Finite size scaling of spinodal suppression in confined blends of strongly segregating polymers

Abstract

We report confinement-controlled scaling relations governing the phase behavior of strongly segregating polystyrene (PS)/polydimethylsiloxane (PDMS) blends in thin films. Below a critical thickness h_c, lateral phase separation is completely suppressed, suggesting a transition from in-plane spinodal decomposition to vertical segregation. Systematic experiments reveal an unexpected chain length (N) dependence of the critical thickness, h_c ∼ N^−0.15. To rationalize this behavior, we incorporate the adsorbing surface fields, finite thickness, and quantization of concentration fluctuation modes along the confining direction into the Cahn–Hilliard framework. The model suggests that the adsorption-induced renormalization of the lateral square-gradient stiffness of the PS–PDMS interface may underlie the intriguing chain length dependence of h_c. A direct consequence of the finite film thickness is a shift in the spinodal fraction, following Δϕ_s ∼ h⁻². Experiments, spanning different h and different initial fractions of PDMS ϕ_w, confirm the finite-size scaling for all thicknesses larger than the unperturbed molecular dimensions of the PS matrix. Together, these results establish confinement-controlled scaling laws for the phase behavior of strongly segregating mixtures.