Diffusivity measured activation energy

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]. 

Thus the rate of change of ip under activation control is much faster than / i, which is under diffusion control, and for the same condition of solution velocity the two rates could become equal at some common temperature, i.e. = ip, and there is no active-passive transition. For many of the systems given in the table this temperature is about 100°C. Above this temperature the measured activation energy is lower and diffusion control is established. 

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. 

Since equations (1), (2a), and (3) are formally the same, it is necessary to find criteria to distinguish the three cases. This is possible because 6 varies so much with stirring speed, and the diffusion coefficient D is affected by viscosity while the parameters in chemical rates usually are not. Different metals dissolve at the same rate in the same solution if the rate is controlled by convection-diffusion. The activation energy of diffusive transport, as measured from temperature coefficients, is normally much lower than the activation energy of chemical processes (3000-6000 cal/mole compared to 10,000-20,000 cal/mole, although some chemical reactions do have lower values). 

In parallel with the HEM experiments, studies using a model porous membrane (Nuclepore ) system, with urea and mannitol as the permeants, were conducted. These studies showed that for these permeants, under experimental conditions identical to those of the HEM studies, the measured temperature dependence of permeation was in line with measured activation energies of bulk diffusion (Longsworth, 1953). The measured temperature-dependent ratios P glP2T) were 1.34 0.03 and 1.38 0.02 N = 4, ave. s.d.) for urea and mannitol, respectively (Peck et al., 1995). These ratios were viewed as a reference point to which the permeation temperature-dependence ratios determined for HEM could be compared. 

Diffusion in porous catalyst affecting experimental activation energy. In case of a porous catalyst diffusion effects existing therein will also reduce the measured activation energy, depending on the temperature dependence of in... 

Fig. 14. Experimental demonstration of the effect of diffusion on the measured activation energy of the cracking reaction of cumene on Si02-Al20s catalyst. (Experimental points and slopes expected theoretically due to diffusion effect.)...

Operative. For the non isothermal case, effectiveness factors greater than unity are possible. Weisz and Hicks have considered this problem in some detail and constructed a number of graphs for various heats of reaction and activation energies. When a reaction is limited by pore diffusion, the reaction rate is proportional to yjky. If the temperature effects can be expressed as a simple Arrhenius relationship = A txp —E/RT), then the measured activation energy E will be about half the true activation energy. Very low values of the activation energy, i.e, 1-2 kcal. mole are only observed when mass transfer to the external catalyst surface is limiting the rate. 

In order to interpret the temperature-dependent experiments it is necessary to assume an activation energy for the diffusion process. Assigning a value of 3 5 kcal./mole (which is reasonable in comparison with other measured activation energies for diffusion processes then the correlation time dependence of the p values obtained by the... 

Abstract Infrared spectroscopic methodsfor the measurement of adsorption and adsorption kinetics of some aromatics (benzene, ethylbenzene, p-xylene), pyridine, and paraffins in solid microporous materials such as zeolites (MOR, ZSM-5, silicalite-1) are described as well as the evaluation of the spectroscopically obtained data. The adsorption isotherms are of the Langmuir-Freundlich type. Isosteric heats of adsorption, transport diffusivities, and activation energies of diffusion as deduced from the spectroscopic measurements are compared with literature data as far as available, and they are found to be in reasonable agreement with results provided by independent techniques. Special attention is paid to sorption and sorption kinetics of binary mixtures, especially the problems of co- and counter-diffusion. ... 

Another complication in comparing data from different techniques may arise from the possibility that several surface diffusion mechanisms may be operative. Evidence for different surface diffusion mechanisms may be revealed by large differences in measured activation energies and by large differences in absolute values of measured surface diffusion coefficients at the same temperature. Hence experimental data, especially if they originate from different techniques, need to be be compared systematically in order to decide whether the effective rates of diffusion (at the same or at different temperatures) may be indicative of different diffusion mechanisms. 

Table 8.2 Measured activation energies for filament growth with those for carbon diffusion in the corresponding metal catalysts.

Because (T in Equation (66) pertains to a hypothetical isotropic nucleus, it cannot be measured. Furthermore, true (anisotropic) solid-liquid interfacial energies are measured near the melting temperature [86], whereas what would be needed for an independent confirmation of the theory is Cf(T) in the supercooled region. Consequently, the theory of homogeneous nucleation, as it applies to supercooled liquids, has been used mainly to calculate effective interfacial tensions from measurements of nucleation rates [82,86]. In summary, the application of nucleation theory to supercooled liquids involves two major simplifications the replacement of the true, anisotropic embryo by an "equivalent" spherical object, and the ad-hoc introduction of a diffusion-like activation energy barrier to account for hindered molecular mobility in the dense supercooled liquid. It is therefore not surprising that the resulting theory has been mostly used descriptively rather than predict vely. 

Akimov and Kraftmakher (1970), using heat capacity measurements, determined the enthalpy of formation AH (23 kcal/mole) of thermally activated defects in /3-La. This value represents one-half of the experimentally measured activation energy for self-diffusion (Dariel et al., 1969b). Since Q = AH + AHm (with AHm the enthalpy of migration of the defects) and since it is well established that AH = AHm for vacancies as diffusion determining defects in fee metals, the heat capacity results seem to constitute further evidence for a vacancy dominated self-diffusion mechanism in the close-packed structures. 

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