Theory and simulation of associating liquid mixtures

Chapman, Walter G.; Gubbins, Keith E.; Joslin, Chris; Gray, C.G.

doi:10.1016/0378-3812(86)85033-6

Cited by 94 publications

(113 citation statements)

References 5 publications

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“…The fact that this temperature dependence is not included in the molecular model outlined above constitutes some degree of approximation. However, many accurate theories for the isotropic state of "real" molecules (e.g., SAFT, 22,23 PC-SAFT, 24 etc.) have been developed based on similar molecular models.…”

Section: Molecular Modelmentioning

confidence: 99%

“…Here, a 1 , a 21 , a 22 , a 31 , a 32 , b 1 , b 21 , and b 22 are adjusted constants. Note that for the case of linear chains (which by definition also includes hard spheres and dimers) Eqs.…”

Section: A Pure Componentsmentioning

confidence: 99%

“…The overall agreement is very good except for a small underestimation of the excluded volume at small angles γ . Since the 8 constants a 1 -b 22 (see Table I) were fitted to excluded volume data for identical chains only, it is expected that predictions based on Eqs. (23)- (26) become less accurate when the two molecules become less similar; a more stringent test is therefore the case of a linear chain and a fully flexible chain.…”

Section: B Mixturesmentioning

confidence: 99%

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An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Westen

Vlugt

Groß

2012

The Journal of Chemical Physics

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Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].

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Section: Molecular Modelmentioning

confidence: 99%

Section: A Pure Componentsmentioning

confidence: 99%

Section: B Mixturesmentioning

confidence: 99%

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An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Westen

Vlugt

Groß

2012

The Journal of Chemical Physics

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“…The physical foundation of the SAFT (Statistical Association Fluid Theory)-family equations of state [72] was built up by Wertheim applying perturbation theory of first and second order for directional interactions [73][74][75][76]. Chapman et al [77] extended the formalism to mixtures and developed an engineering approach for the description of associating fluids. Gross and Sadowski [78] introduced an interaction potential with soft repulsion and called this equation of state PC-SAFT.…”

Section: Introductionmentioning

confidence: 99%

Phase Diagrams for Systems Containing Hyperbranched Polymers

et al. 2012

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Abstract:Hyperbranched polymers show an outstanding potential for applications ranging from chemistry over nanotechnology to pharmacy. In order to take advantage of this potential, the underlying phase behaviour must be known. From the thermodynamic point of view, the modelling of these phase diagrams is quite challenging, because the thermodynamic properties depend on the architecture of the hyperbranched polymer as well as on the number and kind of present functional end groups. The influence of architecture can be taken into account via the lattice cluster theory (LCT) as an extension of the well-known Flory-Huggins theory. Whereas the Flory-Huggins theory is limited to linear polymer chains, the LCT can be applied to an arbitrary chain architecture. The number and the kind of functional groups can be handled via the Wertheim perturbation theory, applicable for directed forces between the functional groups and the surrounding solvent molecules. The combination of the LCT and the Wertheim theory can be established for the modelling or even prediction of the liquid-liquid equilibria (LLE) of polymer solutions in a single solvent or in a solvent mixture or polymer blends, where the polymer can have an arbitrary structure. The applied theory predicts large demixing regions for mixtures of linear polymers and hyperbranched polymers, as well as for mixtures made from two hyperbranched polymers. The introduction of empty lattice sites permits the theoretical investigation of pressure effects on phase behaviour. The calculated phase diagrams were compared with own experimental data or to experimental data taken from literature. OPEN ACCESSPolymers 2012, 4 73

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“…47 In addition to the theoretical work above, there have been several simulation studies of associating systems. Particularly, there have been investigations into bulk two and four site associating fluids, [48][49][50] as well as those located near a wall. 51 Further, there has also been some work done with simulations to study equilibrium chains near a surface 52 and end-adsorbed systems which mimic polymer brushes.…”

Section: Introductionmentioning

confidence: 99%

Fluids density functional theory studies of supramolecular polymers at a hard surface

McGarrity

Thijssen

Besseling

2010

The Journal of Chemical Physics

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We have applied a fluids density functional theory based on that of Yu and Wu ͓J. Chem. Phys. 116, 7094 ͑2002͔͒ to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.

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Theory and simulation of associating liquid mixtures

Cited by 94 publications

References 5 publications

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Phase Diagrams for Systems Containing Hyperbranched Polymers

Fluids density functional theory studies of supramolecular polymers at a hard surface

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