Equilibrium charge distribution

PLASMA FREQUENCY. The oscillation frequency of plasma electrons about an equilibrium charge distribution is called the plasma or Langmuir frequency and is... 

For a rod-like chain, the equilibrium charge distribution was shown to obey [99]... 

Fig. 16 Equilibrium charge distribution on a rigid rod (AT=128, (/)=1/16) at varying screening length. Theoretical results (see Eq. (23) are given as lines, simulation data as...

Fig. 18 Equilibrium charge distribution on a flexible chain (N=1000, (/)=0.083, AD=64b). The theoretical result (see Eqs. (23, 24)) is given as dashed line, simulation data as dots...

It should be observed that for the global equilibrium charge distribution, where /i = /j1. 

We again emphasize that for a non-equilibrium charge distribution, e.g., from independent SCF calculations, f = /i0, may not be equalized. It should be observed that the AIM components of wx indices,... 

Table 12.5 shows the equilibrium charge distribution on various monodisperse aerosols as computed from Eq. 12.40. 

Frictional electrification, 183-184 Frictional resistance, 50 Friedlander, S. K, 312, 316 Fuchs, N. A., 61 and brownian rotation, 138 and coagulation, 313-314 and diffusion charging, 188 and diffusion and collisions, 304 and equilibrium charge distributions, 204-205... 

It is interesting to note that according to Eq. 12.36, the equilibrium charge distribution on aerosols is independent of both ion concentration and aerosol concentration. These factors are important, however, in establishing the length of time necessary for equilibrium conditions to develop. 

With an ion production rate of 104 ions/(cms s) and an aerosol concentration of 5 x 104 particles/cm3, equilibrium would be achieved in about 2 s. For atmospheric aerosols where the ion production rate may be only 10 ions/(cm3 s), even though aerosol concentrations of 5 x 104 particles/cm3 are not uncommon, it takes approximately 1700 s (or about 30 min) for equilibrium to be achieved. O Connor and Sharkey (1960) report that equilibrium conditions usually prevail in air coming from the ocean. Over an industrial city, however, measurements indicated that the equilibrium charge distribution is not attained (Nolan and Doherty, 1950). This difference is attributed to the shorter time span between the production of the aerosol over the city and its measurement. 

Zito T, Seidela C (2002) Equilibrium charge distribution on annealed polyelectrolytes. Eur Phys J E 8 339-346... 

In the following sections, the relationship between surface charge and electrokinetic phenomena is expounded in terms of classical theory. First, a few possible mechanisms and models for the development of charge at a surface in contact with an aqueous solution are described in order to form a basis for the formation of an electrical double-layer at an interface. Secondly, the electrical double-layer is discussed in terms of an equilibrium charge distribution and electrostatic potential near the interface. With an adequate description of the interface, the discussion turns to explication of electrokinetic phenomena according to the charge distribution in the electrical double-layer and the Navier-Stokes equation. A section then follows which describes common methods and experimental requirements for the measurement of electrokinetic phenomena. The discussion closes with a few examples of the use of measurement of the pH dependence of electroosmosis as an analytical characterization technique from this present author s own experience. The intention is to provide... 

We shall examine the computation of the equilibrium charge distribution of the solute later and focus our attention on the geometry of the cavity. Its volume may be defined unambiguously as the fraction of the total volume of the sample which is occupied by the solute e.g. the partial molecular volume of this species. The shape of the cavity is not so easily defined since it corresponds to a fictitious surface which is expected to give rise to an electric potential as close as possible to the actual potential in this region of space. 

Table 4.11 contains bond polar parameter values for carbon-halogen bonds determined from experimental infrared intensities in halomethanes and carbonyl halides. As emphasized before, bond polar parameters are not directly related to the equilibrium charge distribution and, therefore, any relationship between the magnitude or sign of diese quantities and the actual polarity of valence bonds may only be qualitative. It should also be pointed out that parameter values are dependent on the accuracy of experimental measurements and the force fields employed. 

The rate at which an aerosol reaches the Boltzmann equilibrium charge distribution depends on the concentration of bipolar ions and is given by... 

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