Chain immobilization factor

It appears that in these Sclair resins the increased crystallinity is the result of fewer, larger crystallites rather than more of the same size. These larger crystallites have a lower total surface area. The tortuosity is then relatively unaffected, but the chain immobilization factor defined by Equation 2 is reduced significantly, resulting in a larger diffusion coefficient in the denser, more crystalline materials. 

Previous measurements of diffusion in polyethylene (37, 38) have found a diffusion coefficient decreasing with increasing crystallinity. These results were explained by assuming an increased tortuosity with increased crystallinity. These investigators have compared samples of polyethylene prepared by different manufacturers under different conditions. For their samples the increase in crystallinity may be the result of more crystallites of a smaller size, increasing both the tortuosity and the chain immobilization factor. 

The presence of the crystalline phase restricts also the motion of polymer segments causing the diffusion to decrease. The effects of crystalline phase are usually characterized by geometric impedance factor and chain immobilization factor. The diffusion through polymer films is affected by the glassy or rubbery state of the polymer matrix and by stretching of polymer specimen . 

The effects of crystallinity on the diffusion coefficient can be more complex than this simple volumetric exclusion, since the crystallites may act not only as tortuous barriers, but also as effective restrictors of chain motion analogous to chemical cross-linking. This twofold effect has been treated (54) in terms of a tortuosity factor r, and a chain immobilization factor p, both of which increase with increasing crystalline fraction. The parameters D and Da are the diffusion... 

In a treatment of the effects of crystallinity on transport in rubbery polymers using a modification of free-volume expressions (26), it was suggested that the introduction of crystallinity reduces the freedom of motion of amorphous chain segments between crystals. Although these ideas are physically consistent with those described above in terms of the chain immobilization factor p, a rather different analytical form of the diffusion coefficient is obtained. 

Kim, S. and J. M. Krochta. 1998. Pol5mier chain immobilization factors for whey protein-sorbitol/beeswax edible emulsion films. In Paradigm for Successful Utilization of Renewable Resources, D. J. Sessa and J. L. Willett (eds), AOCS Press, Champaign, IL, pp. 198-213. 

D = diffusivity in (totally) amorphous polyethylene X = geometric impedance (tortuosity) factor P = chain immobilization factor... 

Such principles can be used to guide the development of new resin grades and morphologies. However, despite our advanced knowledge of polyethylene morphology it is not possible to determine the tortuosity or chain immobilization factors solely on the basis of morphological parameters. These factors must still be evaluated experimentally. 

Cross-linking polyethylene reduces chain segment motion in the disordered regions, and thus diffusion becomes more dependent upon the size and shape of the penetrant moleeules. The chain immobilization factor will have the greatest effect on penetrants that have a large molecular volume. 

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