Stiff Thin Film Research Articles

Surface wrinkling of a film coated to a graded substrate

We study the surface wrinkling of a stiff thin elastic film bonded to a compliant graded elastic substrate subject to compressive stress generated either by compression or growth of the bilayer. Our aim is to clarify the influence of the modulus gradient on the onset and surface pattern in this bilayer. Within the framework of finite elasticity, an exact bifurcation condition is obtained using the Stroh formulation and the surface impedance matrix method. Further analytical progress is made by focusing on the case of short wavelength limit for which the Wentzel–Kramers–Brillouin method can be used to resolve the eigenvalue problem of ordinary differential equations with variable coefficients. An explicit bifurcation condition is obtained from which the critical buckling load and the critical wavelength are derived asymptotically. In particular, we consider two distinct situations depending on the ratio β of the shear modulus at the substrate surface to that at infinity. If β is of O(1) or small, the parameters related to modulus gradient all appear in the higher-order terms and play an insignificant role in the bifurcation. In that case, it is the modulus ratio between the film and substrate surface that governs the onset of surface wrinkling. If, however, β≫1, the modulus gradient affects the critical condition through leading-order terms. Through our analysis we unravel the influence of different material and geometric parameters, including the modulus gradient, on the bifurcation threshold and the associated wavelength which can be of importance in many biological and technological settings.

A comparative study on the speed-up dynamics of drop spreading on floating and glass-supported polystyrene thin films

The enhanced spreading of a 2D drop on a stiff and free-standing elastic thin film theoretically investigated by Shanahan (Rev. Phys. Appl. 1988, 23, 1031–1037) has not been studied and verified experimentally. To shed a light on this interesting problem, herein, we perform comparison studies on the spreading behavior of a silicone oil drop on stiff polystyrene thin films supported by two different substrates: glass vs. water. Scaling analysis on the time evolution of the contact radius for the drop spreading on the films of varied thickness (∼40 nm to ∼600 nm) reveals the difference on the dynamics for the drop spreading on glass-supported and floating films. Upon fitting the spreading data by using the spreading model developed by de Ruijter et al. (Langmuir 1999, 15, 2209–2216), we are able to identify the speed-up effect for the drop spreading on water supported floating films, which progressively decreases with film thickness and diminishes when the thickness is greater than ∼200 nm. The elastic driving force that is responsible for the speed-up of the drop spreading on the floating film is evaluated empirically, which is found to decay exponentially with contact radius of the drop. The pre-factor and the decay length of the decay function are determined by film thickness and drop volume, resepctively. Our findings expect to facilitate developing new theories with practical relevance on the spreading dynamics of a liquid drop on elastic films.

Buckling of a Stiff Thin Film Embedded Between Two Compliant Substrates

Layered structures consisting of stiff thin films and compliant matrixes are widely observed in flexible electronics, geology and composite materials. In this work, through analytic modelling and numerical simulations, we investigate the buckling instability of a stiff thin film embedded between two compliant substrates under uniaxial compression. Considering the shear stresses at the film/substrate interfaces and the finite geometry change of the film, the critical compressive strain, buckling wavelength and amplitude of sinusoidal wrinkles are analytically derived by the energy method. The analytic predictions agree well with the results obtained by finite element analysis. The post-buckling morphology may be sinusoidal or multiple-period, depending on the compressive strain and the modulus ratio of two compliant substrates. Our results aid in understanding the buckling of compliant substrate/film/compliant substrate tri-layer structures.

An asymptotic modeling and resolution framework for morphology evolutions of multiple-period post-buckling modes in bilayers

A stiff thin film bonded to a compliant substrate initially buckles into wrinkles, following with some intricate advanced instability modes when the compression exceeds higher thresholds. Here, we present an asymptotic modeling and resolution framework to quantitatively predict and continuously trace secondary bifurcation transitions in the non-linear post-buckling region. An advantage of this framework, besides its applicability to finite-strain deformations, is its asymptotic consistency with the three-dimensional (3D) field equations and interface continuity conditions in a pointwise manner. Based on our model, we reveal intricate post-buckling responses involving successive advanced mode transitions, i.e., period-doubling, period-tripling, period-quadrupling, ridge, and hierarchical wrinkles in film–substrate bilayers upon excess compression. Apart from modulus ratio, pre-stretch and pre-compression of the substrate can alter surface morphology of film–substrate bilayers. With substrate pre-compression, a bilayer may eventually involve into a period-tripling or period-quadrupling mode. We observe hierarchical wrinkles and ridges in films attached on pre-stretched substrates. With high substrate pre-tension and modulus ratio, a novel pattern, namely, periodic ridges, appears at the secondary bifurcation. Fundamental understanding and quantitative prediction of non-linear morphology evolutions of soft bilayers play important roles in rational designs of wrinkle-tunable functional surfaces.

Controlled Bi-Axial Buckling and Postbuckling of Thin Films Suspended on a Stretchable Substrate with Square Prism Relief Structures

Stretchable electronics have spurred rapid developments from curvilinear devices to bio-integrated diagnostic and therapeutic devices. The wavy configuration in the device components on a stretchable elastomeric substrate surface plays a prominent role in simultaneously achieving high areal coverage and stretchability without compromising the electric performance, resulting in unique applications in stretchable and flexible light-emitting diodes (LEDs), batteries, supercapacitors, and photovoltaics. In this study, we investigate the buckling behaviors of stiff thin films on the top surface of a biaxially pre-strained elastomeric substrate with square prism micro-patterned structures. Based on energy minimization, a theoretical model is established to study the buckling profiles and the maximum strain for different pre-strain levels along two directions, which agrees reasonably well with those obtained by the finite element analysis (FEA). After revealing the effect of the center-to-center distance in micro-patterned structures and the interfacial contact width between the film and substrate on the buckling behavior, the elastic stretchability of the system is studied.

Control of Surface Wrinkling through Compliant Nanostructured Interfaces

AbstractSurface wrinkling occurs due to the mechanical instability induced by the stiffness mismatch between a soft substrate and a stiff film. In a two‐layer system comprised of a thick compliant substrate and a thin stiff film, the wrinkle pattern, as described by the wrinkle wavelength, amplitude, and orientation, is limited by the material properties and thickness of the two layers. In this work, an interface layer of nanostructures fabricated by glancing angle deposition (GLAD) is introduced to modify the surface wrinkling of polydimethylsiloxane due to a Cu film, thus enabling improved control of wrinkling in an otherwise constrained material system. Isotropic (nanospring) and orthotropic (nanochevron) Cu interfaces are GLAD‐deposited with different geometric parameters to control the in‐plane stiffness of the interface. The isotropic nanospring films provide a novel means to control the physical length scale of wrinkle patterns, namely, both the wavelength and the amplitude of surface wrinkles, while maintaining the amplitude‐to‐wavelength aspect ratio. The anisotropic nanochevron films result in anisotropy ratio of ≈10 which provides a unique means to modify the wrinkle direction independently of the direction of the applied load. The prediction by the experimentally calibrated analytical model is shown to be in good agreement with the experiment.

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

Wrinkling instabilities occur when a stiff thin film bonded to an elastic substrate undergoes compression. Regardless of the nature of compression, this phenomenon has been extensively studied through local models based on classical continuum mechanics. However, the experimental behavior is not yet fully understood and the influence of nonlocal effects remains largely unexplored. The objective of this paper is to fill this gap from a computational perspective by investigating nonlocal wrinkling instabilities in a bilayered system. Peridynamics (PD), a nonlocal continuum formulation, serves as a tool to model nonlocal material behavior. This manuscript presents a methodology to precisely predict the critical conditions by employing an eigenvalue analysis. Our results approach the local solution when the nonlocality parameter, the horizon size, approaches zero. An experimentally observed influence of the boundaries on the wave pattern is reproduced with PD simulations which suggests nonlocal material behavior as a physical origin. The results suggest that the level of nonlocality of a material model has quantitative influence on the main wrinkling characteristics, while most trends qualitatively coincide with predictions from the local analytical solution. However, a relation between the film thickness and the critical compression is revealed that is not existent in the local theory. Moreover, an approach to determine the peridynamic material parameters across a material interface is established by introducing an interface weighting factor. This paper, for the first time, shows that adding a nonlocal perspective to the analysis of bilayer wrinkling by using PD can significantly advance our understanding of the phenomenon.

Capillary-Induced Wrinkle-to-Fold Transitions Under Biaxial Compression.

Wrinkles in bilayer systems comprising a thin stiff film attached to a soft substrate can globally transition into folds under sufficiently large compression. This phenomenon has been extensively studied primarily using uniaxially compressed systems. However, inducing the wrinkle-to-fold transition at designated locations on a wrinkled surface under small biaxial compression remains a challenge. In this study, we describe a method for causing randomly oriented wrinkles to locally evolve into folds using water droplets. When a droplet comes into contact with the random wrinkles that have spontaneously formed upon film deposition owing to residual biaxial compressive strains, radially extended folds instantaneously emerge at the droplet boundary. Upon water evaporation, the wrinkles beneath the droplet also undergo a transition, leaving a fold network. By contrast, the surface regions distant from where the droplet was placed retain the wrinkle morphology. The folded areas can be controlled by adjusting the volume and number of droplets. These transitions are enabled by the capillary forces of water that help to increase the local compressive strains. This capillary-induced wrinkle-to-fold transition provides a simple mechanism to develop folds in selected locations on wrinkled surfaces of film-substrate systems subject to small biaxial compression, which is unachievable with conventional approaches.

Dynamic stability analysis of stiff films by element-free method with strain-rotation decomposition

Buckling and post-buckling analysis of thin films is significant for the design, optimization and fabrication of stretchable electronic devices based on compression buckling. Aiming to achieve a more accurate and reliable way for the dynamic stability analysis of stiff films considering geometric nonlinearity, an implicit dynamic element-free Galerkin method based on the Strain-Rotation decomposition theorem is developed in this paper to investigate the dynamic buckling behavior of stiff films. Convergence and comparison studies are conducted to validate the numerical stability and accuracy of the proposed numerical method. The influences of compression loading rate and thickness to length ratio on the buckling/post-buckling of stiff thin films subjected to dynamic load are numerically analyzed and discussed in parametric studies. This work provides an effective way for the engineering computation of flexible electronic technology.

Buckling behaviour of a stiff thin film on a finite-thickness bi-layer substrate

In engineering stretchable electronics, an intermediate layer between a thin stiff film and a substrate can enhance the adhesion of the film and modulate its buckling shape. Capturing buckling behaviour of the tri-layer film/intermediate layer/substrate structure is essential for designing stretchable electronics. In this paper, considering the shear stress between the film and intermediate layer and using the complete mathematical form of the longitudinal displacement of the film, an improved theoretical model of the buckled tri-layer structure is established and the total energy of this tri-layer structure is derived. Based on the total energy, two buckling regimes, global (Euler) buckling and local wrinkling, influenced by the intermediate layer, are studied. Since local wrinkling is a desirable buckling pattern for stretchable electronics, accurate solutions of buckling wavelength and critical strain of local wrinkling verified by finite element analysis are determined. The influence of the intermediate layer on the wrinkling instability of the tri-layer structure is analysed. These results will aid in the design and manufacture of film/substrate-type stretchable electronics.

Circumferential buckling and postbuckling analysis of thin films integrated on a soft cylindrical substrate with surface relief structures

As a novel tactic, controlled buckling of the stiff thin film device component on a compliant substrate with surface relief structures has been widely explored in the design and demonstration of various flexible and stretchable electronic devices. While flat substrates are mainly used in the current design and demonstration of the buckled thin film on a structured substrate, the use of cylindrical substrates presents alternative opportunities for this technique with direct applications in multifunctional catheters for the treatment of ventricular tachycardia, primary and metastatic malignancies, as well as various smart wearable devices. In this study, we will present the modeling analysis and design considerations of thin film device components on a soft cylindrical substrate with surface relief structures. By investigating the controlled circumferential buckling and postbuckling behaviors of stiff thin film integrated on a compliant cylindrical substrate with surface relief structures, the buckling/postbuckling amplitude and maximum strain in the thin film are found to depend on various material and geometric parameters. Additionally, the results predicted from the analytic model are validated by the finite element analysis, which provides a powerful toolset to inform experimental designs.

Buckling of a stiff thin film on a bi-layer compliant substrate of finite thickness

The buckling of a stiff thin film on a compliant substrate has been widely studied over the past decade due to its wide applications such as stretchable electronics, micro- and nano-metrology, and surface engineering. Instead of a single-layer compliant substrate, a bi-layer compliant substrate is usually encountered in practical applications. In this paper, the buckling of a stiff thin film on a bi-layer compliant substrate of finite thickness is studied theoretically, numerically and experimentally. The theoretical models based on the small-deformation theory and the simple finite-deformation theory accounting for the geometry change by using the energy method are both developed and presented. The good agreement among theoretical predictions, finite element analysis and experimental measurements of the buckling behavior validates the theoretical model. The influences of finite thickness of the bi-layer substrate and substrate modulus ratio on the buckling wavelength and critical buckling strain are systematically investigated. The buckling configurations at various applied strains are also measured to further validate the theoretical model. These results shed light on the influence of finite substrate thickness on buckling of the bi-layer substrate-supported thin films and are helpful to provide design guidelines in practical applications.

Delamination of Stiff Films on Pressure Sensitive Ductile Substrates

Stiff thin films supported by pressure sensitive ductile solids are an ubiquitous architecture appearing in a wide range of applications. The film rupture and delamination of films are important reliability issues of such an architecture. In this study, we investigate the synergistic effects of plastic deformation of substrates and fracture properties of film/substrate interface on the delamination of films. The focus of this study is on the interplay between the debonding of the interface and the plastic deformation of substrates. Finite deformation analyses are carried out for a stiff film deposited on a soft substrate with the substrate subjected to stretching. The fracture process of film/substrate interface is represented by a cohesive zone model, and the substrate is modeled as an elastic–plastic solid with pressure sensitive and plastically dilatant plastic flow. It is found that increasing the degree of pressure sensitivity of substrate can generate large plastic deformation, promoting crack tip blunting and thereby retarding delamination of film/substrate interface. Whereas, the increase in the degree of plastic dilatancy of substrate gives rise to the limited plastic deformation and leads to poor resistance to interface delamination. The strain hardening of substrate also affects the film/substrate debonding; the substrate with weakly post-yield strain hardening behavior contributes to enhanced resistance to interface delamination. It is further identified that the fracture properties of interface play an important role in activating plastic deformation of substrates. The film/substrate interface with high stiffness, large cohesive strength and high toughness enables the substrate to undergo significant plastic deformation, which suppresses the film/substrate delamination.

Buckling configurations of stiff thin films tuned by micro-patterns on soft substrate

Wrinkling and buckling of stiff film/soft substrate system has great potential applications in many areas, especially in stretchable electronics. Inspired by the micro-patterns to tune the interfacial adhesion strength, a novel way to tune three buckling configurations (i.e., wrinkling, upward and downward buckling) by using the micro-patterns on the soft substrate was found experimentally. The established governing equations to distinguish the three buckling configurations are consistent with the experimental observations. Results show that the geometries of the micro-patterns, the material properties and the interfacial adhesion between the stiff film and the micro-patterned soft substrate can tremendously influence the final buckling configurations. The proposed analytical governing equations can not only clarify the mechanism of the micro-patterns on the tuning of different buckling configurations, but also be used to design the buckling configurations as desired.

Controlled buckling and postbuckling behaviors of thin film devices suspended on an elastomeric substrate with trapezoidal surface relief structures

The wavy structure is a simple, practical, and promising structural design scheme widely used in the field of flexible and stretchable electronics. In the development of the strategies to enable stretchable characteristics in the device, buckling of thin film devices suspended on an elastomeric substrate with surface relief structures provides an alternative tactic for applications that require both high areal coverage and large stretchability without compromising electric performance (e.g., flexible photovoltaics, batteries, supercapacitors, etc.). In this study, we utilize the energy method to reveal the mechanical mechanisms of controlled buckling and postbuckling behaviors of the stiff thin film devices suspended on the elastomeric substrate with trapezoidal surface relief structures. Both two- and three-dimensional models are explored to simulate the buckling behaviors of the thin film devices in the finite element analysis (FEA). Theoretical predictions of the buckling profile and the maximum strain in the thin film devices are compared reasonably well with those obtained from the FEA. The influences of thin film width and the contact width (between the thin film and the structured substrate) on the amplitude and the maximum strain of the buckled thin film devices are discussed. Results show that the amplitude of the buckled thin film device decreases as the contact width increases, whereas the maximum strain in the buckled thin film devices increases with the increasing contact width. The elastic stretchability of the buckled film/substrate system is also discussed. The validated analytic tool provides a powerful basis for further experimental designs.

In Situ Measurement of the Plane-Strain Modulus of the Solid Electrolyte Interphase on Lithium-Metal Anodes in Ionic Liquid Electrolytes

We present an experimental approach for in situ measurement of elastic modulus of the solid electrolyte interphase (SEI), which is formed from reactions between a lithium thin-film [on a polydimethylsiloxane (PDMS) substrate] and a room-temperature ionic liquid (RTIL) electrolyte. The SEI forms under a state of compressive stress, which causes buckling of the sample surface. In situ atomic force microscopy is used to measure the dominant wavelength of the wrinkled surface topography. A mechanics analysis of strain-induced elastic buckling instability of a stiff thin film on a soft substrate is used to determine the plane strain modulus of the SEI from the measured wavelength. The measurements are performed for three RTIL electrolytes: 1-butyl 1-methylpiperidinium bis(trifluoromethylsulfonyl)imide (P14 TFSI) without any lithium salt, 1.0 M lithium bis(trifluoromethylsulfonyl)imide (Li TFSI) in P14 TFSI, and 1.0 M lithium bis(fluorosulfonyl)imide (Li FSI) in P14 TFSI to investigate the influence of lithium salts on the plane strain modulus of the SEI. The measurements yield plane-strain moduli of approximately 1.3 GPa for no-salt P14 TFSI and approximately 1.6 GPa for 1.0 M Li TFSI in P14 TFSI and 1.0 M Li FSI in P14 TFSI. The experimental technique presented here eliminates some of the uncertainties associated with traditional SEI mechanical characterization approaches and offers a platform to engineer an SEI with desired mechanical properties by approaches that include altering the electrolyte composition.

Programmable localized wrinkling of thin films on shape memory polymers with application in nonuniform optical gratings

Shape memory polymers (SMPs) can remember different shapes and can be recovered to their permanent shapes from temporary shapes with appropriate stimuli, such as heat, humidity, and electrical field. Using programmed thermal responsive SMPs as substrates, we demonstrate a self-assembly fabrication method for programmable surface wrinkling within a highly confined area that is accurately controllable. Different from global wrinkling reported in most of the literature, Joule heating through a heating wire embedded in the SMP substrate leads to temperature increase and thus recovery in a highly confined area of the SMP substrate, inducing localized wrinkling of the stiff thin film on SMPs. The patterns show good sinusoidal profiles, with the wrinkling wavelength and amplitude decreasing gradually with the distance from the heat source. The surface wrinkling area can be accurately tuned by controlling the heat input, such as power and duration. Based on this unique surface wrinkling phenomenon, we demonstrate a nonuniform reflective optical grating device, whose peak wrinkling wavelength and amplitude decrease gradually away from the heat source. This study offers a simple method to fabricate programmable localized wrinkling patterns, with potential applications in surface engineering, advanced manufacturing, optical gratings, and other demanding areas.

Controlled bending and folding of a bilayer structure consisting of a thin stiff film and a heat shrinkable polymer sheet

Bending pre-designed flat sheets into three-dimensional (3D) structures is attracting much interest, as it provides a simple approach to make 3D devices. Here we report controlled bending and folding of a bilayer structure consisting of a heat shrinkable polymer sheet and a thin stiff film (not thermally responsive). Upon heating, the prestrained polymer sheet shrinks, leading to bending or folding of the bilayer. We studied the effect of relative dimensions of the two layers on the bending behavior and demonstrated the transition from longitudinal bending to transverse bending of the bilayer strip. Transverse bending was utilized to fold origami structures, including several flat letters, a crane, and a corrugated metal sheet via Miura-ori folding. We developed a method to further control the bending orientation based on bio-inspired anisotropic bending stiffness. By bending the metal foil in different orientations, several structures were obtained, including cylindrical surfaces and left-handed/right-handed helical structures.

Buckling of a stiff thin film on an elastic graded compliant substrate.

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

Buckling analysis of stiff thin films suspended on a substrate with tripod surface relief structure

A wavy configuration is a simple yet powerful structural design strategy, which has been widely used in flexible and stretchable electronics. A buckled structure created from a prestretch-contact-release process represents an early effort. Substrates with engineered surface relief structures (e.g., rectangular islands or tripod structure) have enabled stretchability to the devices without sacrificing their electric performance (e.g., high areal coverage for LEDs/photovoltaics/batteries/supercapacitors). In particular, the substrate with a tripod surface relief structure allows wrinkled devices to be suspended on a soft tripod substrate. This minimizes the contact area between devices and the deformed substrate, which contributes to a significantly reduced interfacial stress/strain. To uncover the underlying mechanism of such a design, we exploit the energy method to analytically investigate the buckling and postbuckling behaviors of stiff films suspended on a stretchable polymeric substrate with a tripod surface relief structure. Validated by finite element analysis, the predications from such an analytical study elucidate the deformed profile and maximum strain in the buckled and postbuckled stiff thin device films, providing a useful toolkit for future experimental designs.