Charge regulation

As discussed in the previous section, often neither constant potential nor constant charge conditions describe well the surface behavior, especially at small separation 

FIG U RE 6.9 Force between plane parallel surfaces as a function of distance between them. Initial potentials at infinite separation 0.1 = — 1-8 RT/F. (1) Exact results for constant 

---

To examine this peculiar behavior, we have converted the elastic compressibility modulus, per unit area, Y (Fig. 12a), to the modulus per chain, Y = F/10 F (Fig. 12b). The elastic compressibility modulus per chain is practically constant, 0.6 0.1 pN/chain, at high densities and jumps to another constant value, 4.4 0.7 pN/chain, when the density decreases below the critical value. The ionization degree, a, of the carboxylic acid determined by FTIR spectroscopy gradually decreases with increasing chain density due to the charge regulation mechanism (also plotted in Fig. 12b). This shows that a does not account for the abrupt change in the elastic compressibihty modulus. 

Stahlberg J, Appelgren U, Jonsson B (1995) Influence of charge regulation in electrostatic interaction chromatography of proteins. J Colloid Interf Sci 176 397 107... 

Coulombic, van der Waals, entropic and osmotic forces are coupled in a nontrivial way and give rise to important charge regulation in polyelectrolyte systems. The salt concentration is also an important factor to define the structure and thermodynamic properties of polyelectrolyte solutions. In weak polyelectrolytes the ionization equilibrium is also coupled to these interactions and thus the pKof ionizable groups depends on the organization of the interface and differs from that for the isolated molecule. 

Besides the dependence of peak potential with solution pH, there is other evidence of the acid-base and redox coupling, namely the prediction of amine deprotonation during film oxidation. Deprotonation is a response to the creation of Os(III) sites that increment the concentration of positive charges in the film. This is an example of charge regulation a chemical equilibrium at the interface is displaced as the system tries to reduce its electrostatic charge. 

I. M. Metcalfe and T. W. Healy, Charge-regulation modeling of the Schulze-Hardy rule and related coagulation effects, Faraday Discuss. Chem. Soc. 90 335 (1990). 

It is possible to calculate Vr as a function of separation exactly using numerical techniques. The method of Chan et al. 145] may be used for this purpose. Interested readers are referred to Ref. 45 for further information about these calculations. It is also possible to calculate the interaction for the charge regulation case where knowledge of the surface density of acid groups and their dissociation constants is required. 

If the dissociation of the ionizable groups on the particle surface is not complete, or the configurational entropy Sc of adsorbed potential-determining ions depends on N, then neither of ij/o nor of cr remain constant during interaction. This type of double--layer interaction is called charge regulation model. In this model, we should use Eqs. (8.35) and (5.44) for the double-layer free energy [ 11-13]. 

Figure 14.18. Energy Charge Regulates Metabolism. High concentrations of ATP inhibit the relative rates of a typical ATP-generating (catabolic) pathway and stimulate the typical ATP-utilizing (anabolic) pathway.

Beyond this, the inclusion of the competition for surface sites of different competing species (e.g. H vs. Na" ") gives rise to the further problem of surface charge regulation [22, 27-30], with a concomitant appearance of a so-called "secondary hydration force". Surface localised dipole-dipole correlations give rise to a further force [31, 32], and much of what was confused falls into place. These developments represent a first conceptual step forward on the way to a more complete and necessary stage of... 

Figure 18.41 Energy charge regulates the use of fuels. The synthesis of ATP from ADP and Pj controls the flow of electrons from NADH and FADHj to oxygen. The availability of NAD and PAD in turn control the rate of the citrfc acid cycle (CAC).

Zhmud, B.V. and Sonnefeld, J., Charge regulation at the surface of porous silica,... 

The electrostatic properties of particles can be described by two key parameters, the surface charge density and the kinetic surface potential. The surface charge density (a,) corresponds to the potential at the particle surface ( /o). This charge regulates the interaction of dissolved ions with the surface and the effective charge is dependent on the degree of adsorbed counterions to the surface. In this section we discuss the relative effect of simple ions (no deprotonation and no condensation of aquo ligands) on sol stability when the pH is varied. 

Shubin V, Linse P. Self-consistent field modeling of polyelectrolyte adsorption on charge-regulating surfaces. Macromolecules 1997 30 5944—5952. 

---