Double layer interaction plates

Two classes of interactions are considered (i) London-van der Waals attractions and (ii) electrical double-layer interactions. The unretarded London-van der Waals potential Ad between a sphere and a plate is 5i 6... 

When the sphere and plate are composed of similar material the double-layer interaction potential < DL may be approximated by 2- 1... 

AH rate calculations presented above have used the double-layer interaction given by Eq. [p3 as applied to approach at constant surface potential. Suppose the charge density had been held constant instead. How would this change affect the rate of deposition The answer is illustrated in Fig. 5. When the sphere and plate are many Debye lengths apart, the... 

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...

Therefore, the present treatment of the double layer interaction leads to the same results for the interaction free energy as the imaginary charging approach for systems of arbitrary shapes and constant surfece potential or constant charge density and to the same results as the Langmuir equation for parallel plates and arbitrary surface conditions. It can be, however, used for systems of any shape and any surfece conditions, since it does not imply any of the above restrictions. 

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. 

II.C. Double-Layer Interaction. The calculation of the double-layer interaction accounts for the association-dissociation at the interface. Assuming two parallel plates at a distance x apart, the potential xpm at the middle distance between plates can be very well approximated by the following equation, due to Ohshima and Kondo 13... 

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. 

Double-Layer Interaction. When the copolymer PEO— PPO—PEO precipitates onto the surface of the particles, the PPO segments are attached to the surface, and the PEO segments extend into the solution. The dielectric constant near the surface of the plates is changed by the presence of the polymer chains because the latter have a lower dielectric constant. In addition,... 

The potential energy V h) of the double-layer interaction per unit area between two parallel plates at separation h is given by... 

Double-Layer Interaction Between Two Parallel Similar Plates... 

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... 

First we consider the double-layer interaction between two parallel plates with constant surface charge density cr [3]. 

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