Thermodynamics Of Polymer Solutions Research Articles

Diffusion mediated thermally induced phase separation for preparing poly(vinylidene fluoride) membranes with enhanced separation performances

Thermally induced phase separation (TIPS) process is an appealing method for preparing poly(vinylidene fluoride) (PVDF) membranes for separation. In this work, we developed a diffusion mediated thermally induced phase separation (d-TIPS) to prepare PVDF membranes with great molecules separation performances. We investigated the thermodynamics of ternary polymer solutions including PVDF, caprolactam (CPL), and Polyethylene glycol (PEG). We controlled liquid–liquid phase separation and the CPL diffusion by adjusting the addition of PEG and molecular weight to modulate the evolution of morphology from spherulitic to bicontinuous structure. The resulting membrane was characterized by morphology, surface chemistry, tensile strength, water contact angle, and perm-selectivity. The membrane was further stretched for enhanced strength, permeance, and rejection. This work provides a fundamental understanding of the diffusion mediated thermally induced phase separation and shows the great potential of PVDF membranes in macromolecules separation.

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis.

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

On the Mechanism and Kinetics of Synthesizing Polymer Nanogels by Ionizing Radiation-Induced Intramolecular Crosslinking of Macromolecules.

Nanogels—internally crosslinked macromolecules—have a growing palette of potential applications, including as drug, gene or radioisotope nanocarriers and as in vivo signaling molecules in modern diagnostics and therapy. This has triggered considerable interest in developing new methods for their synthesis. The procedure based on intramolecular crosslinking of polymer radicals generated by pulses of ionizing radiation has many advantages. The substrates needed are usually simple biocompatible polymers and water. This eliminates the use of monomers, chemical crosslinking agents, initiators, surfactants, etc., thus limiting potential problems with the biocompatibility of products. This review summarizes the basics of this method, providing background information on relevant aspects of polymer solution thermodynamics, radiolysis of aqueous solutions, generation and reactions of polymer radicals, and the non-trivial kinetics and mechanism of crosslinking, focusing on the main factors influencing the outcomes of the radiation synthesis of nanogels: molecular weight of the starting polymer, its concentration, irradiation mode, absorbed dose of ionizing radiation and temperature. The most important techniques used to perform the synthesis, to study the kinetics and mechanism of the involved reactions, and to assess the physicochemical properties of the formed nanogels are presented. Two select important cases, the synthesis of nanogels based on polyvinylpyrrolidone (PVP) and/or poly(acrylic acid) (PAA), are discussed in more detail. Examples of recent application studies on radiation-synthesized PVP and PAA nanogels in transporting drugs across the blood–brain barrier and as targeted radioisotope carriers in nanoradiotherapy are briefly described.

Development of Porous Polyacrylonitrile Composite Fibers: New Precursor Fibers with High Thermal Stability

Polyacrylonitrile (PAN) fibers with unique properties are becoming increasingly important as precursors for the fabrication of carbon fibers. Here, we suggest the preparation of porous PAN composite fibers to increase the homogeneity and thermal stability of the fibers. Based on the thermodynamics of polymer solutions, the ternary phase diagram of the PAN/H2O/Dimethylformamide (DMF) system has been modeled to introduce porosity in the fibers. Adding a conscious amount of water (4.1 wt.%) as a non-solvent to the PAN solution containing 1 wt.% of graphene oxide (GO), followed by wet spinning, has led to the preparation of porous composite fibers with high thermal stability and unique physicochemical properties. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) results elucidate that PAN/GO/H2O porous composite fibers have a higher thermal decomposition temperature, increased residual weight, reduced heat release rate, and higher crystallinity in comparison with the pristine PAN fibers, being a promising precursor for the development of high-performance carbon fibers. The results show a promising application window of the synthesized PAN fibers in electronic and electrochemical devices.

Thermodynamics of real polymer solutions in the new Rényi and Tsallis formalism

The generalized non-ideality factor of systems (GNF) was introduced into the Renyi and Tsallis information entropy equations, and new expressions were obtained for information and thermodynamic entropies with a fractional moment of the order entropy gS and thermodynamic gth nonideality factors. Equations in formalism of Renyi and Tsallis: The equations describe self-organized structures of essentially non-equilibrium systems and can be used in studying the topological and conformational properties of solutions of high-molecular compounds. GNF: where is are relative average characteristics (pi are statistical probabilities) of opposite processes. Factor g varies in the range 0 ≤ g ≤ 2 and depends on which of the competitive processes prevails. An algorithm for calculating the thermodynamic functions of the state of the system under study is presented. The equations are intended for calculating the thermodynamic functions of objects of fractal nature, including real solutions of synthetic and natural highmolecular compounds of plant and animal origin (hyper branched structures, dendrimers, lignins, biological systems, dendrites, systems of internal organs, blood vessels, etc.).

Equation of state modeling and force field-based molecular dynamics simulations of supercritical polyethylene + hexane + ethylene systems

The understanding of polymer solution thermodynamics and characterization of pressure effects on fundamental polymer physics of macromolecular systems is significant in the manufacturing of polyolefins. Consequently, numerous experimental and theoretical efforts have been made towards understanding phase behavior of polymer solutions at elevated pressures. Despite this progress, only limited efforts are directed towards understanding the underlying phenomena behind the influence of high pressure upon the thermophysical properties of ternary polymer solutions at a molecular level. The present paper, therefore, reports on the influence of supercritical ethylene on the density of PE + hydrocarbon solvent system by exploring ternary mixtures of PE + hexane + ethylene for ethylene concentrations up to 10 wt% at varied temperatures and in a pressure range from 100 to 1000 bar via fully-atomistic molecular dynamics (MD) simulations. Additionally, the modified Sanchez-Lacombe equation of state (EOS) model is iteratively solved to capture the pressure, concentration, and temperature dependence of ternary PE solution density. It is shown that the small amounts of ethylene dissolved in the liquid mixtures of PE + hexane significantly decreases the polymer solution density. The presence of unreacted monomer in the solution polymerization process utilized in PE manufacturing was found to substantially lower the PE solution density particularly at the lower end of the investigated pressure range. This noteworthy reduction in mixture density as a consequence impacts design and operation of the liquid-liquid phase separator in manufacturing of PE via solution polymerization. Another key point to bear in mind is that the mixture density exhibits fairly less sensitivity to ethylene amount as external pressure raises. Nevertheless, pressure, solvent composition, and temperature dependence of density display less sensitivity as pressure increases. In relation to the characterization of the impact of addition of ethylene an atomistic-level insight is provided, which proves to be of great value in revealing intermolecular interactions in the binary subsystems of polymer/solvent/monomer. The MD computations are shown to be in excellent agreement with the theoretical EOS model, confirming the validity of the proposed methodology. Furthermore, the adopted OPLS-AA has been found a reliable atomistic force field, which provides detailed molecular information on the thermophysical properties of polyolefin in hydrocarbon solutions. Ultimately, it is demonstrated that the MD simulations complement parametric EOS predictions and costly experimental approaches.

A guide to solution‐based additive manufacturing of polymeric structures: Ink design, porosity manipulation, and printing strategy

AbstractThree‐dimensional (3D) printing of polymer solution is a rising research topic as it can utilize polymers without photoreactivity or melting points. Solution‐based additive manufacturing (SBAM) was recently reported to fabricate polymeric objects by depositing ternary polymeric inks (eg, solutions comprising polymer, volatile solvent, and nonvolatile nonsolvent), which undergo rapid phase inversion upon evaporation of a relatively small fraction of the volatile component, resulting in hierarchically porous filaments (eg, pores of diameters ranging from 2 nm to 10 μm). SBAM is conceptually compatible with any solution‐processable polymer, which significantly extends the 3D‐printable polymeric material spectrum. In addition to the architecture of the printed object, its internal porosity can be manipulated for different applications. Compared with typical direct ink writing of binary polymeric inks, which typically only contain the polymer and a volatile solvent, SBAM is capable of (a) eliminating evaporation‐induced shrinkage, and (b) creating nanopores without the need for templating additives or nanoscale nozzles. The development of SBAM processes involves optimization of polymer solution thermodynamics, rheological engineering and mass transfer control, which makes it challenging to develop an SBAM protocol for a new polymer. This paper provides a practical guide toward the development of ternary polymeric inks, the design of 3D printer hardware for SBAM, and the posttreatment of printed objects for desired porosity. It also discusses solutions to common challenges encountered during this new polymer processing technology. A case study of developing the optimal SBAM protocol for a commercial polyimide is provided to illustrate the process design.

Thermodynamic approach to tailor porosity in piezoelectric polymer fibers for application in nanogenerators

Low power density of polymer piezoelectric nanogenerators is a major hurdle for their application as a potential mode of powering wearable and portable electronic devices. To increase the efficiency, here we suggest use of porous piezoelectric poly (vinylidenefluoride-co-trifluoroethylene) (P(VDF-TrFE)) nanofibers. However, designing a process that allows introduction of pores in the nanometric fibers with a diameter of only several 100 nm, is highly challenging due to the intricate physics of polymer/solvent/anti-solvent interactions. Realization of the porous nanofibers would be a breakthrough in the field of piezoelectric nanogenerators. We presents an elegant approach based on the thermodynamics of polymer solutions to tailor porosity in P(VDF-TrFE) nanofibers. By adding a conscious amount of water, carefully chosen as non-solvent based on the ternary phase diagram of P(VDF-TrFE)/water/solvent, we intentionally induce liquid-phase demixing, which leads to formation of nanopores in the electrospun nanofiber. By calculating the mean composition trajectories, we predict and explain formation of the pores in the nanofibers, and show how little variations in initial water content substantially influences fiber porosity. Nanogenerators based on the porous electrospun P(VDF-TrFE) nanofibers show output power that systematically increases with porosity (with 500 times increase in output power for 45% porous fibers). The enhanced output is due to the reduced effective dielectric permittivity of the nanofibers. We unambiguously show that the voltage generation in nanofibers is of the same origin as in neat piezoelectric P(VDF-TrFE) films and is due to the relaxation of segments within the restricted amorphous phase. Understanding how to form nanopores, would have a major contribution to other fields, ranging from nanoporous membranes, as well as porous polymer structures for triboelectric nanogenerators.

Thermodynamics of star polymer solutions: A coarse-grained study.

We consider a coarse-grained (CG) model with pairwise interactions, suitable to describe low-density solutions of star-branched polymers of functionality f. Each macromolecule is represented by a CG molecule with (f + 1) interaction sites, which captures the star topology. Potentials are obtained by requiring the CG model to reproduce a set of distribution functions computed in the microscopic model in the zero-density limit. Explicit results are given for f = 6, 12, and 40. We use the CG model to compute the osmotic equation of state of the solution for concentrations c such that Φp=c∕c*≲1, where c* is the overlap concentration. We also investigate in detail the phase diagram for f = 40, identifying the boundaries of the solid intermediate phase. Finally, we investigate how the polymer size changes with c. For Φp≲0.3, polymers become harder as f increases at fixed reduced concentration c∕c*. On the other hand, for Φp≳0.3, polymers show the opposite behavior: At fixed Φp, the larger the value of f, the larger their size reduction is.

Thermodynamics of high polymer solutions

Thermodynamics of high polymer solutions

Microporous Polymer Particles via Phase Inversion in Microfluidics: Impact of Nonsolvent Quality.

We investigate the impact of ternary phase behavior on the microstructure of porous polymer particles produced by solvent extraction of polymer solution droplets by a nonsolvent. Microfluidic devices fabricated by frontal photopolymerization are employed to produce monodisperse polymer (P)/solvent (S) droplets suspended in a carrier (C) phase before inducing solvent extraction by precipitation in a nonsolvent (NS) bath. Model systems of sodium poly(styrenesulfonate) (P), water (S), hexadecane (C), and either methyl ethyl ketone (MEK) or ethyl acetate (EA) as NS are selected. Extraction across the liquid-liquid interface results in a decrease in the droplet radius and also an ingress of nonsolvent, leading to droplet phase demixing and coarsening. As the concentration of the polymer-rich phase increases, droplet shrinkage and solvent exchange slow down and eventually cease, resulting in microporous polymer particles (of radius ≃50-200 μm) with a smooth surface. The internal structure of these capsules, with pore sizes of ≃1-100 μm, is found to be controlled by polymer solution thermodynamics and the extraction pathway. The ternary phase diagrams are measured by turbidimetry, and the kinetics of phase separation is estimated by stopped-flow small-angle neutron scattering. The higher solubility of water in MEK results in faster particle-formation kinetics than in EA. Surprisingly, however, the lower polymer miscibility with EA/water results in a deeper quench inside the phase boundary and small phase sizes, thus yielding particles with small pores (of narrow distribution). The effects of droplet size, polymer content, and nonsolvent quality provide comprehensive insight into porous particle and capsule formation by phase inversion, with a range of practical applications.

Characterization of poly(N,N-diethylacrylamide) and cloud points in its aqueous solutions

The mean-square radius of gyration, second virial coefficient and intrinsic viscosity were determined in methanol at 25.0 °C for two types of poly(N,N-diethylacrylamide) (PDEA) samples that were synthesized by radical polymerization in tert-butanol and benzene using azobis(isobutyronitrile) as an initiator. Analyses of these results indicated that the primary structure of both PDEA samples was linear. The cloud points of the two PDEA samples were also determined in aqueous solutions. For the two types of PDEA samples, the cloud point decreased as the weight-average molecular weight Mw of the sample increased, which is in contrast to previously reported results for poly(N-isopropylacrylamide) (PNIPA) samples, even though those samples have the same hydrophobic chain-end groups. In addition, the cloud-point curve of each PDEA sample has a critical point, which has not been previously reported for PNIPA. The critical point shifted to the upper right with decreasing Mw, as predicted by conventional polymer solution thermodynamics. Therefore, the aqueous PDEA solutions exhibited typical phase behavior that is consistent with the lower critical solution temperature type, which is substantially different from that observed for aqueous PNIPA solutions. The cloud point was determined in aqueous poly(N,N-diethylacrylamide) (PDEA) solutions. It was found that the cloud-point curve of each PDEA sample has a critical point and each PDEA solution exhibits phase separation into two liquid phases when the temperature is increased above its cloud point, which has not been previously observed for aqueous poly(N-isopropylacrylamide) (PNIPA) solutions. Therefore, the aqueous PDEA solutions exhibit typical phase behavior of lower critical solution temperature type, which is substantially different from that observed for PNIPA.

Characterization of the Flory-Huggins interaction parameter of polymer thermodynamics

Flory-Huggins theory is the main basis of polymer solution and blend thermodynamics. A key piece of this theory is a parameter quantifying the enthalpic interactions between the components; however, experiments have revealed that this parameter is not composition independent, as originally assumed. This composition dependence has been attributed by some theorists to experimental error; others have tried to explain it based on several competing hypotheses. Here, we use atomistic simulations of isotopic blends based on realistic potentials to study this parameter without making any prior hypotheses. Simulations reveal a composition dependence of this parameter that compares well with experimental data, and serve to verify theoretical relationships between the various forms of this parameter.

Nonequilibrium thermodynamics of dilute polymer solutions in flow.

Modern materials processing applications and technologies often occur far from equilibrium. To this end, the processing of complex materials such as polymer melts and nanocomposites generally occurs under strong deformations and flows, conditions under which equilibrium thermodynamics does not apply. As a result, the ability to determine the nonequilibrium thermodynamic properties of polymeric materials from measurable quantities such as heat and work is a major challenge in the field. Here, we use work relations to show that nonequilibrium thermodynamic quantities such as free energy and entropy can be determined for dilute polymer solutions in flow. In this way, we determine the thermodynamic properties of DNA molecules in strong flows using a combination of simulations, kinetic theory, and single molecule experiments. We show that it is possible to calculate polymer relaxation timescales purely from polymer stretching dynamics in flow. We further observe a thermodynamic equivalence between nonequilibrium and equilibrium steady-states for polymeric systems. In this way, our results provide an improved understanding of the energetics of flowing polymer solutions.

Field theoretic simulations of polymer nanocomposites

Polymer field theory has emerged as a powerful tool for describing the equilibrium phase behavior of complex polymer formulations, particularly when one is interested in the thermodynamics of dense polymer melts and solutions where the polymer chains can be accurately described using Gaussian models. However, there are many systems of interest where polymer field theory cannot be applied in such a straightforward manner, such as polymer nanocomposites. Current approaches for incorporating nanoparticles have been restricted to the mean-field level and often require approximations where it is unclear how to improve their accuracy. In this paper, we present a unified framework that enables the description of polymer nanocomposites using a field theoretic approach. This method enables straightforward simulations of the fully fluctuating field theory for polymer formulations containing spherical or anisotropic nanoparticles. We demonstrate our approach captures the correlations between particle positions, present results for spherical and cylindrical nanoparticles, and we explore the effect of the numerical parameters on the performance of our approach.

Thermodynamics and viscosities of dilute polymer solutions in binary solvents

Experiments aimed at comparison of calculated and experimental intrinsic viscosities of PS and PMMA in some binary solvents used as eluents in chromatography are performed. The intrinsic viscosities are determined in mixed solvents of different thermodynamic qualities, including a θ solvent, in a wide composition range. The analysis of the thermodynamic and rheological theoretical equations for ternary systems allowed the interpretation of anomalies observed on the experimental curves of intrinsic viscosity versus solvent composition.

Stable Free Radical Polymerization in Emulsion: Modeling the Thermodynamics of Monomer Transfer between Droplets and Particles

AbstractA mathematical model is developed from polymer solution thermodynamics and stable free radical polymerization kinetics to predict the monomer swelling behavior of large droplets and small particles that coexist during the seeded polymerization of styrene in emulsion. This model is used to predict the sensitivity of polymerized latex stability (based on the persistence of large particles) to changes in seed particle size and final latex target molecular weight. Simulation results show that the use of small seed particles (diameter ≤ 50 nm) in recipe formulation will lead to polymerization occurring preferentially in the large droplets, and offers theoretical evidence that TEMPO‐mediated ab initio emulsion polymerizations will not be feasible. Our predictions are consistent with experimental evidence suggesting that the presence of large particles leads to the formation of undesirable coagulum in the final product.magnified image

Molecular thermodynamics of mixed-solvent polymer solutions

Following our previous work, we developed a new lattice model for systems containing two solvents and a polymer chain. The chain length of solvent molecules is taken as 1, while that of the polymer is treated as r in the model. Comparison with Monte Carlo simulation data shows the great advantages of this model over the traditional Flory–Huggins theory and the revised Freed theory especially in the critical region. When applied to real systems, it is found that this model also exhibits notable practical value for the engineering application.

Morphology development and characterization of the phase-separated structure resulting from the thermal-induced phase separation phenomenon in polymer solutions under a temperature gradient

This paper studied the morphological development during the fabrication of anisotropic polymeric materials using the thermal-induced phase separation phenomenon (spinodal decomposition) in a model binary polymer solution under a linear spatial temperature gradient using mathematical modeling and computer simulation. The model incorporated the non-linear Cahn–Hilliard theory for spinodal decomposition and the Flory–Huggins theory for polymer solution thermodynamics. Moreover, the slow mode theory and Rouse law were used to account for polymer diffusion. The two-dimensional numerical results showed that an anisotropic morphology was developed when a temperature gradient was imposed along the polymer solution sample. The droplet size and droplet density decrease as temperature increases during the intermediate stage of spinodal decomposition. The spatial temperature gradient, however, had insignificant effect on the droplet shape.

Solvent activity changes and phase separation during crosslinking of coating films

AbstractChanges in solvent activity and thermodynamic stability of a system undergoing crosslinking in the presence of a solvent are modeled by combination of branching theory with thermodynamics of polymer solutions and swelling of a crosslinked polymer. The system is considered as a quasiternary one in which the solvent, polydisperse soluble polymer (sol) and crosslinked network, respectively, represent the components. Crosslinking brings about growth of polymer structures but also changes in polymer‐solvent interactions. The results are compared with onset of phase separation and changes in evaporation rates from films formed from a hydroxy‐functional star oligomer and triisocyanate.