Electrochemical phase formation (ECPF): Nucleation growth vis-a-vis adsorption models

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

Adsorption isotherms for neutral organic compounds - A hierarchy in modelling: Part V. Models for the inner layer potential difference in the presence of dipolar adsorption

The relations for the inner layer potential &fference (E) in the presence of adsorbed orgamc molecules are derived for three hterarchlcal models, m terms of molecular constants like permanent &pole moments, polarlzablhtles, etc It is shown how the experimentally observed patterns of the E vs 0 plots (hnear m all ranges of $\sigma^M$, non-linear in one or both regions of o M, etc ) can be understood in a serm-quantltatlve manner from the simplest model in our hierarchy, viz the two-state site panty version Two-state multi-site and three-state (sxte panty) models are also analysed and the slope (3E/80),,M tabulated for these also The results for the Esm-Markov effect are denved for all the models and compared with the earlier result of Parsons. A comparison with the GSL phenomenologlcal equation is presented and its molecular basis, as well as the hmltatlons, is analysed. In partxcular, two-state multa-slte and three-state (site panty) models yield E-o M relations that are more general than the "umfied" GSL equation The posslblhty of vaewlng the compact layer as a "composite medium" with an "effective dlelectnc constant" and obtaimng novel phenomenological descnptions IS also indicated.

Some adsorption-nucleation-based models for electrochemical phase formation

A new class of models which are based on adsorption, nucleation growth and their coupling is discussed. In particular, the potentiostatic response of a model that involves nucleative phase growth via direct incorporation and adsorptive discharge of metal ions on the free area is analysed for both instantaneous and progressive nucleation. This model is able to predict certain experimental features in the potentiostatic transient, like the initial fall, shoulder or maximum (as well as minimum) which have not been predicted by models analysed hitherto.Limiting behaviour for short and long times as well as a description of the above-mentioned features in terms of model parameters are given.A special case of the above model, viz. a reversible adsorption–nucleation model, wherein the adsorption is very fast, is shown to give rise to transients which can be distinguished from the pure nucleation-growth transients only by its parametric dependence, but not by the form.

Adsorption isitherms for neutral organic compounds-A hierarchy in modelling: Part IV. Charge of maximum adsorption-Statistical mechanical basis

The charge at which adsorption of orgamc compounds attains a maximum ( \sigma MAX M) at an electrochenucal interface is analysed using several multi-state models in a hierarchical manner The analysis is based on statistical mechamcal results for the following models (A) two-state site parity, (B) two-state muhl-slte, and (C) three-state site parity The coulombic interactions due to permanent and reduced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the exphcit dependence of ( \sigma MAX M) on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc Other models in the baerarchy bring to hght the influence of the solvent structure and the role of substrate interactions, etc As a result of this approach, the "composition" of oM.x m terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maxamum advantage, the derived results for ( \sigma MAX M) have been converted into those involving experimentally observable parameters lake Co, C 1, E N, etc Wherever possible, some of the earlier phenomenologlcal relations reported for ( \sigma MAX M), notably by Parsons, Damaskm and Frumkln, and Trasattl, are shown to have a certain molecular basis, vlz a simple two-state sate panty model.As a corollary to the hxerarcbacal modelling, \sigma MAX M and the potential corresponding to at (Emax) are shown to be constants independent of 0max or Corg for all models The lmphcatlon of our analysis f o r OmMa x with respect to that predicted by the generalized surface layer equation (which postulates Om~ and Ema x varlaUon with 0) is discussed in detail Finally we discuss an passing o M. and the electrosorptlon valency an this context.

Adsorption isotherms-Microscopic modelling: Part II

A lattice formahsm 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 reduced dipole moments of the solvent and the organic adsorbate,substrate interactions, and &screteness of charge effects is analysed The resulting Generalized Islng Hamaltonian 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 isomorphism existing at the Hamlltonlan level for several diverse realizations, such as adsorption of ions and solvent/orgamc molecules, is indicated The possibility of analysing phase transitions using this generalized approach is briefly indicated.

Microscopic modelling of adsorption and the generalised surface layer hypothesis

Two- and three-state models for the adsorption of organic compounds at the electrodelelectrolyte interface are proposed. Different size requirements, if any, for the neutral molecule and the adsorbing solvent are also considered. It is shown how the empirical, generalised surface layer (GSL) relationship (between the potential difference and the electrode charge) formulated by Damaskin et a / . can be understood at the molecular level.

Adsorption of anionic dyes on chitosan grafted poly(alkyl methacrylate)s

Chitosan grafted poly(alkyl methacrylate)s (namely chitosan grafted poly(methyl methacrylate) (ChgPMMA), chitosan grafted poly(ethyl methacrylate)(ChgPEMA), chitosan grafted poly(butyl methacrylate) (ChgPBMA) and chitosan grafted poly(hexyl methacrylate) (ChgPHMA)) were synthesized and characterized by using FT-IR and C-13 NMR techniques. The adsorption batch experiments on these grafted copolymers were conducted by using an anionic sulfonated dye. Orange-G. A pseudo-second-order kinetic model was used to determine the kinetics of adsorption. The effect of grafting, effect of process variables and the effect of different sulfonated anionic dyes (Orange-C, Congo Red, Remazol Brill Blue R and Methyl Blue) on the adsorption kinetics was determined. The Langmuir and Freundlich models were used to fit the adsorption isotherms and from the values of correlation coefficients (R-2), it was observed that the experimental data fits very well to the Langmuir model. The values of the maximum adsorption capacity of the adsorbents follow the order: ChgPMMA > ChgPEMA > ChgPBMA > ChgPHMA > chitosan. (C) 2010 Elsevier B.V. All rights reserved.

Adsorption-nucleation/growth based model for electrochemical phase formation and Avrami ansatz for a multicomponent competitive growth process

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.

Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with epsilon(aa) as the adsorbate-adsorbate interaction parameter, the comparisons for different values of epsilon(aa)(*)=epsilon(aa)z/2kT, and number of sites per cage, n, illustrate that for -1 adsorption isotherms and heats of adsorption predicted with the two approaches are similar. In general, the deviation between the LMFA and GMFA is greater for smaller n and less sensitive to n for epsilon(aa)(*)> 0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent epsilon(aa)) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages. (C) 1999 American Institute of Physics. [S0021-9606(99)70333-8].

Microscopic modelling of adsorption and the generalised surface layer hypothesis

Two- and three-state models for the adsorption of organic compounds at the electrode/electrolyte interface are proposed. Different size requirements, if any, for the neutral molecule and the adsorbing solvent are also considered. It is shown how the empirical, generalised surface layer (GSL) relationship (between the potential difference and the electrode charge) formulated by Damaskin et al. can be understood at the molecular level.

Adsorption and Desorption Kinetics of Anionic Dyes on Doped Polyaniline

In this study, we report an approach for the adsorption and desorption of anionic (sulfonated) dyes from aqueous solution by doped polyaniline. In this study, we have synthesized PANI with two dopants, namely, p-toluenesulfonic acid (PTSA) and camphorsulfonic acid (CSA), and used these to adsorb various dyes. It was found that the doped PANI selectively adsorbs anionic dyes and does not adsorb cationic dyes. The adsorption of anionic dyes causes the variation in electrical conductivity of PANI, indicating its potential as a conductometric sensor for these dyes at very low concentration. The adsorbed dyes were desorbed from the polymer by using a basic aqueous solution. The adsorption and desorption kinetics of the dye in the presence of doped PANI were also determined.

Multiphase models for simulating hot and slightly miscible DNAPL (dense non-aqueous phase fluids) in a saturated rock fracture under deformation

In the present study a two dimensional model is first developed to show the behaviour of dense non-aqueous phase liquids (DNAPL) within a rough fracture. To consider the rough fracture, the fracture is imposed with variable apertures along its plane. It is found that DNAPL follows preferential pathways. In next part of the study the above model is further extended for non-isothermal DNAPL flow and DNAPL-water interphase mass transfer phenomenon. These two models are then coupled with joint deformation due to normal stresses. The primary focus of these models is specifically to elucidate the influence of joint alteration due to external stress and fluid pressures on flow driven energy transport and interphase mass transfer. For this, it is assumed that the critical value for joint alteration is associated with external stress and average of water and DNAPL pressures in multiphase system and the temporal and spatial evolution of joint alteration are determined for its further influence on energy transport and miscible phase transfer. The developed model has been studied to show the influence of deformation on DNAPL flow. Further this preliminary study demonstrates the influence of joint deformation on heat transport and phase miscibility via multiphase flow velocities. It is seen that the temperature profile changes and shows higher diffusivity due to deformation and although the interphase miscibility value decreases but the lateral dispersion increases to a considerably higher extent.