Combinatorial Entropy Of Mixing Research Articles

Multimonomer partitioning in latex systems with moderately water‐soluble monomers

AbstractSimple equations describing monomer partitioning in latices during intervals 2 and 3 in emulsion polymerization with any number of low to moderately water soluble monomers were derived from the extended Morton equation by making various assumptions. It appears that it is mainly the combinatorial entropy of mixing that governs the partitioning behavior, and that other contributions to the free energy of the monomers in the polymer particles are marginal. Experimental results with styrene, methyl methacrylate, and methyl acrylate confirm the validity of the assumptions. In interval 3 of emulsion polymerization the sum of all contributions to the free energy of the monomers in the particles other than the combinatorial entropy of mixing can be taken as a constant that is dependent only on the monomer composition in the particles and independent of the degree of swelling of the particles. The only parameters one needs to know to calculate the monomer concentrations in all phases with help of the derived equations, are the saturation concentrations of each monomer in the polymer particles, and the saturation concentrations of each monomer in the aqueous phase. © 1994 John Wiley & Sons, Inc.

TEM and image analysis to quantitatively describe the phase behavior in copolymer/homopolymer/homopolymer blends: Effect of the copolymer sequence distribution

Polymers are typically immiscible with one another, that is phase separated, in the absence of specific favorable intermolecular interactions, because the combinatorial entropy of mixing is small. Copolymers, polymer molecules containing more than one type of monomer unit, are frequently used to induce miscibility in homopolymer mixtures. Extensive work has previously established the importance of the copolymer composition, though the sequence of monomers within the copolymer has received less attention. Copolymers with random and with alternating sequences of monomers have been synthesized and mixed with homopolymers to evaluate the importance of the sequence distribution on blend miscibility. Blend miscibility determinations using differential scanning calorimetry and visual inspection can be erroneous when the glass transition temperatures of the phases are similar or the domains are small compared to the wavelength of light. Thus, we have used transmission electron microscopy to study the phase behavior of these polymer blends.Blend samples (∼30 mg) of poly(styrene-co-methyl methacrylate) (PS-PMMA), homopolystyrene (PS), homopoly(methyl methacrylate) (PMMA) were prepared by casting from tetrahydrofuran and annealing at 150°C for 7 days.

Comment on “a new expression for the combinatorial entropy of mixing in liquid mixtures”

Abstract The solution model proposed by Huyskens and Haulait-Pirson is applied to an associated solution. Expressions based on this model show that the equilibrium constant for complex formation is likely to be a function of both mole and volume fraction compositions.

Combinatorial Entropy of Mixing Molecules that Differ in Size and Shape. A Simple Approximation for Binary and Multicomponent Mixtures

For liquid solutions, the combinatorial entropy of mixing is commonly calculated using either (a) the ideal-solution model (suitable for mixtures of simple spherical molecules) or (b) the Flory lattice model (suitable for mixtures of chainlike molecules). Based on the lattice theories of Huggins, Staverman, Tompa, and Lichtenthaler for molecules of arbitrary size and shape, this work proposes an adhoc generalization of Flory's formula for the combinatorial entropy of mixing in binary and multicomponent solutions. The generalized Flory model yields results that are always intermediate between those obtained from (a) and (b). Parameters re quired for the calculations are found from molecular structure data (bond angles and distances). Illustrative calculations are given for the system carbon tetrachloride – octamethylcyclotetrasiloxane.

Entropy of mixing of polymer and solvent as derived from the free‐volume concept

AbstractA theory is proposed for the entropy of mixing of polymer and solvent. The theory is an extension of Hildebrand's derivation of the Flory‐Huggins combinatorial entropy of mixing by use of free‐volume concepts. The noncombinatorial (or equation of state) entropy of mixing originates, according to the proposed theory in the different free volume fractions which characterize ordinary simple solvents and high polymers. Two parameters are introduced: a parameter ρ, which is the ratio of the free volume fractions in the polymer and in the solvent, and a parameter c, which describes the external degrees of freedom of the polymer segments and is equivalent to Prigogine's parameter c. The noncombinatorial entropy of mixing, as derived from the present theory is equivalent (but not identical) to that derived from the newer theory of Flory et al. Concomitantly, the agreement with experiment of the calculated interaction parameter × for the athermal system polyisobutylene‐cyclohexane is about the same as that obtained from the theory of Flory et al.