Diffusion‐Controlled, Self‐Organized Growth of Symmetric Wrinkling Patterns

2009 WILEY-VCH Verlag Gmb Compressing a thin film on a compliant substrate can lead to the spontaneous formation of highly ordered patterns, a phenomenon known as surface wrinkling. These self-organized patterns can occur in a variety of morphologies and spatial configurations due to differences in the applied stress state. A common natural example of this phenomenon is human skin, which wrinkles perpendicular to the compressive stress direction when bunched together between two fingers. The same patch of skin, however, will display a spoke-like radial pattern when indented or pulled up at a localized point due to lateral contraction induced by the Poisson effect, demonstrating that the wrinkles prefer to orient themselves perpendicular to the axis of principal compressive stress. Motivated by these observations, we investigate here the initiation, organization, and growth of surface wrinkling patterns in UV/ozone (UVO)-treated polymer films exposed to solvent vapor. In particular, we demonstrate that unique and previously unreported pattern symmetries are formed in response to in-plain stresses caused by localized diffusion of solvent into the film; furthermore, these patterns can be powerful morphological indicators of the kinetics of solvent diffusion within the film. We focus on two distinct anisotropic patterns, namely spokes and targets. These patterns initially develop at random defect sites in the film, and expand until their growth is stopped by neighboring patterns or film boundaries (Fig. 1), analogous to crystallization and other growth processes involving ordering thermodynamic systems and chemical-reaction processes. Our results suggest that the type of pattern and its speed of growth is coupled to the degree of UVO crosslinking, which in turn governs the rate of solvent diffusion into the film. Spoke and target patterns are associated with Fickian and Case II diffusion behavior, respectively, as these kinetic regimes establish distinct stress fields that favor the formation of wrinkles in those specific morphologies. Moreover, we show that precise positional control and long-range ordering of the patterns can be achieved by producing predefined defects in the film. So far, the study of self-organization via wrinkling processes has largely focused on static structures, but this simple yet novel approach is ideally suited for studying the rich dynamics of wrinkling, which could facilitate a broader understanding of the wrinkling phenomenon. This approach could also serve as a test-bed for studying topography-driven phenomena (e.g., wettability and adhesion) and diffusion-related processes. A sketch of the experimental set-up is depicted in Figure 2a. The films used in this study were prepared by spin-casting a solution of polystyrene (PS) in toluene onto a clean silicon wafer. Film thicknesses on the order of hundreds of nanometers were used in order to constrain the system to a 2D diffusion geometry. The surface of the spin-cast film was treated with UVO for a controlled period of time, leading to oxidation and crosslinking of the PS chains in the near surface region. The film was then placed into a closed chamber saturated with toluene vapor at room temperature. Upon exposure to the vapor, the internal osmotic pressure induced by the preferential swelling of the unmodified PS resulted in a net compressive stress in the system. When the stress exceeded a critical threshold value, surface wrinkles began to form with the pattern morphology exhibiting a clear dependence on the length of UVO exposure. A rich variety of patterns was observed by simply varying the exposure time between 2 and 40min; these included flowerlike patterns, spokes, targets, labyrinths, and dots, as shown in Figure 2b. These patterns persisted for several weeks after removal of the samples from the solvent chamber, consistent with the notion that the polymer undergoes viscous flow during wrinkling, and is kinetically trapped in the wrinkled morphology when the PS returns to a glassy state. The characteristic wavelength of the observed patterns as determined from 2D Fast Fourier Transform (FFT) analysis of microscope images was roughly proportional to the UVO exposure time (tUVO). This fact can be understood knowing that with longer exposure times, the bending stiffness (Bf) of the surface layer increases, due to a growth in both its Young’s modulus (Ef; due to densification and crosslinking) and thickness (hf), as Bf Efhf. These changes in the layer have been qualitatively confirmed using X-ray reflectivity. The equilibrium wrinkling wavelength (l) is expected to vary as l hf(Ef/Es) (Bf/Es) , with Es being the Young’s modulus of the swollen PS underlayer. Thus, l increases with tUVO as shown in Figure 2c, similar to previous reports for poly(dimethylsiloxane) treated with oxygen plasma or UVO. We chose to focus on the details of the spatio–temporal ordering of two distinct anisotropic patterns (i.e., spokes and targets). Spoke patterns (Fig. 3a) were generally observed after relatively short UVO exposures (tUVO 3min, under our experimental conditions). Atomic force microscopy (AFM) imaging revealed pattern features that were nanometers in height and micrometers in width. Although the wavelength (l) as measured in the theta direction remained constant, the amplitude