Free Energy of Distorted Polymer Films in Highly Confined Three-Dimensional Systems

Abstract

We present a calculation of the free energy for an isotropic polymer film deformed according to a sinusoidal perturbation. Our calculation is for two cases. One is for polymer film/substrate structure that requires a simple extension of the earlier two-dimensional case of Fredrickson et al. As expected, the calculation shows that the wave vectors in x and y directions are reduced to one simple wave vector, q = (q(x)(2) + q(y)(2))(1/2). The other is for polymer film/substrate/poly(dimetliylsiloxane) (PDMS) wall structure, which is the geometry of our recent experiment. For this laterally confined system, the free energy is dominated by two wave vectors, q and q(1) where q(1) is given by q(1) = (q(2) + 2/L-2)(1/2) and L is the half channel width. The limiting cases of long and short wavelength regimes of the latter structure are also studied.