Effects of Pressure and Molecular Weight on the Miscibility of Polystyrene and Cyclohexane

Sun, Zhaoyan; An, Lijia; Li, Hongfei; Jiang, Zhenhua; Wang, Zhongwen

doi:10.1002/1521-3919(20010901)10:7<692::aid-mats692>3.0.co;2-u

Cited by 13 publications

(10 citation statements)

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“…Sun et al21 have calculated the FH interaction parameter ( γ ) for polystyrene/cyclohexane (PS/CH) solutions, and found the molecular‐weight dependence of γ has the following form: where M M is the weight‐average molecular weight of PS, and γ M is the part of the FH interaction parameter which is independent of the molecular weight. The const is a negative value for the system of PS/CH solutions.…”

Section: Resultscontrasting

confidence: 86%

“…On the basis of the FH theory, the free energy of mixing per lattice, G , can be expressed by: where $\Delta \overline{\overline F}$ is the free energy of mixing per lattice; k is the Boltzmann constant; T is the temperature; r 1 i is the number of lattices occupied by one chain of the subcomponent i of the polydisperse polymer 1; r 2 j is the number of lattices occupied by one chain of the subcomponent j of the polydisperse polymer 2; and φ 1 i and φ 2 j are the volume fractions of the subcomponent i of the polydisperse polymer 1 and the subcomponent j of the polydisperse polymer 2, respectively. The corresponding definitions are where r is the average number of lattice sites occupied by a molecule chain of the system; N is the total number of molecule chains in the system; N 1 i is the number of chains of the subcomponent i of polymer 1; N 2 j is the number of chains of the subcomponent j of polymer 2; and χ ij is the FH interaction parameter between the subcomponent i of polymer 1 and the subcomponent j of polymer 2, which is given by:8,21 where a is the proportional constant and χ 0 is the part of the FH interaction parameter which is independent of the chain length.…”

Section: Theory Backgroundmentioning

confidence: 99%

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Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

Sun

2006

Macro Theory & Simulations

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Summary: The chain‐length dependence of the Flory‐Huggins (FH) interaction parameter is introduced into the FH lattice theory for polydisperse polymer‐blend systems. The spinodals are calculated for the model polymer blends with different chain lengths and distributions. It is found that all the related variables, rn, rw, rz, and chain‐length distribution, have effects on the spinodals for polydisperse polymer blends.The spinodals at different chain lengths.magnified imageThe spinodals at different chain lengths.

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Section: Resultscontrasting

confidence: 86%

Section: Theory Backgroundmentioning

confidence: 99%

Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

Sun

2006

Macro Theory & Simulations

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“…It has been shown that such effects can be modeled by the Sanchez–Lacombe theory12–15 if one assumes that the difference in the interaction energies of the components depends on the square route of the M of the polymer 16. According to this hypothesis, χ remains chain‐length dependent up to very high polymer concentrations 17…”

Section: Resultsmentioning

confidence: 99%

On what terms and why the thermodynamic properties of polymer solutions depend on chain length up to the melt

Schneider

Schuld

Bercea

et al. 2004

J Polym Sci B Polym Phys

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Theoretical considerations based on chain connectivity and conformational variability of polymers have lead to an uncomplicated relation for the dependence of the FloryHuggins interaction parameter χ on the volume fraction of the polymer, ϕ , and on its number of segments, N. The validity of this expression is being tested extensively by means of vapor pressure measurements and inverse gas chromatography (complemented by osmotic and light scattering data from literature) for solutions of poly(dimethylsiloxane) in the thermodynamically vastly different solvents n-octane (n-C 8 ), toluene (TL), and methylethylketone (MEK) over the entire range of composition for at least six different molecular masses of the polymer. The new approach is capable to model the measured χ (ϕ , N ) very well, irrespective of the thermodynamic quality of the solvent, in contrast to traditional expressions, which are often restricted to good solvents but fail for bad ones and vice versa. At constant polymer concentration the χ values result lowest for n-C 8 (best solvent) and highest for MEK (theta solvent); the data for TL fall between. The influences of N depend strongly on the thermodynamic quality of the solvent and are not restricted to dilute solutions. For good solvents χ increases with rising N. The effect is most pronounced for n-C 8 , where the different curves for χ (ϕ ) fan out considerably. The influences of N become less distinct for TL, and for MEK they vanish at the (endothermal) theta temperature. For worse than theta conditions, the χ values of the long chains become less than that of short ones. This change in the sign of N-influences is in agreement with the present concept of conformational relaxation.

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“…The S-L EOS parameters have been previously reported in the literature for both pure cyclohexane 18,19 and carbon dioxide. 43−48 There are differences between our parameter values and the literature, as well as between the values reported in the literature.…”

Section: Industrial and Engineering Chemistry Researchmentioning

confidence: 99%

Volumetric Properties and Solubility Parameters of Cyclohexane + CO₂ Mixtures at High Pressures and Their Modeling with the Sanchez–Lacombe Equation of State

Williams

Dickmann

Hassler

et al. 2017

Ind. Eng. Chem. Res.

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Densities of mixtures of cyclohexane and carbon dioxide containing 0 to 50 wt % CO2 were determined using a variable-volume view cell at pressures ranging from 5 to 35 MPa and temperatures ranging from 313 to 393 K covering a density range from 0.55 to 0.83 g/cm3. The data were modeled with the Sanchez–Lacombe (S-L) equation of state (EOS). Modeling was conducted both by treating each mixture as a pseudopure compound and by using the S-L parameters for the pure components with a composition- and temperature-dependent interaction parameter. Various thermodynamic properties for the mixtures such as the isothermal compressibility, isobaric expansivity, internal pressure, excess volumes, and solubility parameters were then evaluated. Mixture excess volumes were also determined, and they were modeled with Redlich–Kister type equations. The mixture density data were also modeled using the S-L parameters for pure components and a composition- and temperature-dependent interaction parameter. Isothermal compressibilities ranged from 0.0008 MPa–1 for pure cyclohexane at 313 K and 35 MPa to 0.013 MPa–1 for the mixture containing 50 wt % CO2 at 393 K and 20 MPa. Isobaric expansivities ranged from 0.0008 K–1 for cyclohexane at 35 MPa and 313 K to 0.0035 K–1 for the 50 wt % CO2 mixture at 20 MPa and 393 K. Internal pressures ranged from 83.8 MPa for 50 wt % CO2 mixture at 20 MPa and 393 K to 275.5 MPa for cyclohexane at 35 MPa and 313 K. Solubility parameters ranged from 16.6 MPa0.5 for cyclohexane at 35 MPa and 313 K to 9.2 MPa0.5 for 50 wt % CO2 mixture at 20 MPa and 393 K. The mixtures showed a high degree of nonideality with excess volumes ranging from approximately −20 cm3 mol–1 for 50 wt % CO2 mixture at 20 MPa and 393 K to +2 cm3 mol–1 also for the 50 wt % CO2 mixture at 20 MPa, but at 313 K.

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Effects of Pressure and Molecular Weight on the Miscibility of Polystyrene and Cyclohexane

Abstract: Cloud points measured [90] (open symbols) for the system CH/ PS-X (the molecular weight of PS in kg/mol is indicated at the curves) plus spinodals (dashed lines), binodals (solid lines) and critical points (full symbols) calculated according to the SLLFT.

Cited by 13 publications

References 35 publications

Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

On what terms and why the thermodynamic properties of polymer solutions depend on chain length up to the melt

Volumetric Properties and Solubility Parameters of Cyclohexane + CO₂ Mixtures at High Pressures and Their Modeling with the Sanchez–Lacombe Equation of State

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Effects of Pressure and Molecular Weight on the Miscibility of Polystyrene and Cyclohexane

Abstract: Cloud points measured [90] (open symbols) for the system CH/ PS-X (the molecular weight of PS in kg/mol is indicated at the curves) plus spinodals (dashed lines), binodals (solid lines) and critical points (full symbols) calculated according to the SLLFT.

Cited by 13 publications

References 35 publications

Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

On what terms and why the thermodynamic properties of polymer solutions depend on chain length up to the melt

Volumetric Properties and Solubility Parameters of Cyclohexane + CO2 Mixtures at High Pressures and Their Modeling with the Sanchez–Lacombe Equation of State

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Volumetric Properties and Solubility Parameters of Cyclohexane + CO₂ Mixtures at High Pressures and Their Modeling with the Sanchez–Lacombe Equation of State