Flory-Huggins Model Research Articles

Theory of nematic-isotropic phase transitions in solutions of rodlike aggregates

ABSTRACT A mean-field theory is introduced to describe phase behaviours for solutions of rodlike aggregates. By combining the Onsager model for rodlike aggregates and the Flory-Huggins model for polydisperse polymer solutions, we derive the free energy for the solutions of the rodlike aggregates. We calculate the mean aggregation number and orientational order parameter of rodlike aggregates. The mean aggregation number jumps at the first-order nematic–isotropic transition (NIT). We also derive the Landau-de Gennes expansion of the free energy and calculate the isotropic-nematic coexistence curves on the temperature-concentration plane. The NIT curves are qualitatively consistent with the experimental results of rodlike aggregates.

Exact analytical solution of the Flory-Huggins model and extensions to multicomponent systems.

The Flory-Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at equilibrium have not been determined analytically, and numerical techniques are required that restrict the theory's ease of application. In this work, we derive an implicit analytical solution to the Flory-Huggins theory of one polymer in a solvent by applying a procedure that we call the implicit substitution method. While the solutions are implicit and in the form of composite variables, they can be mapped explicitly to a phase diagram in composition space. We apply the same formalism to multicomponent polymeric systems, where we find analytical solutions for polydisperse mixtures of polymers of one type. Finally, while complete analytical solutions are not possible for arbitrary mixtures, we propose computationally efficient strategies to map out coexistence curves for systems with many components of different polymer types.

A facile strategy to fabricate stretchable, low hysteresis and adhesive zwitterionic elastomers by concentration-induced polymerization for wound healing

Developing high-efficient wound dressing with a combination of good mechanical toughness, conformal adhesion and multiple functions is important in clinical application yet remains challenge. Herein, a multi-functional zwitterionic elastomer (TASM) was developed by directly evaporating the uniform precursor containing zwitterionic monomer 3-[Dimethyl-[2-(2-methylprop-2-enoyloxy) ethyl] azaniumyl] propane-1-sulfonate (SBMA), α-thioctic acid (TA) and [2-(methacryloyloxy) ethyl] trimethyl ammonium chloride (METAC). It is interesting to find that the originally immiscible SBMA could dissolve well in ethanol with the assistance of TA, while some other zwitterionic still cannot. The underlying reason is revealed through Flory-Huggins model that the mixture of SBMA and TA exhibit a very low mixing free energy, making them successfully dissolve in ethanol. The obtained TASM elastomer exhibited good mechanical performance, robust adhesion, self-healing ability, along with wound monitoring potential. Besides, the elastomer also showed excellent biocompatibilities and efficient anti-bacterial capability. Furthermore, the elastomer worked well in promoting wound healing in both of full-thickness wound and incisions models. Specifically, in the incision model, the elastomer treatment can replace suturing treatment thanks to the strong adhesion, showing great advantages as wound dressing materials. This work could offer new insights into the preparation of PolyTA systems and promote their functionalization and applications.

U(VI) sorption on illite in the Co-existence of carbonates and humic substances

The presence of carbonates or humic substances (HS) will significantly affect the species and chemical behavior of U(VI) in solution, but lacking systematic exploration of the coupling effect of carbonates and HS under near real environmental conditions at present. Herein, the sorption behavior of U(VI) on illite was systematically studied in the co-existence of carbonates and HS including both humic acid (HA) and fulvic acid (FA) by batch technique. The distribution coefficients (Kd) increased as function of time and temperature but decreased with increasing concentrations of initial U(VI), Ca2+, and Mg2+, as well as ion strength. At pH 2.0–10.5, the Kd values first increased rapidly and then decreased visibly, with its maximum value appearing at pH 5.0, owning to the changes in the interaction between illite and the dominant species of U(VI) from electrostatic attraction to electrostatic repulsion. The sorption was a heterogeneous, spontaneous, and endothermic chemical process, which could be well described by pseudo-second-order kinetic and Flory-Huggins isotherm models. When carbonates and HA/FA coexisted, the Kd values always increased first and then decreased as a function of pH, with the only difference for HA and FA being the key pH (pHkey) at which the promoting and inhibiting effects on the sorption of U(VI) onto illite undergo a transition. The carbonates and HS have a synergistic inhibitory effect on the U(VI) sorption onto illite at pH 7.8. FTIR and XPS spectra demonstrated that the hydroxyl groups on the illite surface and in the HS were involved in U(VI) sorption on illite in the presence of carbonates. These results provide valuable data for a deeper understanding of U(VI) migration in geological media.

Eco-friendly corrosion inhibition of steel in acid pickling using Prunus domestica Seeds and Okra stems extracts

The corrosion inhibition process during acid pickling in petroleum industries often employs toxic chemicals, facing stringent environmental regulations. This study explores a sustainable alternative by investigating the inhibitory effects of eco-friendly food waste extracts, namely Prunus domestica seeds (P.S) and Okra stems (O.St), on B7 grade steel corrosion in 1.0 M HCl aqueous solution, simulating an acid pickling environment. The corrosion inhibition efficiency was estimated via both electrochemical methods, including electrochemical impedance spectroscopy and potentiodynamic polarization techniques, and chemical methods, such as weight loss measurements. Fourier transform infrared spectroscopy (FTIR) and Gas chromatography-mass spectrometry (GC-MS) elucidated the extracts' main functional groups and potential chemical constituents. Remarkably, both extracts exhibited a maximum inhibitory efficiency of up to 80 %. Adsorption isotherms were employed to analyze the inhibition mechanisms, including Langmuir and Flory–Huggins models, alongside the Kinetic-thermodynamic model. Activation parameters have been obtained using Arrhenius and transition state equations. The synthesis of the activated complex is characterized as an endothermic process, as evidenced by the positive values of enthalpy of activation (ΔH*). Conversely, negative entropy of activation (ΔS*) values indicate that the activated complex signifies a process of association rather than separation. Quantum chemical calculations identified potential active inhibitor compounds within the extracts. The quantum parameters, including ionization potential, electronegativity, softness, and hardness of the chemical constituents of the extracts, were calculated using DFT with the B3LYP/6–31 G(+) method. This study underscores the innovative approach of utilizing waste food extracts as corrosion inhibitors, addressing environmental concerns while offering practical implications for industrial applications.

Removal of phenol from wastewater using Luffa cylindrica fibers in a packed bed column: Optimization, isotherm and kinetic studies

This research entails a comparison of the effectiveness of unmodified Luffa cylindrica fiber in a fully packed bed (RLCF) and NaOH-modified Luffa cylindrica fiber in another fully packed bed (MLCF) in the context of phenol removal from wastewater. Experimental data obtained through batch adsorption experiments were utilized to determine the most suitable model. It was observed that as the initial concentration of phenol increased from 100 to 500 mg/l, the maximum percentage removal increased from 63.5 to 83.1% for RLCF-PB and from 89.9 to 99.5% for MLCF-PB. The correlation coefficient (R2) was calculated for the Langmuir, Freundlich, Temkin, Harkin-Jura, Halsey, and Flory-Huggins models for both materials. The analysis revealed that the pseudo-second-order model was the most suitable, followed by the Elovich model, with the pseudo-first-order model being the least suitable. The Weber-Morris diffusion model suggested that pore diffusion was the rate-determining step, and diffusion at the border layer was determined to be endothermic, feasible, heterogeneous, and spontaneous. In summary, this study indicates that MLCF-PB is a promising material for the efficient removal of phenol from aqueous solutions.

КОЭФФИЦИЕНТЫ ДИФФУЗИИ И АКТИВНОСТЬ КОМПОНЕНТОВ ВОДНОСПИРТОВЫХ СМЕСЕЙ В ПОЛИУРЕТАНОВЫХ ПЛЕНКАХ НА ОСНОВЕ АМИНОЭФИРОВ БОРНОЙ И ОРТОФОСФОРНОЙ КИСЛОТ

The work carried out studies to determine the diffusion coefficients and activities of water, isopropyl and ethyl alcohols in polymer polyurethane films based on amino esters of boric and orthophosphoric acids at temperatures of 22, 40 and 60 °C. To determine the diffusion coefficients, we used data on the dynamics of sorption of low molecular weight components in the polymers under study, presented in our previous study. To describe the process of swelling of a polymer film, the Fick differential equation was used; the process was represented as unsteady diffusion in a flat plate. The initial condition was the absence of a component in the polymer at the initial moment of time; the solution to the differential equation was the non-stationary field of concentrations of the component in the film. The experimental dependences of changes in the volume-mass concentration of components in the polymer were described using the Heaviside switching function; due to the presence of a maximum in the swelling curve, it is associated with a restructuring of the polymer structure that occurs due to possible relaxation processes. By minimizing the discrepancies between the calculated and experimental values of the concentration versus time dependence, the diffusion coefficients of pure components in AEPA and AEBA films were determined. Based on data on the diffusion of components through polymer films, the separation characteristics of polymers were assessed for their use as a selective layer of pervaporation membranes. Based on swelling data over long periods of time for water-alcohol mixtures of various compositions, the parameters of the Flory-Huggins model were determined for calculating the activities of components in the polymer. It was shown that among the solvents under study, water has the highest diffusion coefficient, and isopropyl alcohol has the lowest, regardless of the type of film (AEPA/AEBA). For all films, there is a tendency for the diffusion coefficient to increase with increasing temperature, regardless of the solvent.

Corrosion inhibitory studies of an eco-friendly thiourea derivative of amino acid on aluminium using 0.1M HCl solution

The inhibition efficiency and corrosion rate of aluminium were investigated at varying temperatures and immersion time using thiourea complex with an organic ligand at concentrations of 0.20, 0.40, 0.60, 0.80 and 1.00 M. The results showed that an increase in the concentration of the complex thiourea led to an increase in the inhibition efficiency, which was attributed to the availability of the proton moiety of the thiourea lost as electron in acidic media. The inhibition efficiency decreased as the immersion time increased with temperature and the largest decrease observed at 333 K due to the distortion of molecular structure of the complex thiourea at high temperatures. The corrosion rate decreased with an increase in immersion time but increased with temperature, possibly due to inhibitor molecular rearrangement. The activation energy of the suppression process of high-concentration thiourea was found to be higher than that of low-concentration, indicating that the adsorption process was triggered by physical adsorption. The formation of a thin film on the metal surface was due to the presence of complex thiourea acted as a barrier to both energy and mass transport, leading to an increase in the activation energy. The adsorption of the thiourea derivatives complex on aluminum was primarily physisorption. The Langmuir, Flory-Huggins, Tempkin, and Dubinin-Radushkevich adsorption isotherm models were investigated with Langmuir found to be the most fitted model based on high R2 values of the model.

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.

Rice Husk for Adsorbing Dyes in Wastewater: Literature Review of Agricultural Waste Adsorbent, Preparation of Rice Husk Particles, Particle Size on Adsorption Characteristics with Mechanism and Adsorption Isotherm

This study aims to evaluate the adsorption characteristics of unmodified natural rice husk particles (sizes of 74, 177, and 500 μm) in adsorbing dyes in wastewater. The adsorption isotherm analysis was performed in batch mode. Turmeric was selected as a model for organic dyes. Ten isotherm models were used to predict and determine the characteristic parameters: Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Flory-Huggins, Fowler-Guggenheim, Hill-de-Boer, Jovanovic, Harkin Jura, and Halsey isotherm models. The adsorption isotherm analysis showed the phenomena that occur during adsorption are physical, with multilayer formation on the surface of the adsorbent and the occurrence of adsorbate-adsorbate repulsive interaction. The pore-filling molecules occur at the largest and medium particle sizes, whereas the small particle size has no pore-filling molecules. This study reveals that the natural rice husk (unmodified) could be employed as a low-cost and effective sorbent for wastewater treatment, supporting current issues in the Sustainable Development Goals (SDGs).

Aggregating fluids under centrifugal fields

We present a general theoretical framework designed to interpret the effect of centrifugation of ternary fluids that exhibit weak aggregation. The model includes a buoyancy term with thermodynamic description given by a Flory-Huggins model of ternary systems containing a hydrotrope. The system octanol-ethanol-water used as a numerical example is one of several ternary systems that exhibit dynamic aggregates even far from the critical point and undergo a spontaneous emulsification upon dilution with water (Ouzo effect). The model proposes an explanation from first principles of an increased responsiveness to the centrifugal fields. We illustrate the usage of this system in intensified extraction efficiency of hydrophobic solutes that is at the basis of the dispersive liquid-liquid extraction, and show that its capabilities can be extended from analytical to continuous preparative extraction.

Electrochemical and Solvent-Driven Swelling in a Conducting Polymer Film

Poly(ethylene dioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) is likely the most widely used conducting polymer and a champion material for emerging electrochemical technologies. However, the fundamental polymer science describing this material in an electrochemical context remains an active area of investigation. We employ in situ UV–vis absorption and in situ spectroscopic ellipsometry to measure changes to a cross-linked PEDOT:PSS film under an applied electrochemical potential. Using multiple component regression data analyses, we find that two polaronic charge carriers and two neutral forms of PEDOT are necessary to adequately describe the data. Systematic studies of swelling of PEDOT:PSS films in a range of non-aqueous solvents demonstrate that a traditional Flory–Huggins model is suitable to describe film thickness changes. Electrochemical oxidation and reduction also cause dramatic thickness changes to PEDOT:PSS films. In-operando spectroscopic ellipsometry shows that film thickness increases upon reduction and decreases during oxidation, indicating that cation transport is of primary importance in the electrochemistry of PEDOT:PSS. The changes in film thickness in response to electrochemically driven swelling can also be approached using a Flory–Huggins approach when a voltage dependence is included in the enthalpy of mixing.

Investigation of Nonidealities through an Extended Flory–Huggins Model of Ionic Liquid Mixtures with Ammonia

The phase behavior of ionic liquids and ammonia is critical due to their application in various fields such as sorption-based heating/cooling cycles and direct ammonia capture. To date, various ionic liquids have been developed and investigated to enhance the solubility of ammonia without compromising the reversibility due to recycling concerns and various thermodynamic models have been used to correlate the experimental vapor–liquid equilibria data. Surely, high ammonia sorption capacities are required and understanding the interaction between ammonia and ionic liquids can lead to synthesizing targeted ionic liquids for ammonia. In this study, we developed an extended Flory–Huggins model on ammonia and imidazolium-based ionic liquid systems, where both combinatorial and residual terms are considered, to understand the interaction between ammonia and ionic liquids. The results showed that the nonidealities in ammonia and imidazolium-based IL mixtures are due to both entropic and enthalpic contributions. Therefore, increasing the size of the IL would not be enough to achieve higher solubilities. A deeper understanding of the molecular-level interaction between ionic liquids and ammonia can be investigated via molecular simulations.

Modeling the Formation of Rigid Polyurethane Foams Using Hydrofluorolefin as Expanding Agent

AbstractPolyurethanes are probably the most versatile among polymers of greater industrial use due to the possibility of being produced in a wide range of density, hardness, and mechanical properties and through different conversion processes. Its synthesis involves a great variety of raw materials and proportions between them. A mathematical model that describes the polyurethane foam formation can be very useful for the development of formulations and in the definition of the processing conditions, avoiding great consumption of time and errors in the development and experiments. The present work studies this process using industrial formulation. The kinetic parameters of the reaction between polyol with isocyanate are determined calorimetrically using the adiabatic temperature rise method, obtaining the values of activation energy 22.2 kJ mol−1 and heat of reaction 91.8 kJ mol−1. Data liquid–vapor equilibrium of the hydrofluorolefin blowing agent in a polyol mixture are obtained and treated with Flory–Huggins model with good agreement with experimental data (deviation of 1.6%). The mathematical model is satisfactory to describe the expanding process in a pilot scale, under different conditions.

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.

Approximate analytical solution to the Flory-Huggins model.

Approximate analytical solution to the Flory-Huggins model.

The influence of spinodal decomposition-based phase separation in a hybrid polymer hole transport layer on electroluminescent quantum dot light-emitting diodes

Phase separation exists in a hybrid hole transporting layer system, i.e., hybrid PVK–TFB layer. A phase diagram based on the thermodynamic Flory–Huggins model is established and confirms the phase separation arises from a spinodal decomposition event.

Miscibility and exchange chemical potential of ring polymers in symmetric ring-ring blends.

Generally, differences of polymer topologies may affect polymer miscibility even with the same repeated units. In this study, the topological effect of ring polymers on miscibility was investigated by comparing symmetric ring-ring and linear-linear polymer blends. To elucidate the topological effect of ring polymers on mixing free energy, the exchange chemical potential of binary blends was numerically evaluated as a function of composition ϕ by performing semi-grand canonical Monte Carlo and molecular dynamics simulations of a bead-spring model. For ring-ring blends, an effective miscibility parameter was evaluated by comparing the exchange chemical potential with that of the Flory-Huggins model for linear-linear polymer blends. It was confirmed that in the mixed states satisfying χN > 0, ring-ring blends are more miscible and stable than the linear-linear blends with the same molecular weight. Furthermore, we investigated finite molecular weight dependence on the miscibility parameter, which reflected the statistical probability of interchain interactions in the blends. The simulation results revealed that the molecular weight dependence on the miscibility parameter was smaller in ring-ring blends. The effect of the ring polymers on miscibility was verified to be consistent with the change in the interchain radial distribution function. In ring-ring blends, it was indicated that the topology affected miscibility by reducing the effect of the direct interaction between the components of the blends.