Surface dipole potential

Studies of pzc in mixed solvents were also carried out by Blaszczyk etal n using the dipping method. They worked in mixtures offormamide and NMF and estimated the shift of the standard potential of the hydrogen electrode, of the surface dipole potential atHg, and of the liquid junction potential. 

Here, Ws is the work function of electrons in the semiconductor, q is the elementary charge (1.6 X 1CT19 C), Qt and Qss are charges located in the oxide and the surface and interface states, respectively, Ere is the potential of the reference electrode, and Xso is the surface-dipole potential of the solution. Because in expression (2) for the flat-band voltage of the EIS system all terms can be considered as constant except for tp (which is analyte concentration dependent), the response of the EIS structure with respect to the electrolyte composition depends on its flat-band voltage shift, which can be accurately determined from the C-V curves. 

For electrons in a metal the work function is defined as the minimum work required to take an electron from inside the metal to a place just outside (c.f. the preceding definition of the outer potential). In taking the electron across the metal surface, work is done against the surface dipole potential x So the work function contains a surface term, and it may hence be different for different surfaces of a single crystal. The work function is the negative of the Fermi level, provided the reference point for the latter is chosen just outside the metal surface. If the reference point for the Fermi level is taken to be the vacuum level instead, then Ep = —, since an extra work —eoV> is required to take the electron from the vacuum level to the surface of the metal. The relations of the electrochemical potential to the work function and the Fermi level are important because one may want to relate electrochemical and solid-state properties. 

Show that for an uncharged metal surface A = B = 1/2, and derive a formula for the surface dipole potential. Cesium has an electronic density of 0.9 x 1022 cm 3 and a 2 A 1. Calculate its surface dipole potential. 

This correlation has been explained in terms of two effects (1) the surface energies of the two metals involved and (2) the formation of a surface dipole potential. 

As was pointed out in Chapters 2 and 3, a dipole layer exists at the surface of a metal, which gives rise to a concomitant surface dipole potential x- The magnitude of this potential changes in the presence of an external electric field. A field E directed away from the surface induces an excess charge density, o e0e E, where e is the dielectric constant of the medium outside the metal. The field E pushes the electrons into the metal, producing the required excess charge, and decreasing the dipole potential (see Fig. 3.4). This has consequences for the interfacial capacity. 

So in any case the variation of the surface dipole potential with an external field makes a negative contribution to the inverse capacity. It is natural to define this metal contribution by ... 

In order to estimate the magnitude of the surface dipole potential and its variation with the charge density, we require a detailed model of the metal. Here we will explore the jellium model further, which was briefly mentioned in Chapter 3. 

This equation can be solved by several techniques, for example, by noting that it is a quadratic equation in a2. The sp metals that are relevant for electrochemistry have electronic densities in the range of 10-2 to 3 x 10 2 a.u., over which a is almost constant (see Table 17.1). From simple electrostatics it can be shown that the surface dipole potential... 

As a result, the plots of o- / vs. E for different bulk concentrations of the solute intersect at the same point (Umax. max). which corresponds to the adsorption maximum. This implies that at the adsorption maximum does not vary with increasing F. Consequently, the surface dipole potential due to the adsorbing molecules exactly matches that of the desorbed solvent molecules, " provided that the solvent and solute molecules assume only one orientation at the surface. In practice, however, a single point of intersection of the vs. E plot for different bulk solute concentrations is observed rather rarely. For example, a gradual inaease in the surface concentration of 2-propanol on mercury in aqueous solution brings about a small positive shift of a. A much bigger shift has been observed for hexafluoro-2-propanol (HFP). " It has been ascribed to the reorientation of the HFP molecules in such a way that both -CF3 groups are directed toward the electrode, which in turn results in... 

The work function contributing factors, namely, the relevant chemical potential p experienced by the particle in the bulk material and the surface dipole potential D. Thus, for positrons and electrons the relevant work functions can be written (Tong, 1972 Hodges and Stott, 1973) as — (j> = p D. The chemical potential contains terms due to the electron and positron interactions with the other electrons and with the ion cores. The surface dipole, which is attractive for positrons and repulsive for electrons, arises mainly from the tailing of the electron distribution into the vacuum for a distance of approximately... 

Here, as = -Vrs is the charge density on the -S groups of a hypothetical close-packed monolayer of thiolate anions, P is the distance of the center of charge of the sulfur atoms from the metal surface, d = p + y is the length of the thiol molecule, and p and y are the dielectric constants accounting for the distortional polarization in the (0 < x< P) and (pelectron spillover and Xs is that due to any polar groups of the thiol molecule. For simplicity, the small potential difference (4/ across the diffuse layer is disregarded. 

Here P and y are the thickness of the hydrocarbon tail and of the polar head region of the lipid monolayer, Sp and eY are the corresponding distortional dielectric constants, %e and Xm are the surface dipole potentials due to the electron spillover and to the oriented polar heads, and fa is the potential difference across the diffuse layer. At ion concentrations that are not exceedingly low, fa can be disregarded as a good approximation. Moreover, the orientation of the polar heads of the lipid film is hardly affected by changes in aM. The differential capacity C of the electrode can, therefore, be written ... 

E, measured vs. the SCE, by about 250 mV. From Eq. (86) it also follows that the surface dipole potential Xw due to the water molecules in direct contact with bare mercury at the potential of zero charge is equal to -200 50 mV. This value is somewhat more negative than that, -70 mV, estimated by Trasatti55 from the shift, AEau=(), in the... 

The first term of Eq.(2.330a) equals the surface-dipole potential, equals the Fermi level Ef. Within the jellium model G(n) is given by itz ... 

In the case of a polymer-coated metal substrate in a humid air atmosphere (for simplificity, only the situation of a polymer that is not highly oriented and has rather a small dipole potential is considered), a situation for the correlation of the corrosion potential with the Volta potential difference A R° f measured here (outer polymer surface and the probe as reference) could be derived analogously to the situation of an electrolyte-covered metal substrate (Eq. (10) with xpoI the surface dipole potential of the polymeric phase, which should be constant for a given polymer and a given gas phase as long as the polymer surface is stable). 

Therefore, again assuming that the surface dipole potential of the polymer and the work function of the reference are constant, the Volta potential difference mainly reflects the oxidation state within the oxide surface. 

Uex of DOPS and DOPA are determined at different pH values and at a constant apphed potential E, Eq. (2) allows the surface dipole potential X = —... 

The slopes of the plots for DOPC and DO PS at those pH values at which these monolayers are neutral are similar, and yield a dipole potential of+140—1-150 mV, positive toward the interior of the film. Conversely, the dipole potential for DO PA is much smaller, +30 mV [15]. The DOPS and DOPC monolayers having very similar surface dipole potentials indicate that this potential is not to be ascribed to the serine or choline group of their polar heads, but rather to a group common to these two lipids and buried deeper inside the polar head region. This can be reasonably identified with the glycerol backbone. This also explains the low value of the dipole potential of DOPA, whose polar head consists of the sole phosphate group and whose glycerol backbone is. 

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