Thermodynamic perturbation theory for associating fluids with small bond angles: Effects of steric hindrance, ring formation, and double bonding

Marshall, Bennett D.; Chapman, Walter G.

doi:10.1103/physreve.87.052307

Cited by 38 publications

(60 citation statements)

References 41 publications

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“…Extensions of the theory to include the effects of ring formation have been limited to the cases of particles with two patches [27][28][29][30][31] (i.e. to the competition between chain and ring formation, but no branching) or with one patch, but allowing the formation of rings with 3 particles by double bonding of the patches [32].…”

Section: Pacs Numbersmentioning

confidence: 99%

Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points

2013

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We study the interplay between phase separation and self-assembly in chains, rings and branched structures in a model of particles with dissimilar patches. We extend Wertheim's first order perturbation theory to include the effects of ring formation and theoretically investigate the thermodynamics of the model. We find a peculiar shape for the vapor-liquid coexistence, featuring re-entrant behavior in both phases and two critical points, despite the single-component nature of the system. The emergence of the lower critical point is caused by the self-assembly of rings taking place in the vapor, generating a phase with lower energy and lower entropy than the liquid. Monte Carlo simulations of the same model fully support these unconventional theoretical predictions. PACS numbers:Understanding the competition between self-assembly and phase-separation is central in today's research in different fields encompassing biology, soft-matter, material science, statistical mechanics. Self-assembly of finitesize aggregates requires strong interaction energies compared to the thermal energy to guarantee that the generated structure is persistent. As a result, self-assembly competes with the ubiquitous macroscopic phase separation, the low-temperature tendency common to atoms, molecules and larger particles to maximize the number of bonded neighbours and minimize the potential energy, giving rise to a condensed (liquid) state [1]. When particles can arrange themselves into low energy and weakly interacting finite size aggregates, self-assembly can completely suppress phase separation [2][3][4]. Soft matter and biology offers several examples of three-dimensional stable aggregates (e.g. micelles, vesicles, capsids [5,6]) which constitute the stable phase in wide temperature and density regions.The possibility of hampering the formation of large amorphous aggregates in favor of ordered structures is often facilitated by the presence of strong, directional and saturable interactions (limited valence) [7][8][9]. The renewed focus on the role of directional interactions, stimulated by the synthesis of new-generation patchy colloids [10][11][12][13], has deepened our understanding not only of the role of the valence on the gas-liquid phase separation [14] but also on the competition between selfassembly and phase separation. Two recent investigations have provided insights particularly relevant for this work: (i) a numerical study of Janus colloids in which a gas-liquid critical point and a self-assembly process are simultaneously observed [15,16]. In this model, the formation of energetically stable vesicles stabilizes at low temperature T the gas-phase; (ii) a study of particles with dissimilar patches [17][18][19], promoting respectively chaining and branching, specifically designed to reproduce a mean-field model introduced by Safran and Tlustly [20] to describe the phase behavior of dipolar fluids. Here branching produces a gas-liquid critical point, but on cooling the formation of energetically favored chains stabilizes, thi...

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Section: Pacs Numbersmentioning

confidence: 99%

Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points

2013

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“…This will allow for a tractable and logical extension of our previous work (we will consider the more difficult general case in a future paper). 1 We then validate the theory by comparison to Monte Carlo simulation data for the three patch case. Once validated, we show that bond angle has a huge effect on the liquid-vapor equilibria of three patch colloids.…”

Section: Introductionmentioning

confidence: 87%

“…This means that all interactions which do not involve patches A or B will be treated in TPT1. As in our previous work, 1 we will assume that patches A and B do not self-attract, that is ε AA = ε BB = 0.…”

Section: A Asmentioning

confidence: 99%

“…1 When the angle α AB is large enough that patches A and B are independent → 1, which results in λ → 1 and c (o) ch:AB → 0. When bonding at patch A completely blocks another colloid from approaching to bond at patch B, the blockage integral vanishes → 0.…”

Section: A Asmentioning

confidence: 99%

“…In a recent publication, 1 we extended Wertheim's thermodynamic perturbation theory 2,3 (TPT) to include the effect of bond angle α AB in the equation of state for associating fluids with two association sites (an A association site and a B association site). It was found that various modes of association became dominant in various bond angle ranges.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Molecular theory for the phase equilibria and cluster distribution of associating fluids with small bond angles

Marshall

Chapman

2013

The Journal of Chemical Physics

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We develop a new theory for associating fluids with multiple association sites. The theory accounts for small bond angle effects such as steric hindrance, ring formation, and double bonding. The theory is validated against Monte Carlo simulations for the case of a fluid of patchy colloid particles with three patches and is found to be very accurate. Once validated, the theory is applied to study the phase diagram of a fluid composed of three patch colloids. It is found that bond angle has a significant effect on the phase diagram and the very existence of a liquid-vapor transition. © 2013 AIP Publishing LLC. [http://dx

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Thermodynamic Perturbation Theory for Associating Molecules

Marshall

Chapman

2016

Advances in Chemical Physics

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Thermodynamic perturbation theory for associating fluids with small bond angles: Effects of steric hindrance, ring formation, and double bonding

Cited by 38 publications

References 41 publications

Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points

Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points

Molecular theory for the phase equilibria and cluster distribution of associating fluids with small bond angles

Thermodynamic Perturbation Theory for Associating Molecules

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