Double layer Nemst equation

Based on the previous description of the double layer, it is logical to assume that a direct relationship between the absolute charge at the interface and the concentration of ions in the vicinity of the interface exists. Indeed, several models have been developed in the past that describe the ion concentration as a function of the actual surface charge at a specific distance jc from the interface. Furthermore, the famous Nemst equation, which is the basis for understanding many electrochemical reactions, proves to be helpful as it relates the ion concentration to a quantity called the electrical potential ( j/). The electrical potential is the work (W) required to move a unit charge (q) through the electrical field ... 

The electrostatic aspects of electrochemical systems will be introduced first and the electrochemical potential as a key concept is presented (Sects. 1.2-1.4). The electrochemical equilibrium is discussed and Nemst s equation and standard and formal electrode potentials are introduced (Sect. 1.5). The study of electrochemical interfaces under equilibrium ends with the phenomenological and theoretical treatment of the electrical double layer (Sect. 1.6). 

Relaxed interfaces cannot be polarized unless special precautions are taken. Capacitances can of course be obtained as derived quantities by differentiating the surface charge with respect to the surface potentieil if changes In the latter are known, which is possible if the Nemst equation applies. We now discuss direct capacitance measurements on reversible interfaces. To start with, the response of such an interface to an applied field has to be considered. The basic problem is that not only are double layers built up, but also charge transfer across the interfaces takes place and diffusion of charge-determining ions to or from the surface starts to play a role. With regard to these physical processes only the sum-effect is measured, and this sum has to be divided into its parts to obtain the capacitance. Distinctions can be made because the three constituents mentioned react in a different way to the frequency of the external field. 

In the small nanochaimels (from a few to about 100 nm), the electric double layer (EDL) thickness becomes larger or at least comparable with the nanochaimels lateral dimensions. It affects the balance of bulk ionic concentrations of co-ions and counterions in the nanochannels. Thus, many conventional approaches such as the Poisson—Boltzmann equation and the Helmholtz-Smoluchowski slip velocity, which are based on the thin EDL assumption and equal number of co-ions and counterions, lose their credibility and cannot be utilized to model the electrokinetic effects through these nanoscale channels. The Poisson equation, the Navier-Stokes equations, and the Nemst-Planck equation should be solved directly to model the electrokinetic effects and find the electric... 

Instead of the Nemst-Plank equation for the flux of ionic transportation, the equilibrium Poisson equation can be selected as the starting point for describing the electrical potential because the time required for cellular motion, electrophoresis, coagulation, and deposition is much longer than the diffusion equihbrium of ionic profile in interacting double layers [70-72]. The spatial variation in the electrostatic potential can be described by the Poisson equation... 

To evaluate the integrals in Equations 9.17 and 9.21 the relation between rpo and Oo should be known. This relation may be obtained from Oo(Cedi) represented by the titration curves (see Figure 9.2), provided that Nemst s law, Equation 9.14, applies. If not, a model for the electrical double layer is required to derive rpo (oo ) ... 

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