Configurational diffusion coefficient

Knudsen diffusion is generally encountered in heterogeneous catalysis. In the smallest pores configurational diffusion takes place with diffusion coefficient ranging from 10 to 10 m /s. 

Several investigators have used the two-chamber diffusion cell configuration. This experimental method has been found useful to determine diffusion coefficients [11] and to study drug transport from drug delivery devices [12],... 

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. 

C4 hydrocarbons, presence of water in NaX, self-diffusion coefficients, 39 391-393 Chymotrypsin, 20 344, 356, 386, 387 Cl, see Configuration interaction Cirmarttaldehyde, hydrogenation of, 42 490... 

The viscosity relates to the longest relaxation time in a system. If we consider Rouse diffusion along the tube with a Rouse diffusion coefficient DJ l/ NQ) then an initial tube configuration is completely forgotten when the mean-square displacement along the tube fulfils (r (t))tube=(contour length ly. Thus, for the longest relaxation time, we obtain ... 

The computational efficiency of a FF approach also enables simulations of dynamical behavior—molecular dynamics (MD). In MD, the classical equations of motion for a system of N atoms are solved to generate a search in phase space, or trajectory, under specified thermodynamic conditions (e.g., constant temperature or constant pressure). The trajectory provides configurational and momentum information for each atom from which thermodynamic properties such as the free energy, or time-dependent properties such as diffusion coefficients, can be calculated. 

The error concerned an explicit formula for the translational diffusion coefficient. Kirkwood calculated the diffusion tensor as the projection onto chain space of the inverse of the complete friction tensor he should have projected the friction tensor first, and then taken the inverse. This was pointed out by Y. Ikeda, Kobayashi Rigaku Kenkyushu Hokoku, 6, 44 (1956) and also by J. J. Erpenbeck and J. G. Kirkwood, J. Chem. Phys., 38, 1023 (1963). An example of the effects of the error was given by R. Zwanzig, J. Chem. Phys., 45, 1858 (1966). In the present article this question does not come up because we use the complete configuration space. 

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

Diffusion and adsorption studies with Boscan VO-porphyrin extracts and pure VO-TPP in C0M0/AI2O3 catalysts have been reported by Morales and co-workers (Galiasso and Morales, 1983 Morales and Galiasso, 1982 Andreu et al., 1981 Morales et al., 1984). The Boscan extract contained up to 30 wt. % vanadyl DPEP and vanadyl etioporphy-rin. Effective diffusion coefficients at 300°C in a catalyst with an average pore diameter of 150 A (A < 0.1) are on the order of 10-5 cm2/sec. Configurational effects are minor for this system. 

---