Finite size scaling of spinodal suppression in confined blends of strongly segregating polymers.
basic_science · Level V
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- Also identified by DOI 10.1039/d6sm00074f.
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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 <i>h</i><sub>c</sub>, lateral phase separation is completely suppressed, suggesting a transition from in-plane spinodal decomposition to vertical segregation. Systematic experiments reveal an unexpected chain length (<i>N</i>) dependence of the critical thickness, <i>h</i><sub>c</sub> ∼ <i>N</i><sup>-0.15</sup>. 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 <i>h</i><sub>c</sub>. A direct consequence of the finite film thickness is a shift in the spinodal fraction, following Δ<i>ϕ</i><sub>s</sub> ∼ <i>h</i><sup>-2</sup>. Experiments, spanning different <i>h</i> and different initial fractions of PDMS <i>ϕ</i><sub>w</sub>, 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.