Gels thermodynamic properties

Permeability (P) is usually defined as the product of a thermodynamic property and a transport property which are, respectively, the partition or solubility coefficient, K, and the diffusion coefficient, D. This partition coefficient is defined as the ratio at equilibrium of the solute concentration inside the gel to that in solution. A value of K less than 1 indicates that the solute favors the solution... 

B 9. Boyer, R. F., and R. S. Spencer Some thermodynamic properties of slighty cross-linked styrene-divinylbenzene gels. J. Polymer Sci. 3, 97 (1948). 

More detailed discussion of food polymers and their functionality in food is now difficult because of the lack of the information available on thermodynamic properties of biopolymer mixtures. So far, the phase behaviour of many important model systems remains unstudied. This particularly relates to systems containing (i) more than two biopolymers, (ii) mixtures containing denatured proteins, (iii) partially hydrolyzed proteins, (iv) soluble electrostatic protein-polysaccharide complexes and conjugates, (v) enzymes (proteolytic and amylolytic) and their partition coefficient between the phases of protein-polysaccharide mixtures, (vi) phase behaviour of hydrolytic enzyme-exopolysaccharide mixtures, exopolysaccharide-cell wall polysaccharide mixtures and exopolysaccharide-exudative polysaccharide mixtures, (vii) biopolymer solutes in the gel networks of one or several of them, (viii) enzymes in the gel of their substrates, (ix) virus-exopolysaccharide, virus-mucopolysaccharides and virus-exudative gum mixtures, and so on. 

Considerable effort has been dedicated to understand the changes on thermodynamical properties of gas and liquids due to their confinement in porous media [1-3]. The special case of water in porous silica (silica gels, zeolites, vycor. ..) [4-7] has grown interest due to large field of application, from geophysics (water and silica are the most represented on earth) to industry and environment (phase separation, catalysis...). 

The presence of proteins in the lipid bilayer influences greatly the thermodynamic properties of the membrane. The lipids in the area of immediate protein influence are in gel-state and their molecular movements are restricted. 

Handa, Y.P. Stupin, D. Thermodynamic properties and dissociation characteristics of methane and propane hydrates in 70-A-radius silica gel pores. J. Phys. Chem. 1992, 96, 8599-8606. 

This largely adopted model has eluded to direct thermodynamic confirmation because the formation of gel has been a serious limitation to the reproducibility of measurements. On the other hand, an analysis of the thermodynamic properties is necessary in order to ascertain whether the polymeric conformational "state" has been subjected to changes or not. 

Swelling of polyurethane networks. Proceeding from the general conception of the role of surfactants in the formation of the secondary structure of polyurethanes, studies of the influence of KEP-2 on the distribution of hydrogen bonds in polyurethane networks were required. The literature on the thermodynamic properties of polymer solutions and gels was searched and, in particular, the work of the authors of [117] is of direct interest in this context. This work... 

In contrast to the gel formation at these concentrations, it is well known,30 that from more dilute solution, the polymer will precipitate, or crystallize, in the form of isolated lamella-like crystallites. It is theoretically possible to prepare both the lamella-like crystallites and the gels, of the same molecular weight fraction, at the same undercooling. This possibility exists since there is only an imperceptible change between the equilibrium melting temperature for a concentration of about 0.1%, where the platlets form, and the higher concentrations typical of gel formation.24 Hence, a rationale or natural comparison can be made between the thermodynamic properties of the well-known lamella-like crystallites typical of dilute solution crystallization and those of the crystallites involved in the gel formation when both are crystallized at the same temperature. In Table I, a typical set of such data is given. 

To obtain quantitative representation of fractionation, a model for the thermodynamic properties of the copolymer + solvent + nonsolvent system and the original two-dimensional distribution function are required. Ratzsch et al. [46] presented the application of continuous thermodynamics to successive homopolymer fractionation procedures based on solubility differences. This method is now applied to copolymer fractionation. The liquid-liquid equilibria (LLE) of polymer solutions forms the thermodynamic background for these procedures. The introduction of the precipitation rate (23) permits calculation of the distribution functions in the sol and gel phases of every fractionation step, i, according to ... 

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