The Diffusion Layer

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

The interaction of an electrolyte with an adsorbent may take one of several forms. Several of these are discussed, albeit briefly, in what follows. The electrolyte may be adsorbed in toto, in which case the situation is similar to that for molecular adsorption. It is more often true, however, that ions of one sign are held more strongly, with those of the opposite sign forming a diffuse or secondary layer. The surface may be polar, with a potential l/, so that primary adsorption can be treated in terms of the Stem model (Section V-3), or the adsorption of interest may involve exchange of ions in the diffuse layer. 

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

Figure A2.4.9. Components of the Galvani potential differenee at a metal-solution interfaee. From [16], A2.4.5.2 INTERFACIAL THERMODYNAMICS OF THE DIFFUSE LAYER...

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

Engstrom R C, Webber M, Wunder D J, Burgess R and Winquist S 1986 Measurements within the diffusion layer using a mioroeleotrode probe Anal. Chem. 58 844... 

Winquist, Engstrom R C, Meaney T, Tople R and Wightman R M 1987 Spatiotemporal desoription of the diffusion layer with a mioroeleotrode probe Anal. Chem. 59 2005... 

The diffusion layer widtli is very much dependent on tire degree of agitation of tire electrolyte. Thus, via tire parameter 5, tire hydrodynamics of tire solution can be considered. Experimentally, defined hydrodynamic conditions are achieved by a rotating cylinder, disc or ring-disc electrodes, for which analytical solutions for tire diffusion equation are available [37, 4T, 42 and 43]. 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

Not all of the ions in the diffuse layer are necessarily mobile. Sometimes the distinction is made between the location of the tme interface, an intermediate interface called the Stem layer (5) where there are immobilized diffuse layer ions, and a surface of shear where the bulk fluid begins to move freely. The potential at the surface of shear is called the zeta potential. The only methods available to measure the zeta potential involve moving the surface relative to the bulk. Because the zeta potential is defined as the potential at the surface where the bulk fluid may move under shear, this is by definition the potential that is measured by these techniques (3). 

The physical separation of charge represented allows externally apphed electric field forces to act on the solution in the diffuse layer. There are two phenomena associated with the electric double layer that are relevant electrophoresis when a particle is moved by an electric field relative to the bulk and electroosmosis, sometimes called electroendosmosis, when bulk fluid migrates with respect to an immobilized charged surface. 

Electrokinetics. The first mathematical description of electrophoresis balanced the electrical body force on the charge in the diffuse layer with the viscous forces in the diffuse layer that work against motion (6). Using this force balance, an equation for the velocity, U, of a particle in an electric field... 

A tangential electric field VE acting on these charges produces a relative motion between the interface and the solution just outside the diffuse layer. In view of the thinness of the diffuse layer, a balance of the tangential viscous and electrical forces can be written... 

From the ion density profiles it is obvious that the surface charge is screened within less than 10 A. Thus, the thickness of the diffuse layer is of the same order of magnitude as the one derived from the Debye... 

The mechanism by which analytes are transported in a non-discriminate manner (i.e. via bulk flow) in an electrophoresis capillary is termed electroosmosis. Eigure 9.1 depicts the inside of a fused silica capillary and illustrates the source that supports electroosmotic flow. Adjacent to the negatively charged capillary wall are specifically adsorbed counterions, which make up the fairly immobile Stern layer. The excess ions just outside the Stern layer form the diffuse layer, which is mobile under the influence of an electric field. The substantial frictional forces between molecules in solution allow for the movement of the diffuse layer to pull the bulk... 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

It should also be noted that both reactions will result in an increase in pH in the diffusion layer. 

Figure 1.3 la to c shows how an increase in the concentration of dissolved oxygen or an increase in velocity increases /Y and thereby increases. It has been shown in equation 1.73 that /Y increases with the concentration of oxygen and temperature, and with decrease in thickness of the diffusion layer, and similar considerations apply to. Thus Uhlig, Triadis and Stern found that the corrosion rate of mild steel in slowly moving water at... 

Temperatures well in excess of 400°C can be used for processing in this case much deeper coatings are obtained, but the iron content of the surface alloy is higher and the diffusion layer is very brittle and less corrosion-resistant. This effect is easily explained when it is remembered that the rate of interdiffusion is far more rapid when the temperature is above the melting point of zinc (420°C). 

The interchange reaction implies the removal of one atom of /I at the surface for each atom of B deposited. It therefore takes place with a minimum change in weight or dimensions of the article (A). U A and B have similar atomic weights, as in the case of iron and chromium, interchange reaction will produce little change in weight and no measurable increase in dimension, whatever the thickness of the diffusion layer. 

On the other hand, both reduction and thermal-dissociation reactions will result in an increase in weight (equivalent to the solute deposited) and a slight increase in dimensions which will depend on the average composition of the diffused layer. 

Fig. 20.1 Potential and concentration gradients in the electrolytic cell CU/CUSO4/CU. (a) The electrodes are unpolarised the potential dilference is the equilibrium potential and there is no concentration gradient in the diffusion layer. (f>) The electrodes are polarised Ep of the anode is now more positive than E. whilst E of the cathode is more negative and concentration gradients exist across the diffusion layer c, C), are the concentrations at the electrode...

I.H.P. and O.H.P. (the diffuse layer being disregarded), and adistinction is made between contact-adsorbed ions and ions electrostatically adsorbed by long-range coulombk forces, Wroblowa, Kovac and Bockris showed that when = 0(pzc). the B,D.M. isotherm can be expressed in the form... 

Fig. 20.18 Concentration gradient and potential gradient in the diffusion layer for a cathodic process (note that the potential drop through the solution has not been included)...

If it is assumed that transport is entirely by diffusion and that there is a linear concentration gradient through the diffusion layer, the concentration gradient at. v = 0, i.e. can be expressed as (Cb - c o)/b. From... 

Example 5 A stainless steel pipe is to be used to convey an aerated reducing acid at high velocity. If the concentration of dissolved Oj is 10 mol dm (10 mol cm ) calculate whether or not the steel will corrode when (a) the acid is static, (b) the acid is moving at high velocity. Assume that the critical current density for passivation of the steel in the acid is 200/iAcm the thickness of the diffusion layer is 0-05 cm when the acid is static and 0-005 cm when the acid flows at a high velocity assume the diffusion coeffi-... 

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