Diffusion between finite layers solute

Occasionally (e.g., thin-layer electrochemistry, porous-bed electrodes, metal atoms dissolved in a mercury film), diffusion may be further confined by a second barrier. Figure 2.7 illustrates the case of restricted diffusion when the solution is confined between two parallel barrier plates. Once again, the folding technique quickly enables a prediction of the actual result. In this case, complete relaxation of the profile results in a uniform finite concentration across the slab of solution, in distinct contrast to the semi-infinite case. When the slab thickness t is given, the time for the average molecule to diffuse across the slab is calculable from the Einstein equation such that... 

In regards to the stationarity of the reaction-diffusion process, it should be emphasised that the number of the B atoms diffusing across the ApBq layer is always equal to their number combined by the A surface into the ApBq compound at interface 1, if the growth of this layer is not accompanied by the formation of other compounds or solid solutions. The case under consideration is characterised by a kind of forced stationarity due to (z) the impossibility of any build-up of atoms at interfaces between the solids, (z z) the limited number of diffusion paths in the ApBq layer for the B atoms to travel from interface 2 to interface 1 and (Hi) the finite value of the reactivity of the A surface towards the B atoms. The stationarity is only... 

A lattice model for an electrolyte solution is proposed, which assumes that the hydrated ion occupies ti (i = 1, 2) sites on a water lattice. A lattice site is available to an ion i only if it is free (it is occupied by a water molecule, which does not hydrate an ion) and has also at least (i, - 1) first-neighbors free. The model accounts for the correlations between the probabilities of occupancy of adjacent sites and is used to calculate the excluded volume (lattice site exclusion) effect on the double layer interactions. It is shown that at high surface potentials the thickness of the double layer generated near a charged surface is increased, when compared to that predicted by the Poisson-Boltzmann treatment. However, at low surface potentials, the diffuse double layer can be slightly compressed, if the hydrated co-ions are larger than the hydrated counterions. The finite sizes of the ions can lead to either an increase or even a small decrease of the double layer repulsion. The effect can be strongly dependent on the hydration numbers of the two species of ions. 

The treatment given above of the diffuse double layer is based on the assumption that the ions in the electrolyte are treated as point charges. The ions are, however, of finite size, and this limits the inner boundary of the diffuse part of the double layer, since the center of an ion can only approach the surface to within its hydrated radius without becoming specifically adsorbed (Fig. 6.4.2). To take this effect into account, we introduce an inner part of the double layer next to the surface, the outer boundary of which is approximately a hydrated ion radius from the surface. This inner layer is called the Stern layer, and the plane separating the inner layer and outer diffuse layer is called the Stern plane (Fig. 6.4.2). As indicated in Fig. 6.4.2, the potential at this plane is close to the electrokinetic potential or zeta ( ) potential, which is defined as the potential at the shear surface between the charge surface and the electrolyte solution. The shear surface itself is somewhat arbitrary but characterized as the plane at which the mobile portion of the diffuse layer can slip or flow past the charged surface. 

A finite length diffusion layer thickness cannot only be caused by constant concentrations of species in the bulk of the solution but also by a reflective boundary, that is, a boundary that cannot be penetrated by electroactive species (dc/dr = 0). This can happen when blocking occurs at the far end of the diffusion region and no dc current can flow through the system, for example, a thin film of a conducting polymer sandwiched between a metal and an electrolyte solution [6]. The impedance in this case can be described with the expression... 

A common arranganent for thin layer geometry is to sandwich the solution between glass and an rrO electrode using a Teflon or Kapton spacer such cells are now commercially available. For a thin layer arrangement, the cell width through which the excitation beam is directed ranges between 50 and 250 pm and the electrolysis rate is controlled by finite diffusion. 

In the case when there is an externally imposed electron injection/extraction into/from the electrode, ET processes between the electrode and electroactive species in solution can proceed continuously, which would result in a concentration distribution layer (CDL) of electroactive species at the interface due to their finite mass transport (MT) rates. If assuming that the solution species approximately have the same PCA, one can imagine that the CDL and diffuse EDL would start similarly at the OHP and would merge into each other at the electrode interface when an ET process proceeds continuously (Figure 2.1). To this end, the diffuse EDL will be dynamic in nature, and interfacial MT and ET processes will be impacted by the high electrostatic gradient (on the order of 10 V/m) in the EDL. 

Several additional physical processes potentially exist that can create somewhat more complicated equivalent circuit diagrams, as is evident for example from discussions in Chapter 10 on conductive polymer films. For instance, additional macrodefect corrosion and diffusion effects may develop between the coating and the surface, with an additional low frequency relaxation becoming visible in the Nyquist plot. The interface between a pocket of solution and the bare metal is modeled as a double-layer capacitance in parallel with a kinetically controlled charge-transfer resistance R, which can also often include the diffusion element associated with corrosion products in series with R. If the diffusion element represents a finite diffusion, an additional Rpiipp I element appears and a third relaxation at low frequencies,... 

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