Diffusion partial immobilization model

Application of the dual mode concept to gas diffusion in glassy polymers was originally subject to the limitation that DT2 = OinEq. (6) ( total immobilization model )6-Later this simplifying assumption was shown to be unnecessary, provided that suitable methods of data analysis were used 52). Physically, the assumption DX2 = 0 is unrealistic, although it is expected that DT2 < DX1 52). Hence, this more general approach is often referred to as the partial immobilization model . 

The concentration dependent diffusion coefficient defined by Eq. (9) can be evaluated by differentiation of steady state permeation data without reference to tile partial immobilization model The concentration dependent diffusion coefficient calculated from the partial immobilization model agrees very well with values calculated in this way, and one can consider them to be essentially identical mathematically The partial inunobilization theory, therefore, serves to explain the source of the concentration dependency of Dgfr in Eq. (9). 

At least in the sterns studied, errors of less than a factor of two are found between the total and partial immobilization cases. In contrast the diffusion constants obtained by the simple time lag equation [Eq. (6)] are as small as one ei th of those estimated for the Henry s law mode diffiisivity using the completly immobilized model (F = 0) in some cases. This means that actual errors of iqj to four fold in estimation of the true Henry s law mode diffiisivity, Dp, can possibly be introduced by use of the simple time lag technique for assy polymers if one faQs to acccaint for the effect of immobilization. 

When the temperature is lower than the critical temperature 7 of gas the solubility of the permeant gas in the membrane may become so high that the diffusion constant no longer remains constant. A modification was done in the above dual transport model with partial immobilization of the Langmuir sorption mode to include the concentration dependency of the diffusion coefficient [153]. Instead of Equation 5.204 the following equation expresses the permeability coefficient ... 

Adhesion of different immune cells to one another or to epithelial cells has also been studied using planar bilayer models. For example, lymphocyte function-associated protein-1 (LFA-1) promotes cell adhesion in inflammation [i.e., a reaction that can be mimicked by binding to purified ICAM-1 in supported membranes (70)]. Similarly, purified LFA-3 reconstituted into supported bilayers mediates efficient CD2-dependent adhesion and differentiation of lymphoblasts (71). This work was followed by a study in which transmembrane domain-anchored and GPl-anchored isoforms of LFA-3 were compared (72). Because this research occurred before the introduction of polymer cushions and because the bilayers were formed by the simple vesicle fusion technique, the transmembrane domain isoform was immobile, whereas the GPl isoform was partially mobile. By comparing results with these two isoforms at different protein densities in the supported bilayer, the authors showed that diffusible proteins at a sufficient minimal density in the supported membrane were required to form strong cell adhesion contacts in this system. 

Petropoulos [20] and Paul and Koros [21] independently developed models where the diffusion of the gas species adsorbed in the Langmuir region is partially, or even totally, immobilized. In this case, a parameter Fa is introduced, defined either as the ratio of diffusion coefficients in the Langmuir (Du) and Henry s Law region (Do) or as the fraction of the Langmuir species that are fully mobile. In this case, the concentration of mobile species is given by ... 

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