Absence Of Adsorption Research Articles

Finite-difference scheme for solving dynamic multicomponent diffusion problems

A linearized implicit finite-difference scheme for solving diffusion equations is developed. The algorithm has been used for modelling multicomponent diffusion dynamics in a pellet of porous catalyst under unsteady-state conditions caused by a change of gas composition at the pellet outer surface. This allows us to prove the reliability of the unsteady-state Stefan—Maxwell diffusion equations and to check textural parameters of porous solids under dynamic conditions in the absence of adsorption and reaction. The method has been applied to modelling of unsteady diffusion of a ternary H 2/N 2/He gaseous mixture in a porous pellet. The procedure developed can be used for a wide class of diffusion processes on porous materials (catalysts, adsorbents etc.).

Stability of displacement processes in porous media in radial flow geometries

The linear stability of certain displacement processes in porous media for two-dimensional radial flows induced by a point source is examined. Both two-phase, immiscible displacement and single-phase miscible displacement in the presence of equilibrium adsorption are discussed. In agreement with Tan and Homsy [Phys. Fluids 30, 1239 (1987)], it is found that disturbances grow or decay algebraically in time. Via appropriate transformations the eigenvalue problems are shown to be identical to those in rectilinear flow geometries with suitably modified base states and parameters. Thus several stability features are inferred directly from the analysis in rectilinear geometries. The results indicate the existence of critical values for the capillary (NCa) or Peclet (Pe) number, above which the displacement is unstable for wavenumbers in a band of finite width. For large NCa or Pe the most dangerous and the highest cutoff modes scale linearly with NCa or Pe. The different scaling found by Tan and Homsy [Phys. Fluids 30, 1239 (1987)] follows directly as a singular limit of the miscible displacement problem in the absence of adsorption.

Oxygen uptake by thin lead deposits on polycrystalline gold

The oxidation of thin lead overlayers on a predominantly (111) polycrystalline gold surface at room temperature and oxygen pressure of 8×10 −6 Torr was investigated using Auger electron spectroscopy (AES). Oxidation was monitored using the oxide lead peak obtained by spectral decomposition. This peak experiences a shift from pure lead of 2.3±0.1 eV for deposits up to 3 monolayer-equivalents (ME) and 2.7±0.1 eV for deposits greater than about 4 ME. The oxygen signal for a 1 ME deposit at saturation exposure is about 20% of the value expected for a complete oxygen monolayer. This is explained in terms of clusters of about 5 Pb atoms for each oxygen atom. This differs from the PbO stoichiometry which has been observed under similar conditions on bulk lead and also claimed for the oxidation of thin lead deposits on Ag and Cu. Also contrary to results on Ag and Cu is the rate of oxygen uptake on Au which increases with lead coverage in the submonolayer region; this is explained by the absence of adsorption and surface diffusion of oxygen on gold, and the need for clusters of about 5 lead atoms for oxidation to occur. Deposition of more than 1 ME of lead results in lead-gold compound formation as observed by previous authors. Exposure of this compound to oxygen causes oxidation of the surface lead with inward migration of gold from the surface. The oxide layer is about 2 monolayers thick and greatly reduces the rate of further oxidation. The large decrease in the gold substrate signal on oxidation is a sensitive method for differentiating between compound formation and altermative growth modes for the bimetallic surface.

Theory of chromatography of oligomers on porous adsorbents

The authors look at the theory of the chromatographic behaviour of short chains modelled by one, two and three freely articulated rigid portions (“rods”). The distribution coefficients have been obtained as a function of the length of the rigid portion, the energy of the polymer-adsorbent interaction, pore width and the thickness of the adsorption layer. In absence of adsorption on the walls of the pores the distribution coefficient of the oligomers is determined by the ratio of the mean spen of the molecule to the pore width. In the field of adsorption chromatography the dependence of the retained volume on M of the oligomers is non-monotonic. The degree of coherence of the oligomer with the pore surface essentially depends on the contour length, the number of fractures and the energy of interaction. Expressions are obtained for the distribution coefficients of the oligomers with terminal functional groups.

Evaluation of effective diffusivity of adsorbate in the absence of adsorption and surface diffusion

AbstractA method is suggested for the evaluation of effective diffusivity of adsorbate in the absence of adsorption and surface diffusion, the precise value of which is required for estimating the effective surface diffusivity and the extent of influence of adsorption on the overall mass flux in a porous solid. The method does not require the knowledge of tortuosity factor, the accurate values of average pore radius for micro, transitional and macro pores, or the porosities corresponding to micro and macro pores, which are required in case of diffusion in the transitional region and in the solids containing bimodal pore size distribution.

On the ionic displacement current in lipid bilayer membranes

It is shown that the constant field approximation must be amended to make it apply to time-dependent signals. The necessary additional term corresponds to the ionic displacement current. In the absence of adsorption, this ionic displacement current is found to have a characteristic time of the order of a fraction of a microsecond. We confirm its mathematical form as given by Cole (1965). When the membrane-soluble ions are strongly adsorbed, an additional, purely exponential transient of much larger time constant is calculated, with a time dependence identical to that of the translocation of adsorbed ions. Our results support the pseudostationary approximation used by Andersen and Fuchs (1975) in the description of such exponential transients. Explicit expressions are given for the current after a voltage step as for the admittance, both in the absence and presence of adsorption, for a membrane with a rectangular potential energy profile.

High amplitude periodic signal theory: I. Potential controlled

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).

Effects of langmuirian adsorption on potentiostatic relaxation of diffusion-limited reversible electrode reactions

A theoretical treatment is given of the effect of Langmuirian adsorption on Nernstian, diffusion-limited electrode reactions at a plane electrode under potentiostatic conditions. Relaxation currents generally consist of three components, an instantaneous initial conversion of adsorbed reactant to product, the same diffusional component that would be observed in the absence of adsorption, and a time-distributed adsorptive component due to interconversion between adsorbed and diffusing species. The magnitude, sign, and time-constant associated with the time-distributed adsorptive component vary widely with experimental conditions. In favorable situations the magnitudes of both adsorptive components can be determined conveniently by extrapolation of two separate linear segments of a chronocoulometric plot of charge vs. square root of time to time zero. This feature and other prominent effects of adsorption are shown to be qualitatively independent of the detailed form of the adsorption isotherms.

Effects of Langmuirian adsorption on potentiostatic relaxation of diffusion-limited reversible electrode reactions

A theoretical treatment is given of the effect of Langmuirian adsorption on Nernstian, diffusion-limited electrode reactions at a plane electrode under potentiostatic conditions. Relaxation currents generally consist of three components, an instantaneous initial conversion of adsorbed reactant to product, the same diffusional component that would be observed in the absence of adsorption, and a time-distributed adsorptive component due to interconversion between adsorbed and diffusing species. The magnitude, sign, and time-constant associated with the time-distributed adsorptive component vary widely with experimental conditions. In favorable situations the magnitudes of both adsorptive components can be determined conveniently by extrapolation of two separate linear segments of a chronocoulometric plot of charge vs . square root of time to time zero. This feature and other prominent effects of adsorption are shown to be qualitatively independent of the detailed form of the adsorption isotherms.

Adsorption of sulphite, oleate and manganese(II) ions by β‐manganese dioxide and its activation in flotation

AbstractA high‐grade ore sample A and a synthetic sample B of β‐MnO2 were characterised by a number of physical methods. The points of zero zeta potential were found at pH4.4 and 4.6 for A and B, respectively. Below the critical micellar concentration and at pH 7, the adsorption isotherms of oleate on to sample B followed the Freundlich equation, the adsorption density decreasing with rising temperature. Over a wider concentration range, the isotherm had a Langmuir shape and was displaced to higher adsorption densities in presence of NaCl. The adsorption density was slightly affected by pH, but it gradually decreased beyond pH 9. From a comparison of the adsorption and ζ potential results, the adsorption mechanism could not be electrostatic only but may also involve van der Waals and π interactions.The adsorption isotherm of sulphite ions exhibited a broad maximum and was shifted to lower adsorption densities in presence of oleate. The amount of Mn2+ ions released on conditioning sample A in sulphite solutions increased with increasing sulphite concentration. It could be assumed that sulphite ions were adsorbed prior to reaction with MnO2 producing Mn2+ ions, which were the activating species in flotation. Although there was an adsorption competition between sulphite and oleate ions, the adsorption of the latter was enhanced in presence of sulphites.The adsorption density of Mn2+ ions on to sample B increased linearly with increase in their equilibrium concentration. Assuming the low‐coverage form of the Langmuir isotherm, the heat of adsorption was found to be 51.9 kJ/mole.The adsorption density of Mn2+ ions increased with increasing the pH of the medium from 5 to 6.5, in agreement with the more negative surface charge on the MnO2 particles. Above a certain Mn2+ concentration, the charge was reversed. The adsorption of Mn2+ ions is interpreted in terms of an Na+/Mn2+ exchange mechanism. Tentatively, the cations are assumed to be in the outer Helmholtz layer of the electric double layer of MnO2.The activating effect of Mn2+ cations was demonstrated by the increased adsorption density of oleate in presence of Mn2+ ions and by the corresponding increase in flotation recovery. Oleate adsorption was exothermic, i.e. similar to its adsorption in absence of activating cations. It is assumed that activation involves electrostatic attraction between the activating Mn2+ and the oleate ions.

Specific adsorption of fluoride ions on mercury and the structure of the mercury/solutions interface

The specific adsorption of fluoride ion on mercury has been studied at two temperatures. The unusual adsorption isotherm of the fluoride ion has been analyzed in terms of the equilibrium conditions prevailing across the double layer; a Freundlich-type isotherm describes the surface pressure of the adsorbed ionic film. The inner layer capacitance has been analyzed and its various components calculated, and from the variations of the inner layer capacitance at constant amount of adsorbed charge, the inner layer capacitance in the absence of adsorption has been evaluated. The anodic hump in the capacitance of fluoride solutions is due mainly to the adsorption of F– ions, and not to adsorbed solvent reorientation. The adsorption of SiF2–6 does not lead to a large increase in the double-layer capacitance at anodic potentials.

Measurement of charge passed following application of a potential step-application to the study of electrode reactions and adsorption

The integral of the equation for the current-time behaviour following application of potential step to an electrode has been evaluated. After sufficient time, Q is given by an asymptotic expression which is linearly dependent on t 1 2 . In the absence of adsorption, the kinetic parameters of the electrode reaction may be determined from the slope and extrapolated intercept on the t 1 2 axis of a plot of Q vs. t 1 2 If the electro-active species is adsorbed, steps to potentials far from E° will yield Q vs. t 1 2 plots which are linear, but which have positive intercepts on the Q axis. The magnitude of this intercept is a measure of the amount of adsorbed material which has reacted at the electrode. These conclusions have been experimentally verified in the study of the Cd-Cd(II) and I 2 − I − systems.

The Rotated Dropping Mercury Electrode

A review is given of the characteristics of the limiting current, reversible and irreversible waves, criterion of reversiblity of the wave form, the kinetic current and the adsorption waves (prewave and postwave) at the rotated dropping mercury electrode (RDME). The limiting current at the RDME in the presence of a suitable curl tce active substance is hardly affected by variation of the mercury pressure, while the etcct of drop time and hence of potential is much greater at the RDME (t1/2) than at the DME (t1/6). The large drop time effect is particularly important when a mixture of two or more electroactive species is analyzed. Reversible waves at the RDME cars be analyzed in the same way as those at the DME. The half-wave potential of reversible reduction waves at the RDME of simple ions of metals which are soluble in mercury is depcnclcrlt on characteristics of the electrode and is more negative than that at the DME. When oxidized and reduced species are both soluble in the solution, the half-wave potential at the RDME is independent of characteristics of the electrode. The half-wave potential of totally irreversible waves is much more negative at the RDME than at the DME. An expression for the difference in half wave potential at the two electrodes is derived and illustrated by comparing the waves of nickel ion in sodium perchlorate solution obtained at the DME and at the RDME. Criteria of reversibility of waves obtained with the RDME and with the DME are compared. Because of the greater rate of mass transfer at the RDME, the specific rate constant must be greater for the wave to be reversible at the RDME than at the DME. When the rate constant is not sufficiently large, a species yielding a reversible wave at the DME may give an irreversible wave at the RDME. This situation is illustrated by composite waves obtained with a mixture of vanadic and vanadous ions in sulfuric acid solution. Kinetic currents at the RDME are treated on the basis of the concept of reaction layer. When the current is entirely controlled by the rate of the chemical step involved, the expression for the kinetic current is the same at the DME and at the RDME. Since the kinetic current and the mass-transfer controlled limiting current are both practically independent of the mercury pressure, the dependence of current on the mercury pressure cannot be used to detect kinetic nature of the current at the RDME. On the other hand, the kinetic current at the RDME decreases with increasing speed of rotation of the electrode, the decrease corresponding to the decrease in drop time. Thus kinetic currents can be identified at the RDME by determining the effect of speed of rotation upon the value of the limiting current. The RDME is particularly useful in the study of polarograms involving adsorption owing to the fact that maxima of the second kind always appear in the absence of adsorption. This is demonstrated by the application of the RDME to the study of the potwave observed with copper (ll)-thiocyanate system and the anodic prewave observed with solutions containing iodide ions.