Excess chemical potential, definition

The definition of the terms can be found in Refs. 91, 92. The excess chemical potential, computed from the direct correlation function of the... 

In Flory s theory (/< ), a polymer-solvent system is characterized by a temperature 0 at which (i) excluded-volume effects are just balanced by polymer-solvent interactions, so that os=l, (ii) the second virial coefficient is zero, irrespective of the MW of the polymer, and (iii) the polymer, of infinite molecular weight, is just completely miscible with the solvent The fundamental definition of the temperature is a macroscopic one, namely that for T near 0 the excess chemical potential of the solvent in a solution of polymer volume fraction v2 is of the form (18) ... 

The relative chemical potentials can be obtained from the relative excess chemical potentials given by Eq. (70) by the definition... 

The reference state of each component in a system may be defined in many other ways. As an example, we may choose the reference state of each component to be that at some composition with the condition that the composition of the reference state is the same at all temperatures and pressures of interest. For convenience and simplicity, we may choose a single solution of fixed composition to be the reference state for all components, and designate xf to be the mole fraction of the /cth component in this solution. If (Afikx) represents the values of the excess chemical potential based on this reference state, then (A/if x ) [T, P, x ] is zero at all temperatures and pressures at the composition of the reference state. That this definition determines the standard state is seen from Equation (8.71), for then... 

Equations similar to Equation (8.203) are written for the chemical potentials of the ionic species. We take the pure liquid component as the reference state, and hence the standard state for the component, and express the chemical potential of the component in terms of the chemical potentials of the ionic species to obtain equations similar to Equation (8.206). In this particular case x + is unity but both x A- and x%2- have fixed values whose sum must be unity. Finally, with appropriate definitions of the excess chemical potentials, we obtain either... 

We now return to the definition of the surface excess chemical potential fta given by Equation (2.19) where the partial differentiation of the surface excess Helmholtz energy, Fa, with respect to the surface excess amount, rf, is carried out so that the variables T and A remain constant. This partial derivative is generally referred to as a differential quantity (Hill, 1949 Everett, 1950). Also, for any surface excess thermodynamic quantity Xa, there is a corresponding differential surface excess quantity xa. (According to the mathematical convention, the upper point is used to indicate that we are taking the derivative.) So we may write ... 

Consider the excess chemical potential obtained for a definite configuration,... 

Equation (7.8) offers a clear separation of inner-shell and outer-shell contributions so that different physical approximations might be used in these different regions, and then matched. The description of inner-shell interactions will depend on access to the equilibrium constants K. These are well defined, observationally and computationally (see Eq. (7.10)), and so might be the subject of either experiments or statistical thermodynamic computations. Eor simple solutes, such as the Li ion, ab initio calculations can be carried out to obtain approximately the Kn (Pratt and Rempe, 1999 Rempe et al, 2000 Rempe and Pratt, 2001), on the basis of Eq. (2.8), p. 25. With definite quantitative values for these coefficients, the inner-shell contribution in Eq. (7.8) appears just as a function involving the composition of the defined inner shell. We note that the net result of dividing the excess chemical potential in Eq. (7.8) into inner-shell and outer-shell contributions should not depend on the specifics of that division. This requirement can provide a variational check that the accumulated approximations are well matched. 

Using these definitions we identify the enthalpic contribution to the excess chemical potential of a Cluster of size n as... 

Thus, surface tension changes have been related to changes in the absolute potential differences across an electrode/electrolyte interface and to changes in the chemical potential of all the species, i.e., to changes in solution composition. Only one other quantity is missing, the surface excess. This can be easily introduced by recalling the definition of surface excess [Eq. (6.66)], i.e.,... 

Because of their rigid cell walls, large hydrostatic pressures can exist in plant cells, whereas hydrostatic pressures in animal cells generally are relatively small. Hydrostatic pressures are involved in plant support and also are important for the movement of water and solutes in the xylem and in the phloem. The effect of pressure on the chemical potential of water is expressed by the term VWP (see Eq. 2.4), where Vw is the partial molal volume of water and P is the hydrostatic pressure in the aqueous solution in excess of the ambient atmospheric pressure. The density of water is about 1000 kg m-3 (1 g cm-3) therefore, when 1 mol or 18.0 x 10-3 kg of water is added to water, the volume increases by 18.0 x 10-6 m3. Using the definition ofV,., as a partial derivative (see Eq. 2.6), we need to add only an infinitesimally small amount of water (dnw) and then observe the infinitesimal change in volume of the system (dV). We thus find that Vw for pure water is 18.0 x 10-6 m3 mol-1 (18.0 cm3 mol-1). Although Vw can be influenced by the solutes present, it is generally close to 18.0 x 10-6 m3 mol-1 for a dilute solution, a value that we will use for calculations in this book. 

The equations that are commonly used to represent experimental data of (Z = G, y ) and p, are expressed as a function of Xj, whereas in Equation 4.14 derivatives with respect to are required. We need therefore to express than in a fnnction of X,. Taking into account the definition of the excess partial molar quantity, 7, as a function of the relationship between x, and the differentials of 7F- =f(X with respect to x, and of X with respect to and applying the treatment to one mole of mixture, after some substitutions and rearrangements, the diagonal elements p, can be expressed in a function of X and of four derivatives of the chemical potential of components 1 and 2,... 

Notice that since A/j. is negative then by definition IT is positive.) The excess surface energy,, is obtained from the product of the surface excess, r, and the change in chemical potential, provided the surface is flat. Using the above equation then... 

The exact definition of the theta state is given by chemical thermodynamics. The chemical potential of a solvent 1, Afi i, can be split into an ideal term and an excess term ... 

Where e is the excess acid in mol/L and ionic concentrations are expressed as mol/L. While this more precise definition may apply in some strictly chemical responses such as soil erosion, Biydges and Summers 19) have considered the more complete reactions including biological ionic utilizations and have defined an "acidifying potential" of precipitation as ... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Guidelli model of, 899 Habib and Bockris, 899 at the interface, importance of, 918 -ion interaction energy, 924 -metal interactions, 896 chemical forces, 897, 972 lateral forces, 897 monomers of, definition, 899 orientation of, 898 Parsons model of, 899 and potential of the electrode. 900. 924 preferential orientation of, 912 and solvent excess entropy, 912 the "three-state water model 898, 899 Wave nature of electrons, 788 Wavenumber, 799 Waves... 

FLAVOR ENHANCERS AND POTENTIATORS. A, /tamr enhancer is a substance which when present in a food accentuates the taste of the food without contributing any flavor of its own. This is reminiscent ol the role of a catalyst in a chemical reaction which promotes a reaction without chemically participating in the reaction. Although not usually regarded as a flavor enhancer, common sail, if not used excessively, enhances the taste ol food substances. Sail does not fully meet the definition of an enhancer, however, because the sail is detectable as such. 

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