Colloids get hardcore: New simulation technique yields thermodynamic theory of hard-disk fluids

Colloids have the unique feature of being large enough to disregard quantum effects and observe optically while being small enough to experience Brownian motion. Focusing on the strong repulsions between molecules at short distances, hardcore interactions have become vital to understanding how colloids and other liquids behave in two dimensions. Work on the thermodynamics of hard-disk fluids at the walls of their planes is leading to a new theory that helps explain how these systems work.

Martin et al. derived a new generalized scaled-particle theory for uniform hard-disk mixtures. Assessed using Monte Carlo simulations coupled with Gibbs-Cahn integration, the theory provides a simple result for interfacial free energy of the hard-disk fluid at a planar hard wall in terms of the equation of state. The simulations achieve an accurate result for solid-liquid interfacial properties of a 2-D system.

“The paper represents an ideal collaboration between theory and simulation, applying the novel ideas of Gibbs-Cahn integration to a 2-D system,” said Hendrik Hansen-Goos, an author on the paper. “Theory and simulation have informed and guided each other.”

Standard scaled-particle theory, which has received broad support among liquid-state physicists, falls short when colloid densities become too high. This new theory mitigates these issues. It uses the small number of scaled-particle variables available in 2-D to approximate excess free energy density of a fluid of hard disks. The small number of variables limits the accuracy of the resulting interfacial free energies.

Hansen-Goos said he hopes the group’s findings will spark further interest in theory and simulation work on two-dimensional fluids.

Source: “Thermodynamics of the hard-disk fluid at a planar hard wall: Generalized scaled-particle theory and Monte Carlo simulation,” by Seth C. Martin, Brian B. Laird, Roland Roth, and Hendrik Hansen-Goos, The Journal of Chemical Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5043185 .