Solvent chemical potential, stability

Polyphosphazene-based PEMs are potentially attractive materials for both hydrogen/air and direct methanol fuel cells because of their reported chemical and thermal stability and due to the ease of chemically attaching various side chains for ion exchange sites and polymer cross-linking onto the — P=N— polymer backbone. Polyphosphazenes were explored originally for use as elastomers and later as solvent-free solid polymer electrolytes in lithium batteries, and subsequently for proton exchange membranes. 

Here, the quantities jn ° and ji are, respectively, the chemical potentials of pure solvent and of the solvent at a certain biopolymer concentration V is the molar volume of the solvent and n is the biopolymer number density, defined as n C/M, where C is the biopolymer concentration (% wt/wt) and M is the number-averaged molar weight of the biopolymer. The second virial coefficient has (weight-scale) units of cm mol g. Hence, the more positive the second virial coefficient, the larger is the osmotic pressure in the bulk of the biopolymer solution. This has consequences for the fluctuations in the biopolymer concentration in solution, which affects the solubility of the biopolymer in the solvent, and also the stability of colloidal systems, as will be discussed later on in this chapter. 

Knowledge of the expressions for the chemical potentials of each of the components allows theoretical prediction of the critical concentration boundaries of the phase diagram for ternary solutions of biopolymeri + biopolymer2 + solvent. According to Prigogine and Defay (1954), a sufficient condition for material stability of this multicomponent system in relation to phase separation at constant temperature and pressure is the following set of inequalities for all the components of the system ... 

A characteristic manifestation of the coexistence of two gel phases and hence of the first-order phase transition in a swollen network consists of the van der Waals loop which appears in the dependence of the swelling pressure P (or of the chemical potential of the solvent plf see Eq. (1)) on 0. The composition of coexisting gel phases at the collapse (values

2) is given by the condition of equality of the chemical potentials of the solvent px and polymer p2 in both phases... 

By far the biggest problems with the stability and the magnitude of the liquid junction potentials arise in applications where the osmotic or hydrostatic pressure, temperature, and/or solvents are different on either side of the junction. For this reason, the use of an aqueous reference electrode in nonaqueous samples should be avoided at all cost because the gradient of the chemical potential of the solvent has a very strong effect on the activity coefficient gradients of the ions. In order to circumvent these problems one should always use a junction containing the same solvent as the sample and the reference electrode compartment. 

As the guiding principle we use the thermodynamic equilibrium requirement that in a system of identical monomer units in equilibrium with its aggregates the chemical potential of the various r-mers in different states of assembly be the same. We further ignore the role of solvent in considering the stability of the... 

One particular advantage of chemically anchored as opposed to physically adsorbed species such as Rh complexes on 7-AI2O3 is that no migration of Rh occurs over the surface of the support. At the same time the absence of solvent stabilization in gas-phase reactions gives rise to a greater potential for deactivation of catalyst due to thermal degradation or poisoning. 

A polymer is generally dissolved in a solvent to enable its manipulation into a usable, profitable, and marketable product. Hence, dissolution per se, is not the ultimate objective. In addition to rendering the polymer soluble, the resulting solution must have certain desirable characteristics, such as chemical and thermal stability, proper viscoelastic properties, environmental friendliness, and a general ease of manipulation, including ease of recovery. The first five solvents discussed exhibit some of these desirable characteristics. The steam explosion process is mentioned more for completeness than as a potential contender in the cellulose fiber production market. 

The excess chemical potential of solute, or the solvation free energy , at infinite dilution is of particular interest, because it is the quantity which measures the stability of solute in solvent, and because all other excess thermodynamic quantities are derived from the free energy. The excess chemical potential, which is defined as an excess from the ideal gas, can be expressed in terms of the so called Kirkwood coupling parameter. The excess chemical potential is defined as the free energy change associated with a process in which a solute molecule is coupled into solvent [41]. The coupling procedure can be expressed by. 

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