Linearized theory penetration model

The problems of penetration of polymers with arbitrary connectivity into confined spaces (for examples, pores or slits) have been discussed [62]. It has been noted that the Flory theory, the blob model [62] and the scaling concept provide identical results for linear chains however, in the case of branched polymers, the Flory theory and scaling can lead to contradictory results when applied without invoking additional information. 

Within the context of this model, c and f are adjustable constants that vary from polymer to polymer. The ratio f /c is a crude measure of the average interchain separation. As polymer chain stif ess increases and free volume decreases, c should increase (20), and as fractional free volume increases, /c should increase. This theory is based on four hypotheses (1) the solution-di sion mechanism (equation 2) governs gas transport (2) diffusion obeys an Arrhenius expression (equation 8) (3) the linear free energy relation (equation 12) is valid and (4) the effect of penetrant size on activation energy is given by equation 13. 

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