Concentration, definition electrostatic

Equations 12.39, 12.35, and 12.40 form a coupled system of equations describing the surface function S, charge concentrations Pa, and electrostatic potential. This coupled system differs from the original PNP equations through the coupling of the surface definition are to charge concentrations and electrostatics. We call this DG-based system the "Laplace-Beltrami Poisson-Nernst-Planck" (LB-PNP) model. 

According to the definition, electrostatic interactions must play an important role. From the Debye-Hiickel theory, it can be concluded that in dilute systems these interactions should be long ranged, whereas in concentrated or neat systems, they are screened and therefore short ranged. However, it should be stressed that very often other interactions (e.g., due to the ions polarizability and geometry) are of the same order of magnitude and must not be neglected. 

This important equation expresses the fact that the conductance A of a solution is an additive property and that it equals the sum of the cation conductance X+ and of the anion conductance X. When applying the equation (111-21) we must, however, bear in mind that the ionic conductances Af and A (as well as the velocities y+ and v ) are dependent on concentrations, so that in every particular case their respective values have to agree with the composition of the solution in question. Apart from this it must be remembered that the mutual electrostatic attractions of ions vary at definite concentrations according to the nature of the electrolyte so that the equation (III-21) does not. always yield quite accurate results for arbitrary combinations of cations and anions. 

Adsorbed films between two immiscible liquids. The question of the meaning of the term pn in the surface layer has been raised by Crax-ford, Gatty, and Teorell,2 without, however, coming to any very clear decision. Danielli s estimate was a very rough one, based on the application of the Donnan equilibrium between the surface layer and the interior, and suffers from the difficulties always attending an attempt to consider concentrations in the surface layer in a similar way to concentrations in a bulk phase the surface layer is not homogeneous. pH is closely related to, and is determined by, the electrochemical potential (see Chap. VIII, pp. 304 ff.), and this depends on the electrostatic potential, which varies rapidly at different levels near to the surface it appears possible that the only satisfactory definition of pa in the surface may be one which varies rapidly at different depths. The question appears one which would repay... 

For nonspherical particles, Muller (1928) postulated that since the diffusion equation applicable to aerosol problems is the same (except for definition of terms) as the general equation for electric fields (Laplace s equation), there should be analogs among the electrostatic terms for various properties of coagulation. For example, the potential should be analogous to particle number concentration, and field strength to particle agglomeration rate. Zebel (1966) pointed out that... 

Some papers60-61 have been devoted to phase separation of polyionic complexes from partially furated (PVA-S) and aminoacetylated (PVA-AAC)poly(vinyl alcohol) in aqueous salt solutions. The separation liquid-liquid or complex coacervation occurs at a definite value of the charge density on the macromolecule. From the concentration dependence of the reduced viscosity of the initial components PVA-S, PVA-AAc and their equivalent mixture in water it follows that the viscosity of the components noticeably increases with dilution, and the curve of the equivalent mixture is concentration independent. This fact confirms the formation of the neutral polymer salt, due to electrostatic interactions of PVA-S (strong polyadd) and PVA-AAc (weak polybase). 

The theory is evidence based it can explain (1) the presence of different theoretical curves when k is plotted as a function of the stationary phase concentrations for different IPRs (2) the influence of IPR concentration on the ratio of the retention of two different analytes and (3) the influence of analyte nature on the klk ratio if the experimental conditions are the same. These experimental behaviors cannot be explained by other genuine electrostatic retention models because they arise from complex formation. The present model was the first to take into account at a thermodynamic level these recently definitively demonstrated equilibria in the mobile phase. 

Here is by definition the diffusion coefficient and has the dimensions of cm sec if J is expressed in the conventional units given above, and is the concentration, in molecules/cm. Strictly speaking, this equation is correct only for a two-component system it is applicable in multicomponent systems only if the interaction between flows can be neglected [29]. If the flow of substance A is affected by an external potential (for example, electrostatic interactions greatly influence ionic reactions), Eq. (2-83) can be modified to give... 

Let us consider first a surface-inactive solution, whose properties have already been outlined in Sects. 2.1.3 to 2.1.6. By definition, this term means that the compact layer is solely composed of solvent molecules. The distribution of components within the diffuse layer is determined mostly by the electrostatic forces. If the image forces (see Sect. 2.1.11.3) can be disregarded the concentrations of solute species, ionic or neutral, at the p.z.c. are identical to their bulk values, and the integral (66) over the diffuse layer vanishes. Inside the compact layer the concentration, Ci(z), is zero, and the integration in (66) yields Eq. (12) for the Gibbs adsorption of surface-inactive components, F = —zhc, which allows one to measure the thickness of the ion-free layer of the solvent, zh-... 

Orbital interactions are complex and depend on the combination of stabilizing delocalizations, sterics, and electrostatics. Again, in the spirit of the definition of stereoelectronic effects in the introduction, we will concentrate on stabilizing effects, such as hyperconjugation and conjugation. 

Although no definite stand-point can be reached it appears that these sequences provide some support for the electrostatic model. Especially for aqueous LiCl solutions the electronic distortion model seems not to apply. Thus in this case the halide ion shielding becomes diamagnetic (relative to infinite dilution) at high concentrations [250], whereas marked increases in the halide ion relaxation rate divided by either water relaxation rate or viscosity take place. 

More extensive measurements on the I-N transition in TMV suspensions with added PEO (M = lOOkDa, Rg = 10 nm) were carried out by Adams and Fraden [26]. They observed at TMV concentrations of 20 mg/ml, at which the pure rod system is in the isotropic phase, the first signs of I-N phase separation at 5 mg/ml added PEO and a more definite transition for 10 mg/ml added PEO. To compare this experimental observation with theory we present in Fig. 6.13 also the theoretical phase diagram for L/D = 17 (TMV virus as before) but now with q = 2Rg/D = 2 -10/18 =1.1, which are the relevant parameters for this mixed TMV-PEO suspension. From this calculated phase diagram we observe that at low TMV concentration a relative polymer concentration phase separation which corresponds in this case to a mass concentration of Cp = 3(j)pM/4nNAR g = 10 mg/ml. This is again in reasonable agreement with theory. As mentioned before the electrostatic interactions that certainly play a role have not been taken into account, and therefore the comparison with experiment should be considered with care. 

Reference has already been made to the interesting finding by Laurent and Scott (65) that precipitation of various polyanion/cationic surfactant systems can be totally inhibited by the addition of a sufficient amount of simple salt. This work allowed the definition of a critical electrolyte concentration (c.e.c.), which was found to vary from system to system. Clearly, electrostatic screening effects are again involved. This phenomenon has been confirmed and examined in some detail by Lindman and co-workers (see next section). Less work has been carried out in this respect on polycation/anionic surfactant systems and, at least in some systems involving cationic cellulosic polymer/SDS combinations, resolubilization by salt addition was found not to be facile (59,103). 

---