Periodically Ordered Wrinkles in Gradient Patterned Polymer Stripes

Abstract

We demonstrated a versatile and robust strategy to create spatially defined periodic wrinkles in gradient striped polymer films through the coupled process of controlled evaporative self-assembly (CESA) and mechanically driven surface wrinkling. The mechanical properties of patterned-gradient polymer thin films were investigated by wrinkling methodology in a fast and simple manner. Understanding of the complex wrinkles can provide insights into the growth mechanism of most biological species that can be explained by competition between bending and stretching energies, e.g., leaves with gradient thickness range from the central area to edges. Furthermore, it also benefits a wide range of micro-to-nanotechnologies that strongly depend on the mechanical stability and performance of thin polymer membranes for semiconductor applications.

1. Introduction

Wrinkling in soft materials has received increasing attention due to the ease of using self-organization in such systems to generate well-defined and complex topological features [1]. Spontaneous organization of complex, intriguing, highly ordered structures in simple systems is both arresting and potentially useful in micro-to-nanometer scale technological fields. Wrinkling of thin, high modulus polymer films on a relatively compliant support opens a powerful platform for creating intricate yet well-ordered periodical sinusoidal wave-like patterns that can be controlled and aligned by elastomeric foundation in the surface of the polymer film [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. The periodically riffled structures with characteristic spatial features such as wavelength and amplitude can potentially function as a wide range of practical applications such as diffraction gratings [19,20] and optical sensors [21,22], smart adhesives [23,24,25,26,27], mechanical strain sensors [28,29,30,31,32], microfluidic sorters [33], cell culture surfaces [34], stretchable electronics [35,36,37], thin film metrology [13], etc. In this regard, several pioneering works based upon controlled wrinkling, not as a nuisance but as a ubiquitous platform for creating spatially defined mechanical instabilities, have been reported, including thermally induced wrinkling [2], mechanically driven wrinkling [6,8,9,13], and swelling or drying-mediated wrinkling [5,15]. Most approaches to the formation of wrinkles in selectively patterned areas have been successfully made by the synergy of lithographical techniques for mesoscale patterning of the polymeric thin films and spontaneous wrinkle alignment through well-defined patterns. However, the above-mentioned methods suffer from complex processing steps and high cost. For example, e-beam or deep UV lithography for generating spatially defined capping layers is expensive and sophisticated for its operation and maintenance, although the resulting pattern dimensions are well-controlled. In addition, various topological patterns with different widths and heights require multi-step processing and come with a higher cost. Therefore, fully combining controlled evaporation of confined microfluids as an alternative tool to conventional lithographic technique for generating well-ordered polymer patterns with strain-mismatch induced surface wrinkling may pull off a much simpler and more masterful methodology for structuring of periodic surface wrinkles over patterned areas and provide a new platform for characterizing mechanical properties of patterned polymer films with multi-dimensional scale ranging from micrometers to nanometers. This means that the wrinkles confined in limited areas with a gradient fashion in terms of width and height can be created via a cost-effective and fast method to determine the mechanical properties of various organic or inorganic functional materials including glassy, semicrystalline, conductive or conjugated polymers, block copolymers, graphitic materials, carbon nanotubes, etc., thus establishing a library for characterizing mechanical properties of patterned-gradient polymers.

In the present study, we introduce a simple and robust route to the formation of periodically structured wrinkles in patterned-gradient media enabled by the synergetic process of controlled evaporative self-assembly (CESA) and mechanically driven surface wrinkling. This approach creates a new arena for fundamental studies of how the surface wrinkles can be confined and aligned in patterned areas with gradient fashion in terms of height and width, opening the door to characterization of the material properties of various organic thin film patterns, which would be valuable for designing and implementing flexible and/or stretchable organic electronics.

2. Experimental

We developed a versatile and robust approach for the assembly of periodic wrinkles in gradient patterned areas using the process schematically summarized as 1% tensile d in Figure 1. Our approach is in complete contrast to previously reported studies on the wrinkling behaviors of heterogeneously patterned films produced by stamping [38] or lithographic patterning [39], which can barely produce thickness-gradient patterned films.

Wedge-on-Flat Geometry and CESA: A wedge-shaped lens made of aluminum and a flat Si wafer with 2 nm thick native silicon oxide were used as the upper and lower surfaces, respectively, which is called “wedge-on-flat geometry” as shown in Figure S1. The size of the wedge and the wedge height were 1 × 1 cm² (≈the meniscus size) and 1000 µm, respectively. The silicon substrate was vigorously cleaned using a mixture of sulfuric acid and NOCHROMIX, and then clearly rinsed with deionized water and blown dry with nitrogen gas. The wedge-on-flat geometry was placed in a home-made sealed chamber to minimize possible unexpected variables raised from air convection and temperature change during the controlled evaporative self-assembly (CESA) process. Poly(methyl methacrylate) (PMMA, Mn = 534 kg mol⁻¹, PDI = 1.57, Sigma Aldrich, St. Louis, MO, USA) was selected to prepare 0.25 mg mL⁻¹ PMMA toluene solution. Gradient polymer stripes of PMMA are systematically created by controlled evaporative self-assembly (CESA) based on repetitive pinning/depinning cycles of a three-phase contact line when a drop of polymer solution is forced to evaporate in the wedge-on-flat geometry, as described elsewhere [40,41]. As a result, solvent evaporation is expected to be fastest at the capillary edge. As a volatile solvent becomes depleted, a three-phase contact line at the capillary edge is subject to pinning by spontaneous transportation of nonvolatile polymer molecules from the contact center of the upper wedge and lower flat Si substrate (i.e., “stick”). During this process, the initial contact angle of the meniscus gradually reaches a critical value due to evaporative loss of solvent, at which the depinning force (i.e., capillary force) become larger than the pinning force, causing the contact line to jerk toward the wedge/Si contact center (i.e., “slip”) and become arrested at a new position, thereby leaving behind a straight line pattern [40,41,42,43,44,45,46,47].

Wrinkling Formation: The gradient polymer stripes of PMMA are readily transferred onto a soft, elastomeric polydimethyl siloxane (PDMS) substrate (Figure 1c) with uniaxial tensile pre-strain (dL) (Figure 1d). For preparing the PDMS, a Sylgard 184 (Dow Corning, Midland, MI, USA) silicon base and a curing agent were mixed at a 10:1 ratio by weight. Then the resulting mixture was degassed to remove any tiny air bubbles and poured into the petri dish. The PDMS was baked under a vacuum for curing and to evacuate all entrapped air bubbles. After cooling, the cured PDMS was peeled and cut. The PDMS substrate was directly used without additional surface modification such as plasma or oxygen treatment. When the applied tensile pre-strain is released, the gradient polymer stripes begin to wrinkle periodically with a spatially defined wavelength (d), and amplitude (A), as schematically illustrated in Figure 1f. The wavelength of the wrinkles assembled in the patterned-gradient stripes changes linearly with the maximum thickness (h_max) of the polymer stripe (d~h_max).

Characterization of Surface Morphologies: The PMMA stripes formed on the flat Si substrate and the wrinkles were thoroughly examined using an optical microscope (OM; BX51 optical microscope in reflection mode (Olympus, Shinjuku City, Tokyo)) and atomic force microscope (AFM; Dimension 3100 scanning force microscope in tapping mode (Digital Instrument, Santa Barbara, CA, USA)). BS-tap 300 tips (Budget Sensors, Sofia, Bulgaria) with spring constants ranging from 20 to 75 Nm⁻¹ were used as scanning probes.

3. Results and Discussion

Figure 2 obviously visualizes mesoscale wrinkles periodically assembled in the patterned-gradient poly(methyl methacrylate) (PMMA) stripes supported by an elastomeric poly(dimethyl siloxane) (PDMS) foundation. As schematically depicted in Figure 2a, the initial PMMA stripes were in a gradient fashion in terms of thickness (h_max), width (w_s), and center-to-center spacing (λ_c-c), which were measured to be 96 ± 4 nm, 11.4 ± 0.3 µm, and 22.8 ± 0.7 µm at X₁, 78 ± 4 nm, 9.1 ± 0.1 µm, and 16.0 ± 1.7 µm at X₂, 62 ± 3 nm, 8.4 ± 0.2 µm, and 13.8 ± 1.1 µm at X₃, 50 ± 2 nm, 7.1 ± 0.1 µm, and 10.8 ± 0.5 µm at X₄, and 28 ± 2 nm, 4.3 ± 0.2 µm, and 7.1 ± 0.4 µm at X₅, respectively. This gradient fashion can be effectively explained by nonlinear volume loss of the solvent resulting from the imbalance between linear pinning force and nonlinear capillary force during the whole evaporation process [46]. At five regions (i.e., X₁ to X₅) marked in the OM images (Figure 2b–f)), spatially ordered wrinkles were crafted in the patterned-gradient stripes. The slight tilt of the wrinkles is presumably due to a mismatch between the long axis of the PMMA line pattern and the direction of the applied compressive force. AFM measurements confirmed that periodically aligned wrinkles formed over the entire area, more clearly showing a gradual decrease in the wrinkle wavelength with decreasing strip width (Figure 3a–e). All characteristic wavelengths of the wrinkles were determined both in real space using the distance averaged over multiple waves displayed in atomic force microscopy images (Figure 3f–j) and in reciprocal space using a fast Fourier transform (FFT; Figure 3k–o). The wrinkle wavelengths (real space and FFT) at five regions were measured to be 4.6 ± 0.2 µm (4.68 µm) at X₁, 3.6 ± 0.2 µm (3.92 µm) at X₂, 2.8 ± 0.1 µm (3.01 µm) at X₃, 2.2 ± 0.1 µm (1.98 µm) at X₄, and 1.1 ± 0.1 µm (1.05 µm) at X₅. Two-dimensional (2D) FFT analysis of the wrinkled topography assures the improved sensitivity for periodically ordered domains within the gradient polymer stripes. All wrinkle wavelengths were taken at the maximum thickness levels due to gradient divergence of thickness level in a single stripe (i.e., stripes are not uniformly flat, but topologically semi-elliptical), as schematically described in Figure 2a.

Generally, surface wrinkles of a thin film supported by a thick, elastomeric foundation can be well-described using an energy balance between the film bending (~Eh³) and the in-plain substrate deformation (~Eh²). Short wavelengths are suppressed by the sizable bending energy of the thin, stiff film, whereas long wavelengths are suppressed by the large strain energy associated with deformation of the thick, elastomeric foundation [2,3,4,6,13,48]. The characteristic wavelength of the wrinkle, d, is highly expected to be dominant as a function of the initial stripe thickness. A close investigation of the plots displayed in Figure 4a reveals that the wrinkle wavelengths experimentally observed at five regions (solid red circles) show a reasonably close fitting with theoretically predicted values (dotted line) derived from a classic theory $\mathrm{d}=2\mathsf{\pi }{\mathrm{h}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\left({\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{M}\mathrm{M}\mathrm{A}}/3{\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{D}\mathrm{M}\mathrm{S}}\right)}^{1/3}$, where h_max is the maximum film thickness, $\overline{\mathrm{E}}=\mathrm{E}/\left(1-{\mathsf{\nu }}^2\right)$ is the plain strain modulus (2.34 MPa for PDMS and 2.96 GPa for PMMA), E is Young’s modulus (1.8 MPa for PDMS and 2.6 GPa for PMMA), and ν is Poisson’s ratio (0.48 for PDMS and 0.35 for PMMA). Mechanically induced wrinkling instabilities can be readily used for characterizing the elastic modulus of polymer thin films, as reported in a pioneering work by Stafford et al., which was a study about how the elastic modulus of the polymer thin film with thickness gradient fashion can be measured by applying well-established wrinkling mechanics [13]. In Figure 4b, the plain strain moduli of PMMA stripes (${\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{M}\mathrm{M}\mathrm{A}}$) at five regions are plotted against their height levels based on the following equation: ${\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{M}\mathrm{M}\mathrm{A}}=3{\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{D}\mathrm{M}\mathrm{S}}{\left(\mathrm{d}/2\mathsf{\pi }{\mathrm{h}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)}^3$. The plain modulus of the patterned PMMA stripe gradually decreases with decreasing thickness. This trend is consistent with previous work based on continuous glassy polystyrene (PS) and PMMA thin films on PDMS [14]. In this reference work, they experimentally proved that the modulus of the polymer thin films with thickness ranges from 5 nm to 190 nm, and apparently decreased as the film thickness decreased. In Figure 4c, the plain strain modulus ratio of PMMA and PDMS is plotted against the ratio of wrinkle wavelength and thickness. The relationship between the two quantities is well described by a linear dependence and the best-fit power law is 2.98 ± 0.16, verifying the theoretical prediction that ${\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{M}\mathrm{M}\mathrm{A}}/{\overline{\mathrm{E}}}_{\mathrm{P}\mathrm{D}\mathrm{M}\mathrm{S}}~{\left(\mathrm{d}/{\mathrm{h}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)}^3$. A key parameter is the amount of strain required to induce wrinkling in the system. The critical strain can be calculated by the modulus ratio of the substrate and film as follows: ${\mathsf{\epsilon }}_{\mathrm{c}}=1/4{\left(3{\overline{\mathrm{E}}}_{\mathrm{s}}/{\overline{\mathrm{E}}}_{\mathrm{f}}\right)}^{2/3}$. It is worth noting that ${\mathsf{\epsilon }}_{\mathrm{c}}$ is not mainly affected by the film thickness. Once strain is externally applied beyond a critical point and thus wrinkles with a specific range of wavelength are formed, the exceeding strain should be accommodated by increasing the wrinkle amplitude (A), whereas the wrinkle wavelength should theoretically remain constant since the wrinkle wavelength is not affected by the amount of applied stress based on a classic theory, not experimentally [48]. In this study, the critical strain for wrinkling formation of the gradient patterned PMMA stripes was calculated to be 0.4% and thus 1% tensile strain was externally applied. In Figure 4d, the wrinkle amplitudes experimentally measured at five regions (solid red circles; 110 ± 7 nm at X₁, 84 ± 5 nm at X₂, 69 ± 6 nm at X₃, 54 ± 5 nm at X₄, and 27 ± 8 nm at X₅) show a reasonable fitting with theoretically predicted values (dotted line) based on a classic theory, $\mathrm{A}={\mathrm{h}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\left({\mathsf{\epsilon }}_{\mathrm{a}}/{\mathsf{\epsilon }}_{\mathrm{c}}-1\right)}^{1/2}$, which is very close to the best-fit power law component (1.09 ± 0.05). All characteristic amplitudes of the wrinkles were determined in real space using the half-depth averaged over multiple waves displayed in the AFM images. The amplitudes of the wrinkles formed in gradient patterned stripes decreased as a function of the maximum stripe thickness, as expected from wrinkling mechanics for constant applied strain [2,3,4,6,13,48].

Well-ordered gradient concentric polymer stripes obtained by controlled evaporative self-assembly (CESA) of a confined microfluid in the curve-on-flat geometry can be readily multi-transferred on to a pre-stretched flexible substrate to generate wrinkles within finite areas. As illustrated in Figure 5, to study confinement of the wrinkles, the first transfer of the CESA PMMA stripes were made and then the second stripes were successively overlaid normal to the axis of the first transferred stripes. Figure 5a shows a schematic cartoon for the formation of PMMA mesh patterns comprised of gradient patterned PMMA stripes double layered onto a pre-stretched PDMS. Compressive force was applied parallel to the axis of the 2nd transferred PMMA stripes, i.e., normal to the 1st transferred PMMA stripes. Figure 5b is a representative optical micrograph of confined wrinkles taken from the overlaid web pattern of the outermost region (X₁) in the 1st transferred stripes and the innermost region (X₅) in the 2nd transferred stripes. As clearly shown in a representative SEM image of Figure 5c,d, the wrinkles were locally confined within the open areas of the 1st transferred PMMA stripes, whereas in intersection areas, no wrinkles were formed. Topological features of the wrinkles strongly depend on thickness and lateral size of the open area of the 1st transferred PMMA stripe. In addition, the number of confined wrinkles decreased with decreasing area. Apparently, only one wrinkle was formed. This is a simple and robust approach to hierarchical assembly of confined wrinkles, dispensing with the need for complex and expensive conventional lithographical or external fields for micro-to-nanometer scale patterning of the target films.

4. Summary

In summary, we successfully demonstrated a versatile and robust route to the formation of periodically aligned wrinkles through the coupled process of controlled evaporative self-assembly (CESA) as a mesoscale patterning of nonvolatile organic elements and mechano-dynamically driven wrinkling originated from the mismatch between equilibrium strains in a thin, stiff epidermis coupled with a relatively softer, thicker dermis. This process serves as a simple and rapid tool for creating topographically defined areas with a gradient fashion in terms of the height on pre-stretched compliant substrate by transferring patterned-gradient polymer thin films onto a pre-stretched elastomeric foundation. The spatially defined moduli-mismatch regions lead to the controlled alignment of surface wrinkles in patterned-gradient polymer films, which is very sensitive to the geometrical feature size of the areas (i.e., thickness), opening a cost-effective and fast method to determine the mechanical properties of various organic or inorganic functional materials including glassy, semicrystalline, conductive, or conjugated polymers, block copolymers, graphenes or graphites, carbon nanotubes, etc. Spatially defined polymer patterns obtained from controlled evaporation of capillary-held microfluids can be further used as templates for generating patterned-gradient metallic wrinkles. The biggest advantage of the proposed approach is to save cost and time.