Polystyrene in cyclopentane: Dilute solution properties from the upper critical to the lower critical solution temperature

Dilute solutions of polystyrene in cyclopentane are studied with four narrow-distribution polymer fractions ranging in molecular weight from 1.6 × 10⁵ to 1.8 × 10⁶. Light scattering (total intensity) and viscosity measurements cover a temperature range spanning both “theta” temperatures: the limiting upper critical solution temperature (19.6°C) and the limiting lower critical temperature (154.5°C). Within experimental uncertainty, chain dimensions are the same at the two theta temperatures. Correlations among second virial coefficients, mean-square molecular radii of gyration, and intrinsic viscosities, are analyzed. Temperature and molecular-weight dependences are correlated satisfactorily in terms of the excluded-volume parameter z that is central to the “two-parameter” theories of dilute solution behavior. The data can also be correlated in the framework of the newer renormalization theories.     

Structural changes of the molecular complexes and consolute phenomena in binary liquid mixtures

Consolute phenomena in the aqueous solutions of the polymers are considered In view of the temperature induced structural changes of the hydrogen bonds between water and functional groups of polymer. The lower and upper critical consolute points are attributed to the appearance of the “critical” concentration of the complexes with one hydrogen bond between single water molecule and functional group of polymer. Namely such kind of the hydrogen bonds are responsible for the formation of the strongly associated water clusters, that may be followed by phase separation. Experimentally observed dependences of the critical consolute temperatures for the aqueous solutions of polyethylene glycol on the molecular weight of polymer and adding of salts are well reproduced in the framework of the proposed model.     

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.     

Molecular modeling of polymers. IV. Estimation of glass transition temperatures

A method is described which allows molecular modeling to be combined with a group additive property model to estimate glass transition temperatures of linear polymers. T_g is assumed to be a function of conformational entropy and mass moments of the polymer. These two molecular properties are estimated in terms of the torsion angle units composing the polymer using conformational energy calculations. A “universal” T_g equation is derived using 30 structurally diverse polymers and multidimensional linear regression analysis. “Designer” T_g equations are also derived specifically for acrylate and methacrylate polymers. The work described here demonstrates how molecular modeling can be combined with group additivity theory to yield open-ended models that are not restricted by lack of requisite group additive parameters and take advantage of three-dimensional molecular information.     

Group contribution methods for molecular mixtures. III. Solution of groups tested via computer simulation

In this paper computer simulation results for model molecular fluids are used to test ideas underlying group contribution methods. The focus of attention is on the extent to which group contributions in one fluid (or two) can be used to estimate properties in other mixtures. This study is based on group—group distribution functions that were introduced in the first paper in this series.We propose two versions of an approach to a ”solution of groups“: a one-fluid theory and a two-fluid theory. The one-fluid theory subdivides into two forms and both result in group contributions to the residual internal energy that are independent of composition. The strong form of the one-fluid theory fails in comparisons with simulation data, but the weak form reliably predicts residual internal energies at low temperatures and low-to-moderate densities. The two-fluid version of the theory is somewhat better at estimating residual and excess internal energies.     

Surface tension of water droplets upon homogeneous droplet nucleation in water vapor

A method has been proposed for determining interfacial free energy from the data of molecular dynamics simulation. The method is based on the thermodynamic integration procedure and is distinguished by applicability to both planar interfaces and those characterized by a high curvature. The workability of the method has been demonstrated by the example of determining the surface tension for critical nuclei of water droplets upon condensation of water vapor. The calculation has been performed at temperatures of 273–373 K and a pressure of 1 atm, thus making it possible to determine the temperature dependence of the surface tension for water droplets and compare the results obtained with experimental data and the simulation results for a “planar” vapor–liquid interface.     

Liquid-liquid equilibria and theta temperatures in homopolymer-solvent solutions from a perturbed hard-sphere-chain equation of state

The perturbed hard-sphere-chain (PHSC) equation of state is used to calculate liquid-liquid equilibria of binary nonpolar solvent/homopolymer systems exhibiting both an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST). Systems studied include polyisobutylene, polyethylene, and polystyrene solutions. Equation-of-state parameters of homopolymers are obtained by regressing the pressure-volume-temperature data of polymer melts. In polymer solutions, however, theory overestimates the equation-of-state effect which causes the LCST at elevated temperature. To correct the overestimated equation-of-state effect, an empirical adjustable parameter is introduced into the perturbation term of the PHSC equation of state. An entropy parameter is also introduced into the Helmholtz energy of the mixture to correlate quantitatively the dependence of critical temperatures on polymer molecular weight. For systems exhibiting a LCST, two adjustable parameters are required to obtain quantitative agreement of theoretical critical temperatures with experiment as a function of polymer molecular weight. For systems exhibiting both an UCST and a LCST, three adjustable parameters may be necessary. The need for so many empirical binary parameters is probably due to the oversimplified perturbation term which is based on the mean-field assumption. © 1996 John Wiley & Sons, Inc.     

Research on Configuration of Polymer Molecular Aggregate and Its Reservoir Applicability

This article researches the effect of configuration of polymer molecular aggregate on the performance of polymer solution and its reservoir applicability, taking configuration of polymer molecular aggregate, first normal stress difference, resistance coefficient, residual resistance coefficient, and oil recovery as the evaluation indexes, guided by physical chemistry, polymer materials science, and reservoir engineering, by means of chemical analysis, instrument detection, and physical simulation. Results show that the apparent viscosity of polymer solution is closely related to the configuration of molecular aggregate. However, that reflects neither the transporting and migrating ability of molecular aggregate in porous media nor the applicability of polymer solution for reservoir core pore. Compared with “linear-branched chain” polymer, network polymer has a regional “laminated-net” structure, which has a stronger ability to adsorb and wrap hydrone, when deformation occurs, internal friction of which is larger, and apparent viscosity of which is higher with isoconcentration. Changing the configuration of molecular aggregate can enhance the tackify performance of polymer, but crosslinking or association degree must be controlled properly. Otherwise, the applicability of polymer solution for reservoir core pore will become poor, thus influencing the oil incremental effect of polymer flooding.     

Stability conditions for the solutions of the hartree-fock equations. VII. Stability of some closed-shell nonalternant systems

The instabilities of the solutions to the Hartree-Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry-adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off-diagonal charge-density wave (CDW ) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked-ethylenic (bond alternating) structure is obtained.     

The state of the art in the rheology of polymers: Achievements and challenges

The state of the art in the rheology of polymer fluids (polymer solutions and melts) and filled composites is reviewed. This review includes two parts: analysis of the basic principles for the construction of rheological constitutive equations in terms of the continuum mechanics and finding correlations between the rheological characteristics and molecular structure of polymers on the basis of molecular models. Possible approaches to the formulation of constitutive equations are discussed. Special attention is focused on the correct selection of the form of the elastic potential for rubbery deformations induced under the flow of polymer fluids. The use of a power-law potential leads to the best results. To gain unequivocal results and minimize the number of free constants, viscoelastic characteristics of polymer fluids should be described in terms of a continuous relaxation spectrum as a power-law function limited by the maximum relaxation time. To solve the boundary problems by the selected constitutive equation, analysis of the dynamic stability is required, because the combination of viscosity and elasticity controls the limits of flow upon shear and tensile. Deformation can also lead to changes in the phase state of a polymer system. Furthermore, correct formulation of the boundary conditions is necessary because, in many cases, polymer fluids and, in particular, filled materials tend to efficient slip along walls. The existing molecular models adequately describe the characteristics of monodisperse polymers; however, on passing to polydisperse polymers, the additional use of semiempirical approaches is required. The modern level of experimental studies allows test measurements over a wide range of deformation rates, frequencies, and temperatures. However, in this field, the mainstream tendency in experimental studies is concerned with hybrid methods, which combine direct rheological measurements with optical observations of local structure and its evolution in the material. In this case, various physical principles of measurements are applied. In recent years, much interest has been focused on studying polymer compositions containing nanosized fillers, which are able to produce their structures in melt.     

Mechanical structures in polymer melts. II. Roles of entanglements in viscosity and elastic turbulence

Current theories of polymer flow processes often sacrifice realistic molecular models for simplicity of their mathematical equations. An analysis of what might happen to molecules of more realistic sizes and shapes under shear flow, shows the importance of the rapid Brownian motion of chain segments, the elastic deformations of polymer random coils, and the dissipation of this elastic random coil energy by the relatively slow slippage of the chains past each other at a few entanglements where steric hindrance causes long relaxation times. This makes the energy loss depend on the time at each local deformation, and not on the overall shear rate. At high shear rates this model leads to “cluster flow” and low loss cyclic deformations, rather than the high loss processes of steady-state shear. This model gives reasonable qualitative explanations for many anomalous flow properties, and it has predicted new effects that have since been observed.     

The validity of the “few-level” approximation in gaseous relaxation phenomena

The Bloch equations including damping are formulated for a molecular system excited by incident radiation. In contrast with a previous treatment the present formalism gives an intuitively satisfactory form of relaxation terms. A three-level system irradiated by a single oscillating field is specifically considered, and using this manifold as a model for a two-level system immersed in a heat bath, the problem of “embedding” a pair of levels connected by radiation within a multi-level manifold is treated. A brief discussion of transient solutions to the Bloch equations is included.     

Thermodynamics of Swelling of Poly(N-vinylpyrrolidone)-Poly(ethylene glycol) Complex Due to Water Sorption

The deformation of sorbent caused by the sorption is new method of quantitative investigation “in situ” of interaction in system host-quest. The deformation of PVP-PEG complex, ϕ_PEG=0.36 and ϕ_PEG=0.20 due to water sorption has been studied by the measuring of the relative elongation of the polymer samples and the isotherms of water sorption simultaneously. The investigation of the sorption deformation gives the possibility of direct estimation of polymer sample free volume and it's variation during sorption, also the variation of Gibbs energy of system due to sorption according to the vacancy solution theory. The glassy-plastic state transition of polymer during water sorption has been observed.     

On the nature of phase separation of polymer solutions at high extension rates

Experiments with stretching moderately concentrated polymer solutions have been carried out. Model experiments were carried out for poly(acrylonitrile) solutions in dimethyl siloxane. Just the choice of concentrated solutions allowed for a clear demonstration of a demixing effect with the formation of two separate phases—an oriented polymer fiber and solvent drops sitting on its surface. An original experimental device for following all subsequent stages in the demixing process was built. It combined two light beams, one transverse to the fiber and a second directed along (inside) the fiber, the latter played the role of an optical line. This gives a unique opportunity to observe processes occurring inside a fiber. The process of demixing starts from the volume phase separation across the whole cross section of a fiber at some critical deformation and the propagation of the front of demixing along the fiber. Then a solvent cylindrical skin appears which transforms into a system of separate droplets. New experimental data are discussed based on a comparison of the current different points of view on the phenomenon of deformation‐induced phase separation: thermodynamic shift of the equilibrium phase transition temperature, growth of stress‐induced concentration fluctuations in two‐component fluids, and mechanically pressing a solvent out from a polymer network. The general belief is that a rather specific (so‐called “beads‐on‐a‐string”) structure of a filament is realized in stretching dilute solutions: beads of a polymer solution connected by oriented polymer bridges forming a single object. The situation in stretching moderately concentrated solutions appears quite different: real phase separation was observed. So, the alternative phenomenon to the formation of the “beads‐on‐a‐string” structure has been experimentally proven. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 559–565     

Prediction of phase equilibrium behavior of quasibinary polymer solutions

A chronological review is given of typical contributions which played a role in approaching quantitative predictions of phase equilibria in binary and quasibinary polymer solutions. It describes step by step findings of the variables which govern phase separations in these systems. These variables are temperature, overall polymer concentration, and chain length distribution of the polymer mixture making up the solution. The last variable gives rise to a considerable difficulty in formulating the free energy of quasibinary solutions.     

Upper critical solution temperature phase behavior, composition fluctuations, and complex formation in poly (vinyl methyl ether)/D2O solutions: small-angle neutron-scattering experiments and wertheim lattice thermodynamic perturbation theory predictions

Small-angle neutron-scattering measurements are presented for homogeneous mixtures of poly (methyl vinyl ether) (PVME) and deuterium oxide (D(2)O) at high polymer concentrations and for temperatures lower than the equilibrium melting point of the solvent. The experimental data are analyzed to give values for the second-order compositional derivative of the Gibbs energy and the Ornstein-Zernike correlation length. The experimental data together with earlier SANS data determined at higher temperatures cannot be represented with an extended Flory-Huggins (F-H) interaction function depending on composition and temperatures. The experimental data confirm the existence of a narrow upper critical solution temperature (UCST) miscibility gap at high concentrations in agreement with theoretical predictions of the Wertheim lattice thermodynamic perturbation theory (LTPT). The Wertheim LTPT incorporates the influence of hydrogen bonding and predicts not only the existence of bimodal lower critical solution temperature (LCST) phase behavior but also the occurrence of highly unconventional two narrow adjacent UCST miscibility gaps. Finally, the experimental data do not support the existence of a stable molecular complex at the investigated temperatures and compositions. Even at the lowest investigated temperature, the energy required to induce typical Ornstein-Zernike-like concentration fluctuations is smaller than the thermal energy. Also, in this case, the Wertheim LTPT provides a theoretical basis to understand the formation of polymer solvent associations in PVME/water.     

Modelling rheology and free energy of entangled polymers. State of the art

Significant progress made in recent times on the basic molecular theory of Doi and Edwards for entangled polymers is briefly reviewed. In particular we present a recent version of the theory that is entirely described by a set of differential equations, and is therefore especially useful for simulations of complex flows as encountered in polymer processing. The model also provides an expression for the excess free energy that can be of use to predict the onset of flow-induced crystallisation.     

Rheological properties of aqueous solutions of polyethylene glycols with various molecular weights

The dependences of the kinematic viscosity of dilute aqueous solutions of polyethylene glycols (PEGs) with various molecular weights in the temperature range of 293.15–323.15 K were investigated. The intrinsic viscosity, the Huggins constant, and the activation energy of a viscous flow were calculated for these solutions. Proposals regarding the structure of polymer macromolecules in solution are made. The constants of the Mark-Kuhn-Hauvink equation required to estimate the polymer molecular weights were determined for PEG-water systems at various temperatures.     

Application of Continuous Thermodynamics to the Stability of Polymer Systems. III

Based on the stability theory of continuous thermodynamics for polymer solutions, necessary and sufficient conditions for multiple critical points are derived assuming the segment-molar excess Gibbs free energy to be independent of the distribution function. Equations for calculating double and triple critical points are given. Higher order critical points may be obtained in a successive way. For polymers possessing a Schulz-Flory molecular weight distribution, general conditions for an m-fold critical point are presented.