Self-diffusion activation energy

In order to develop a consistent free-volume diffusion model, there are some issues which must be addressed, namely i) how the currently available free-volume for the diffusion process is defined, ii) how this free-volume is distributed among the polymer segments and the penetrant molecules and iii) how much energy is required for the redistribution of the free-volume. Any valid free-volume diffusion model addresses these issues both from the phenomenologic and quantitative points of view such that the diffusion process is described adequately down to the microscopic level. Vrentas and Duda stated that their free-volume model addresses these three issues in a more detailed form than previous diffusion models of the same type. Moreover, it was stated that the model allows the calculation of the absolute value of the diffusion coefficient and the activation energy of diffusion mainly from parameters which have physical significance, i.e. so-called first principles . In the framework of this model the derivation of the relation for the calculation of the self-diffusion coefficient of the sol-... 

Fig. 5.28. The dependence of the experimental energy of activation for self-diffusion on the melting point (1 cal = 4.184 J).

The first point to note about this expression, apart from the fact that it is of the form of the experimentally observed variation of D with temperature (i.e., D = is that the energy of activation for self-diffusion of cations and anions... 

Figures 1 and 2 show the self-diffusivities of the various adsorbates in NaX and CsNaX, respectively. Acetone and isopropanol are the largest of the molecules studied and have the lowest mobilities. Specific interactions of the adsorbate oxygen atoms with the cations of the zeolite may also reduce the mobility. The smaller molecules, propene and water, are considerably more mobile. Water is seen to have the highest activation energy for diffusion of the adsorbates investigated.

Membrane Diffusion in Nonaqueous Solvent Environments. Self-diffusion coefficients of Na+ and Cs+ for 1200 EW Nafion membranes in dilute methanol and acetonitrile solutions have been measured (5). Arrhenius plots of these results are shown in Figure 7 along with corresponding results for aqueous experiments activation energies of diffusion are listed in Table IV. Diffusion coefficients of Na+ in methanol and water-equilibrated membranes are very similar, and the activation energy of diffusion for the methanol system is only slightly higher than the respective value for Na+ in pure methanol solvent, 12.9 kJ mol 1 (27). Thus a solution-like diffusion mechanism is inferred for both solvent systems. Cesium ion diffusion in the methanol equilibrated membrane is much slower than sodium ion diffusion in fact the... 

Diffusion coefficients provide two kinds of information. First, their absolute magnitudes, combined with membrane sodium ion concentrations, are useful indicators of the temperature dependence of ionic self-diffusion and thereby they yield the activation energy for diffusion. They thereby provide insight into the nature of the diffusion mechanism (16). When activation energies are measured for various types of related membranes, the influence of different membrane structural design features can thus be separated and determined directly. 

Dyer and Gettins (27) have made a more comprehensive study of self-diffusion in zeolite ZK-4. This zeolite is isostructural with zeolite A but more siliceous (39), having a Si/Al atom ratio of 1.33, and it is of interest to compare it to their study of zeolite A (25). The activation energy for diffusion and D0 in the Arrhenius equation D = D° exp (— Ea/RT), along with the entropy of activation ASJ, are shown in Table II. 

Q is the activation energy for diffusion. Fig. 5.22 shows this temperature dependence for the diffusion coefficient of phenanthrene in anthracene crystals. In the relatively small temperature range between 400 and 450 K, D changes by a factor of about 100 [35]. Table 5.7 lists measured values of D for self diffusion in naphthalene crystals, and Table 5.8 contains characteristic values for D in naphthalene and anthracene crystals. The two important experimental results are the following ... 

Pulsed field gradient NMR (PFG-NMR) is primarily used for measuring molecular difiusion coefficients in solution. In ILs, diffusion is the process of charge transport via cations or anions activated by internal kinetic energy. Self-diffusion in combination with other bulk properties, such as viscosity, density, and electrical conductivity, provides a thorough understanding of molecular transport in ILs. 

To obtain a clearer indication of the activation energy for diffusion-limited transport, the activation energy for the self-diffrision coefficient of NPOE can be measured. The activation energy for self-diffusion of a solvent often correlates well with the activation energy for diffusion of a solute species, since on a molecular level diffusion of a solute can be considered as a process in which either a solute or solvent molecule jumps from solvent cavity to cavity. Since the activation energy for self-diffusion varies with the solvent used, it is important to determine the activation energy E for the self-diffusion of NPOE first. The temperature dependency of the viscosity of organic solvents T has an Arrhenius-type behaviour. 

This theoretical prediction is satisfied when the self-reaction of trichloromethyl radicals is assumed to be diffusion controlled, that is, when E. is equated to the activation energy of diffusion in cyclohexane of 4.54 kcal. The Arrhenius expression for % obtained from the results of Table III, assuming that E = 4.54 kcal/mole is ... 

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... 

The ESR spectrum of the pyridazine radical anion, generated by the action of sodium or potassium, has been reported, and oxidation of 6-hydroxypyridazin-3(2//)-one with cerium(IV) sulfate in sulfuric acid results in an intense ESR spectrum (79TL2821). The self-diffusion coefficient and activation energy, the half-wave potential (-2.16 eV) magnetic susceptibility and room temperature fluorescence in-solution (Amax = 23 800cm life time 2.6 X 10 s) are reported. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

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