Surface charge density calculations

Sufficient charge must be available to supply the required critical surface charge density. Calculations show that 50-pound plastic bags and plastic lined 55-gallon drums are too small to represent a credible risk. 

Fig. 6 Variation of the effective position of the image plane with the electronic density and with the surface charge density, calculated within the jellium model.

Assume is -25 mV for a certain silica surface in contact with O.OOlAf aqueous NaCl at 25°C. Calculate, assuming simple Gouy-Chapman theory (a) at 200 A from the surface, (b) the concentrations of Na and of Cr ions 10 A from the surface, and (c) the surface charge density in electronic charges per unit area. 

In this expression, Wp is the weight of particles titrated (g), Cb and Vb are the concentration of the base (i.e., titrant) and the volume of the base at equivalence point. The surface charge density can be calculated for the particles having a known diameter by means of the following expression ... 

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. 

In characterizing layered silicate, including layered titanate (HTO), the surface charge density is particularly important because it determines the interlayer structure of the intercalants as well as the cation exchange capacity (CEC). Lagaly proposed a method of calculation consisting of total elemental analysis and the dimensions of the unit cell [15] ... 

Fig. 9.3 Illustration of a model of interlayer structure of intercalant N-(cocoalkyl)-N,N-[bis (2-hydroxyethyl)]-N-methyl ammonium cation (qCi4(OH)) in the gallery space of layered titanate (HTO). The average distance between exchange sites is 0.888 nm, calculated from the surface charge density of 1.26e /nm2. For qCi4(OH), the obtained molecular length,...

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. 

Consider two different metals in contact and assume that both are well described by the Thomas-Fermi model (see Problem 3.3) with a decay length of Ltf 0.5 A. (a) Calculate the dipole potential drop at the contact if both metals carry equal and opposite charges of 0.1 C m 2. (b) If the work functions of the two metals differ by 0.5 eV, how large is the surface-charge density on each meted ... 

To calculate the surface charge densities c p and <3%r eq [cf. (2.11)], one has to solve numerically the integral equations on the solute cavity surface domain[ll]... 

The description of the sorption of charged molecules at a charged interface includes an electrostatic term, which is dependent upon the interfacial potential difference, Ai//(V). This term is in turn related to the surface charge density, electric double layer model. The surface charge density is calculated from the concentrations of charged molecules at the interface under the assumption that the membrane itself has a net zero charge, as is the case, for example, for membranes constructed from the zwitterionic lecithin. Moreover,... 

The surface potential, y, cannot be measured directly. It can be estimated however, e.g., with the help of Eq. (3.8a) from the surface charge density. Discuss the assumptions involved in applying such a calculation. 

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