Gouy-Chapman theory spherical surfaces

Before we proceed to the Gouy-Chapman theory of electrical double layers, it is worthwhile to note that relations similar to Equations (45) and (47) can also be derived for double layers surrounding spherical particles. The equation for surface charge density takes the form... 

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],... 

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