Chain immobilization

Fig. 4.11 Illustration of the typical cell wall structure showing a rigid and porous network of peptoglycan chains immobilized with tetratpeptide crosslinks. Observe the fatty acid (pentanoic) easily penetrating the cross-linked structure...

Figure 19. Distribution of the end-to-end distance of terminal subchains for polymer chains immobilized at one interface and reflected at the other one.

The chain immobilization term indirectly reflects the amount of increase in activation energy of diffusion that is observed in the amorphous phase upon crystallization. 

It is probably a function of both effective crystal surface area and penetrant size. It was noted, however, that the concept of chain immobilization loses its significance as the rigidity of the polymer backbone increases (22.). ... 

In brief, unlike solubility, the effects of crystallinity on the effective diffusivity intimately involve the details of the polymer morphology. Because of the chain immobilization effect, crystallinity may cause an increase in the activation energy of diffusion. However, observed decreases for the activation energy of diffusion for helium in semicrystalline materials have been attributed to "grain boundary" effects (22.) For a first approximation, some authors have found it sufficient to use the following relationship for the correlation of amorphous volume fraction and effective diffusivity,... 

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 . 

Influence of the Polymer Architecture. The time dependence of the friction reduction with PLL- -PEG adsorption suggests that the frictional properties of these interfaces are closely related to the areal density of the PEG chains immobilized near the surface. The full effect of this areal density is revealed through an analysis of the coupled contribution of the PEG chain length and grafting ratio to the... 

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. 

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