Range Of Surface Charge Densities Research Articles

Restricted primitive model for electrical double layers: Modified HNC theory of density profiles and Monte Carlo study of differential capacitance

Interfacial properties of an ionic fluid next to a uniformly charged planar wall are studied in the restricted primitive model by both theoretical and Monte Carlo methods. The system is a 1:1 fluid of equisized charged hard spheres in a state appropriate to 1 M aqueous electrolyte solutions. The interfacial density profiles of counterions and coions are evaluated by extending the hypernetted chain approximation (HNC) to include the leading bridge diagrams for the wall–ion correlations. The theoretical results compare well with those of grand canonical Monte Carlo computations of Torrie and Valleau over the whole range of surface charge density considered by these authors, thus resolving the earlier disagreement between statistical mechanical theories and simulation data at large charge densities. In view of the importance of the model as a testing ground for theories of the diffuse layer, the Monte Carlo calculations are tested by considering alternative choices for the basic simulation cell and are extended so as to allow an evaluation of the differential capacitance of the model interface by two independent methods. These involve numerical differentiation of the mean potential drop as a function of the surface charge density or alternatively an appropriate use of a fluctuation theory formula for the capacitance. The results of these two Monte Carlo approaches consistently indicate an initially smooth increase of the diffuse layer capacitance followed by structure at large charge densities, this behavior being connected with layering of counterions as already revealed in the density profiles reported by Torrie and Valleau.

The nature and stability of aluminum hydroxide precipitated on wyoming montmorillonite

A freeze—fracture technique was used to prepare replicas of interlayer surfaces of a hydroxy-aluminum montmorillonite (OH-Al-SWy-1), synthesized by titrating an Al-clay with NaOH. Aqueous suspensions containing 0.01 M NaClO 4 and 4% OH-Al-SWy-1 were frozen rapidly with Freon 22 to vitrify the solution phase and stored in liquid N 2. The frozen samples were fractured at 10 −6 Torr and 158K and C-Pt replicas were made of the exposed surface. Transmission electron microscopy (TEM) of the replicas showed a randomly distributed surface precipitate. The precipitate was flat and angular, resembling gibbsite morphologically. Gibbsite crystals were observed outside the interlayer when the suspension was air-dried on microscope grids, underscoring the value of the freeze—fracture technique in minimizing alteration of the OH-Al-SWy-1 complex. Using the mass of Al(OH) 3 fixed by the clay and the average particle perimeter observed by TEM (49.3 nm), we estimated the maximum Al(OH) 3 surface charge density and site density available for phosphate adsorption. The range of surface charge density for the Al(OH) 3, estimated from crystallographic data, was very close to the range of surface charge density for montmorillonite, suggesting that the latter may influence the maximum particle size of the precipitate. The total charge and edge [-Al(OH)(H 2O)] site density were less than the observed CEC reduction on SWy-1 and maximum phosphate retention on OH-Al-SWy-1 at pH 5.3, respectively. Interlayer Al(OH) 3 is known to be unstable with respect to gibbsite and it is possible that a relatively high specific surface area was responsible for the high solubility.

A numerical analysis of the resurf diode structure

The results of a 2-dimensional numerical analysis of medium and high-voltage diode structures that incorporate a ‘resurf’ field reduction layer are presented. The work illustrates the effect of surface charge on the optimisation of the design and indicates the requirements that will ensure bulk breakdown for a wide range of surface charge densities. The results are used to assess the analytical design equation presented by Appels et al., modified to take account of surface charge. A comparison is also made with results obtained from an analysis of the field limiting ring technique, and the relative performance of the two methods is assessed.

Electrical double layers. I. Monte Carlo study of a uniformly charged surface

This paper reports grand canonical Monte Carlo computations on the diffuse double layer in an ionic system next to a uniformly charged plane surface. The boundary conditions and the grand canonical techniques are discussed. Calculations were carried out for the 1:1 restricted primitive model at several concentrations and over a range of surface charge densities. The results are compared with the modified Gouy–Chapman theory, and some remarks are also possible with respect to the modified Poisson–Boltzmann and the hypernetted chain approaches. At high concentrations and surface charge densities the counterions are packed closely at the surface and begin to show a layered structure. This results in a large electrostatic potential drop, but only very slight charge oscillations are observed in the solution. None of the theories seems able to describe this behavior.

Generalized flux equations for osmotic transport through charged membranes

The equations for a model of water and solute transport across membranes bearing surface charges are derived. Charged species can be transported actively and by a combination of passive diffusion and convection through pores. Separate pores for each ion can be incorporated. Because convection is present, no simple Goldman-like equation for the overall potential difference across the membrance is obtainable. It is shown that for the range of surface charge densities reported in the literature, the potential drop through the external double layers is a significant portion of the measured transmembrane potential difference.

Comparison of double layer potentials in lipid monolayers and lipid bilayer membranes

It is shown that the Gouy-Chapman double layer analysis adequately describes the variation of the surface potential of monolayers of acidic natural lipids over a wide range of surface charge density and salt concentration. It is also shown that the potential which initially appears when an electrolyte gradient is rapidly imposed across a bilayer membrane is due to a difference in the double layer potentials on the two sides of the membrane. This conclusion follows from the fact that the observed bilayer potentials arise much more rapidly than can be accounted for by charge migration across the membrane and from the observation that the bilayer membrane concentration potentials, when measured immediately after establishment of a gradient, are equal to the surface potential change observed when the subphase concentration of a monolayer of the same lipid is changed by an amount equal to the gradient across the bilayer. The bilayer potential and monolayer potential changes, so measured, agree in a number of different electrolyte solutions over a wide range of electrolyte concentrations and surface charge densities. Because of this agreement and the applicability of the Gouy theory to monolayers, initial bilayer potentials may be calculated if the composition of the mixture used to form the membrane is known, provided that the pK's and areas of such components are available. In the absence of this information, membrane potentials may be calculated from electrophoretic data on the membrane lipid mixture; the conditions under which the latter approach is possible have been determined. The experimental results indicate that the composition of monolyers and bilayers spread from the same lipid mixture in decane are very similar, that the composition of the two types of film closely resembles the composition of the solution used to generate them, and that bilayer membranes are close-packed. The evidence further indicates that if any hydrocarbon solvent remains in these bilayers, it must be so situated that it contributes little, if anything, to the surface area. The steady state potential in the bilayer membrane system is frequently not identical with the initial potential which supports the hypothesis that in many cases only a fraction of the electrical conductance of unmodified membranes is caused by the ions which constitute the bulk electrolyte. An expression for the relationship between diffusion and double layer potentials has been derived which shows that, in the absence of any intrinsic selectivity of the hydrocarbon region of the membrane for hydrogen, hydroxyl, or impurity, the two potentials should be identical.