Critical state in chain-molecule mixtures

Patterson, D.; Delmas, G.

doi:10.1039/tf9696500708

Cited by 115 publications

(26 citation statements)

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“…Patterson and Delmas (1969) recommended a set of reference parameters for alkanes to be used with PPCS based on considerations put forward by Flory and collaborators (Flory, 1964; Orwoll, 1967). The parameters for ethane and n-heptane are listed in Table 1.…”

Section: Molar Volumesmentioning

confidence: 99%

Volumetric properties of supercritical ethane‐n‐heptane mixtures: Molar volumes and partial molar volumes

Ehrlich

1973

AIChE Journal

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SCOPEA good deal is known about gas-liquid equilibria of paraffin mixtures, and the location of the gas-liquid critical lines (critical locus) has been determined for many binary mixtures of this type (Kay, 1968). Little information, on the other hand, is available on their thermodynamic properties in the supercritical phase. Some of these properties, for example the negative partial molar volumes of mixtures containing polar components (Ehrlich and Fariss, 1969) and presumed to exist in binary paraffin mixtures with components of sufficient size difference as well, appear quite anomalous in the context of the behavior of liquid mixtures at low reduced temperatures. The paraffin pair chosen represents two components of a most important homologous series which differ substantially in chain length. Any generalization of the results obtained in a study of the system ethane-n-heptane to mixtures in which the components exhibit varying molecular sizes and size differences is likely to be of interest in petroleum recovery and refining, as well as in the engineering of high pressure polyethylene processes. (The mixture ethane-polymethylene is a good model for ethylene-polyethylene.) Since, according to transition state theory, the pressure-coefficient of the reaction rate constant can be represented in terms of the compressibility of the mixture and the partial molar volumes of reactants and activated complex, a knowledge of the volumetric properties of supercritical systems should help in a solution of kinetic as well as thermodynamic problems.Molar volumes of the mixture ethane-n-heptane were therefore measured in the supercritical region, including the vicinity of the critical locus, over a pressure, temperature, and composition range corresponding to nearly pure ethane to about 20 mole #Yo heptane, and partial molar volumes were obtained by the analysis of volume-composition plots constructed from pressure-volume isotherms. The results were compared with two different sets of calculations based on equations of state. CONCLUSIONS AND SIGNIFICANCETwo approaches were found which were, in general, qualitatively successful in predicting the molar volumes and partial molar volumes in the region investigated. One of these was based on the reduced equation of state of Flory, Orwoll, and Vrij (FOV), used in conjunction with Prigogine's principle of corresponding states (PPCS) for chain molecule mixtures, the other on the Redlich-Kwong (RK) equation of state. The former method, in its original form, involves fewer arbitrary assumptions and can be extended in a straightforward manner to other binary mixtures of the same homologous series. The FOV equation was, however, proposed for liquids (negligible reduced pressure and low reduced temperature), and an empirical adjustment of its parameters was required for a good fit of the experimental data. The RK equation, on

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Section: Molar Volumesmentioning

confidence: 99%

Volumetric properties of supercritical ethane‐n‐heptane mixtures: Molar volumes and partial molar volumes

Ehrlich

1973

AIChE Journal

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“…In a previous paper [1], this phenomenon was investigated in terms of the thermodynamic free volume theory for polymer solutions proposed by Prigogine [2], Patterson [3][4][5][6] and Flory [7,8]. The notion of the apparent theta temperature (point) TO ap was then introduced for a temperature at which the second virial coefficient becomes zero [9].…”

Section: Introductionmentioning

confidence: 99%

Lower critical solution temperature (LCST) and theta temperature of aqueous solutions of nonionic surface active agents of various polyoxyethylene chain lengths

Fujimatsu

Ogasawara

Kuroiwa

1988

Colloid & Polymer Sci

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Cloud points of aqueous solutions of homogeneous poly(oxyethylene)dodecyl ether derivatives (C12(OE)n : 1"/= 2-8) and the apparent theta temperature TO ap were determined from the abrupt changes in optical transmittance and the temperature dependence of the second viriai coefficient obtained by light scattering measurements. It was found that the lower critical solution temperature (LCST) shifts to a lower temperature and lower concentration as the number of oxyethylene units in a molecule decreases. Because of this behavior of LCST, the modified Flory-Schultz plot of phase separation was applied to the present nonionie surfactant-water system, and its theta temperature obtained. The dependence of TO ap on the number of oxyethylene units suggests that the polyoxyethylene chain has different effects on the solubility of C12(OE)n in water for n less than or equal to 3 from those for n greater than or equal to 4.

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“…(27)]. Delmas and Patterson [10] calculated binary critical curves of polymer-solvent systems using the Flory equation of state [11,12]. Many polymer-solvent systems, at temperatures above the UCST, show a second region with liquid-liquid immiscibilty (Figure 2.2), which is characterized by the occurrence of a lower critical solution temperature (LCST) [9].…”

Section: Flory-huggins Theory and Liquid-liquid Equilibriamentioning

confidence: 99%

Polymer Thermodynamics

Loos¹

2005

Handbook of Polymer Reaction Engineering

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Critical state in chain-molecule mixtures

Cited by 115 publications

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Volumetric properties of supercritical ethane‐n‐heptane mixtures: Molar volumes and partial molar volumes

Volumetric properties of supercritical ethane‐n‐heptane mixtures: Molar volumes and partial molar volumes

Lower critical solution temperature (LCST) and theta temperature of aqueous solutions of nonionic surface active agents of various polyoxyethylene chain lengths

Polymer Thermodynamics

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