Tailoring Long-range Force Induced Surface Instability Mode Of Soft Solids By Pre-stretch

We consider a kind of soft elastomers with extreme flexibility, taken Polydimethylsiloxane (PDMS) as a representative. Such soft elastomers are wildly used in both daily life and scientific research, due to their excellent material properties.Here we focus on the surface stability of the soft elastomeric substrate with external interactions, which can be sorted into the van der Waals interaction between the surface of elastomer and a rigid contactor, and the uniformly pre-deformation of the elastomer itself. The former facilitates the perturbation on the surface, while the latter inhibits. As a result, it provides a promising way to fabricate well-ordered pattern on the elastomer surface. By a linear analysis, we show how the finite pre-deformation affects the surface morphology of the soft elastomers, and discuss the regulating of the pattern.By applying the theory of nonlinear elasticity, we obtain the equilibrium equations and the boundary conditions in terms of the additional fluctuations in the finitely deformed state taken as the reference configuration. The stress-strain relations of such soft elastomers are discussed in detail, and the stress tensor with respect to the general finite deformation and additional disturbance is derived explicitly.First of all, we study a simple two-dimensional problem under plane strain condition, viz. elastic buckling of an equi-biaxially pre-tensioned soft elastic film due to van der Waals interaction between the surface of film and a rigid contactor. By a linear stability analysis, we reveal the dependence of critical buckling pattern on the pre-tension. And with increasing the magnitude of pre-tension, the critical wave number and corresponding interaction parameter increase. Accordingly the buckling of elastic film can be regulated by equi-biaxial pre-tension.Secondly, we consider the buckling of a uni-axially pre-tensioned soft elastic film due to van der Waals interaction. The uni-axial pre-tension leads to that the film material behaves anisotropically with respect to the reference configuration. It is shown that the film will buckle into stripe parallel to the tensile direction by a linear stability analysis. Moreover the spacing of the stripe pattern decreases with increasing the magnitude of the pre-tension.Then we develop the foregoing discussion into a general case, which is the stability of an elastic film pre-deformed homogeneously due to van der Waals interaction. Consider the surface buckling of an isotropic incompressible soft film, which is deformed uniformly in two perpendicular directions respectively. The expression of the interaction parameter is deduced through a linear stability analysis. Furthermore, we investigate the criterion and pattern of the surface buckling, which are dependent on three principal extension ratios related to the finite pre-deformation. Besides, we take a soft elastomeric film with shear pre-deformation for instance, which is coincident with the general conclusion.Finally, we study the instability of a thin liquid film resting on a uniformly stretched soft elastomeric substrate driven by van der Waals forces by a linear analysis. By adopting the lubrication approximation, the growth rate of a fluctuation of the liquid surface is derived. The corresponding instability criterion has been obtained, and the most unstable mode of the fluctuation has been discussed. It is shown that the pre-stretch stabilize the liquid film in the direction parallel to the tension while destabilize it in other directions. The liquid film is most unstable against the periodic fluctuation normal to the tensile direction with a special wavelength depend on the magnitude of the principal stretch. Therefore, the pre-stretch of the substrate leads to anisotropic dewetting of the thin liquid film, and the degree of anisotropy can be tuned by varying the principal stretch. This phenomenon may be used to create microstructures with elongated features.