Search

The degree of personalization that a Web site offers in presenting its services to users is an important attribute contributing to the site's popularity. Web server access logs contain substantial data about user access patterns. One way to solve this problem is to group users on the basis of their Web interests and then organize the site's structure according to the needs of different groups. Two main difficulties inhibit this approach: the essentially infinite diversity of user interests and the change in these interests with time. We have developed a clustering algorithm that groups users according to their Web access patterns. The algorithm is based on the ART1 version of adaptive resonance theory. In our ART1-based algorithm, a prototype vector represents each user cluster by generalizing the URLs most frequently accessed by all cluster members. We have compared our algorithm's performance with the traditional k-means clustering algorithm. Results showed that the ART1-based technique performed better in terms of intracluster distances. We also applied the technique in a prefetching scheme that predicts future user requests.

We develop a theory for the electrical admittance of a rough interface under diffusion-limited and partial diffusion-limited charge transfer conditions. The large and small-frequency expansion brings out the relationships between the various morphological features of the rough electrode i.e. area, curvature and width, and the average admittance. The diffusion-limited reaction admittance is determined on an approximately self-affine corrugated random surface fractal. We obtain exact results for the low roughness and the asymptotic results (in three frequency regions) for the arbitrary and large roughness surfaces. These results show an anomalous frequency dependence for the mean admittance and the mean excess admittance for the large and small roughness surfaces, respectively. The intermediate frequency behavior of the reaction admittance for small roughness interfaces has the following form: 〈Y〉∼(iω)1/2+const.(iω)3/2−H, where H is Hurst's exponent, for the large roughness interfaces it has same form as predicted earlier: 〈Y〉∼(iω)1−H/2. This non-universality and dependence of intermediate-frequency behavior on the strength of interfacial fractality has not been previously conceived. We also show the localization of the active zones in the presence of roughness. Finally, these results unravel the connection between the total reaction admittance and the crossover frequency to the roughness characteristics likes the fractal dimension, lower and upper fractal cutoff lengths, and the amplitude of the fluctuations of the fractal.

Tubular components subjected to severe thermal conditions are widely used by industry in many applications such as radiant burners and heat exchangers. As would be expected, these applications often involve thermal transients that are severe enough to induce fatigue, and eventually failure. In order to be able to predict these failures and the thermoelastic stresses that are the underlying cause, a detailed understanding of the transient temperature distributions is essential. Although there have been numerous analytical models, they have been limited to severe and often unrealistic step or linear temperature changes [1, 2] . More recent studies [3–5] have shown the potentially complicated time dependence of the surface temperature loading and need for improved estimates using finite-element analysis along with a temperature-matching scheme when temperature dependent materials properties are involved. However, the finite element calculations were iterative and required an analytical starting point for the prescribed surface temperatures, as well as a means for verifying the numerical solution. Because of these needs, an analytical model of the thermal transients developed within tubular components subjected to a more realistic, time dependent boundary condition is ultimately required. Accordingly, this paper derives the equations for a hollow cylinder with a plausible exponential boundary condition of the form H ( t ) = V (1− e −ct ) for the internal surface with external convection to the external environment. Additionally, the unit response of a cylinder subjected to an internal step load with external convection is also derived.

The effects of anodic and cathodic overvoltages given by Butler–Volmer expressions on the determination of bypass parasitic currents are studied in detail, as a function of several design parameters like the bypass resistance and the number of plates as well as other electrochemical parameters like the cell current, the anodic/cathodic exchange currents and the transfer coefficients. The failure of Tafel approximation in the middle plates (even when the cell current is large) is illustrated. Exact expressions for an approximate model are compared with our calculations.

An analysis of leakage currents in bipolar systems is carried out, using an equivalent circuit approach. The resulting non-linear difference equations appropriate to the Tafel regime are solved by four different methods: 1. (a) piecewise linear method (PLM), 2. (b) iterative piecewise linear method (IPLM), 3. (c) Adomian decomposition method (ADM), 4. (d) Piecewise linear continuum (PLC). On the basis of the numerical analysis, it is seen that PLM is a good approximation, and IPLM as well as ADM converge rapidly to the true values. These results are also compared with a continuum version.

The effect of a one-dimensional field (1) on the self-absorption characteristics and (2) when we have a finite numerical aperture for the objective lens that focuses the laser beam on the solid are considered here. Self-absorption, in particular its manifestation as an inner filter for the emitted signal, has been observed in luminescence experiments. Models for this effect exist and have been analyzed, but only in the absence of space charge. Using our previous results on minority carrier relaxation in the presence of a field, we obtain expressions incorporating inner filter effects. Focusing of a light beam on the sample, by an objective lens, results in a three-dimensional source and consequently a three-dimensional continuity equation to be solved for the minority carrier concentration. Assuming a one-dimensional electric field and employing Fourier-Bessel transforms, we recast the problem of carrier relaxation and solve the same via an identity that relates it to solutions obtained in the absence of focusing effects. The inner filter effect as well as focusing introduces new time scales in the problem of carrier relaxation. The interplay between the electric field and the parameters which characterize these effects and the consequent modulation of the intensity and time scales of carrier decay signals are analyzed and discussed.

A general expression derived for the scanning tunnelling microscopy current in the presence of chemisorbed intermediate is analysed for the dependence of the current on temperature and potential. It is demonstrated that weak and strong chemisorption states can be distinguished through such studies. The inverse problem of deducing the density of states of the adsorbate from the measurement of current is discussed briefly.

We develop a perturbation formalism for diffusion accompanying the finite charge transfer rates on an arbitrary rough electrode. Second-order perturbation expressions are obtained for the concentration, current density and measured current transients for an arbitrary surface profile electrode. Various results obtained by earlier workers in the area of complex interfacial geometry are generalized. The results reported earlier for diffusion-limited (Nernstian) charge transfer at an arbitrary roughness about plane, sinusoidal, curvature expansion and realistic random surface models are generalized for the case where the effects of finite rates of charge transfer are incorporated. The problems of the screened electrostatic potential of the electric double layer for the one-dimensional arbitrary roughness are generalized for a two-dimensional arbitrary surface. In the random surface model (the gross geometrical property of an electrochemically active rough surface) the surface structure factor is related to the average electrochemical current, the current density and the concentration. Under the short- and long-time regimes, various morphological features of the rough electrode, i.e. roughness factor (related to excess area and slope due to roughness), curvature, correlation length etc. are related to the (average) current transients. The expressions for inner and outer cross-over times are obtained. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how roughness and finite charge transfer rates affect the overall quasi-reversible charge transfer current.

Analytical expressions which include depletion layer effects on low-injection carrier relaxation are being presented for the first time here. Starting from the continuity equation for the minority carriers, we derive expressions for the output signal pertinent to time-resolved microwave and luminescence experiments. These are valid for the time domain that usually overlaps with the time scales of surface processes, such as charge transfer and trapping. Apart from the usual pulse form of illumination, theoretical expressions pertaining to other forms of illumination such as switch-on and switch-off transient modes, a periodic mode, and a steady state and their various inter-relationships are derived here. The expressions obtained are seen to be generalizations of existing flat-band low-injection results in the Limit of early or initial band bendings. The importance of the depletion layer as an experimental parameter is clearly seen in the limit of larger band bendings wherein it is shown, unlike the flat-band case, to exhibit pure exponential forms of carrier relaxation. Our results are consistent with the main conclusions of the numerical and experimental work published recently. Furthermore, this work provides the actual functional relationships between the applied potential and observed carrier decay. This should enable one to extract the surface kinetic parameters, after deciding on the dominant mode of carrier relaxation at the interface, whether charge transfer or trapping, by studying the potential dependence of the fate of relaxation.

A semiquantitative evaluation of lead sulfate film formation on lead in sulfuric acid solution was done by current-time transient studies. The effects of acid concentration, potential, and expander are explored. Crucial parameters of film formation and passivation are identified which could be used for selection of an electrolyte concentration as well as screening of expanders and their concentration for lead-acid battery negative plate operation. The mechanism of formation of Pb 2+ (PbSO 4 ) from lead was confirmed to involve two, one-electron, steps ; the second electron transfer being the rate-determining step. Expanders do not affect the Tafel slope but favor the mechanism through dissolution-precipitation mode. The kinetics of lead sulfate formation do not follow any of the reported/known models. The dissolution-precipitation model coupled with nucleation and a growth model/theory is indicated.

A general mean field formalism for the two-component multilayer competitive growth processes by random irreversible deposition is presented. Overhangs and screening effects are ignored. The effects of the individual rates of the elementary act of deposition on the extent of growth, the overall growth rates (or currents) of the individual components and the composition at each deposited layer and in the bulk of the deposit are analysed. Transient and asymptotic behaviours of such quantities are derived. Various limiting growth situations of practical importance, namely poisoning of the growth of one component by the other, blocking of the multilayer growth by the monolayer coating of one of the components etc., are discussed in detail as special cases. Generalization of the formalism for more than two components is also indicated.

The brush plating technique has been employed for the first time to obtain CdSe films on Ti and conducting glass substrates. These films have been annealed in an argon atmosphere and their structural, optical and photoelectrochemical properties are discussed. The power conversion efficiency has been found to be 7.43% under an illumination of 80 mW cm-2. A peak quantum efficiency of 0.64 is obtained for an incident wavelength of 720 nm. Donor concentration of 3.42 x 10(17) cm-3, electron mobility of 3 cm2 V-1 s-1 and minority carrier diffusion length of 0.013 mum have been obtained.

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.

The phenomenological theory of hemispherical growth in the context of phase formation with more than one component is presented. The model discusses in a unified manner both instantaneous and progressive nucleation (at the substrate) as well as arbitrary growth rates (e.g. constant and diffusion controlled growth rates). A generalized version of Avrami ansatz (a mean field description) is used to tackle the ''overlap'' aspects arising from the growing multicentres of the many components involved, observing that the nucleation is confined to the substrate plane only. The time evolution of the total extent of macrogrowth as well as those of the individual components are discussed explicitly for the case of two phases. The asymptotic expressions for macrogrowth are derived. Such analysis depicts a saturation limit (i.e. the maximum extent of growth possible) for the slower growing component and its dependence on the kinetic parameters which, in the electrochemical context, can be controlled through potential. The significance of this model in the context of multicomponent alloy deposition and possible future directions for further development are pointed out.

A new model for describing electrochemical aggregation and growth via a layer-by-layer mode is described, where there are competing phases. The earlier version of “the cascade approach” is generalized to accommodate two components, i.e. phases A and B, growing with their own mechanisms of nucleation and accretion. The overlap corrections under such competing situations are made through an extended Avrami ansatz. Several possible outcomes are indicated including the exact predictions of the steady state limit for the current, exhibiting different Tafel regimes, with slopes determined by the relative importance of the parameters characterizing the A-on-A, A-on-B, B-on-A and B-on-B transitions. Special cases to reflect partial and total blocking of the growth of one by the other are also discussed.

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

The brush plating technique has been employed for the first time to obtain CdSe films on Ti and conducting glass substrates. These films have been annealed in an argon atmosphere and their structural, optical and photoelectrochemical properties are discussed. The power conversion efficiency has been found to be 7.43% under an illumination of 80 mW cm-2. A peak quantum efficiency of 0.64 is obtained for an incident wavelength of 720 nm. Donor concentration of 3.42 x 10(17) cm-3, electron mobility of 3 cm2 V-1 s-1 and minority carrier diffusion length of 0.013 mum have been obtained.

A supramolecular host—guest assembly based on zeolite YMHCF (M  Ni, Co) is examined electrochemically. Using well-known metal hexacyanoferrate (MHCF) redox chemistry in response to alkali metal cations, revealed by cyclic voltammetric “signatures”, we present the first results on the effects of the zeolite medium and confirm the intrazeolitic presence of MHCF complexes.

Current-potential characteristics are obtained numerically for a lone-adsorbate-mediated anodic charge transfer at the electrode-solution interface. An increase in the overpotential leads to the appearance of maxima in the anodic current-potential plots instead of the extended activationless region (i.e. a saturation current at large positive overpotentials) predicted by the direct heterogeneous outer-sphere anodic charge transfer process. A detailed analysis of the dependence of current-potential profiles and other kinetic parameters on various system parameters is also presented.

The recombination and the faradaic fluxes are shown to be sensitive to the location of a single level recombination center, when it is located near the band edges. As the surface level is shifted deeper into the band gap from either of the band edges, the back emission terms are dominated by electron capture and hole capture terms, and the occupancy of the surface level is no longer determined by its location in the band gap. However, when one of the back emission terms determines the surface state occupancy, it is shown that there exists a simple relation between the value of the surface level and the recombination and the faradaic fluxes respectively. Expressions to this effect are derived and verified in the case of the recombination flux, which characterized by the potential at which it attains its maximum value. For the faradaic flux the results are qualitative.

The imprint of the changing surface concentration of minority carriers in photocurrent transients is marginalized in “switch off” transients as compared to “switch on” transients. When the surface level is situated close to either one of the band edges, it is shown that in principle it must be possible to obtain the energy of the surface level from “switch off” transients. The time constants for the “switch on” and “switch off” cases behave differently with potential. While in “switch off”, transient plots, the magnitude of the slope decreases monotonically with increasing band bending potentials; for the “switch on” however, though it decreases and is identical to “switch off” initially, beyond a certain increase in potential the magnitude of the slope shows an increase.

The existing models describing electrochemical phase formation involving both adsorption and a nucleation/growth process are modified. The limiting cases leading to the existing models are discussed. The characteristic features of the potentiostatic transients are presented. A generalization of the Avrami ansatz is given for two or more competitive irreversibly growing phases.

In this paper we report, for the first time, the preparation of pulse plated CdSe films with an increased average grain size and more uniform grain distribution compared to conventional electrodeposition techniques

Potential transients are obtained by using “Pade approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pade expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

Mmorlty carrier relaxation and surface state relaxation are the two time dependent coupled processes that occur at semiconductor interfaces [1,2] Surface state relaxation 1s usually viewed as purely temporal with no spatial extension mto the bulk and hence 1s modelled as a first order kmetlc equation [31 However, mmorlty carrier relaxation 1s a volume process and Its time behavlour at the surface needs to be derived from the transport equation usmg appropriate boundary condltlons In the presence of a space-charge layer, whether it 1s possible to derive a kinetic form or not for the minority carriers 1s a question that has not been addressed so far Such kmetlc forms have been assumed previously, but as they were not rigorously derived, the order of magnitude of the length parameter needed to project a volume process at the surface has remained speculative [1,4] In this note, we report some of the results concerning minority carrier relaxation at the surface, whose general form 1s given by an integral equation which can be reduced to a simple kinetic form under certain condltlons From this kinetic equation we obtain the exact form of the earlier mentioned length parameter and more importantly the potential dependent rate constant for the mmorlty carrier relaxation, as we have included space-charge effects The rate of relaxation of the integral of the mmorlty carners m the semiconductor electrode can be shown to be approximately the same as that of the minority carriers at the surface [5] As a result the potential dependence of transient photomduced microwave conductlvlty [61 and the time resolved fluorescence signals [71, which are proportional to the total mmorlty carrier concentration, can be understood from the rate constant of the kinetic equation of mmorlty carriers at the surface

Electrodeposition of GaAs thin films by the pulse plating technique is reported for the first time. The films have been characterized by X-ray diffraction studies and the bandgap has been found to be 1.43 eV by the optical method.

Pulse deposition at room temperature was applied to obtain CdSe thin filmsfrom an aqueous bath consisting of CdSO,and Se02 on titanium substrates, employinga range of current densities from 80—550 mA cm .2• The films were polycrystallinewith a hexagonal structure. The pulse deposited films were observed to show greateruniformity and larger grain sizes than the conventionally deposited ones. The films,heat—sensitized and vacuum annealed, showed a flat—band potential of —1.17 V (SCE)and a high energy conversion efficiency of 6.3% at 60 mW cm 2in polysulphide redoxafter photoetching. The optical band gap was 1.7 eV.1. INTRODUCTIONCdSe, with a direct band gap of 1.7 eV, is a promising candidate for solarenergy conversion. MIS type solid state solar cells and PEC cells based on CdSeare being actively investigated. Several methods like vacuum evaporation, spraypyrolysis, chemical bath deposition, screen printing, electrodeposition etc., havebeen employed for the preparation of CdSe films. We report here results on pulse

Studies on slurry painted CdSexTe1-x photoactive films prepared from CdSe and CdTe synthesized by a low temperature wet process are reported. The films on Ti sub- strates, heat treated at 550°C in argon were polycrystalline with the bandgap increasing and room temperature conductivity decreasing with the x value. In poly- sulphide electrolyte, the films with a composition CdSe0.5Te0.5 gave a Voc of 425 mV, Jsc of 8.5 mA cm-2, FF of 0.54 and η of 3.25% at an illumination of 60 mW cm-2.

Thin films of cadmium selenide were prepared for the first time by a selective plating technique on conducting glass and titanium substrates. The films were characterised bymeans of x-ray diffraction, scanning electron microscopy, optical absorption, photoconductivity, and photoelectrochemical (PEC) studies.

A model Hamiltonian to describe adsorbate-mediated electron transfer is proposed and analyzed for the (electrochem.) currents. This Hamiltonian differs fundamentally from the ones used earlier (cf. Schmickler 1980, 1982). Three situations are treated, viz., (1) a lone adsorbate picture; (2) presence of an inactive neighboring adsorbate; and (3) electrostatic effects due to an adsorbate lattice. In all 3 cases, the mediation is via a single adsorbate only. Several limiting cases are considered and related to the earlier results of Marcus and Schmickler.

Summary We show in this paper how the unified formalism obtained in a previous communication 1 embraces several situation discussed in the literature thus far. Several new results are also given. The special cases range from the classical results of Warburg 3 , Randles-Ershler 2 , Frumkin-Melik-Gaikazyan 5 , Lorenz 7 and others to more recent ones of Delahay et al . 11 on the faradaic-non-faradaic coupling. No conscious distinction between the polarizable and the non-polarizable electrode and no undue preoccupation with the mass transfer problem are required. The straightforward methodology given makes it possible to write down immediately the various formulae by forming the suitable matrix representations for the variables and the coefficients. Multi-step electron transfer processes are especially easy to handle with this formalism. Interesting schemes for which results have been obtained as illustrations include the e.e. and e.c.e. mechanisms under varied mass transfer conditions and with adsorption coupling. The non-equilibrium desad case and even processes such as two-dimensional association do not cause any undue difficulty, and it is indicated how to obtain impedance/admittance expressions for such involved reaction schemes and mass-transfer mechanisms.

A simple semiempirical quantum chemical approach (Extended Huckel Theory) is shown to give a reasonable description of the electronic structural aspects of chemisorption on the mercury model surface. Chemisorptive interaction of alkali metal atoms and cations, halogen atoms and anions, and water molecules with a charge-neutralized hexagonal close-packed cluster of seven Hg atoms is studied. Adsorption of H, C, N and O atoms on the same model cluster is studied for comparison with earlier work. Chemisorption energies, charge transfer, interaction distance and hydration effects are discussed and compared with experimental results where available.

A two-state Ising model has been applied to the two-dimensional condensation of tymine at the mercury-water interface. The model predicts a quadratic dependence of the transition potential on temperature and on the logarithm of the adsorbate concentration. Both predictions have been confirmed experimentally.

A theory for Fournier polarography and higher order harmonics is presented. This is valid for reversible systems under semi-infinite diffusion to stationary and expanding plane electrodes. The algorithm is simple, accurate and exploits the identities holding for the interfacial concentrations. The computations — minimal in nature — can be carried out easily and the results given here were evaluated taking into account the presence of harmonics to, at least, the twenty-fifth order.

Current-potential relationships are derived for porous electrode systems following a homogeneous model and whenadsorbed intermediates participate in the electrode reaction. Limiting Tafel slopes were deduced and compared with thecorresponding behavior on planar electrode systems. The theoretical results showed doubling of Tafel slopes when theslow-step is a charge-transfer reaction and a nonlogarithmic current-voltage behavior when the slow-step is a chemical reaction.Comparison of the experimental results with theory for the case of oxygen reduction on carbon surfaces in alkalinemedia indicates that a slow chemical reaction following the initial charge-transfer reaction to be the likely rate-controllingstep. Theoretical relationships are utilized to determine the exchange current density and the surface coverage by the adsorbedintermediates during the course of oxygen reduction from alkaline solutions on "carbon." Tafel slope measurementson planar and porous electrodes for the same reaction are suggested as one of the diagnostic criteria for elucidatingthe mechanistic pathways of electrochemical reactions.

The relations for the inner layer potential difference ( E ) in the presence of adsorbed organic molecules are derived for three hierarchical models, in terms of molecular constants like permanent dipole moments, polarizabilities, etc. It is shown how the experimentally observed patterns of the E vs. θ plots (linear in all ranges of σ M , non-linear in one or both regions of σ M , etc.) can be understood in a semi-quantitative manner from the simplest model in our hierarchy, viz. the two-state site parity version. Two-state multi-site and three-state (site parity) models are also analysed and the slope (∂ E /∂θ) σ M tabulated for these also. The results for the Esin-Markov effect are derived for all the models and compared with the earlier result of Parsons. A comparison with the GSL phenomenological equation is presented and its molecular basis, as well as the limitations, is analysed. In particular, two-state multi-site and three-state (site parity) models yield E −σ M relations that are more general than the “unified” GSL equation. The possibility of viewing the compact layer as a “composite medium” with an “effective dielectric constant” and obtaining novel phenomenological descriptions is also indicated.

A lattice formalism using “spin variables” is employed to analyse multi-state models for the adsorption of neutral dipoles. In particular, a spin-1/2 (two-state) model incorporating permanent and induced dipole moments of the solvent and the organic adsorbate, substrate interactions, and discreteness of charge effects is analysed. The resulting Generalized Ising Hamiltonian is solved under mean field approximation (MFA) in order to derive the adsorption isotherm for organic molecules. A few spin-1 (three-state) models are also analysed under MFA to describe the competitive adsorption of multi-state solvent and organic dipoles, and the appropriate equilibrium relations are derived. The unification and isomorphosm existing at the Hamiltonian level for several diverse realizations, such as adsorption of ions and solvent/organic molecules, is indicated. The possibility of analysing phase transitions using this generalized approach is briefly indicated.

A new technique for measuring rate constants of moderately fast electrode reactions is proposed. The input is a decreasing current ramp of the form i ( t ) = Δ i (1 − t /τ). The overpotential transient-response expected for the activation/diffusion model is confirmed through experiments on the system K 4 Fe(CN) 6 +K 3 Fe(CN) 6 /Pt. The rate constant and the transfer coefficient are obtaine presence of several interesting features (a maximum, a zero crossing etc.) in the η− t profile makes this technique almost unique.

Summary A theoretical framework is given to evaluate the non-linear response of a halfcell when a periodic potential is superimposed on a base potential. Some interesting features of this approach are: o (i) no restriction is placed on the magnitude of the periodic signal; (ii) formally, all the infinite harmonics in the output current can be evaluated; (iii) the time-averaged part of the current (the so called “rectification” component) is also obtained and its identity in form with its d.c. counter part viz. “the bias response”, is established for the case E * =a constant; (iv) the influence of the bias state on the harmonics ( i.e. the time modulation) and the influence of the harmonics on the time averaged part (Fournier polarogram) become explicit; (v) the formalism deduced here is common to several models like those with parallel electron transfers with or without preceding chemical reactions, numerous mass-transport models, any given non-linear dependence of the rates on the overpotential etc. (vi) the applicability of these results are immediate to different input profiles such as (a) the sinusoidal, (b) the square wave, (c) pulse trains of various forms, (d) the triangular ones etc. (vii) the presentation is not restricted to constant “bias” conditions: it is capable of handling all time deependent bias profiles too, provided the latter are sufficiently slowly varying (as compared to the frequency of the periodic part). The computational procedure is briefly sketched. The limitations on our results arise from the assumptions on (i) the absence of adsorption, (ii) the presence of the supporting electrolyte, and (iii) the linear (in the generalized sense) relationship between the interfacial concentrations and the current (faradaic).

The modular formalism of Rangarajan [J. Electroanal. Chem., 55 (1974) 297] has been applied to the admittance of lipid bilayer membranes. The method leads to equations which clearly show the interrelations between the various partial processes involved in ion transport, and which allow examination of model assumptions without the need for a complete rederivation of the membrane admittance. Explicit expressions are given for both the continuum and single jump models. The former includes the ionic displacement component, important mostly at high frequencies.

Linear and nonlinear transformation occuring when noise is fed from outside to the electrochemical interface are analysed. Expressions for the rectified components in the mean are given for both the current and potential controlled situations; these are based on the functional-method approach. It is also shown how interesting techniques based on extrinsic noise signals are possible, under Tafel-regime conditions.

The nucleation growth model of electrochemical phase formation is analysed for the linear potential sweep input. Apart from deducing diagnostic criteria and methods of estimating model parameters, the predictions of the nucleation growth model are compared and contrasted with those of a simple adsorption model. A distinction is made possible between adsorption and phase transition, which seems useful for understanding the nature of ECPF phenomena, especially underpotential deposition (UPD).

An analytical solution is given for the kinetics of reversible homogeneous one-dimensional growth, assuming that all association rate constants have the same value ⇀k , that all dissociation rate constants are likewise equal to ⇀k , and that the monomer concentration has a constant value, C. Such growth tends to generate a maximally polydisperse (“white”) distribution of cluster concentrations ci all approaching a limiting value equal to that of the critical nucleus, ci. Continued growth merely increases the range of cluster sizes over which this white distribution applies. A simple expression is obtained for the flux ϵi = n∞ dci/dt, which becomes constant and equal to ( ⇀kC−⇀k)c n . The monomer uptake increases with time, and is given approximately by (kC-k)2Cnt.

Summary We seek here a formalism which would unify results obtained (A) for different schemes like O+ ne R YO+ ne R O+ ne R 1 O 1 + n 1 e I R 1 + n 2 e R 2 IY Y+ n 2 e R (B) for different geometries of the electrode e.g. stationary, expanding plane, spherical,… and (C) for several relaxation techniques such as the faradaic impedance, second harmonic, modulation-demodulation, linear and non linear response to noise input etc. What makes such an attempt possible is the recasting of these problems in an operator form and solving this operator equation by perturbation methods. The non-linear dependence of the faradaic current with respect to the potential E is retained, but it is assumed that the concentrations are linear with respect to i in a generalized sense. The latter assumption implies that it is possible to write, Δ c i = i i where { i } are appropriate operators determined by the boundary value problem. Only the i 's are to be known and not the actual interfacial concentrations, Δ c . The elimination of Δ c 's results in explicit operator equations for i involving i 's and the rate constants. Consequently our solutions too are expressed in terms of i 's and the k 's, only, for any specified potential input. The Volterra functional expansion approach of this paper leads to higher order describing functions in a natural way. Any variation in schemes or geometries is manifest only through its appropriate i and as will be shown in the subsequent reports, the procedure adopted here truly unifies all the known results for such models besides enabling us to tackle in a straight-forward manner more complex schemes. Adsorption is assumed absent.