Tunable Nanowrinkles on Shape Memory Polymer Sheets

Final page numbers not assigned Researchers have long been fascinated by wrinkles as a pervasive natural phenomenon. Recently, there has been a resurgence of interest in emulating and leveraging wrinkles for various applications. Polymeric wrinkles are finding increased utility as complex quasiperiodic structures important in applications, including cell-fate studies. Flexible integrated circuits promising many new applications, such as wearable systems, have been demonstrated using thin buckled films of single-crystalline silicon based on elastomeric substrates. Metal wrinkles, thin films of metal on polymer substrates, have promise for applications in molecular detection, optical devices, filters and sorters, high-surface-area conductors and actuators, and even metrology. We have developed a rapid approach to create metal nanowrinkles of tunable size and demonstrable utility on a shapememory polymer, pre-stressed polystyrene (PS) sheets commercially available as the children’s toy Shrinky-Dinks. Previous demonstrations of wrinkles exhibited relatively large wrinkle wavelengths. For instance, Bowden et al. deposited metal onto a thermally expanded polydimethylsiloxane (PDMS) polymer; the cooling of the PDMS causes a compressive stress, which buckles the deposited metal film to achieve ca. 30mm structures. Huck et al. augmented this approach with photochemically patterned areas that differ in stiffness and thermal expansion. Watanabe and Hirai more recently developed the very simple approach of simply pre-stretching the PDMS sheet to achieve 6–20mm striped patterns. Lacour et al. used this approach to create stretchable gold conductors. Yoo et al. imposed order on the buckling of polystyrene by applying a physical mold during the buckling process. While this group was able to achieve higher resolution wrinkles than previously reported (down to 2mm periodicity) as well as directionality, the process required a microfabricated mold and took several hours. Here, by just leveraging the stiffness mismatch of materials, we present a simple and ultra-rapid two-step (metal deposition and subsequent heating) method to controllably create nanometer-scale metal wrinkles. First, a 10 nm thick gold film is deposited on the PS sheets. Heating at 160 8C causes the substrates to retract to less than half of its original size and therefore induces the stiffer, nonshrinkable metal film to buckle (Fig. 1a, left). Scanning electron microscopy (SEM) images (Figs. 1b and 2a) show that large areas of uniform biaxial nanowrinkles can be produced. To determine the resulting wrinkle wavelengths, we took the two-dimensional fast Fourier transform (2D FFT, shown in the inset of Fig. 2a) of the SEM images. The resulting disc-shaped power spectral densities indicate a broad distribution of wrinkle wavelength in k-space. From this, we can determine the distribution of wavelengths as a probability function. As shown by the black line in Figure 2b, the prevailing wavelengths peak near 400 nm and range from ca. 200 nm to ca. 1mm. This range is smaller but more heterogeneous than those reported from other approaches, where the wrinkles had periodicities ranging from 20mm to 50mm. As discussed below, we can adjust this broader range to our advantage for sensing applications. In order to tune the wavelength of the wrinkles, it is important to understand how the length scales of the wrinkles depends on the thickness of the metal film, the material properties of the film and substrate, and the overall shrinking strain produced. Wrinkles arise from competition between the elastic bending energy of a stiff skin and the elastic energy of deformation of the soft substrate on which it is supported. For a skin of thickness h and Young’s modulus Yskin supported on a substrate of Young’s modulus Ysub, minimization of the overall elastic energy yields an equilibrium wrinkle wavelength of l/ hh, where h/Yskin/Ysub. For large compressive stresses, it is known that hierarchical wrinkling can occur because the amplitude of the smaller, first generation wrinkles saturate, forming an effective skin that can undergo a similar wrinkling process with wavelengths l/ heffheff, where heff and heff are the parameters corresponding to the new effective skin. For biaxial strains, another critical length scale is the distance j, over which