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

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.