Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P-(1)(X,R,t)) and the product (p((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent, As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

Flow structure and heat transfer characteristics behind a diaphragm in the presence of a diffusion flame

The characteristics of the separated flow behind a diaphragm over a burning surface are investigated experimentally. This complex problem of practical significance involving recirculation, blowing and combustion reactions is studied in a two-dimensional combustion tunnel. The flame structure, recirculation patterns and heat transfer to the surface are presented for a range of values of free stream and fuel injection velocities as well as for different heights of the diaphragm. The trends of heat transfer vs axial distance are shown to be similar to those resulting from a non-reactive heated stream with a diaphragm. Treating the case of a boundary layer diffusion flame as that corresponding to the zero height of the diaphragm, the heat transfer augmentation due to recirculation is estimated. It is found that at considerable downstream distances (xfh > 3), the heat transfer rates with diaphragm overtake the rates from a developing boundary layer case. Flow visualization studies with particle track photography show that there are many similarities between the reactive and the non-reactive cases.

A molecular dynamics study of cage-to-cage migration in sodium Y zeolite: role of surface-mediated diffusion

The details of cage-to-cage migration have been obtained from an analysis of the molecular dynamics trajectory of a probe adsorbate. It is observed that particles utilize the region within a radius of 2 angstrom from the window center but with diffusion taking place predominantly at 1.6 angstrom from the window center and a potential energy of nearly -12 kJ/mol. A barrier of about 0.5 kJ/mol is observed for surface-mediated diffusion. Surprisingly, for diffusion without surface mediation for a particle going from one cage center to another, there is an attractive well near the window instead of a barrier. At low adsorbate concentrations and room temperature, the predominant mode for cage-to-cage migration is surface-mediated diffusion. The analysis suggests that particles slide along the surface of the inner walls of the alpha-cages during migration from one cage to another.

Diffusion coefficients for selected binary liquid systems: cyclohexanes and n-alkyl alcohols

In the present work the integral diffusion coefficients are estimated by using the diaphragm cell technique. The diffusion coefficients are measured at various compositions for two sets binary systems: one of cyclohexane and n-paraffinic alcohols and the other of methylcyclohexane and n-paraffinic alcohols. The alcohols used are seven members of homologous series of n-paraffinic alcohols from ethanol to octanol. The maximum possible error in the experimental diffusion coefficient could be 8% for both the cyclohexane-n-alkyl alcohol system and methylcyclohexane-n-alkyl alcohol system. A correlation for each of the two sets of binary systems is given. The maximum deviation in the correlations was less than 6.5 and 3.5% for cyclohexane-n-alkyl alcohols and methylcyclohexane-n-alkyl alcohols, respectively.

Mutual diffusion coefficients of some binary liquid systems: benzene-n-alkyl alcohol

The mutual diffusion coefficients for binary liquid systems of benzene-n-alkyl alcohol at various compositions have been determined by the diaphragm cell method at 28-degrees-C. The alcohols used were the members of n-paraffinic alcohols ranging from C1 to C8. The maximum possible experimental error is 14%. The data were fitted with a generalized correlation, giving the deviation from the experimental data to within 2.75%, on average.

Large-amplitude chirped coherent phonons in tellurium mediated by ultrafast photoexcited carrier diffusion

We report femtosecond time-resolved reflectivity measurements of coherent phonons in tellurium performed over a wide range of temperatures (3-296 K) and pump-laser intensities. A totally symmetric A(1) coherent phonon at 3.6 THz responsible for the oscillations in the reflectivity data is observed to be strongly positively chirped (i.e., phonon time period decreases at longer pump-probe delay times) with increasing photoexcited carrier density, more so at lower temperatures. We show that the temperature dependence of the coherent phonon frequency is anomalous (i.e, increasing with increasing temperature) at high photoexcited carrier density due to electron-phonon interaction. At the highest photoexcited carrier density of (1.4 x 10(21) cm(-3) and the sample temperature of 3 K, the lattice displacement of the coherent phonon mode is estimated to be as high as similar to 0.24 angstrom. Numerical simulations based on coupled effects of optical absorption and carrier diffusion reveal that the diffusion of carriers dominates the nonoscillatory electronic part of the time-resolved reflectivity. Finally, using the pump-probe experiments at low carrier density of 6 x 10(18) cm(-3), we separate the phonon anharmonicity to obtain the electron-phonon coupling contribution to the phonon frequency and linewidth.

Impurity diffusion in bismuth single-crystals

Measurements of impurity diffusion of 86Rb, 90Sr, 133Ba, and 137Cs in single crystal Bi were carried out. Diffusion samples were prepared from single crystal Bi by ion implantation. About 1012-1013 ions were implanted, resulting in surface activities approx =104 cpm. After implantation, specimens were annealed for specified times at 220-265 deg C, and tracer penetration profiles were determined by an electrolytic method. A typical penetration profile for 137Cs in Bi showed a linear relationship for log C vs x in with Fick's law for volume diffusion. Laws of grain boundary diffusion were not obeyed and the order of magnitude of the penetration distances was much less than on a grain boundary mechanism. Results were interpreted in terms of a modified Fischer analysis using a kinetic trapping term. Effective half lengths for trapping at a twin boundary were determined for each impurity.

Atmospheric boundary-layer across Hadley and Ferrel cells over the Indian Ocean

A Southern Ocean Pilot cruise covering the latitudes from 10 degrees N to 56 degrees S in the open Indian Ocean was carried out during January February 2004. Surface and upper air data collected during this cruise are reported here. It is shown that the broad features of the atmosphere, in particular that of temperature, follow the tropical and mid-latitude weather expected during January February in this region. However, the atmospheric boundary-layer shows large variations, both in its height and structure between tropics and high latitudes. Strong influence of the surface heat flux on boundary layer structure is clearly seen. Humidity field reveals several local maxima and minima, suggesting a laminated atmosphere with air from different sources moving almost unmixed in adjacent layers.

Influence of non-geometrical factors on intracrystalline diffusion -- Role of sorbate-zeolite interactions

Molecular dynamics simulations on Xe in NaY and Ar in NaCaA zeolite are reported. Rates of cage-to-cage crossovers in the two zeolites exhibit trends which are contrary to that expected from geometrical considerations. The results suggest the important role of the sorbate-zeolite interactions in determining the molecular sieve properties of zeolites for small sized sorbates. The results are explained in terms of the barrier height for cage-to-cage crossover in the two zeolites.

Sorbate properties and cage-to-cage diffusion of argon in NaCaA: a molecular dynamics study

Detailed molecular dynamics simulations of argon in zeolite NaCaA are reported. Thermodynamic, structural, and dynamical properties of the sorbate as a function of temperature have been obtained. The properties calculated include various site-site radial distribution functions, different energy distribution functions, selfdiffusion coefficients, the power spectra, and properties relating to cage-to-cage diffusion. The results suggest that sorbate is delocalized above 300 K. Both modes of cage-to-cage diffusion-the surface-mediated and centralized diffusion-are associated with negative barrier heights. Surprisingly, rate of cage-to-cage diffusion is associated with negative and positive activation energies below and above 500 K. The observed differences in the behavior of the rate of cage-to-cage diffusion between Xe-NaY and Ar-NaCaA systems and the nature of the potential energy surface are discussed. Presence of sorbatezeolite interactions results in significant enhancement in the rate of cage-to-cage diffusion and rate of cage visits. It is shown that properties dependent on the long-time behavior such as the diffusion coefficient and the rate of cages visited exhibit the expected Arrhenius dependence on temperature.

Growth mechanism of phases by interdiffusion and diffusion of species in the niobium-silicon system

The integrated diffusion coefficient of the phases and the tracer diffusion coefficients of the species are determined in the Nb-Si system by the diffusion couple technique. The diffusion rate of Si is found to be faster than that of Nb in both the NbSi2 and Nb5Si3 phases. The possible atomic mechanism of diffusion is discussed based on the crystal structure and on available details of the defect concentration data. The faster diffusion rate of Si in the Nb5Si3 phase is found to be unusual. The growth mechanism of the phases is also discussed on the basis of the data calculated in this study. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Effect of sodium diffusion on the structural and electrical properties of Cu2ZnSnS4 thin films

Cu2ZnSnS4 (CZTS) is a kesterite semiconductor consisting of abundantly available elements. It has a band gap of 1.5 eV and a large absorption coefficient. Hence, thin films made of this material can be used as absorber layers of a solar cell. CZTS films were deposited on soda lime and Na free borosilicate glass substrates through Ultrasonic Spray Pyrolysis. The diffusion of sodium from soda lime glass was found to have a profound effect on characteristics like grain size, crystal texture and conductivity of CZTS thin films. Copper ion concentration also varied during the deposition and it was observed that the carrier concentration was enhanced when there was a deficiency of copper in the films. The effect of sodium diffusion and copper deficiency in enhancing the structural and electrical properties of CZTS films are presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.