Diffusion in polymers - The computational approach

It was shown in the above section that as a rule, at the base of the classical or microscopic diffusion models, there are ad hoc (heuristic) assumptions on a certain molecular behaviour of the polymer penetrant system. The fact that the mathematical formulae developed on such bases often lead to excellent correlations and even semipredictions of diffusion coefficients must be aknowledged. It is true that the classical models are not capable to predict diffusion coefficients only from first principles but this is often not an obstacle to hinder their use in certain types of investigations. Therefore we are quiet sure that this type of diffusion models will certainly be used in the future too for the interpretation of diffusion experiments. 

The problem of diffusion modeling in polymers changes to some degree when one envisages to develop a really atomistic model, with trully predictive capabilities and without making any ad hoc assumption on the molecular behaviour and/or motions in the polymer penetrant system. In principle, a possibility to develop such diffusion modelings, is to simulate theoretically the process of penetrant diffusion in a polymer matrix by computer calculations. 

The prerequisites which make possible the development of atomistic simulations of diffusion in polymers are the development of powerful methods for the simulation of polymer microstructures and dynamics and also great computation capabilities of supercomputers. 

The first attempts in the direction of simulating theoretically at an atomistic level the diffusion of simple gas molecules in a polymer matrix were made more than two decades ago (100). But, the systematic development of ab initio computer simulations of penetrant diffusion in polymeric systems dates only from the late 80 s (101-104). At the beginning of the 90 s it was achieved to simulate some qualitative aspects such as the diffusion mechanism, temperature, and pressure dependence of diffusion coefficients (105-109). The polymers chosen for investigation mainly fell into two categories either they were easily described (model elastomers or polyethylene) or they were known to have, for simple permanent gases like H2, 02, N2, H20 or CH4, 

Based on these encouraging achievements, in the last five or six years, the interest of the researchers shifted from easy-to-compute polymer penetrant systems to those which have interesting technological potentials in such fields as gas barriers (114— 117), gas or liquid separation processes (118-121), molded objects (packagings for example) (122) or swelling of polymers by solvents (123-126). 

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