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.

Effect of Ni content on the diffusion-controlled growth of the product phases in the Cu(Ni)-Sn system

A strong influence of Ni content on the diffusion-controlled growth of the (Cu,Ni)(3)Sn and (Cu,Ni)(6)Sn-5 phases by coupling different Cu(Ni) alloys with Sn in the solid state is reported. The continuous increase in the thickness ratio of (Cu,Ni)(6)Sn-5 to (Cu,Ni)(3)Sn with the Ni content is explained by combined kinetic and thermodynamic arguments as follows: (i) The integrated interdiffusion coefficient does not change for the (Cu,Ni)(3)Sn phase up to 2.5 at.% Ni and decreases drastically for 5 at.% Ni. On the other hand, there is a continuous increase in the integrated interdiffusion coefficient for (Cu,Ni)(6)Sn-5 as a function of increasing Ni content. (ii) With the increase in Ni content, driving forces for the diffusion of components increase for both components in both phases but at different rates. However, the magnitude of these changes alone is not large enough to explain the high difference in the observed growth rate of the product phases because of Ni addition. (iv) Kirkendall marker experiments indicate that the Cu6Sn5 phase grows by diffusion of both Cu and Sn in the binary case. However, when Ni is added, the growth is by diffusion of Sn only. (v) Also, the observed grain refinement in the Cu6Sn5 phase with the addition of Ni suggests that the grain boundary diffusion of Sn may have an important role in the observed changes in the growth rate.

Electric current induced flow of liquid metals: Mechanism and substrate-surface effects

Long range, continuous flow of liquid metals occurs upon application of an electric current. Here, we report experimental results elucidating the mechanism of current-induced liquid metal flow, and its dependence on substrate surface condition. It is shown that the observed flow is diffusion-controlled, with the flow-rate depending linearly on applied current density, indicating that it is driven by electromigration. The effective charge number for liquid electromigration, Z*, of several pure metals, such as Al, Bi, Ga, Sn, and Pb, were deduced from the experimental results and were found to be close to the elemental valency. With the exception of liquid Pb, Z* for all liquid metals tested in this study were positive, indicating that: (i) electron wind contributes much less to Z* in liquid metals than in solids, and (ii) with a few exceptions, liquid metals generally flow in the direction of the electric current. On smooth substrates which are wetted well by the liquid metal, flow occurs in a thin, continuous stream. On rough surfaces which are poorly wetted, on the other hand, discrete beads of liquid form, with mass transport between adjacent beads occurring by surface diffusion on the substrate. A rationale for the role of substrate roughness in fostering this observed transition in flow mechanism is presented. (C) 2014 AIP Publishing LLC.

A Comparative Study of Electrochemical Kinetic Parameters by the Potential Step Method. Electrode Reactions of CyDTA and EDTA Complexes of Cu(II) at DME

By using the same current-time (I-t) curves, electrochemical kinetic parameters are determined by two methods, (a) using the ratio of current at a given potential to the diffusion-controlled limiting current and (b) curve fitting method, for the reduction of Cu(II)–CyDTA complex. The analysis by the method (a) shows that the rate determining step involves only one electron although the overall reduction of the complex involves two electrons suggesting thereby the stepwise reduction of the complex. The nature of I-t curves suggests the adsorption of intermediate species at the electrode surface. Under these circumstances more reliable kinetic parameters can be obtained by the method (a) compared to that of (b). Similar observations are found in the case of reduction of Cu(II)–EDTA complex.

Influence of surface chemistry of mesoporous alumina with wide pore distribution on controlled drug release

The crucial role of the drug carrier surface chemical moeities on the uptake and in vitro release of drug is discussed here in a systematic manner. Mesoporous alumina with a wide pore size distribution (2-7 nm) functionalized with various hydrophilic and hydrophobic surface chemical groups was employed as the carrier for delivery of the model drug ibuprofen. Surface functionalization with hydrophobic groups resulted in low degree of drug loading (approximately 20%) and fast rate of release (85% over a period of 5 h) whereas hydrophilic groups resulted in a significantly higher drug payloads (21%-45%) and slower rate of release (12%-40% over a period of 5 h). Depending on the chemical moiety, the diffusion controlled (proportional to time(-0.5)) drug release was additionally observed to be dependent on the mode of arrangement of the functional groups on the alumina surface as well as on the pore characteristics of the matrix. For all mesoporous alumina systems the drug dosages were far lower than the maximum recommended therapeutic dosages (MRTD) for oral delivery. We envisage that the present study would aid in the design of delivery systems capable of sustained release of multiple drugs.

Effect of surface roughness on diffusion-limited charge transfer

A theory is developed for diffusion-limited charge transfer on a non-fractally rough electrode. The perturbation expressions are obtained for concentration, current density and measured diffusion-limited current for arbitrary one- and two-dimensional surface profiles. The random surface model is employed for a rough electrode\electrolyte interface. In this model the gross geometrical property of an electrochemically active rough surface - the surface structure factor-is related to the average electrode current, current density and concentration. Under short and long time regimes, various morphological features of the rough electrodes, i.e. excess area (related to roughness slope), curvature, correlation length, etc. are related to the (average) current transients. A two-point Pade approximant is used to develop an all time average current expression in terms of partial morphological features of the rough surface. The inverse problem of predicting the surface structure factor from the observed transients is also described. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how the surface roughness enhances the overall diffusion-limited charge transfer current.

Electrochemical copolymerization of thiophene derivatives; a precursor to photovoltaic devices

This work presents an electrochemical technique for the polymerization and copolymerization of thiophene derivatives like 7,9-dithiophene-2yl-8H-cyclopenta[a]acenaphthalene-8-one and 3-hexylthiophene. The structural characterization of chemically synthesized monomers and electro-chemically synthesized polymers was carried out by nuclear magnetic resonance and Fourier transform infrared spectroscopy. Thermal characterizations indicate that copolymer has increased thermal stability than that of homopolymer. Morphological studies of the polymerized films carried out by scanning electron microscopy shows network structure of copolymer. Optical properties of the homopolymers and copolymer were studied by UV-visible spectrometer and it was observed that band gap of copolymer is less than the homopolymers. HOMO and LUMO levels, band gap values of the respective polymers were also calculated from the cyclic voltammetry technique with various scan rates. By the peak current obtained from various scan rates shows that all polymerization reactions are diffusion controlled process. Charge transfer resistances of polymers were determined using Nyquist plots. Conductivity of synthesized polymers shows higher conductivity for copolymer than homopolymers. (C) 2011 Elsevier Ltd. All rights reserved.

Dislocation mechanisms for plastic flow of nickel in the temperature range 4.2 – 1200 K

The temperature ranges of thermal and athermal deformation behaviour of nickel are identified by employing the temperature-dependence of flow-stress and strain-rate cycling data. The results are used to present a unified view of dislocation mechanisms of glide encompassing the two thermally activated and the intermediate athermal regimes of plastic flow.In the low-temperature thermally activated region (<250 K) the strain rate is found to be controlled by the repulsive intersection of glide and forest dislocations, in accordance with current ideas. The athermal stress in this region can be attributed mainly to the presence of strong attractive junctions which are overcome by means of Orowan bowing, a small contribution also coming from the elastic interactions between dislocations. The values of activation area and activation energy obtained in the high-temperature region (> 750 K) negate the operation of a diffusion-controlled mechanism. Instead, the data support a thermal activation model involving unzipping of the attractive junctions. The internal (long-range) stress contribution here results solely from the elastic interactions between dislocations. This view concerning the high-temperature plastic flow is further supported by the observation that the Cottrell–Stokes law is obeyed over large strains in the range 750–1200 K.

Growth of hafnium and zirconium suicides by reactive diffusion

Diffusion controlled growth of the phases in Hf-Si and Zr-Si systems are studied by bulk diffusion couple technique. Only two phases grow in the interdiffusion zone, although several phases are present in both the systems. The location of the Kirkendall marker plane, detected based on the grain morphology, indicates that disilicides grow by the diffusion of Si. Diffusion of the metal species in these phases is negligible. This indicates that vacancies are present mainly on the Si sublattice. The activation energies for integrated diffusion coefficients in the HfSi2 and ZrSi2 are estimated as 394 +/- 37 and 346 +/- 34 kJ mol(-1), respectively. The same is calculated for the HfSi phase as 485 +/- 42 kJ mol(-1). The activation energies for Si tracer diffusion in the HfSi2 and ZrSi2 phases are estimated as 430 +/- 36 and 348 +/- 34 kJ mol(-1), respectively. (C) 2013 Elsevier B.V. All rights reserved.

Growth of hafnium and zirconium suicides by reactive diffusion

Diffusion controlled growth of the phases in Hf-Si and Zr-Si systems are studied by bulk diffusion couple technique. Only two phases grow in the interdiffusion zone, although several phases are present in both the systems. The location of the Kirkendall marker plane, detected based on the grain morphology, indicates that disilicides grow by the diffusion of Si. Diffusion of the metal species in these phases is negligible. This indicates that vacancies are present mainly on the Si sublattice. The activation energies for integrated diffusion coefficients in the HfSi2 and ZrSi2 are estimated as 394 +/- 37 and 346 +/- 34 kJ mol(-1), respectively. The same is calculated for the HfSi phase as 485 +/- 42 kJ mol(-1). The activation energies for Si tracer diffusion in the HfSi2 and ZrSi2 phases are estimated as 430 +/- 36 and 348 +/- 34 kJ mol(-1), respectively. (C) 2013 Elsevier B.V. All rights reserved.

Curing Reactions in Elastomers. 11. Carboxy- Terminated Polybutadiene

Attempts have been made to understand the curing reactions in carboxy-terminated polybutadiene (CTPB), which happens to be the most practical binder in advanced solid composite propellants. The curing of CTPB has been studied for different ratios of curing agents (MAPO and Epoxide) by gel content, molecular weight, crosslink density, and penetration temperature measurements, and the optimum composition of curators for effective curing of CTPB has been determined. Activation energy calculations on the curing of CTPB with 9.5% epoxide and 0.5% MAPO in the temperature range 75100°C gave 14.1 kcal/mol for which a diffusion-controlled or acid-catalyzed epoxide ring opening mechanism has been suggested for the curing process in CTPB.

Electrochemical phase formation (ECPF) and macrogrowth Part I. Hemispherical models

The phenomenological theory of hemispherical growth is generalised to time-dependent nucleation and growth-rates. Special cases, which include models with diffusion-controlled rates, are analysed. Expressions are obtained for small and large time behaviour and peak characteristics of potentiostatic transients, and their use in model parameter estimation is discussed. Two earlier equations are corrected. Numerically calculated transients which are presented exhibit some interesting features such as a maximum preceding the steady state, oscillations and shoulder.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

Inhibition of self-quenching in thioketones by micellar compartmentalization

The technique of micellar compartmentalization has been used to inhibit the diffusion-controlled self-quenching process in thioketones. By adjusting the ratio of the bulk concentration of the thioketone solute to the bulk concentration of micelles multiple occupancy of the micelles was avoided. Under these conditions enhanced phosphorescence intensity was observed in nitrogen-purged micellar solutions compared with that in acetonitrile solutions, indicating that the thioketone triple was indeed protected from deactivation by a ground statet