Generalized Flory-Huggins Theory Research Articles

Generalized Flory-Huggins theory-based equation of state for ring and chain fluids

By modeling the ring-like molecule as a pearl necklace of freely jointed hard sphere, we develop a new equation of state (EOS) for the ring-like fluids on the basis of generalized Flory-Huggins (GFH) theory. Before proposing the new EOS of the ring-like fluids, we first modify the generalized Flory-Huggins theory for the chain fluids by incorporating a function related to the packing fraction into the insertion probability. The results indicate that the modified GFH EOS can predict the compressibility factors more accurately than the GFH EOS, especially for the intermediate and high packing fractions (η ≥ 0.157). Subsequently, the modified GFH theory-based EOS for the ring-like fluids is proposed. Compared to the Monte Carlo data of 3-mer, 4-mer, 5-mer, 6-mer, 16-mer, and 32-mer ring-like fluids, our EOS exhibits the best prediction among four EOSs for the compressibility factors at intermediate and high packing fractions (η ≥ 0.157), although our EOS also shows a slight underestimation for the compressibility factors at low packing fractions. In summary, this is the first report on the generalized Flory-Huggins theory-based EOS for the ring-like fluids. It is expected that the same strategy can be applied to these fluids with more complex architectures.

Quaternary (liquid + liquid) equilibria of aqueous two-phase poly (ethylene glycol), poly (DMAM–TBAM), and KH 2PO 4: Experimental and generalized Flory–Huggins theory

Quaternary (liquid + liquid) equilibrium (LLE) data of the aqueous two-phase poly (ethylene glycol), poly (N,N-dimethylacrylamide- t-butylacrylamide) with abbreviation name poly (DMAM–TBAM) as a hydrophobic association water-soluble copolymer and KH 2PO 4 has been determined experimentally at T = 338.15 K. Furthermore, the generalized Flory–Huggins theory with two electrostatic terms (the Debye–Hückel and Pitzer–Debye–Hückel) was used for correlation of the phase behavior of the quaternary system and the interaction parameters between all species were calculated. It was found that addition of poly (DMAM–TBAM) copolymer as well as changing the temperature can shift the binodal curves of aqueous two-phase systems containing polyethylene glycol (PEG) and salt. Also, the phase behavior of the DMAM–TBAM copolymer with some salts containing sodium chloride, ammonium hydrogen phosphate, potassium hydrogen phosphate, and sodium carbonate were studied experimentally at T = 338.15 K and the effect of the salt type on the their binodal curves was determined.

Reentrant Three-Phase Equilibrium of Homologous Polystyrene Solution

Phase equilibrium behavior was studied for a four-component system which consists of three polystyrene homologs with different molecular weights in methylcyclohexane. By using a refractive index method, a reentrant three-phase equilibrium was observed for the first time. The lower three-phase region appeared near the critical temperature of the binary system of polystyrene with the lowest molecular weight in methylcyclohexane. The characteristics of the observed phase equilibrium behavior was compared with the calculation using a generalized Flory-Huggins theory with an empirically determined interaction parameter.

Salt-induced liquid-liquid phase separation of protein-surfactant complexes.

We report the cloud-point curve determination of lysozyme-sodium-doderyl-sulfate (SDS) complexes in solution. By varying the pH, salt concentration, and relative ratio of lysozyme to SDS, the phenomenon of clouding and liquid-liquid phase separation is investigated under different solution conditions. For the temperature, concentration, and pH ranges used in this study, the clouding phenomenon appears to be controlled by the electrostatic interaction between the lysozyme-SDS complexes. Any change in the solution condition that leads to a decrease in the charge on the lysozyme-SDS complexes results in an increase in cloud-point temperature. A generalized Flory-Huggins theory for polydisperse polymers is used to describe the cloud-point curve.

Liquid—liquid phase separation in blends of polydisperse linear and branched polyethylenes

A generalized Flory—Huggins theory is employed to investigate liquid—liquid phase separation in a blend of polydisperse linear and branched polyethylenes (LPE/BPE). A temperature- and concentration-dependent χ parameter is used. The temperature- and composition-dependent coefficients of χ are obtained by fitting to experimental cloud-point data, and having a detailed knowledge of the molecular weight distributions of the two components. The value of χ is found to be small and positive (3.4 × 10 −4 ( ϕ BPE = 0.0) to 2.6 × 10 −4 ( φ BPE = 1.0), T = 423 K) over the temperature composition range of interest, consistent with an approximately athermal blend with small, non-combinatorial entropic contributions to the free energy of mixing. The magnitude of χ determined here is also in reasonable agreement with values measured previously on related systems. The best-fit cloud-point curve obtained for the LPE/BPE blend is a closed immiscibility loop, which is consistent with the experimental observations. However, no critical point(s) or spinodal(s) are found to exist. It is suggested, based on the limited data available, that a blend comprising two monodisperse LPE/BPE components, with molecular weights corresponding to the weight-average molecular weights of the polydisperse linear and branched polyethylenes, would not undergo liquid—liquid phase separation.

Solvation: Effects of molecular size and shape

Sharp et al. have raised the question: If a solute and its solvent have different molecular sizes, how should solvation interaction energies be extracted from transfer experiments? Is the chemical potential more appropriately given by ‘‘classical’’ solution theory or by Flory–Huggins theory? We study a general statistical mechanical treatment of solvation, a generalized Flory–Huggins theory, and related treatments by Hildebrand and by Sharp et al. to determine the physical basis for size-dependent terms in the chemical potential, and their limitations and applicabilities. We find that the extra entropy in the Flory–Huggins theory does not arise from the disparity of sizes of solute and solvent, from free volume, or from artifacts of approximations. Rather, when solutes and solvents have sufficient complexity that they can ‘‘interfere’’ with each other in solution, there is an ‘‘entropy of coupling’’ of translational freedom to excluded volume or internal or rotational degrees of freedom. The Flory–Huggins theory approximates this coupling entropy for polymeric solutes or solvents, but not for other systems. Proper extraction of contact free energies requires proper subtraction of the coupling term. This study rationalizes several experimental and simulation studies, and indicates that coupling entropies that depend on molecular size and shape are often needed to treat complex solvation processes.

Determination of .chi. from liquid-liquid phase data and the computation of phase diagrams for quasi-binary polymer solutions and blends

A generalized Flory-Huggins theory is described that permits the investigation of the phase behavior for quasi-binary polymer solutions or blends in which, for blends, both components may be polydisperse. A temperature- and concentration-dependent χ interaction parameter is used. Itis demonstrated that the χ parameter may be readily extracted from experimental phase data. This is illustrated by using a robust fitting procedure to obtain the composition and temperature dependence of χ for the cyclohexane/ polystyrene system from experimental phase data. The result (eq 22) is in excellent agreement with previous determinations of χ for this system, and the method employed here has several advantages over other approaches

Phase diagrams of quasi-binary polymer solutions and blends

Abstract A generalized Flory-Huggins theory is presented for use in fitting and predicting liquid-liquid phase diagrams of quasi-binary polymer solutions and blends, in which one component may be polydisperse. A temperature- and concentration-dependent χ parameter is employed. As has been demonstrated previously for simple binary systems, the form chosen for χ is sufficient to fit phase diagrams having upper and lower critical solution temperatures (UCST and LCST), combination of the two with the LCST lying above the UCST, closed loop and hour-glass shapes. In extending this work to quasi-binary systems, the phase diagrams obtained are compared with those for binary solutions and blends. It is illustrated how polymer solutions, in which the polymeric component has the same weight-average molecular weight and even the same polydispersity index, although having identical spinodals, may exhibit markedly different cloud-point curves. Comparison is also made with experimental data determined on a model quasi-binary system. Such comparisons may be used to extract the temperature and concentration dependence of χ for the system.

Phase diagrams of quasi-binary polymer systems with LCST/UCST spinodals and hour-glass cloud-point curves

A generalized Flory-Huggins theory is utilized to investigate liquid-liquid phase diagrams of quasi-binary polymer solutions and blends, in which one component may be polydisperse. A temperature and concentration dependent χ parameter is employed. It is illustrated that a polymer solution, in which the polymeric component has a Schulz-Zimm molecular weight distribution, may exhibit combined lower critical solution temperature/upper critical solution temperature spinodals and hour-glass cloud-point curves (CPCs). This is a direct consequence of the critical points being offset from the extrema of the CPCs and spinodals for quasi-binary systems, in contrast to true binary systems (such as solutions and blends of monodisperse polymers). Thus, for quasi-binary systems, it may be hazardous to infer the behaviour of spinodals from observations of CPCs or vice versa.

Observation of polymerlike phase separation of protein-surfactant complexes in solution.

Protein solution at appropriate pH and ionic strength has been shown to phase separate upon addition of suitable amount of anionic surfactant, sodium dodecylsulfate (SDS). We determine a series of cloud-point curves for bovine serum albumin-SDS complexes in aqueous solutions at different pH. Small angle neutron-scattering and light-scattering studies give strong evidence that these denatured proteins in solution are multicomponent polymerlike objects. We show that the generalized Flory-Huggins theory for polydisperse polymers can describe the cloud-point curves satisfactorily.