On the effects of association in fluids with spherically symmetric interactions

Kalyuzhnyi, Yu. V.; Stell, G.

doi:10.1080/00268979300100821

Cited by 105 publications

(102 citation statements)

References 17 publications

Supporting

Mentioning

101

Contrasting

Order By: Relevance

“…Elimination of this element eliminates the doubly counted diagrams which required the 1/2 factor. To see this, consider the diagram pair, (29) which is generated from two different source terms in Eq. (1), i.e., the diagram on the left is generated by the term, while the diagram on the right, which is obviously equivalent due to the normalization of the molecular S-bond, is generated from the source term in the OZ equations.…”

Section: B Low Order Angular Expansion Of the Site-site Equationsmentioning

confidence: 99%

A site-renormalized molecular fluid theory

Dyer

Perkyns

Pettitt

2007

The Journal of Chemical Physics

View full text Add to dashboard Cite

The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335(1982]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.

show abstract

Section: B Low Order Angular Expansion Of the Site-site Equationsmentioning

confidence: 99%

A site-renormalized molecular fluid theory

Dyer

Perkyns

Pettitt

2007

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Mueller and Gubbins 38 correlated this quantity as a function of bond angle ω as y (0) = (1 + aη + bη 2 )/(1 − η) 3 where a and b are constants which depend on ω and are tabulated in the original paper. 38 For our case θ (c) is fixed not ω.…”

Section: Appendix B: Expressions For the Integrals E (11) E (21) mentioning

confidence: 99%

“…In the previous two papers 1, 2 thermodynamic perturbation theory for central force (TPT-CF) associating potential, [3][4][5] which was formulated for one multiply bondable attractive site, placed in the center of the particle, was extended to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. The theory, which we call resummed TPT-CF (RTPT-CF) was applied to describe the properties of multiply bondable one-patch 1 and multi-patch 2 models of associating fluid.…”

Section: Introductionmentioning

confidence: 99%

Second-order resummed thermodynamic perturbation theory for central-force associating potential: Multi-patch colloidal models

Kalyuzhnyi

Marshall

Chapman

et al. 2013

The Journal of Chemical Physics

View full text Add to dashboard Cite

We propose a second-order version of the resummed thermodynamic perturbation theory for patchy colloidal models with arbitrary number of multiply bondable patches. The model is represented by the hard-sphere fluid system with several attractive patches on the surface and resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. The theory represents an extension of the earlier proposed first order resummed thermodynamic perturbation theory for central force associating potential and takes into account formation of the rings of the particles. In the limiting case of singly bondable patches (total blockage), the theory reduces to Wertheim thermodynamic perturbation theory for associating fluids. Closed-form expressions for the Helmholtz free energy, pressure, internal energy, and chemical potential of the model with an arbitrary number of equivalent doubly bondable patches are derived. Predictions of the theory for the model with two patches appears to be in a very good agreement with predictions of new NVT and NPT Monte Carlo simulations, including the region of strong association.

show abstract

“…In addition to perturbation theory, the more complex formalism of integral equation theory (IET) can be employed. 24,25 Given the remarkable success in applying TPT1 to describe the self-assembly and phase behavior of patchy colloid fluids. It would be equally valuable to have such a tool to describe the self-assembly and phase behavior of competitive colloids.…”

Section: I: Introductionmentioning

confidence: 99%

A theory for the effect of patch/non-patch attractions on the self-assembly of patchy colloids

Marshall

2017

Soft Matter

View full text Add to dashboard Cite

In this paper, we develop a thermodynamic perturbation theory to describe the selfassembly of patchy colloids which exhibit both patch-patch attractions as well as patch / non-patch attractions. That is, patches attract other patches as well as the no patch region (we call this region Ψ). In general, the patch-patch and patch-Ψ attractions operate on different energy scales allowing for a competition between different modes of attraction. This competition may result in anomalous thermodynamic properties. As an application, we tune the patch parameters to reproduce the liquid density (suitably scaled) maximum of water. It is then shown that the liquid branch of the colloids phase diagram has liquid densities consistent with both saturated and super-cooled liquid water. Finally, it is shown that the colloids reproduce water's anomalous minimum in isothermal compressibility and negative volume expansivity.

show abstract

On the effects of association in fluids with spherically symmetric interactions

Cited by 105 publications

References 17 publications

A site-renormalized molecular fluid theory

A site-renormalized molecular fluid theory

Second-order resummed thermodynamic perturbation theory for central-force associating potential: Multi-patch colloidal models

A theory for the effect of patch/non-patch attractions on the self-assembly of patchy colloids

Contact Info

Product

Resources

About