Composition-dependent Interaction Parameter Research Articles

Water Swelling Behavior of Poly(ethylene glycol)-Based Polyurethane Networks.

Defects in a polymer network complicate an accurate calculation of structural parameters such as the molar mass between cross-links Mc, typically obtained from experimental swelling data. In this paper the formation and structure of poly(ethylene glycol) (PEG)-based polyurethane networks containing PEG-mono methyl ether dangling chains are studied. The phantom network model can describe the swelling behavior of these networks only when a composition-dependent interaction parameter is used and the formation of allophanates is accounted for. A clear transition in the network formation is found at the PEG network precursor molar mass at which entanglements are formed in the melt. Correction factors based on structure calculations using the Miller–Macosko–Vallés probability approach are proposed and validated for an accurate calculation of the Mc of these defect-containing networks. This provides a new approach for studies that requires an accurate estimate of the Mc, only based on experimentally straightforward swelling experiments.

Theoretical and experimental investigation of drug-polymer interaction and miscibility and its impact on drug supersaturation in aqueous medium

Amorphous solid dispersions (ASDs) have the potential to offer higher apparent solubility and bioavailability of BCS class II drugs. Knowledge of the solid state drug-polymer solubility/miscibility and their mutual interaction are fundamental requirements for the effective design and development of such systems. To this end, we have carried out a comprehensive investigation of various ASD systems of dipyridamole and cinnarizine in polyvinylpyrrolidone (PVP) and polyacrylic acid (PAA) at different drug loadings. Theoretical and experimental examinations (by implementing binary and ternary Flory-Huggins (F-H) theory) related to drug-polymer interaction/miscibility including solubility parameter approach, melting point depression method, phase diagram, drug-polymer interaction in the presence of moisture and the effect of drug loading on interaction parameter were performed. The information obtained from this study was used to predict the stability of ASDs at different drug loadings and under different thermal and moisture conditions. Thermal and moisture sorption analysis not only provided the composition-dependent interaction parameter but also predicted the composition dependent miscibility. DPM-PVP, DPM-PAA and CNZ-PAA systems have shown molecular level mixing over the complete range of drug loading. For CNZ-PVP, the presence of a single Tg at lower drug loadings (10, 20 and 35%w/w) indicates the formation of solid solution. However, drug recrystallization was observed for samples with higher drug weight fractions (50 and 65%w/w). Finally, the role of polymer in maintaining drug supersaturation has also been explored. It has been found that drug-polymer combinations capable of hydrogen-bonding in the solution state (DPM-PVP, DPM-PAA and CNZ-PAA) are more effective in preventing drug crystallization compared to the drug-polymer systems without such interaction (CNZ-PVP). The DPM-PAA system outperformed all other ASDs in various stability conditions (dry-state, in the presence of moisture and in solution state), which was attributed to the drug’s low crystallization tendency, the strong DPM-PAA interaction, the robustness of this interaction against moisture or water and the ability of PAA in maintaining DPM supersaturation.

Biopolymer gel swelling analysed with scaling laws and Flory–Rehner theory

The swelling of biopolymer gels is analysed with scaling laws from polymer physics, as an alternative for the classical Flory-Rehner theory. With these scaling laws, holding for polymer concentrations in the semi-dilute regime, experimental data on deswelling of gels can be collapsed to a single universal master curve. The predictions made with the scaling laws are similar to those made with the modified Flory-Rehner, where the osmotic pressure is described with a composition-dependent interaction parameter. For gels in the semi-dilute regime we recommend the use of the scaling laws, because their compact, and universal character.

Phase equilibrium of water in different types of PEDOT:PSS

It is well-known, that humidity and thus water absorption have a strong influence on electrical and optical properties of electrochemical devices containing layers of PEDOT:PSS. Sorption isotherms have to be determined to correlate the air humidity with the exact amount of absorbed water. Here we report on phase equilibrium data for different commercially relevant types of PEDOT:PSS. The measured data can be correlated well by a Flory–Huggins approach with composition-dependent interaction parameter.

Miscibility of In x Ga1−x As alloys: a study using atomistic simulations

Atomistic simulations are used in combination with the two potential energy functions, namely, the Valence Force Field (VFF) model and the Tersoff model, to study the solution thermodynamics of In x Ga1−x As alloy. The simulation data, in the form of a T − x diagram, is contrasted with the results obtained by using the Ho and Stringfellow approach. It is observed that for the VFF model, the upper critical solution temperature obtained from simulation data is approximately 850 K, which is higher than the 729 K predicted by the Ho and Stringfellow treatment. The composition range for which the two-phase heterogeneous region exists is wider than that predicted by the Ho and Stringfellow approach. The Tersoff model predicts a complex miscibility diagram, where the 850 K temperature corresponds to the approximate ‘eutectic’ temperature. Further improvement of model predictions may be made possible by investigation of temperature and composition dependent interaction parameter in a modified regular solution theory, and investigation of non-random, non-ideal solution models in the Ho and Stringfellow treatment, development of temperature dependent VFF model parameters and adjustment of Tersoff model parameters to account for longer range interactions which exist at temperatures above 850 K. The miscibility diagram constructed using the Tersoff model simulation data can be used to provide information on the phase stability and equilibrium Indium content at any given temperature for the crystalline solid solution.

Cloud-Point Measurements for (Water + Poly(ethylene glycol) + Salt) Ternary Mixtures by Refractometry Method

The cloud-point temperatures and phase separation of (water + poly(ethylene glycol) + salt) ternary systems were studied by the refractometry method. The salts were K3PO4, K2HPO4, Na2HPO4, or Na2CO3. The phase separation was also observed by visual inspection. Differences between the measured cloud point using the refractometry method, and visual inspection was up to ±1 °C. The measured cloud-point temperatures are compared with those obtained by viscometry and laser beam scattering methods. These comparisons indicate complete agreement between the different methods for cloud-point temperature measurements for the (water + poly(ethylene glycol) + salt) ternary system. The salt-included liquid−liquid separation is studied by using the Flory−Huggins polymer solution theory. A simple linear temperature composition-dependent interaction parameter (χ) was applied for correlation of the measured cloud-point temperatures. The comparison between measured and correlated cloud-point temperatures indicates that average absolute deviation is less than 0.61 °C. Therefore, the Flory−Huggins model was successfully applied to determine the phase separation conditions of the (water + poly(ethylene glycol) + salt) ternary systems.

Determination of water/polymer interaction parameter for membrane-forming systems by sorption measurement and a fitting technique

The water/polymer interaction parameter plays an important role in the thermodynamic description of membrane-forming water/solvent/polymer solutions with the Flory-Huggins (FH) model. In order to discuss reasons for the wide variety of values for this parameter reported in the literature, interaction parameter was determined utilizing two different methods for polysulfone, poly(ether sulfone), cellulose acetate and poly(ether imide) (PSU, PES, CA, and PEI). In a “direct” determination, water sorption isotherms have been measured and analyzed with the FH model. In a second, “indirect”, method an optimal parameter value was found by fitting experimental cloud point data of ternary polymer systems with the FH model. Liquid–liquid equilibrium (LLE) calculations have been carried out under the assumption that the water/solvent and solvent/polymer interactions are correctly described by known composition dependent interaction parameters. For a given polymer, the water/polymer interaction parameters resulting from fits of ternary systems with different solvents agree well. But the obtained values are smaller than the ones resulting from the sorption experiment. The difference is smaller for a more hydrophilic polymer with a higher water uptake than for hydrophobic polymers with a lower uptake. Reasons for this difference will be discussed.

Excess Enthalpy Data in Binary Systems Containing a Supercritical Fluid and Their Correlation

Excess enthalpy data measured in the critical regions were collected from the literature for the period of 1983−1995. The database contains 231 datasets of 23 binary systems (6434 data points) covering the temperature and pressure ranges of 263.15−573.15 K and 43.3−175 bar, respectively. The experimental data were correlated by Redlich−Kister equation. The following thermodynamic models were also tested: Peng−Robinson EOS, NRTL, and MHV1 models. A modified Peng−Robinson EOS with composition-dependent interaction parameters was proposed. The correlation of the excess enthalpy data in the database using this model provides good results.

Excess molar enthalpies of (carbon dioxide+ethylene glycol dimethyl ether or 2-methoxyethyl ether) at the temperatures 298.15 K and 308.15 K and pressures from 7.5 MPa to 12.5 MPa

The excess molar enthalpies H m Eof { xCO 2+ (1 − x)CH 3(OCH 2CH 2) n OCH 3}, where n= 1 (ethylene glycol dimethyl ether) and n= 2 (2-methoxyethyl ether) were measured at the temperatures 298.15 K and 308.15 K and pressures (7.5, 10.0, and 12.5) MPa. No (vapour + liquid) phase boundaries were observed from the H m Ebehaviour. The values of H m Eof all the mixtures are negative over the entire composition, temperature and pressure range. An analysis using the Peng-Robinson equation with a composition-dependent interaction parameter confirms that the large negative values of H m Eobserved at T= 308.15 K and p= 7.5 MPa are due to the proximity to the critical point of CO 2. In contrast to the behaviour of ethylene glycol dimethyl ether mixtures, for which (∂ H m E/∂ p) Tx is positive, the pressure dependence of H m Efor the 2-methoxyethyl ether mixtures became negative in the solvent-rich region at T= 298.15 K. The Peng-Robinson equation reproduces the main features observed, but fails to predict the reversal in (∂ H m E/∂ p) Tx .

Excess enthalpies of (carbon dioxide + propylene carbonate or N-methyl-ε-caprolactam or 1-formyl piperidine) at the temperatures 298.15 K and 308.15 K and pressures from 7.5 MPa to 12.5 MPa

The excess molar enthalpies H E mof [ xCO 2+ (1 − x){C 4H 6O 3(propylene carbonate) or C 7H 13NO ( N-methyl-ε-caprolactam) or C 6H 11NO (1-formyl piperidine)}] were measured at the temperatures 298.15 K and 308.15 K and pressures (7.5, 10.0, and 12.5) MPa. (Vapour + liquid) phase boundaries were determined from the H E ms. The excess enthalpies for all of the mixtures are negative over the entire composition, temperature, and pressure range. Large changes in the values of H E mwere observed near the critical temperature and pressure of carbon dioxide. The Peng-Robinson equation of state with a composition-dependent interaction parameter was used to model the behaviour of H E m. At low xthe Peng-Robinson equation provided a satisfactory fit for all mixtures studied over the full range of pressures and temperatures. For { xCO 2+ (1 − x)C 4H 6O 3}, the predicted H E mvalues for x> 0.5 were more negative than the experimental results. The fits to the other mixing curves were somewhat better, but show similar discrepancies at T= 308.15 K and p= 7.5 MPa.

Dense polymer film and membrane formation via the dry-cast process part I. Model development

The dry-cast membrane-formation process is a major phase-inversion technique by which asymmetric membranes are manufactured. In this paper a fully predictive model which incorporates coupled heat and mass transfer is developed to describe the evaporation of both solvent and nonsolvent from an initially homogeneous polymer/solvent/nonsolvent system. This unsteady-state, one -dimensional, coupled heat- and mass-transport model allows from local film shrinkage owing to excess volume of mixing effects as well as evaporative solvent and nonsolvent loss. The model can predict composition paths into the ternary phase diagram which determine the onset of phase transition. The ternary phase diagram is predicted using the Flory-Huggins theory allowing for composition-dependent interaction parameters. The model is applied to the well-characterized cellulose acetate/acetone/water-system for which sufficient experimental data are available to permit determination of the friction coefficients in the ternary mass-transport model. The model is solved numerically using a software package based on the method of lines which is capable of handling moving boundary problems. The modeling studies indicate that for a given polymer/solvent/nonsolvent/support system, the most influential parameters are the gas-phase mass transport, initial cast film thickness, and initial composition. Of particular importance, the model can predict the general morphological characteristics associated with the formation of dense polymer films and symmetric as well as asymmetric membranes.

Tacticity effects on polymer blend miscibility. 1. Flory-Huggins-Staverman analysis

Flory-Huggins-Staverman (F-H-S) theory is used to relate shifts in miscibility to changes in the entropic component of the composition-dependent interaction parameter, «g», and to changes in the Staverman parameter, «c» for the poly(methyl vinyl ether) (PVME)/polystyrene (PS) system. In the F-H-S approach a composition-dependent interaction parameter is explicitly related to the relative surface areas for lattice sites of the two componentsThe relative surface are can be determined from low molecular weight materials using the method of Bondi, from simple molecular models, and from a fit to the cloud-point curve. For tactic blends these methods are compared

Tacticity effects on polymer blend miscibility. 2. Rate of phase separation

The functional form g for the composition-dependent interaction parameter previously obtained for the isotactic and atactic poly(vinyl methyl ether) (i- and a-PVME)/atactic polystyrene (PS) blends are used to predict the rate of phase separation in terms of the apparent diffusion constant. The Flory-Huggins-Staverman (F-H-S) analysis of cloud-point curves predicts a drastically slower rate of phase separation for i-PVME in blends with PS in comparison with a-PVME blends. The rate of phase separation is experimentally determined for these blends using light scattering.

ON THE COMPOSITION-DEPENDENT INTERACTION PARAMETERS IN EQUATIONS OF STATE

Composition-dependent interaction parameters have been applied to the calculation of vapor-liquid equilibria (VLE) in mixtures containing components of different chemical nature. Binary VLE have been correlated and ternary VLE have been predicted from binary data using five different mixing rules. Binary data can be accurately correlated for systems with moderate deviations from ideality using mixing rules with two binary parameters. For very strongly nonideal mixtures three binary parameters are needed. For the prediction of ternary VLE from binary information only the mixing rules of Panagiotopoulos and Reid (1986) and Schwartzentruber et al. (1987) are reliable. For most systems the quality of predicting ternary data is comparable to the quality of correlating binary data. Significant deviations are noted only for strongly nonideal systems close to phase separation. In these cases it is recommended to use models incorporating association in an explicit form. KEYWORDS Equations of state Mixing rules Multicomponent Vapor-liquid equilibria.