The electrochemical behavior of a system with a limited number of molecules

In this paper, based on Einstein relationship between diffusion and random walk, the electrochemical behavior of a system with a limited number of molecules was simulated and explored theoretically. The transition of the current vs time responses from discrete to continuous was clearly obtained as the number of redox molecules increased from 10 to 10(6).

What has brought on the effects of number-average molecular weight on the spinodals in polymer mixtures?

On the basis of the thermodynamics of Gibbs, the spinodal for the quasibinary system was derived in the framework of the Sanchez-Lacombe lattice fluid theory. All of the spinodals were calculated based on a model polydisperse polymer mixture, where each polymer contains three different molecular weight subcomponents. According to our calculations, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights, whereas that of the z-average molecular weight is invisible. Moreover, the extreme of the spinodal decreases when the polydispersity index (eta = (M) over bar (w)/(M) over bar (n)) of the polymer increases. The effect of polydispersity on the spinodal decreases when the molecular weight gets larger and can be negligible at a certain large molecular weight. It is well-known that the influence of polydispersity on the phase equilibrium (coexisting curve, cloud point curves) is much more pronounced than on the spinodal. The effect of M, on the spinodal is discussed as it results from the infuluence of composition temperatures, molecular weight, and the latter's distribution on free volume. An approximate expression, which is in the assumptions of v* v(1)* = v(2)* and 1/r --> 0 for both of the polymers, was also derived for simplification. It can be used in high molecular weight, although it failed to make visible the effect of number-average molecular weight on the spinodal.

A novel electrochemical method for simultaneously measuring diffusion coefficient and ion transference number

This paper introduces a new method to estimate the diffusion coefficient and transference number of a salt or an electroactive ion in a solution with little or no supporting electrolyte. The above two parameters can be obtained from a single potential step experiment without previous knowledge of either one. It would appear that the method could also be used in the study of ion transport in a high viscosity solvent or a solid electrolyte. (C) 1998 Elsevier Science S.A.

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.

Effect of pore ring number of zeolites on catalytic performance of Mo/Zeolite in methane aromatization under non-oxygen condition

The catalytic behavior of Mo-based zeolite catalysts with different pore structure and size, particularly with 8 membered ring ( M R), 10 M R, coexisted 10 and 12 M R, and 12 M R, was studied in methane aromatization under the conditions of SV=1500 ml/(g.h), p=0.1 MPa and T = 973 K. It was found that the catalytic performance is correlated with the pore structure of the zeolite supports. The zeolites that possess 10 MR or 10 and 12 MR pore structure with a pore diameter equal to or slightly larger than the dynamic diameter of benzene molecule, such as ZSM-5, ZSM-11, ZRP-1 and MCM-22, are fine supports. Among the tested zeolite supports, MCM-22 exhibits the highest activity and selectivity for benzene. A methane conversion of 10.5% with benzene selectivity of 80% was achieved over Mo/MCM-22 catalyst. The Mo/ERS-7 catalyst with 8 MR (0.45 nm) does not show any activity in methane dehydro-aromatization, while Mo/JQX-1 and Mo/SBA-15 catalysts with 12 MR pore exhibit little activity in the reaction. It can be concluded that the zeolites with 10 MR pore or coexisted 10 and 12 MR, having pore size equal to or slightly larger than the dynamic diameter of benzene molecule, are fine supports for methane activation and aromatization.