Solubility thermodynamic concepts

The qualitative discussion of solubility has focussed so far on the attractive forces in solute-solvent interactions. However, where water is concerned, it is also important to consider the forces of repulsion due to the so-called hydrophobic interactions that may arise in certain cases (Franks, 1975). These hydrophobic interactions may be explained in terms of thermodynamic concepts. 

The initiation of the cationic polymerisation of alkenes is examined in detail by means of simple thermodynamic concepts. From a consideration of the kinetic requirements it is shown that the ideal initiator will yield a stable, singly charged anion and a cation with a high reactivity towards the monomer by simple, well defined reactions. It must also be adequately soluble in the solvent of choice and for the experimental method to be used. The calculations are applied to carbocation salts as initiators and a method of predicting their relative solubilities is described. From established and predicted data for a variety of carbocation salts the position of their ion molecule equilibria and their reactivity towards alkenes are examined by means of Born-Haber cycles. This treatment established the relative stabilities of a number of anions and the reason for dityl, but not trityl salts initiating the polymerisation of isobutene. 

The solubility parameter approach is a thermodynamically consistent theory and it has some links with other theories such as the van der Waals internal pressure concept, the Lennard-Jones pair potentials between molecules, and entropy of mixing concepts of the lattice theories. The solubility parameter concept has found wide use in industry for nonpolar solvents (i.e. solvent selection for polymer solutions and extraction processes) as well as in academic endeavor (thermodynamics of solutions), but it is unsuccessful for solutions where polar and especially hydrogen-bonding interactions are operating. 

Concurrent with these developments of the solubility parameter concept, other approaches to the treatment of solution thermodynamic problems were being undertaken, A review of some of these approaches has been given by Prigogine (6), Increasing emphasis,... 

The predictions that can be made for solvent mixtures on the basis of the solubility diagram are not strictly valid because they involve thermodynamic simplifications and empirical parameters, and disregard temperature effects [14.29], [14.33]. A strong warning must therefore be given against the uncritical use of solubility parameters. Nevertheless, description of the solvents with the aid of the solubility parameter concept often provides useful information about their solvency and reveals similarities which can otherwise only be characterized empirically (e.g., latent solvents or dilutability). 

The thermodynamic affinity between components of a solution is important for quantitative estimation of mutual solubility. The concept of solubility parameters is based on enthalpy of the interaction between solvent and polymer. Solubility parameter is the square root of the cohesive energy density, CED ... 

These effects are part of the solubility parameters concept. This concept allows to predict compatibility qualitatively (see Section 6.2). Within the framework of the general principles of the thermodynamics of solutions, the numerical evaluation of compatibility implies the evaluation of the value of the free energy (the Gibbs energy) of mixing over the whole range of solution concentration. However, sueh evaluations are difBcult and often excessive for most practical purposes. Therefore, for the estimation of compatibility, it is more convenient to know the value of aity numerical criterion mentioned in the previous subchapters. 

The idea of solubility parameters was first introduced by Hildebrand using the concept of regular solutions and was further developed by Scatchard [6,7]. Hildebrand s solubility parameter concept is based on Gibbs free energy relationship. Thermodynamically two compounds (e.g. polymer in solvent) do mix when the change in their free energy is negative ... 

The Phaser experiments reveal a surprising thermodynamic principle of polymer-solvent-carbon dioxide mixtures. Whereas most polymers have very low solubility (often below 1%) in supercritical carbon dioxide, supercritical carbon dioxide can have appreciable solubility in many types of polymers. Carbon dioxide solubilities ranging from 20 to 60% have been measured for several pure liquid polymer systems having no organic solvent. In these systems, the thermodynamic concepts of solvent and solute are reversed the carbon dioxide is the solute and the polymer is the solvent. 

Regarding the chapters not yet mentioned suffice it to say that this book altogether elucidates the interplay of solubility phenomena, thermodynamic concepts, and environmental problems. I congratulate the editor and the authors on this remarkable achievement in such a comparatively short time. 

The quantity /if may be hypothetical, but the thermodynamic concept is very distinct, as is evidenced by Henry s law on solubility of gases in solution. Henry s law will be explained later by the lattice theory of solution. ... 

The simple Flory-Huggins approach and the solubility parameter concept are inadequate when tested against experimental data for polymer solutions. Even for mixtures of n-alkanes, the excess thermodynamic properties cannot be described satisfactorily - Flory et In particular, changes of volume upon mixing are excluded and observed... 

Several thermodynamic properties are related to partitioning between water and other phases, for example octanol (Kow) or the pure compoimd itself (water solubility). These partitioning processes can be understood from thermodynamic concepts—like free energy, chemical potential and fugacity. The equilibrium partition constant between two phases, on a mole fraction basis, can be expressed as ... 

Nernst was only 25 years old when he formulated his equation relating cell voltages and concentrations. He is also credited with proposing the solubility product concept in the same year. In 1906, he announced his "heat theorem," which we now know as the third law of thermodynamics. 

The qualitative thermodynamic explanation of the shielding effect produced by the bound neutral water-soluble polymers was summarized by Andrade et al. [2] who studied the interaction of blood with polyethylene oxide (PEO) attached to the surfaces of solids. According to their concept, one possible component of the passivity may be the low interfacial free energy (ysl) of water-soluble polymers and their gels. As estimated by Matsunaga and Ikada [3], it is 3.7 and 3.1 mJ/m2 for cellulose and polyvinylalcohol whereas 52.6 and 41.9 mJ/m2 for polyethylene and Nylon 11, respectively. Ikada et al. [4] also found that adsorption of serum albumin increases dramatically with the increase of interfacial free energy of the polymer contacting the protein solution. 

The values of % and 8 are much less widely available for aqueous systems than for nonaqueous systems, however. This reflects the relative lack of success of the solution thermodynamic theory for aqueous systems. The concept of the solubility parameter has been modified to improve predictive capabilities by splitting the solubility parameter into several parameters which account for different contributions, e.g., nonpolar, polar, and hydrogen bonding interactions [89,90],... 

Indeed, in the world of tomorrow we can expect new aspects of polymer solids to extend the conventional and successful structure ideas of this century. These, of course, were the recognition as molecular identities of the chains of repeating chemical monomers. The circumstances of those entities have resulted in interesting concepts of solubilities, viscosity, and other mechanics, and especially thermodynamic limitations m mutual solubility or comparability of polymer mixtures. But we have known for decades that even homogeneous regular chain polymers such as Carothers polyesters and polyamides formed solids with manifold imperfections and irregularities, such as order-disorder crystal configurations.(22,23)... 

J The concept of counter-phases. When a stable compound penetrates from a binary into a ternary system, it may extend right across the system or exhibit only limited solubility for the third element. In the latter case, any characterisation also requires thermodynamic parameters to be available for the equivalent metastable compound in one of the other binaries. These are known as counter-phases. Figure 6.16 shows an isothermal section across the Fe-Mo-B system (Pan 1992) which involves such extensions for the binary borides. In the absence of any other guide-... 

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