Distribution of physical clusters

Coniglio, Antonio; Angelis, U. de; Forlani, A.; Lauro, G.

doi:10.1088/0305-4470/10/2/011

Cited by 92 publications

(51 citation statements)

References 14 publications

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“…In other words, probabilistic clusters are much smaller on average than the deterministic Hill clusters. On the other hand, the mean cluster size of the probabilistic Hill clusters can be calculated using an integral equation theory 29 (Coniglio et al, 1977a). The percolation density is then determined by the divergence of the mean cluster size.…”

Section: Percolation Lines In Simple Fluidsmentioning

confidence: 99%

Clusters in simple fluids

Sator

2003

Physics Reports

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This article concerns the correspondence between thermodynamics and the morphology of simple fluids in terms of clusters. Definitions of clusters providing a geometric interpretation of the liquid-gas phase transition are reviewed with an eye to establishing their physical relevance. The author emphasizes their main features and basic hypotheses, and shows how these definitions lead to a recent approach based on self-bound clusters. Although theoretical, this tutorial review is also addressed to readers interested in experimental aspects of clustering in simple fluids.

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Section: Percolation Lines In Simple Fluidsmentioning

confidence: 99%

Clusters in simple fluids

Sator

2003

Physics Reports

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“…The division of the Mayer f-function into two parts results in the decomposition of a grand partition function into contributions determined by the particles that are contained in physical clusters and "free" unbonded particles. Hill's ideas were further developed by Coniglio et al [38] as applied to the problem of percolation. They succeeded in separating the subset of graphs from a standard cluster f-expansion of the theory of simple liquids that determines the special pair-correlation function h + (r), which relates only to the particles belonging to the same physical cluster.…”

Section: Clustering and Continuum Percolationmentioning

confidence: 99%

Structural Organization of Water-Containing Nafion: The Integral Equation Theory

Khalatur¹,

Talitskikh²,

Khokhlov³

2002

Macromol. Theory Simul.

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Using the mutually consistent variant of the integral equation polymer reference interaction site model (RISM) theory and the chemically realistic rotational isomeric state (RIS) model, we perform a molecular level modeling of the specific structural organization of perfluorosulfonic acid ionomer (Nafion) with certain amount of physisorbed water. Our results establish molecular scale information necessary for understanding the equilibrium structure and thermodynamics of water‐containing Nafion as well as water distribution and ionic (molecular) transport phenomena in hydrated Nafion membranes. As a first step in this direction, semi‐empirical quantum mechanical calculations on the molecular structures and energies of the polymeric backbone and pendant chains of Nafion with and without additional water molecules are carried out. These data are used in the single‐polymer RIS Monte Carlo simulation, in which the short‐range intramolecular interactions are taken into account via appropriate matrices of statistical weights. The local structure and morphology of the entire bicomponent water‐containing system is calculated consistently on the basis of the RISM theory at different contents of absorbed water. We find that the addition of even a relatively small amount of water leads to the strong intensification of aggregation processes observed for polar sulfonic acid (SO3H) groups. Water molecules and polar SO3H groups form mixed aggregates with a three‐layer structure. Incorporation of water molecules inside the aggregates results in an increase of their stability and leads to the increase of the number of associating groups in a stable aggregate. With increasing the number of incorporated solvent molecules, the average size of mixed aggregates increases. The results obtained in the present study support the concept of an irregularly shaped cluster surfaces. Such geometries are favorable to the formation of long channels of connected water‐containing aggregates providing the unique permeability characteristics of Nafion membranes. In addition, we investigate the clustering and continuum percolation in the water phase, using the formalism of pair‐connectedness correlation functions. The mean cluster size found theoretically is in reasonable agreement with the corresponding experimental estimates existing in the literature.

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“…Including these interactions augments the connectivity of the system and favours percolation. Since gas-liquid criticality is commonly preceded by percolation, 45 a phase separation sustained by s = 4, w = 4 defect clusters, which are not suppressed by rings, could occur at low T. However, we note that it is possible to have percolation but not phase separation. This suggests that a patchy particle model for DHS, in which chaining and branching are modelled via dissimilar patches, 30 may require not only chain-chain or chain-branching interactions, but also an additional, weaker branching-branching contribution to mimic the s = 4, w = 4 defect clusters.…”

Section: Discussionmentioning

confidence: 74%

Branching points in the low-temperature dipolar hard sphere fluid

Rovigatti

Kantorovich

Иванов

et al. 2013

The Journal of Chemical Physics

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Branching points in the low-temperature dipolar hard sphere fluid In this contribution, we investigate the low-temperature, low-density behaviour of dipolar hardsphere (DHS) particles, i.e., hard spheres with dipoles embedded in their centre. We aim at describing the DHS fluid in terms of a network of chains and rings (the fundamental clusters) held together by branching points (defects) of different nature. We first introduce a systematic way of classifying inter-cluster connections according to their topology, and then employ this classification to analyse the geometric and thermodynamic properties of each class of defects, as extracted from state-of-the-art equilibrium Monte Carlo simulations. By computing the average density and energetic cost of each defect class, we find that the relevant contribution to inter-cluster interactions is indeed provided by (rare) three-way junctions and by four-way junctions arising from parallel or anti-parallel locally linear aggregates. All other (numerous) defects are either intra-cluster or associated to low cluster-cluster interaction energies, suggesting that these defects do not play a significant part in the thermodynamic description of the self-assembly processes of dipolar hard spheres.

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Distribution of physical clusters

Cited by 92 publications

References 14 publications

Clusters in simple fluids

Clusters in simple fluids

Structural Organization of Water-Containing Nafion: The Integral Equation Theory

Branching points in the low-temperature dipolar hard sphere fluid

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