Coefficient of self diffusion

Free shear flows, 77 757-760 Free sintering, 73 300 Free spectral range (FSR), 74 671-672 Free surface vaporization, 24 724-725 Free-vibration instruments, 27 745 Free-volume coefficient of self-diffusion, 23 102... 

This quantity is called the coefficient of self-diffusion. Equation (87) also describes the interdiffusion of ortho- and para-forms. 

Fig. 3. Generalized chart for calculation of the coefficient of self-diffusion of gases at high densities, prepared by Slattery (S10),...

In both cases, ctj i depends on PO2- Figure 1.43 shows that eqn (1.167) is dominant in the pressure range I O2 > 10 atm and eqn (1.168) is dominant in the pressure range 02 < 10 atm. In the former case, CT , depends on temperature because ion mobility is temperature dependent. The relation between the ionic and electronic conductivity for solid electrolytes is shown schematically in Fig. 1.44. Since ionic conductivity originates from diffusion of ions in the solid phase, (Tio is closely related to the coefficient of self diffusion of ions ( X,o ) shown by the following equation... 

The coefficients of self diffusion for each of these simulations (see Tables II, III, IV, and V), are all very close to those measured experimentally for liquid CO.52 If we were dealing with solids these coefficients would be an order of magnitude or more smaller. 

Theoretical formulas show that the self-diffusivity of interstitial metal atoms decreases with an increase in the concentration of included hydrogen, which blocks free interstitial sites. A calculation of the coefficient of self-diffusion in the QCA is presented in Fig. 8.14. To calculate concentration dependences of the self-diffusivity, authors used eHh = 0-6 kcal/mol [217]. The curves are normalized to a self-diffusivity of 2.9 x 1CT3 sm/sec at 0H = 0 [218]. As can be seen, the character of curves 1-3 and 5 substantially depends on the value of an = hh/shh, which reflects the difference between... 

Relation (5.4) is used to describe the dependence in the region of lengths below 2Me, whereas in the region above 2Me, the two mechanisms of the displacement of the centre of mass of the macromolecule are optional, so that the resulting coefficient of self-diffusion has to be defined as... 

The results of estimation of coefficient of self-diffusion due to simulation for macromolecules with different lengths are shown in Fig. 12. The introduction of local anisotropy practically does not affect the coefficient of diffusion below the transition point M, the position of which depends on the coefficient of local anisotropy. For strongly entangled systems (M > M ), the value of the index —2 in the reptation law is connected only with the fact of confinement of macromolecule, and does not depend on the value of the coefficient of local anisotropy. At the particular value ae = 0.3, the simulation reproduces the results of the conventional reptation-tube model (see equation (5.21)) and corresponds to the typical empirical situation (M = 10Me). 

Equation (6-17) can be easily adapted for the critical state, if p is substituted with the critical pressure, pc, obtained with Eq. (6-12) and if W/ in the exponent is substituted with w, e. This takes into account the absence of a pure translational energy contribution in the critical state. On the contrary, an additional negative term, the critical compression factor Zc = -w,lw, is introduced in the exponent, taking into account the decrease in diffusion velocity caused by attraction between the particles. As a result the following equation gives the coefficient of self-diffusion in the critical state ... 

Single-component diffusion under equilibrium conditions can be monitored either by labeling some of the molecules or by following their trajectories. Considering the diffusion flux of the labeled molecules, again a proportionality relation of the type of eq 2 may be established. The factor of proportionality is called the coefficient of self-diffusion (or tracer diffusion). In a completely equivalent way [2], the self-diffusion coefficient may be determined on the basis of Einstein s relation... 

Diffusivities are often measured under conditions which are far from those of catalytic reactions. Moreover, corresponding to their different nature, the various measuring techniques are limited to special ranges of application. The possibility of a mutual transformation of the various diffusivities would therefore be of substantial practical relevance. Since each of the coefficients of self-diffusion and transport diffusion in single-component and multicomponent systems refers to a particular physical situation, one cannot expect that the multitude of information contained in this set of parameters can in general be adequately reflected by a smaller set of parameters. Any correlation which might be used in order to reduce the number of free parameters must be based on certain model assumptions. 

At 0°C the coefficient of viscosity of N2 = 1.66 X 10 poise. From this compute the collision diameter of N2 and compare it with the diameter of N2 computed from (a) the volume of solid N2 assuming hexagonal close packing (i.e., 12 nearest neighbors), (h) Van der Waals constant b, computed from the critical volume of N2 gas. (c) Compute the coefficient of self-diffusion of N2 gas at STP. 

The quantities Db and rjg denote the Boltzmann coefficients of self-diffusion and viscosity determined by the expressions... 

This is called a Green-Kubo relation25 (see Chapters 10 and 11, andZwanzig, 1965). Thus we expect the results of the diffusion equation to be valid for times long compared to the velocity-correlation time, and the coefficient of self diffusion to be proportional to the area under the velocity correlation function. 

The preliminaries to Eqs. (48) contain the following (exact) expression for the coefficient of self diffusion [identical with Eq. (46)] ... 

In conventional sorption experiments it is the process of adsorption or desorption itself that is considered in determining the transport behavior of the adsorbate. Referring as they do to different physical situations (namely to equilibrium and nonequilibrium states), the coefficients of self-diffusion and transport cannot be expected to be identical. However, for various microdynamic models [4,5, 111-114] the relation between the two coefficients is found to be given by Eq. (5),... 

For pure liquids the relationship between the transfer coefficient L or coefficient of self-diffusion D is determined via the ratio (Eq. 33), which can be rewritten in a form of the Walden s rule (L=D)... 

The relationships below give the energy required for the diffusion process and compare the sizes of holes required for the solvent and polymer jumping unit to move within the system. The free-volume coefficient of self-diffusion is given by the equation ... 

The microscopic theory based on the Liouville equation leads to diffusion equation (235) for t with the coefficient of self-diffusion D given by an equation identical to (236) except that in the microscopic theory the angular bracket is taken to be the average over an equilibrium ensemble. To be... 

Moreover, one can also show that the time integral of (248) for PD,o(t) leads to exactly the same values for the coefficient of self-diffusion D as given by the Boltzmann equation. Similarly the time integral of po e(0 Eq- (250), leads to an expression for D that is identical to the Enskog theory result. ... 

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