The Ion Distribution

The micellar surface has a high charge density and the stability of the aggregate is heavily dependent on the binding of counterions to the surface. From the solution of the Poisson-Boltzmann equation one finds that a large fraction (0.4—0.7) of the counterions is in the nearest vicinity of the micellar surface300. These ions could be associated with the Stern layer, but it seems simpler not to make a distinction between the ions of the Stern layer and those more diffusely bound. They are all part of the counterions and their distribution is primarily determined by electrostatic effects. 

5 Variation of the CMC with Salt Concentration, Alkyl Chain Length and 

In the limit of an infinite micellar radius, i.e. a charged planar surface, the salt dependence of Ge is solely due to the entropy factor. A difficult question when applying Eq. (6.13) to the salt dependence of the CMC is if Debye-Hiickel correction factors should be included in the monomer activity. When Ge is obtained from a solution of the Poisson-Boltzmann equation in which the correlations between the mobile ions are neglected, it might be that the use of Debye-Hiickel activity factors give an unbalanced treatment. If the correlations between the mobile ions are not considered in the ionic atmosphere of the micelle they should not be included for the free ions in solution. 

An example of a calculation of the salt concentration dependence of the CMC on the basis of Eq. (6.13) is shown in Fig. 6.2. A fair agreement between theory and experiment is observed using only one adjustable parameter which fixes the absolute value of the calculated CMC. The slope (=. 73) of the approximately straight line is 

One contribution, AGe, to the electrostatic free energy comes from Gf in the region rm r r,. Since no charges are present in that region Eq. (6.5) can be integrated directly using Eq. (6.4) and the assumption of a constant dielectric permittivity to give 

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Debye and Htickel [42] assumed that the ion distribution fiinctions are related to by... 

At each phase boundary there exists a thermodynamic equilibrium between the membrane surface and the respective adjacent solution. The resulting thermodynamic equilibrium potential can then be treated like a Donnan-potential if interfering ions are excluded from the membrane phase59 6,). This means that the ion distributions and the potential difference across each interface can be expressed in thermodynamic terms. 

Space charge arises because the character of cation distribution differs from that of anion distribution (the signs of Zj are different). The volume charge density depends on the ion distribution,... 

The volume charge density depends on the ion distribution, which obeys the Boltzmann equation ... 

However, these classical models neglect various aspects of the interface, such as image charges, surface polarization, and interactions between the excess charges and the water dipoles. Therefore, the widths of the electrode/electrolyte interfaces are usually underestimated. In addition, the ion distribution within the interfaces is not fixed, which for short times might lead to much stronger electric helds near the electrodes. 

Bedzyk and co-workers used the XSW technique to probe the ion distribution in the electrolyte above a charged cross-linked phospholipid membrane adsorbed onto a silicon-tungsten layered synthetic microstructure (LSM) as shown in Figure 2.80(a). The grazing-angle incidence experimental set-up... 

One of the first studies of multiple ions at the water/solid interface was by Spohr and Heinzinger, who carried out a simulation of a system of 8 Li" and 81" ions dissolved in 200 water molecules between uncharged flat Lennard-Jones walls.However, the issues discussed in their paper involved water structure and dynamics and the single-ion properties mentioned earlier. No attempt was made to consider the ions distributions and ion-ion correlations. This work has recently been repeated using more realistic water-metal potentials. ... 

Figure 9.30 Flow diagram of the energy chain from food to essential processes in human life. The ATP utilised by the NayK ATPase maintains the ion distribution in nerves that is essential for electrical activity and, in addition, maintains neurotransmitter synthesis, both of which provide communication in the brain and hence consciousness, learning and behaviour (Chapter 14). ATP utilisation by myosin ATPase is essential for movement and physical activity. ATP utilisation by the flagellum of sperm is essential for reproduction and ATP utilisation for synthesis of macromolecules is essential for growth.

The positive-positive particles will show repulsion. On the other hand, the positive-negative particles will attract each other. The ion distribution will also depend on the concentration of any counterions or coions in the solution. Even glass, when dipped in water, exchanges ions with its surroundings. Such phenomena can be easily investigated by measuring the change in the conductivity of the water. 

Under ordinary mass spcctrometric conditions only unimolecular reactions of excited ions occur, but at higher ionization chamber pressures bimolecular ion molecule reactions are observed in which both the parent ions and their unimolecular dissociation product ions are reactants. Since it requires a time of 10 5 sec. to analyze and collect the ions after their formation all of the ions in the complete mass spectrum of the parent molecule are possible reactants. However, in radiation chemistry we are concerned with the ion distribution at the time between molecular collisions which is much shorter than 10 5 sec. For example, in the gas phase at 1 atm. the time between collisions is 10 10 sec. and in considering the ion molecule reactions that can occur one must know the amount of unimolecular decomposition within that time. By utilizing the quasi-equilibrium theory of mass spectra6 it is possible to calculate the ion distribution at any time. This has been done for propane at a time of 10 10 sec.,24 and although the parent ion is increased by a factor of 2 the relative ratios of the other ions are about the same as in the mass spectrum observed in 10 r> sec. Thus for gas phase radiolysis the observed mass spectrum is a fair first approximation to the ion distribution. In... 

The stoichiometric measurements were made using a similar dialysis technique. Exactly 50 mg zeolite ( 0.1-0.2 mg) was weighed into a dialysis membrane to which 5 ml 0.01 NaCl (or NaNOs) was pipetted. The mixture was equilibrated with 40 ml of a mixed electrolyte solution of 0.01 total normality, containing sodium and the bivalent cation (Ni, Zn, Co) in various proportions. Each combination requires two identical experiments, involving either a 22Na or a label of the transition element. Equilibrations were made in an end-over-end shaker (5 or 25°C) for one to two weeks. The ion distributions were calculated from the amounts of radioactivity of the initial and the equilibrium solutions for assays of duplicate 5 ml samples. For precision, the total number of counts collected in the 22Na-labeled samples was always about 10 . 

In concluding this section on liquid-liquid phase transitions, we briefly consider the available experimental information on the ion distribution near criticality. In the absence of scattering experiments, most experimental data come from electrical conductance data [72, 137, 138]. Moreover, there are some data on the concentration dependence of the dielectric constant in low-s solutions [139] and near criticality [138]. 

More refined continuum models—for example, the well-known Fumi-Tosi potential with a soft core and a term for attractive van der Waals interactions [172]—have received little attention in phase equilibrium calculations [51]. Refined potentials are, however, vital when specific ion-ion or ion-solvent interactions in electrolyte solutions affect the phase stability. One can retain the continuum picture in these cases by using modified solvent-averaged potentials—for example, the so-called Friedman-Gumey potentials [81, 168, 173]. Specific interactions are then represented by additional terms in (pap(r) that modify the ion distribution in the desired way. Finally, there are models that account for the discrete molecular nature of the solvent—for example, by modeling the solvent as dipolar hard spheres [174, 175]. 

At a quantitative level, near criticality the FL theory overestimates dissociation largely, and WS theory deviates even more. The same is true for all versions of the PMSA. In WS theory the high ionicity is a consequence of the increase of the dielectric constant induced by dipolar pairs. The direct DD contribution of the free energy favors pair formation [221]. One can expect that an account for neutral (2,2) quadruples, as predicted by the MC studies, will improve the performance of DH-based theories, because the coupled mass action equilibria reduce dissociation. Moreover, quadrupolar ionic clusters yield no direct contribution to the dielectric constant, so that the increase of and the diminution of the association constant becomes less pronounced than estimated from the WS approach. Such an effect is suggested from dielectric constant data for electrolyte solutions at low T [138, 139], but these arguments may be subject to debate [215]. We note that according to all evidence from theory and MC simulations, charged triple ions [260], often assumed to explain conductance minima, do not seem to play a major role in the ion distribution. 

They are often plasticized PVC matrices, which occlude an ionophore as the key selective element, a chromoionophore or a fluoroionophore as the chemical-optical transducer and, sometimes, ionic additives to maintain electroneutrality. Such optodes follow ion-exchange mechanisms between the membrane and the aqueous solution and the analytical response originates from the ratio of the concentration of ions in the solution or from their product (Fig. 3). Moreover, selectivity is ruled by the ion distribution coefficients between both phases and by the formation constants of complexes within the membrane. 

The catalytic effect for reactions involving an ionic reactant usually shows a strong dependence on the total amphiphile concentration. The maximal effective rate constant is attained at concentrations just over the CMC. Romsted284 showed that this occurs due to the competition between the ion binding of the reactive ions (OH- in the example above) and the counterions of the amphiphile. Recently, Diekman and Frahm285 286 showed that it is possible to rationalize the kinetic data by describing the ion distribution through a solution of the Poisson-Boltzman equation. (See Fig. 5.1). 

Since the ion association in micellar systems is due to the long-range electrostatic interactions it is preferable to describe the ion distribution around the charged micelle explicitly. This is customarily made in a model where the water is approximated by a dielectric continuum in which the counterions are distributed. Within such a model, there is a multitude of different degrees of refinements. We choose here to describe the, in our view, most straightforward scheme and postpone a discussion of the possible modifications to a later stage. 

The use of centrifugation to separate the liquid from solid phases in traditional batch or tube techniques has several disadvantages. Centrifugation could create electrokinetic effects close to soil constituent surfaces that would alter the ion distribution (van Olphen, 1977). Additionally, unless filtration is used, centrifugation may require up to 5 min to separate the solid from the liquid phases. Many reactions on soil constituents are complete by this time or less (Harter and Lehmann, 1983 Jardine and Sparks, 1984 Sparks, 1985). For example, many ion exchange reactions on organic matter and clay minerals are complete after a few minutes, or even seconds (Sparks, 1986). Moreover, some reactions involving metal adsorption on oxides are too rapid to be observed with any batch or, for that matter, flow technique. For these reactions, one must employ one of the rapid kinetic techniques discussed in Chapter 4. 

Counterion binding is not a well defined quantity, with various experimental techniques weighing the ion distribution slightly differently. Thermodynamic methods (e.g. ion activities or osmotic coefficients) monitor the free counterion concentration, transport methods (e.g. ion self diffusion or conductivity) the counterions diffusing with the micelle, and spectroscopic methods (e.g. NMR) the counterions in close contact with the micelle surface. Measurement of the effect of Na+ counterions on the symmetric S-O stretching modes would also be expected to be highly dependent on the distance of the counterion from the micelle surface (similar to the NMR method). 

Recently, Forsman developed a correlation-corrected PB model by introducing an effective potential between like-charge ions (Forsman, 2007). The effective potential at large ion-ion separation approaches the classical Coulomb potential and becomes a reduced effective repulsive Coulomb potential for small ion-ion separation. Such an effective potential represents liquid-like correlation behavior between the ions. For electric double layer with multivalent ions, the model makes improved predictions for the ion distribution and predicts an attractive force between two planes in the presence of multivalent ions (Forsman, 2007). However, for realistic nucleic acid structures, the model is computationally expensive. In addition, the ad hoc effective potential lacks validation for realistic nucleic acid structures. 

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