Metal surface charge density

Lang, N. D., and Kohn, W. (1970). Theory of metal surfaces charge density and surface energy. Phys. Rev. B 1, 4555-4568. 

N.D. Lang and W. Kohn. Theory of Metal Surfaces Charge Density and Surface Energy. Phys. Rev. B 1 4555 (1970). 

A simplified approach, based on the Stern-Grahame double layer model, gives the following relation for the metal surface charge density,... 

FIGURE 3.25 Solution of the single pore model in the ID Poisson-Boltzmann limit (a) the electrostatic effectiveness factor, as a function of the metal surface charge density, ctm, for various values of Rp (b) radial variation of the normalized proton concentration in the pore for various values of Rp at gm = —0.05 C (Reprinted from Chan, K. and Eikerling, M. 2011. /. Electrochem. Soc., 158(1), B18-B28, Figures 1,2,3,4,5,6. Copyright (2011), the Electrochemical Society. With permission.)... 

This is used to measure charge, surface charge density, volumetric charge density or charge-to-mass ratio. It comprises an all-metal container, such as... 

The capacity of the metal phase (CM) and the potential drop in the thin metal surface layer have been discussed by Amokrane and Badiali,122,348 as well as by Damaskin et a/.349 353 The value of was found to increase in the order Ga < In(Ga) < Tl(Ga) Hg if it was assumed that the capacity of a solvent monolayer C = const. The negative value of the surface charge density <7, at which the Cs,ff curve has a maximum, decreases in the order Ga > In(Ga) > Hg, i.e., as the hydrophilicity of the electrode decreases. 

For the metal in the electrochemical interface, one requires a model for the interaction between metal and electrolyte species. Most important in such a model are the terms which are responsible for establishing the metal-electrolyte distance, so that this distance can be calculated as a function of surface charge density. The most important such term is the repulsive pseudopotential interaction of metal electrons with the cores of solvent species, which affects the distribution of these electrons and how this distribution reacts to charging, as well as the metal-electrolyte distance. Although most calculations have used parameterized simple functional forms for this term, it can now be calculated correctly ab initio. 

Figure 2.1 (a) A schematic representation of the apparatus employed in an electrocapillarity experiment, (b) A schematic representation of the mercury /electrolyte interface in an electro-capillarity experiment. The height of the mercury column, of mass m and density p. is h, the radius of the capillary is r, and the contact angle between the mercury and the capillary wall is 0. (c) A simplified schematic representation of the potential distribution across the metal/ electrolyte interface and across the platinum/electrolyte interface of an NHE reference electrode, (d) A plot of the surface tension of a mercury drop electrode in contact with I M HCI as a function of potential. The surface charge density, pM, on the mercury at any potential can be obtained as the slope of the curve at that potential. After Modern Electrochemistry, J O M. 

This relates the change in surface tension with the applied potential at constant electrolyte composition to the surface charge density on the metal, [Pg.44]

Consider a plane metal electrode situated at z = 0, with the metal occupying the half-space z < 0, the solution the region z > 0. In a simple model the excess surface charge density a in the metal is balanced by a space charge density p(z) in the solution, which takes the form p(z) = Aexp(—kz), where k depends on the properties of the solution. Determine the constant A from the charge balance condition. Calculate the interfacial capacity assuming that k is independent of a. 

Figure 3.4 Distribution of the electronic density in the jellium model the metal occupies the region x < 0. The unmarked curve is for an uncharged surface, the other two curves are for the indicated surface-charge densities. The distance along the x axis is measured in atomic units (a.u.), where 1 a.u. of length = 0.529 A.

The Thomas-Fermi model of a metal is similar to the Gouy-Chapman theory for electrolytes. In this model the surface-charge density o is... 

---