Constant surface potential

Physical model for colloid stability. Net energy of interaction for spheres of constant potential surface for various ionic strengths (1 1 electrolyte) (cf. Verwey and Overbeck). 

A computer program which evaluates the interaction of two charged plates in a 2 1 1 electrolyte solution for either case of constant charge surfaces or constant potential surfaces as a function of their separation is available from the author. 

The double layer free energy is naturally divided into contributions, FL and Fr from each surface. F(oo) is also a sum of two contributions. For constant potential surfaces this is... 

For constant potential surfaces the variable surface charges are derivatives of the potential at the surfaces, approaching each from within the double layer. That is,... 

Interestingly, Carnie et al. [17] point out that the linear Derjaguin approximation for constant charge density surfaces is attractive for all kH only when other case, the force becomes repulsive at very small separations, because the need for counterions to balance the extra charge leads to high osmotic stresses. Conversely, the linear Derjaguin approximation for constant potential surfaces is repulsive for all k i only when... 

Figure 3 Above Radial distribution functions for water samples at 25 C using the TIP4P potential (solid line) and the TIP4P potential plus a localized repulsive barrier (dashed line), as discussed in the text. Below Constant potential surfaces of the localized repulsion added to the TIP4P model. The surfaces correspond to an energy value of 1 kT.

This is the simplest model of an electrocatalyst system where the single energy dissipation is caused by the ohmic drop of the electrolyte, with no influence of the charge transfer in the electrochemical reaction. Thus, fast electrochemical reactions occur at current densities that are far from the limiting current density. The partial differential equation governing the potential distribution in the solution can be derived from the Laplace Equation 13.5. This equation also governs the conduction of heat in solids, steady-state diffusion, and electrostatic fields. The electric potential immediately adjacent to the electrocatalyst is modeled as a constant potential surface, and the current density is proportional to its gradient ... 

Constant potential surfaces Under the assumption of a constant potential, the potential distribution near the surface remains constant. In order to maintain electro-neutrality, as the electrical doublelayers overlap, the concentration of the counterion... 

Finally, the linear superposition approximation (LSA) is a simple way to try to take into account that real interfaces most often behave neither as constant potential surfaces nor as constant charge ones LSA is a simple average between those two cases for the linear PB, it results in... 

Repassivation potentials are readily determined by using the galvanostatic method (Ref 59) or the constant potential-surface scratch test (Ref 59, 60). The galvanostatic method involves impressing an anodic current density of approximately 200 mA/cm (1290 mA/in. ) on the specimen for at least several minutes before measuring the repassivation potential of the sample. Reproducible, anambi-guous repassivation potentials are more difficult to derive by using reverse scan potentiodynamic techniques. 

For constant charge, surfaces with carges of equal sign repel each other at all distances. For constant potential surfaces of equal sign in potential also repel each other at large distances. If the surface potentials are not equal for very short distance the force becomes attractive. (Figure 4.8) [426]. 

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