Modified Flory-Huggins Model Research Articles

Effect of thermodynamic instability on viscous fingering of binary mixtures in a Hele-Shaw cell

The coupled effects of thermodynamic and hydrodynamic instabilities are studied during viscous fingering (VF). We introduced a modified Cahn–Hilliard phase-field model in conjunction with the Korteweg force in the classical VF model and derived consistent governing equations. The free energy of the partially miscible system is described using a modified Flory–Huggins model, which allows us to investigate the temporal evolution of spatial inhomogeneities. The mass flux in the Cahn–Hilliard equations is modified according to modern diffusion theory. The governing equations have been solved through an in-house model implementation using the COMSOL multiphysics software. We successfully demonstrated the transition from the finger-like structures to the droplet formation during spinodal decomposition as demonstrated experimentally in the literature. Our results are also in agreement with earlier numerical results obtained using a classical Landau type mixing energy. We further systematically studied the effects of the Margules parameter (interaction parameter) and the gradient parameter, which is associated to the thermodynamic length scale and capillary number on the VF. Aysmmetric features of the binary mixture are also investigated showing a stronger thermodynamic effect on the system with increasing phase separation and, hence, droplet formation.

Using the Intrinsic Geometry of Binodal Curves to Simplify the Computation of Ternary Liquid-Liquid Phase Diagrams.

Phase diagrams are powerful tools to understand the multi-scale behaviour of complex systems. Yet, their determination requires in practice both experiments and computations, which quickly becomes a daunting task. Here, we propose a geometrical approach to simplify the numerical computation of liquid-liquid ternary phase diagrams. We show that using the intrinsic geometry of the binodal curve, it is possible to formulate the problem as a simple set of ordinary differential equations in an extended 4D space. Consequently, if the thermodynamic potential, such as Gibbs free energy, is known from an experimental data set, the whole phase diagram, including the spinodal curve, can be easily computed. We showcase this approach on four ternary liquid-liquid diagrams, with different topological properties, using a modified Flory-Huggins model. We demonstrate that our method leads to similar or better results comparing those obtained with other methods, but with a much simpler procedure. Acknowledging and using the intrinsic geometry of phase diagrams thus appears as a promising way to further develop the computation of multiphase diagrams.

Extraction of estrogenic pollutants in aqueous solution using poly(lactic acid)

Biologically active estrogenic hormones that may have endocrine disrupting effects on organisms, including humans, have been detected recently in water effluent. Development of cost effective and reliable absorptive extraction methods is an area of active research, not only for applications in pollutant in detection but also for environmental remediation. In this paper a systematic analysis of the extraction of the nano-sized compounds estradiol, estriol. estrone, ethinylestradiol, diethylstilbestrol, mestranol, progesterone, and testosterone using poly(lactic acid) is assessed using atomistic Monte Carlo simulations. This polymer is ubiquitous in 3D filament printing, a common additive manufacturing technique and technology of emerging significance. The configurational spaces of the polymer + estrogenic pollutant systems are investigated. Mixing energies, molecular configurations, and sensitivity of poly(lactic acid) to each estrogenic compound was analysed using a combination of Monte Carlo molecular simulation and a modified Flory-Huggins model. The new predictions reported in this study yield insight into the suitability of this widely used additive manufacturing material for applications related to detecting these pollutants in the environment as well as their removal from contaminated aqueous media.

PEO-PU block copolymer membrane for air dehumidification

Membrane separation was an efficient process for air dehumidification. In this study, an environmentally friendly and low-cost polyethylene oxide (PEO)-polyurethane (PU) block copolymer (Permax232) membrane was prepared successfully using water as solvent. An aqueous polycarbondiimide (PCD) crosslinking agent was added into the membrane to improve its water stability property. The physicochemical properties and the crosslinking mechanism of the membrane were investigated using various analytical methods. Compared with the Permax232 membrane, the cross-linked Permax232 membrane exhibited improved water stability and mechanical properties. The surface roughness of the cross-linked membrane increased, and the intensity of the crystalline peak decreased. The crosslink density increased with the PCD content based on the water swelling method. The modified Flory-Huggins model showed excellent agreement between the crosslink density and water vapor sorption. When the appropriate amount of PCD was added, the Permax232 membrane exhibited a high water vapor permeability of 1.45 × 105 Barrer and a water vapor/N2 selectivity of 8.2 × 104. In addition, the water vapor permeability of the cross-linked Permax232 membrane did not change significantly with increasing temperature at the same humidity.

Lewis Adduct-Induced Phase Transitions in Polymer/Solvent Mixtures.

Functionalization-induced phase transitions in polymer systems in which a postpolymerization reaction drives polymers to organize into colloidal aggregates are a versatile method to create nanoscale structures with applications related to biomedicine and nanoreactors. Current functionalization methods to stimulate polymer self-assembly are based on covalent bond formation. Therefore, there is a need to explore alternative reactions that result in noncovalent bond formation. Here, we demonstrate that when the Lewis acid, tris(pentafluorophenyl) borane (BCF), is added to a solution containing poly(4-diphenylphosphino styrene) (PDPPS), the system will either macrophase-separate or form micelles if PDPPS is a homopolymer or a block in a copolymer, respectively. The Lewis adduct-induced phase transition is hypothesized to result from the favorable interaction between the PDPPS and BCF, which results in a negative interaction parameter (χ). A modified Flory-Huggins model was used to determine the predicted phase behavior for a ternary system composed of a polymer, a solvent, and a small molecule. The model indicates that there is a demixing region (i.e., macrophase separation) when the polymer and small molecule have favorable interactions (e.g., χ < 0) and that the phase separation region coincides well with the experimentally determined two-phase region for mixtures containing PDPPS, BCF, and toluene. The work presented here highlights that Lewis adduct-induced phase separation is a new approach to functionalization-induced self-assembly (FISA) and that ternary mixtures will undergo phase separation if two of the components exhibit a sufficiently negative χ.

Molecular Dynamics Simulations of Molecular Diffusion Equilibrium and Breakdown Mechanism of Oil-Impregnated Pressboard with Water Impurity.

The water molecule migration and aggregation behaviors in oil-impregnated pressboard are investigated by molecular dynamics simulations in combination with Monte Carlo molecular simulation technique. The free energy and phase diagram of H2O-dodecylbenzene (DDB) and H2O-cellulose mixtures are calculated by Monte Carlo technique combined with the modified Flory-Huggins model, demonstrating that H2O molecules can hardly dissolved with infinitesimal content in cellulose system at temperature lower than 650 K, based on which the oil/cellulose layered structure with water impurity representing three-phase coexistence in oil-impregnated pressboard are modeled and performed for molecular dynamics. The molecular dynamics of H2O/DDB/cellulose three-phase mixture simulating oil-paper insulating system with H2O impurity indicates that DDB molecules can thermally intrude into the cellulose-water interface so as to separate the water phase and cellulose fiber. The first-principles electronic structure calculations for local region of H2O/DDB interface show that H2O molecules can introduce bound states to trap electrons and acquire negative charges, so that they will obtain sufficient energy from applied electric field to break DDB molecular chain by collision, which are verified by subsequent molecular dynamics simulations of H2O−/DDB interface model. The electric breakdown mechanism under higher than 100 kV/m electric field is presented based on the further first-principles calculations of the produced carbonized fragments being dissolved and diffusing in DDB phase. The resulted broken DDB fragments will introduce impurity band between valence and conduction bands of DDB system, evidently decreasing bandgap as to that of conducting materials in their existence space. The conductance channel of these carbonized DDB fragments will eventually be formed to initiate the avalanche breakdown process by the cycle-feedback of injected charge carriers with carbonized channels.

Liquid phase extraction of nanosized biologically active estrogenic pollutants by using an efficient adsorbent

Dangerous nanosized micropollutants and estrogenic hormones which might severely affect the environment are more found in water effluents, recently, and detection of them is of high importance. As the result, reliable and inexpensive absorptive extraction and removal applications are favored. As the second most abundant biomolecule on earth, a lignocellulosic material can be a potential choice as nanosized adsorbent. In this paper, quantum chemistry techniques are employed as the state of the art approach for predictive modeling, to investigate the feasibility of using this material in extraction and removal of eight estrogens including estradiol, estrone, testosterone, progesterone, estriol, mestranol, ethinylestradiol and diethylstilbestrol. Due to nano-scaled dimensions of these pollutants, removing them by using current commercial methods is challenging and a new approach needed to be developed. The mechanism of removing micropollutants from water affluent is based on adsorption. This fact motivated us to simulate the adsorption process, and check how well the adsorbent interact with nanosized micropollutants. In order to evaluate the affinity of lowest energy sites on structure of the lignocellulosic material toward each estrogenic hormones and micropollutants, we carried out configurational bias Monte Carlo search of the configurational space of the lignocellulosic material-estrogenic micropollutants systems according to a simulated annealing schedule. To check the response and sensitivity of the lignocellulosic material to each estrogenic micropollutants, a combination of modified Flory-Huggins model and molecular simulation techniques was used. Evaluation of detachment energy revealed the potential of the lignocellulosic material as a reusable material for removing these compounds in an aqueous media.

Predictive construction of phase diagram of ternary solutions containing polymer/solvent/nonsolvent using modified Flory-Huggins model

The Flory-Huggins (FH) model has been one of the most used models in theoretical calculations which has been proved to be sensitive to values assigned as interaction parameters. In this work, a predictive equation is implemented to implicitly couple the concept of compressible regular solution theory of Ruzette and Mayes into the original FH model to obtain a new concertation-dependent interaction parameter equation. Then, the modified model (m-FH) is applied for construction of phase diagram of ternary solutions containing polymer/solvent/nonsolvent where experimental data for ternary systems were collected from the literature. In order to compare and analyze the model performance, the individual absolute relative deviation (IARD (%)) was used. The m-FH model revealed acceptable accuracy in calculations without prior need for correlation to experimental data.

Measurement and Correlation of Activity, Density, and Speed of Sound for Binary Mixtures of 1-Propanol + Poly(Propylene Glycol) 400, 725, and 1025

The improved isopiestic method was used to measure 1-propanol activity data for several binary mixtures of 1-propanol + poly(propylene glycol) 400 (PPG400)/poly(propylene glycol) 725 (PPG725)/poly(propylene glycol) 1025 (PPG1025) at 298.15 K. The effect of polymer molar mass was studied on the solvent activity and vapor pressure of the studied systems. The results indicate that solvent activity increases with the increasing of the polymer molar mass. These data have been correlated with different activity models including Flory–Huggins (FH), modified Flory–Huggins, NRTL, NRF-NRTL, Wilson, and NRF–Wilson models. The obtained values of standard deviations for the models represent that modified Flory–Huggins model have good agreement with the experimental data. The apparent specific volume, excess specific volume, isentropic compressibility, isentropic compressibility increments, and apparent specific isentropic compressibility quantities were obtained with use of density and speed of sound data in the 1-propanol + poly(propylene glycol) 400/poly(propylene glycol) 725 systems at T = 288.15 to 318.15 K which supplies the strong solute–solvent interactions and more compatibility between 1-propanol with PPG400 rather than the other polymers.

An enquiry on appropriate selection of polymers for preparation of polymeric nanosorbents and nanofiltration/ultrafiltration membranes for hormone micropollutants removal from water effluents

To analyze polymeric nanosorbents and nanofiltration/ultrafiltration membranes for hormone micropollutants removal from water effluents, here an in-through investigation on the suitability and compatibility of various polymers has been carried out. For this work, estradiol, estrone, testosterone, progesterone, estriol, mestranol, and ethinylestradiol were considered. A total number of 452 polymers were analyzed and initially screened using Hansen solubility parameters. The identified good pairs of hormones and polymers then were examined to obtain the equilibrium capacity of hormones removal from water effluents using a modified Flory–Huggins model. A distribution coefficient was defined as the ratio of hormones in water effluent phase and polymer phase. For removal of mestranol, estradiol and ethinylestradiol, no compatible polymer was identified based on initial screening of collected database. Three compatible polymers were identified for estriol. For progesterone, a wide variety of polymers was identified as good matching of polar, dispersion and hydrogen forces contributions can be observed for these pairs. For estrone, only two polymers can be proposed due to the mismatch observed between polar, dispersion and hydrogen forces contributions of other polymers and this hormone. The phase calculations showed that not all the identified good pairs could be used for practical separation applications. The domain of applicability of each good pair was investigated and potential polymers for practical micropollutants removal together with their removal capacity were represented in terms of phase envelops. The theoretical approach follows fundamental chemical thermodynamic equations and then can be simply applied for any system of interest.

Thermodynamic modeling of polyamide-6 (PA-6)/cellulose acetate (CA) blend membrane prepared via casting technique

Abstract Thermodynamic behavior of a ternary system with one low molecular weight component, formic acid (FA) as the solvent, water (non-solvent), and two high molecular weight polymers [polyamide-6 (PA-6) and cellulose acetate (CA)] was investigated using an extended modified Flory-Huggins model. Where, all chemicals were purchased from Leuna Werke AG (Germany). The model was solved by MATLAB SIMULINK software manufactured in the USA. The predicted results from the model explained that the miscibility of the two blend polymers, PA-6 and CA, completed over all compositions at room temperature, and the minimum point where the miscibility of the two polymers completed was in the composition of 0.2 volume fraction of PA-6 at Gibbs free energy change on mixing (ΔGm) of -1.74015 kJ/mole. The critical temperature (Tc) for superiority properties of the polymer blend solution are in the range between the upper critical saturation temperature (UCST) 323K and the lower critical saturation temperature (LCST) 338K. The diffusion model on the solution of the immersion precipitation process in the coagulation bath indicates that the solvent volume fractions increase with time, while the polymer solution volume fraction decreases, due to solvent removal from the polymer solution and membrane formation. According to the mathematical model, it was found that the annealing temperature can affect the densification of the membrane top layer. However, the heat treatment process leads to a decrease in thickness of the membrane bottom layer, as a result of reduced and distributed membrane pores.

Strong polyelectrolyte – Induced mixing in concentrated biopolymer aqueous emulsions

Using a rheo-small angle light scattering methodology, optical microscopy, phase analysis, static light scattering, rheology, and isoelectric focusing (IEF), we studied the effect of a polyelectrolyte (sodium salt of dextran sulfate/DSS/) on phase equilibrium, intermacromolecular interactions and structure of water-inwater biopolymer emulsions. These emulsions resulted from the mixture of a conformationally variable protein chain (alkaline gelatin type B), and a highly branched non-ionic high molecular weight coil (dextran). Addition of DSS to the emulsion leads to its compatibilization and subsequent homogenization in both liquid (at +45 °C) and gel (at +18 °C) states, and to substantial increase in viscosity and moduli (G′, G″). Homogenization is observed at DSS/gelatin weight ratio (q) = 0.04 and 0.08 respectively. Increasing the ionic strength in the resulting single-phase system induces phase separation, showing that DSS-induced compatibilization is reversible. The zeta potential and IEF measurements showed that interaction between DSS and gelatin is weak and results mainly in an increase of the negative charge of gelatin and in a slight shift of its isoelectric point to the acid range. Our results suggest that the change of the total charge of gelatin molecules in the presence of sulfate polysaccharide is the main driving force for compatibilization and mixing. This is in agreement with a modified Flory–Huggins model, in which dissociated counter ions are included as a separate component contributing to the entropy of mixing. The proposed mechanism of strong polyelectrolyte-induced compatibilization could be generalized to other biphasic concentrated protein–polysaccharide mixtures, provided that the capacity of the protein to form large polymer complexes is weak and provided that the polysaccharide does not contain charged functional groups.

Modeling of Osmotic Pressure of Aqueous Poly(Ethylene Glycol) Solutions Using the Artificial Neural Network and Free Volume Flory Huggins Model

In this work, the modified Flory-Huggins coupled with the free-volume concept and the artificial neural network models were used to obtain the osmotic pressure of aqueous poly(ethylene glycol) solutions. In the artificial neural network, the osmotic pressure of aqueous poly(ethylene glycol) solutions depends on temperature, molecular weight and the mole fractions of poly(ethylene glycol) in aqueous solution. The network topology is optimized and the (3-1-1) architecture is found using optimization of an objective function with batch back propagation (BBP) method for 134 experimental data points. The results obtained from the neural network in obtaining of the osmotic pressure of aqueous poly(ethylene glycol) were compared with those obtained from the free volume Flory-Huggins model (FV-FH). The results showed that the modified Flory-Huggins model and also the artificial neural network can accurately predict the osmotic pressure of aqueous poly(ethylene glycol) solutions but the accuracy of ANN is much better than the modified Flory-Huggins model.

Prediction of the Partition Coefficients of Biomolecules in Polymer–Polymer Aqueous Two-Phase Systems Using the Artificial Neural Network Model

In this work, an artificial neural network model was used to obtain the partition coefficients of biomolecules in polymer–polymer aqueous two-phase systems. In the artificial neural network, the partition coefficient of a biomolecule depends on the difference between concentrations of poly (ethylene glycol), dextran in the top and bottom phases, temperature and molecular weights of poly (ethylene glycol), dextran, and the biomolecule. The network topology is optimized and the (6-1-1) architecture is found using optimization of an objective function with sequential quadratic programming (SQP) method for 450 experimental data points. The results obtained from the neural network of the partition coefficients of biomolecules in polymer–polymer aqueous two-phase systems were compared with those from the modified Flory–Huggins model. Comparisons showed that the artificial neural network is 50% more accurate than the Flory–Huggins model in obtaining partition coefficients of biomolecules in polymer–polymer aqueous two-phase systems.

Influence of molar mass of polymer on the solvent activity for binary system of poly N-vinylcaprolactam and water

The water activity in aqueous solution of poly N-vinyl caprolactam with different molecular weights is measured by isopiestic method at T = 308.15 K. The results show that water activity and vapour pressure of poly N-vinylcaprolactam solution increases with increasing the molecular weight. The Flory-Huggins model, the modified Flory-Huggins model and Freed Flory-Huggins equation + NRTL model are used for correlation of the experimental solvent activity. It is found that the Freed Flory-Huggins + NRTL model is better than the others.

Phenomena and Mechanism for Separation and Recovery of Penicillin in Ionic Liquids Aqueous Solution

In this paper, an integrated process based on hydrophilic and hydrophobic ionic liquids is proposed to extract penicillin G frorn its fermentation broth and recover it into fresh water. With the aid of buffer salt, hydrophilic ionic liquids [C(4)mim]BF(4)(1-butyl-3-i-nethylimidazolium tetrafluoraborate) could form an ionic liquids aqueous two-phase systern (ILATPS) and extract penicillin into the ionic liquids-rich phase of ILATPS, while leaving miscellaneous proteins in the ionic liquids-poor phase. Subsequently, hydrophobic [C(4)mim]PF(6)(1-butyl-3-methylimidazolium hexafluoraphosphate) is introduced into the ionic liquids-rich phase of ILATPS, which transfers the system into a hydrophobic ionic liquids phase in equilibrium with a water-phase system (HOILWS). The majority of hydrophilic [C(4)mim]BF4 is transferred into the ionic liquids-rich phase of HOILWS, leaving most of the penicillin in the conjugated water phase. In comparison with the butyl acetate/water system or the polymer- aqueous two-phase system, the integrated ionic liquids system shows several advantages: (1) Penicillin is efficiently extracted into the ionic liquids-rich phase at neutral pH, so the protein emulsification met in the organic solvent system is avoided. (2) Hydrophobic ionic liquids could separate hydrophilic ionic liquids away from the penicillin-containing aqueous phase. Consequently, the trouble for recovering the phase-forming material in the polymer- aqueous two-phase system is overcome. Moreover, the experimental results suggest that the partitioning behaviors of penicillin in ILATPS and HOILWS are different. In ILATPS, the logarithm of the partitioning ratio of penicillin (In K) increases proportionally with the concentration difference of ionic liquids between ionic liquids-rich and liquids-poor phases (A[ionic liquids]), and the partitioning ratio exceeds 1000 at A[ionic liquids] = 2.5 mol/L. While in HOILWS, In K decreases monotonically with A[ionic liquids], and more than 90% penicillin could be recovered from the ionic liquids-rich phase of ILATPS when the mole ratio of [C(4)mim]PF(6)/[C(4)mim]BF(4) exceeds 1. Moreover, the partitioning ratio approaches that in the [C(4)mim]PF(6)/water systern when the [C(4)mim]PF(6)/[C(4)mim]BF(4) ratio in HOILWS is sufficiently large. A modified Flory-Huggins model is proposed to elucidate the partitioning behaviors in the two ionic liquids systems, which emphasizes the key role of energic equilibrium in determining In K ionic liquids solution. In ILATPS, the distance between ionic liquids aggregates is relatively large, which makes the long-range selfenergy dominating the partitioning behaviors of penicillin. In contrast, in HOILWS the distance between ionic liquids aggregates is greatly suppressed, which magnifies the entropic loss and hydration repulsion between ionic liquids aggregates and makes them as determinants for the partitioning of penicillin in HOILWS. The conclusions from this model are validated by a series of experimental observations, including the salt's type and concentration, hydrophobic/hydrophilic ionic liquids ratio, and ionic liquids species.

Application of a new cubic equation of state to computation of phase behavior of fluids and asphaltene precipitation in crude oil

In this study, a new equation of state has been presented based on the perturbation theory. The vapor phase volume, liquid density, saturation pressure enthalpy and entropy of 20 pure components have been calculated by this new EOS. The average absolute deviations of the predicted saturation pressure, liquid density and vapor phase volume are 0.64, 2.69 and 2.390%, respectively. Also, liquid densities of n-alkanes (C 1–C 20) have been estimated by the new EOS whose average absolute deviation is 4.3%. The obtained results have been compared to PR and M–PR equations of state and the accuracy of the new EOS has been approved. Then, the Flory–Huggins model has been modified for prediction of the amount of asphaltene precipitation in crude oil. The estimated amounts of asphaltene precipitation by this model and the new EOS have been compared to the amounts obtained by the Flory–Huggins model and the experimental data. This comparison shows that the modified Flory–Huggins model is more accurate for prediction of asphaltene precipitation in crude oil.

A modified Flory-Huggins model for prediction of asphaltenes precipitation in crude oil

The Flory-Huggins model has been modified to predict the phase behavior of asphaltene precipitation process by adding solvents such as n-C5, n-C6 and n-C7 to an oil sample. The adjustable parameters of this model are calculated by optimization of an objective function and experimental data of asphaltene precipitation. The amount of asphaltene precipitation has been calculated based on the modified Flory-Huggins model compared with the Flory-Huggins model and the experimental data of references. It is shown that the modified Flory-Huggins model can accurate predict the asphaltene precipitation. Also, the differential solubility parameters of asphaltene and oil at different proportions of solvent have been calculated. The results show that the values of this parameter increases when solvent ratio enhancement.

A GENERAL MODEL FOR MULTICOMPONENT TRANSPORT IN NONPOROUS MEMBRANES BASED ON MAXWELL-STEFAN FORMULATION

A “general” model of membrane transport was formulated using the mechanistic Maxwell-Stefan approach and generalized driving forces, which included the contribution from the various internal and external driving forces. Transient models of dialysis and pervaporation were developed that used exactly the same general model to describe the transport through the membrane. In this model, the bulk solution/polymer equilibria were described by a modified Flory-Huggins model, and the concentration dependence of ternary Maxwell-Stefan diffusivities was described by a natural extension of the binary Vignes relationship to a multicomponent system. A notable advantage of the general model lies in the fact that the Maxwell-Stefan diffusivities retain their physical significance irrespective of the number of components present. This offers the opportunity of recovering many of the model parameters from relatively simple binary experiments. The results obtained indicate that the general model is capable of describing the transient dialysis and pervaporation of the {ethanol-water}/silicone rubber system with an identical set of concentration dependent equilibrium and diffusive parameters. The general model provides a solid framework for the theoretical description of diverse processes employing a nonporous polymer as the selective separation barrier.

Effect of metal clusters on the swelling of gold–fluorocarbon–polymer composite films

We have investigated the swelling of acetone in fluorocarbon polymer films doped with different gold concentrations below the percolation threshold. The presence of the gold clusters in the polymer improves the mixing between the polymer and the acetone, which is not a good solvent for this kind of polymer. To explain our results, the stoichiometry and the morphology of the polymer–metal system have been studied and a modified Flory–Huggins model has been developed.