S. Saeki

Upper and lower critical solution temperatures in poly (ethylene glycol) solutions

Upper and lower critical solution temperatures have been determined for solutions of poly(ethylene glycol) in t-butyl acetate and water over the molecular weight range of Mη = 2.18 × 103 to ∼1020 × 103. The phase diagram for solutions of poly(ethylene glycol) (Mη = 719 × 103) in t-butyl acetate was expressed as the ‘hour glass’ type, while the phase diagram for solution of poly(ethylene glycol) (Mη = 2.18 × 103 to ∼2.29 × 103) in water was expressed as the ‘closed loop’ type. The value of the pressure dependence of the lower critical solution temperature (dTdP)c in the poly(ethylene glycol) (Mη = 1020 × 103)/water system over the pressure range of 0 to ∼50 atm was negligibly small and positive.

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

Abstract The pressure dependence of the upper critical solution temperature ( d T d p ) c in the polystyrene-cyclohexane system has been measured over the pressure range of 1 to 50 atm. The value of ( d T d p ) 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 ( d T d p ) 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.

Phase separation of poly(ethylene glycol)-water-salt systems

Abstract Phase separation temperatures, each corresponding to lower critical solution temperature (LCST) for solutions of poly(ethylene glycol) (PEG) in water-sodium chloride (NaCl) and in water-propionic acid-sodium salt (Pro-Na), have been determined for PEG with molecular weights of Mη = 2.18 × 103, 8 × 103 and 719 × 103 over concentration ranges from 0–1.09 M (mol/1000 g solvent) NaCl and 1.02 M Pro-Na. The phase separation temperature decreases with an increase of salt concentration and depends on polymer molecular weight. The thermal pressure coefficient, thermal expansion coefficient, and density have been determined from 20° to approximately 60°C for ethylene glycol-water solutions over the entire concentration range and also for aqueous salt solutions over the concentration ranges from 0–1.7 M NaCl and 0–0.5 MPro-Na. The excess thermal pressure coefficient, γEV, excess thermal expansion coefficient, αE, and excess of temperature dependence of γV, [ ( ∂ γV ∂T ) E ϱ ], for the EG-water system are all positive, while the excess volume of mixing VE is negative. The thermal pressure coefficient and thermal expansion coefficient for aqueous salt solutions water-Pro-Na and water-NaCl increase with an increase of salt concentration. The behaviour of the two polymer-salt-water solutions is discussed in terms of a thermodynamic equation of state, and a shortcoming of the usual formulation of the corresponding states theory of polymer solutions is pointed out.

Upper and lower critical solution temperatures in polyethylene solutions

Abstract Upper and lower critical solution temperatures have been determined for solutions of polyethylene in n-butyl acetate and n-amyl acetate over the molecular weight range of M η = 1·36 × 10 4 to 17·5 × 10 4 . Polyethylene solution in n-butyl acetate displays a smaller miscibility region than that of the polyethylene/n-amyl acetate system, as indicated by the relative positions of their upper and lower critical solution temperatures. Contributions of the energy and the equation of state terms to the χ1 parameter have been examined by an application of the Patterson-Delmas corresponding state theory to the experimental results of the polyethylene solutions.

Temperature dependence of polymer chain dimensions in the polystyrene-cyclopentane system

Abstract The limiting viscosity number in polystyrene-cyclopentane system has been determined over the temperature range of θ u to θ l in which θ u and θ l are the θ or Flory temperature for the upper and lower critical solution temperatures. The temperature coefficient of unperturbed mean square end-to-end distance observed for the polystyrene ( M w =20×10 4 , M w M n and M w =67×10 4 , M w M n ) in cyclopentane is negligibly small. The observed temperature dependence of the polymer chain dimension over the temperature range of θ u =19·6° to θ l =154·2°C shows a parabolic curve with a maximum in the neighbourhood of 90°C and is qualitatively interpreted by the free volume theory of polymer solution, which gives a new χ 1 -temperature function.

Thermodynamic properties of the system polystyrene‐trans‐decalin

Osmotic pressure measurements were performed on solutions of polystyrene in trans‐decaline in the temperature range from 20° to 90 °C and in concentrations of segment fraction φ2 ranging from 0.06 to 0.26. The cloud‐point curves for this system were observed for samples of molecular weights from 3.7 to 270×104. Values of the interaction parameter χ obtained from osmotic pressure data were compared with those calculated from the new Flory theory for liquid mixtures. The behavior of χ was well represented by the simple relation: χ= (127.1+72.6φ2+48.7φ22)/T +(2.32×10−4+2.07×10−4φ2) T, where the terms proportional to temperature and to reciprocal temperature were found to be ascribed mainly to the difference of the liquid properties of the respective components and the exchange energy, respectively. Behaviors of the cloud‐point curves were well explained by the above expression for χ.

Semi-empirical equation of state for polymers and simple liquids in non-critical and critical regions

The semi-empirical equation of state for the polymers polystyrene (PS), polyisobutylene (PIB) and polydimethyl siloxane (PDMS) and the simple liquids benzene, n-heptane, carbon tetrachloride and argon at a negligible external pressure has been determined using the experimental data of thermal pressure coefficient γv, molar volume V and thermal expansion coefficient αp. The equation of state obtained in this work is expressed by P = (XβoV)c1exp(α−1oIo)T − coexp(a−1oIo), where X = (Vc − V)V and Io = ∫VVcXβoVdV, Vc is the critical volume and α0, β0, a0, c1 and c0 are constants determined experimentally. We have obtained good agreement between the values of αp and γv calculated and observed, within 1–2% over a wide temperature range. The semi-empirical equation of state in the critical region is expressed by Vc − V∝(Tc − T)0.33, P − Pc∝(Vc − V)5.0, β−1T∝(Tc − T)1.33 and α−1p∝(Tc − T)0.67 for β0 = 2.0, which agrees semi-quantitatively with the experimental critical indices.

Semiempirical equation of state for polymers and simple liquids under high pressure

Abstract The semiempirical equation of state for polymers polyethylene (PE), poly(n-butyl methacrylate) (PNBMA) and polystyrene (PS) for pressures up to 2 kbar, five hydrocarbons from n-heptane to n-octadecane over 0 to 1.2–9.0 kbar, five organic liquids, including carbon tetrachloride (CCl4), over 0 to 2.0–12.0 kbar, water up to 10 kbar and argon up to 3 kbar has been derived by using experimental data for specific volume V, compressibility βT and thermal expansion coefficients αP under high pressure published by Simha et al., Hellwege et al., Bridgman, Streett and others on the basis of the homogeneous function approach. The equations derived in this work under a constant temperature are: ln V∼-(P+P 0 ) 1-m 0 β T ∼(P+P 0 ) -m 0 α P ∼(P+P 0 ) 1-m 0 where P0 is a constant with respect to pressure but depends on temperature, and m0 and n0 are constants determined from the experimental data. Values of m0 range from 0.76 to 0.99, with an average value 0.87 for polymers and simple liquids including water and argon, while values of n0 for αP for argon are around 0.50 over 90–150 K.

Theoretical prediction of the upper and lower critical solution temperatures in aqueous polymer solutions based on the corresponding states theory

Abstract The upper and lower critical solution temperatures in aqueous polymer solutions have been predicted by the Flory-Huggins theory with a particular temperature dependence of the χ parameter characterized by a parabolic-like function of temperature with a maximum. The closed-loop type of phase diagram for an aqueous polymer solution is discussed using an equation derived from the thermodynamic equation of state on the basis of the corresponding states theory, which is able to explain the particular temperature dependence of χ in aqueous polymer solutions.

Correlation between the equation of state and the pressure dependence of glass transition and melting temperatures in polymers and rare-gas solids

Abstract A correlation between the equation of state and the pressure dependence of the glass transition temperature Tg in polymers such as polystyrene (PS) and poly (methyl methacrylate) (PMMA) and the pressure dependence of the melting temperature Tm in polymers such as polyethylene (PE), in rare-gas solids such as argon (Ar) and in hydrogen (H2) has been examined based on the experimental data by Simha, Zoller and Rehage for polymers and Cheng, Mills and Zha for rare-gas solids and an equation of state derived in a previous work. The volume-pressure relation at constant temperature for solid and liquid states is expressed by: V x (P 0 , T)/V x (P, T)= A x (P + P x ) m x where Vx (P0, T) is the volume at constant pressure P0 and temperature T, Vx (P, T) is the volume at P and T, Px is a function of temperature, mx is a constant and the subscript x means a state such as x = 1 for liquid and x = s for solid. It is found that values of Px change discontinuously with increasing temperature in the vicinity of Tg, while mx changes discontinuously at Tm where Px is continuous with respect to temperature. Values of Fm,s defined by F m,s = 1 − V s (P m , 0) V s (P m , T m ) for a rare-gas solid such as Ar are calculated based on the experimental data and are around 0.09 for Ar, independent of pressure, where Vs(Pm, Tm) is the volume of solid phase at Tm. Values of Fg defined by F g = 1 − V s (P g , T 0 ) V(P g ), T g ) at Tg are 0.036-0.055 for PS and 0.018–0.036 for PMMA. A three dimensional P-V-T surface over the temperature region including Tg and Tm is established based on the experimental data.