Single-component diffusion coefficients

For the systems described in this chapter, the values for om and ow are om = 5.8 and om = 7.0 A for / -xylene and o-xylene, respectively [11,12] and ow = 7 A for the SSZ-24 channel windows and ow = 5.8 A for the ZSM-11 zeolite [112], Therefore, p-xylene and o-xylene relatively, freely move in H-SSZ-24 during single-component diffusion, inasmuch as r p x = 0.83 and T 0, = 1.00. In addition, for H-ZSM-11, the single-component diffusion of o-xylene is hindered by steric factors inasmuch as rp= 1.21, but the single-component diffusion for / -xylene is relatively free since rp, = 1. These facts are reflected on the reported single-component diffusion coefficients (see Table 5.3). Besides, the results reported in Table 5.3 reasonably agree with data previously reported in the literature for the diffusion of xylenes in zeolites with 10- and 12-MR channels [88,116-120],... 

The current work indicates the strong effect of acid sites on the interaction and diffusivity of hydrocarbons. To further study this effect, we determined the single-component diffusion coefficients and specifically the activation energy for diffusion. Activated diffusion is described by the Arrhenius-type Eq. 8. The pre-exponential factor Djnf is related to the jump frequency between adsorption sites in the zeolite lattice, while the exponential expresses the chance that the molecules are able to overcome the free energy barrier - act between these sites. The loadings of n-hexane and 2-methylpentane in H-ZSM-5 and silicalite-1 have been measured at temperatures between 373 and 533 K at intervals of 20 K. The hydrocarbon pressure was taken identical... 

The diffusion coefficients for Rb, Cs and Sr in obsidian can be calculated from the aqueous rate data in Table 1 as well as from the XPS depth profiles. A simple single-component diffusion model (9j characterizes onedimensional transport into a semi-infinite solid where the diffusion coefficient (cm2-s 1) is defined by ... 

D is the chemical diffusion coefficient in the case of the single-component diffusion of hydrogen... 

This equipment can be used for the study of a single-component diffusion, and the measurement of the corresponding Fickean diffusion coefficient made using a solution of Fick s second law for a geometry appropriate for the experimental setup [87-92], In this case, the flow rates were adjusted to get the desired partial pressure (6.7 Pa, P/Pn = 0.006) [90],... 

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... 

Diffusion in multicomponent system is difficult to analyze. Transport of one component is affected by the presence of the other component due to their mumal interaction. This results in the coupling of fluxes. Thus, single-component diffusion equation cannot be used to predict diffusion in a multicomponent system. Greenlaw et al. [38] proposed a simple relationship in which the diffusion coefficients for components i and j are interdependent on both component concentrations ... 

G. J. Janz and N. P. Bansal, J. Phys. Chem. Ref 11 (1982) 505 Molten Salts Diffusion Coefficients in Single and Multi-Component Salt Systems, American Chemical Society-American Institute of Physics-National Bureau of Standards, Washington, DC, 1982. 

Chemical diffusion has been treated phenomenologically in this section. Later, we shall discuss how chemical diffusion coefficients are related to the atomic mobilities of crystal components. However, by introducing the crystal lattice, we already abandon the strict thermodynamic basis of a formal treatment. This can be seen as follows. In the interdiffusion zone of a binary (A, B) crystal having a single sublattice, chemical diffusion proceeds via vacancies, V. The local site conservation condition requires that /a+/b+7v = 0- From the definition of the fluxes in the lattice (L), we have... 

There are many experiments which determine only specific frequency components of the power spectra. For example, a measurement of the diffusion coefficient yields the zero frequency component of the power spectrum of the velocity autocorrelation function. Likewise, all other static coefficients are related to autocorrelation functions through the zero frequency component of the corresponding power spectra. On the other hand, measurements or relaxation times of molecular internal degrees of freedom provide information about finite frequency components of power spectra. For example, vibrational and nuclear spin relaxation times yield finite frequency components of power spectra which in the former case is the vibrational resonance frequency,28,29 and in the latter case is the Larmour precessional frequency.8 Experiments which probe a range of frequencies contribute much more to our understanding of the dynamics and structure of the liquid state than those which probe single frequency components. 

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

We write the exact solution of the diffusion in a velocity field with a single Fourier-component. The expression for the effective diffusion contains the molecular diffusion coefficient as a factor this ensures correct behavior of the result with respect to time reversal. 

Figure 2.16 Illustration of isotopic fractionation effects in diffusion. The model is that 132Xe and 134Xe are initially uniformly distributed throughout spheres in the ratio 134Xe/132Xe = 0.382 and then allowed to escape by diffusion with the boundary condition that the concentration vanishes on the surface. The figure shows the instantaneous composition of the released gas at various stages, assuming that the diffusion coefficients varies as m 112. The single-component locus is for all spheres having the same radius the mixed-component locus is for distribution of sizes. Reproduced from Funk, Podosek, and Rowe (1967).

When the relative volumes are known and the diffusion coefficients in the capsule core and capsule membrane can be estimated a priori in single component adsorption, the parameter to work with is the effective diffusivity in the adsorbent pore (Dn). Then, with the above estimated parameter values, the parameters of competitive adsorption are the maximum concentration at the solid phase of the adsorbent (CsmT), and the equilibrium constants of the target product (KS1) and byproduct (KS2)-... 

Figure 4.7. Determination of translational diffusion coefficient. Plots of ln[(G(nAf))/B) - 1] versus time for collagen a chains (top) and mixtures of a chains and P components (bottom). The translational diffusion coefficient is obtained by dividing the slope of each line by -2Q2, where Q is the scattering vector. B is the baseline of the autocorrelation function. Note for single molecular species, the slope is constant, and for mixtures with different molecular weights, the slope varies (molecular weight for a chains is 95,000 and for y components is 285,000). (reproduced from Silver, 1987).

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