Diffuse electrical layer

An electroosmotic flux is formed as a result of the effect of the electric field in the direction normal to the pores in the membrane, delectric diffuse layer in the pore with a charge density p. The charges move in the direction of the x axis (i.e. in the direction of the field), together with the whole solution with velocity v. At steady state... 

The process of particle collision is governed by physical factors such as diffusion, temperature, fluid shear, particle and fluid density, and the size of particles and aggregates. Whether particles will adhere when they collide is considered to be a function of conditions at the interface between the two solid particles and the fluid medium. Chemical interactions at the solid-liquid interface are responsible for the development of surface charge and potential, the electric diffuse layer, and hydration and hydrophobic effects which determine the probability of particle attachment. 

The system considered consists of a charged interface including a compact layer between two immiscible ionic solutions with dielectric constants c and e. The surface charge density is compensated by the integral charges of two electrical diffuse layers of thickness k =(0RT/8 ttz (with the concentration in... 

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]. 

Outside the OHP, there may still be an electric field and hence an imbalance of anions and cations extending in the fomi of a diffuse layer into the solution. 

Splelman L A and Friedlander S K 1974 Role of the electrical double layer In particle deposition by convective diffusion J. Colloid. Interfaoe. Sol. 46 22-31... 

Fig. 7. (a) Simple battery circuit diagram where represents the capacitance of the electrical double layer at the electrode—solution interface, W depicts the Warburg impedance for diffusion processes, and R is internal resistance and (b) the corresponding Argand diagram of the behavior of impedance with frequency, for an idealized battery system, where the characteristic behavior of A, ohmic B, activation and C, diffusion or concentration (Warburg... 

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... 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

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... 

Tafel slope (Napieran loop) transfer coefficient diffusion layer thickness dielectric constant, relative electric field constant = 8.85 x 10 F cm overvoltage, polarization ohmic voltage drop, resistance polarization specific conductance, conductivity electrochemical potential of material X,... 

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 explicit mathematical treatment for such stationary-state situations at certain ion-selective membranes was performed by Iljuschenko and Mirkin 106). As the publication is in Russian and in a not widely distributed journal, their work will be cited in the appendix. The authors obtain an equation (s. (34) on page 28) similar to the one developed by Eisenman et al. 6) for glass membranes using the three-segment potential approach. However, the mobilities used in the stationary-state treatment are those which describe the ion migration in an electric field through a diffusion layer at the phase boundary. A diffusion process through the entire membrane with constant ion mobilities does not have to be assumed. The non-Nernstian behavior of extremely thin layers (i.e., ISFET) can therefore also be described, as well as the role of an electron transfer at solid-state membranes. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

While from a structural point of view metal/solution and metal/vac-uum interfaces are qualitatively comparable even if quantitatively dissimilar, in the presence of ionic adsorbates the comparability is more difficult and is possible only if specific conditions are met.33 This is sketched in Fig. 7. A UHV metal surface with ions adsorbed on it is electrically neutral because of a counter-charge on the metal phase. These conditions cannot be compared with the condition of a = 0 in an electrochemical cell, but with the conditions in which the adsorbed charge is balanced by an equal and opposite charge on the metal surface, i.e., the condition of zero diffuse-layer charge. This is a further complication in comparing electrochemical and UHV conditions and has been pointed out in the case of Br adsorption on Ag single-crystal faces.88... 

The model more generally accepted for metal/electrolyte interfaces envisages the electrical double layer as split into two parts the inner layer and the diffuse layer, which can be represented by two capacitances in series.1,3-7,10,15,32 Thus, the total differential capacitance C is equal to... 

The interaction between two double layers was first considered by Voropaeva et a/.145 These concepts were used to measure the friction between two solids in solution. Friction is proportional to the downward thrust of the upper body upon the lower. However, if their contact is mediated by the electrical double layer associated with each interface, an electric repulsion term diminishes the downward thrust and therefore the net friction. The latter will thus depend on the charge in the diffuse layer. Since this effect is minimum at Eam0, friction will be maximum, and the potential at which this occurs marks the minimum charge on the electrode. 

Figure 10. Theoretical model for the electrical double layer at an electrode with a polycrystalline surface, (a) Model of independent diffuse layers [Eq. (S3)], and (b) model of common diffuse layer [Eq. (54)).

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y, whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the face j.262,263 In the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc electrode and depends on the average charge density <7pc = R ZjOjOj [Fig. 10(b)]. The capacitance Cj al is obtained by the equation... 

The electrical double-layer structure at Ga/DMF, In(Ga)/DMF, and Tl(Ga)/DMF interfaces upon the addition of various amounts of NaC104 as a surface-inactive electrolyte has been investigated by differential capacitance, as well as by the streaming electrode method.358 The capacitance of all the systems was found to be independent of the ac frequency, v. The potential of the diffuse layer minimum was independent of... 

The electrical double layer at a pc-Ag/aqueous solution interface has been discussed by LeiMs et al., Valette and Hamelin, and Beck et al. in many papers.24 63 67146 223 272363-368 Detailed reviews have been given by Hamelin63 and Vorotyntsev74 in this work only a few comments will be added. First, the diffuse-layer minimum in the C,E curve was obtained363... 

The electrical double-layer structure of a Pt/DMSO interface has been investigated using the potentiostatic pulse method.805 The value of C at E = const, as well as the potential of the diffuse layer minimum, have been found to depend on time, and this has been explained by the chemisorption of DMSO dipoles on the Pt surface, whose strength depends on time. Eg=Q has been found11 at E = -0.64 V (SCE in H2O). 

Various pc electrode models have been tested.827 Using the independent diffuse layer electrode model74,262 the value of E n = -0.88 V (SCE) can be simulated for Cd + Pb alloys with 63% Pb if bulk and surface compositions coincide. However, large deviations of calculated and experimental C,E curves are observed at a 0. Better correspondence between experimental and calculated C,E curves was obtained with the common diffuse-layer electrode model,262 if the Pb percentage in the solid phase is taken as 20%. However, the calculated C, at a Ois noticeably lower than the experimental one. It has been concluded that Pb is the surface-active component in Cd + Pb alloys, but there are noticeable deviations from electrical double-layer models for composite electrodes.827... 

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

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