Segmental diffusion concentration dependence

Fig. 58a, b. Segmental diffusion in semi-dilute polymer solutions. Schematic view of the Q-dependence of the relaxation rates Q(Q) at a fixed concentration. a Good solvent conditions b -conditions. (Reprinted with permission from [168]. Copyright 1994... 

Concentration Dependence. By varying the diffusant concentration in a series of absorption experiments, the variation of D with concentration can be determined. This concentration dependence is the normal situation in polymer-organic vapor systems. Since the addition of small molecules to a polymer increase segmental mobility (plasticization), the diffusion coefficient of an organic vapor in a polymer should increase with increasing diffusant concentration (3). 

Figure 3.33. Concentration dependence of the diffusion coefficient D in the polystyrcne-f-ethylbenzciic sy.stem at 20 (i), 30 (2), 40 ( ), 50 U), and OO C (5). Xj is the segment mole fraction of polymer, i.c. x = zn2l(ni -t- Wi), where rii and 7(2 are the number of moles of the solvent and polymer, respectively, z is the degree of polymerization (Rehage et al., 1970) [G.Rehage, O.Ernst, J.Fulirmaiin. Disc. Faraday Soc. 49 (1970) 208-221. Copyright 1970 by the Royal Society of Chemistry]...

Mahabadi and O Driscoll also studied the effect of dissolved polymer upon the termination rate coefficient [82, 83]. They derived a theoretical relationship for the dependence of kt upon conversion [82], based on a previously derived segmental diffusion model [100] that allowed for a concentration dependent linear expansion coefficient and polymer-solvent interactions. Also Mahabadi and O Driscoll pointed out that the rate of segmental diffusion would increase if the segment density gradient was increased as a result of coil shrinkage. In a simplified form, the dependence of kt upon polymer concentration, C, could be represented by ... 

The solubility is relatively unaffected except at very high degrees of cross-linking or when the penetrant significantly swells the polymer. The constraint of crosslinking on segmental mobility of the polymer makes the diffusion process more dependent on the size and shape of penetrant molecules. The decreases in inherent segmental mobility makes the diffusion process more concentration dependent. 

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