Solutions Of Polystyrene In Cyclohexane Research Articles

Phase Equilibrium and Interfacial Tension of Binary and Ternary Polymer Solutions

The liquid–liquid equilibrium (LLE) and interfacial tensions of binary and ternary polymer solutions of polystyrene in cyclohexane and methylcyclohexane are investigated. The chain length dependent modified double lattice model (MDL-CL) is applied to describe experimental phase diagrams measured by thermo-optical analysis. The proposed model is also combined with the modified density gradient theory to calculate interfacial tension between two coexisting liquid phases of the investigated systems. The calculated results of LLE and interfacial tensions using the MDL-CL model combined with the modified density gradient theory show good agreement with experimental data. The interfacial tension of the ternary system (polystyrene + cyclohexane + methylcyclohexane) is described with the parameters obtained from the binary subsystems (polystyrene + cyclohexane and polystyrene + methylcyclohexane). A comparison of experimental and theoretical phase behaviors and interfacial tensions demonstrates that the theoretic...

Broadband ultrasonic spectrometry of polystyrene-cyclohexane critical mixtures

Mutual diffusion coefficients, shear viscosities, and broadband ultrasonic attenuation spectra in the frequency range 100 kHz to 300 MHz have been measured for solutions of polystyrene in cyclohexane at two degrees of polymerization N and various temperatures near the critical. The exponent y(η) in the power law representation of the critical part in the viscosity deviates substantially from the universal value y(η) = 0.0435: y(η) = 0.028 (N = 288) and y(η) = 0.014 (N = 6242). Also, the adiabatic coupling constant g and the amplitudes ξ(0) and Γ(0) in the power laws of the correlation length and the relaxation rate of fluctuations, respectively, depend on N. This is especially obvious with the relaxation rates, for which Γ(0) = 5.8×10(9) at N = 288 and Γ(0) = 6.1×10(7) with the larger polymer results. A noteworthy feature is the difference between the relaxation rates from the diffusion coefficients and shear viscosities on the one hand and from the ultrasonic spectra on the other. Near the critical temperatures the latter Γ values deviate from power law behavior, indicating a coupling between the concentration fluctuations and structural isomerizations of the polymers.

Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.

The Two Critical Concentrations in Polymer Science

Several years ago Utracki and Simha reported a remarkable independence of molar mass of the ratio of the thermodynamic critical (consolute) concentration and the concentration of incipient coil overlap, also known as “critical” concentration. They investigated solutions of polystyrene in cyclohexane and also found the consolute concentration at the critical temperature to be approximately equal to the average segmental concentration within the coils. Here we supply an explanation for these indisputable experimental findings. To this end we examine three systems for which experimental information about the true consolute state and coil dimensions is available in the literature, viz. cyclohexane/polystyrene, methylcyclohexane/polystyrene, and diphenyl ether/polyethylene. The conclusion is that the two concentration ratios will usually vary with molar mass. The constancy observed by Utracki and Simha can be explained if it is assumed that their anionic polystyrene samples, though having narrow molar-mass distributions as expressed in Mw/Mn, were contaminated with small amounts of high molar-mass material responsible for considerable deviations between maximum-demixing and consolute concentrations. This conclusion is independent of whether the temperature- and concentration dependence of the coil dimensions are taken into account. For the concentration dependence we made use of an expression not published hitherto. Light-scattering data published earlier by Borchard and Rehage clearly demonstrate that the maximum in the 45/135 angular dissymmetry does not occur at the consolute concentration but close to, or at, the concentration at which the spinodal exhibits an extremum. Here we prove the latter point theoretically. The extremum of the spinodal is a consolute point in strictly binary systems only. Hence, the term “spinodal”, rather than “critical”, opalescence appears to be appropriate to indicate the phenomenon.

Dynamic crossover to tricriticality and anomalous slowdown of critical fluctuations by entanglements in polymer solutions.

We have performed accurate dynamic light-scattering measurements near critical demixing points of solutions of polystyrene in cyclohexane with polymer molecular weight ranging from 200 000 to 11.4 x 10(6). Two dynamic modes have been observed, "slow" and "fast," which result from a coupling between diffusive relaxation of critical fluctuations of the concentration and viscoelastic relaxation associated with the entanglement network of the polymer chains. The coupling with the viscoelastic mode causes an additional slowdown of the critical mode on top of the uncoupled diffusion mode. By implementing crossover from the critical to the theta-point tricritical behavior for both static and dynamic properties, we are able to present a quantitative description of the phenomenon and obtain a scaling of the viscoelastic parameters as a function of the molecular weight.

Competition of mesoscales and crossover to tricriticality in polymer solutions

We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200 000 up to 11.4x10(6) clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length.

Osmotic compressibility in dilute polystyrene-cyclohexane and polystyrene-methylcyclohexane solutions: Correlation of polystyrene virial coefficients with solvent quality

Osmotic compressibilities were determined as a function of temperature for solutions of polystyrene in cyclohexane and methylcyclohexane by static light scattering, the measurements extending well below the theta temperature, T = θ. Virial coefficients extracted from the data are compared with literature values obtained by light scattering, membrane osmometry, and phase equilibrium measurements, and successfully correlated over wide ranges of molecular weight, temperature, and solvent quality. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 184–196, 2001

Static and dynamic light scattering experiments on semidilute solutions of polystyrene in cyclohexane between the Θ-temperature and the binodal curve

Static and dynamic light scattering experiments are carried out with solutions of a high molar mass polystyrene (Mw=0.96×106 g mol-1) in cyclohexane at different concentrations of the polymer. At the Θ-temperature TΘ the critical concentration of the system is located in the semidilute regime. The temperature is varied between TΘ and the temperature of phase separation TP of the solutions. At TΘ the distribution of the amplitudes of the relaxation rates of the autocorrelation function of the electric field is bimodal (slow and fast relaxation rates) in the semidilute regime. It becomes monomodal approaching TP. The contribution of the fast relaxation rates disappears and the weak q-dependence of the slow mode changes over to a q-dependence similar to that of the critical relaxation rate in binary liquid mixtures of low molar mass components close to the critical temperature Tc. On approaching the temperature of phase separation by decreasing the temperature, concentration fluctuations with long range correlations develop. The change of the q-dependence of the slow relaxation rate is rationalised using the transient gel model of Brochard and de Gennes. Here it is assumed that approaching TP transient gels formed by interpenetrating polymer coils become part of the concentration fluctuations with long range correlations. The dynamics of the solutions in the vicinity of the binodal curve monitored by dynamic light scattering experiments is dominated by the dynamics of the concentration fluctuations with long range correlation.

Interfacial tension of demixed polymer solutions: augmentation by polymer additives

AbstractThe interfacial tension between phase separated polymer solutions increases pronouncedly upon the addition of small amounts of incompatible polymers. This feature is demonstrated by means of measurements with solutions of polystyrene in cyclohexane and the following additives: poly(styrene‐block‐dimethylsiloxane), polyisobutylene and polydimethylsiloxane. Theoretical considerations based on a correlation between the lengths of tie lines and the corresponding interfacial tension corroborate this finding.

The scaling behavior of critical adsorption in critical polymer solutions

The critical adsorption ellipsometric measurements of five solutions of polystyrene in cyclohexane for different polystyrene molecular weights collapse to a single universal curve when scaled as a function of nBξ/λ, where nB is the polymer solution refractive index, ξ=ξ0Nnt−ν is the correlation length, and λ is the wavelength of incident light in vacuum. From this universal feature we deduce the value of the polymerization critical exponent n=0.258±0.017. We consider both the volume fraction order parameter (φ) and a symmetrized order parameter (ψs) together with both the renormalization group (RG) and Monte Carlo (MC) simulation forms for the surface scaling function P+(x). The symmetrized order parameter gives significantly better agreement with experiment than the volume fraction order parameter. The combination of RG and ψs provides better agreement with experiment than does the combination of MC and ψs.

Dynamic Light Scattering from Polymer Solutions: The Subtraction Technique

Correlation functions measured in dynamic light scattering on polymer solutions often contain a strong sharp decay which obscures and renders difficult a reliable analysis of other decay processes. We demonstrate that this problem can be circumvented by performing a two-step inverse Laplace transformation. The strong component obtained in the first step is subtracted from the correlation function which is then re-analyzed in the second step. We illustrate this technique on semidilute solutions of polystyrene in cyclohexane and tetrahydrofuran.

Viscometric study of extremely dilute macromolecular solutions: Critical concentration c and the intrinsic viscosity of the polystyrene through scaling laws. The values of the Huggins constant

AbstractA crossover is observed in the variation of the reduced viscosity, ηsp/c, as a function of the concentration, c, for polystyrene solutions in cyclohexane and dioxane. This crossover is attributed to the critical concentration c at which the macromolecular coils start to contact. The critical concentration c is related to the molecular weight and the intrinsic viscosity of the polystyrene through scaling laws. The values of the Huggins constant k' determined in the concentration regions below c (extremely dilute solutions) confirm the Peterson‐Fixman theory.

Studies of linear polymer dimensions of polystyrene in cyclohexane over a wide range of temperature by intrinsic viscosity

Intrinsic viscosities ([η]) of polystyrene solutions in cyclohexane above and below the θ temperature have been measured using a capillary viscometer. The viscosity measurements were performed on five polystyrene samples with molecular weights of 6.3 × 10 4, 9.0 × 10 4, 6.0 × 10 5, 2.8 × 10 6 and 10 × 10 6. A smooth and continuous contraction was observed below the θ temperature (34.5°C). The temperature dependence of [η] can be represented by a master curve in a α 3 η|τ|M 1 2 ( g 1 2 mol − 1 2 ) versus |τ|M 1 2 ( g 1 2 mol − 1 2 ) plot, where α η = [η(T)] [η(θ)] 1 3 is a viscosity expansion factor and τ = (T − θ) T is the reduced temperature. A universal plot of reduced viscosity ( α η ) versus reduced blob parameter ( N N c ) shows the achievement of the collapsed state for the T < θ region. The prediction of the temperature blob theory is also verified for the T > θ region.

Static and dynamic light-scattering studies on semidilute solutions of polystyrene in cyclohexane as a function of temperature

Static and dynamic light-scattering studies on semidilute solutions of polystyrene in cyclohexane as a function of temperature

Small-angle X-ray scattering and coexistence curve of semidilute polymer solutions

Small-angle X-ray scattering from semidilute solutions of polystyrene in cyclohexane has been studied in a poor solvent regime. The values of binary and ternary cluster integrals of polymer segments were determined from the concentration dependences of the correlation length and the osmotic compressibility, as obtained from the absolute intensity at zero scattering angle, at various temperatures in the poor solvent regime. By using these interaction parameters the coexistence curve was calculated via a mean field theory. Excellent agreement was achieved between the calculated coexistence curve and the experimental phase separation points which we have measured.

Coexistence curve of semidilute polymer solutions

By using the interaction parameters deduced from small-angle neutron and X-ray scattering, we have calculated, via mean-field theory, the coexistence curve of the semidilute solutions of polystyrene in cyclohexane. We obtain substantial agreement between the theoretical coexistence curve and the observed phase-separation points reported in the literature. General features of the temperature-concentration diagram of polymer solutions in the semidilute poor solvent regime are also discussed.

Quasielastic light scattering from semidilute solutions in θ-solvent: Distribution functions of decay times

Measurements of composite autocorrelation functions extending over a broad time range on semidilute theta solutions of polystyrene in cyclohexane are reported. Three mathematical methods were used to obtain the corresponding distribution functions of decay times, F(τ). Results of the different methods are in mutual agreement. It is found that F(τ) consists of several separated bands. The shortest and longest decay times have been extracted from F(τ) and, on the basis of their concentration and angular dependences, attributed to the gel mode and reptation process, respectively.

Structure and thermodynamics of polymer solutions near the upper and lower consolute temperatures

Phase equilibrium investigations have been carried out for solutions of polystyrene in cyclohexane, and for polyoxypropylene diol in water, hexane and octane, and temperature dependences of the light scattering, optical density and viscosity of the solutions have been determined. Association of macromolecules was detected in the vicinity of temperatures for phase separation, and these association processes have been compared with the thermodynamic criteria of upper and lower consolute temperatures.

Small-angle neutron scattering from polymer solutions: 2. The semi-concentrated region near the upper critical solution temperature

Small-angle neutron scattering experiments have been made on solutions of polystyrene in cyclohexane. From these experiments the radius of gyration has been determined as a function of polymer concentration at a fixed temperature (60°C). Additionally, the screening length has been determined as a function of temperature for a fixed polymer concentration of 36% (w/v). The results support the notion of an additional region of solution behaviour, the semi-concentrated region, predicted by mean field-type theory.

Analysis of macromolecular polydispersity by dynamic light scattering and thermodiffusion

We show that the ratio between the average diffusion coefficient D LS determined by dynamic light scattering and the average diffusion coefficient D TD determined by dynamic thermodiffusion can be used to characterize sample polydispersity. As an example, we present data on solutions of polystyrene in cyclohexane.