Effective diffusivity, polymer

Sorption curves obtained at activity and temperature conditions which have been experienced to be not able to alter the polymer morphology during the test, i.e. a = 0.60 and T = 75 °C, for as cast (A) and for samples previously equilibrated in more severe conditions, a = 0.99 and T = 75 °C (B), are shown in Fig. 13. According to the previous discussion, the diffusion coefficient, calculated by using the time at the intersection points between the initial linear behaviour and the equilibrium asymptote (a and b), for the damaged sample is lower than that of the undamaged one, since b > a. The morphological modification which increases the apparent solubility lowers, in fact, the effective diffusion coefficient. 

Lin, TH Phillies, GDI, Prohe Diffusion in Polyacrylic Acid Water—Effect of Polymer Molecular Weight, Journal of Colloid and Interface Science 100, 82, 1984. 

Kinetic Parameters of Free Valence Migration in Polymers [13,14] Effective Diffusion Coefficient D and Average Distance of Diffusion r... 

The mechanism of antioxidant action on the oxidation of carbon-chain polymers is practically the same as that of hydrocarbon oxidation (see Chapters 14 and 15 and monographs [29 10]). The peculiarities lie in the specificity of diffusion and the cage effect in polymers. As described earlier, the reaction of peroxyl radicals with phenol occurs more slowly in the polymer matrix than in the liquid phase. This is due to the influence of the polymeric rigid cage on a bimolecular reaction (see earlier). The values of rate constants of macromolecular peroxyl radicals with phenols are collected in Table 19.7. 

Much research into radiation effects on polymers is done with samples sealed under vacuum. However, polymer materials may, in practical applications, be subjected to irradiation in air. The effect of irradiation is usually substantially different in air, with increased scission at the expense of crosslinking, and the formation of peroxides and other oxygen-containing structures. Diffusion rates control the access of oxygen to radicals produced by the radiation, and at high dose rates, as in electron beams, and with thick samples, the behaviour may be similar to irradiation in vacuum. Surface changes may be quite different from bulk due to the relative availability of oxygen. 

Summarising, the paint-seawater mechanism includes the following rate-influencing steps hydrolysis and erosion of the active TBT-polymer binder, effective diffusion in the leached layer of dissolved pigment species and TBTC1,... 

Deff effective diffusivity of solute in porous membrane Dim diffusivity of solute i in polymer membrane... 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

At finite polymer concentrations, the intermolecular hydrodynamic interaction may also alter polymer dynamics. Except for spherical particles, the hydrodynamic calculations of the effective diffusion coefficients including this... 

In polyisobutylene in the melt and in solution (CC14, CS2), McCall, Douglass, and Anderson 17) found that the activation energies for polymer diffusion increased with polymer concentration from the value at infinite dilution (approaching the pure solvent value) to the value in the melt. Solvent diffusion, and solvent effect on polymer diffusion, were also measured. The Stokes-Einstein model applied to this data yielded molecular dimensions too small by a factor of two or three. 

The collapse of the networks was studied experimentally mainly for the case of mixed solvents. From the practical point of view, it would be interesting to generate the collapse in a purely aqueous medium. In this case, by changing the interactions between subchains of the network in aqueous solution it is possible, for example, to influence effectively diffusion in gels that are used as carriers of enzymes or pharmacologically active substances. One of the new directions in the research of network polymers is the study of their interaction with linear macromolecules. The results of the theoretical analysis of the behavior of polymer networks swollen in polymer solutions have been discussed in Ref. [34,35] (see Sect. 2.4.2). 

This sieve effect cannot be considered statically as a factor that only determines the amount of accessible acid groups in the resin in such a way that the boundary between the accessible and non-accessible groups would be sharp. It must be treated dynamically, i.e. the rates of the diffusion of reactants into the polymer mass must be taken into account. With the use of the Thiele s concept about the diffusion into catalyst pores, the effectiveness factors, Thiele moduli and effective diffusion coefficients can be determined from the effect of the catalyst particle size. The apparent rates of the methyl and ethyl acetate hydrolysis [490] were corrected for the effect of diffusion in the resin by the use of the effectiveness factors, the difference in ester concentration between swollen resin phase and bulk solution being taken into account. The intrinsic rate coefficients, kintly... 

Table I lists also the apparent diffusion coefficients, Da, calculated from the time lag, 0. The dependence of the apparent diffusion coefficients on additive concentration is similar to the dependence of the permeability coefficients on this concentration. We will show later that the diffusion coefficients in PVC are dependent on the gas concentration in the polymer, and we emphasize here that the values quoted in Table I are the apparent diffusion coefficients and are not the values of either the real or effective diffusion coefficients, D and D, respectively. We recognize that Da actually underestimates both D and D, but we can still use the apparent diffusion coefficients to show the...

H. Nishide, H. Kawakami, T. Suzuki, Y. Azechi, Y. Soejima and E. Tsuchida, Effect of Polymer Matrix on the Oxygen Diffusion via a Cobalt Porphyrin Fixed in a Membrane, Macromolecules 24, 6306 (1991). 

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 ... 

For pore sizes ranging from 50 to 200 A, which are comparable to the sizes of the diffusing solute molecules and are called microporous, the diffusion of solutes may be substantially restricted by polymer materials. A diffusing molecule may be hindered from entering the pores and be chafed against the pores walls. Equation (6.30) incorporates these factors into the effective diffusion coefficient as ... 

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