Arrhenius rate expression, diffusion coefficient

From this molecular theory, we see that the diffusion coefficient depends on the frequency of cooperative main-chain motions of the polymer, v, which cause chain separations equal to or greater than the penetrant diameter. Pace and Datyner were able to estimate v by adopting an Arrhenius rate expression in which the pre-exponential factor, A, is a function of both AE and T. The diffusion coefficient is given by,... 

Pk temperature exponent in Arrhenius rate expression (—) r generalized diffusion coefficient (variable units)... 

Increasing temperature permits greater thermal motion of diffusant and elastomer chains, thereby easing the passage of diffusant, and increasing rates Arrhenius-type expressions apply to the diffusion coefficient applying at each temperature," so that plots of the logarithm of D versus reciprocal temperature (K) are linear. A similar linear relationship also exists for solubUity coefficient s at different temperatures because Q = Ds, the same approach applies to permeation coefficient Q as well. 

Self diffusion coefficients can be obtained from the rate of diffusion of isotopically labeled solvent molecules as well as from nuclear magnetic resonance band widths. The self-diffusion coefficient of water at 25°C is D= 2.27 x 10-5 cm2 s 1, and that of heavy water, D20, is 1.87 x 10-5 cm2 s 1. Values for many solvents at 25 °C, in 10-5 cm2 s 1, are shown in Table 3.9. The diffusion coefficient for all solvents depends strongly on the temperature, similarly to the viscosity, following an Arrhenius-type expression D=Ad exp( AEq/RT). In fact, for solvents that can be described as being globular (see above), the Stokes-Einstein expression holds ... 

This expression has the Arrhenius form and E is the maximum value of the potential energy, an activation energy for deposition. This is expected because the potential profile of fig. 2 resembles the plot of the energy against reaction coordinate used in the theory of rate processes. The factor /(//m) accounts for the dependence of the diffusion coefficient on the distance and evaluations show that it can decrease the frequency factor in eqn (16) by two orders of magnitude. 

Transport through a dense polymer may be considered as an activated process, which can be represented by an Arrhenius type of equation. This implies that temperature may have a large effect on the transport rate. Equations 4.7 and 4.8 express the temperature dependence of the diffusion coefficient and solubility coefficient in Equation 4.5 ... 

There is a large amount of data on nonhomogeneous track chemistry of energetic electrons at room temperature, and the track structure and diffusion-limited kinetics are well parameterized. This wealth of knowledge contrasts with the limited information about the effects of radiation on aqueous solutions at elevated temperatures. The majority of the studies at elevated temperatures have been performed at AECL, Canada [93], or at the Cookridge Radiation Laboratory, University of Leeds, UK [94]. These two groups have focused on measuring the rate coefficients of the reactions of the radiation-induced radicals and ions of water. The majority of the temperature dependencies can be fitted with an empirical Arrhenius-type expression, k = A This type of parameterization provides a... 

The rate of diffusion is governed by the diffusion coefficient in conjunction with Pick s laws of diffusion. Because diffusion is thermally activated, the diffusion coefficients follow the Arrhenius behavior and it is a common practice to express their thermal dependence in terms of a pre-exponential coefficient Do and an activation energy Q,... 

Quantum effects can also be included artificially by a tunneling correction in the expression for the rate eonstant of the process, proportional to the diffusion coefficient D [33]. In this way, the diffusion coefficient is obtained as a modification of the Arrhenius temperature dependence of the rate constant ... 

The temperature dependence of the hydrogen permeability can be expressed by the well-known Arrhenius expression P exp( - )], formally similar to the self-diffusivity coefficient mentioned in Section 15.3. However, in this case, the activation energy for diffusion, E , is referred to the jumps of the hydrogen atoms in the bulk of the Pd-aUoy (the rate-determining step is the H diffusion according to the Richardson equation). Considering that 0 depends on the partial pressure of the carbon monoxide, in addition to the temperature of the mixture, that is 0 (T, ), the scaling factor g(T,p ) can... 

In the resulting expression, only constant k varies significantly with temperature, since the diffusion of gas in a pore varies little with temperature. Passing to the logarithm of the rate and expressing the temperature, we notice that Arrhenius law is still followed but the temperature coefficient is half the activation energy of the reaction interface ... 

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