Charge-dipole potential

Provided that microscopic reversibility is properly accounted for, thermal averaging of specific rate constants leads to thermal capture rate constants such that a relation between /rigid and /ngid( ,7) can be established. As the charge-dipole potential is particularly simple, the behavior is transparent such that a reference for comparison with other types of interaction potentials is available. 

We consider a situation where the interaction potential between two associating/dissociating species is described sufficiently well by the simple charge-dipole potential... 

The complete W(E, J) is obtained by convolution of the contributions of conserved modes and transitional modes. For the charge-dipole potential, the transitional modes are the free-rotor modes of the ion and two perturbed rotor modes of the linear neutral fragment, only the latter being governed by... 

In the following we elaborate VTST expressions for various charge-dipole potentials. For demonstrative purposes, we further consider the isotropic locked permanent-dipole case where SACM and PST are identical. We also consider the real anisotropic permanent-dipole case in the quantum low-temperature and classical high-temperature oscillator limits. Finally we show comparisons for real permanent and induced-dipole cases. We always employ explicit adiabatic channel eigenvalues for calculating partition functions or numbers of states. 

Lennard-Jones, dipole-dipole, and charge-dipole potentials, given by... 

Fig. 6 The electrical potential, ij/, profile across a lipid bilayer. The transmembrane potential, Aij/, is due to the difference in anion and cation concentrations between the two bulk aqueous phases. The surface potential, ij/s, arises from charged residues at the membrane-solution interface. The dipole potential, J/d, results from the alignment of dipolar residues of the lipids and associated water molecules within the membrane...

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. 

The inner and outer potential differ by the surface potential Xa — (fa — ipa- This is caused by an inhomogeneous charge distribution at the surface. At a metal surface the positive charge resides on the ions which sit at particular lattice sites, while the electronic density decays over a distance of about 1 A from its bulk value to zero (see Fig. 2.1). The resulting dipole potential is of the order of a few volts and is thus by no means negligible. Smaller surface potentials exist at the surfaces of polar liquids such as water, whose molecules have a dipole moment. Intermolecular interactions often lead to a small net orientation of the dipoles at the liquid surface, which gives rise to a corresponding dipole potential. 

The changes in the dipole potentials are typically small, of the order of a few tenths of a volt, while work functions are of the order of a few volts. If we keep the solvent, and hence 3>ref, fixed and vary the metal, the potential of zero charge will be roughly proportional to the work function of the metal. This is illustrated in Fig. 3.6. A more detailed consideration of the dipole potentials leads to a subdivision into separate correlations for sp, sd, and transition metals [3]. 

In general a polar bond is formed when an ion is specifically adsorbed on a metal electrode this results in an uneven distribution of charges between the adsorbate and the metal and hence in the formation of a surface dipole moment. So the adsorption of an ion gives rise to a dipole potential drop across the interface in addition to that which exists at the bare metal surface. 

Consider two different metals in contact and assume that both are well described by the Thomas-Fermi model (see Problem 3.3) with a decay length of Ltf 0.5 A. (a) Calculate the dipole potential drop at the contact if both metals carry equal and opposite charges of 0.1 C m 2. (b) If the work functions of the two metals differ by 0.5 eV, how large is the surface-charge density on each meted ... 

On the whole, the Gouy-Chapman theory seems to work well for ITIES, indicating that any contribution from the dipole potential is small. In particular the interfacial capacity exhibits a minimum at the potential of zero charge for low electrolyte concentrations (see Fig. 12.3). 

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. 

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. 

The distribution of charges on an adsorbate is important in several respects It indicates the nature of the adsorption bond, whether it is mainly ionic or covalent, and it affects the dipole potential at the interface. Therefore, a fundamental problem of classical electrochemistry is What does the current associated with an adsorption reaction tell us about the charge distribution in the adsorption bond In this chapter we will elaborate this problem, which we have already touched upon in Chapter 4. However, ultimately the answer is a little disappointing All the quantities that can be measured do not refer to an individual adsorption bond, but involve also the reorientation of solvent molecules and the distribution of the electrostatic potential at the interface. This is not surprising after all, the current is a macroscopic quantity, which is determined by all rearrangement processes at the interface. An interpretation in terms of microscopic quantities can only be based on a specific model. 

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