Potential, chemical elasticity

At constant chemical potentials, electric potential, and elastic strain, the dependence of the surface tension on temperature is given by the surface entropy. Inserting into Eq. (I9) yields 192,931... 

Only because the remarkable biocompatibility of chemically synthesized poly(GVGVP) was already known was there adequate impetus to purify microbially prepared (GVGVP)2si. Otherwise, it would have been presumed, as had been widely expected, that the toxicity of inadequately purified (GVGVP)25i was an inherent property of the protein-based polymer. To be left in such a state of misunderstanding would have meant that the dramatic potential of elastic protein-based polymers for use in medical applications would be neither appreciated nor realized. The inflammatory response elicited by an inadequately purifled biosynthetic elastic protein-based polymer would have overwhelmed most considered medical applications. 

Freund, L. B. (1998), A surface chemical potential for elastic solids. Journal of the Mechanics and Physics of Solids 46, 1835-1844. 

The details of chemical crosslinking need not concern us, but some examples will illustrate materials with the potential to display elasticity ... 

The interface region in a composite is important in determining the ultimate properties of the composite. At the interface a discontinuity occurs in one or more material parameters such as elastic moduli, thermodynamic parameters such as chemical potential, and the coefficient of thermal expansion. The importance of the interface region in composites stems from two main reasons the interface occupies a large area in composites, and in general, the reinforcement and the matrix form a system that is not in thermodynamic equiUbhum. 

Whereas the quasi-chemical theory has been eminently successful in describing the broad outlines, and even some of the details, of the order-disorder phenomenon in metallic solid solutions, several of its assumptions have been shown to be invalid. The manner of its failure, as well as the failure of the average-potential model to describe metallic solutions, indicates that metal atom interactions change radically in going from the pure state to the solution state. It is clear that little further progress may be expected in the formulation of statistical models for metallic solutions until the electronic interactions between solute and solvent species are better understood. In the area of solvent-solute interactions, the elastic model is unfruitful. Better understanding also is needed of the vibrational characteristics of metallic solutions, with respect to the changes in harmonic force constants and those in the anharmonicity of the vibrations. 

A close analogy exists between swelling equilibrium and osmotic equilibrium. The elastic reaction of the network structure may be interpreted as a pressure acting on the solution, or swollen gel. In the equilibrium state this pressure is sufficient to increase the chemical potential of the solvent in the solution so that it equals that of the excess solvent surrounding the swollen gel. Thus the network structure performs the multiple role of solute, osmotic membrane, and pressure-generating device. 

The first three terms occurring in the right-hand member of Eq. (38), represent dAFu/ ni] they correspond to mi Mi according to Eq. (XII-26) for a polymer of infinite molecular weight (i.e., a = 00). The last member introduces the modification of the chemical potential due to the elastic reaction of the network structure. The activity ai... 

If the chemical potential difference ah "Mi calculated according to Eq. (38) is plotted against it will be found that, owing to the positive contribution of the elastic term (with j e>0), the chemical potential Ml exceeds mi for the pure solvent for all concentrations below a certain polymer concentration In other words, the activity a would... 

Donnan-Type Equilibria in Polyelectrolyte Gels.—In a somewhat more rigorous fashion we consider the reduction of the chemical potential of the solvent in the swollen gel to be separable into three terms which severally represent the changes due to the mixing of polymer and solvent, to the mixing with the mobile ionic constituents, and to the elastic deformation of the network. Symbolically... 

The formal definition of the electronic chemical hardness is that it is the derivative of the electronic chemical potential (i.e., the internal energy) with respect to the number of valence electrons (Atkins, 1991). The electronic chemical potential itself is the change in total energy of a molecule with a change of the number of valence electrons. Since the elastic moduli depend on valence electron densities, it might be expected that they would also depend on chemical hardness densities (energy/volume). This is indeed the case. 

In Eq. (2), mi is the chemical potential of the solvent in the polymer gel and /al 0 is the chemical potential of the pure solvent. At equilibrium, the difference between the chemical potentials of the solvent outside and inside the gel must be zero. Therefore, changes of the chemical potential due to mixing and elastic forces must balance each other. The change of chemical potential due to mixing can be expressed using heat and entropy of mixing. 

The change of chemical potential due to the elastic retractive forces of the polymer chains can be determined from the theory of rubber elasticity (Flory, 1953 Treloar, 1958). Upon equaling these two contributions an expression for determining the molecular weight between two adjacent crosslinks of a neutral hydrogel prepared in the absence of... 

Peppas and Merrill (1977) modified the original Flory-Rehner theory for hydrogels prepared in the presence of water. The presence of water effectively modifies the change of chemical potential due to the elastic forces. This term must now account for the volume fraction density of the chains during crosslinking. Equation (4) predicts the molecular weight between crosslinks in a neutral hydrogel prepared in the presence of water. 

One key experimental observation regarding the ZP films is that the films found on the tops of asperities are stiffer and exhibit chemical spectra indicative of longer phosphate chain lengths than films found in the valleys between asperities. These observations that differences in the conditions at the two distinct locations alter the elastic and chemical properties of the films. One of the key differences between the tops of asperities and the valleys is the pressure experienced by the zinc phosphates. Since the highest pressures, and greatest potential for wear, are achieved at the tops of the asperities, determining the response of ZPs to these pressures may aid in developing a clear picture of how the anti-wear films work. 

An alternative theory, first proposed by Rettori and Villain (1988). takes the point of view which corresponds to the variation depicted in Fig. 1 (a), in which case the excess chemical potential of the top terrace is much lower than Eq. (6) suggests. In fact, in their treatment, the shrinkage of the top terrace is drivrii by the pressure from the step trains on either side, which has its origin in the repulsive interaction (of elastic or entropic origin) of like steps. This yields an effective chemical potential for the top terrace,... 

This equates the difference between the ionic contributions from the chemical potentials outside ( ) and inside the gel to the contributions of the two forces used to describe neutral networks. The contributions from the mixing and elastic portions of Eq. (17) may be described as discussed in Sect. 1.1 [13]. 

It must be noted that Eqs. (35) and (36) are for the case in which the crosslinks in the polymer network were introduced in solution as with the Peppas-Merrill equation for neutral hydrogels and also that a Gaussian chain distribution is assumed. The complete equilibrium expressions accounting for the mixing, elastic-retractive, and ionic contributions to the chemical potential for anionic networks in the two cases described above are then... 

---