Solvent diffusion temperature dependence

The diffusivity data were analyzed using the Vrentas-Duda version of the foee-volume theory. Hie basic equation describing the solvent and temperature dependence of the diffusion coefficient in the limit of zero mass fraction above the glass transition temperature is given by the expression... 

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

The temperature dependence of a diffusion-controlled rate constant is very small. Actually, it is just the temperature coefficient of the diffusion coefficient, as we see from the von Smoluchowski equation. Typically, Ea for diffusion is about 8-14 kJ mol"1 (2-4 kcal mol-1) in solvents of ordinary viscosity. 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Recall that the diffusion coefficient of a molecule will decrease with increasing viscosity of the solvent. Thus, the rate of encounter complex formation will decrease in a viscous medium. Since viscosity is itself temperature dependent, such encounters in solution will have their own activation energy. 

EXAMPLE 2.6 Temperature Dependence of Diffusion Coefficients. Suppose the diffusion coefficient of a material is measured in an experiment (subscript ex) at some temperature Tex at which the viscosity of the solvent is qgx. Show how to correct the value of D to some standard (subscript s) conditions at which the viscosity is j s. Take 20°C as the standard condition and evaluate D°20 for a solute that displays a D° value of 4.76-10 11 m2 s 1 in water at 40°C. The viscosity of water at 20 and 40°C is 1.0050-10 2 and 0.6560 -10 2 P, respectively. 

The temperature-dependence of solvent diffusion obeyed the free-volume — based expression of Williams, Landel, and Ferry59) adapted to diffusion ... 

The rate coefficients for f-butyl radical reaction to form 2,2,4,4-tetra-methylbutane are typically 1010 dm3 mol s-1. The exact value depends on the solvent and temperature, becoming greater in more mobile solvents and at high temperatures, that is when the diffusion coefficient is larger. Indeed, Schuh and Fischer [40] found a good correlation between the rate coefficient, k, which they had measured, and the ratio... 

Figure 5. Segmental diffusion constant depending on temperature and solvent viscosity data are calculated according to Equation 1 and the graph according to Equation 2...

TEMPO, which is commercially available, traps carbon-centred radicals with rate constants an order of magnitude lower than the diffusion-controlled limit in most organic solvents at <120°C (e.g. kc = 3.1 x 108 dm3 mol-1 s 1 with benzyl radical at 50°Cin tert-butylbenzene) [6], and somewhat more slowly if the radical is sterically congested (e.g. kc = 5.7x 107 dm3 mol-1 s 1 with cumyl radical under the same conditions, Scheme 10.6) [6]. Non-Arrhenius behaviour or non-temperature dependence has been observed for several radical coupling reactions [6, 7]. 

The rate of deprotonation of an acid by a base depends on their structures [41], on the solvent and temperature, and on the difference (ApKa) between the pKa of the acid and that of the base. When acid and base have the same pfCa (ApKa=0) the change of free energy for proton transfer becomes zero and the reaction becomes thermoneutral. Under these conditions the rate of proton transfer is limited only by the so-called intrinsic barrier [34], which is particularly sensitive to structural changes in the reaction partners [39]. When ApKa increases, the rate of proton transfer also increases and approaches a limiting value, which depends on the structures of the acid and base and on the experimental conditions. For normal acids (O-H, N-H) in water the rate of proton transfer becomes diffusion-controlled (ka=10loL mol-1 s"1) when ApKa>2, but in aprotic solvents the limiting proton transfer rate can be substantially lower [42]. 

The above equation provides a basis for correlating the temperature dependence of a transport coefficient such as mass diffusivity in the supercritical region. The effects of composition, solute, and solvent characteristics can also be introduced into the correlations via and A which are system-dependent amplitudes. However, a rigorous ftest of the applicability of equation 5 requires independent measurements of the decay rate of the order-parameter fluctuations, the correlation length, and the viscosity. 

Electron spin resonance (ESR) studies of radical probe species also suggest complexity. Evans et al. [250] study the temperature dependence of IL viscosity and the diffusion of probe molecules in a series of dissimilar IL solvents. The results indicate that, at least over the temperature range studied, the activation energy for viscous flow of the liquid correlates well with the activation energies for both translational and rotational diffusion, indicative of Stoke-Einstein and Debye-Stokes-Einstein diffusion, respectively. Where exceptions to these trends are noted, they appear to be associated with structural inhomogeneity in the solvent. However, Strehmel and co-workers [251] take a different approach, and use ESR to study the behavior of spin probes in a homologous series of ILs. In these studies, comparisons of viscosity and probe dynamics across different (but structurally similar) ILs do not lead to a Stokes-Einstein correlation between viscosity and solute diffusion. Since the capacities for specific interactions are... 

Similarly to Fig. 5-4 for other glassy polymer-solvent systems also the predictions of this free-volume theory are in general agreement with experimental data on the temperature dependence of D in the vicinity of Tg2. In particular, the theory predicts a step change in Ed at Tg2, and this is consistent with most experimental investigations of polymer-solvent diffusion at temperatures just above and below the glass transition temperature (6,11,15). 

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