Concentration-dependent transport in finite sized composites: Modified effective medium theory

Abstract

Current models for transport in dispersions, while grounded in well-established effective medium theory (EMT), rely on the assumption of uniformity of the driving force. As consequence, theoretical approaches cannot accommodate driving force inhomogeneities as well as variations over the space occupied by the dispersed phase particles, and existing EMT-based models therefore fail to represent finite particle size effects. Moreover, because transport coefficients are generally considered uniform, such models largely pertain to the Henry's law region. Here, using the context of permeation in mixed-matrix membranes (MMMs), we introduce a self-consistent theory for transport in dispersion-based composites, which captures effects of isotherm nonlinearity and dispersant size without introducing fitting parameters, and accurately predicts concentration-dependent permeabilities. The model is validated against rigorous 3d simulations of transport in filler-polymer composite MMMs, with excellent agreement between theoretical results and those from simulation. Both model and simulations confirm isotherm nonlinearities to have a very significant effect on effective MMM permeability, which is found to be more sensitive to isotherm nonlinearity in the filler phase than in the continuous phase. These effects disappear when the filler phase is much more permeable than the continuous phase, although additional system size effects related to exclusion regions at the ends due to finite particle size lead to decrease in permeability with increase in particle size even for linear isotherms.