Assessment of the micro-structure and depletion potentials in two-dimensional binary mixtures of additive hard-disks

Abstract

Depletion forces are a particular class of effective interactions that have been mainly investigated in binary mixtures of hard-spheres in bulk. Although there are a few contributions that point toward the effects of confinement on the depletion potential, little is known about such entropic potentials in two-dimensional colloidal systems. From theoretical point of view, the problem resides in the fact that there is no general formulation of depletion forces in arbitrary dimensions and, typically, any approach that works well in three dimensions has to be reformulated for lower dimensionality. However, we have proposed a theoretical framework, based on the formalism of contraction of the description within the integral equations theory of simple liquids, to account for effective interactions in colloidal liquids, whose main feature is that it does not need to be readapted to the problem under consideration. We have also shown that such an approach allows one to determine the depletion pair potential in three-dimensional colloidal mixtures even near to the demixing transition, provided the bridge functions are sufficiently accurate to correctly describe the spatial correlation between colloids [E. López-Sánchez et al., J. Chem. Phys. 139, 104908 (2013)]. We here report an extensive analysis of the structure and the entropic potentials in binary mixtures of additive hard-disks. In particular, we show that the same functional form of the modified-Verlet closure relation used in three dimensions can be straightforwardly employed to obtain an accurate solution for two-dimensional colloidal mixtures in a wide range of packing fractions, molar fractions, and size asymmetries. Our theoretical results are explicitly compared with the ones obtained by means of event-driven molecular dynamics simulations and recent experimental results. Furthermore, to assess the accuracy of our predictions, the depletion potentials are used in an effective one-component model to reproduce the structure of either the big or the small disks. This demonstrates the robustness of our theoretical scheme even in two dimensions.

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids

“…We also use the simulation and theoretical results to provide new insights concerning the physics of ultra-dense highly correlated fluids. Concerning the new theoretical aspect, we consider the Modified-Verlet (MV) closure [20][21][22][23]. It was shown long ago [20,21] to produce very accurate results for pair structure and thermodynamic properties of monodisperse hard spheres in the "normal" liquid regime below the crystallization packing fraction of ~0.495 where glassy dynamics has not yet emerged.…”

Determining depletion interactions by contracting forces

“…An interesting and natural result obtained from Eq. ( 2), and confirmed by independent experiments and molecular simulations [12], is that the effective potential tends to the potential of mean force when only a few large particles are present (the leading term in b eff ll (r) is quadratic in n l [11]), even for high concentrations of small particles. The correlation terms in Eq.…”

Colloidal Soft Matter Physics

“…As stressed out above, one focus of colloidal science research is concerned with determining particle-particle effective interactions. More specifically, by means of the multicomponent Ornstein-Zernike equation, a theoretical approx-imation that accounts for the effective interactions between colloids when part of the system is integrated out of the description has been successfully developed [49,50]. As we will explain in detail in the following section, this approximation can be used, for example, to determine the phase behavior of a colloidal binary mixture and the depletion forces between large colloids [49].…”

“…For example, within the integral equations theory of liquids for the effective interactions, one takes advantage of the covariant property of the Ornstein-Zernike equation when the degrees of freedom of the unobservable components of the fluid are integrated out from the description and are fully taken into account within the effective potential between the observable molecules [75,76], i.e., colloids. This theoretical approximation represents a good starting point since it has been demonstrated that it quantitatively describes the effective potential among macromolecules when compared with either molecular simulations or experiments [50] and can be accurately applied near to non-equilibrium conditions [49]. In particular, this formalism has been used to understand the depletion forces between colloids, see, e.g., Refs.…”

“…In particular, this formalism has been used to understand the depletion forces between colloids, see, e.g., Refs. [50,75,76] and references therein, and the effective interactions in chargestabilized colloidal dispersions [77].…”