Glassy polymers diffusive jump

In a rubbery polymer with flexible macromolecular chains (PDMS for example) the cavities forming the free-volume are clearly separated from each other. The detailed evaluation of the movement of a penetrant particle from cavity (1) to the neighboring (2), did not show any immediate back jumps (2) — (1). This is mainly do to the fact that the channel between (1) and (2) closes quiet quickly. In a polymer with stiff chains (glassy polyimide (PI) for example) the individual cavities are closer to each other and a rather large number of immediate back jumps ocurred during the time interval simulated (120). This indicates that once a channel between two adjacent cavities in a stiff chain polymer is formed it will stay open for some 100 ps. This makes the back jump (2) - (1) of the penetrant more probable than a jump to any other adjacent hole (3). This process seems to be one cause for the general tendency that the diffusion coefficient of small penetrants in stiff chain glassy polymers is smaller than in flexible chain rubbery polymers. 

Transport Properties. Sorption and transport properties are highly dependent on the post-vitrification history of glassy polymers (77) hence one would expect parameters such as physical aging, antiplasticization and amorphous orientation to affect transport properties. The reduction in diffusivity and permeability due to aging, orientation, and antiplasticization can be modeled via entropy or fi ee volume arguments (77). In addition, diffusive jumps of penetrant molecules in glassy polymers can be affected by (facilitated by) the segmental mobility that is manifested in sub-Tg relaxations 78),... 

More recently Takeuchi reported details of a jump mechanism of a small diffusant molecule in a system of endless polymer chains that is quenched at the glassy state (T < T ). For most diffusant species (simulating O2 molecules) trapped in rigid cages formed by strands of the glassy polymer, the time evolution of the... 

Figure 5.4 Transition State Theory for diffusion in condensed media, (a) General representation of the transition state theory, (b) Diffusive jump in glassy polymer [ 17j. Reprinted from journal of Membrane Science, 73, E. Smit, M. H. V. Mulder, C. A. Smolders, H. Karrenbeld, j. van Eerden and D. Eeil, Modelling of the diffusion of carbon dioxide in polyimide matrices by computer simulation, 247 257, Copyright (1992), with permission from Elsevier, (c) Diffusive jump in microporous silica, reprinted with permission from AlChE, Theory of gas diffusion and permeation in inorganic molecular-sieve membranes by A. B. Shelekhin, A. C. Dixon and Y. H. Ma, 41, 58 67, Copyright (1995) AlChE...

Fig. 41. N2 diffusion through PEEK shows back-and-forth diffusion jumps that have been observed in many glassy polymers. Reprinted from Ref 200, with permission from Elsevier.

The final step in obtaining a diffusion coefficient is to simulate the dynamics of a penetrant molecule on the network of sorption states and rate constants. Analogous to the frozen positions of voids and channels in a glassy polymer, the relative sorption probabilities and jump rate constants typically remain constant throughout the diffusion simulation. For uniform rate constants on an ordered lattice, it is possible to solve the dynamics analytically. For the disordered network found for voids through a polymer matrix, a numerical solution is required. 

The transport properties of glassy and rubbery polymers are related to their microstructural morphology. For a penetrant to diffuse, a minimum characteristic packet of imoccupied volume is required. The penetrant diffuses by jumping through transient gaps between packets of unoccupied volume. The lifetime, size, and shape of these volume packets and the transient gaps that connect them are dependent upon the micromotions of the polymeric media. New techniques such as... 

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