Interaction between Electrical Double Layers

Generally, both the protein molecule and the surface are electrically charged and surrounded by counterions and co-ions. A fraction of the countercharge may be bound to the surface and/or the protein molecule and the other part is diffusely distributed in the solution (see Section 9.4). 

The Gibbs energy G to invoke a charge distribution can be calculated as the 

FIGURE 15.16 Schematic representation of charge distributions before (left) and after (right) protein adsorption. The charge on the surface and the protein molecule are indicated by +/-. The low-molecular-weight electrolyte ions are indicated by 0/ . 

FIGURE 15.17 Proton charge (net number of charged groups per protein molecule) as a function of pH for (X-lactalbumin in solution (—) and adsorbed on a negatively (—) and 

FIGURE 15.18 Variation in the electrokinetic charge density resulting from plateau-adsorption of lysozyme (o) and a-lactalhumin ( ) on negatively charged polystyrene particles. The arrows indicate the isoelectric points of the two proteins. (Adapted from Norde, W. et al., Polym. Adv. Technol., 6, 518, 1995.) 

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Hon, T. et al.. Interaction between electrical double layers of soil colloids and Fe/Al oxides in suspensions, 7. Colloid Interf. Sci., 310, 670, 2007. 

That ideal solution behavior is essential to the derivation of Eq. 6.7a has been shown in W. Olivares and D. A. McQuarrie, Interaction between electrical double layers, J. Phys. Chem. 84 863 (1980). 

The zeta potential is the potential at the surface between a stationary solution and a moving charged colloid particle. This surface defines the plane of shear. Its definition is somewhat imprecise because the moving charged particle will have a certain number of counterions attached to it (for example ions in the Stern layer, plus some bound solvent molecules), the combined flowing object being termed the electrokinetic unit. The stability of colloidal suspensions is often interpreted in terms of the zeta potential, because, as we shall see, it is more readily accessible than the surface potential (Eq. 3.7), which describes the repulsive interaction between electric double layers. 

J. C. Hansen and H. Lowen, Annu. Rev. Phys. Chem., 51,209 (2000). Effective Interactions between Electric Double Layers. 

Repulsive forces caused by the interaction between electrical double layers and controlled by the physicochemical parameters of the system. In Section 6.2, we saw that the surface charge and the size of the counterion diffuse layer are linked to the pH and to the ionic strength of the solution. 

The interaction between two double layers was first considered by Voropaeva et a/.145 These concepts were used to measure the friction between two solids in solution. Friction is proportional to the downward thrust of the upper body upon the lower. However, if their contact is mediated by the electrical double layer associated with each interface, an electric repulsion term diminishes the downward thrust and therefore the net friction. The latter will thus depend on the charge in the diffuse layer. Since this effect is minimum at Eam0, friction will be maximum, and the potential at which this occurs marks the minimum charge on the electrode. 

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

The influence of the electric potential of the surface of the drops was shown by Watanabe and Gotoh (W3) for the case of mercury droplets in aqueous solutions. In the case of oil drops in water the electric double layer is in the water phase, which makes possible a real interaction between the double layers of the two drops that approach each other. In the case of water drops in an oil phase, however, the electric double layers are on the inside of the drops, so that the interaction of these layers when two drops approach each other is much smaller [see Sonntag and Klare (S5)], which means that the potential barrier is much smaller or may even be absent, and the attraction by London-van der Waals forces predominates. This at least is a first explanation of why systems in which water is the dispersed phase show much higher interaction rates than systems in which oil is the dispersed phase. 

A similar calculation can be carried out for the potential energy of repulsive forces between two identical spherical particles. In the case when the thickness of the electrical double layer around these particles is small compared to their radii, interaction of electrical double layers of these spheres may, according to Derjaguin, be considered as a superposition of interactions of infinitely narrow parallel rings (Fig. 10.2) [53]. 

It is well known that Verwey and Overbeek and Derjaguin and Landau " " (DLVO) have given a quantitative treatment of the interaction of electrical double layers. According to them, the free energy of a double layer may be expressed as a difference between the surface energy G, of the system in its equilibrium state and the surface free energy G of a standard state in which no double layer is present ... 

The DLVO theory of stability takes into account the interaction of two kinds of long-range forces which determine the closeness of contact of two particles approaching as a result of Brownian movement. The forces concerned are (i) the London-van der Waals forces of attraction, and (ii) the electrostatic repulsion between electrical double layers. 

Here we consider the total interaction between two charged particles in suspension, surrounded by tlieir counterions and added electrolyte. This is tire celebrated DLVO tlieory, derived independently by Derjaguin and Landau and by Verwey and Overbeek [44]. By combining tlie van der Waals interaction (equation (02.6.4)) witli tlie repulsion due to the electric double layers (equation (C2.6.lOI), we obtain... 

Fig. 1. Potential energies of interaction between two coUoidal particles as a function of their surface-surface separation, for electrical double layers due...

In some cases, e.g., the Hg/NaF q interface, Q is charge dependent but concentration independent. Then it is said that there is no specific ionic adsorption. In order to interpret the charge dependence of Q a standard explanation consists in assuming that Q is related to the existence of a solvent monolayer in contact with the wall [16]. From a theoretical point of view this monolayer is postulated as a subsystem coupled with the metal and the solution via electrostatic and non-electrostatic interactions. The specific shape of Q versus a results from the competition between these interactions and the interactions between solvent molecules in the mono-layer. This description of the electrical double layer has been revisited by... 

The situations would be totally different when the two surfaces are put in electrolyte solutions. This is because of formation of the electrical double layers due to the existence of ions in the gap between solid surfaces. The electrical double layers interact with each other, which gives rise to a repulsive pressure between the two planar surfaces as... 

A force-distance curve between layers of the ammonium amphiphiles in water is shown in Figure 8. The interaction is repulsive and is attributed to the electric double-layer... 

Fig. 2. Schematic diagram of the tunnel gap between sample and tip, with the extension of the electric double layers indicated by the outer Helmholtz plane(OHP). (a) No tip interaction at large tip-sample separation, (b) Overlap of the electric double layers at a distance s = 0.6 nm, which can be achieved by conventional imaging conditions (e.g., Uj = 50 mV It = 2 nA Rt = 2.5 x 107 Q). Inset Dependence of the tunnel gap s on the tunnel resistance Rt for a tunnel barrier of 1.5 eV.

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