Flory-Huggins Research Articles

Effect of End Groups on the Cloud Point Temperature of Aqueous Solutions of Thermoresponsive Polymers: An Inside View by Flory-Huggins Theory.

In an effort to gain insight into the origin of the effects of end groups on the cloud point temperature (Tcp) as a function of the polymer molar mass of thermoresponsive polymers with lower critical solution behavior in dilute aqueous solutions, we use the Flory-Huggins (FH) theory amended for end groups. The theory was applied to available experimental data sets of poly(N-isopropylacrylamide) (PNIPAM), poly(4-vinylbenzyl methoxytris(oxyethylene) ether) (PTEGSt), and poly(α-hydro-ω-(4-vinylbenzyl)tetrakis(oxyethylene) ether) (PHTrEGSt). The theory relates the variations in TcpM,ϕcp for different end groups to the effective FH χ parameter of the end groups and explains the qualitative notion that the influence of the end groups is related to the hydrophobicity/hydrophilicity of the end groups relative to that of the so called intrinsic TcpM,ϕcp response of a polymer without end groups. The limits to the applicability of the FH theory are established, and a set of possible theoretical improvements is considered. The ultimate scrutiny of the simple FH theory and suggested improved theories must await the measurement of truly thermodynamic cloud points; the available cloud points are merely estimations of the thermodynamic cloud point, for which the deviation to the true cloud point cannot be established with sufficient accuracy.

Integrating theory with machine learning for predicting polymer solution phase behavior

Flory-Huggins (FH) theory is foundational to understanding macro-phase separation in polymer solutions; however, its predictions often quantitatively disagree with experiment. Recent machine-learning (ML) methods have generated predictive models of phase behavior across a broad range of chemistries and state variables with uncertainty comparable to experiment, but they lack interpretability. In this work, we develop several hybrid frameworks that combine Flory-Huggins theory with ML to (i) further improve interpolation and extrapolation with less experimental data, as well as (ii) provide interpretability of the ML model. Using the well-studied binodal of polystyrene-cyclohexane as a case study, we compare data-derived ML models to hybrid models where the prediction is confined by a theoretical expression (theory-constrained model), or the feature vector input incorporates theoretical expressions (theory-informed model). Even though Flory-Huggins theory is imperfect, its incorporation improves performance under data sparse situations, such as when only 2 or 3 molecular masses are in the training set. However, neither approach to integrate theory provides advantages in accuracy or computational efficiency when greater coverage of the parameter space or quantities of experimental data are available, indicating that the greatest impact on predictability occurs in data sparse situations. More important than impacting the accuracy of predictions though, these hybrid models provide physical relationships, such as the molecular mass dependence of the critical point or the coefficients within a FH expression. They also afford determination of scaling behavior of theoretical parameters from cloud point experiments instead of more complicated methods. This aspect of physics-incorporated ML models enhances trust in predictions, as well as providing a systematic means to identify anomalous behavior, assess experimental data quality, and reveal unanticipated correlations among factors.

Effective removal of cationic dyes from aqueous solutions by using black cumin (Nigella sativa) seed pulp and biochar

Black cumin seed pulp (C), as well as biochar (CC) produced via pyrolysis of black cumin seed pulp were used to remove methylene violet 2B (MV) and basic yellow 28 (BY28) from aqueous solution. Adsorption isotherms and kinetics were applied at 10, 25, and 35 °C. The adsorption of methylene violet 2B and basic yellow 28 on the black cumin seed pulp and biochar surface was exothermic; the heat of adsorption values were lower than 0. The adsorption capacities of BY28-C, BY28-CC, MV-C, and MV-CC were 212.8, 625, 164, and 909 mg g-1 at 25 °C, respectively. The adsorption of black cumin seed pulp and biochar data were examined with the Freundlich, Langmuir, Temkin, Dubinin-Radushkevich (D-R), and Flory-Huggins (F-H) isotherm models. The kinetics of the adsorption were fitted to the pseudo first-order and pseudo second order equations. The pseudo second order equation gave a better fit than the pseudo first-order equation.

The Flory–Huggins Isotherm and Water Contaminant Adsorption: Debunking Some Modeling Fallacies

The Flory–Huggins (FH) isotherm first appeared in the literature of water contaminant adsorption in the mid-2000s. It has come into the limelight and received considerable attention in recent years, in large part due to regular coverage in review articles. Here, we point out that a linear form of the FH isotherm is incompatible with the original nonlinear version. We show conclusively that the original FH isotherm was destroyed beyond recognition by the linearization method. As a result, the linearized FH isotherm suffers from the following serious defects: (1) Its parameter estimates are incorrect and nonsensical. (2) It is not possible to plot standard isotherm curves in the form of adsorbed phase concentration versus liquid phase concentration. These anomalies, or “red flags”, that arise in the use of the linearized FH isotherm in data correlation are reported for the first time. To avoid publishing meaningless research, it is advisable to use the original form of the FH isotherm in data fitting. To go beyond routine application (e.g., simple data correlation and thermodynamic calculation), this work describes a novel application that uses the FH isotherm to evaluate the energy distribution of heterogeneous adsorbents.

Interactions in plasticizer mixtures used for sugar replacement

In our quest for novel ingredients to be used in sugar replacement strategies, we have investigated the thermodynamics of polycarboxylic acids, such as citric acid. We have demonstrated the applicability of the Flory-Huggins (FH) theory to describe the thermodynamics of polycarboxylic acids solutions. Moreover, for citric acid we can describe the complete phase diagram with the theory. It shows that polycarboxylic acids have similar plasticizing and hygroscopic properties as sugars and polyols.Regarding mixtures of polycarboxylic acids and carbohydrates, the FH theory is able to describe a) the water activity of the mixtures, b) the solubility of ternary mixtures of acids and sugars, c) the lowering of the deliquescence point for binary mixtures of crystals, and d) the melting point depression in eutectic mixtures. Unexpectingly, our investigations show there is a strong non-zero FH interaction parameter between carboxylic acids and carbohydrates. In our prior sugar replacement strategy we have assumed zero interactions between plasticizers. Here, we will readdress this assumption. Carefull investigations of solid-liquid equilibrium of eutectic mixtures involving polycarboxylic acids and/or carbohydrates, shows nearly zero interaction in eutectic mixtures consisting only of two carbohydrates or two polycarboxylic acids. We now hold the hypothesis that there is strong non-zero interaction if the mixture contains plasticizers strongly differing in the amount of hydrogen bonding groups. This strong interaction explains why these mixtures, like polycarboxylic acids and carbohydrates, are excellent candidates as deep eutectic solvents. Furthermore, we conclude that polycarboxylic acids are useful additions to the toolbox of sugar replacers, albeit that there are some limitations to their amounts used.

Prediction and Construction of Drug-Polymer Binary System Thermodynamic Phase Diagram in Amorphous Solid Dispersions (ASDs).

Amorphous solid dispersion (ASD) has been well known as a potential strategy to improve the bioavailability and dissolution performance of poorly water-soluble drugs. The primary concern of this approach is the long-term stability of the amorphous drug in the solid dispersion. Accurate prediction and detection of the solubility and miscibility of drug in polymeric binary system will be a milestone to the development of ASDs. In this investigation, a method based on Flory-Huggins (F-H) theory was proposed to predict and calculate the solubility and miscibility of the drug in polymeric matrix and construct the phase diagram to identify the relevance between drug loading and temperature for ASDs development. Indomethacin (Indo) was chosen as the model drug, and polyvinyl pyrrolidone vinyl acetate (Kollidon® VA 64) was used as a polymeric carrier for the ASD systems. Physical mixtures were prepared with different drug loadings (10 to 90%) and analyzed by differential scanning calorimetry (DSC). The interaction parameter χ was calculated for physical mixtures by the melting point depression and solubility parameter contribution methods. The phase diagram was constructed to investigate the impact of other parameters like drug loading, processing temperature, and Gibbs free energy of mixing (ΔGmix). For further validation, formulations were developed using HME to verify the accuracy of the phase diagram and to guide in the hot-melt extrusion (HME) process design space and optimization.

Thermodynamic insights on the liquid-liquid fractionation of gluten proteins in aqueous ethanol

Wheat gluten includes two major proteins classes, gliadin (25–60 kg/mol) and glutenin polymers (100 to > 2,000 kg/mol) each comprising several polypeptides routinely identified by size-exclusion chromatography and electrophoresis. Gluten proteins are rich in glutamine (30%) and contain several repeated sequences, linking them to the wide class of intrinsically disordered protein (IDP). Here we showed that an ethanol/water (EtOH/W, 50/50, v/v) extract of an industrial gluten, comprising 1/3 of glutenin polymers and 2/3 of gliadin, underwent liquid-liquid phase separation (LLPS) below 14 °C, leading to two coexisting phases, respectively rich and poor in protein. As the quenching depth increased, proteins of lower and lower molecular weight joined the rich phase, akin to what would have been obtained for a polydisperse polymer sample. Within the rich phase the mass ratio of glutenin over gliadin decreased from 2.5 to 0.5 as the temperature dropped from 14 °C to −0.8 °C. Concomitantly the concentration in glutenin polymers increased up to 143 ± 6 g/L (at 9 °C) and then stopped to evolve, suggesting that the binodal line intersected the gelation line below this temperature. Applying the Flory-Huggins (FH) lattice model for each gluten protein classes, we demonstrated that their partitioning in the coexisting phases followed a same temperature dependency. However, some gliadin species joined the rich phase above their critical temperature. Here, specific interactions with the glutenin polymers through weak forces were exemplified. The study demonstrated the relevance of the Flory-Huggins (FH) lattice model in predicting phase behavior even when applied to complex protein mixtures.

An empirical model for sorption by glassy polymers: An assessment of thermodynamic parameters

A new fitting model for sorption by glassy polymers is suggested based on the Flory–Huggins (FH) equation with a composite formula for the FH interaction parameter, χ, which is applicable if sorption experimental data shows a single-maximum variation of the FH parameter. Namely, a power-like and a linear approximation is assumed for χ(φ1), as a function of solvent volume fraction φ1, before and after the point of its maximum. After determining the maximum point from a direct inspection of the sorption data, the three fitting parameters are evaluated by solving two independent least-square minimization problems. Several sorption studies of biopolymers taken from the literature show that the endset of the glass transition region is correlated with the position of the maximum of the FH interaction parameter. Based on this hypothesis and the Vrentas–Vrentas model for sorption of glassy polymers, a theoretical framework for the glass transition analysis is developed. In particular, the solvent-induced glass transition temperature variation can be estimated from the sorption isotherm as a function of the solvent content corresponding to temperatures above the temperature of sorption.

Alkali Lignin from Rice (Oryza sativa L.) Husk as Adsorbent for Aqueous Methyl Orange and Bromothymol Blue: Analysis of the Adsorption Kinetics and Mechanism

In this study, lignin was isolated from rice (Oryza sativa L.) husk using alkaline extraction method and was used as an adsorbent for aqueous solutions of methyl orange (MO) and bromothymol blue (BTB). The equilibrium removal rate of MO was found to be at 61.4%, with experimental equilibrium adsorbate uptake, qe, of 1.23 mg·g-1, achieved at 150 minutes contact time. For BTB, the equilibrium removal rate was found to be at 78.3%, with an experimental qe of 1.57 mg·g-1, achieved at 150 minutes contact time. Pseudo-first order (PFO) and pseudo-second order (PSO) kinetic models were then used to investigate the kinetics of the adsorption process. Both MO and BTB on lignin were found to follow a PSO kinetic model, with rates of 6.84 x 10-3 g·mg-1·min-1 and 0.69 g·mg-1·min-1, respectively. Langmuir, Freundlich, Dubinin-Radushkevich (DR), Brunauer-Emmett-Teller (BET), Flory Huggins (FH), and Temkin adsorption isotherm models were then used to determine the appropriate equilibrium adsorption model for both substrates. Based on the calculations performed, the Temkin model best described the adsorptive removal of both MO and BTB. Based on the Temkin model, the adsorption processes of both MO and BTB were found to occur spontaneously, with equilibrium rate constants of 0.083 L·mg-1 and 0.012 L·mg-1, respectively.

A critical assessment of the Flory-Huggins (FH) theory to predict aqueous two-phase behaviour

This article provides an analysis on published models used to calculate phase separation in aqueous two-phase systems (ATPS) based on Flory-Huggins (FH) theory, in terms of problem formulation and mathematical solving algorithm. An integrated algorithm is presented, showing different mathematical approaches of using the FH theory. The algorithm involves the estimation of interchange energy, and the calculation of phase compositions. Based on experimental data, the thermodynamic model can provide a useful framework to perform a sensitivity analysis on parameters, in order to understand the influence of salt type, polymer molecular mass, and ionic strength on phase separation. However, this model, restricted to entropic and enthalpic terms, cannot quantitatively describe the data. This occurs mainly because of the strong influence of random experimental errors on the estimation of interchange energy and FH not being an exact description of phase separation in salt based ATPS. After providing a literature overview and mathematical analysis, we bring to the field the application of the FH theory for selecting ATPS and its limitations.

Amino acids, polyols and soluble fibres as sugar replacers in bakery applications: Egg white proteins denaturation controlled by hydrogen bond density of solutions

In this paper we demonstrate that the denaturation behavior, i.e. Tden, of egg white proteins in sugar and sugar replacer solutions is explained by the volumetric density of hydrogen bonds in the solutions, i.e. nOH,eff. The validity of the presented approach is demonstrated using 18 solutions comprising single compounds as well as 7 ternary/quaternary mixtures. Different classes of plasticizers are used at various concentrations and at various ratio with proteins. Sweet amino acids such as l-proline and glycine are included as novel alternatives to polyols. The experimental data are modelled with the Flory-Huggins (FH) theory for biopolymer melting. For such purpose, solutions are treated as a single solvent, which is described by the effective volume fraction of the solvent Φw,eff (⁓nOH,eff). Overall, the FH model can well describe the denaturation behavior of egg white proteins in sugar and sugar replacer solutions up to 30% concentration. Deviations from the model become particularly evident at high sugar concentrations (i.e. 50%), which relate to conditions of phase separation in a protein-rich and sugar-rich domain. In such conditions, Φw,eff does not reflect the composition of the solvent around the proteins. An elevation in Tden is observed due to a reduction in hydrogen bond density in the protein-rich domain. The results indicate that phase separation is driven by both the concentration and the molar volume density of effective hydroxyl groups NOH,s/vs of the plasticizers or plasticizer mixtures. Finally, the proposed approach can predict key phase-transitions which result in protein network formation in pound cake baking.

Thermodynamic aspects of the preparation of amorphous solid dispersions of Naringenin with enhanced dissolution rate.

Amorphous ternary solid dispersions of poorly water-soluble Naringenin (NRG) in Poloxamer 188 (POX) and Neusilin US2 (NSL) were prepared in a Hot- Melt Extruder (HME) using the principle of Low-Temperature Solubilization (LTS). Before HME, the NRG-POX solid-state interaction was investigated using Flory Huggins (F-H) theory. Construction of the composition-phase diagram showed Gibbs free energy to be negative close to the melting temperature of NRG, indicating a miscible system. The temperature-composition phase diagram provided insights on the phase behavior of the active-polymer solid dispersion system. The interactions and phase behavior predicted within the framework of the F-H theory were further investigated using Differential Scanning Calorimetry (DSC), X-Ray Diffraction (XRD), Hot Stage Microscopy (HSM) and Fourier-transform infrared spectroscopy (FT-IR). Based on the findings, amorphous solid dispersions of NRG were prepared via HME, which demonstrated a significant increase in the dissolution rate (p≤0.05). The enhancement of the dissolution rate is due to conversion from crystalline to amorphous form, as confirmed by DSC and XRD. The amorphous NRG prepared in the current study exhibited a release of 77% at the end of 2h, which is an increment of 250% from that of pure crystals.

Predicting Solubility of Small Molecules in Macromolecular Compounds for Nanomedicine Application from Atomistic Simulations

AbstractSolubility of small molecules in macromolecular compounds is of fundamental importance for a number of applications, including the growing field of nanomedicine. Here, approaches for in silico solubility predictions based on atomistic models are evaluated. A computationally efficient atomistic simulation procedure based on the concept of inherent structures is proposed for statistical sampling of polymer conformations. Comprehensive test simulations of several polymers and common solvents confirm the accuracy of the procedure for calculation of physicochemical properties such as cohesive energy densities, which along with the Hansen solubility parameters and the Flory–Huggins (FH) theory facilitate rapid, qualitative solubility predictions. However, the FH theory fails to model specific interactions such as hydrogen bonding. Therefore, more accurate predictions are obtained employing the perturbed hard sphere chain (PHSC) equation of state (EOS). As test case, aqueous poly(ethylene oxide) (PEO) solutions revealing strong hydrogen bonding are used. The physicochemical properties including the PEO‐water phase diagram calculated by the PHSC EOS show good agreement with experimental observations. Consequently, the combination of qualitative predictions using the FH theory for rapid prescreening with computationally more demanding parameterization of the PHSC EOS provides a promising tool for in silico solubility predictions with potential applications in nanomedicine.

Molecular dynamics simulation of polystyrene copolymer with octyl short-chain branches in toluene.

In this study, dimensional, conformational and dynamic behaviors of a short-chain branched styrene/1-octene copolymer chain with different 1-octene percentages, i.e., 0, 2, 4 and 6%, in toluene are investigated at the temperature of 298.15K via molecular dynamics simulation. The chain dimensions and flexibility in the solvent are evaluated by calculating the radius of gyration (Rg), end-to-end distance (<r0>), surface area (Ach), and volume (Vch) of the copolymer chain. The mean square displacement (MSD) and diffusivity coefficient for each copolymer chain are measured to determine its dynamic behavior and mobility in aromatic media. To consider the effect of increasing the 1-octene co-monomer percentage on the copolymer chain affinity to the solvent molecules, the interaction energy (Eint) and Flory-Huggins (FH) interaction parameter are calculated for each equilibrated solution model. The simulation results indicate that the co-monomer level increment in the copolymer structure reduces the chain Rg amount and its interaction with the solvent. The <r0> of the chain increases up to 4% co-monomer content, while further co-monomer content decreases the <r0> value. Additionally, the viscosity of the equilibrated dilute solutions is calculated via non-equilibrium molecular dynamics simulation (NEMD). Moreover, the steric hindrance of the copolymers and the solvent molecules capturing in the dilute solution is determined via radial distribution function (RDF) analysis. Helmholtz free energy and the system entropy changes are calculated to evaluate the tendency of the copolymer to the solvent molecules and its dilute solution irregularity, respectively. Graphical abstract The figure shows the variations trend of the poly(styrene-co-1-octene) chain dimensions in toluene aromatic solvent by increasing the 1-octene content (x), after the equilibration state. Red and blue colors represent the carbon atoms of the copolymer chain backbone and 1-octene side chains, respectively. The styrene rings and the hydrogen atoms of the chains were removed for better view.

Evaluation of different thermodynamic models in predicting asphaltene precipitation: A comparative study

One of the major issues in the oil industry is asphaltene precipitation. Modeling asphaltene precipitation is still considered as a complex problem due to various characteristics of different heavy components existing in the crude oil. Thermodynamic models have been found as accurate models for studying asphaltene precipitation in the past few years and a great deal of effort has been devoted to model this process by using different empirical models and equations of state. In this study, the obtained results of asphaltene precipitation from different models based on perturbed-chain statistical associating fluid theory (PC-SAFT), cubic-plus-association (CPA), solid model, Flory-Huggins (FH), and the modified Flory-Huggins (MFH) are compared and their accuracy and reliability are analyzed in detail. For this purpose, twelve crude oil types with different characteristics and asphaltene precipitation behavior are used. Additionally, the performance of the introduced models in predicting asphaltene precipitation during gas injection into the studied oil is investigated. Results demonstrated that PC-SAFT and CPA models have the highest accuracy for both precipitation estimation and behavior trend prediction. Afterward, sensitivity analysis is performed by using Monte-Carlo algorithm for better understanding of the effect of different adjusting parameters, which were used during the tuning process, on each model outputs. Results indicated that cross-association energy between asphaltene and heavy component (HC), self-association energy of asphaltene, and binary interaction coefficient between asphaltene and CO2 are the most sensitive tuning variables for PC-SAFT, CPA, and solid models, respectively. Finally, the CPU times of various models for simulating this process were compared. This comparison showed that the PC-SAFT model has more computational time due to the involved iterative processes for phase equilibrium calculations.

Insights into the miscibility of polymethyl methacrylate (PMMA) and nile blue oxazone (NBO) flurophores: tacticity and chain length aspects

Polymethyl methacrylate (PMMA) based florescent nanoparticles are noteworthy carriers that may be explored for the delivery of numerous anti-cancer and anti-viral drugs. Particularly, the PMMA-nile blue oxazone (NBO) carriers are one of the most frequently used fluorescent probes. Despite various PMMA-based cargos being explored for drug delivery, the spatial arrangement of the methyl and ester groups on the PMMA chains with respect to the encapsulated agent remains a largely unexplored area.In the present work Molecular dynamics simulation and docking studies were carried out to explore the effect of chain length of PMMA and its tacticity on its miscibility with NBO dye molecules. Energetic behavior of the modeled chains was assessed using COMPASS force field. Total potential energy of the chains increased as their length increased. The total potential Intermolecular energy of the isotactic chains was higher as compared to their syndiotactic counterparts, for all the chain lengths considered unlike the intramolecular energy, which was higher for syndiotactic chains. Flory huggins interaction parameter (χ) was calculated for polymer chains of varying lengths and tacticities, with respect to NBO. Interaction parameter increased with increase in the chain length of the polymer chains, which indicated superior interaction with smaller chains. Syndiotactic chains showed strongest interactions with the dye molecule for all the chain lengths of the polymer, whereas isotactic chains exhibited the weakest interactions. Binding energy analysis validated the patterns obtained from flory huggins theory and also established that the polymer chains had higher propensities to self- assemble within themselves, as compared to interactions with NBO molecules. Analysis of the radius of gyration of the polymer chains in the PMMA- NBO complexes, at the end of dynamics run, exhibited that the syndiotactic chains formed smallest coiled structures while the isotactic chains formed the largest coiled structures. Flexibility of the polymer chains was calculated by determining the ratio of the radius of gyration at beginning and at the end of simulation run. Here, isotactic chains were found to have maximum flexibility, followed by atactic and syndiotactic chains. These results were more coherent when the calculations were performed on larger systems, differing in the relative number of PMMA chains and NBO molecules.

In-situ changes of thermo-mechanical properties of poly(lactic acid) film immersed in alcohol solutions

Poly (lactic acid) (PLA) has properties suitable for many applications. However, PLA's properties are affected by environmental conditions. In this study, the glass-rubber transition temperatures (Tg) of PLA films were measured during immersion (i.e., in-situ) in pure alcohols and alcohol aqueous solutions using a dynamic mechanical analysis technique. The Tg of PLA decreased when immersed in alcohols. For pure aliphatic alcohols, the Tg reduction became smaller as the number of carbons (C1–C10) in the alcohol main chains increased. The Fox equation and the Hansen solubility parameters (HSP)/Flory-Huggins (FH) model were used to explain the Tg reduction. The relationships explained the interactions between PLA and pure alcohols with small molecules (C1–C8), but bigger pure alcohols (C9–C10) did not fit the prediction. The chemical isomerism in pure propanol (i.e., propan-1-ol and propan-2-ol) did not affect the Tg reduction. The Tg reduction in propan-2-ol aqueous solutions was concentration dependent although the partition coefficients based on the HSP and the FH parameters did not fit this relationship. The in-situ immersion of PLA in alcohol solutions could be used to evaluate the change in Tg from the Tg of dry PLA.

Salt-induced LCST-type thermal gelation of methylcellulose: quantifying non-specific interactions via fluctuation theory.

What drives the phase separation of water-soluble polymers in the presence of electrolytes was quantified on a molecular scale via statistical thermodynamic fluctuation theory. Quantifying polymer-water and polymer-salt interactions enabled us to identify the dominant interaction for phase separation. As a model system, the lower critical solution temperature (LCST) type thermal gelation of methylcellulose (MC) in aqueous salt solutions was chosen. The Kirkwood-Buff integrals for intermolecular interactions, calculated from the published calorimetric and volumetric data, showed that (1) the accumulation of salts around MC molecules (favourable interaction between salts and MC) inhibits thermal gelation and the depletion of salts from MC (unfavourable interaction between salts and MC) promotes the gelation, and (2) this salt-MC interaction is the dominant factor (50-100 times stronger than the water-MC interaction). This insight from the fluctuation theory is at odds with the age-old consensus regarding the driving force of thermal gelation: water structure change in the presence of salts induces the promotion or inhibition of thermal gelation. However, our conclusion is founded upon the ability of the fluctuation theory to quantify water-MC and salt-MC interaction independently via the Kirkwood-Buff integrals. Flory-Huggins (FH) theory, on the contrary, could not separate these two interactions owing to the lack of a thermodynamic degree of freedom because the lattice solution is assumed to be fully packed. In addition, the dominant contribution from salt depletion poses difficulty for the χ parameter, which is essentially the difference of contact energies. Our approach, requiring calorimetric and volumetric data alone as input, provides a simple and versatile method towards elucidating the effect of cosolvents on biopolymer phase separation of physiological importance.

Rivaroxaban polymeric amorphous solid dispersions: Moisture-induced thermodynamic phase behavior and intermolecular interactions

The present study evaluates the physical stability and intermolecular interactions of Rivaroxaban (RXB) amorphous solid dispersions (ASDs) in polymeric carriers via thermodynamic modelling and molecular simulations. Specifically, the Flory-Huggins (FH) lattice solution theory was used to construct thermodynamic phase diagrams of RXB ASDs in four commonly used polymeric carriers (i.e. copovidone, coPVP, povidone, PVP, Soluplus, SOL and hypromellose acetate succinate, HPMCAS), which were stored under 0%, 60% and 75% relative humidity (RH) conditions. In order to verify the phase boundaries predicted by FH modelling (i.e. truly amorphous zone, amorphous-amorphous demixing zones and amorphous-API recrystallization zones), samples of ASDs were examined via polarized light microscopy after storage for up to six months at various RH conditions. Results showed a good agreement between the theoretical and the experimental approaches (i.e. coPVP and PVP resulted in less physically-stable ASDs compared to SOL and HPMCAS) indicating that the proposed FH-based modelling may be a useful tool in predicting long-term physical stability in high humidity conditions. In addition, molecular dynamics (MD) simulations were employed in order to interpret the observed differences in physical stability. Results, which were verified via differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FTIR), suggested the formation of similar intermolecular interactions in all cases, indicating that the interaction with moisture water plays a more crucial role in ASD physical stability compared to the formation of intermolecular interactions between ASD components.

Phase Diagrams of n-Type Low Bandgap Naphthalenediimide-Bithiophene Copolymer Solutions and Blends.

Phase diagrams of n-type low bandgap poly{(N,N′-bis(2-octyldodecyl)naphthalene -1,4,5,8-bis(dicarboximide)-2,6-diyl)-alt-5,5′,-(2,2′-bithiophene)} (P(NDI2OD-T2)) solutions and blends were constructed. To this end, we employed the Flory–Huggins (FH) lattice theory for qualitatively understanding the phase behavior of P(NDI2OD-T2) solutions as a function of solvent, chlorobenzene, chloroform, and p-xylene. Herein, the polymer–solvent interaction parameter (χ) was obtained from a water contact angle measurement, leading to the solubility parameter. The phase behavior of these P(NDI2OD-T2) solutions showed both liquid–liquid (L–L) and liquid–solid (L–S) phase transitions. However, depending on the solvent, the relative position of the liquid–liquid phase equilibria (LLE) and solid–liquid phase equilibria (SLE) (i.e., two-phase co-existence curves) could be changed drastically, i.e., LLE > SLE, LLE ≈ SLE, and SLE > LLE. Finally, we studied the phase behavior of the polymer–polymer mixture composed of P(NDI2OD-T2) and regioregular poly(3-hexylthiophene-2,5-dyil) (r-reg P3HT), in which the melting transition curve was compared with the theory of melting point depression combined with the FH model. The FH theory describes excellently the melting temperature of the r-reg P3HT/P(NDI2OD-T2) mixture when the entropic contribution to the polymer–polymer interaction parameter (χ = 116.8 K/T − 0.185, dimensionless) was properly accounted for, indicating an increase of entropy by forming a new contact between two different polymer segments. Understanding the phase behavior of the polymer solutions and blends affecting morphologies plays an integral role towards developing polymer optoelectronic devices.