High throughput adhesion energy measurements using a roll-to-roll method

Abstract

A device may conduct a roll-to-roll dry transfer experiment. A device may record peeling forces and peeling angles during the roll-to-roll dry transfer experiment. A device may record peeling forces without peeling angles durring the roll-to-roll dry transfer experiment. A device may process the real-time measurements using a peeling front finite element model that assumes a constant web length before and after a peeling front. A device may determine normal stress and shear stress in adhesion elements of the peeling front finite element model. A device may determine a maximum failing state of the adhesion elements based on the normal stress and the shear stress. A device may determine an adhesion energy based on the maximum failing state.

Description

HIGH THROUGHPUT ADHESION ENERGY MEASUREMENTS USING A ROLL-TO-ROLL METHODCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit ofU.S. Provisional Patent Application No. 63 / 665,100 filed on June 27, 2024, the entire contents of which are incorporated herein by reference.GOVERNMENT LICENSES RIGHTS

[0002] This invention was made with government support under Grant No. CMMI2041470 awarded by the National Science Foundation. The government has certain rights in the invention.BACKGROUND

[0003] This disclosure relates to roll-to-roll dry transfer systems. More specifically, this disclosure relates to the determination of adhesion energy in roll-to-roll dry transfer systems.SUMMARY

[0004] In some aspects, the techniques described herein relate to a method of determining adhesion energy, the method including: conducting a roll-to-roll dry transfer experiment; recording peeling forces with or without peeling angles measurements during the roll-to-roll dry transfer experiment; processing the recorded peeling forces using a peeling front finite element model that assumes a constant web length before and after a peeling front; determining normal stress and shear stress in adhesion elements of the peeling front finite element model; determining a maximum failing state of the adhesion elements based on the normal stress and the shear stress; and determining an adhesion energy based on the maximum failing state.

[0005] In some aspects, the techniques described herein relate to a method, wherein conducting a roll-to-roll dry transfer experiment includes conducting multiple experiments including different peeling forces.

[0006] In some aspects, the techniques described herein relate to a method, wherein recording peeling forces and peeling angles includes recording a relationship between the peeling forces and peeling angles.

[0007] In some aspects, the techniques described herein relate to a method, wherein recoding peeling forces includes recording a tension in a web using a tension sensor.

[0008] In some aspects, the techniques described herein relate to a method, wherein recording peeling angles includes processing image information received from a camera.

[0009] In some aspects, the techniques described herein relate to a method, wherein recording peeling forces and peeling angles occurs when the peeling front is in steady state.

[0010] In some aspects, the techniques described herein relate to a method, wherein the peeling forces and the peeling angles are the only variables input into the peeling front finite element model.

[0011] In some aspects, the techniques described herein relate to a method, wherein determining an adhesion energy occurs concurrent with the experiment.

[0012] In some aspects, the techniques described herein relate to a method, wherein recording peeling angles includes determining a linear first web section tangential to a first roller and a linear second web section tangential to a second roller.

[0013] In some aspects, the techniques described herein relate to a method, wherein determining an adhesion energy includes averaging a plurality of maximum failing states determined over a plurality of experiments.

[0014] In some aspects, the techniques described herein relate to a method of determining a peeling angle without the use of imaging techniques, the method including: assuming an adhesion energy of a roll-to-roll dry transfer process; determining a roller diameter of the roll-to-roll dry’ transfer process; recording peeling forces during the roll-to-roll dry transfer process; generating a peeling front finite element model of webs adhered together; applying the assumed adhesion energy’, roller diameter, and peeling forces to the peeling front finite element model; determining the peeling angle and adhesion energy based on outputs of the peeling front finite element model.

[0015] In some aspects, the techniques described herein relate to a method, further including determining a peeling front location based on outputs of the peeling front finite element model.

[0016] In some aspects, the techniques described herein relate to a method, wherein the peeling front finite element model defines a first pinned end of the webs adhered together and applies the peeling forces to a second free end of the webs adhered together.

[0017] In some aspects, the techniques described herein relate to a method, wherein the peeling front finite element model assigns fixed beam lengths before and after a peeling front until a match between the peeling forces and beam asymptotes is achieved.

[0018] In some aspects, the techniques described herein relate to a method, further including: enumerating a peeling angle difference of a first web and a second web () between zero and 180 degrees; solving a structure deformation based on the peeling angle difference; determining an energy of a maximum failing state in a cohesive zone; and correlating the recorded adhesive energy and the determined energy of the maximum failing state in the cohesive zone, wherein determining the peeling angle includes the correlation of the recorded adhesive energy and the determined energy of the maximum failing state in the cohesive zone.

[0019] In some aspects, the techniques described herein relate to a method, wherein the peeling front finite element model is based on beam asymptotes defined by tangents of the roller diameter.

[0020] In some aspects, the techniques described herein relate to a non-transitory computer readable media having computer-executable instructions embodied therein that, when executed by a circuit of a roll-to-roll dry transfer system, causes the roll-to-roll dry transfer system to perform functions including: recording peeling forces and peeling angles; processing the recorded peeling forces and peeling angles using a peeling front finite element model; determining normal stress and shear stress in adhesion elements of the peeling front finite element model; determining a maximum failing state of the adhesion elements based on the normal stress and the shear stress; and determining an adhesion energy based on the maximum failing state

[0021] In some aspects, the techniques described herein relate to a non-transitory computer readable media having computer-executable instructions, wherein the functions further include: determining the adhesion energy with only the peeling forces and the peeling angles as variables input into the peeling front finite element model.

[0022] In some aspects, the techniques described herein relate to a non-transitory computer readable media having computer-executable instructions, wherein the functions further include: determining adhesion energy' concurrent with recording peeling forces and peeling angles.

[0023] In some aspects, the techniques described herein relate to a non-transitory computer readable media having computer-executable instructions, wherein the functions further include:determining the adhesion energy based on an average of a plurality of maximum failing states determined over a plurality7of experiments.

[0024] This summary is illustrative only and is not intended to be in any way limiting. Other aspects, features, and advantages of the devices or processes described herein will become apparent in the detailed description set forth herein, taken in conjunction with the accompanying figures, wherein like reference numerals refer to like elements.BRIEF DESCRIPTION OF DRAWINGS

[0025] The device is explained in even greater detail in the following drawings. The drawings are merely exemplary7and certain features may be used singularly or in combination with other features. The drawings are not necessarily drawn to scale.

[0026] Fig. 1. (a) Schematic of a R2R peeling process, (b) A detailed view of the peeling front geometry7.

[0027] Fig. 2. (a) Schematic of a R2R peeling process without bending, (b) bending of the web sections during the R2R process.

[0028] Fig. 3. The R2R mechanical peeling system.

[0029] Fig. 4. The composite sample structure in the R2R graphene peeling process.

[0030] Fig. 5. (a) R2R peeling front progression of a graphene sample of 8 cm wide, (b) realtime tension measurements during peeling, and (c) the adhesion energy estimation.

[0031] Fig. 6. (a) R2R peeling front geometry at different graphene sample widths, and (b) corresponding bending radius measurements.

[0032] Fig. 7. (a) Plot of U2 / (Adl *b), where U2 is the potential energy changes due to the work done by the external tension forces. The image in the figure shows the dimension of the graphene- on-copper sample, (b) Plot of U4 / (Adl *b), where U4 is the bending energy change during the peeling process. The image shows the measurement of the bending radii, (c) Adhesion energy without the bending effect correction, (d) Adhesion energy with the bending effect correction.

[0033] Figure 8a) Two peeling front simulation results with different peeling forces, b) Finite element modeling of peeling front, c) Simulated adhesion forces (energy) in different cohesive elements, d) Identical configuration with rotated peeling forces.

[0034] Figure 9 is a schematic representation of a roll-to-roll dry transfer system, according to some implementations.DETAILED DESCRIPTION

[0035] Following below are more detailed descriptions of concepts related to, and implementations of, methods, apparatuses, and systems for estimation of adhesion energy. The figures illustrate exemplary implementations in detail and the present disclosure is not limited to the details or methodology set forth in the description or illustrated in the figures. The terminology used herein is for the purpose of description only and should not be regarded as limiting.

[0036] Generally, implementations of this disclosure estimate adhesion energy between two substrates in a roll-to-roll (R2R) process, thus achieving a high throughput rate. The method and device can also be used to transfer materials from one substrate to another in an R2R fashion. For adhesion measurements, typical techniques all operate in discrete processes, measuring one sample at a time. The methods, apparatuses, and system described herein measure the adhesion energy in a continuous process. The materials can be either long webs or samples mounted on long webs. The R2R adhesion energy measurement method also includes a sophisticated mathematical algorithm, which allows the adhesion energy to be estimated with only web tension and speed measurements. No measurements are needed to measure web curvatures during the peeling process. This allows adhesion energy’ to be measured in a fast and high throughput fashion. In some examples, the throughput of systems described herein is one-hundred times faster than ty pical processes. It also allows adhesion energy to be estimated online and in real time in a R2R material transfer process.

[0037] Adhesion energy determines the bonding strength of adhesives and coatings to their substrate material. It in turn determines the energy required to peel them off the substrate that they are bonded to. Therefore, the tension forces required to peel the adhesives and coatings, together with other information, can be used to deduce the adhesion energy. Using a roll-to-roll process, the adhesion energy of rolls of material, or adhesion samples mounted on a carrier film, can be measured in a high throughput fashion in real-time.Graphene Example

[0038] 1. Introduction

[0039] The interfacial adhesion energy of as-grown graphene on its metal growth substrate is an important variable in designing, monitoring, and controlling a roll-to-roll (R2R) graphene transfer process using mechanical peeling. In this study, we develop a novel method to estimate the adhesion energy of as-grown graphene during the R2R dry transfer process. An energy balance model is established to derive the adhesion energy based on web tension and bending curvature measurements. Experiments were conducted under various mechanical peeling conditions. The adhesion energy of as-grown graphene on copper foil was determined to be from 1.22 J / m2to 2.58 J / m2depending on the peeling front geometry. The developed adhesion energy estimation method is compatible with the R2R process and can be used to monitor and control the large-scale graphene transfer process with in-process measurements.

[0040] Graphene grown on catalytic metal via chemical vapor deposition (CVD) has been envisioned for many advanced applications such as wearable electronics, solar cells, and flexible displays. Large-scale graphene growth on copper and nickel has been demonstrated using a roll- to-roll (R2R) CVD process. After the growth. CVD graphene needs to be transferred from its growth substrate to a target substrate for device fabrication. A R2R dry transfer system was recently developed based on mechanical peeling. Compared with the wet transfer processes, the mechanical peeling process is fast and environmentally benign and does not leave undesirable chemical residues on the transferred graphene. Furthermore, the dry transfer process allows reuse of the metal substrate for graphene growth, reducing the overall fabrication cost.

[0041] In a R2R dry transfer system, the interfacial adhesion energy between the as-grown graphene and its growth substrate is an important parameter that needs to be determined for designing, monitoring, and controlling the mechanical peeling process.

[0042] Previous techniques for adhesion energy measurement relied on special configurations and procedures that are not compatible with the R2R process. More importantly, previous studies all focused on a quasi-static measurement methods that cannot be used for in-process adhesion energy estimation. As the adhesion energy could vary due to process conditions such as peeling angle and peeling speed, a method to estimate the adhesion energy during the R2R mechanical peeling process is needed for monitoring and controlling the R2R dry transferred graphene. In this study, we develop a novel approach to determining the adhesion energy of as-grown graphene using real-time in-process measurements. An energy balance model is developed that includes the web bending effect in the R2R process. Experiments were conducted with graphene-on-copper samples of different sizes to introduce various adhesion force conditions. To our knowledge, thisis the first study to report the adhesion energy of as-grown graphene with a R2R configuration. It provides a method to estimate a key process variable that can be used for monitoring and control of the large-scale graphene transfer process.

[0043] 2. Energy balance in a R2R dry transfer process of graphene

[0044] For R2R dry transfer of graphene, a layer of polymer is first laminated onto graphene on metal foil. The laminate is then sandwiched between two carrier films and loaded on an unwinding roller. After peeling, graphene is transferred to the polymer film and collected by a rewinding roller. The metal foil is collected by another rewinding roller. Fig. 1 shows a schematic of the R2R dry transfer process. Fig. 1(a) shows that the incoming laminate is peeled with two guiding rollers, whose radius is denoted as R. The unwinding roller speed is denoted as and the linear film speeds before and after peeling are denoted as Vi. V2 and V3. respectively. Correspondingly, the tension forces are denoted as Ti, T2, and T3 and the resulting elastic strains in each of the films as si, £2 and £3, respectively. Fig. 1(a) also shows the composition of the web sections before and after peeling. The sample preparation and loading procedure will be described later in the experimental setup section. Fig. 1(b) shows geometric configuration of the peeling front. The peeling angle 0 is defined as the angle between T2 and T3. The angle a is defined as the angle between tensions Ti and T2. The extension line of Ti further divides the peeling angle into 0i and O2.

[0045] For the peeling process to be feasible, the energy release rate G of the peeling action should be equal to the adhesion energy T. The adhesion energy T characterizes the bonding strength between the two materials at the interface. As shown in Fig. 2(a), three terms of energy' are included: the energy dissipated due to the creation of a new interface area (Ui), the potential energy change due to the work done by the external forces (U2). and the elastic potential energy due to the change of strains in the films during the peeling process (U3). Consider that a small peeling length Adi is created under tensions Ti, T2 and T3 with peeling angles 0i and 02. The energy dissipated due to the creation of a new interface area Ui can be expressed as

[0046] Ui = - TbAdi [1]

[0047] where b is the width of the web. The potential energy changes due to the work done by the external forces U2 can be defined as

[0048] U2 =T2Adi( 1 - cos 02 +E2 - EI) + TsAdi(l - cos 0i +£3 - £1) [2]

[0049] The elastic potential energy due to the change of strain in the films during the peeling process U3 is given by

[0051] where he and he are the thicknesses and E2 and Es are the elastic moduli of the corresponding web section. The above formulation did not consider the web bending effect in the R2R mechanical peeling process. In reality, however, all three web sections before and after the peeling point will bend due to the complex force balance condition in the peeling process. A more realistic peeling front geometry' is shown in Fig. 2(b). The curvature due to bending of the unpeeled section is denoted as Ki, and those of the peeled sections are denoted as K2 and K3, respectively. The bending effect of a hyper-elastic film in a mechanical peeling process is substantial, and the bending energy can be expressed as

[0052] Ub= ^-EbIbK [4]

[0053] where Kb is the curvature. Eb is the elastic modulus, and lb is the moment of inertia of the film. When a new surface is created, the curvature of the unpeeled web section is changed from Ki to K2 and K3 after peeling. Therefore, the potential energy' changes due to bending during the peeling process can be expressed as

[0055] where the subscripts indicate the web sections as shown in Fig. 2. Based on energy conservation, which requires SUi = 0, for i = 1 to 4, the adhesion energy' can then be obtained as

[0057] Unlike classic adhesion mechanics formulation, the above energy balance model considers the R2R peeling geometry, strain energy stored in flexible substrates, and the film bending effect during the peeling process. The angles in the above equations 0 and a can be determined based on the force balance equations below.

[0058] T2+T3 cos 0 + Ti cos a = 0 [7]

[0059] Ti sin a=Ta sin 0 [8]

[0060] where 0=0i + 02 [9]

[0061] a=ir - 02

[0010]

[0062] 3. Experimental setup

[0063] Experiments were conducted on a lab-built R2R testbed as shown in Fig. 3. The unwinding roller was driven by a NEMA 23 stepper motor (1- DM542S-23HS45), while the rewinding rollers were driven by two brushless DC motors (Aerotech BM130). Three of the idler rollers were instrumented with cantilevered load cells (MAGPOWR CL- 1-50) to measure web tensions. A digital camera was used to measure the film bending during the R2R peeling process. Two feedback controllers were implemented to track the tension set-points of T2 and T3 independently. The web speed at the unwinding roller was controlled by the stepper motor. Both tension forces T2 and T3 were set at 5 N in this study. The linear speed of peeling was fixed at 1.0 m / min. The graphene samples used in this study were CVD-grown monolayer graphene on copper foil (25 pm thickness) from Grolltex, CA. As-received graphene-on-copper sheets were cut into smaller samples to reduce the material cost of the experiment. The sample size across the peeling direction, defined as sample width, was varied from 2 cm to 10 cm. The sample size along the peeling direction was fixed at 1 cm. The samples were first coated with polyvinyl alcohol (PVA, Mw 9000-10,000 g / mol, 80% hydrolyzed) solution and dried in a vacuum oven. Coated samples were then sandwiched between two rolls of polyethylene terephthalate (PET) carrier film (MYLAR® A, 100 pm thick) with double-sided pressure-sensitive tape (Scotch Tape 6137H). Fig. 4 shows a schematic of the composite structure of the samples after loading onto the carrier films. The sample size and material property parameters are listed Table 1. Based on the equivalent area method, the equivalent flexural rigidity of each web (E2I2 and E3I3) of the composite beams can be determined for graphene-on-copper samples of different widths.Table 1Parameters used in the experimentParameters ValueEPET film 2.7 GPaEcopper film 121 GPaEtape 1.8 GPaEpVA film 0.7 GPa hpET film 100 pm hcopper film 25 pm htape 60.96 pm HPVA film 80 pm bppT 0.1016 m bsample 2, 4, 6, 8, 10 cmRroller 0.0381 m

[0064] 4. Results and discussion

[0065] 4.1. Tension monitoring and adhesion energy estimation

[0066] The results from a R2R dry peeling experiment with a graphene sample of 8 cm wide are shown in Fig. 5. To confirm the successful graphene transfer, Raman spectroscopy and scanning electron microscopy were used to inspect the peeled graphene-on-PVA sample. Fig. 5(a) is a series of still images showing the peeling front progression as the graphene sample going through the peeling process. During the peeling process, the carrier films were pulled away from the guiding roller surface, causing further bending of the web sections. Fig. 5(b) shows the corresponding tension force measurements on the three sections of the web. In the R2R system, the film tensions T2 and Ts were controlled by automatic controllers. Although the initial tensions T2 and T3 were set at 5 N, the tension forces would change due to the peeling action. As shown in Fig. 5 (b), the peeling tensions can be divided into four regions of interest. In region A, the tension forces increase to build up enough strain energy for the peeling process to start. Once the peeling process begins, the tension forces start to drop as shown in region B, with T2 drops more significantly than T3 and Ti. The sudden drop of T2 easily marks the starting point of the peeling process. Region C is the period when the peeling front geometry and tension forces remain relatively stable. After the peeling process is complete, the stretching and bending of the film is suddenly released, resulting in sudden drops and oscillations in the tension forces, as seen in region D. Fig. 5(c) shows the real-time adhesion energy estimate during the R2R peeling process. The curvatures K2 and K3 were obtained based on the bending radius measurements Raand Rb from the peeling front images as shown in Fig. 5(a). It was found that all the elastic strains (si, i = 1, 2, 3) due to tension were substantially smaller than the rest of the terms in Eq. (6). Therefore, the terms of S3 - ei, 82 - 81, and

[0068] in the equation were ignored. In addition, a baseline constant was subtracted from the strain energy to compensate for the friction effect in the R2R system. This baseline constant was obtained by running the R2R system without peeling graphene samples. Although the adhesion energy is plotted for the entire duration of the experimental run in Fig. 5(c), only region C provides meaningful adhesion energy estimation, because it is the only region with stable peeling. All other regions are affected by disturbances such as sudden release of elastic energy due to the start and end of the peeling process.

[0069] 4.2. Effects of film bending on adhesion energy estimation

[0070] The effect of film bending on the adhesion energy estimation was investigated using graphene samples of different widths. Although the same tension force of 5 N was used throughout this study, wider samples generated more bending (Fig. 6(a)) in the two peeled web sections. The digital images were used to measure the bending radius during the peeling process. Fig. 6(b) shows the results of bending radius measurements. When the sample width was small, such as 2 cm and 4 cm, graphene was readily peeled from the copper substrate and almost no additional film bending beyond the curvature of the guiding rollers was observable. When the sample width became larger, in the cases of 6, 8, and 10 cm, the peeling front location shifted away from the nipping point of the two guiding rollers. Larger curvatures resulted in each arm, leading to greater bending effects.

[0071] The adhesion energy' estimation as a function of sample width is shown in Fig. 7. Fig. 7(a) shows the work done by the external tension forces (U2). Correspondingly, Fig. 7(b) shows the strain energy due to bending (U4). As discussed previously, the energy change due to tensile strains (U3) was negligible. Fig. 7(c) shows the adhesion energy estimation without accounting for the bending effect, whereas Fig. 7(d) shows that with the bending effect accounted. As can be seen from Fig. 7(c), if the bending effect was not accounted, the estimated adhesion energy was as high as 100 J / m2, almost two orders of magnitude higher than those reported previously. Such a high value indicates that the strain energy due to bending (LU) plays a significant role in measuring the adhesion energy' and cannot be ignored. After accounting for the bending effect, the adhesion energy was found to be between 1.22 J / m2and 2.58 J / m2, agreeing well with previous studies. Table 2 summarizes the estimated adhesion energy under different sample width conditions. Three samples were measured under each condition. As seen in Table 2, the experimental results in thisstudy suggested dependency of the adhesion energy on the graphene sample width. The adhesion energy initially decreased as the sample width increased from 2 cm to 8 cm. It then almost doubled when the sample width increased to 10 cm. This change is caused by the difference in the peeling front geometry. As seen in Fig. 6(a), when the sample width increased from 2 cm to 10 cm, the peeling angle 9 increased from approximately 20°-130°. From a fracture mode-mix perspective, interfacial toughness often increases with the shear component of the interfacial traction. The shear component decreases as the peeling angle increases when the peeling angle is smaller than 90°. Beyond 90°, the shear component will increase. The adhesion energy trend observed in this study in general is consistent with the fracture mode-mix understanding. However, the relationship between the adhesion energy and peeling angle in the R2R transfer process may be complex and require further investigation in a future study.Table 2Adhesion energy estimateSample width (cm) Average adhesion energy ±Standard deviation (J / m2)(J / m2)2 1.62 ±0.814 1.37 ±0.616 1.22 ±0.218 1.27 ±0.3410 2.58 ±0.63

[0072] In summary, a novel method for estimating the adhesion energy' of as-grown graphene in a R2R dry transfer process is developed. An energy balance model is established to obtain the adhesion energy based on web tension and bending curvature measurements before and after the peeling point. It is found that the film bending effect is a major factor in the strain energy change during the R2R dry transfer process, and thus needs to be corrected in adhesion energy' estimation. After the bending energy correction, the adhesion energy of as-grown graphene on copper foil is estimated to be from 1.22 J / m2to 2.58 J / m2depending on the peeling angle. The method developed in this study provides a unique approach to estimating the adhesion energy of as-grown graphene with a roller configuration. It enables the monitoring and controlling the quality' of transferred graphene using in-process tension measurements in the R2R dry transfer process and paves theway for large-scale graphene applications in multifunctional materials such as those that are both optically transparent and electrically conductive for organic solar cells.A High Throughput Roll-to-Roll Method for Adhesion Energy Measurement Without measured Web Curvatures

[0073] Peeling Front Finite Element Modeling

[0074] As shown in FIG. 8, the deformation of the materials in the peeling front, together with the peeling process, can be modeled using finite element methods. More specifically, 2D corotational Euler-Bernoulli beam elements are adopted to simulate the deformation of materials before and after the peeling front. An updated Lagrangian method is used to track the structure deformed coordinates with geometric nonlinearities (large displacement and rotation of the elements). Meanwhile, the adhesion / fracture between materials is modeled using discrete cohesive zone elements for mixed normal-shear failure modes. Nonlinear adhesion failing behavior is considered for peeling analysis. System peeling angles, bending / tension energy, and peeling front location can be easily simulated and extracted using the developed model, given the system peeling force amplitudes, material mechanical properties, adhesion energy, and roller diameters as inputs.

[0075] It is important to note that mechanical behaviors of adhesion / cohesion and its failure process are extensively studied for bonding / fracture / crack analysis. Different approaches, such as penalization barrier function, spring-damper approximation, traction-separation law etc., have been proposed to simulate the failure of materials / structures in specific patterns but none of them are applied to the peeling mechanics and control in roll-to-roll manufacturing. Here a comprehensive adhesion energy estimation process and a peeling angle modeling framework are first proposed.

[0076] 2. Estimation of Adhesion Energy

[0077] With the proposed model, the adhesion energy' (or the maximum cohesive tensile / shear stress) can be identified with roll-to-roll manufacturing experiments. The estimation process can be divided into following steps:

[0078] Step 1 - Conduct roll-to-roll dry transfer experiments using different peeling force combinations. It is suggested that, for the sake of accuracy, peeling forces pair should beenumerated extensively in the 2D space for its feasible values with appropriate intervals. The same material and adhesive should be used to obtain consistency.

[0079] Step 2 - Record the relation between peeling forces and peeling angles in each of the experiments. Peeling forces, or tensions in webs, can be measured through the tension sensors. The peeling angles can be measured through the camera. The measurement should be taken when peeling front is in steady state.

[0080] Step 3 - Run the peeling front finite element model with the recorded peeling forces and peeling angles, assuming constant web lengths before and after the peeling front. Note that this assumption is made because webs are observed to be mostly straight (or in other words, subject to little bending stress) when approaching points of tangency at rollers. In the finite element model, this can be reproduced by ensuring enough web lengths before and after the peeling front. The modeling results, especially the deformation near the peeling front, should see marginal differences with the parallel moving of the force vectors as long as enough nodes are assigned.

[0081] Step 4 - Extract the normal and shear stress in the adhesion (discrete cohesive zone) elements, identify the maximum failing state, and average it over different simulations. As the peeling of materials happens in real-time in all the conducted experiments, the energy of the maximum failing state in the cohesive zone should be equal with the adhesion energy between materials.

[0082] Taking the two simulation results in Fig. 8a for example, say peeling forces and angles along QiAi, QiBi, and QiCi are measured in a roll-to-roll manufacturing experiment in Step 1 and 2. Then a finite element simulation can be run in Step 3 to reproduce the structure deformation shown as dotted P1A1B1C1. Then the stress state in the cohesive elements, similar to that is shown in Fig. 8c, can be extracted in Step 4 and the energy of the maximum failing state is denoted as the identified adhesion energy in this configuration. The same process can be repeated for different setups, for example Q2P2A2B2C2 to obtain the average estimation of adhesion energy.

[0083] During this adhesion energy estimation process, the bending / tension energy of the structure is inherently considered in the finite element modeling framework. Since the adhesion energy is an independent variable from the peeling configuration, the average of the identified energy states over different experiments eliminates the variation of the uncontrollable factors on adhesion energy. With this physics-based method, a better and more accurate understanding ofthe peeling front mechanics, adhesion failing mechanisms, and their correlation to manufacturing qualities can be achieved.

[0084] 3. Modeling of Peeling Angle

[0085] Besides the adhesion energy estimation introduced in the previous section, the peeling front finite element model can be used to model peeling angles. In this case, the calculation is reversed compared with the last section and the prerequisite now is the knowledge of the adhesion energy, roller diameters, and material properties. The input of the calculation is peeling forces while the peeling angles and the peeling front location are derived based on an iterative process.

[0086] Firstly, the peeled webs are modeled as two beams with (known) equivalent cross section bending / tension properties. As shown in Fig. 8b, the beams are pinned (fixed the x and y displacement) at left ends and are discretized into aligned beam elements. Discrete cohesive zone elements are added betw een the aligned red nodes of the beams to construct the unpeeled material and peeling forces are applied at the right ends of the beams.

[0087] Due to the change of peeling front and points of tangency at rollers in different peeling scenarios, lengths of the webs betw een rollers are not definite for different simulations. The solution here is to assign a fixed and long enough beam lengths before and after the peeling front until the match between peeling forces and beam asymptotes is achieved. In a simpler word, what is actually cared about is the modeling of the web bending near the peeling front. Peeling configurations are not essentially affected if the roller constraints are removed, the w ebs are extended following their roller-tangent directions, and peeling forces are parallelly moved outwards along the webs. This convergence of configuration is achieved here as the simulated angular rotations at the last beam elements share negligible differences from peeling force directions (0.2% in this case) and the bending at the end of the beam is marginal.

[0088] Using Fig. 8a for example, the dotted part of the webs are the part of the structure shares a large bending deformation and the structure beyond the dotted part mainly follows the dashed tangent line to the rollers. Any beam length that covers the dotted part should yield a similar simulation result. Note that the dashed structure Q-ABC is composed of straight webs, which is the configuration calculated through peeling force balance considering no bending effects. While the dotted structure P-ABC is the finite element simulation result and a clear difference can be seen for the exact peeling front position.

[0089] Secondly, simulations are conducted enumerating the peeling angle difference+ 92between zero and 180 degrees. In each of the simulations, the Newton-Raphson method is adopted to solve the structure deformation as displacements / rotations of the elements are geometrically nonlinear. After the deformation converges, the energy of the maximum failing state in the cohesive zone (usually the rightmost cohesive element) is extracted and recorded against the peeling angle difference. By matching or correlating the given adhesion energy with the enumerated cohesive element energy, the peeling angle difference can be determined.

[0090] Here the peeling angle difference (0] + 02)- instead of the specific values of the 2D peeling angle pairs (91and 92), are enumerated because of the pinned boundary condition at the left ends of the structure. Similar to the argument on parallel movements of peeling forces, the configuration of the structure is essentially identical if peeling forces are rotated at the same angle in the same direction (see Fig. 8d). For example, with the same peeling forces, peeling at +60 / -40 degrees gives a rotated but identical structure deformation compared with peeling at +30 / -70 degrees. Note that the same conclusion cannot be achieved with a fixed left boundary.

[0091] Lastly, the geometric constraints of the rollers (roller diameters and center positions) are added and the deformed structure configuration is rotated to match the beam asymptotes with the tangents of rollers. As discussed, the peeling configuration is physically correct when extending web lengths along the web asymptotes or rotating the entire structure. With the given peeling forces and calculated peeling angle difference 9* in last step, the tension and tangent direction of the unpeeled material (red parts of the beams in Fig. 8a) can be calculated based on force balance. Then the upper peeling angle is increased from 180° — 9* to 180° while calculating the distances from two roller centers to three web asymptotes (QA, QB, and QC). The geometric constraints are satisfied when these distances match the corresponding roller diameters.

[0092] Following the prominent fracturing analysis procedure, the determination of peeling angle (the second step above) can also be achieved by extending the cohesive region all the way to the entire beams and incorporating a fracture propagation criterion. More specifically, the beams are assumed to be adhered from left to right and the cohesive elements are added at each aligned node before the simulation. A failure criterion is checked for all the cohesive elements during the simulation: when the normal / shear stress in an element reaches a threshold (related with the adhesion energy) the element is removed from the simulation. While the enumeration of peeling angle is still un-avoidable but can be earned out under some guidance: 1) if no cohesive elements fail and no peeling happens, the peeling angle difference 9r+ 92should be increased; 2) if all thecohesive elements fail and the peeling penetrates all the way to the pinned end at the left, the peeling angle difference 01+ 02should be decreased; 3) if part of the cohesive elements fail and the peeling pauses in the middle of the material, the current peeling angle difference+ 02should be taken and the simulation can be stopped. Theoretically, this approach might share a higher computation time, can be unstable, but gives a same result compared with the proposed procedure. The difference is that the proposed procedure checks the adhesion energy after the enumeration while this approach proceeds both at the same time.As shown in FIG. 9, a roll-to-roll dry transfer system 20 includes a roller assembly 24 structured to move / process webs of material, a controller 28 structured to control operation of the roller assembly 24, a camera 32 positioned to record peeling angles and generate image information, and a tension sensor 36 positioned to record peeling forces including generating tension information indicative of a tension in one or more webs. Referring now to FIG. 9, a schematic diagram of the controller 28 is shown according to an example implementation. As shown in FIG. 9, the controller 28 includes a processing circuit 40 having a processor 44 and a memory' device 48. a control system 52 having a peeling force circuit 56, a finite element analysis (FEA) circuit 60, a stress circuit 64, a fail state circuit 68, and an adhesion energy circuit 72, and a communications interface 76. Generally, the controller 28 is structured to operate rollers and winders of the roller assembly 24 to conduct the roll-to-roll dry transfer process. The controller 28 records peeling forces and peeling angles during the roll-to-roll dry transfer process via the peeling force circuit 56, and processes the recorded peeling forces and peeling angles using a peeling front finite element model of the FEA circuit 60. The FEA circuit 60 assumes a constant web length before and after a peeling front. The controller 28 further determines normal stress and shear stress in adhesion elements of the peeling front finite element model via the stress circuit 64, determines a maximum failing state of the adhesion elements based on the normal stress and the shear stress via the fail state circuit 68, and determines an adhesion energy based on the maximum failing state via the adhesion energy circuit 72. In some implementations, the controller 28 continues operation of the roller assembly 24 and adjusts operation of the in view of the determinations of the control system 52 in real time. The measurements and determinations of the controller 28 are made on-line and allow for continuous optimization of the roll-to-roll dry transfer process. The details of the operations of the control system 52 are discussed in more detail above and all discussions of this disclosure are contemplated as being implemented using the controller 28. In some implementations, the roll-to-roll dry transfer system 20 and the roll-to-roll dry transfer process are using an a graphene manufacturing process.

[0093] In one configuration, the circuits of the control system 52 are in the form of machine or computer-readable media that is executable by a processor, such as processor 44. As described herein, the machine-readable media facilitates performance of certain operations to enable reception and transmission of data. For example, the machine-readable media may provide an instruction (e.g., command, etc.) to acquire data. In this regard, the machine-readable media may include programmable logic that defines the frequency of acquisition of the data (or, transmission of the data). The computer readable media may include code written in any programming language. The computer readable program code may be executed on one processor, multiple co located processors, multiple remote processors, or any combination of local and remote processors. Remote processors may be connected to each other through any type of network (e.g., CAN bus, etc.).

[0094] In another configuration, the circuits of the control system 52 are implemented as hardware units, such as electronic control units. As such, the circuits of the control system 52 may be implemented as one or more circuitry components including, but not limited to, processing circuitry, network interfaces, peripheral devices, input devices, output devices, sensors, etc. In some implementations, the circuits of the control system 52 may take the form of one or more analog circuits, electronic circuits (e.g., integrated circuits (IC), discrete circuits, system on a chip (SOCs) circuits, microcontrollers, etc.), telecommunication circuits, hybrid circuits, and any other type of "‘circuit.’7In this regard, the circuits of the control system 52 may include any type of component for accomplishing or facilitating achievement of the operations described herein. For example, a circuit as described herein may include one or more transistors, logic gates (e.g., NAND, AND, NOR, OR, XOR, NOT. XNOR, etc.), resistors, multiplexers, registers, capacitors, inductors, diodes, wiring, and so on). The circuits of the control system 52 may also include programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like. The circuits of the control system 52 may include one or more memory devices for storing instructions that are executable by the processor(s) of the circuits of the control system 52. The one or more memory devices and processor(s) may have the same definition as provided below with respect to the memory device 48 and processor 44. In some hardware unit configurations, the circuits of the control system 52 may be geographically dispersed throughout separate locations. Alternatively and as shown, the circuits of the controlsystem 52 may be implemented in or within a single unit / housing, which is shown as the controller 28.

[0095] In the example shown, the controller 28 includes the processing circuit 40 having the processor 44 and the memoty device 48. The processing circuit 40 may be structured or configured to execute or implement the instructions, commands, and / or control processes described herein with respect to the circuits of the control system 52. The depicted configuration represents the circuits of the control system 52 as machine or computer-readable media. However, as mentioned above, this illustration is not meant to be limiting as the present disclosure contemplates other implementations where the circuits of the control system 52, or at least one circuit of the circuits of the control system 52, is configured as a hardware unit. All such combinations and variations are intended to fall within the scope of the present disclosure.

[0096] The hardware and data processing components used to implement the various processes, operations, illustrative logics, logical blocks, modules and circuits described in connection with the implementations disclosed herein (e.g., the processor 44) may be implemented or performed with a general purpose single- or multi-chip processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, or, any conventional processor, or state machine. A processor also may be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some implementations, the one or more processors may be shared by multiple circuits (e.g., the circuits of the control system 52 may comprise or otherwise share the same processor which, in some example implementations, may execute instructions stored, or otherwise accessed, via different areas of memory). Alternatively or additionally, the one or more processors may be structured to perform or otherwise execute certain operations independent of one or more co-processors. In other example implementations, two or more processors may be coupled via a bus to enable independent, parallel, pipelined, or multi -threaded instruction execution. All such variations are intended to fall within the scope of the present disclosure.

[0097] The memory’ device 48 (e.g., memory’, memory unit, storage device) may include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage) for storing data and / orcomputer code for completing or facilitating the various processes, layers and modules described in the present disclosure. The memory device 48 may be communicably connected to the processor 44 to provide computer code or instructions to the processor 44 for executing at least some of the processes described herein. Moreover, the memory device 48 may be or include tangible, non-transient volatile memory or non-volatile memory. Accordingly, the memory device 48 may include database components, object code components, script components, or any other ty pe of information structure for supporting the various activities and information structures described herein.

[0098] While various circuits with particular functionality are shown in FIG. 9, it should be understood that the controller 28 may include any number of circuits for completing the functions described herein. For example, the activities and functionalities of the circuits of the control system 52 may be combined in multiple circuits or as a single circuit. Additional circuits with additional functionality may also be included. Further, the controller 28 may further control other activity beyond the scope of the present disclosure. In some implementations, the circuits described herein may include one or more processing circuits comprising one or more memory' devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to perform the operations performed herein and described w ith reference to circuits.

[0099] As mentioned above and in one configuration, the “circuits"’ may be implemented in machine-readable medium for execution by various types of processors, such as the processor 44 of FIG. 9. An identified circuit of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions, which may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified circuit need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the circuit and achieve the stated purpose for the circuit. Indeed, a circuit of computer readable program code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within circuits, and may be implemented in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.

[0100] While the term “processor” is briefly defined above, the term “processor” and “processing circuit” are meant to be broadly interpreted. In this regard and as mentioned above, the “processor” may be implemented as one or more general-purpose processors, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), digital signal processors (DSPs), or other suitable electronic data processing components structured to execute instructions provided by memory. The one or more processors may take the form of a single core processor, multi -core processor (e.g., a dual core processor, triple core processor, quad core processor, etc.), microprocessor, etc. In some implementations, the one or more processors may be external to the apparatus, for example the one or more processors may be a remote processor (e.g.. a cloud based processor). Alternatively or additionally, the one or more processors may be internal and / or local to the apparatus. In this regard, a given circuit or components thereof may be disposed locally (e.g., as part of a local server, a local computing system, etc.) or remotely (e.g., as part of a remote server such as a cloud based server). To that end. a “circuit” as described herein may include components that are distributed across one or more locations.

[0101] Implementations within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.

[0102] For purposes of this description, certain advantages and novel features of the aspects and configurations of this disclosure are described herein. The described methods, systems, and apparatus should not be construed as limiting in any way. Instead, the present disclosure is directed toward all novel and nonobvious features and aspects of the various disclosed aspects, alone and in various combinations and sub-combinations with one another. The disclosed methods, systems,and apparatus are not limited to any specific aspect, feature, or combination thereof, nor do the disclosed methods, systems, and apparatus require that any one or more specific advantages be present or problems be solved.

[0103] Although the figures and description may illustrate a specific order of method steps, the order of such steps may differ from what is depicted and described, unless specified differently above. Also, two or more steps may be performed concurrently or with partial concurrence, unless specified differently above. Such variation may depend, for example, on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations of the described methods could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps, and decision steps.

[0104] Features disclosed in this specification (including any accompanying claims, abstract, and drawings), and / or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and / or steps are mutually exclusive. The claimed features extend to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract, and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0105] As used in the specification and the appended claims, the singular forms “a”, "an", and ■‘the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another aspect includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about”, it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. The terms “about” and “approximately” are defined as being “close to” as understood by one of ordinary skill in the art. In one non-limiting aspect the terms are defined to be within 10%. In another non-limiting aspect, the terms are defined to be within 5%. In still another non-limiting aspect, the terms are defined to be within 1%.

[0106] The terms “coupled”, “connected”, and the like as used herein mean the joining of two members directly or indirectly to one another. Such joining may be stationary (e.g., permanent)or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another. If "coupled" or variations thereof are modified by an additional term (e.g., directly coupled), the generic definition of “coupled7’ provided above is modified by the plain language meaning of the additional term (e.g., “directly coupled” means the joining of tw o members w ithout any separate intervening member), resulting in a narrower definition than the generic definition of “coupled” provided above. Such coupling may be mechanical, electrical, or fluidic.

[0107] Certain terminology' is used in the following description for convenience only and is not limiting. The words “right”, “left”, “lower”, and “upper” designate direction in the drawings to which reference is made. The words “inner” and “outer” refer to directions toward and away from, respectively, the geometric center of the described feature or device. The words “distal” and “proximal” refer to directions taken in context of the item described and, with regard to the instruments herein described, are ty pically based on the perspective of the practitioner using such instrument, with “proximal” indicating a position closer to the practitioner and “distal” indicating a position further from the practitioner. The terminology7includes the above-listed words, derivatives thereof, and words of similar import.

[0108] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises”, means “including but not limited to”, and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary ” means “an example of’ and is not intended to convey an indication of a preferred or ideal aspect. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0109] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below' are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description but is not intended to be exhaustive or limited to the form disclosed. Many modifications and variations will be apparent to those of ordinary7skill in the art w ithout departing from the scope and spirit of the present disclosure.

Claims

What is claimed is:

1. A method of determining adhesion energy, the method comprising: conducting a roll-to-roll dry transfer process; recording peeling forces and peeling angles during the roll-to-roll dry transfer process; processing the recorded peeling forces and peeling angles using a peeling front finite element model that assumes a constant web length before and after a peeling front; determining normal stress and shear stress in adhesion elements of the peeling front finite element model; determining a maximum failing state of the adhesion elements based on the normal stress and the shear stress; and determining an adhesion energy based on the maximum failing state.

2. The method of claim 1, wherein conducting a roll-to-roll dry transfer process includes conducting multiple roll-to-roll dry transfer processes including different peeling forces.

3. The method of claim 1. wherein recording peeling forces and peeling angles includes recording a relationship between the peeling forces and peeling angles.

4. The method of claim 1, wherein recording peeling forces includes recording a tension in a web using a tension sensor.

5. The method of claim 1 , wherein recording peeling angles includes processing image information received from a camera.

6. The method of claim 1. wherein recording peeling forces and peeling angles occurs when the peeling front is in steady state.

7. The method of claim 1, wherein the peeling forces and the peeling angles are the only variables input into the peeling front finite element model.

8. The method of claim 1, wherein determining an adhesion energy occurs concurrent with the roll-to-roll dry transfer process.

9. The method of claim 1, wherein recording peeling angles includes determining a linear first web section tangential to a first roller and a linear second web section tangential to a second roller.

10. The method of claim 1, wherein determining an adhesion energy includes averaging a plurality of maximum failing states determined over a plurality of roll-to-roll dry transfer processes.

11. A method of determining a peeling angle, the method comprising: determining an adhesion energy of a roll-to-roll dry transfer process; determining a roller diameter of the roll-to-roll dry transfer process; recording peeling forces during the roll-to-roll dry transfer process; generating a peeling front finite element model of webs adhered together; applying the recorded adhesion energy, roller diameter, and peeling forces to the peeling front finite element model; determining the peeling angle based on outputs of the peeling front finite element model.

12. The method of claim 11. further comprising determining a peeling front location based on outputs of the peeling front finite element model.

13. The method of claim 11, wherein the peeling front finite element model defines a first pinned end of the webs adhered together and applies the peeling forces to a second free end of the webs adhered together.

14. The method of claim 11, wherein the peeling front finite element model assigns fixed beam lengths before and after a peeling front until a match between the peeling forces and beam asymptotes is achieved.

15. The method of claim 11, further comprising: enumerating a peeling angle difference of a first web and a second web (0! + 02) between zero and 180 degrees; solving a structure deformation based on the peeling angle difference; determining an energy of a maximum failing state in a cohesive zone; andcorrelating the recorded adhesive energy and the determined energy of the maximum failing state in the cohesive zone, wherein determining the peeling angle includes the correlation of the recorded adhesive energy and the determined energy of the maximum failing state in the cohesive zone.

16. The method of claim 11, wherein the peeling front finite element model is based on beam asymptotes defined by tangents of the roller diameter.

17. A non-transitory computer readable media having computer-executable instructions embodied therein that, when executed by a circuit of a roll-to-roll dry transfer system, causes the roll-to-roll dry transfer system to perform functions comprising: recording peeling forces and peeling angles; processing the recorded peeling forces and peeling angles using a peeling front finite element model; determining normal stress and shear stress in adhesion elements of the peeling front finite element model; determining a maximum failing state of the adhesion elements based on the normal stress and the shear stress; and determining an adhesion energy based on the maximum failing state18. The non-transitory computer readable media having computer-executable instructions of claim 17. wherein the functions further comprise: determining the adhesion energy with only the peeling forces and the peeling angles as variables input into the peeling front finite element model.

19. The non-transitory computer readable media having computer-executable instructions of claim 17, wherein the functions further comprise: determining adhesion energy concurrent with recording peeling forces and peeling angles.

20. The non-transitory computer readable media having computer-executable instructions of claim 17, wherein the functions further comprise:determining the adhesion energy based on an average of a plurality of maximum failing states determined over a plurality of experiments.

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