Diffusion in polymers - The classical approach

Many theoretical models have been proposed in the last six decades to describe the diffusion of small penetrant molecules in polymer matrices. According to the distance-time scale at wich the basic physico-chemical processes involved in these models have been set one could classify them in two main categories, namely microscopic and atomistic diffusion models. 

In this section we will present briefly some relevant aspects of the classical approach to model diffusion in polymers along with representative features and results of the most often cited of these models. 

Since about 15 years, with the advent of more and more powerfull computers and appropriate softwares, it is possible to develop also atomistic models for the diffusion of small penetrants in polymeric matrices. In principle the development of this computational approach starts from very elementary physico-chemical data - called also first-principles - on the penetrant polymer system. The dimensions of the atoms, the interatomic distances and molecular chain angles, the potential fields acting on the atoms and molecules and other local parameters are used to generate a polymer structure, to insert the penetrant molecules in its free-volumes and then to simulate the motion of these penetrant molecules in the polymer matrix. Determining the size and rate of these motions makes it possible to calculate the diffusion coefficient and characterize the diffusional mechanism. 

Nowdays the atomistic simulation of diffusional processes in polymers is a domain of vivid research activity which already shows remarcable results and brings continously new achievements. The second section of this chapter is devoted to a concise presentation of this topic. 

In approaching the problem of modelling diffusion in polymers, regardless if in a classical or computational manner, an important feature must be highlighted, namely that markedly different diffusion mechanisms operate at temperatures above and below the glass transition temperature, Tg, of the polymer. This is due in principal to the fact that polymers at temperatures T Tg, so-called rubbery polymers, respond rapidly to changes in their physical condition. Therefore, the penetrant polymer system adjusts immediately to a new equilibrium when a penetrant species is 

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