Polymers, diffusion through

AT DiBenedetto, DR Paul. Interpretation of gaseous diffusion through polymers by using fluctuation theory. J Polym Sci Part A 2 1001-1015, 1964. 

Numerous models have been proposed to interpret pore diffusion through polymer networks. The most successful and most widely used model has been that of Yasuda and coworkers [191,192], This theory has its roots in the free volume theory of Cohen and Turnbull [193] for the diffusion of hard spheres in a liquid. According to Yasuda and coworkers, the diffusion coefficient is proportional to exp(-Vj/Vf), where Vs is the characteristic volume of the solute and Vf is the free volume within the gel. Since Vf is assumed to be linearly related to the volume fraction of solvent inside the gel, the following expression is derived ... 

S Sato, SW Kim. Macromolecular diffusion through polymer membranes. Int J Pharm 22 229-255, 1984. 

The characteristics of pore structure in polymers is a key parameter in the study of diffusion in polymers. Pore sizes ranging from 0.1 to 1.0 pm (macroporous) are much larger than the pore sizes of diffusing solute molecules, and thus the diffusant molecules do not face a significant hurdle to diffuse through polymers comprising the solvent-filled pores. Thus, a minor modification of the values determined by the hydrodynamic theory or its empirical equations can be made to take into account the fraction of void volume in polymers (i.e., porosity, e), the crookedness of pores (i.e., tortuosity, x), and the affinity of solutes to polymers (i.e., partition coefficient, K). The effective diffusion coefficient, De, in the solvent-filled polymer pores is expressed by ... 

Diffusion through polymers is influenced not only by the polymer s structure, but also by the molecular structure of the solute. The solute structure may also influence the rate of partitioning into the elution medium. However, there is only a low relationship between these factors. The influence of gel structure on the diffusion characteristics of solutes through polyHEMA hydrogels has been reported [146]. 

C. Stradowski, Methylviologen cation radical as probe of oxygen diffusion through polymer, J. Appl. Polym. Sci., 1990, 41, 2511 B. Maiti and S. Schlick, Oxygen permeation in perfluorinated ionomers based on the reaction with the methylviologen cation radical. An ESR and optical study, Chem. Mater., 1992, 4, 458. 

Pressure or concentration difference serves as the driving force for isothermal diffusion through polymer films. Molecules at higher concentration sorb into the solid polymer and can move through the matrix of polymer chains with subsequent desorption from the film surface of different concentration. If the polymer membrane separating two solutions is permeable, the diffusion of molecules from the high concentration side to the low concentration side is called osmosis or dialysis. 

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 . 

Section 2 presents nomenclature and a theoretical background. Sections 3 cind 4 review, respectively, (i) self-diffusion of polymers in solution and (ii) probe diffusion through polymer solutions. Section 5 notes other experimental papers that do not lend themselves to our analytic approach. Section 6 treats experimented studies on polymers in porous media and true gels. Section 7 treats universal phenomenological features in our lncdysis. Section 8 summarizes conclusions. 

F. Jagodic, B. Borstnik, A. Azman, Model calculation of gas-diffusion through polymer bulk, Makrontol. Chem., 173, 221-231 (1973). 

Solution diffusion through polymer selective layers is used exclusively in current commercial devices. High-performance polymeric membranes based on the solution-diffusion mechanism can achieve high permeation rates favoring a given component in a feed gas mixture. Such membranes form the basis for simple, convenient processes to separate a wide spectrum of gas pairs [164]. 

For metals such as Ni, Cd, and Pt, where gases such as Hj and Oj are diffusing, it is found experimentally that the flux is approximately proportional to(VPxi -s/Pxz), so Eq. (6.5-8) does not hold (B5). When water is diffusing through polymers, unlike the... 

Overall, the in situ method remains very poorly characterised. Relying as it does on diffusion through polymer to the filler surface, where conditions must be right for hydrolysis and condensation. It sounds very haphazard, but seems to work remarkably well in practice. 

Litt, M. H. (1986), Free volume concepts connecting PVT behavior and gaseous diffusion through polymers, /. Rheol., 30,853-868. 

If we work back from solid polymer by adding progressively more amounts of liquid monomer, we see that the glass transition temperature of the now plasticised polymer decreases with the amount of monomer added. Monomer cannot diffuse through polymer below the glass transition temperature, so the reaction stops when the amount of monomer decreases by the amount necessary to raise the transition temperature of the mixture above the reaction temperature. However, the reaction will continue to proceed if the temperature of the reaction is raised, and will go to 100% conversion if the final temperature is above the transition temperature of the soHd polymer. For this reason, many industrial processes carry out the polymerisation using a temperature profile that finishes with a high temperature to ensure that there is no unreacted monomer left in the final product. 

FIGURE 6 Idealized morphology for diffusion through polymer nanocomposite containing dispersed clay platelets (David and Gupta, 2007). 

The penneability of gases in the polymeric material depends upon the diffusion rate of the diffusant through polymer matrix (Cussler, 1988). The adsorption rate depends upon the rate of formation of free volume holes in the polymer created due to random Brownian motion or thermal motion of the polymeric chains and diffusion caused by jumps of molecular gas molecules to neighboring empty holes during polymer formation (Yang, 2007). Permeability of polymer films is also dependent on the intrinsic polymer chemistry, polymer-polymer, and polymer-gas interactions. 

Diffusion coefficients were also determined in the mass-transfer investigations, when citric acid reacts with calcite [169], in citric acid solutions saturated with 1-butanol [170] and when citric acid diffuses through polymer membranes [171-173],... 

As seen in other chapters, the Ogston sieving model also does not describe sedimentation or diffusion through polymer solutions (cross-linked gels are a separate question not considered here), so its invocation in electrophoresis seems problematic. Conclusions about transport mechanics, drawn from relationships between measurements and a hypothesized Ogston model, are therefore subject to reservations. 

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