Classification of electrical potentials at interfaces in .NET

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3.1.1 Classification of electrical potentials at interfaces
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The distribution equilibrium for uncharged species distributed between two phases is determined by the equality of the chemical potentials of the
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146 components in the two phases. The chemical potential of the ith component in phase a is defined by the relationship (cf. Section 1.1.3)
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where G' is the Gibbs energy, V is the internal energy of phase a and nt is the amount of the given component (in moles). According to an alternative definition, the chemical potential is a measure of the work that must be done under otherwise constant conditions for reversible transfer of one mole of uncharged species from the gaseous state with unit fugacity (assigned purely conventionally as zero on the chemical potential scale) into the bulk of the given phase. If one mole of charged particles is to be transferred from the given reference state, further specified by the absence of an electric field, into the bulk of an electrically charged phase, then work must be expended not only to overcome chemical bonding forces but also to overcome electric forces. The work expended is given by jkif termed the electrochemical potential by Guggenheim and also defined by Eq. (3.1.1), where G' and U' are replaced by G and U; these are analogous to G' and U' and apply to an electrically charged phase. In general, the electrochemical potential cannot be separated into chemical and electrical components, as the chemical interaction of a species with its environment is also electric in nature. Nonetheless, the separation of the electrochemical potential is frequently made according to the equation ft^. + zlty (3.1.2) In this equation, the second term describes purely electrostatic work, connected with an infinitely slow transfer of charge zF from infinity in a vacuum into the bulk of the second phase, i.e. to a point with electric potential <j>. Here only electric charge is transferred, not a material species with which it might be connected. The ratio of this work to the transferred charge is equal to the inner electrical potential <p of the given phase. Equation (3.1.2) would imply separation of the effect of short-range forces (also including dipole interactions) and of the individual ionic atmospheres, related to \iiy from the long-range forces related to 0, identical with purely coulombic interaction between excess charges. It will be seen later that such splitting, although arbitrary, is very useful. The inner electrical potential (p may consist of two components. Firstly, the phase may possess some excess electrical charge supplied from outside. This charge produces an outer electrical potential ip. This is defined as the limit of the ratio w/q for q 0, where w is the work expended for the infinitely slow transfer of charge q from an infinite distance to a point in the vacuum adjacent to the surface of the given phase and just outside the range of image forces. A particle transferred from this point further on in the
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147 direction of the other phase must overcome the effect of electric forces in the interphase. This component is called the surface electrical potential %. The component % is defined as the limit of the ratio w'/q for q 0, where w' is the work expended in the transfer of charge q, from a point at which the outer electrical potential ip is defined, into the bulk of the phase. The surface potential x consists of the contributions of ions present in the interphase x(ion) and contributions from dipoles oriented in this region (3.1.3) (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 (/> = ip + x ( t m s equation is the definition of the inner electrical potential 0). Equation (3.1.2) can then be written in the form fiL^M + zFip + zFx (3.1.4)
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For uncharged species z = 0 and /2f- = \it. The first term in Eq. (3.1.2) is thus the chemical potential of a charged species in the phase considered. If two phases oc and / , with common species /, are brought into contact, then for uncharged species the tendency to pass from phase oc into phase j3 is expressed by the difference ^(a) jU,()3), and for charged species by the difference &{&) /(|8). For equilibrium of uncharged species, ju^ar) = jM/(j8), while the condition for equilibrium of charged species is
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fc(a) = |S,03)
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The result of the establishment of phase equilibrium is the formation of differences of inner and outer potentials of both phases. These differences are defined by the equations
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It should be noted that phase equilibrium can be attained for charged species through far smaller transfer of particles from one phase into the other than for uncharged species, as the potential difference formed, 0(/3) 0(ar), decreases the original tendency for transfer between the two phases much faster than the changes in the original chemical potentials. The difference of the inner electrical potentials of the phases, A^0, is also called the Galvani potential difference and the analogous difference of the outer electrical potentials, A^/T/;, is termed the Volta potential difference.
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