A novel analytical method for prediction of gas permeation properties in ternary mixed matrix membranes: Considering an adsorption zone around the particles

Mixed Matrix Membranes (MMMs) are composed of dispersed (nano) particles into a continuous polymer matrix with a complex structure. Here, we present a new analytical model for calculation of gas concentration in the MMMs. In this regard, it is determined the gas concentration in the two zones of an MMM including the polymer matrix and the outer surface of a dense nanoparticle which is called adsorption zone. Therefore, mass transfer equations developed for polymer matrix/nanoparticles interface. A 3D model for MMM considered in which the spherical shape dense nanoparticles are randomly dispersed in the polymer matrix. In the vicinity of a nano particle, gas molecules attract to the adsorption zone. Achieved results indicated that when a gas molecule passing from up-to downstream side of an MMM, its concentration changes linearly through the polymer matrix, however changes nonlinearly near to the adsorption zone. Indeed, gas molecules pass the adsorption zone much faster than the polymer matrix and abandon the membrane non-uniformly. It was also concluded that penetrant concentration at the adsorption zone is directly related to the gas diffusion coefficient at the nanoparticle surface (D-adsorp) which is two orders of magnitude higher than gas diffusion coefficient in the polymer matrix (D-p). Moreover, the results showed that at the nanoparticle surface where the theta (azimuthal angle) is equal to zero, the gas concentration has its minimum value. The more molecules adsorb on the nanoparticle surface, the higher concentration gradient between the polymer matrix and the nanoparticle surface is achieved. Gas concentration gradient in the polymer matrix deviates from its linear behavior on the upper hemispherical of nanoparticle surface (which is first facing point of the gas-adsorption zone). In addition, it is observed that the gas concentration at the bottom of the adsorption zone (the lower hemispherical of nanoparticle surface) is higher than that of the polymer matrix in a same width of the membrane because at this zone the gas molecules are desorbed in the polymer matrix again. An important result obtained here is that the concentration gradient in the adsorption zone is much higher than that for the polymer matrix along the membrane width. This makes mass transfer in the absorption zone to be greater than the polymer matrix.