Polystyrene-cyclohexane System Research Articles

Classical Nucleation and Lattice Model Unite

Classical nucleation theory predicts the limit of superheat of liquids quite well. To come up with an equation for the limit of superheat of polymer solutions, the lattice model for polymer solutions was used to give the surface tension of polymer solutions. A formula for bubble nucleation in polymer solutions was derived by Jennings with the precursor equation dlnA/dK=1/(6K) where J=AexpK gives the nucleation rate for liquids. The aim of this paper was to show that the precursor equation holds for monomer in the polystyrene-cyclohexane system. Thus, the precursor equation is true for all molecular weight polymer. This happens because the surface tension of polystyrene is significantly more than cyclohexane and the influence of the surface tension dominates.

Solvent H/D isotope effects on miscibility and Θ-temperature in the polystyrene–cyclohexane system

High-accuracy cloud-point temperatures for polystyrene–cyclohexane (PS–CH) and polystryrene–deuterated cyclohexane (PS–CH-d) solutions were measured over a broad range of molecular weights: 2.5 × 104 ≤ Mw ≤ 1.32 × 107. All polystyrene samples were characterized by low polydispersity indexes. Deuterium substitution in cyclohexane shifts the UCSTs to higher values and this isotope shift increases with increasing molecular weight, reaching at the limit of infinite Mw the value 4.53 K. No isotope effect on the critical concentration has been detected. Using different methods, Θ-temperatures for both PS–CH and PS–CH-d systems were determined. All approaches generate consistent results and a remarkable isotope effect on the Θ-temperature is observed. It is shown that isotopic shifts on UCST and Θ-temperature translate as a red shift of the C–H stretching frequency of cyclohexane on its transfer from a pure liquid to polymer solution at infinite dilution. The effect of pressure on the Θ-temperature has also been analyzed and it appears to mimic that of the pressure dependence of the critical temperatures of polystyrene–cyclohexane solution. It is also shown that the frequency shift of C–H vibrations changes with pressure in a similar fashion.

Multiphase multicomponent equilibria for mixtures containing polymers by the perturbation theory

The correlating and predictive capabilities of a thermodynamic model based on the perturbation theory are investigated, with reference to mixtures containing components of different size and molecular interactions. The simplified Perturbed-Hard-Sphere-Chain (PHSC) equation of state is applied to a series of pure polymers, a number of solvents and pure carbon dioxide, and both volumetric and equilibrium properties are considered. The ability of the proposed model to reproduce experimental phase equilibrium data is discussed and tested with reference to binary and multicomponent mixtures, in the presence of vapor–liquid, liquid–liquid and vapor–liquid–liquid equilibria. Attention is focused on the ternary system polystyrene–cyclohexane–carbon dioxide, to test the proposed thermodynamic model in view of simulating supercritical antisolvent-induced fractionation processes. It is shown that the PHSC equation of state can be reliably used for calculating the phase behavior of such a complex system in different conditions.

Dynamic light scattering studies of poly(4-chlorostyrene) and poly(2-chlorostyrene) in theta solvents

Most studies of coil-to-globule transitions of macromolecules have dealt exclusively with the standard polystyrene–cyclohexane system. In this work we aim to extend such investigations to halogenated polystyrenes, namely poly(4-chlorostyrene)(PPCS), poly(2-chlorostyrene)(POCS) and poly(chlorostyrene)(PCS),a mixture of 2- and 4- isomers. Changes in R h of these polymers with temperature in their respective theta solvents were investigated by dynamic light scattering. The hydrodynamic size of PPCS in n-propyl benzene( M w: 2.25×10 6 g mol −1, M w/ M n: 1.16) decreases to 75% of that in the unperturbed state at 22.2°C. POCS ( M w: 10.32×10 6 and M w: 4.30×10 6, M w/ M n: 1.10) in 2-butanone exhibited LCST behaviour and a limited chain collapse was observed with increasing temperature above theta point. The parameters α h= R h/ R h( θ) for POCS with two different molecular weights, (10.32 M and 4.30 M) were found to be 0.67 and 0.77, respectively at 37.0°C. A smooth and continuous contraction was also observed for the mixture of 2- and 4- isomers, PCS ( M w: 2.32×10 6 g mol −1, M w/ M n: 1.06).

Scaling of the shear viscosity of the system polystyrene-cyclohexane in the critical region

The shear viscosity of the system polystyrene-cyclohexane was measured along the isochores near the critical concentration. The value of the critical exponent for the shear viscosity (phi/sub eta/ = 0.029 +- 0.003) is obtained by analyzing the results from the viewpoint of multiplicative renormalization of transport coefficients. In addition, it is shown that the shear viscosity satisfies scaling-law relations and the pseudospinodal generalization previously established for fluids and binary mixtures.

Forces between mica surfaces bearing adsorbed macromolecules in liquid media

The forces between two molecularly smooth curved mica surfaces a distance D apart immersed in a liquid have been measured, both in the absence and in the presence of macromolecules adsorbed from the liquid.The forces between bare mica surfaces in 0.2 mol dm–3 KNO3 aqueous solution are repulsive for D≲ 5 nm and correspond reasonably well to electrostatic double-layer (DLVO) theory. Following adsorption of soluble monomeric collagen onto the surfaces from the solution, repulsion commences at D≲ 600–700 nm and increases monotonically with decreasing D, suggesting that the collagen monomers are adsorbed in an upright configuration normal to each surface.The forces between bare mica surfaces in cyclohexane are monotonically attractive for D≲ 10 nm, and appear to obey a van der Waals-like potential acting across the non-polar medium. Following adsorption of polystyrene (of two molecular weights) onto the mica from the cyclohexane, interactions between the surfaces are found to commence at D≲ 2.5 Rg(unperturbed radius of gyration of the respective polymers) and are initially attractive. For D≲Rg the attraction decreases, and on further reducing D strong repulsion between the surfaces is observed. These results may be understood in terms of the phase equilibrium of the polystyrene–cyclohexane system (which under the experimental conditions is below its critical temperature), and are in good accord with the predictions of a recent theory for interaction between adsorbed polymer layers in a poor solvent.

An analysis of excluded‐volume effects in a polystyrene‐cyclohexane system

AbstractAn attempt was made to analyse Miyaki's data for the radius of gyration <s2> and the intrinsic viscosity [η] of very high molecular weight samples of polystyrene in cyclohexane. The excluded‐volume variable z was estimated by adopting the temperature dependence of the excluded‐volume integral as predicted by Eichinger. It was found that the volume expansion as given by the ratio of <s2> to <s2>0 under the unperturned state was a function of z only, as required by two‐parameter theories. These data were in good agreement with the Domb‐Barrett and the Suzuki equations. On the other hand, the ratio of [η] to [η] 0 under the unperturbed state also gave a single composite curve when plotted against z. However, it was found that the observed hydrodynamic behaviour was not satisfactorily explained by two‐parameter theories of [η]. A brief comment was made on the validity of two‐parameter theories from the experimental point of view.

Forces between two polymer layers adsorbed at a solid-liquid interface in a poor solvent

The forces between mica surfaces a distance D apart immersed in cyclohexane, bearing adsorbed layers of polystyrene, have been measured at temperatures lower than the corresponding critical temperatures. Polymers of two different molecular weights were used. The results show that these forces are attractive for 3R g > D >. R g (where R g is the polymer radius of gyration) and repulsive at lower D, and may be understood in terms of the phase equilibrium of the polystyrene-cyclohexane system. The adsorption of the polymer under these conditions appears to be effectively irreversible over the time of our experiments. The adsorbance of polymer and the thickness of the adsorbed layers are comparable with values measured in other studies using entirely different techniques.

Coexistence curve of polystyrene in methylcyclohexane. II. Comparison of coexistence curves observed and calculated from classical free energy

Comparison of coexistence curves observed and calculated from the classical free energy was made for the systems polystyrene–methylcyclohexane and polystyrene–cyclohexane. Classical free energy was determined from the molecular weight dependence of the critical point. At low molecular weight, the numerically calculated coexistence curve was well represented by the leading term with the exponent β=1/2. The shape of the calculated coexistence curve is very different from the observed one because of the comparable values of the coefficient and different values of the exponent β observed and calculated. At high molecular weight, the entire shape of the observed coexistence curve is fairly well described by the calculated one. This fair description was caused by the large value of the calculated coefficient compared with the observed one and the narrow range of simple scaling. The numerically calculated coexistence curve was found to deviate from the leading term with β=1/2 at high molecular weight. Both in diameter and concentration difference, a transition from the critical region to the classical region was observed for the system polystyrene–cyclohexane with molecular weight Mw=156×104.

Molecular dimensions of polystyrene in solution near the theta point

Hydrodynamic dimensions of polymer coils in solution were investigated around the theta point for the polystyrenecyclohexane system by quasielastic light scattering. Below the theta point, the hydrodynamic radius decreases very slightly and does not exhibit the collapse of the coil near the critical solution temperature in contrast with the radius of gyration.

Temperature dependence of hydrodynamic lengths in the polystyrene-cyclohexane system

We present experimental data on the dynamic temperature behaviour of the polystyrene-cyclohexane system in the neighbourhood of the 03B8 point (0 ~

Intrinsic viscosity of polystyrene in mixed solvents

AbstractThe intrinsic viscosity of a single sample of polystyrene was measured as a function of the composition of solvent in three mixed solvent pairs. The parameter Y introduced by Shultz and Flory was useful for prediction of trends, but severely overestimated the effect of solvent (1)–solvent (2) interaction on the expansion of polymer coils. The system polystyrene–cyclohexane–ethyl acetate was studied in detail for five samples of polystyrene. The analysis of the data provided strong experimental proof of a strict validity of the Mark–Houwink–Sakurada relation. The dependence of the Mark–Houwink–Sakurada exponent α on the composition of the solvent mixture was unexpectedly unsymmetrical. The unperturbed dimentions of the polystyrene chain are reduced by specific interaction of polystyrene with carbonyl groups in the solvent mixture.

Phase equilibria in polymer solutions

A theoretical study of phase equilibria in multicomponent polymer solutions is presented. The treatment is based on the virial expansion of the osmotic pressure. A program for the numerical determination of phase diagrams is worked out and applied to the polystyrene-cyclohexane system. The present approach is compared with the Flory-Huggins theory of polymer solutions, which is shown to represent a special class of approximations in the present treatment.

Light scattering and pseudospinodal curve of the system polystyrene–cyclohexane in the critical region

The angular distribution of scattered light intensity from polystyrene (Mw = 1.1×105, Mw/Mn<1.02) in cyclohexane has been measured over a range of temperatures using a specially designed light-scattering photometer and then a ’’pseudospinodal curve’’ Tsp(φ) described by Tc − Tsp(φ) ∝ (φ(1) − φ(2))1/β+, where φ is the volume fraction of polymer on the spinodal curve, has been investigated for various equilibrium states in the critical neighborhood of the temperature–concentration diagram. An empirical equation of the form (Ic,0/T)−1 ∝ (T−Tsp)γ, in which Ic,0 is the extrapolated zero-angle scattering intensity, is used to effect an extrapolation for the determination of Tsp inside the coexistance curve. The temperature dependence of Ic,0 obeys the same relation with γ=1.20–1.24 for several samples. The long-range correlation length ξ obeys a relation ξ∝ (T−Tsp)−ν with ν=0.59∼0.64. As expected on the ground of the homogeneity hypotheses, the value of β+?0.38 found in the present work is essentially the same as the value of the critical exponent β=0.34±0.01 for the coexistence curve near its critical mixing point.

Pressure dependence of upper critical solution temperatures in the polystyrene - cyclohexane system

The pressure dependence of the upper critical solution temperature ( dT dp ) c in the polystyrene-cyclohexane system has been measured over the pressure range of 1 to 50 atm. The value of ( dT dp ) c determined over the molecular weight ( M w ) range of 3.7 × 10 4 to ∼145 × 10 4 greatly depends on the molecular weight of polystyrene. The value of ( dT dp ) c for a polystyrene solution of low molecular weight ( M w = 3.7 × 10 4) is positive (3.14 × 10 −3 degree atm −1), while the values are negative (−0.52 × 10 −3∼−5.64 × 10 −3 degree atm −) for solutions of polystyrene over the high molecular weight range of 11 × 10 4 to ∼145 × 10 4. The Patterson-Delmas theory of the corresponding state and the newer Flory theory have been used to explain this behaviour.

Coexistence curve for polystyrene–cyclohexane near the critical point

The coexistence curves for the system polystyrene–cyclohexane have been determined with a specially designed differential refractometer, which determines concentrations of the two coexisting phases with a precision of ± 0.01%. The plots of the coexistence curve data represented by log(X+−Xc) and log(Xc−X−) versus the reduced temperature ε = (Tc−T)/Tc yield largely curved lines. The shape of the coexistence curve very near the critical point, however, is asymptotically symmetric. The coexistence curve obtained with an over-all concentration at the critical concentration is represented by the relation X+−X− = Bεβ with β=0.348 and B=0.97 in the temperature region of Tc −T<2.0 °C. The critical point exponent β and the coefficient B vary only slightly depending on the over-all concentration. Although the data give a curved diameter, a precision of the present experiment is not sufficient to determine the asymptotic behavior of the diameter.

Computer analysis of light scattering data—I: Polystyrene-cyclohexane system

A Fortran computer program has been written to perform the bivariate least squares analysis of light scattering data introduced by Miller and Stepto. The program also carries out the necessary extension to the computer plotting of the results. In the conventional Zimm plot analysis, terms of order c 2 (where c = concentration) and x 2 [where x = sin 2 ( ϑ 2) ] , are effectively ignored without theoretical justification, although (i) the intramolecular scattering function P( ϑ) is not generally a linear function of x. and (ii) the effect of the third (and higher) virial coefficients cannot always be neglected. Results for the theta system polystyrene cyclohexane, and also for the systems poly x-methyl styrene in benzene and trans-decalin using published data indicate that the inclusion of these terms provides further insight into the dilute solution properties of macromolecules.

Precision measurements of osmotic pressure in concentrated polymer solutions—II

Precision measurements of osmotic pressure have been carried out with several polymers (polystyrene, polymethylmethacrylate and polyvinyl acetate) in organic solvents. The concentration dependence of the osmotic pressure over a wide range of concentrations (up to 0·2 g/cm 3) was established and the osmotic virial coefficients were evaluated. From the temperature dependence of the osmotic pressure, the partial molar heats and entropies of mixing were also determined. In the system polystyrene-cyclohexane, measurements were carried out near the θ-temperature; variation of the virial coefficients with temperature and molecular weight was studied. It was found that the conventionally defined θ-temperature is molecular weight dependent. At the θ-temperature, the third virial coefficient is positive and tends to a nonzero limit when the molecular weight tends to infinity.

Pulse-induced critical scattering (PICS) from polymer solutions

Abstract

Cloud-point curves of the polystyrene-cyclohexane system near the critical point

Cloud-point curves for solutions of five polystyrene samples, including three well-fractionated polystyrenes, in cyclohexane have been examined near their critical points. Even for a solution of polystyrene characterized by M w M n<1.03 , the critical point determined by the phase-volume method is generally situated on the right hand branch of the cloud-point curve. The precipitation threshold concentration is appreciably lower than the critical concentration, while the threshold temperature slightly deviates from the critical temperature. The agreement of the precipitation threshold point with the critical point has been found for a solution of polystyrene characterized by M w =20×10 4 and M w M n<1.02 in cyclohexane. The η(φ) function derived from critical miscibility data is expressed by χ(φ) = 0.2798+ 67.50 T +0.3070φ+0.2589φ 2 , which yields θ of 33.2°C and ψ 1 of 0.22.