Work function dielectric constant

When a solute is added to an acidic solvent it may become protonated by the solvent. If the solvent is water and the concentration of solute is not very great, then the pH of the solution is a good measure of the proton-donating ability of the solvent. Unfortunately, this is no longer true in concentrated solutions because activity coefficients are no longer unity. A measurement of solvent acidity is needed that works in concentrated solutions and applies to mixed solvents as well. The Hammett acidity function is a measurement that is used for acidic solvents of high dielectric constant. For any solvent, including mixtures of solvents (but the proportions of the mixture must be specified), a value Hq is defined as... 

The present work is a report of the properties of polyimide which define functionality as an interlevel dielectric/passivant. Thus, the planarizing and patterning characteristics and electrical characteristics of current vs voltage, dissipation, breakdown field strength, dielectric constant, charge and crossover isolation are discussed in addition to the reliability-related passivation properties. 

The charge density p of the solute may be expressed either as some continuous function of r or as discrete point charges, depending on the theoretical model used to represent the solute. The polarization energy, Gp, discussed above, is simply the difference in the work of charging the system in the gas phase and in solution. Thus, in order to compute the polarization free energy, all that is needed is the electrostatic potential in solution and in the gas phase (the latter may be regarded as a dielectric medium characterized by a dielectric constant of 1). 

Some work has also appeared describing MD with implicit solvation for solutes described at the DFT level. Fattebert and Gygi (2002) have proposed making the external dielectric constant a function of the electron density, thereby achieving a smooth transition from solute to solvent instead of adopting a sudden change in dielectric constant at a particular cavity surface. Non-electrostatic components of the solvation free energy have not been addressed in this model. 

In their studies of the effect of solvent upon the N—H stretching frequency in pyrrole, Fuson and Josien [1] have shown the distinction between the solvent-solute interaction which is a function of dielectric constant alone [2, 3] and that which is more specific, involving N—H hydrogen bonding. The most pronounced frequency shifts are those caused by pyridine [4] (K—M N bonding) and by acetone (N—H 0 bonding). The choice of pyrrole for these studies was presumably partly governed by convenience since the N—H band in pyrrole is considerably more intense than in the more basic secondary amines. We have attempted an extension of this work in two directions ... 

As zero state of our system we chose that state in which all constituents are dispersed to infinite dilution within a dielectric of dielectric constant Dq (which value may or may not be chosen as D0 = 1). Then we obtain the contribution to the work function by imagining the system charged (in the way calculated above) at the given concentrations in a system of dielectric constant D and subsequently discharged at infinite dilution in a medium of dielectric constant Do. Adding over all species of particles we obtain an expression for the work function which can be written in the form... 

The subscripts i which have been added refer to the different species of ion-dipoles, and the symbols ax(D),... indicate that the respective coefficients have to be calculated with the value of D and n2. From the way our work function A has been derived, it is evident that it contains the contributions which are caused by the presence of the solutes and by the change in dielectric constant of the solvent. The contributions which result from the first term in Equation 19 and which represent the work which is required to build up the ion-dipole in a standard environment (e.g., a vacuum) have disappeared from Equation 24 (being identical in A and A o). This self-energy of the particles is without interest for the present investigation and depends, of course, in a decisive way on the underlying model. 

The work and results reported in Part I led us to believe that the first-order coulombic interactions among the ions and the ions and the solvent molecules are the significant interactions in solvents of bulk dielectric constant 40 or higher. This in turn led us to believe that a simple electrostatic model might be used for generating functions that would correlate the ionization processes in two solvents both of moderate bulk dielectric constants. 

One of the diflSculties in applying the Born equation is that the effective radius of the ion is not known further, the calculations assume the dielectric constant of the solvent to be constant in the neighborhood of the ion. The treatment has been modified by Webb who allowed for the variation of dielectric constant and also for the work required to compress the solvent in the vicinity of the ion further, by expressing the effective ionic radius as a function of the partial molal volume of the ion, it was possible to derive values of the free energy of solvation without making any other assumptions concerning the effective ionic radius. 

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