Fluids with competing interactions: II. Validating a free energy model for equilibrium cluster size

Abstract

Using computer simulations, we validate a simple free energy model that can be analytically solved to predict the equilibrium size of self-limiting clusters of particles in the fluid state governed by a combination of short-range attractive and long-range repulsive pair potentials. The model is a semi-empirical adaptation and extension of the canonical free energy-based result due to Groenewold and Kegel [J. Phys. Chem. B, 105 (2001)], where we use new computer simulation data to systematically improve the cluster-size scalings with respect to the strengths of the competing interactions driving aggregation. We find that one can adapt a classical nucleation like theory for small energetically-frustrated aggregates provided one appropriately accounts for a size-dependent, microscopic energy penalty of interface formation, which requires new scaling arguments. This framework is verified in part by considering the extensive scaling of intracluster bonding, where we uncover a superlinear scaling regime distinct from (and located between) the known regimes for small and large aggregates. We validate our model based on comparisons against approximately 100 different simulated systems comprising compact spherical aggregates with characteristic (terminal) sizes between six and sixty monomers, which correspond to wide ranges in experimentally-controllable parameters.

Expanded discussion on size-dependent interfacial energies of droplets

References in corpus (5)

• Phase behavior of a fluid with competing attractive and repulsive interactions
• Colloidal systems with competing interactions: from an arrested repulsive cluster phase to a gel
• Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers
• Origin and Detection of Microstructural Clustering in Fluids with Spatial-Range Competitive Interactions
• Fluids with competing interactions: I. Decoding the structure factor to detect and characterize self-limited clustering

Cited by in corpus (8)

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• Self-Assembly of Spiral Patterns in Confined System with Competing Interactions
• Non-Equilibrium View of the Amorphous Solidification of Liquids with Competing Interactions
• Postponing the dynamical transition density using competing interactions
• Discontinuous Structural Transitions in Fluids with Competing Interactions