The Role of Interfacial Morphology in the Gas Transport Behavior of Nanocomposite Membranes: A Mathematical Modeling Approach

Abstract

The presence of polymer–particle interactions in composite materials leads to the formation of interfacial layers with physical properties significantly different from those of the polymer matrix and fillers. Mathematical modeling of the interfacial morphology in mixed matrix membranes (MMMs) not only considerably depends on the assumed interface thickness, but also is related to the applied modeling algorithm. In the current study, a new algorithm is developed to estimate the interface thickness based on findings of molecular dynamics and Monte Carlo simulations in the literature as well as the size and the loading of the particles. Moreover, effective permeability of the MMMs is predicted with no need to evaluate the permeability of the particles and the type of interfacial morphology by only adjusting the reduced permeability factor in the range of −0.5 to 1. On the basis of the proposed modeling approach, characteristic parameters of encapsulated particles by interfacial layer, β and γ, can be simply determined from the corresponding contour line of γ and β for the description of permeability through it. Initially, the effective permeability of composites comprising encapsulated particles by the interfacial layer is assessed by adjusting only one parameter after determining effective interface thickness. The comparison between the predictions and the reported experimental permeability data of 17 series of the MMMs confirmed that the accuracy of the modified Maxwell model based on the proposed modeling approach is more than 95% for more than 90% of the predictions, while the maximum average absolute relative error (AARE) is 8.3%.

Influence of Blend Composition and Silica Nanoparticles on the Morphology and Gas Separation Performance of PU/PVA Blend Membranes

“…Membrane technology plays an important role in reducing the manufacturing cost and energy consumption in industrial processes [1,2,3,4]. For many practical applications, such as CO 2 removal from natural gas or CO 2 /N 2 separation, seeking new materials with high gas permeability and selectivity is great importance [5,6].…”

Determination of maximum possible contribution of porous particles in gas transport properties of their corresponding mixed matrix membranes

“…Consequently, the obtained value of β will be the maximum. As presented in our previous study, [29] F I G U R E 4 Contour line of P ps,opt as a function of β and γ T A B L E 1 Estimation of maximum possible permeability of dispersed porous particles in different polymer matrices using the proposed the optimal values of β and γ are considered to the depth the contour line of P ps,opt as a function of β and γ, Figure 4.…”

“…Ф d , Ф I and Ф 2 are the volume fractions of the particles and interface in MMM and volume fraction of particles in the pseudo-dispersed phase, respectively. After determining l I based on the proposed method in our previous study, by comparing the values of 3δ and D 6 , [29] λ eff is the only unknown of Equation [ (4 ] ). To this end, the percentage of average absolute relative error (% AARE) is calculated for −0.5 ≤ λ eff ≤ 1 as:…”

“…The obtained value for interface thickness may be restricted not only at high particle loadings but also at low loadings of very small particles. Therefore, in the case of restrictions created by the packing of the fillers, by supposing a regular arrangement with no agglomeration for the particles in a cubic structure (see Figure 1), the half maximum distance between the surface of a particle and its six nearest neighbors, D 6 , is considered as interphase thickness and can be calculated as follows [29] :…”

“…As the interfacial layer is difficult to be characterized by experimental techniques, our previous studies indicated that mathematical modeling can be used to gain insight into it. [ 29,30 ] We showed that modeling of the interfacial properties not only significantly depends on the assumed interface thickness but also is related to the modeling algorithm. In that study, a new algorithm was developed to estimate the layer thickness based on findings of molecular dynamics, Monte Carlo simulations, particle size, and loading level.…”