Faradaic Impedance of Polarized Porous Electrodes

Abstract

the radius of curvature of the fringes is relatively large and the two types can exist simultaneously, it is easy to confuse the two. The error was not discovered until a large number of tedious hand measurements had been made.For wedge fringes, the fringes appear on a uniform wedge at positions where the thickness of the wedge is an integral multiple of the wavelength of the monochromatic light, that is since nk : 2~t cos r whenever the thickness has increased by k/2 from the last fringe, bright or dark, a new fringe appears, n is the order of interference, ~ the refractive index, t the thickness, and r the angle of incidence of the light. If r becomes a very little less than 90 ~ for thick wedges, Brewster's fringes result.Brewster's fringes are located at infinity and appear on the wedge as rings. The fringes will appear at positions governed by nk = ~t(cosine of the angle of refraction in the first glass flat minus cosine of the angle of refraction in the second glass flat) assuming cos r is about equal to 1, since the light passes only once through the cell.Variations in the refractive index of the wedge of electrolyte cause displacement of the fringes up and down the wedge (toward the apex if the change is an increase in concentration) which takes the form of a perturbation to the arc of the circle seen between the electrodes. The fringes measured for the S/V position were a 2 ~ 35' arc of a circle of 3.43 cm radius and those for the C/A position had a similar radius of cur-vature. A detailed account of how to relate wedge fringe perturbation to concentration has been given by O'Brien and Rosenfield (7) and complete review of the theory by O'Brien (9).To allow plots of concentration changes to be made on cartesian coordinates, these arcs had to be converted to straight lines. Frequently the increments at successive positions at which measurements were made were smaller than the expected precision of measurement. However, to ensure that some systematic method of correction for fringe curvature was used, a transparent plastic template whose plotting edge was cut in the mirror image of the curve was used in replotting the uncorrected values read from the display of the original fringes. In this way the curvature was plotted out and also any rotation of axis needed to correct the angle of the fringes to the electrode to 90 ~ . Of course since both the plastic template and the pencil point had thickness, a further, but it is thought, random scatter of points resulted. A smooth curve was then drawn through the points. A scale in which fringe perturbations are shown as concentration change in moles per liter has been added to the figures where necessary. The limit of accuracy of the measurements is that with which the center of any fringe can be located relative to the center of another fringe. In this case it is thought from the results of repeated measurements to be about • of a fringe width or about •x 10-41VL Details of this type of calculation have been given previously (4). ABSTRACTThe a-c impedance characte...

Optimized nanoporous materials.

“…He and others have explored the charging behavior of porous electrodes over several decades, although the emphasis has been directed more toward electrochemical reaction kinetics and not to supercapacitor optimization. [5][6][7][8][9] Refinements on the model including electrostatic charging only include treatment of finite pore length, [10,11] variable pore cross section, [12] an ensemble of pores of different size, [13], spatially nonuniform resistivity [14] and capacitance, [15] including generalized impedance elements. [16,17] A model starting from the Nernst-Planck equation has also been developed.…”

“…Solutions can be found by assuming that they can be separated into time-and space-dependent factors. If a solution is (1)(2)(3)(4)(5)(6)(7)(8)(9) then the governing equation becomes…”

“…the previous equation (3)(4)(5)(6)(7)(8) can be expressed as: (3)(4)(5)(6)(7)(8)(9)(10) This is the basic de Levie model, rearranged to account for position-dependent concentration. We now consider Fick's second law of diffusion to model concentration with respect to time:…”

“…For the current for the entire electrode, the pore cross-sectional area A can be substituted with the electrode surface area multiplied by its porosity (the percentage of that area occupied by pore entrances). Within the pore, voltage, concentration, and current can be computed through the discretization of equations (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20); however, the different solution environment outside ...…”

“…This technology could also be applied to gridwired electric vehicles such as commuter and light rail systems that currently dissipate much of their braking energy, providing opportunity for reduction of the financial and environmental cost of public transportation, and increasing its use. A 1000 kg vehicle requires 3x10 5 J or about 90 Wh to accelerate to 55 mph, so a target energy density for a device is about 10 Wh/kg, resulting in a device comparable to a standard car battery. This should fully charge in about 1 second to ensure that ohmic losses do not inhibit energy capture, requiring a power density of 3x10 4 W/kg.…”