Phase Diagrams Of Polymer Solutions Research Articles

Modeling Swelling Behavior of Thermoresponsive Polymer Brush with Lattice Density Functional Theory

A key problem in designing thermoresponsive polymer brushes on a solid surface is to find a relation between the targeted thermoresponsive properties and controllable conditions. Usually, a temperature-thickness curve showing the heating-induced swelling behavior of polymer brushes is chosen as the relation by either experimental or theoretical investigation. In this work, a lattice density functional theory (LDFT) developed previously is employed to investigate the temperature-thickness curves for five different types of polymer brushes, where the density profiles of polymer brushes calculated by LDFT are compared directly with simulation. It is found that the thermoresponsive behavior of a polymer brush can be characterized by the bulk phase behaviors of its corresponding polymer solution, including UCST, LCST, both UCST and LCST, closed LOOP and hourglass-shaped, which implies that the bulk phase diagram of polymer solutions can help us to find an appropriate polymer brush for a targeted thermoresponsive behavior. As an example, we show that the swelling behavior of a thermoresponsive polymer brush found in the experiment could be predicted by our LDFT results with the bulk phase diagram of real polymer solution only.

Mapping Phase Diagrams of Polymer Solutions by a Combination of Microfluidic Solution Droplets and Laser Light-Scattering Detection

Conventional mapping of a phase diagram of a polymer in a solvent requires a substantial amount of polymer (e.g., at least of the order of ∼100 mg of narrowly distributed samples with different molar masses) and may take months or even years to reach the true two phase equilibrium at each given temperature, especially when the polymer concentration is high. This is why good phase diagrams of polymer solutions are rare in the literature. To solve such a problem, we developed a Teflon microfluidic device to prepare and store a series of droplets (∼10 nL) at different polymer concentrations inside a glass capillary. The phase transition inside each polymer solution droplet sealed and isolated in immiscible fluorohydrocarbon could be quickly and precisely monitored by a newly developed small angle laser light scattering detector. Using poly(vinyl acetate) (PVAc) in isobutyl alcohol and in benzene as two examples, we demonstrated that a combination of microfluidic device and small angle light scattering enables us to map the phase diagram of a polymer in a given solvent within hours by using only a few mg of the sample because (1) each droplet contains no more than ∼10 μg polymer and (2) the phase-transition induced interchain association inside each droplet can be quickly and sensitively detected. We have demonstrated that two sets of a total of eight precisely mapped phase diagrams of four PVAc fractions in the two solvents can be reasonably scaled together to form a master curve.

Dynamic Crossover Scaling in Polymer Solutions

The crossover region in the phase diagram of polymer solutions, in the regime above the overlap concentration, is explored by Brownian dynamics simulations to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations, our simulation results, and recently reported data on the polymer contribution to the viscosity obtained from rheological measurements on DNA systems support the assumption that there are simple relations between these functions, such that they can be inferred from one another.

Unusual Lower Critical Solution Temperature Phase Behavior of Poly(ethylene oxide) in Ionic Liquids

We describe the LCST-type phase behavior of poly(ethylene oxide) (PEO) dissolved in imidazolium-based tetrafluoroborate ionic liquids (ILs). Phase diagrams were determined by a combination of small-angle neutron scattering (SANS) and cloud point (CP) measurements. Unlike typical LCST phase diagrams of polymer solutions, the PEO/IL phase diagram is either roughly symmetric with a critical composition near 50% polymer or asymmetric with a critical composition shifted to an even higher concentration of PEO. As the molecular weight decreases from 20 500 to 4200 g/mol, the critical temperature (Tc) increases slightly (∼10 °C). However, a larger increase in Tc (27 °C) was observed as the molecular weight decreases from 4200 to 2100 g/mol, likely due to the increasing importance of hydrogen bonds between the −OH end groups of PEO and the fluorine atoms of the anions. This inference is supported by the strong dependence of the phase diagram on the identity of the PEO end groups (hydroxy vs methoxy). Furthermore, ...

Phase Behavior of Polymer‐Containing Systems: Recent Advances Through Computer Simulation

AbstractComputer simulations dealing with the phase transitions and phase diagrams of polymer solutions, polymer mixtures, and polymers in heterogeneous environments are still a methodological challenge, since nontrivial structure occurs from the Angstrom‐scale of covalent chemical bonds to the micrometer scale in the resulting multiphase materials. A brief review of strategies that were developed to deal with these problems will be given, and a few highlights of recent results from the research groups of the authors will be described.magnified image

Exploiting interfacial polarization to detect phase transitions in dilute solutions: Crystallization and melting of P3HT in toluene down to ppm contents

Determination of phase diagrams of polymer solutions with conventional techniques, like differential scanning calorimetry (DSC), is limited to sufficiently high concentrations due to a low signal/noise ratio. Controlling the nanoscale morphology formation upon solution processing of dilute conjugated polymer solutions however requires this information. In this work, we introduce an experimental methodology able to detect phase transitions in solutions over a wide concentration regime, by means of dielectric spectroscopy. We tested the validity of our method for solutions of poly(3-hexylthiophene) in toluene. Apart from providing crystallization and melting temperatures consistent with DSC data for the overlapping sample concentrations, our method turned out to be able to detect phase transition down to trace level mass fractions as low as 10 ppm.

Predicting flow induced change in phase diagram of polymer solutions in simple shear flow

AbstractThe change in the phase diagram of polymer mixtures under flow is an important issue since flow may promote mixing or demixing of the phases in a polymer mixture. This work, compared to previous studies, presents a different approach with special attention to the rheology of polymer solutions and flow conditions. Different approaches including Marrucci's approach in calculating stored elastic free energy (ΔGE) have been reviewed. Marrucci’s equation is obtained based on a fundamental analysis of polymer chains microstructure. The new approach introduces the proper viscoelastic constitutive equations to estimate ΔGE. Selecting the appropriate rheological model is essential to correctly estimate the state of stress and deformation rates due to the flow. Moreover, the parameters of viscoelastic constitutive equations were defined, from the microstructural viewpoint, as functions of composition and temperature in semi-concentrated regions. Finally, flow induced change in the phase diagram of polymer solutions is predicted for a well-defined flow condition (constant shear rate and stress), and the results are compared with the previously reported experimental observations of mixing and demixing.

Towards the Quantitative Prediction of the Phase Behavior of Polymer Solutions by Computer Simulation

AbstractThe phase diagram of polymer solutions (cf. e.g. alkanes dissolved in supercritical carbon dioxide) is complicated, since there are four control parameters (temperature, pressure, monomer volume fraction, chain length of the polymer) and due to the interplay of liquid‐vapor transitions and fluid‐fluid unmixing. As a result very intricate phase diagram topologies can result. An attempt to develop coarse‐grained models that can deal with this task will be described. As usual, the polymers will be modelled as off‐lattice bead‐spring chains, where several chemical monomers are integrated into one effective bond, torsional degrees of freedom being disregarded. But also a coarse‐grained description of the solvent is needed: we show that using a simple point particle with a quadrupole moment and suitable Lennard‐Jones interaction yields a very good description of pure carbon dioxide (better than fully atomistic models with potentials from ab initio quantum chemistry calculations). The strength of the quadrupole moment is taken from experiment, and the Lennard‐Jones parameters are adjusted such that the experimental critical temperature and density is correctly reproduced. This procedure works for other solvents as well, such as benzene. The pure alkane phase diagram is also reproduced by similarly chosen Lennard‐Jones (LJ) potentials among the monomers, and the monomer‐carbon dioxide LJ parameters are chosen from Lorentz‐Berthelot mixing rules. These parameters are then used as input both for Monte Carlo calculations and approximate methods to calculate the equation of state, such as density functional and perturbation theory methods. Apart from the region close to critical points, where mean‐field type methods fail, the analytical calculations agree well with the simulations. The solvent model, in which quadrupolar interactions are explicitly considered, is important in order to obtain a fair agreement with mixture experimental results.

Ultrasonic studies on the phase transition from the dilute‐good to the theta regimes in polymer solution

AbstractThe phase transition from the dilute‐good solvent (I) to the theta (I′) regimes, which does not exist in the earlier phase diagram presented by Flory and has not been detected by common methods such as intrinsic viscosity, was observed clearly by measurements of ultrasonic velocity in the MHz range. Furthermore, ultrasonic absorption measurements revealed that the thermal relaxation, due to local segmental motions, observed in phase I disappeared in phase I′. Ultrasonic methods allow us to ascertain the existence of a second‐order phase transition from phase I to phase I′ above the theta temperature in the phase diagram of polymer solutions. Copyright © 2004 Society of Chemical Industry

Calculation of phase diagram of polymer solution over supercritical fluid region based on the Patterson-Delmas theory of corresponding state

Based on the Patterson-Delmas theory of corresponding state and the equation of state by Flory, the polymer–solvent interaction parameter χ 1 in the Flory–Huggins theory has been calculated over a temperature range including the supercritical fluid region of solvent and a wide range of pressure up to 1.0×10 4 bar. The temperature dependence of χ 1 parameter at constant pressure over the supercritical fluid region is expressed by a parabolic-like with a maximum, and a closed-loop phase diagram is calculated in nonpolar polymer solution by the Flory–Huggins theory and the temperature dependence of χ 1 parameter in this work.

Study of the phase separation in polymer solutions using the pair approximation of the CVM: analytical solution of the problem

The phase diagrams of polymer solutions are studied using the pair approximation of the Cluster Variational Method (CVM). In this model the solvent (oligomers) and the solute (polymers) are chains with different lengths. In particular, the dependence of the phase diagram on the lengths of the components of the mixture, on the lattice, and on the relative size of the components of the mixture is investigated. The critical temperature and the critical concentration are also studied. Some comparison of our results with the Flory and Guggenheim approximations are done for the symmetric case (when oligomer chains and polymer chains have the same length) and the asymmetric case (when oligomer chains and polymer chains have different length). A novel technique to solve the set of equations derived from the CVM is presented, and an analytical solution of the problem is given

Semi‐interpenetrating polymer networks with controllable morphology ‐ arrest of demixing by thermoreversible gelation

AbstractSemi‐interpenetrating polymer networks with well defined morphologies were obtained using a three‐step process, separating morphology formation and polymerization/crosslinking. Different phase textures were formed when (spinodal) liquid/liquid demixing of a solution of atactic polystyrene in methacrylate monomers was arrested by thermoreversible gelation (vitrification) of the polymer‐rich phase at a desired stage. Subsequent UV‐polymerization of the methacrylate allowed to study the morphology by transmission electron microscopy. Phase diagrams of polymer solutions with low and high viscosities are reported. Depending on the initial solution viscosities and the applied cooling conditions, morphologies both with a dispersed as well with a continuous polystyrene phase could be obtained at PS concentrations already below 10 %. Mechanical measurements indicated only partial demixing in the semi‐IPN's.