Particle charge density

It is well known that the exact electronic energy can also be given explicitly in terms of the spinless 1-RDM and the two-particle charge density (2-CD). This suggests an alternative viewpoint regarding D-functional theory. One could employ the exact functional but with an approximate 2-CD that is built from... 

These calculations reflect equation i of Table 14.3, which shows that different types of surface charges contribute to the net total particle charge density on a colloid. 

In the RPA, the induced potential V" (r, t) is simply obtained as the potential induced in a noninteracting Fermi system by both the probe-particle charge density p (r, t) and the induced electron density p (r, Z), i.e.,... 

The ideal probe potential probe is seen to be proportional to the individual particle charge Q in the bed, or equivalently, to the particle charge density pq... 

Giese, T. J., and York, D. M. (2008). Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities,/. Comput Chem. 29(12), 1895-1904. 

Yamanaka, J., Yoshida, H., Koga, T., Ise, N., and Hashimoto, T. (1999). Reentrant order-disorder transition in ionic colloidal dispersions by varying particle charge density. Langmuir 15, 4198-4202. 

Equation 4.17 adds an extra parameter, namely the particle charge density, to the list ofunknovms, but if the degree of dissociation ofthe charged group is known then it should be po s sible to relate this charge density to the thickness of the polymer layer, so that the number of parameters stays the same. Unfortunately, there have been no attempts made so far to apply this theory to the characterization of adsorbed polyelectrolyte layers. One possible application would be to explore whether this relationship can explain the occasional occurrence of DC mobilities that are greater than the maximum anticipated by the computer calculations of O Brien and White [18]. 

The physical significance of the zeta potential is discussed in the following section. The suspension could be characterised by particle charge density, which can in principle be determined from the electrophoretic mobility, but which requires certain assumptions regarding the particle size and shape distribution and conductivity effects. The zeta potential is the most commonly used parameter for characterising a suspension, and can be determined from measurements of particle velocity or mobility in an applied field using commercially available electrophoresis cells. In practice electrophoretic mobilities are not easy to measure accurately, and since the Smoluchowski equation is based on a model of doubtful validity, the view sometimes expressed that "zeta potentials are difficult to measure and impossible to interpret" has a ring of truth but is probably unduly pessimistic. The Smoluchowski relation is valid provided that the double... 

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

Radicals generated from water-soluble initiator might not enter a micelle (14) because of differences in surface-charge density. It is postulated that radical entry is preceded by some polymerization of the monomer in the aqueous phase. The very short oligomer chains are less soluble in the aqueous phase and readily enter the micelles. Other theories exist to explain how water-soluble radicals enter micelles (15). The micelles are presumed to be the principal locus of particle nucleation (16) because of the large surface area of micelles relative to the monomer droplets. 

Electrostatic Interaction. Similarly charged particles repel one another. The charges on a particle surface may be due to hydrolysis of surface groups or adsorption of ions from solution. The surface charge density can be converted to an effective surface potential, /, when the potential is <30 mV, using the foUowing equation, where -Np represents the Faraday constant and Ai the gas law constant. 

For particles, the maximum field intensity occurs at the particle surface and decays inversely with distance. This highly nonuniform field allows greater surface charge densities before breakdown takes place, depending on the curvature of the particle surface. Empirical studies reviewed in [18] ... 

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