Double layers, interaction between

The observed equilibrium thickness represents the film dimensions where the attractive and repulsive forces within the film are balanced. This parameter is very dependent upon the ionic composition of the solution as a major stabilizing force arizes from the ionic double layer interactions between any charged adsorbed layers confining the film. Increasing the ionic strength can reduce the repulsion between layers and at a critical concentration can induce a transition from the primary or common black film to a secondary or Newton black film. These latter films are very thin and contain little or no free interlamellar liquid. Such a transition is observed with SDS films in 0.5 M NaCl and results in a film that is only 5 nm thick. The drainage properties of these films follows that described above but the first black spot spreads instantly and almost explosively to occupy the whole film. This latter process occurs in the millisecond timescale. 

D.C. Prieve, E. Ruckenstein The double-layer interaction between dissimilar ionizable surfaces and its effect on the rate of deposition, JOURNAL OF COLLOID AND INTERFACE SCIENCE 63 (1978) 317-329. 

The Double-Layer Interaction between Dissimilar lonizable Surfaces and Its Effect on the Rate of Deposition1... 

Rates of deposition were calculated for cases in which sol and collector surfaces are dissimilar and acquire their charge by the dissociation of multiple acidic and/or basic sites. The double-layer interaction between such dissimilar surfaces can induce a sign reversal in the surface charge or the force. These sign reversals are not observed between identical surfaces. 

Such calculations were first performed by Ninham and Parsegian (1) for the case of two identical plane, acidic surfaces. Later, Pricve and Ruckenstein (2, 3) and Chan et al. (4, 5) independently published numerical results of similar calculations for the case of two identical, plane, amphoteric surfaces. Rates of hydrosol adsorption were calculated by Prieve and Ruckenstein (6), who used the double-layer interaction between the particle and collector corresponding to identical and acidic or amphoteric surfaces. However, in a real situation the particle and collector surfaces are different. 

Figures 1 and 2 summarize the results computed for the double-layer interaction between two parallel plates. Each figure presents the charge density and electrostatic potential of both interacting surfaces, together with the double-layer force per unit area (p > 0 denotes repulsion), as a function of the dimensionless separation...

The electrostatic stabilization theory was developed for dilute colloidal systems and involves attractive van dcr Waals interactions and repulsive double layer interactions between two particles. They may lead to a potential barrier, an overall repulsion and/or to a minimum similar to that generated by steric stabilization. Johnson and Morrison [1] suggest that the stability in non-aqueous dispersions when the stabilizers are surfactant molecules, which arc relatively small, is due to scmi-stcric stabilization, hence to a smaller ran dcr Waals attraction between two particles caused by the adsorbed shell of surfactant molecules. The fact that such systems are quite stable suggests, however, that some repulsion is also prescni. In fact, it was demonstrated on the basis of electrophoretic measurements that a surface charge originates on solid particles suspended in aprotic liquids even in the absence of traces of... 

In this Appendix, equations will be derived for the double layer interaction between two charged, planar surfaces in an electrolyte-free system. W e assume that the potential ip(x) obeys the Poisson—Boltzmann equation... 

The present approach reduces to the traditional ones within their range of application (imaginary charging processes for double layer interactions between systems of arbitrary shape and interactions either at constant surface potential or at constant surface charge density, and the procedure based on Langmuir equation for interactions between planar, parallel plates and arbitrary surface conditions). It can be, however, employed to calculate the interaction free energy between systems of arbitrary shape and any surface conditions, for which the traditional approaches cannot be used. 

At low electrolyte concentrations, the experimental results can be explained within the DLVO theory. A well-known approximation for the double layer interaction between weakly charged spheres, at constant surface charge, is1... 

H. Huang, E. Ruckenstein Double-layer interaction between two plates with haiiy surfaces JOURNAL OF COLLOID AND INTERFACE SCIENCE 273 (2004) 181-190. 

Double-layer interaction between two plates with hairy surfaces... 

Colloidal dispersions can be stabilized by attaching polymer chains to their surface [1-9]. When neutral polymer chains grafted on two parallel plates interpenetrate, a steric repulsion is generated. If the polymer chains grafted to the plates are charged, the double layer interaction between the two plates is also affected by the presence of the chains. 

H. Ohshima, Diffuse double layer interaction between two spherical particles with constant surface charge density in an electrolyte solution, Colloid Polymer Sci. 263, 158-163 (1975). 

This chapter has been written with the intention of introducing the reader to some analytical methods which can be employed to describe the structure of the electrical double layer adjacent to a charged surface and double layer interactions between two charged surfaces across an electrolyte. Since the... 

Force and Potential Energy of the Double-Layer Interaction Between Two Charged Colloidal Particles... 

When two charged colloidal particles approach each other, their electrical double layers overlap so that the concentration of counterions in the region between the particles increases, resulting in electrostatic forces between them (Fig. 8.2). There are two methods for calculating the potential energy of the double-layer interaction between two charged colloidal particles [1,2] In the first method, one directly calculates the interaction force P from the excess osmotic pressure tensor All and... 

The potential energy V(R) of the double-layer interaction between two spheres at separation R is given by... 

In this chapter, we give exact expressions and various approximate expressions for the force and potential energy of the electrical double-layer interaction between two parallel similar plates. Expressions for the double-layer interaction between two parallel plates are important not only for the interaction between plate-like particles but also for the interaction between two spheres or two cylinders, because the double-interaction between two spheres or two cylinders can be approximately calculated from the corresponding interaction between two parallel plates via Deijaguin s approximation, as shown in Chapter 12. We will discuss the case of two parallel dissimilar plates in Chapter 10. 

DOUBLE-LAYER INTERACTION BETWEEN TWO PARALLEL SIMILAR PLATES... 

The boundary conditions at the plate surface depends on the type of the double--layer interaction between plates 1 and 2. If the surface potential of the plates remains constant at ij/o, then... 

For the low potential case, simple analytic expressions for the force and potential energy of the double-layer interaction between two plates can be derived. In this case Eq. (9.26) for the interaction force P h) per unit area between the plates at separation h reduces to... 

The potential energy per unit area of the double-layer interaction between plates 1 and 2 is obtained by integrating Eq. (9.47) with respect to h with the result that... 

The calculation of the potential energies V" h) and h) of the double-layer interaction between two parallel plates requires numerical solutions to transcendental equations (9.105) and (9.137), respectively. In the following we give approximate analytic expressions for V (h), which does not require numerical calculation. The obtained results, which are correct to the order of the sixth power of the unperturbed surface potential i//q, are applicable for low and moderate potentials. 

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