Free volume mixing rules

This equation shows that the excess Gibbs free energy computed from a cubic EOS of the van der Waals type and the one-fluid mixing rules contains three contributions. The first, which is the Flory free-volume term, comes from the hard core repulsion terms and is completely entropic in nature. The second term is very similar to the excess free-energy term in the regular solution theory, and the third term is similar to a term that appears in augmented regular solution theory. Consequently, one is led... 

MSE/MST and MSEE/MST blends were miscible by DSC measurements. Their density vs. composition curves showed positive deviations from the linear additivity rule volume contraction upon mixing two miscible polymer pairs was confirmed. Permeability vs. composition plot also showed large negative deviations from the semilogarithmic mixing rule. The permeability coefficient of the 50/50 MSE/MST blend was the lowest of all the materials tested it is comparable to EVAL-F and much lower than any other commercial barrier polymers. The volume shrinkage in the compatible blends show that the free volume is reduced, thus reducing the permeability. 

For several years, polymers were expected to be miscible only when there was favorable specific interaction between them. Gibbs free energy of mixing was developed and shown to contain three different contributions combinatorial entropy of mixing, exchange interaction, and a free volume term. Specific interactions are a prerequisite for the miscibility of polymers. This was the drift that the Nobel laureate P. Flory indicated as discussed in Chapter 1. A number of exceptions to this rule have been found. A number of miscible systems have been found to have a random copolymer as one of the blend constituents. Both the copolymers that were found miscible with random microstructure are butadiene-styrene copolymer and vinyl chloride and vinyl acetate copolymers. The homopolymers PBd, PS, PVC, and PVA can form six binary blends. This is from C2 = 6. They are not miscible in any of the six binary blends that can be formed from four homopolymers. This would mean that there are no specific interactions... 

He, H2, O2, Ar, N2, CH4 and CO2 are lower than those calculated from the semi-logarithmic additivity rule, indicating that PMMA is miscible with BCPC over the whole blend composition range. These permeation results can be interpreted in terms of the free volume contraction which has been proposed to describe gas transport behavior in polymer mixtures. Similar observations for the miscible blends of polycarbonate with a copolyester formed from 1,4-cydohexanedimetha-nol and a mixture of terephthalic and isophthaUc adds have been made using CO2 [100]. Negative deviations of both permeability and diffusion coeffidents from simple additivity relations have been observed, and interpreted qualitatively to have resulted from the decrease in volume when the blends were mixed. 

In the first following section some of the principles of the glass transition will be outlined, free volumes will be related to T in accordance with established viewpoints, and mixing rules for binary and ternary mixtures will be reformulated and discussed... 

It is shown that the present model for a polymer network as a copolymer of chain ends, chain segments and branch points provides a workable hypothesis, from which useful conclusions can be derived. To arrive at a set of consistent expressions, the mixing rules for free volumes of copolymers and polymer mixtures had to be reformulated. Where possible, these results have been checked with data from the literature on the effects of chain ends and branch points on T. Thus it was shown that a unified free volume theory for polymer solutions, copolymers, or polymer networks exists which is in agreement with most experimental data. 

Many characteristics of a protein in aqueous solvents are connected to its preferential solvation (or preferential hydration). The protein stability is a well-known example. Indeed, the addition of certain compounds (such as urea) can cause protein denaturation, whereas the addition of other cosolvents, such as glycerol, sucrose, etc. can stahihze at high concentrations the protein stiucture and preserve its en2ymatic activity [4-7]. The analysis of literature data shows that as a rule Ffor the former and r23 " <0 for the latter compounds. Recently, the authors of the present paper showed how the excess (or deficit) number of water (or cosolvent) molecules in the vicinity of a protein molecule can be calculated in terms of F2 the molar volume of the protein at infinite dilution and the properties of the protein-free mixed solvent [8]. The protein solubility in an aqueous mixed solvent is another important quantity which can be connected to the preferential solvation (or hydration) [9-13] and can help to understand the protein behavior [9-17]. 

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