Experimental evidence for slow theory of mutual diffusion coefficients in phase separating polymer blends

Abstract

Small Angle Neutron Scattering (SANS) is used to study the kinetics of spinodal decomposition of a blend of polymethyl methacrylate (PMMA) with solution chlorinated polyethylene. The early stages of phase separation are quantified using Cahn‐Hilliard theory. Temperature and molecular weight dependences of interdiffusion are studied and it is shown that data can be better interpreted in terms of a wave vector dependent diffusional mobility M(q).

Spinodal nanostructures in polymer blends: On the validity of the Cahn-Hilliard length scale prediction

“…Nevertheless, these results demonstrate that  can confidently be predicted from G''(T), obtained by extrapolated from the one-phase region. Figure 10 shows further SANS data, this time for a 50/50 blend of solution chlorinated polyethylene (SCPE) with PMMAd following a temperature jump to 150°C, inside the LCST [50]. In line with Fig 8 and 9, a clear intensity maximum appears in S(q), whose position remains invariant over the initial time.…”

“…( 14) may not be appropriate as R(q)/q 2 may not be linear with q 2 . Both Binder [20] and Pincus [43] discussed this point and in Higgins et al [50] attempts are made to compare theory with experiment. For the purpose of this review it suffices to note a potential deviation from C-H-C behaviour for high Mw polymers (and thus large Rg) in SANS observations of spinodal decomposition.…”

Stress-Diffusion Coupling and Viscoelastic Effects on Early Stage Spinodal Decomposition in Polymer Solutions

“…Thus the plot of R(q)/q 2 vs q 2 should be linear. However, as shown in Figure 2(b), the plot of R(q)/q 2 vs q 2 does not show the linear relationship but rather a quite remarkable nonlinear behavior as characterized by large downward curvature, in contrast with the CHC prediction and the previous results [20][21][22][23][24] . We investigated possibility that this curvature in the plot of R(q)/q 2 vs q 2 originates from the viscoelastic effects.…”

“…This change in I(q,t) is similar to that in the early stage spinodal decomposition in polymer blends or dilute polymer solutions except for the fact that the peaks here are much broader than others. It is well confirmed [20][21][22][23][24] that the dynamics of the early stage SD can be approximated by Cahn-Hilliard-Cook theory (CHC theory) 19,25,26) . According to the CHC theory, the change in the q-Fourier mode of the scattered intensity I(q,t) at time t can be described by the following equation: ,…”

Phase-Field Simulation of Liquid–Vapor Equilibrium and Evaporation of Fluid Mixtures

“…Several theories have been proposed to derive correct expressions for the flux, among which the “slow-mode theory” and the “fast-mode theory” are the most successful ones. Their names come from the fact that the mutual diffusion coefficient in a binary system is controlled by the slowest component in the “slow-mode theory,” while it is controlled by the fastest component in the “fast-mode theory.” Because the controversy between both theories is not fully resolved yet despite significant efforts, − both have been implemented in the model. The expressions of the mobility coefficients in the liquid phase read for the fast mode as and for the slow mode as Here, the coefficients ω i are related to the self-diffusion coefficients D s, i liq of the material i through the relationship ω i = N i φ i D s, i liq .…”