Diffuse electric double layer spherical

Double Layer Interactions and Interfacial Charge. Schulman et al (42) have proposed that the phase continuity can be controlled readily by interfacial charge. If the concentration of the counterions for the ionic surfactant is higher and the diffuse electrical double layer at the interface is compressed, water-in-oil microemulsions are formed. If the concentration of the counterions is sufficiently decreased to produce a charge at the oil-water interface, the system presumably inverts to an oil-in-water type microemulsion. It was also proposed that for the droplets of spherical shape, the resulting microemulsions are isotropic and exhibit Newtonian flow behavior with one diffused band in X-ray diffraction pattern. Moreover, for droplets of cylindrical shape, the resulting microemulsions are optically anisotropic and non-Newtonian flow behavior with two di-fused bands in X-ray diffraction (9). The concept of molecular interactions at the oil-water interface for the formation of microemulsions was further extended by Prince (49). Prince (50) also discussed the differences in solubilization in micellar and microemulsion systems. 

The most widely used theory of the stability of electrostatically stabilized spherical colloids was developed by Deryaguin, Landau, Verwey, and Overbeek (DLVO), based on the Poisson-Boltzmann equation, the model of the diffuse electrical double layer (Gouy-Chapman theory), and the van der Waals attraction [60,61]. One of the key features of this theory is the effective range of the electrical potential around the particles, as shown in Figure 25.7. Charges at the latex particles surface can be either covalently bound or adsorbed, while ionic initiator end groups and ionic comonomers serve as the main sources of covalently attached permanent charges. 

In the years 1910-1917 Gouy2 and Chapman3 went a step further. They took into account a thermal motion of the ions. Thermal fluctuations tend to drive the counterions away form the surface. They lead to the formation of a diffuse layer, which is more extended than a molecular layer. For the simple case of a planar, negatively charged plane this is illustrated in Fig. 4.1. Gouy and Chapman applied their theory on the electric double layer to planar surfaces [54-56], Later, Debye and Hiickel calculated the potential and ion distribution around spherical surfaces [57],... 

The calculation of the interaction energy, VR, which results from the overlapping of the diffuse parts of the electric double layers around two spherical particles (as described by Gouy-Chapman theory) is complex. No exact analytical expression can be given and recourse must be had to numerical solutions or to various approximations. 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

Ionic strength of medium, surface structure and non-spherical particles can affect diffusion speed of particles. The thickness of the electric double layer (Debye length) changes with the ions in the medium and the total ionic concentration. An extended double layer of ions around the particle results from a low conductivity medium. So, the diffusion speed reduces and hydrodynamic diameter increases. The diffusion speed can be affected with a change in surface area. The diffusion speed will reduce with an adsorbed polymer layer. Polymer conformation can alter the apparent size. 

Two general theoretical approaches have been applied in the analysis of heterogeneous materials. The macroscopic approach, in terms of classical electrodynamics, and the statistical mechanics approach, in terms of charge-density calculations. The first is based on the application of the Laplace equation to calculate the electric potential inside and outside a dispersed spherical particle (11, 12). The same result can be obtained by considering the relationship between the electric displacement D and the macroscopic electric field Em a disperse system (12,13). The second approach takes into account the coordinate-dependent concentration of counterions in the diffuse double layer, regarding the self-consistent electrostatic poton tial of counterions via Poisson s equation (5, 16, 17). Let us consider these approaches briefly. 

The consequences of these restrictive assumptions have been reviewed by Dukhin " and others, who noted that the neglect of the outer regions leads to error in assessing the source of the polarization. The diffuse outer, and not the inner ionic double layer is according to Dukhin, the major source of polarization. The details of this comparison were recently reviewed. So much for the effective electrical polarization of rigid spherical bodies surrounded by an ionic double layer, i.e., for a large class of colloidal particle suspensions. 

In a similar way we may understand another remarkable point ro be derived from M ii 11 e r s tables. For a flat double layer we found that the form of the electric potential curve is radically changed by an increase in the ionic charge. M ii 11 e r s data however, show, that for a spherical particle (with jco 1) the valency of the ions in the solution has only a minor influence upon the decline of the electric potential in the diffuse layer. Hence, also in this respect the Debyc-Hiickel theory is a much better approximation for the spherical double layer field than for the flat double layer, once we wish to apply this theory to cases where the potential is no longer small. 

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