Diffusion coefficients comparison with penetration

The quantities of prime interest here are the solubility and diffusion coefficient of the penetrant molecules and how these quantities are related to the structure of the host polymer. Comparisons with the extensive experimental data available for a wide range of polymers provides a stiff test not only of the accuracy of potential functions but perhaps more importantly of the method of preparation techniques and methods of sampling representative polymer structures. So far only limited quantitative success has been achieved, and that is under system conditions where the diffusion rate is... 

In Table 5-2 a comparison between diffusivities obtained with the TSA method and experimental D is presented. From this table one can see that, in all cases computed D agree with experimental data to within an order of magnitude. Moreover most of these D are considerably smaller than the 5 10-7 cm2/s lower threshold assumed to be in reach of nowadays MD simulations Section 5.2.1. This is an encouraging sign that computer simulations of diffusional processes are already able to predict, with a reasonable accuracy and for small and simple penetrants, diffusion coefficients around 10-10 cm2/s. From the point of view the packaging sector it would be interesting to learn if and when further theoretical developments of the TSA method will be able to simulate (predict) such slow diffusional processes for organic penetrants with a much more complex structure, see Chapter 3 and Appendix I. 

A substantial number and variety of models of gas transport in polymers have been proposed during the last 20-30 years, in view of the great practical and scientific importance of this process. Molecular-type models are potentially most useful, since they relate diffusion coefficients to fundamental physicochemical properties of the polymers and penetrant molecules, in conjunction with the pertinent molecular interactions. However, the molecular models proposed up to now are overly simplified and contain one or more adjustable parameters. Phenomenological models, such as the dual-mode sorption model and some free-volume models, are very useful for the correlation and comparison of experimental data. 

Molecular dynamics studies of penetrant diffusion have so far been performed for polyethylene, polyisobutylene and polydimethylsiloxane. Calculated diffusion coefficients have not been in particularly good agreement with experiment. In the case of polyethylene, modeled using the united atom approximation, diffusion coefficients were much higher than expected and the activation energies too small although much better results have been obtained using PE IV. Reliable comparisons with experimental data are made difficult by uncertainties as to the true diffusion coefficients... 

To understand the effect of network structure on permeability, the diffusion coefficients for each system were calculated based on independent sorption studies, and the result is presented in Figure 35.6b. Comparison with Figure 35.6a. reveals similar trends such that the observed permeability variation can be attributed mostly to a change in penetrant diffusivity in the networks. In a homogeneous blend, gas transport properties (X) such as permeability or diffusivity are often modeled empirically as (Paul, 1984)... 

---