-third deflations, respectively.

2D crumple features could be obtained by conducting the isotropic deflation of either sphere- or tube-shaped balloons as elastomeric substrates, while ID wrinkle features could be obtained by undergoing ID anisotropic deflation of tube-shaped balloons. The diverse characteristics of hierarchical 2DM topographies, including hierarchical level, feature size, feature type, and deformation sequences, can be programmably tuned by adjusting various fabrication parameters, such as numbers of deflation stages, \ _< v. _\ / \;; at each deflation stage, directions and sequences of deflations. Environmental stability tests

The Gi GO and MXene PUF patterns were characterized before and after their exposures to various harsh treatments, including organic solvent immersion (in DCM for 1 minute), UV light illumination (with wavelength of 254 nm and energy density of 0.12 J cm ^-2 for 1 hour), strong acid immersion (in 6 M HC1 for 1 minute), strong base immersion (in 6 M NaOH for 1 minute), low temperature (at -20 °C for 1 hour), high temperature (at 150 °C for 3 minutes), low humidity (under 0% relative humidity for 12 hours), and high humidity (under 90% relative humidity for 12 hours). In addition, the long-term stabilities of the Gi GO and MXene PUF patterns were verified before and after the exposure to daylight for 30 days.

Convolutional neural network (CNN) deep learning (DL)

Based on Pytorch library, a CNN DL model was built to classify various 2DM PUF patterns. The network consisted of one input layer (PUF patterns), three convolutional layers, three max-pooling (MP) layers, one fully connected (FC) layer, and one output layer (classification model). The output of the last fully connected layer produced a distribution of 5 class labels (Gi/ID, Gi /2D, G i/lDUD, Gi/2D-2D and GT2D-2D-2D). The first convolutional layer filtered the 300 x 200 x 3 input image with 8 kernels of size 5 x 5 x 3 with a stride of 1 pixel, and a MP layer with kernel size of 5 was used to filter its output. The second convolutional layer took the pooled output of the first layer as input and filtered it with 16 kernels of size 5 x 5 x 16, and a MP layer with kernel size of 2 was used to filter its output. The third convolutional layer possessed 32 kernels of size 5 x 5 x 32 connected to the pooled outputs of the second layer, after the filter of a 5 x 5 MP layer, the output of third layer was connected to the last layer, the FC layer, which possessed 32 x 6 x 4 neurons and 5 linear output. NVIDIA Quadro P2000 was used to conduct the calculation.

Calculations of threshold SSIM values for differentiating the REAL and FAKE.

To determine the proper threshold SSIM values for differentiating REAL and FAKE patterns in practical applications, 1,168 SEM images of PUF patterns from five categories taken under diverse practical scenarios were used for SSIM calculations. The threshold SSIM value for REAL was determined by calculating the SSIM between HQ SEM image and corresponding LQ SEM image of the same 2DM PUF pattern (i.e., under practical scenarios, such as out of focus, off brightness & contrast, etc.). The threshold SSIM value for FAKE was determined by calculating SSIM between SEM images of different 2DM PUF patterns.

Determination of threshold SSIM values for validation step.

For Gi/ID category, the SSIM of REAL distributed from 0.212 to 0.920 with the first quartile (Ql), median, and third quartile (Q3) being 0.430, 0.546, and 0.661, respectively. The SSIM of FAKE distributed from 0.022 to 0.368 with Ql, median, and Q3 of 0.069, 0.088, and 0.118, respectively. Based on the SSIM distribution of REAL and FAKE, the threshold SSIM value was set to be 0.37, leading to zero “false -positive” case out of 9,204 cases (i.e., FAKE pattern is mis-authenticated as REAL), while the “false-negative” cases (i.e., REAL pattern fails the authentication) appeared with the rate of 30/196 due to the low image quality.

For Gi I2D category, the SSIM of REAL distributed from 0.053 to 0.883 with Ql, median, and Q3 being 0.519, 0.656, and 0.760, respectively. The SSIM of FAKE distributed from 0.000 to 0.050 with Ql, median, and Q3 of 0.011, 0.016, and 0.021, respectively. As such, the threshold SSIM value was set to be 0.06, leading to zero “false -positive” case out of 9,048 cases, while the “false-negative” cases appeared with the rate of 6/192 due to the low image quality.

For G21 ID- ID category, the SSIM of REAL distributed from 0.137 to 0.179 with Ql, median, and Q3 being 0.508, 0.644, and 0.727, respectively. The SSIM of FAKE distributed from 0.006 to 0.074 with Ql, median, and Q3 of 0.027, 0.033, and 0.039, respectively. As such, the threshold SSIM value was set to be 0.08, leading to zero “false -positive” case out of 8,892 cases, while the “false-negative” cases appeared with the rate of 6/188 due to the low image quality.

For G2 /2D-2D category, the SSIM of REAL distributed from 0.350 to 0.890 with Ql, median, and Q3 being 0.655, 0.725, and 0.798, respectively. The SSIM of FAKE distributed from 0.000 to 0.061 with Ql, median, and Q3 of 0.018, 0.023, and 0.029, respectively. As such, the threshold SSIM value was set to be 0.07, leading to zero “false -positive” case out of 9,360 cases, and no “false-negative” case appeared (0/200).

For G3 /2D-2D-2D category, the SSIM of REAL distributed from 0.174 to 0.856 with Ql, median, and Q3 being 0.509, 0.617, and 0.702, respectively. The SSIM of FAKE distributed from 0.015 to 0.223 with Ql, median, and Q3 of 0.047, 0.058, and 0.072, respectively. As such, the threshold SSIM was set to be 0.23, leading to zero “false-positive” case out of 9,360 cases, while the “false-negative” cases appeared with the rate of 10/200 due to the low image quality.

In summary, out of the total tested 46,840 cases regarding the second validation step, we achieved zero rate of “false-positive” validation and low "false-negative" rate of 0.1% (52/46,840). Taking the first classification step ((0% + 0% + 7% + 3% + 4%)/5 = 2.8%) into account, the overall “false-negative” rate reaches 2.9% mainly due to the mis-classification at the first step because of low image quality, which could be avoided by taking multiple images of the same tag during practical exploitation.

Characterization and measurements

The surface morphologies of multigenerational GO and MXene topographies and their cross-section information were obtained by using a scanning electron microscope (SEM, FEI Quanta 600), a benchtop SEM (JCM-7000 NeoScope™ Benchtop), and a field emission SEM (JEOL-JSM-6610LV) operated at 15.0 kV. The as-prepared MXene and as-received GO nanosheets were characterized by using a high-resolution transmission electron microscopy (HRTEM, JEOL 2010F). X-ray diffraction (XRD) patterns were recorded by an X-ray diffractometer (Bruker, D8 Advance X-ray Powder Diffractometer, Cu Ka (l = 0.154 nm) radiation) with a scan rate of 2° min ^-1 . Uniaxial tensile tests and delamination tests were conducted by using a Universal Testing System (Instron 5567, Instron, Canton, MA) at room temperature with a 500 N load cell. X-ray photoelectron spectroscopy (XPS) was measured by Kratos AXIS Ultra ^DLD by using a microfocused (100 pm, 25 W) A1 X-ray beam with a photoelectron take off angle of 90°. Regarding the multigenerational GO and MXene topographies presented in Figure 3, the specific fabrication routes are listed below.

GO genealogy

Gi I2D\ One-stage full deflation with \ _< v, _\ of 200%; both sphere- and tube-shaped balloons could be applied.

G _\ l ID : One-stage full deflation with \s of 100%; tube-shaped balloon was applied with uniaxial deflation along its axis direction.

G212D-2D: Two-stage deflations of 200%-200% ( \ _< v, _\ at first stage- \s, _\ at second stage); both sphere- and tube-shaped balloons could be applied; Cl treatment was applied between the first-second deflations.

G212D-1D: Two-stage deflations of 200%- 100% ( \s, _\ at first stage- \s at second stage); tube-shaped balloon was applied for the second-stage uniaxial deflation along its axis direction; Cl treatment was applied between the first-second deflations.

G211D-2D: Two-stage deflations of 100%-200% (As at first stage- \s, _\ at second stage); tube-shaped balloon was applied for the first-stage uniaxial deflation vertical to its axis direction; Cl treatment was applied between the first-second deflations.

G2/IDIID: Two-stage deflations of 100%-100% (As at first stage- \s at second stage); tube-shaped balloon was applied for the first-stage uniaxial deflation vertical to its axis direction and the second-stage uniaxial deflation along its axis direction; Cl treatment was applied between the first-second deflations.

G312D-2D-2D: Three-stage deflations of 200%-200%-200% ( \ _< v, _\ at first stage- \s, _\ at second stage- \s, _\ at third stage); both sphere- and tube-shaped balloons could be applied; Cl and MIL (at -80 °C) treatments were applied between the first-second and second-third deflations, respectively.

G312D-1D-2D: Three-stage deflations of 200%-100%-200% ( \s, _\ at first stage- \s at second stage- \s, _\ at third stage); tube-shaped balloon was applied for the second-stage uniaxial deflation vertical to its axis direction; Cl and MIL (at -80 °C) treatments were applied between the first-second and second-third deflations, respectively. G ₃ /2D-IDIID: Three-stage deflations of 200%-100%-100% ( \ _< v, _\ at first stage- \s at second stage- \s at third stage); tube-shaped balloon was applied for the second-stage uniaxial deflation vertical to its axis direction and the third stage uniaxial deflation along its axis direction; Cl and MIL (at -80 °C) treatments were applied between the first-second and second-third deflations, respectively.

G ₃ 11D\\1D-2D\ Three-stage deflations of 100%-100%-200% (Ae at first stage- \s at second stage- \ _< v, _\ at third stage); tube- shaped balloon was applied for the first and second-stage uniaxial deflations vertical to its axis direction; Cl and MIL (at -80 °C) treatments were applied between the first-second and second- third deflations, respectively.

MXene genealogy

Gi I2D One-stage full deflation with \ _< v, _\ of 200%; both sphere- and tube-shaped balloons could be applied.

G _\ l ID : One-stage full deflation with \s of 100%; tube-shaped balloon was applied with uniaxial deflation along its axis direction.

G212D-2D·. Two-stage deflations of 200%-200% ( \ _< v, _\ at first stage- \s, _\ at second stage); both sphere- and tube-shaped balloons could be applied; MIL treatment was applied between the first-second deflations.

G ₂ /2D-ID: Two-stage deflations of 200%- 100% ( \SA at first stage- \s at second stage); tube-shaped balloon was applied for the second-stage uniaxial deflation along its axis direction; MIL treatment was applied between the first-second deflations.

G2 HD-2D Two-stage deflations of 100%-200% (As at first stage- \SA at second stage); tube-shaped balloon was applied for the first-stage uniaxial deflation vertical to its axis direction; MIL treatment was applied between the first-second deflations.

G ₂ UDIID: Two-stage deflations of 100%-100% (As at first step- \s at second step); tube-shaped balloon was applied for the first-stage uniaxial deflation vertical to its axis direction and the second-stage uniaxial deflation along its axis direction; MIL treatment was applied between the first-second deflations.

G3 /2D-2D-2D: Three-stage deflations of 200%-200%-200% ( \ _< v, _\ at first stage- \ _< v. _\ at second stage- \ _< v. _\ at third stage); both sphere- and tube-shaped balloons could be applied; MIL treatments (at 4 °C and at -80 °C) were applied between the first-second and second-third deflations, respectively.

G3 /2D-2D-1D: Three-stage deflations of 200%-200%-200% ( \ _< v, _\ at first stage- \ _< v. _\ at second stage- \ _< v. _\ at third stage); tube-shaped balloon was applied for the third stage uniaxial deflation along its axis direction; MIL treatments (at 4 °C and at -80 °C) were applied between the first-second and second-third deflations, respectively.

G3 /2D-1D-2D: Three-stage deflations of 200%-100%-200% ( \ _< v, _\ at first stage- \;; at second stage- \ _< v. _\ at third stage); tube-shaped balloon was applied for the second-stage uniaxial deflation vertical to its axis direction; MIL treatments (at 4 °C and at -80 °C) were applied between the first-second and second- third deflations, respectively.

G3 /1D-2D-1D: Three-stage deflations of 200%-100%-200% ( \ _< v, _\ at first stage- \;; at second stage- \ _< v. _\ at third stage); tube-shaped balloon was applied for the first-stage uniaxial deflation vertical to its axis direction and the third stage uniaxial deflation along its axis direction; MIL treatments (at 4 °C and at -80 °C) were applied between the first-second and second-third deflations, respectively.

It will be appreciated that many further modifications and permutations of various aspects of the described embodiments are possible. Accordingly, the described aspects are intended to embrace all such alterations, modifications, and variations that fall within the spirit and scope of the appended statements.

Throughout this specification and the statements which follow, unless the context requires otherwise, the word “comprise”, and variations such as “comprises” and “comprising”, will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

The reference in this specification to any prior publication (or information derived from it), or to any matter which is known, is not, and should not be taken as an acknowledgment or admission or any form of suggestion that that prior publication (or information derived from it) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates.