Flory-Huggins Research Articles

Modeling non-electrolyte hydrogel swelling using the adjusted parameters from liquid-liquid equilibrium data of the linear polymer

Hydrogels are tridimensional elastic hydrophilic cross-linked polymers with the ability to absorb water in a process called swelling. The Flory-Huggins (FH) theory can be applied to model hydrogel swelling with appropriate adjustments. In the literature the FH model parameter is directly estimated from experimental data on swelling. The target of this paper is to evaluate the effect of using parameters estimated from liquid-liquid equilibria of the linear polymer directly in the swelling modeling of the respective cross-linked polymer as these data can be easily found in literature. Three methods that use different equations for the FH parameter and two methods for the mechanical contribution are evaluated. These models were applied to the polymer poly(N-isopropylacrylamide), PNIPA, and compared in three swelling intervals: the volume contraction region; the transition temperature; and the region of volume expansion. The most relevant and important behaviors of each region are shown, analyzed and discussed.

Describing mixture permeation across polymeric membranes by a combination of Maxwell-Stefan and Flory-Huggins models

The primary objective of this article is to develop an analytic procedure for calculating the permeation fluxes of mixtures of penetrant molecules across polymeric membranes. The developed approach combines (1) the Flory-Huggins (F-H) description of phase equilibrium thermodynamics, and (2) the Maxwell-Stefan (M-S) diffusion formulation. For compatibility reasons, the M-S equations are re-formulated in terms of volume fractions, rather than the more commonly used mole fractions. Using matrix algebra, explicit expressions are derived for calculation of the trans-membrane fluxes and component permeabilities. The accuracy of the developed procedure is demonstrated by comparison with published experimental data on CO2/C2H6 and water/ethanol mixture permeation.

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.

Mixing of Two Immiscible Liquids within the Polymer Microgel Adsorbed at Their Interface.

We report on the behavior of two immiscible liquids within polymer microgel adsorbed at their interface. By means of dissipative particle dynamics (DPD) simulations and theoretical analysis in the framework of the Flory-Huggins (FH) lattice theory, we demonstrate that the microgel acts as a "compatibilizer" of these liquids: their miscibility within the microgel increases considerably. If the incompatibility of the liquids is moderate, although strong enough to induce phase separation in their 1:1 composition, they form homogeneous mixture in the microgel interior. The mixture of highly incompatible liquids undergoes separation into two (micro)phases within the microgel likewise out of it; however, the segregation regime is weaker and the concentration profiles are characterized by a weaker decay (gradient) in comparison with those of two pure liquids. The enhanced miscibility is a result of the screening of unfavorable interactions between unlike liquid molecules by polymer subchains. We have shown that better miscibility of the liquids is achieved with densely cross-linked microgels. Our findings are very perspective for many applications where immiscible species have to be mixed at interfaces (like in heterogeneous catalysis).

Phase behavior and second osmotic virial coefficient for competitive polymer solvation in mixed solvent solutions

We apply our recently developed generalized Flory-Huggins (FH) type theory for the competitive solvation of polymers by two mixed solvents to explain general trends in the variation of phase boundaries and solvent quality (quantified by the second osmotic virial coefficient B2) with solvent composition. The complexity of the theoretically predicted miscibility patterns for these ternary mixtures arises from the competitive association between the polymer and the solvents and from the interplay of these associative interactions with the weak van der Waals interactions between all components of the mixture. The main focus here lies in determining the influence of the free energy parameters for polymer-solvent association (solvation) and the effective FH interaction parameters {χαβ} (driving phase separation) on the phase boundaries (specifically the spinodals), the second osmotic virial coefficient B2, and the relation between the positions of the spinodal curves and the theta temperatures at which B2 vanishes. Our classification of the predicted miscibility patterns is relevant to numerous applications of ternary polymer solutions in industrial formulations and the use of mixed solvent systems for polymer characterization, such as chromatographic separation where mixed solvents are commonly employed. A favorable comparison of B2 with experimental data for poly(methyl methacrylate)/acetonitrile/methanol (or 1-propanol) solutions only partially supports the validity of our theoretical predictions due to the lack of enough experimental data and the neglect of the self and mutual association of the solvents.

Communication: Cosolvency and cononsolvency explained in terms of a Flory-Huggins type theory.

Standard Flory-Huggins (FH) theory is utilized to describe the enigmatic cosolvency and cononsolvency phenomena for systems of polymers dissolved in mixed solvents. In particular, phase boundaries (specifically upper critical solution temperature spinodals) are calculated for solutions of homopolymers B in pure solvents and in binary mixtures of small molecule liquids A and C. The miscibility (or immiscibility) patterns for the ternary systems are classified in terms of the FH binary interaction parameters {χαβ} and the ratio r = ϕ A /ϕ C of the concentrations ϕ A and ϕ C of the two solvents. The trends in miscibility are compared to those observed for blends of random copolymers (AxC1-x) with homopolymers (B) and to those deduced for A/B/C solutions of polymers B in liquid mixtures of small molecules A and C that associate into polymeric clusters {ApCq}i, (i = 1, 2, …, ∞). Although the classic FH theory is able to explain cosolvency and cononsolvency phenomena, the theory does not include a consideration of the mutual association of the solvent molecules and the competitive association between the solvent molecules and the polymer. These interactions can be incorporated in refinements of the FH theory, and the present paper provides a foundation for such extensions for modeling the rich thermodynamics of polymers in mixed solvents.

Modeling study of a pervaporation membrane reactor for improving oxime hydrolysis reaction

The conversion of equilibrium-limited reactions can be efficiently improved by selective removal of product using a Pervaporation Membrane Reactor (PVMR), which attracts substantial attentions due to its excellent performance. For modeling the PVMR process, a pseudo-binary system was often assumed, nevertheless, it is inadequate to predict the performance when both the reactant and product have the similar properties and can simultaneous permeate through the membrane. A detailed model was established by coupling multi-component pervaporation and reaction kinetics with the butanoxime hydrolysis reaction employed as the experiment system. A modified Flory–Huggins (FH) approach and the Maxwell–Stefan (MS) formulation were used to describe the pervaporation model. The mass transfer fluxes and the concentration profiles of permeants within the membrane were modeled by a finite difference approach. Two coexisted behaviors, i.e. competitive adsorption and plasticizing effects were considered to influence mass transfer. The PVMR performance was predicted and a good agreement between experiment and calculation was obtained. The mechanism that how the simultaneous permeation of reactant and product influence the PVMR performance were further clarified in different operating conditions, including initial reactant concentration, downstream pressure, membrane thickness, ratio of membrane area to reaction volume, and temperature.

Construction and Validation of Binary Phase Diagram for Amorphous Solid Dispersion Using Flory-Huggins Theory.

Drug-polymer miscibility is one of the fundamental prerequisite for the successful design and development of amorphous solid dispersion formulation. The purpose of the present work is to provide an example of the theoretical estimation of drug-polymer miscibility and solubility on the basis of Flory-Huggins (F-H) theory and experimental validation of the phase diagram. The F-H interaction parameter, χ d-p, of model system, aceclofenac and Soluplus, was estimated by two methods: by melting point depression of drug in presence of different polymer fractions and by Hildebrand and Scott solubility parameter calculations. The simplified relationship between the F-H interaction parameter and temperature was established. This enabled us to generate free energy of mixing (ΔG mix) curves for varying drug-polymer compositions at different temperatures and finally the spinodal curve. The predicted behavior of the binary system was evaluated through X-ray diffraction, differential scanning calorimetry, and in vitro dissolution studies. The results suggest possibility of employing interaction parameter as preliminary tool for the estimation of drug-polymer miscibility.

Probing the effects of experimental conditions on the character of drug-polymer phase diagrams constructed using Flory-Huggins theory.

Amorphous drug-polymer solid dispersions have been found to result in improved drug dissolution rates when compared to their crystalline counterparts. However, when the drug exists in the amorphous form it will possess a higher Gibb's free energy than its associated crystalline state and can recrystallize. Drug-polymer phase diagrams constructed through the application of the Flory Huggins (F-H) theory contain a wealth of information regarding thermodynamic and kinetic stability of the amorphous drug-polymer system. This study was aimed to evaluate the effects of various experimental conditions on the solubility and miscibility detections of drug-polymer binary system. Felodipine (FD)-Polyvinylpyrrolidone (PVP) K15 (PVPK15) and FD-Polyvinylpyrrolidone/vinyl acetate (PVP/VA64) were the selected systems for this research. Physical mixtures with different drug loadings were mixed and ball milled. These samples were then processed using Differential Scanning Calorimetry (DSC) and measurements of melting point (Tend) and glass transition (Tg) were detected using heating rates of 0.5, 1.0 and 5.0°C/min. The melting point depression data was then used to calculate the F-H interaction parameter (χ) and extrapolated to lower temperatures to complete the liquid-solid transition curves. The theoretical binodal and spinodal curves were also constructed which were used to identify regions within the phase diagram. The effects of polymer selection, DSC heating rate, time above parent polymer Tg and polymer molecular weight were investigated by identifying amorphous drug miscibility limits at pharmaceutically relevant temperatures. The potential implications of these findings when applied to a non-ambient processing method such as Hot Melt Extrusion (HME) are also discussed.

Evaluation of Thermodynamic Models for Prediction of Sorption Behavior into the Polydimethylsiloxane Membrane in Pervaporation Process

This work focuses on modeling of the sorption step as a main step in the mass transport through the pervaporation process. For this purpose, four thermodynamic models including Flory–Huggins (FH), Universal Quasichemical (UNIQUAC), modified Non-Random Two-Liquid (M-NRTL), and modified Wilson (M-Wilson) were used to predict the equilibrium sorption of ethanol/water mixtures into the polydimethylsiloxane (PDMS) membrane. In the M-Wilson model, the reference state based on pure enthalpy of components was used to determine the residual term. Moreover, the influences of ethanol feed content and temperature on the liquid sorption level and sorption selectivity were studied experimentally and theoretically. The results indicated that the proposed models were successfully able to determine the sorption level of the ethanol aqueous solutions into the PDMS membrane. Moreover, the M-NRTL and M-Wilson models were found to be much more accurate than the FH and UNIQUAC models to determine the volume fraction of the penetrants in the PDMS membrane. It was also observed that the total and ethanol sorptions increased with an enhancement in the ethanol feed concentration, while the membrane sorption selectivity decreased. Moreover, increasing the operating temperature led to higher sorption of both ethanol and water, whereas the sorption selectivity did not show significant changes with temperature.

Upper critical solution temperature-type thermosensitive hydrogel phase equilibrium of poly(2-hydroxyethyl methacrylate)/water/n-alkanol mixtures

We investigated the swelling behavior of upper critical solution temperature (UCST)-type nano-sized poly(2-hydroxyethylmethacrylate) (PHEMA) particle gel with n-propanol and n-butanol in the presence of water. Because PHEMA is a biocompatible hydrogel and is highly water absorptive, it is worthwhile to investigate the phase behavior between PHEMA and water. The swelling behavior of the cross-linked PHEMA particle gel and the phase miscibility of the linear PHEMA mixed with the n-alkanol/water solution were evaluated. Our experimental results showed that increasing the water fraction in the mixed solvent gradually reduces the swelling temperature. Moreover, the two phase region of the PHEMA/water/n-butanol mixture showed sudden expansion at ∼15 vol% water in the ternary diagram. In these systems, oriented interactions among each component exist, which strongly affect the chemical association. The modified double lattice (MDL) and Flory-Huggins (FH) models were employed to describe the swelling and phase behaviors of the given ternary systems. The MDL model matched our data much better than the FH model because it was able to correctly represent the oriented interactions from hydrogen bonding or other specific forces encountered in the systems. To demonstrate the model compatibility to UCST-type swelling behavior, we also examined other polymer solutions. Polyvinyl acetate (PVAc) gel/2-propanol was studied as an associating system and polystyrene (PS)/cyclohexane was evaluated as a non-associating system.

A Solution Model for Predicting Asphaltene Precipitation

Formation of asphaltene deposition during oil production, processing and synthesis is known as a fundamental problem of petroleum reservoir worldwide. Asphaltene is a petroleum fraction that can lead to increasing the operating costs in these industries. Variations in operational pressure, temperature and fluid composition are generally the significant cause of asphaltene precipitation. In this study, a regular solution model with liquid-liquid equilibrium criteria between asphaltene-rich phase and solvent-rich phase (maltene phase) is presented in order to calculate asphaltene precipitation. As a result, to achieve this objective, the Flory-Huggins (F-H) theory is applied and the definition of the interaction parameter in the traditional form of F-H model is modified. In this work, an empirical correlation is adapted using regular solution theory to predict the solubility parameters and eventually the DE (Differential Evolution) optimization strategy is applied to calculate optimum values of the justifiable parameters in the model. The results of the developed model are finally compared with the existing asphaltene precipitation data in various solvent ratios from the literature and it is shown that they are in acceptable agreement with the experimental data. Hence, the proposed model is capable of good prediction of asphaltene precipitation in a widespread range of the solvent ratios.

Trends in the Athermal Entropy of Mixing of Polymer Solutions

Polymeric mixtures of hydrocarbons and alcohols have been simulated with discontinuous potential models to characterize the Helmholtz energy of the repulsive reference fluids. This quantity is equivalent to the athermal mixture entropy. The reference compressibility factor and Helmholtz free energy have been correlated for various molecular structures from single to infinite chain lengths. The mixtures included small n-alkanes, branched alkanes, aromatics, and alcohols, with polymeric molecules of: n-alkanes, ethyl-styrenes, ethyl-propylenes, and isoprenes. We find that the athermal entropy of mixing at constant packing fraction deviates significantly from ideality as the volume ratio increases, but the nonideality is fairly insensitive to structural details like branching and rings. Volume ratio alone does not provide a complete characterization, however. For example, a mixture of C40 and C80 would yield a small deviation whereas a mixture of C2 and C4 would provide a relatively large deviation. This observation leads to the introduction of a characteristic parameter in terms of entropy density, designated as an entropic solubility parameter. In both ideal and nonideal solutions, the trends still follow van der Waals (vdW) mixing. This leads to an accurate characterization of the entropic contribution to the χ parameter (χS) of Flory–Huggins theory for mixtures of all sizes, shapes, and compositions of molecular structures. A general rule is developed for predicting the athermal entropy of mixing based on knowledge of the volume ratios and entropic solubility parameter of the constituent molecules. The simulations are compared to Flory–Huggins (FH), group contribution lattice fluid theory (GCLF), statistical associating fluid theory (SAFT), Sanchez–Lacombe (SL), and Guggenheim-Staverman (GS) theories of polymer chains.

Molecular thermodynamic characterization of LCST fluid phase behavior and exploring electrostatic algorithms to compute polymer/solvent solubility parameters in the canonical ensemble

The present study aims to characterize the temperature dependence of polyethylene (PE) solubility in hexane at high pressure using an atomistic-level simulation technique, without the need for expensive and time-consuming experimental methods, to gain significant miscibility insights in polymer processes that are present in a wide range of industrial applications. To this end, various molecular dynamics (MD) simulations based upon the OPLS-AA force field are carried out over a range of 425–500 K at 50 and 200 bar to predict the temperature dependence of Hildebrand's solubility parameter of high-density polyethylene (HDPE) and hexane at these high pressures. The NVT simulation results compare quite favorably with the available experimental and theoretical data. The effect of electrostatic potential energy contribution to cohesive energy is also investigated, and it is shown that the solubility parameter decreases with increasing temperature for both molecular mechanical models with and without electrostatic terms. Subsequently, the Flory–Huggins (FH) binary interaction parameter is predicted from the knowledge of temperature dependence of solubility parameters. It is demonstrated that the computed binary interaction parameter increases upon increasing the temperature, indicating that the miscibility of the PE/hexane system decreases by raising the temperature. This conclusion is in agreement with the widely recognized lower critical solution temperature (LCST) fluid phase behavior. Moreover, it is shown that the increase in system temperature decreases the chemical potential factor of the phase stability condition, indicating that at higher temperatures this effect tends to destabilize the polymer–solvent system. Comparisons of electrostatic forces evaluated based on shift functions and the Particle-Mesh Ewald (PME) methods show slight difference, and it is also found that the grid spacing has no noticeable influence on non-bonded energy terms and total potential, employed in the calculation of cohesive energy, a result that is useful to increase the efficiency of future MD simulations.

Effect of mixing rule and activity coefficient model on prediction of solid–liquid–gas equilibria for carbon dioxide + organic compound mixtures using Peng–Robinson equation of state and GE type mixing rule

Solid–liquid–gas equilibria (SLGE) for carbon dioxide+organic compound mixtures were predicted by Peng–Robinson (PR) equation of state with excess Gibbs free energy (GE) type mixing rule. Activity coefficient models using molecular surface charge density were applied for the calculation of activity coefficient and GE in the mixing rules. Two types of GE type mixing rule, Modified Huron–Vidal (MHV1) and Linear Combination of Vidal and Michelsen (LCVM) mixing rules were applied for the energy and size parameters on PR equation of state. The activity coefficient models used in this work were Conductor-like Screening Model Segment Activity Coefficient (COSMO-SAC) and COSMO-UNIQUAC. In these activity coefficient models, two kinds of the combinatorial equations, Stavermann–Guggenheim (SG) and Flory–Huggins (FH) equations were used. Consequently, the eight combinations with the GE type mixing rule, the activity coefficient model and the combinatorial equation were applied for the prediction of SLGE for carbon dioxide+organic compound mixtures. The organic compounds interested in this work were aromatic hydrocarbons, alcohols and acids. On the SLVE calculation in this work, the temperatures at the phase equilibria were calculated by fixed pressure. The effects of mixing rule and activity coefficient model on the prediction performance of the solid–liquid–gas equilibria were investigated.The combination of MHV1/COSMO-SAC/SG presented the best performance of the SLVE prediction for carbon dioxide+aromatic hydrocarbon systems. The absolute deviation between experimental and predicted result of the temperature at the SLGE was 3.6K in temperature. For alcohols and acids, the smallest absolute deviations between experimental and predicted results of the temperature at the SLGE were given by the combinations of MHV1/COSMO-SAC/FH and LCVM/COSMO-SAC/FH, respectively. The values of the absolute deviations were 1.1 and 4.1K for alcohols and acids.

Solvation of polymers as mutual association. I. General theory

A Flory-Huggins (FH) type lattice theory of self-assembly is generalized to describe the equilibrium solvation of long polymer chains B by small solvent molecules A. Solvation is modeled as a thermally reversible mutual association between the polymer and a relatively low molar mass solvent. The FH Helmholtz free energy F is derived for a mixture composed of the A and B species and the various possible mutual association complexes AiB, and F is then used to generate expressions for basic thermodynamic properties of solvated polymer solutions, including the size distribution of the solvated clusters, the fraction of solvent molecules contained in solvated states (an order parameter for solvation), the specific heat (which exhibits a maximum at the solvation transition), the second and the third osmotic virial coefficients, and the boundaries for phase stability of the mixture. Special attention is devoted to the analysis of the "entropic" contribution χ(s) to the FH interaction parameter χ of polymer solutions, both with and without associative interactions. The entropic χ(s) parameter arises from correlations associated with polymer chain connectivity and disparities in molecular structure between the components of the mixture. Our analysis provides the first explanation of the longstanding enigma of why χ(s) for polymer solutions significantly exceeds χ(s) for binary polymer blends. Our calculations also reveal that χ(s) becomes temperature dependent when interactions are strong, in sharp contrast to models currently being used for fitting thermodynamic data of associating polymer-solvent mixtures, where χ(s) is simply assumed to be an adjustable constant based on experience with solutions of homopolymers in nonassociating solvents.

Physicochemical characterization of nimodipine–polyethylene glycol solid dispersion systems

This study investigates the solid–solid interactions between nimodipine (NIM) and polyethylene glycol (PEG) of different mean molecular weights (PEG 2000, 4000 and 6000), in solid dispersion systems, applying differential scanning calorimetry (DSC), Fourier-Transform infrared spectroscopy, powder X-ray diffraction (PXRD), hot stage microscopy (HSM) and theoretical modeling by the Flory–Huggins (FH) solution theory. Phase diagrams constructed with the aid of DSC and FH solution theory showed sensitivity on the estimated values of the FH interaction parameter (χ). When χ is considered a constant number (χ = α, α ≠ 0), formation of a eutectic mixture is predicted in the 70–80% w/w PEG concentration region, while when χ was considered as a function of concentration and temperature (χ = f(φ,Τ)), the model predicts the formation of monotectic systems. Construction of more precise phase diagrams by HSM to the aid of Kofler’s “contact preparation” method confirmed the monotectic nature of the examined systems. Studies on NIM’s re-crystallization process in the solid dispersions revealed a strong dependence of the crystallization rate, as well as the resulting crystal form, on the mean molecular weight and concentration of PEG: NIM crystallization rates decrease as PEG’s MW increases, while NIM mod II crystals predominate in dispersions prepared at temperatures above NIM’s liquidus and growth of NIM mod I prevailing in PEG-rich samples.

Asphaltene precipitation in live crude oil during natural depletion: Experimental investigation and modeling

The complicated nature of asphaltene molecules besides the unknown mechanism of phase separation of asphaltene-containing systems as well as lack of a suitable characterization parameter has questioned the generality of the available thermodynamic models.The scaling equation developed by Rassamdana et al. [10,13] and its generalized form presented by Hu et al. [20] proved existence of a general relationship to model the asphaltene precipitation envelope and the onset. However, it works only for dead oil systems; here it has been tried to extend this technique for live oil fluids at reservoir condition. In this study, three types of experiments were conducted on five live reservoir fluid samples. The samples were collected from a giant Iranian oil field to measure the amount of precipitated asphaltene for a wide range of temperature and pressure.The results of this study developed a new live oil scaling equation and successfully applied to predict a new real data-set. The predictions of the model were compared with the two widely used thermodynamic methods of single component solid and modified Flory–Huggins (FH) models. The results show that the phase stability and the regions where asphaltene precipitates from the live crude oil were predicted using this new scaling equation with an acceptable accuracy.

Probe dependency of flory–huggins interaction parameters between solvents: Cases of hydrocarbons and isosteric derivatives

AbstractInverse gas chromatography has been widely used to determine the Flory–Huggins parameter, χ, between two solvents. Many studies showed that interaction parameters were probe dependent. In recent studies, it was proposed that the interaction between two solvents may lead to different contact probability between solutes and solvent mixtures and create an apparent solubility parameter different from volume average rule. An equation was previously derived to relate the probe dependency to the deviation of solubility parameter from the volume average rule. By plotting ϕ2ϕ3RT(χ23/V2) versus the solubility parameter of solutes, a linear trend could be observed with a negative slope for miscible mixtures. When there was an unfavorable interaction between two solvents, an opposite situation would be observed. In this study, mixtures of 19,24‐dioctadecyldotetracontane (C78) and its derivatives were tested. The solubility parameters of mixtures showed negative deviation from the volume average. The plots of ϕ2ϕ3RT(χ23/V2) versus solubility parameter of solutes had positive slopes. For two derivatives the best estimated values of RT(χ23/V2) were negative in certain temperatures. Enthalpy–entropy compensation plot showed that these two derivatives have higher entropy of mixing. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2013

State diagram of phase transition temperatures and solvent‐induced recovery behavior of shape‐memory polymer

AbstractIn this study we analyzed the phase and state transitions of shape‐memory polymers (SMPs)/solvent mixtures using the Flory–Huggins (FH) theory by extension of Vrentas and the Couchman–Karasz theory for glass transition, as well as Clausius–Clapeyron relation for melting transition. Using scaling relations of model parameters, we have obtained a theoretical prediction of state diagrams of the phase transition temperature and solvent‐induced recovery in SMPs. The inductive decrease in transition temperature is identified as the driving force for the solvent‐induced shape‐memory effect in SMPs Consequently, the thermodynamics of the polymer solution and the relaxation theory were employed to characterize the dependencies of shape recovery time on the FH parameter and the ratio of the molar volume of solute to solvent. With the estimated model parameters, we constructed the state diagram for SMP, which provides a powerful tool for design and analysis of phase transition temperatures and solvent‐induced recovery. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013