The Charge Double Layer

The charge double layer is a complex and interesting electrode phenomenon, and whole books have been written on the topic (Bokins et al., 1975). However, a much briefer account will suffice in this context. The charge double layer is important in understanding the dynamic electrical behaviour of fuel cells. 

The resistor Rr models the ohmic losses. A change in current gives an immediate change in the voltage drop across this resistor. The resistor Ra models the activation 

---

Here C is the specific differential double layer capacitance. The two terms on the left side of Eq. (4) describe the capacitive and faradaic current densities at a position r at the electrode electrolyte interface. The sum of these two terms is equal to the current density due to all fluxes of charged species that flow into the double layer from the electrolyte side, z ei,z (r, z = WE), where z is the direction perpendicular to the electrode, and z = WE is at the working electrode, more precisely, at the transition from the charged double layer region to the electroneutral electrolyte. 4i,z is composed of diffusion and migration fluxes, which, in the Nernst-Planck approximation, are given by... 

Proteins in the body liquids may be considered as a colloidal electrolyte solute in a water solvent. Contact with water is the natural state of a protein. In more or less dry form, a protein powder loses some of its electrolytic character it loses the charged double layer on the surface and behaves electrically very differently from protein with water. Such materials may well be mixed conductors—electronic in the dry state and ionic with water content. Keratin is a more or less dry protein found in the natural state of no longer living biological materials such as hair, nails, and the stratum corneum. The water content of such materials is dependent on the relative humidity of the ambient air. The question of ionic or electronic conductivity in proteins is important, and an electronic conduction mechanism must be considered in many cases. 

The potentials can be described by a discretized form of the Poisson equation combined with transient charge balances at the charged double layers. In order to clarify the variables spatial and temporal dependences, they are explicitly given in the following formulations ... 

Fig. 18.1 Activation energy for a one-electron transfer reaction as a function of the reaction ccxrrdinate. The activation energy contains a contribution from the potential difference across the charged double layer at the electrode-electrolyte interface...

The electrochemical reactions and the migration of ions introduce the electric potential as a dependent variable. The electric potential is usually treated with two independent variables and a discontinuity is introduced to avoid the sharp gradients in the charged double layer between the electronic and ionic conductor. Charge and current balances give the equations for the... 

The only part of the electrolyte where there is substantial deviation from electroneutrality is in the charged double layer. However, this problem is avoided by introducing the abovementioned discontinuity in the electric potential. For electrolytes with constant composition, a conservation of current and Ohm s law form the model equations. This equation can be derived from Faraday s law and the electroneutrality condition. Faraday s law gives the current density vector as a function of the transport of ions ... 

An A.C. polarization is caused by an alternating current (A.C.), which in turn, affects the concentration periodically in the vicinity of the cathode electrode surface, but the charged double-layer is assumed to remain undistuibed [31]. Under these A.C. conditions, eq. (3.55) becomes... 

Figure 3.6 The charge double layer at the surface of a fuel cell cathode.

---