The system methylcyclohexane/polystyrene. Experimental critical curves, cloud‐point and spinodal isopleths, and their description with a semi‐phenomenological treatment

Abstract

Cloud-point and spinodal pressures up to 900 bar were investigated for the system methylcyclohexane/polystyrene using a pressure-pulse-induced scattering technique based on the theory of Debye. The molar-mass range of the polymer samples is 9-50 kg/mol. The values determined isothermally in a large concentration range for a polymer sample with weight-average molar mass Hw = 17,5 kg/mol lead to isopleths which allow the construction of phase diagrams displaying cloud-point and spinodal curves (in terms of temperature or pressure against concentration). Critical isopleths have been determined for three further samples with M,,, = 9,0, M, = 28,5 and M, = 50,O kg/mol. A semi-phenomenological treatment of the data is presented which allows an accurate description of experimental phase diagrams and isopleths for one single sample (PS 17,5). A prediction of the critical P ( T ) curves for the other samples, of different average molar mass, then fails completely. Fitting the model parameters to the critical data of all four samples improves the description of the critical curves but produces phase diagrams showing considerable deviations from the data. One reason for the failure of the model may be sought in its inherent incapability to deal with dilute polymer solutions in which the individual coils are separated by regions of pure solvent. A first rough attempt to deal with this effect already brings a marked improvement in the agreement between experiment and model calculation for the critical curves, albeit at the cost of introduction of a number of adaptable parameters.

Thermodynamic Properties of Poly(ethylene glycol)/Water Systems. 1. A Polymer Sample with a Narrow Molar Mass Distribution

“…A distinct improvement of the quality of the calculated CPC is not reached by changing the concentration dependence of the g function from the linear type of b g to the squared type of c g . The closed form of the g function d g , which has been introduced by Koningsveld and Kleintjens, leads to a reasonable locus of the calculated CPC . But the shape of the calculated curve, which is the dotted curve in Figure , also deviates from the very flat one of the experimental CPC.…”

“…For a Gibbs free enthalpy of mixing according to eq 3 it follows that and where γ represents the phase indices ‘ or ‘‘ and i = 2, 3, ..., N and r̄ n is the number average of r i . The parameter χ 1 γ represents the interaction parameter of the solvent in the phase γ, and the parameter χ p γ represents the same of the polymer. ,,, They are defined by and By the use of the distribution coefficient σ, it follows that ,, with which reflects the fractionation of a polymer component i enriched either in the dilute or in the concentrated coexisting phase. By a summation over all polymer species i , eq 7a leads to the polymer concentration φ p ‘‘: Assuming a certain mmd in the original polymer sample and assuming an appropriate thermodynamic framework, a stepwise iteration may be performed that should give the CPC and the shadow curve of the system.…”

Dynamic Light Scattering of Polymer/Solvent Solutions Under Pressure. Near-Critical Demixing (0.1 < P/MPa < 200) for Polystyrene/Cyclohexane and Polystyrene/Methylcyclohexane

“…PS/MCH solutions form examples of at least the lower part of the reentrant diagram illustrated in Figure 4. Previous observations of the demixing diagram for PS/ MCH at modestly elevated pressures have been reported by Vanhee et al 44 (0.1 < P/MPa < 90), Van Hook et al, 4,9,10 Enders and de Loos, 45 Hosokawa, Nakata, and Dobashi, 46 and Wells et al 47 and correlated by Imre and Van Hook. 6 The earlier work establishes the existence of a lower hypercritical temperature (T hyp L ) 305 K, 55 MPa, at M w (PS) ) 3 × 10 4 ), and points to the existence of a lower hypercritical pressure at P < 0, but not too deep (P hyp L ) ∼34 010 K, ∼-15 ( 3 MPa at M w (PS) ) 3 × 10 4 , dropping off to P hyp L ) ∼360 ( 10 K, ∼-10 ( 3 MPa, at M w (PS) ) 2 × 10 6 ).…”

Pressure dependence of the second virial coefficient of dilute polystyrene solutions

“…Although in most cases increased pressure improves SQ, that behavior is not universal. Others have reported that increasing the pressure improves SQ by transforming a θ solvent into a good solvent17–21 or a poor solvent into a θ solvent 22, 23. The results at room temperature show that SQ improves with pressure ( d SQ/ dP > 0) in the good (PS/toluene and PS/chloroform) and poor (PS/MCH) solvents studied.…”

“…Others have employed liquid–liquid phase equilibria to determine dT UCST / dP , another measure of SQ. In this way, several groups have reported that increasing pressure improves SQ by transforming a θ solvent into a good solvent17–21 or a poor solvent into a θ solvent 22, 23. Although in most cases increased pressure does improve SQ, that behavior is not universal.…”