Adsorption isotherms for neutral organic compounds-A hierarchy in modelling: Part II

A two-state model allowing for size disparity between the solvent and the adsorbate is analysed to derive the adsorption isotherm for electrosorption of organic compounds. Explicity, the organic adsorbate is assumed to occupy "n" lattice sites at the interface as compared to "one" by the solvent. The model parameters are the respective permanent and induced dipole moments apart from the nearest neighbour distance. The coulombic interactions due to permanent and induced dipole moments, discreteness of charge effects, and short-range and specific substrate interactions have all been incorporated. The adsorption isotherm is then derived using mean field approximation (MFA) and is found to be more general than the earlier multi-site versions of Bockris and Swinkels, Mohilner et al., and Bennes, as far as the entropy contributions are concerned. The role of electrostatic forces is explicity reflected in the adsorption isotherm via the Gibbs energy of adsorption term which itself is a quadratic function of the electrode charge-density. The approximation implicit in the adsorption isotherm of Mohilner et al. or Bennes is indicated briefly.

Adsorption isotherms for neutral organic compounds-A hierarchy in modelling: Part III

A simple three-state model permitting two different configurational states for the solvent, together with one for the organic adsorbate, is analysed to derive the adsorption isotherm. The implications of this model regarding pseudo-two-state and pseudo-Frumkin adsorption isotherms are indicated. A critique of the earlier theory of Bockris, Devanathan and Müller is presented in brief.

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.

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.

Adsopption isotherms-A critique

The possibility or the impossibility of separating the particle and the electrode interactions is discussed in a wider context of the effects due to any two interaction potentials on the equation of state. The involved nature of the pressure dependence on two individually definable forces is illustrated through the Percus Yevick results for the adhesive hard spheres. An alternative form of the adsorption isotherm is given to bring home the intimate relationship between the actual equation of state and the free energy of adsorption. Thermodynamic consequences of congruence with respect to E (or q) as reflected through the linear plots of q (or E) vs. θ are well known. Mathematical consequences of simultaneous congruence have been pointed out recently. In this paper, the physical nature of congruence hypothesis is revealed. In passing "the pseudo-congruence" is also discussed. It is emphasised that the problem is no less ambiguous with regard to modelling the particle/particle interaction. The ad hoc nature of our dependence of the available equations of state is emphasised through a discussion on the HFL theory. Finally, a heuristic method for modelling ΔG mathematically-incorporating its behaviour at saturation coverages-is advanced. The more interesting aspects of this approach, which generalises almost all isotherms hitherto known, are sketched.

Adsorption isotherms-microscopic modelling

The phenomenon of adsorption is governed by the various interactions among the constituents of the interface and the forms of adsorption isotherms hold the clue to the nature of the se in teractions. An understanding of this phenomenon may be said to be complete only when the parameters occurring in such expres - sions for isotherms are interpretable in terms of molecular/electronic interactions.This objective viz. expressing the composition of the isotherm parameters through a microscopic modelling is by no means a simple one. Such a task is particularly made difficult in the case of charged interfaces where idealisation is difficult to make and, when made, not so easy to justify.

Mean field lattice model for adsorption isotherms in zeolite NaA

Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate-adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a "coverage-dependent interaction'' model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate-adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions. (C) 1999 American Institute of Physics. [S0021-9606(99)70515-5].

Adsorption Isotherms and Heat of Adsorption of Difluoromethane on Activated Carbons

Experimental adsorption data of difluoromethane (HFC-32) on activated carbon in powder (ACP) and fiber (ACF) forms over a range of (25 to 75) degrees C and pressures up to 1400 kPa are reported. The data are fitted to Toth and Dubinin-Astakhov isotherm equations. Adsorbed phase volume is derived from the data. Isosteric heats of adsorption are extracted, and their dependence on relative loading and relative pressure is analyzed.

Experimental and theoretical studies on static and dynamic pressure-concentration isotherms of MmNi(5-x)Al(x) (x=0, 0.3, 0.5 and 0.8) hydrides

The static and dynamic pressure concentration isotherms (PCIs) of MmNi(5-x)Al(x). (x = 0, 0.3, 0.5 and 0.8) hydrides were measured at different temperatures using volumetric method. The effect of Al substitution on PCI and thermodynamic properties were studied. The plateau pressure and maximum hydrogen storage capacity decreased with Al content whereas reaction enthalpy increased. The plateau pressure, plateau slope and hysteresis effect was observed more for dynamic PCIs compared to static PCIs. Different mathematical models used for metal hydride-based thermodynamic devices simulation are compared to select suitable model for static and dynamic PCI simulation of MmNi(5)-based hydrides. Few important physical coefficients (partial molar volume, reaction enthalpy, reaction entropy, etc.) useful for development of thermodynamic devices were estimated. A relation has been proposed to correlate aluminium content and physical coefficients for the prediction of unknown PCI. The simulated and experimental PCIs were found matching closely for both static and dynamic conditions. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Studies on porphyrin and phthalocyanine monolayers by means of compression-recompression isotherms and BAM

Monolayers of porphyrin and phthalocyanine at the air-water interface were studied by means of film balance and Brewster angle microscopy (BAM). Results showed that the final point of compression isotherm and that of recompression isotherm were coincident or not coincident depending on the target pressures. Results were discussed in terms of the morphology of monolayers observed by BAM.

Prediction of bisolute dye adsorption isotherms on activated carbon

The removal of acid dyes, Tectilon Blue 4R, Tectilon Red 2B and Tectilon Orange 3G, from single solute, bisolute and trisolute solutions by adsorption on activated carbon (GAC F400) has been investigated in isotherm experiments. Results from these experiments were modelled using the Langmuir and Freundlich adsorption isotherm theories with the Langmuir model proving to be the more suitable. The Ideal Adsorbed Solution (IAS) model was coupled with the Langmuir isotherm to predict binary adsorption on the dyes. The application of the IAS theory accurately simulated the experimental data with an average deviation of approximately 3% between modelled and experimental data.