Low surface charge density

There are only few main group metal ion hydrates open to detailed mechanistic study of water exchange by NMR Be , Mg , Al" , Ga" and to a less extent, In" . They provide the opportunity to study the influence of size and charge on exchange rate constant and mechanism without the complicating effects of the variation of the electronic occupancy of the d-orbitals. All of the alkali ions as well as Ca , Sr, and Ba are very labile as a consequence of their relatively low surface charge density. However, indications on water exchange on Sr " can be obtained from... 

Various lines of experimental evidence confirm the very low surface charge density, at least for symmetrical plenary Keggin- and Dawson-type POMs [33a,d, 84]. For example, a simple linear variation... 

With alkali metal cryptates, cations and anions are well separated (except for the KNCS complex of [2.2.1] in which the ligand is too small to effectively shield the cation). Indeed the cryptated cation may be regarded as a very large, spheroidal cation (—10 A in diameter) of low surface charge density. 

Stability in nonaqueous solvents with low dielectric constants and low surface charge densities,... 

Equation (6.6) cannot be solved analytically but its approximate solution for the case of dilute suspensions has been obtained by Imai and Oosawa [3,4]. They showed that there are two distinct cases separated by a certain critical value of the surface charge density cr or the total surface charge Q, that is, case 1 low surface charge density case and case 2 high surface charge density case, as schematically shown in Fig. 6.2. For case 1, there are two regions I R [Pg.135]

We compare the exact numerical solution to the Poisson-Boltzmann equation (6.6) and the approximate results, Eq. (6.37) for case 1 (low surface charge density case) and Eq. (6.50) for case 2 (high surface charge density case) in Fig. 6.3, in which the scaled surface potential jo = zeij/JkT is plotted as a function of the scaled... 

Althongh derived based on the low surface charge density. Equation 7.11 has been found to be valid for situations where the zeta potential is as high as 50 mV. 

Highly hydrated surface Low surface charge density No or low adsorption... 

All alkali ions and Ca +, Sr + and Ba + are very labile as a consequence of their relatively low surface charge density. The only direct experimental data on water exchange in some of these ions comes from incoherent quasi-elastic neutron scattering (IQENS) [74-76]. IQENS has an observation time scale fobs 1 ns and allows for the calculation of limits for ion to water-proton binding times Tj (Table 4.4). Mean lifetimes of H2O in the first shell of Ca + and Sr " can be estimated to 0.2 ns from the chemically similar Eu " ion (see Sect. 4.3.2). 

Low Surface Charge Densities. In this limit / , and therefore q = + p /2. Substituting these results into the expressions above, one obtains... 

Figure 4 Schematic diagram of the role of surface charge in the oil displacement process. High surface charge density results in high oil recovery, while low surface charge density results in low oil yields.

In liquid crystals, being poor solvents, a low concentration of dissociated ions is expected, as well as relatively low surface charge densities, so that the DH approximation can be used. In this case, the free energy per unit surface area T due to the electrostatic interaction between two parallel plates at the separation D is [42]... 

Low surface charge density High interfacial tension -High interfacial viscosity -Low electrical repulsion between oil droplets and sand -Low recovery... 

Analytical formulas in closed forms for the diffusiophoretic mobility of a charged sphere [6] and circular cylinder [7] of radius a in symmetric electrolytes at low surface charge density <7 (valid for ( up to 50 mV) and arbitrary Ka have been obtained. The diffusiophoretic velocity of the charged particle can be expressed as an expansion in powers of ( ... 

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