Polystyrene In Methylcyclohexane Research Articles

Universality in eight-arm star polystyrene and methylcyclohexane mixtures near the critical point

Measurements of the coexistence curve and turbidity were made on different molecular mass samples of the branched polymer-solvent system eight-arm star polystyrene in methylcyclohexane near its critical point. We confirmed that these systems belong in the Ising universality class. The location of the critical temperature and composition as well as the correlation length, susceptibility, and coexistence curve amplitudes were found to depend on molecular mass and the degree of branching. The coexistence curve diameter had an asymmetry that followed a "complete scaling" approach. All the coexistence curve data could be scaled onto a common curve with one adjustable parameter. We found the coexistence curve amplitude to be about 12% larger for branched than linear polystyrenes of the same molecular mass in either solvent cyclohexane or methylcyclohexane. The two-scale-factor universality ratio R was found to be independent of molecular mass or degree of branching.

Modeling of the phase equilibria of polystyrene in methylcyclohexane with semi-empirical quantum mechanical methods I

A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethyl-benzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum mechanical method AMI, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model mole-cules, and used to calculated UNIQUAC interaction parameters, a ij and a ji. Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methyl-cyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement.

Free Energy of Mixing for Polymer Solutions

The validity of the correction for the interaction parameter g of the Flory−Huggins free energy (Langmuir 2003, 19, 5240) was examined by taking the contributions of spatial variation in the volume fraction into account. Developing the statistical-mechanical view of the invariance conjecture and the Landau expansion with the nonanalytic coefficients for the polymer solutions, we showed that the chain-length dependent correction term H in the interaction parameter g was reasonably introduced. We derived the explicit function form of H as a function of chain-length and temperature to be consistent with the critical power laws for both the concentration difference and the diameter in coexisting phases. It was successfully applied to the systems polystyrene in methylcyclohexane and poly(methyl methacrylate) in 3-octanone.

Eight‐arm star polystyrene in methylcyclohexane: Cloud‐point curves, critical lines, and coexisting densities and viscosities

AbstractWe measured the cloud‐point curves of eight‐arm star polystyrene (sPS) in methylcyclohexane (MCH) for polymer samples of three total molecular masses [weight‐average molecular weight (Mw) × 10−3= 77, 215, or 268]. We found a downward shift of 5–15 K in the critical temperature (Tc) of the star polymer solutions with respect to linear polystyrene (PS) solutions of the sameMw. The shift inTcbecame smaller asMwincreased. The critical volume fraction for eight‐arm sPS in MCH was equal within experimental uncertainty (10–40%) to that of linear PS in MCH. For sPS ofMw= 77,000 in MCH, we studied the mass density (ρ) as a function of temperature (T). As for linear polymers in solution, the difference in ρ between coexisting phases (Δρ) could be described overt= (Tc−T)/Tcfor 1.1 × 10−4<t< 4.7 × 10−3with the Ising value of the exponent β in the expression Δρ =Btβ. Both ρ(T) aboveTcand the average value of ρ belowTcwere linear functions of temperature; no singular corrections were observed. The measurements of the shear viscosity (η) nearTcfor sPS (Mw= 74,000) in MCH indicated a strong critical anomaly in η, but the data were not precise enough for a quantitative analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 129–145, 2004

Modeling of the phase equilibria of polystyrene in methylcyclohexane with semi-empirical quantum mechanical methods I.

A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethylbenzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum chemical method AM1, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model molecules, and used to calculated UNIQUAC interaction parameters, a(ij) and a(ji). Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methylcyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement. Figure Solvent activities for the methylcylcohexane(1)+polystyrene(2) system at 316 K. Parameters aij (blue line) obtained with the AM1 method; parameters aij (pink line) from VLE data for the ethylbenzene+methylcyclohexane system. The abscissa is the polymer weight fraction defined as y2(x1)=(1mx1)M2/[x1M1+(1mx1)M2], where x1 is the solvent mole fraction and Mi are the molecular weights of the components.

Gibbs Free Energy Expression for the System Polystyrene in Methylcyclohexane and Its Application to Microencapsulation

A semiempirical equation of Gibbs free energy of mixing ΔG for the system polystyrene in methylcyclohexane has been determined based on the Flory−Huggins equation by using a series of coexistence curve data. The functional form of the interaction parameter g with respect to chain length of the polymer was determined so as to express the critical universality. The resultant equation of ΔG was used to prepare microcapsules of controlled size distribution by means of coacervation in the spinodal region.

Molecular weight distributions of polydisperse polymers in coexisting liquid phases

We present new experimental measurements of the molecular weight (MW) distributions in coexisting liquid phases for three polymer/solvent systems. We studied samples at the critical compositions and at four temperatures in the two-phase regions. For polystyrene in methylcyclohexane (with an upper critical solution point), we observed the expected fractionation between phases, with a higher average MW in the lower, polymer-rich phase. For poly(ethylene oxide) in 2, 6-lutidine+water (with a lower critical solution point), the total polymer mass is nearly equal in the two phases, but the polymers of higher average MW equilibrate into the upper, 2,6-lutidine-rich phase. For poly(ethylene oxide) in isobutyric acid+water (with an upper critical solution point), most of the total polymer mass is in the upper, isobutyric acid-rich phase, but the polymers of higher average MW equilibrate into the lower, water-rich phase; moreover, the fractionation in this case is quite dramatic, with almost a factor of 2 difference in average MW between the phases and a significant decrease in polydispersity for the lower phase. Our results support prior experimental results on this phenomenon that find that a basic Flory–Huggins (FH) theory is inadequate. More recent theoretical considerations suggest that the difference between FH theory and experiments is due to non-mean field effects, but this theory awaits direct comparison to experiments.

Turbidity measurements and amplitude scaling of critical solutions of polystyrene in methylcyclohexane

We report turbidity measurements for a series of solutions of polystyrene in methylcyclohexane with varying polymer molecular weights. The obtained correlation length ξ and the osmotic compressibility χ shows power law dependence on both the reduced temperature t (=|T−Tc|/Tc) and the molecular weights Mw of the polymers. We find that the relations ξ0(1−φc)0.85∝Mw0.18, and χ0(1−φc)−1.20∝Mw−0.09 proposed by An, Jiang, Chen, and Shen [Chem. Phys. Lett. 282, 403 (1998)] can be used to describe the present experimental results. Moreover, these relations appear to be better suited than a simple scaling for extracting the Mw-exponents. The exponents so obtained are found to be in excellent agreement with theoretical predictions.

Coexistence curve near the tricritical point in ternary polymer solutions.

Two-phase coexistence curves were measured for ternary solutions of bimodal polystyrene in methylcyclohexane with the molecular weight ratio near the tricritical value 23. Coexistence curves were determined by the refractive index method on a diagram of temperature versus volume fraction of total polystyrene. The diameter was strongly curved near the top. The double logarithmic plots of volume fraction difference between two coexisting phases versus reduced temperature yielded the critical exponent beta=0.250+/-0.005 for the tricritical solution and, 0.412+/-0.005 and 0.383+/-0.016 for solutions not far from the tricritical one. The former value could be compared with the classical tricritical exponent beta=1 / 4 and the latter values near 0.40 could be explained by a crossover between the ordinary critical exponent 0.32 or the tricritical exponents 1 / 4 and the classical exponent 1 / 2.

Dilute-solution properties of arborescent polystyrenes: further evidence for perturbed-hard-sphere behavior

Toward improved understanding of the dilute-solution properties of arborescent polystyrenes, new measurements are reported for osmotic second virial coefficients and for intrinsic viscosities in three common organic solvents. As observed for other branched polymers, branching decreases the second virial coefficient in good solvents and lowers the theta temperature for a polymer–solvent system. For generation-zero arborescent polystyrene in methylcyclohexane, the theta temperature is 36±2°C.A correspondence between intrinsic viscosity and second virial coefficient, valid for hard-spheres solutions, holds in good solvents; this correspondence improves with decreasing branch molecular weight.The osmotic-pressure data are interpreted with a colloid-like thermodynamic framework using a van der Waals-type equation of state. The reference state is the hard sphere and the perturbation is given by an attraction decaying with the sixth power of the center-to-center distance between polymers. The hard-sphere diameter is obtained from intrinsic-viscosity data. Predicted and observed osmotic pressures are in good agreement.

Osmotic Second Virial Coefficient, Intrinsic Viscosity and Molecular Simulation for Star and Linear Polystyrenes

Experimental osmotic second virial coefficients are reported for polystyrene in toluene (good solvent), cyclohexane (ϑ solvent) and methylcyclohexane (poor solvent) in the temperature range 10−60 °C. The ϑ temperature for eight-arm star polystyrene in methylcyclohexane is 29 ± 3 °C. Intrinsic viscosity for polystyrene in cyclohexane and methylcyclohexane has been measured over a wide temperature range. A coil-globule transition has been observed for eight-arm star polystyrene in methylcyclohexane at temperatures close to the ϑ temperature. The ϑ point for star polymers with three, four, five, and six arms have been determined by standard Monte Carlo simulation calculations. For six-arm star polymers at the ϑ point, defined as the well depth at which the radius of gyration squared scales linearly with the number of segments, the osmotic second virial coefficient is zero. As shown by others, for a branched polymer, the osmotic second virial coefficient at good solvent conditions and the ϑ temperature are lo...

Correlation length and amplitude scaling in critical polymer solutions

We present a light scattering measurement of the correlation length for a series of critical solutions of polystyrene in methylcyclohexane with different molecular weights. Our results show that the correlation length ξ∼Nζνε−0.63, where N is the polymerization index and ε=(T−Tc)/Tc is the reduced temperature. The N exponent ζν is found to be 0.18±0.02, which is contrary to most earlier direct experimental results but in excellent agreement with theoretical predictions by de Gennes and Stepanow.

Coexistence curve of polystyrene in methylcyclohexane. X. Two-phase coexistence curves for ternary solutions near the tricritical compositions

Tricritical phase equilibrium properties were studied for the ternary solution of two polystyrene homologs in methylcyclohexane by numerical analysis of the generalized Flory–Huggins equation with an empirical interaction parameter and by experimental measurements. For critical solutions at the tricritical molecular weight ratio two-phase coexistence curves were calculated very near to the critical points as 10−7 in the reduced temperature. The shape of the coexistence curves changed markedly depending on the overall compositions of the solution. For the tricritical solution the coexistence curve was asymmetric due to an interference with the critical line but the asymptotic behavior near the tricritical point was not revealed by the present calculation. Two-phase coexistence curves were measured for ternary solutions with the molecular weight M1=1.87×104 and M2=41.2×104 which yielded the molecular weight ratio 22 close to the empirical tricritical value 23 found in literatures. The coexistence curves measured for solutions not far from the tricritical one exhibited the characteristic features calculated for solutions near the tricritical one.

Pressure dependence of the phase behaviour of polystyrene in methylcyclohexane

The influence of pressure on the upper critical solution temperature (UCST) as well as on the lower critical solution temperature (LCST) behaviour of the system methylcyclohexane (MCH)/polystyrene PS 405 was studied. Cloud-point pressures up to 120 bars were measured with a Cailletet apparatus. Cloud-point and spinodal pressures were obtained with a pressure pulse-induced critical scattering apparatus (PPICS) up to 800 bars. Also, some three-phase equilibria liquid-liquid-vapour were determined. The lower demixing temperature is found to decrease with increasing pressure. The upper demixing temperature increases with increasing pressure. The experimental data were described qualitatively with a simple G E -model. This G E -model is able to describe the dependence of the demixing temperature on the pressure. Also, the model is able to predict the merging of the regions of immiscibility that can occur in systems of methylcyclohexane/polystyrene .

Coexistence curve of polystyrene in methylcyclohexane. IX. Pressure dependence of tricritical point

The effect of pressure on the tricritical point (TCP) of a ternary system, polystyrene (PS) I+PS II+methylcyclohexane, was studied by numerical analysis of the generalized Flory–Huggins equation for the Gibbs free energy. For the ternary system, the molecular weight of PS II M2t, total volume fraction of PS φst, volume fraction of PS II with respect to total volume of PS ξ2t, and temperature Tt at TCP were calculated for various values of the molecular weight of PS I M1 in the pressure range from 0 to 100 MPa. As M1 increases, the ratio rt=M2t/M1 and φst decrease, while Tt and ξ2t increase monotonically irrespective of p. The curves of rt and φst vs p have a maximum, while the curves of Tt and ξ2t vs p have a minimum, irrespective of M1. For small M1 these curves are nearly flat and roughly symmetrical with respect to the extrema. From these calculated results it is predicted that the tricritical solution at atmospheric pressure remains very near the tricritical state along the cloud-point curve in the temperature vs pressure diagram.

Coexistence curve of polystyrene in methylcyclohexane. VIII. Crossover from Ising to renormalized Ising behavior in ternary system

In order to examine the crossover from the Ising behavior to the renormalized Ising behavior, we have measured the coexistence curves of the ternary system, polystyrene I+ polystyrene II+ methylcyclohexane, by varying the molecular weight ratio r of polystyrene II to polystyrene I and volume fraction ξ2 of polystyrene II in total polystyrene. The observed critical exponent βt for the concentration difference between two coexisting phases varies from 0.33 to 0.38 with the increase of parameter k=ξ2r(r−1)2. This result is consistent with the theory of Broseta and Leibler [J. Chem. Phys. 90, 6652 (1989)]. The exponent for the diameter μt was found in the range from 0.81 to 0.92. The average of μt=0.86 is close to the exponent μ for binary systems.

Coexistence curve of polystyrene in methylcyclohexane. VI. Two-phase behavior of ternary system near the tricritical point

Tricritical two-phase behavior of bimodal polystyrene (PS) in methylcyclohexane (MCH) was studied by using the Flory–Huggins theory combined with an empirically determined interaction parameter. In the ternary system PSI+PSII+MCH with the molecular weight M1=1.73×104 for PSI, the tricritical system was obtained for PSII with M2=2.24×105, which yielded a coincidence of the upper and lower critical end points. For the tricritical mixture the two-phase coexistence curve was calculated in the temperature range 0.01<Tt−T<6 K with Tt being the tricritical temperature. In a diagram of temperature, total PS volume fraction, the dilute and concentrated branches of the coexistence curve showed very different behavior. The log–log plots to estimate the exponent β for the dilute branch, concentrated branch, and the difference between them were curved, and the slopes of the plots, which decreased with decreasing temperature, were much larger than the exponent expected for the nonsymmetric tricritical point. This observation suggested that the asymptotic range is limited very near the tricritical point (TCP). According to analytical arguments with the original Flory–Huggins theory, the critical line of the tricritical system was conjectured to be tangent to the dilute branch of the coexistence curve at the TCP.

Coexistence curve of polystyrene in methylcyclohexane. VII. Coexistence surface and critical double point of binary system in T–p–φ space

Cloud-point measurements were made for binary systems of polystyrene (PS) +methylcyclohexane (MCH) with three PS samples in the pressure range up to 90 MPa. On a temperature (T)–pressure (p) plane, observed cloud-point curves, which were determined at various compositions for the molecular weight Mw=1.61×104 and at the critical composition for Mw=1.02×104 and 3.49×104, decrease first, reach a minimum and increase with increasing pressure. For Mw=1.61×104 the coexistence surface was investigated in a T–p–φ space, where φ denotes the volume fraction of PS. On a T–φ plane the coexistence curves give a critical composition independent of pressure. On a p–φ plane one phase region appears between two coexistence curves. The top and the bottom of the coexistence curves give an upper critical solution pressure (UCSP) and a lower critical solution pressure (LCSP), respectively. The two critical points coincide forming a critical double point (CDP) at T=19.28 °C, p=48.6 MPa, and φ=0.1719. The shape of the coexistence curves near the CDP is very sensitive to temperature and is characterized by the critical exponent 2β. The Gibbs free energy of the present system was evaluated as a function of T, p, and φ from the molecular weight dependence of the observed critical lines.

Phase separation in polymer solutions

Since the early work of Flory we have understood the causes and main features of the separation of dilute polymer solutions into coexisting phases below the theta point of the polymer-solvent pair. Some issues concerning corrections to the mean-field theory and the reconciliation of theory with experiment remain unresolved, and these are pointed out. In recent years attention has turned to questions about the structure and tension of the interface between those dilute polymer phases. The present status of the scaling theory is reviewed. The application of the theory to the interpretation of the pioneering measurements by Shinozaki et al. of the temperature and chain-length dependence of the interfacial tension in phase-separated solutions of polystyrene in methylcyclohexane, and a more recent test of the scaling theory through measurements of the capillary length of the interface in phase-separated solutions of polymethylmethacrylate in 3-octanone (Xia, Franck and Widom), are described.

Interfacial tensions of phase-separated polymer solutions

Measurements of the capillary length in phase-separated solutions of polymethylmethacrylate in 3-octanone (PMMA/3-OCT) for each of five different molecular weights of PMMA, and in phase-separated solutions of polystyrene in methylcyclohexane (PS/MCH) for a single molecular weight of polymer, are reported. Measurements on PMMA/3-OCT were by the sessile-drop method; those on PS/MCH were by both the sessile-drop and capillary-rise methods. Interfacial tensions are estimated from estimated density differences and the measured capillary lengths. A theoretically predicted scaling law for the dependence of capillary length on polymer molecular weight and temperature is tested and at least semiquantitatively verified. As by-products of the sample preparation, the molecular-weight dependences of the critical composition and critical solution temperature of PMMA/3-OCT were also determined. The volume fraction of polymer at the critical point, φc, is found to be proportional to the −0.37±0.01 power of the molecular weight, in agreement with values of this exponent found by others for polystyrene solutions.