Coefficient of free diffusion

Plasma-Chemical Kinetics, Thermodynamics, and Electrodynamics Table 3-2. Coefficients of Free Diffusion of Electrons and Ions at Room Temperature... 

Components of gas mixtures generally have unequal M, fi, and with ions that result in different fl(T) functions. The coefficient of free diffusion for an ion in mixture, is governed by " ... 

A second point is that the coefficients of free diffusion are always higher than the equilibrium parameter (Table I). 

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... 

From a theoretical point of view, charge propagation in films containing space-distributed redox centers can be achieved either by the physical displacement of the sites or by the transference (hopping) of electrons from neighboring reduced to oxidized sites or by the combination of both processes. In the case of free diffusing couples immobilized in oppositely charged polyelectrolytes, both processes occur and an apparent diffusion coefficient can be defined and measured [136, 142, 143] ... 

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... 

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. 

If we assume that the solute penetrates only through the water-filled channels in the membrane (with volume fraction c/jw), then the solute-water frictional coefficient is close to that of free diffusion D°... 

Constants Dv and Co are determined as free parameters in the non-linear regression of the experimental J(t) dependence along with the theoretical one calculated by the least square root method. The theoretical curve calculated at Co = 1. 7-10 4 mol dm 3 and >v = 4-1 O 6 cm2 s 1 is presented with solid line in the figure. The approximation of the lattice model of the amphiphile bilayer Dv is related to the coefficient of lateral diffusion of surfactant molecules building up the bilayer by the degree of filling 0 (respectively, of vacancies 6V)... 

Figure 13 shows the absorption spectra for a nitroxide spin probe and compares the case of free diffusion (P2 0) with those obtained for various values of the orienting potential. Such spectra have been calculated for an isotropic diffusion coefficient. Note the drastic change in lineshape at the onset of molecular order. 

It had been previously derived from the theoretical equations of free diffusion that when the precipitation zone does not move the ratio of its distance to the respective sources of antigen and antibodies is equal to that of the square roots of the diffusion coefficients of these reagents.In double diffusion in two dimensions from circular reservoirs, the shape of the precipitation zone depends on the relative diffusion coefficients of the antigen and the antibodies. When these diffusion coefficients are sufficiently different from one another, the shape of the precipitation zone is that of an arc with its convexity toward the reservoir of the reagent with the smaller diffusion coefficient. ... 

Ambipolar Diffusion. Estimate the coefficient of ambipolar diffusion in room- temperature atmospheric-pressure nitrogen at electron temperature about 1 e V Compare the coefficient with that for the free diffusion of electrons and nitrogen molecular ions (take ion temperature as room temperature). 

Here Do is the coefficient of Brownian diffusion determined by the formula (8.70), and corresponding to the free Brownian motion of particles. The factor X depends on the relative distance between approaching particles and can be determined from the resistance law F = 6nftaUX r/a), which is applicable to the relative motion of particles along their line of centers with the velocity U (see expression (8.36)). 

The two-site model leads to the definition of the degree of counterion binding, p, as the ratio of counterions to surfactant ions in a surfactant self-assembly. This is a useful but incomplete characterization of the counterion distribution. The value of p can be obtained directly from self-diffusion data because the self-diffusion coefficients of free ions are easily obtainable. For free counterion diffusion a correction is made for the obstruction effect. The micellar D value is obtained as described above or estimated as Dm free. an exact Dm value is not critical. 

The diffusion coefficient under free-diffusion conditions can be measured by analysis at the termination of the experiment or by continuous or intermittent analysis while diffusion continues. Care has to be taken not to disturb the system, and the most widely employed methods for measuring diffusion coefficients in liquids are interferometric, resulting from the original work of Gouy in the 19th century. 

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 ... 

Diffusion coefficient of free ferrocene derivative. Diffusion coefficient of CD-bound ferrocene derivative. 

In Equation 3.54, r] is the viscosity of the polymerizing medium, t]o the viscosity of the pure monomer, and k rj represents the rate coefficient of translational diffusion at zero conversion fit to experimental data [10]. Equation 3.55 has been used to fit, for example, styrene polymerization rate data to high conversion over a range of temperatures [16]. In the free-volume (vf) approach [48, 49], parameters are fitted to experimental data, with the effect of polymer MW on system viscosity being captured by expressing Ci as a function of Mw Further details and variations of these modeling approaches can be found in the literature [10, 50-53]. 

The z = 0 plane does not correspond to the average concentration (Q -I- C )/2 unless 2>ab independent of composition. Duda and Vrentas have analyzed the more complex case of free diffusion, where there is a volume change of mixing, and have shown that neglecting volume changes may introduce significant errors in the diffiision coefficients calculated. 

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