Activation energies of diffusion

When using the microporous zeolite membrane (curve 3) the N2 permeance decreases when the pressure increases such a behaviour can be accounted for by activated diffusion mechanisms [21], which are typical of zeolite microporous systems. In such systems the difflisivity depends on the nature and on the concentration of the diffusing molecule which interacts with the surface of the pore. For gases with low activation energies of diffusion, a decrease of the permeability can be observed [22]. 

Figure 5.19 Arrhenius plot of diffusion data, In D versus 1/T. The slope of the straight-line graph allows the activation energy of diffusion, a, to be determined, and the intercept at 1/T = 0 gives a value for the pre-exponential factor.

Thus ((Ax)2) becomes independent of the starting configuration of the cluster. The same equation is obtained if one averages over all configurations in a large number of events. The activation energy of diffusion of the center of mass of the cluster, A cm, as derived from an Arrhenius plot, is related to AE+ and AE by... 

To estimate the activation energy of diffusion at lower temperatures let us assume the pre-exponential factor Du to be independent of T and, by the order of magnitude, to be equal to D = A2vk % 10 4cm2s 1 (A % 10 8 cm is the characteristic value of a diffusion jump, vk 1012s 1 is the characteristic frequency of atomic oscillations in a solid). Then from the experimental values of D one can find the activation energy of diffusion Ea = 9 kcalmol 1... 

It has been pointed out (Anbar and Hart, 1967 Logan, 1967) that reactions near the diffusion-controlled limit are expected to have a constant apparent activation energy of 3-4 kcal mole-1, which is equal to the activation energy of diffusion of solutes in water (AE f), irrespective of their actual energy of activation (AEaet). For reactions proceeding at rates slower than 108 m-1 sec-1, the measured activation energy represents the actual enthalpy barrier of the reaction. 

Krevelen (4) has summarized much of the published data on gas diffusion, including the graphic relationship between the activation energy of diffusion, E., the relative size of the diffusing molecule, (dN2/dX)2, and the glass transition temperature (Tg) of... 

Activation, dextran and inulin, 189-195 Activation energy of diffusion, 50-52 Additives, effect on percutaneous absorption of drugs in rabbits, 275 Agarose gel, use in liposomal drug delivery system, 267-270 Albumin microspheres intramuscular and intraarticular drug delivery, 204,206,211 preparation, 204,207/... 

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-... 

If one selects the nitrogen molecule as a reference molecule then one can set up the following relationship between the activation energy of diffusion, Eq, of a gas i, its molecular diameter Oj and the glass temperature Tg of the polymer (van Krevelen, 1990) ... 

Figure 10. Dependence of mobility of particles versus viscosity and activation energy of diffusion.

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