Modeling of transport of small molecules in polymer blends: Application of effective medium theory

Abstract

This article concerns itself with the prediction of effective diffusion coefficients of small permeants in binary polymer blends of varying degrees of miscibility and microstructural order. Several models have been critically evaluated with the help of previously published experimental data and in terms of consistency of morphological information provided by small permeants serving as morphological probes. Completely random, two‐phase media have been modeled in terms of Effective Medium Theory with the coordination number (z) describing the average morphology. A comprehensive analysis of experimental data has shown a correlation between z and various physical situations. Near the percolation threshold, z attains a maximum value while, above it, z tends to decrease with increasing content of the conductive component. Accurate predictions of effective diffusivity can be made for volume fractions between 0.3 and 0.8 by letting z = 6. Evidence for phase inversion was studied in terms of models with ordered microstructure and transport data.

Ion transport in sulfonated polymers

“…In contrast, the gyroid-forming sample exhibited apparently high morphology factor in the range of 0.6 to 0.7. Although these values are a bit lower than the theoretical expectations of 0.67 (LAM) and 1.0 (gyroid), 89 we can infer that the higher morphology factor of the gyroid-forming membranes is intimately related to the better connectivity of ionic channels along the co-continuous PSS phases in this structure. Thus, the creation of gyroid morphology in the PEMs should be beneficial for improved transport efficiency.…”

Transport-morphology relationships in segmented polybutadiene polyurethanes: 2. Analysis

“…It replaces an actual heterogeneous system with an effective homogeneous system that exhibits the same steady state transport properties as the original composite. Using the value of the pure component properties (diffusivities and solubilities) the overall transport properties (D 0 rr) can be predicted 26 • The model results for the transport of C0 2 , 0 2 and N 2 for the series of segmented polybutadiene polyurethanes are presented in Figures 1, 2 and 3. (Refer to Part 1 for the system description and the experimental results.)…”

Ion Conduction in Microphase-Separated Block Copolymer Electrolytes

“…In contrast, films aligned by magnetic fields were reported to achieve an enhancement in ion conductivity of A =10, 17 which exceeds predictions based on effective medium theory (EMT) that suggest a maximum of A = 2 for polymer blends with heterogeneous structure. 43 The theoretical maximum of A = 2 is achieved from reductions in tortuosity and path length for an already percolated network. We postulate that the enhancement in conductivity larger than A = 2, which was for a magnetically aligned system, was due to the addition of new percolating pathways that participate in ion conduction which was not considered in the theoretical predictions.…”