(437f) A Novel Universal Diffusion Model for Gas and Solvent Molecules in Polymer
Molecular diffusivity in polymer matrices is a fundamental dynamic physical property, and several models have been developed so far. From the point of molecular motion, gas molecule and solvent molecule must display the same diffusive motions, and therefore fundamentally both of their diffusivity should follow one universal functional form. Moreover, with respect to the model application to real system designs, pure prediction model, which includes no fitting parameter, is required. However, up until now, there have never been both of the universal model and the pure prediction model. These problems can be solved to add microscopic viewpoints into the model. Vrentas-Duda (VD) model is one of free volume models, and is well known as the model that can reproduce experimental values well. However, even VD model contains a fitting parameter ξ and a parameter Do unknown for gas molecules. Thus, VD model cannot treat gas diffusivity in polymer and cannot work as prediction model. These problems result from lack of microscopic viewpoints in the model. In our study, a novel universal diffusivity prediction model was developed by incorporating microscopic viewpoints of molecular motion into free volume model. Here, free volume model is one of the previous models, and its diffusivity expression can be described as follows,
D = Do exp( -v*/vf )
, where Do is pre-exponential factor, v* is core volume, and vf represents free volume per molecule. VD model includes a fitting parameter ξ in vf, and a parameter Do unknown for gas molecules. In this study, the two microscopic concepts, molecular collision and random walk movement, were introduced into the parameters vf and Do. These concepts are the origin of molecular diffusive motion.
First, the microscopic concept of collision frequency was introduced as a concept of ?shell-like free volume? into vf. The shell-like free volume was defined as free space existing around a diffusing molecule. In order to calculate the shell-like free volume, the information about molecular surface area is required, and in this study, was determined using semi-empirical quantum chemical calculation (the method of PM3).
Second, the other microscopic concept of random walk movement was introduced into Do. In VD model, Do was obtained by using pure solvent viscosity data, and thus Do for gas molecule cannot be acquired. In this study, by regarding Do as self-diffusivity of random walk movement with a jumping width of molecular diameter, Do for gas molecules could be also determined.
Both of the focused parameters, shell-like free volume and Do, can be determined using only pure component parameters. Therefore, the newly developed model can universally predict diffusivity for both of gas and solvent molecules in many polymer matrices without using any fitting parameter. The comparison between experimental and predicted values ascertained sufficient predictive property of the present model. This model will provide valuable diffusive properties for wide application areas.