Relation to the dipole moment

The electrosorption valence can be related to the dipole moment of an adsorbed species introduced in Chapter 4. For this purpose consider an electrode surface that is initially at the pzc and free of adsorbate. When a small excess charge density o is placed on the metal, its potential changes by an amount A j given by  

The tilde indicates that the value is not corrected for the diffuse layer. The corrected value is obtained by eliminating the Cgc terms  

To obtain the dipole moment we set o = —o% in Eq. (18.14) so that the diffuse double layer is free of excess charge (see Section 4.3). 

The dipole moment m% per adsorbate is obtained by dividing this potential drop by N%/eo, and changing the sign, so that a positive charge on the adsorbate corresponds to a positive dipole moment  

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The microscopic origin of x and hence of Pis the non-unifonnity of the charge distribution in the medium. To lowest order this is given by the dipole moment, which in turn can be related to the dipole moments of the component molecules in the sample. Thus, on a microscopic quantum mechanical level we have the relation... 

The partial electron transfer parameter kj is directly related to the dipole moment, Pj, of adsorbed j via ... 

It is important to know the influence of the physicochemical parameters of the mobile phase (dipole moment, dielectric constant, and refractive index) on solvent strength and selectivity. The main interactions in planar chromatography between the molecules of the mobile phases and those of solutes are caused by dispersion forces related to the refractive index, dipole-dipole forces related to the dipole moment, induction forces related to a permanent dipole and an induced one, hydrogen bonding, and dielectric interactions related to the dielectric constant. Solvent strength depends mainly on the dipole moment of the mobile phase, whereas the solvent selectivity depends on the dielectric constant of the mobile phase. 

Having shown that the weighting coefficient (A) of the term giving the contribution of an ionic structure to the molecular wave function is related to the dipole moment of the molecule, it is logical to expect that equations could be developed that relate the ionic character of a bond to the electronegativities of the atoms. Two such equations that give the percent ionic character of the bond in terms of the electronegativities of the atoms are... 

As before, the x direction has been taken normal to the metal surface. In electrochemistry, the dipole moment mx associated with an adsorbate bond can be defined in the following way For simplicity suppose that the electrode has unit area. At the beginning the electrode surface is bare and kept at the pzc. Then a number nad of ions with charge number z are adsorbed simultaneously a counter charge —zeon is allowed to flow onto the metal surface. The change A(j> in the electrode potential is related to the dipole moment through ... 

From the framework depicted, it emerges that photocatalytic activity seems strictly related to the dipole moment generated by a distorted crystal structure, namely electron-hole separation upon photoexcitation is promoted by a local electric field due to a dipole moment and, in turn, this promotes vectorial movement of electron and holes. 

Another specific interaction involves solute dipole-solvent dipole pairing. This is usually proposed when the change in the coupling constant seems to be linearily related to the dipole moments of the solvents. 

The dielectric constant D is related to the dipole moment fi by the Debye expression... 

A quantum-mechanical discussion of the structure of these molecules in relation to the dipole moments has been reported by W. N. Lipscomb, J. Chem. Phys. 25, 38 (1956). 

From the Causius-Mosotti-Debye relationship (equation 6), show that a plot of the dielectric constant, Dy for a gas vs. the reciprocal of the absolute temperature should approach a straight line (remember that D is near unity) and that the slope, S, of this line is related to the dipole moment by the relationship ... 

In this review, we will consider the adsorption of a single species coadsorption phenomena will not be considered, since it is generally impossible to divide the flow of charge among several species. We will present the thermodynamics on which the concept of the electrosorption valency is based, discuss methods by which it can be measured, and explain its relation to the dipole moment and to partial charge transfer. The latter can be explained within an extension of the Anderson-Newns model for adsorption, which is useful for a semi-quantitative treatment of electrochemical adsorption. Our review of concepts and methods will be concluded by a survey of experimental data on thiol monolayers, which nowadays are adsorbates of particular interest. 

Electrochemistry shares many concepts with surface science, and for the last two decades there has been an exchange of methods and ideas between these two neighboring disciplines. However, the electrosorption valency has no equivalent in surface science, since experiments at the solid/gas or solid/vacuum interface cannot be performed at constant potential. However, for low coverages, and near the potential of zero charge, the electrosorption valency can be related to the dipole moment of the adsorbate, which can be measured both in surface science and, though with greater difficulty, also in electrochemistry. In the following, we point out the relation between these two quantities. 

According to Pauling the polarity p of a chemical bond is the measure of its ionicity. It is related to the dipole moment /x by the equation p = iXi/d, where d is the interatomic distance. The polarity of M—X bonds in MX4 molecules is illustrated in Table 4. The polarity of a specific M—X bond increases significantly as M changes from C to Si, and it diminishes slightly on going from Si to Ge, Sn and Pb. At the same time, the polarity of a specific M—X bond decreases sharply as the atomic number of the halogen X increases. 

For many years, the polymer was thought to have little influence on transport. Recent evidence, however, has shown that the polymer can have a very considerable effect on the mobilities (Sasakawa et al., 1989 Yuh and Pai, 1990, 1990a, 1990b, 1992 Kanemitsu and Eiinami, 1990 Aratani et al., 1990 Kanemitsu, 1992 Hirao et al., 1993). In part, these effects are related to the dipole moment of the polymer repeat unit, as described above. The mobilities of... 

The experimentally determined specific Kerr constant, BfC, is related to the dipole moment of the particle, /r, in the form (18) ... 

In relation to the dipole moments of (CH2)2X and (CH3)2X, the overall outcome apparent from the data in Table 3 is that, with the diffusely polarized 6-31G(+sd+sp) basis set, the experimental results come much closer to the MP2 values than the SCF values, as expected. The weak trends that... 

Solvent polarity is related to the dipole moment as discussed in the earlier section. A solvent without a permanent dipole must be classified as nonpolar. However, a solvent may exhibit local polarity, if it possesses two mutually canceling dipoles. One such example is... 

Optical absorption in a medium can take place because of the existence of electric or magnetic dipole moments associated with atomic, molecular or crystal entities. Unless otherwise specified, only electric dipoles are considered here. In quantum mechanics, the condition related to the dipole moment for discrete optical absorption appears in terms of transition probability between the initial and final states. It can be formally expressed as the modulus squared of a matrix element involving the wave functions and final states and the electric dipole operator, which reduces, within a proportionality factor to the general displacement coordinate ra ... 

The relaxation strength (e -e ) of the dipole which shows the high frequency absorption is related to the dipole moment, y,... 

Guided by the result in classical mechanics, that the amount of energy radiated by an oscillating charge is related to the dipole moment, the new quantum theory attempts to construct in terms of wave functions the quantity which will represent a fluctuating electric dipole moment. The function... 

Low field or contact potential measurements on well-defined macroscopic surfaces have an advantage here. The total amount of adsorbed material can be measured separately by flash desorption. Moreover, the contact potential A corresponds to an area average, which is also approached in low field emission measurements. The change in the contact potential in adsorption can therefore be unequivocally related to the dipole moment per adatom through Eq. (32). The difficulty in this approach lies in the preparation of a truly uniform surface of macroscopic size, which has not as yet been accomplished. 

The next term is of the order of k. Within the MSA, the dielectric constant e is related to the dipole moment n and the density ps of the solvent through... 

A number of molecules have, when they are free, a non-negligible dipole moment, for example the sulfur dioxide molecule SO2, whose dipole moment is g = 1.61 debye. The dipole component is related to the dipole moment of adsorbed molecules through ... 

An extension of corresponding states to highly polar substances has been based on the acentric factor correlation. A fourth parameter related to the dipole moment must be introduced. A similar four-parameter description of the virial coefficients of polar fluids and their mixtures has been developed by Halm and Stiel and for mixtures of quadrupolar fluids by Ramaiah and Stiel. ... 

Alternatively, an average dipole moment on a bulk sample can be obtained through measurement of the potential difference between charged plates with and without the dielectric present. The latter is, of course, a macroscopic property of the sample, which assumes that the microscopic structure, from which the dipole moment comes, does not actually exist that is, the entire medium is continuous and isotropic. However, despite the assumption of continuity, this macroscopic property, e, the dielectric constant of the medium, can be related to the dipole moment, p, through the density of the medium, the number of molecules between the charged plates, and thus the induced dipole per unit volume (but taking into account an initial contribution of preferential orientation). 

The solvation energy can be related to the dipole moment and the polarizabilities of the solute and solvent molecules. The most significant contribution to the solvatochromic shift comes from the dipole-dipole and solute polarization-solvent dipole interactions. For solvatochromism, the energy shift is given by... 

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