Intramolecular screening effects in nondilute polymer solutions: An equation‐of‐state approach

In a previous article, we presented a simple modification of the traditional Flory–Huggins theory that took intramolecular screening effects (or same chain contacts) into account. In this article, we present a natural extension of that work, in which free‐volume effects are also explained with an equation‐of‐state model. The predictions of the interaction parameter, χ, for several polymer–solvent systems are presented, over the entire concentration range, in θ solvents and good solvents. A geometric mean assumption is applied to the calculation of an exchange energy interaction term. The predictions of χ are successful to various degrees when internal pressures are used, whereas the use of solubility parameters in most cases produces fairly good agreement with experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2911–2922, 2003     

Prediction of Nitrogen Solubility in Pure Water and Aqueous NaCl Solutions up to High Temperature, Pressure, and Ionic Strength

A thermodynamic model for the solubility of nitrogen in pure water (273–623 K, 0–600 bar) and in aqueous NaCl solutions (0–4m, 273-473 K, 0–600 bar) is presented. The model is based on a specific interaction model for the liquid phase and a highly accurate equation of state for the vapor phase. Comparison of the model predictions with experimental data indicates that the model predictions are within or close to experimental uncertainty. Most experimental data sets are consistent within errors of about 7%. Although the parameters were evaluated from data for binary and ternary systems, the model can be used to predict nitrogen solubility in much more complicated systems like seawater.     

Molecular model for solubility of gases in flexible polymers

We propose a model for a priori prediction of the solubility of gases in flexible polymers. The model is based on the concept of ideal solubility of gases in liquids. According to this concept, the mole fraction of gases in liquids is given by Raoult's law with the total pressure and the vapor pressure of the gas, where the latter may have to be extrapolated. However, instead of considering each polymer molecule as a rigid structure, we estimate the effective number of degrees of freedom from an equivalent freely jointed bead‐rod model for the flexible polymer. In this model, we associate the length of the rods with the molecular weight corresponding to a Kuhn step. The model provides a tool for crude estimation of the gas solubility on the basis of only the monomer unit of the polymer and properties of the gas. A comparison with the solubility data for several gases in poly(dimethylsiloxane) reveals agreement between the data and the model predictions within a factor of 7 and that better model results are achieved for temperatures below the critical temperature of the gas. The model predicts a decreasing solubility with increasing temperature (because of the increasing vapor pressure) and that smaller gas molecules exhibit a lower solubility than larger ones (e.g., CH₄ has a smaller solubility than CO₂), which agrees with the experimental data. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 701–706, 2003     

Methyl methacrylate emulsion polymerization at low monomer concentration: Kinetic modeling of nucleation,particle size distribution,and rate of polymerization

The results of a mathematical model developed in the authors' previous work are discussed and compared against final number (N) and size distribution of particles (PSD) and the rate of polymerization (RP) experimental data of methyl methacrylate (MMA) emulsion polymerization above the critical micelle concentration (cmc) of the surfactant. On the basis of the model results, the hypothesis that the observed bimodal PSD can be ascribed to secondary nucleation as proposed in the literature is questionable. It is discussed that this PSD can also be caused by differences in the growing rate of different‐size particles as predicted for styrene emulsion polymerization. Because of the small particle size obtained at low initial monomer concentration, the high rate of free‐radical desorption reduces the accumulation of these species; therefore, the autoacceleration effect is less pronounced for the conditions under study compared with the usual behavior of the RP during MMA emulsion polymerization above cmc. Similarities and differences between model predictions and experimental data are discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2547–2556, 2001     

Photochromic polymers: effects of structure and environment on photoresponsiveness

In this review paper the photoresponsiveness of photochromic macromolecules under different structural and environmental conditions is discussed with reference to results from the authors' laboratories. Polypeptides, in particular poly(L -glutamic acid) and poly(L -lysine), with spirobenzopyrane side chains show photoinduced conformational variations which are amplified by addition of organic acids or bases to hexafluoro-2-propanol (HFP) solutions. Thus combination of light and environment effects allows modulation of order–disorder conformational transitions. Such photoindiced conformational changes are not observed in the case of macromolecules with a hydrocarbon main chain and azobenzene or stilbene side chains, obtained by polymerization of acrylic monomers. However, even in these systems structural variations affect the dependence of optical properties on irradiation. Moreover, the combination of organic solvents and water shows that polymer solubility can be modulated by light.     

A new approach in modelling phase equilibria and gas solubility in electrolyte solutions and its applications to gas hydrates

This paper presents a new predictive model for phase equilibria and gas solubility calculations in the presence of electrolyte solutions. It treats salts as pseudo-components in an equation of state (EoS) by defining the critical properties and acentric factor for each salt. The water–salt, gas–salt and salt–salt binary interaction parameters (BIP) have been determined by using available experimental data on freezing point depression and boiling point elevation as well as gas solubility and salt solubility data in saline solutions.The methodology has been applied in modelling sodium chloride, potassium chloride and their mixtures, as well as solubility of methane and carbon dioxide in aqueous single and mixed electrolyte solutions.The developed model is capable of accurately predicting the phase behaviour, gas hydrate stability zone and potential salt precipitation in single and mixed electrolyte solutions. The model predictions are compared with available independent experimental data, including hydrate inhibition characteristics of single and mixed electrolyte solutions, and good agreement is demonstrated.     

Solubility of hydrocarbons in water: Experimental measurements and modeling using a group contribution with association equation of state (GCA-EoS)

In this communication, new experimental data on the solubility of n-hexane, cyclo-hexane and iso-octane in pure water are reported. The data have been measured using a static-analytic technique that takes advantage of a Rolsi™ sampling device in the temperature range of 298–353 K and at pressures up to 0.5 MPa. The experimental data measured in this work at 298 K have been compared with some selected data from the literature and good agreement is found. A group contribution plus association equation of state, namely the GCA-EoS, is used to model the phase equilibrium of water + hydrocarbon (C₂ to n-C₆, cy-C₆, i-C₄ and i-C₈) system. The predictions of the model are found in good agreement with the experimental data measured in this work and some selected data from the literature.     

Solubility of light hydrocarbons and their mixtures in pure water under high pressure

New solubility data of methane, ethane, n-butane and their mixtures in pure water are obtained at 344.25 K, from 2.5 to 100 MPa. The results agree well with those of the literature in the case of pure hydrocarbons in water, but differ significantly for hydrocarbon mixtures. In contrast to the conclusion reached by Amirijafari and Campbell [B. Amirijafari, J. Campbell, Solubility of gaseous hydrocarbon mixtures in water, Soc. Pet. Eng. J. (1972) 21–27.], the experimental solubility data of methane–ethane mixtures shows an ideal solution behavior, while the solubility data of methane–n-butane mixtures shows a weaker non-ideality than that observed by McKetta and Katz [J.J. McKetta, D.L. Katz, Methane–n-butane–water system in two-and three-phase regions, Ind. Eng. Chem. 40 (1948) 853–863]. The pure hydrocarbon solubility data are satisfactorily correlated using the Soreide and Whitson modification [I. Soreide, C.H. Whitson, Peng–Robinson predictions for hydrocarbons, CO2, N2, and H2S with pure water and NaCl brine, Fluid Phase Equilib. 77 (1992) 217–240] of the Peng–Robinson equation of state.     

Effect of molecular association on solubility,diffusion, and permeability in polymeric membranes

The filling‐type membrane is composed of grafted polymer and solvent‐resistant substrate; the calculation of solubility, diffusivity and swelling‐suppression effect by the substrate permits the prediction of solvent permeability. As noted in our previous article, the use of this approach, called membrane design, resulted in accurate prediction of the permeability of aromatic compounds. In this study, the influence of hydrogen bonding on solubility and diffusivity is investigated both theoretically and experimentally. The solubility of chloroform and dichloromethane in poly(acrylate)s increases, and their diffusivity decreases, compared with that estimated without considering the hydrogen‐bonding effect. Solubilities predicted by the lattice‐fluid hydrogen‐bonding (LFHB) model show good agreement with the results of vapor sorption. Comparison of diffusion coefficients measured by vapor permeation with those predicted from free volume theory reveals that the decrease of solvent diffusion coefficient is approximately proportional to the fraction of associated molecules. Fluxes of chloroform and dichloromethane were measured by vapor permeation experiments through filling‐type acrylate membranes, and predictions agree well with experiments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 171–181, 2000     

CO2 solubility in aqueous solutions of N-methyldiethanolamine+piperazine by electrolyte NRTL model

Accurate modeling of the solubility behavior of CO₂ in the aqueous alkanolamine solutions is important to design and optimization of equipment and process. In this work, the thermodynamics of C_O2 in aqueous solution of N-methyldiethanolamine (MDEA) and piperazine (PZ) is studied by the electrolyte non-random two liquids (NRTL) model. The chemical equilibrium constants are calculated from the free Gibbs energy of formation, and the Henry’s constants of CO₂ in MDEA and PZ are regressed to revise the value in the pure water. New experimental data from literatures are added to the regression process. Therefore, this model should provide a comprehensive thermodynamic representation for the quaternary system with broader ranges and more accurate predictions than previous work. Model results are compared to the experimental vapor-liquid equilibrium (VLE), speciation and heat of absorption data, which show that the model can predict the experimental data with reasonable accuracy.     

Application of the perturbed Lennard–Jones chain equation of state to solute solubility in supercritical carbon dioxide

The perturbed Lennard–Jones chain (PLJC) equation of state is a thermodynamic model based on the perturbation theory of liquid state. This equation has been shown in the past to be a successful model for phase equilibria calculations of binary and ternary fluid mixtures and polymer solutions. In this work, we employed for the first time the PLJC equation to model the solubility of 39 solids in supercritical carbon dioxide. It was shown that the model achieves good correlation with three temperature independent parameters. A comparison of the PLJC with the commonly used Peng–Robinson equation reveals the PLJC equation gives better correlation to the solubility data than the Peng–Robinson model that utilizes temperature dependent parameters.     

A new kinetic model for bulk polymerization of vinyl chloride based on two-phase hypothesis

A kinetic model has been developed for the bulk polymerization of vinyl chloride using Talamini's hypothesis of two-phase polymerization and a new concept of kinetic solubility which assumes that rapidly growing polymer chains have considerably greater solubility than the thermodynamic solubility of preformed polymer molecules of the same size and so can remain in solution even under thermodynamically unfavourable conditions. It is further assumed that this kinetic solubility is a function of chain length. The model yields a rate expression consistent with the experimental data for vinyl chloride bulk polymerization and moreover is able to explain several characteristic kinetic features of this system. Application of the model rate expression to the available rate data has yielded 2.36 × 10⁸l mol^?1 sec^?1 for the termination rate constant in the polymer-rich phase; as expected, this value is smaller than that reported for homogenous polymerization by a factor of 10–30.     

Kinetics of radiation-induced bulk polymerization of vinyl chloride in the temperature range of −50 to 90°c

Kinetic investigations on the bulk polymerization of vinyl chloride initiated by exposure to ⁶⁰Co γ-rays were carried out in the temperature range of ?50 to 90°C at dose rates varying from 0.15 to 50 rad/c. Some polymerization runs were also carried out in a centrifugal field. As generally reported for this polymerization system, in which the polymer is insoluble in the monomer, the polymerization rate was found to change as a function of the amount of the polymer formed in a special fashion. This particular function has been shown to be greatly influenced by the polymerization temperature and to be independent of the rate of initiation, or, more rigorously, of the dose rate. Thus, at any given temperature the equation of the polymerization conversion rate could be written in the form of the product of two separate functions, one for the polymerization conversion and the other for the dose rate. While for the latter the results gave an essentially square-root dependence on dose rate as is normally found for homogeneous polymerization, the former has been discussed in the terms of recently advanced kinetic schemes, based on a two-phase polymerization model. The kinetic parameters found in this work are in agreement with previous authors' data.     

Solubility of CO2 in room temperature ionic liquid [hmim][Tf2N

Solubility measurements of carbon dioxide in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide have been performed with a gravimetric microbalance at temperatures of about 282, 297, 323, and 348 K and pressures up to about 2 MPa. Two different sources for the ionic liquid are examined in this work: an ultrapure sample from NIST (the IUPAC task force sample) and a commercially available sample. Both samples show nearly identical solubility behaviors, being undistinguishable within experimental uncertainties. Solubility (pressure-temperature-composition) data have been well correlated with an equation-of-state (EOS) model used in our previous works. The EOS model calculations are compared with experimental solubility data for the same system in the literature. The present EOS has predicted partial immiscibility at the CO2-rich side solutions. To prove this prediction, vapor-liquid-liquid equilibrium experiments have been made, and our predictions have been confirmed.     

Preparation of polymer nanocomposites with “ultrahigh” refractive index

Nanocomposites of lead sulfide and several polymers, especially poly(ethyleneoxide), were prepared by coprecipitation of lead sulfide and polymer, followed by a drying and pressing procedure. Such nanocomposites consist of ca. 90% w/w (or ca. 50% v/v) lead sulfide, of particle dimensions of 2–40 nm. The refractive index of these materials is on the order of 3 and therefore, to the authors' best knowledge, is the highest reported for any polymer composite.     

Prediction of thermodynamic properties of polymer solutions by a group-contribution method

The Flory–Huggins lattice-theory expression for solvent activity in a polymer-solution is commonly used to calculate the thermodynamic interaction parameter χ with the aid of experimental data from vapor pressure osmometry. This expression assumes that χ is independent of composition. However, experimental data for a variety of polymer-solvent mixtures indicate that χ exhibits an appreciable concentration dependence. A group contribution method, UNIFAC (UNIQUAC Functional-Group Activity Coefficients) incorporating the free-volume correction of Oishi and Prausnitz is used to predict the dependence of χ on solvent concentration. Agreement with previously reported experimental data is within 15%. Calculated values of χ obtained from the Flory–Huggins expression for solvent activity and from the corresponding Gibbs free energy of mixing (which does not assume that χ is independent of composition) are compared. Calculations based on the Gibbs free energy of mixing predict a somewhat larger value of χ relative to those based on solvent activity. The specific Gibbs free energy of mixing for polystyrene-solvent mixtures is calculated using the UNIFAC model, and is found to represent qualitatively the phase equilibrium behavior. Quantitative discrepancies are observed, however, for the polystyrene-acetone system in light of the actual experimental solubility reported by Suh and Clark (20). Most of the thermodynamic predictions for polymer-solvent systems investigated herein are correlated qualitatively with the relative mismatch between solubility parameters of both components.     

Binary classification of aqueous solubility using support vector machines with reduction and recombination feature selection

Aqueous solubility is recognized as a critical parameter in both the early- and late-stage drug discovery. Therefore, in silico modeling of solubility has attracted extensive interests in recent years. Most previous studies have been limited in using relatively small data sets with limited diversity, which in turn limits the predictability of derived models. In this work, we present a support vector machines model for the binary classification of solubility by taking advantage of the largest known public data set that contains over 46?000 compounds with experimental solubility. Our model was optimized in combination with a reduction and recombination feature selection strategy. The best model demonstrated robust performance in both cross-validation and prediction of two independent test sets, indicating it could be a practical tool to select soluble compounds for screening, purchasing, and synthesizing. Moreover, our work may be used for comparative evaluation of solubility classification studies ascribe to the use of completely public resources.     

Modeling of solid–liquid equilibria in naphthalene,normal-alkane and polyethylene solutions

A solid–liquid equilibrium (SLE) model is developed on the basis of an equation of state referred to as copolymer SAFT. This SLE model is demonstrated for hydrocarbon solutions containing totally and partially crystallizable solutes. Initially regressed and tested on the solubility data for naphthalene, normal-alkane, and polyethylene, this model is used in a sensitivity study to understand the effects of crystallizability, melting temperature, molecular weight, and pressure on solid–liquid and liquid–liquid transitions of polyethylene in subcritical and supercritical propane.     

Water Activity and Solubility Measurements and Pitzer Model Simulation of the MgCl<Subscript>2</Subscript>–RbCl–H<Subscript>2</Subscript>O Ternary System at 298.15 K

Water activities for the MgCl₂–RbCl–H₂O ternary system and its sub-binary MgCl₂–H₂O and RbCl–H₂O systems at 298.15 K have been measured using the isopiestic method. The measured results for the binary systems agree well with literature data. The measured equal water activity lines for the MgCl₂–RbCl–H₂O ternary system deviate from Zdanovskii’s rule. The solubilities for the MgCl₂–RbCl–H₂O ternary system also have been measured using a isothermal visual first/last crystal method, and the results are consistent with one reported set of solubility data. Pitzer’s model was selected to correlate the measured water activity and solubility data and the parameters reported in the literature are re-examined by comparing the model-calculated equal water activity lines and solubilities with experimental values measured in this work. New and reasonable parameters are obtained by fitting the water activity and solubility data measured in this work and those reported in the literature. The water activities and solubilities were simulated with the new parameters and the results show that the Pitzer model can successfully represent the thermodynamic properties and be used to calculate the solubility isotherms.