Surface potential, definition

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

Nonadiabatic transitions due to potential energy surface crossings definitely play cmcial roles in chemical dynamics. They (1) are important to comprehend the... 

Recent molecular dynamics studies of properties of the water surface have led to predictions of the surface potential of water that differ not only in magnitude but also in sign. The main problem is connected with the difficulty of proper definition of the surface potential of a real polar... 

Because of the influence of potential gradients, the work function depends on the position of the point to which the electron is transferred. As in the definition of surface potential, a point a) situated in the vacuum just outside the metal is regarded as the terminal point of transfer. It is assumed, moreover, that when the transfer has been completed, the velocity of the electron is close to zero (i.e., no kinetic energy is imparted on it). 

It should be recalled that the term surface potential is used quite often in membranology in rather a different sense, i.e. for the potential difference in a diffuse electric layer on the surface of a membrane, see page 443.) It holds that 0 = 0 + X (this equation is the definition of the inner electrical potential 0). Equation (3.1.2) can then be written in the form... 

The rate constants for the reaction of a pyridinium Ion with cyanide have been measured in both a cationic and nonlonic oil in water microemulsion as a function of water content. There is no effect of added salt on the reaction rate in the cationic system, but a substantial effect of ionic strength on the rate as observed in the nonionic system. Estimates of the ionic strength in the "Stern layer" of the cationic microemulsion have been employed to correct the rate constants in the nonlonic system and calculate effective surface potentials. The ion-exchange (IE) model, which assumes that reaction occurs in the Stern layer and that the nucleophile concentration is determined by an ion-exchange equilibrium with the surfactant counterion, has been applied to the data. The results, although not definitive because of the ionic strength dependence, indicate that the IE model may not provide the best description of this reaction system. 

Electrostatic and EDL forces are found to play a very important role in a variety of systems in science and engineering. It would be useful to consider a specific example in order to understand these phenomena. Let us take a surface with positive charge that is suspended in a solution containing positive and negative ions. There will be a definite surface potential, /0, which decreases to a value zero as one moves away into solution (Figure 7.5). 

Fermi-level DOS 115 Jellium model 92—97 failures 97 schematic 94 surface energy 96 surface potential 93 work function 96 Johnson noise 252 Kohn-Sham equations 113 Kronig-Penney model 99 Laplace transforms 261, 262, 377 and feedback circuits 262 definition 261 short table 377 Lateral resolution... 

Some systems do show excellent agreement between zeta and the surface potential, whilst others differ significantly. Since no definitive results have yet been obtained, it is perhaps best to assume as a first approximation that these two potentials are similar. 

Willis, underpotential deposition. 1313 Wojtowicz, 1381 Work function of the metal, 887 and chemical potential 835 definition, 835 in electrochemistry, 835 and surface potential, 835 underpotential deposition and, 1316 Working electrode, potential, 1061 Wright, 1495... 

At first sight it would look as if the definition of surface potential (x) described in Section 6.4.8 would overlap with the definition of the workfunction. Does this mean that both quantities are the same but with opposite signs To answer this question, let us look closer to the trajectory of the electron as defined in the work function (Fig. 6.45). The electron starts in a point deep inside the metal, where all different types of chemical bondings and interactions exist. After breaking all these forces, the electron moves itself free from inside the metal to a point close to the surface. Then, from here it has to cross the barrier of dipoles (see Section 6.3.8) to reach a point just outside the metal. 

As for the theory of this phenomenon, it was first observed by Onsager [27a] that, since in the limit a — 0 an LCD a is expected to yield a singularity of the type —surface potential, the statistical-mechanical phase integral for counterions should diverge for a greater than some critical value, characteristic of a given valency. Indeed consider a counterion (for definiteness anion) of valency z. The appropriate phase integral is of the form... 

Both ions appear to desorb from the DPPC bilayer surfaces as they come closer. We cannot infer an association constant for the binding of Mg2+ or Ca2+ to DPPC if we use a definition based on mass action. The apparent binding coefficient as well as surface potential and charge density vary with bilayer separation (I). 

Figure 2 gives an overview on the definition of and relation between quantities used in surface science and in electrochemistry such as work function or surface potential. In the following we distinguish between (i) cells to which we apply a current (I >0, the current direction being opposite to the short-circuit current direction, U = E+ LaIRa > E), named polarization cells (cells under load), (ii) cells from which we extract current (7<0, in short-circuit direction, U < E), named current-generating cells, and finally (iii) open-circuit cells (I-0, U-E). In all cases we... 

The first contribution, er° or represents the uniform, i.e., area-average charge or potential on the surface. By definition, it is independent of surface position and represents the n = m = 0 term of the second contribution which accounts for heterogeneities. The summations in Eqs. (33) or (34) exclude the n = m = 0 term. cr° or Tq is singled out for special consideration later in this section. 

Our experimental conclusion — that s is constant and equal to 2.6 0.4 in the range 3 mM < cex <120 mM — accords well with the prediction from the new generalized Donnan equilibrium made in Chapter 4. We recall that the coulombic attraction theory, with the constant surface potential boundary condition s = 70 mV, predicts that. v is constant and equal to 2.8. A factor of x40 in c provides a severe test of the prediction and it passes, although the quantitative agreement between the theoretical and experimental values of s in this case should be treated with caution because of the severity of the approximations used in deriving the theoretical result. The pure Donnan prediction that s = 4.0 for s = 70 mV is definitely invalidated by... 

As far as I am aware, independent experimental evidence for the values of the surface potential and salt fractionation factor have not been obtained for any system other than the n-butylammonium vermiculite gels. For this isolated system, the predicted values of 5 from the Donnan equilibrium and the new equilibrium based on the coulombic attraction theory, namely 4.0 and 2.8, respectively, are definitely distinguished by the experimental results. It would be highly desirable to obtain further tests of our prediction for 5 in systems of interacting plate macroions, both in clay science and lamellar surfactant phases. 

FIGURE 103 Electrostatic repulsion force, F/njAg T versus separation, h, between two identically charged plates with surface potentials of 25 mV in a 1 1 electrolyte solution at 0.001 Hf according to the exact theory with either constant charge or constant potential boundary conditions. Calculated from F = n Jk T (A - A ) with definitions of Aj given in the text for constant charge and potential boundary conditions. 

Two parameters were introduced into the description of double electrical layer. One of them is the point of zero charge (PZC) which according to lUPAC definition [101] can be expressed as concentration of potential-determining ions PDI at which the surface charge is equal to zero ( o = 0), as well as the surface potential (V>o = 0). Another parameter is isoelectric point (lEP) defined [101] as concentration of PDI at which the electrokinetic potential is equal to zero (( = 0). 

The models describing hydrolysis and adsorption on oxide surfaces are called surface complexation models in literature. They differ in the assumptions concerning the structure of the double electrical layer, i.e. in the definition of planes situation, where adsorbed ions are located and equations asociating the surface potential with surface charge (t/> = f(5)). The most important models are presented in the papers by Westall and Hohl [102]. Tbe most commonly used is the triple layer model proposed by Davis et al. [103-105] from conceptualization of the electrical double layer discussed by Yates et al. [106] and by Chan et al. [107]. Reviews and representative applications of this model have been given by Davis and Leckie [108] and by Morel et al. [109]. We will base our consideration on this model. 

Fig. 8.5 Illustration of the definitions of the outer potentials, v / and the surface potentials, x and x, and the Galvani potential difference o Ap for two condensed phases a and p in contact.

A (j) is the potential drop due to the net free charge at the interface is the dipolar potential due to the metal phase, more specifically, to the electron overspill that occurs at the surface of the metal finally, is the dipolar potential due to the solution phase which arises because of the orientation of solvent molecules at the interface due to their proximity to the metal, and because of the unequal distances of closest approach of the cations and anions to the interface. is defined in the opposite direction to because the concept of the dipolar potential originates at the condensed phase vacuum interface where the definition of the potential drop is always from vacuum to the condensed phase. The dipolar potential arises for the same reasons as the surface potential x at the metal vacuum interface. However, it is not the same because of the effect that the proximity of the molecules and ions of the solution phase have on the electron overspill. 

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