Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids with small bond angles: Effects of steric hindrance and ring formation

Marshall, Bennett D.; Haghmoradi, Amin; Chapman, Walter G.

doi:10.1063/1.4871307

Cited by 18 publications

(19 citation statements)

References 20 publications

(34 reference statements)

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“…Wertheim's theoretical framework has now been extended to deal with association into ring-like structures [53,54,[79][80][81][82][83][84][85], double bonding [85,86], and the effects of cooperative bonding on the energetics of the association interactions [84,87,88]. A number of recent developments have been made to increase the scope and general applicability of Wertheim's approach [89][90][91][92][93][94][95][96], largely motivated by a new found interest in the theory as applied to the description of the effect of association on the properties and phase behaviour of proteins and patchy colloids (e.g., see references [97][98][99][100][101][102][103][104][105][106][107][108]).…”

Section: Introductionmentioning

confidence: 99%

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

et al. 2015

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(2015) The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids, Molecular Physics, 113:9-10, 948-984, DOI: 10.1080/00268976.2015 An accurate representation of molecular association is a vital ingredient of advanced equations of state (EOSs), providing a description of thermodynamic properties of complex fluids where hydrogen bonding plays an important role. The combination of the first-order thermodynamic perturbation theory (TPT1) of Wertheim for associating systems with an accurate description of the structural and thermodynamic properties of the monomer fluid forms the basis of the statistical associating fluid theory (SAFT) family of EOSs. The contribution of association to the free energy in SAFT and related EOSs is very sensitive to the nature of intermolecular potential used to describe the monomers and, crucially, to the accuracy of the representation of the thermodynamic and structural properties. Here we develop an accurate description of the association contribution for use within the recently developed SAFT-VR Mie framework for chain molecules formed from segments interacting through a Mie potential [T. Lafitte, A. Apostolakou, C. Avendaño, A, Galindo, C. S. Adjiman, E. A. Müller, and G. Jackson, J. Chem. Phys. 139, 154504 (2013)]. As the Mie interaction represents a soft-core potential model, a method similar to that adopted for the Lennard-Jones potential [E. A. Müller and K. E. Gubbins, Ind. Eng. Chem. Res. 34, 3662 (1995)] is employed to describe the association contribution to the Helmholtz free energy. The radial distribution function (RDF) of the Mie fluid (which is required for the evaluation of the integral at the heart of the association term) is determined for a broad range of thermodynamic conditions (temperatures and densities) using the reference hyper-netted chain (RHNC) integral-equation theory. The numerical data for the association kernel of Mie fluids with different association geometries are then correlated for a range of thermodynamic states to obtain a general expression for the association contribution which can be applied for varying values of the Mie repulsive exponent. The resulting SAFT-VR Mie EOS allows for a much improved description of the vapour-liquid equilibria and single-phase properties of associating fluids such as water, methanol, ammonia, hydrogen sulphide, and their mixtures. A comparison is also made between the theoretical predictions of the degree of association for water and the extent of hydrogen bonding obtained from molecular simulations of the SPC/E and TIP4P/2005 atomistic models.

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Section: Introductionmentioning

confidence: 99%

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

et al. 2015

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“…It was demonstrated by Marshall et al 13,14 that TPT could be used to enforce cooperative effects in 2 site associating fluids. For the two site case, Δc (o) was evaluated in a resummed perturbation expansion over all possible chain lengths.…”

Section: A) Definition Of Free Energymentioning

confidence: 99%

“…Evaluating (5) subject to Eqns. (6), (7) and (10) (12) From (6) and (12) we obtain (13) The densities of the various bonding states can be calculated through the relation 5 (14) From (12) and (14) the density of molecules bonded at site A is given by (15) In Eq. (15) we have enforced that all one site densities are equal.…”

Section: B) Evaluation Of Bonding Fractionsmentioning

confidence: 99%

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A second order thermodynamic perturbation theory for hydrogen bond cooperativity in water

Marshall

2017

The Journal of Chemical Physics

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It has been extensively demonstrated through first principles quantum mechanics calculations that water exhibits strong hydrogen bond cooperativity. Equations of state developed from statistical mechanics typically assume pairwise additivity, meaning they cannot account for these 3-body and higher cooperative effects. In this paper, we extend a second order thermodynamic perturbation theory to correct for hydrogen bond cooperativity in 4 site water. We demonstrate that the theory predicts hydrogen bonding structure consistent spectroscopy, neutron diffraction, and molecular simulation data. Finally, we implement the approach into a general equation of state for water.

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“…It was observed [23,24] that this approximation is most accurate at a reduced density of 0.5. This approximation under-predicts bonding at the lower densities and over-predicts bonding at the higher densities, leading to a much too negative chemical potential at higher densities.…”

Section: B Simplifications -Single Bonding Patchmentioning

confidence: 99%

Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

Bansal

Chapman

Asthagiri

2017

The Journal of Chemical Physics

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We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f -functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graphtheoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere, a Janus particle, and a solute whose entire surface is available for association.

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Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids with small bond angles: Effects of steric hindrance and ring formation

Cited by 18 publications

References 20 publications

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

A second order thermodynamic perturbation theory for hydrogen bond cooperativity in water

Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

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