The effect of size ratio on the sphere structure factor in colloidal sphere-plate mixtures

Abstract

Binary mixtures of colloidal particles of sufficiently different sizes or shapes tend to demix at high concentration. Already at low concentration, excluded volume interactions between the two species give rise to structuring effects. Here, a new theoretical description is proposed of the structure of colloidal sphere-plate mixtures, based on a density expansion of the work needed to insert a pair of spheres and a single sphere in a sea of them, in the presence or not of plates. The theory is first validated using computer simulations. The predictions are then compared to experimental observations using silica spheres and gibbsite platelets. Small-angle neutron scattering was used to determine the change of the structure factor of spheres on addition of platelets, under solvent contrast conditions where the platelets were invisible. Theory and experiment agreed very well for a platelet/sphere diameter ratio D/d = 2.2 and reasonably well for D/d = 5. The sphere structure factor increases at low scattering vector Q in the presence of platelets; a weak reduction of the sphere structure factor was predicted at larger Q, and for the system with D/d = 2.2 was indeed observed experimentally. At fixed particle volume fraction, an increase in diameter ratio leads to a large change in structure factor. Systems with a larger diameter ratio also phase separate at lower concentrations.

Observation of isotropic–isotropic demixing in colloidal platelet–sphere mixtures

“…Still in question is the demixing between two isotropic fluids from the mixture of colloidal platelets and spheres. In previous studies, I-N demixing 13,16 was frequently observed, but isotropicisotropic (I-I) demixing has seldom been observed. Several theoretical studies were carried out with the goal of better understanding of I-I demixing.…”

“…[8][9][10] During the past few years, binary colloidal mixture systems have attracted much attention. [11][12][13] As the second component is incorporated, many new phenomena emerge, such as the dependence of demixing on size ratio, 14 the re-entrant phase boundaries, 15 and phase transitions due to the depletion interaction. 16,17 However, many mixture systems are inclined to gelation, 16,[18][19][20] presenting a challenge in the research of phase transitions in mixtures.…”

Sedimentation of colloidal plate-sphere mixtures and inference of particle characteristics from stacking sequences

“…Experimental works include studies on the structure [4] and the rheology [5] of mixtures of silica nanospheres and kaolinite plates, the observation of a slowdown of the crystallization transition of spheres due to the addition of plates [6], the occurrence of isotropic-columnar coexistence in charged mixtures of gibbsite plates and silica spheres [7,8], enhanced density fluctuations of the spheres due to the addition of plates in dilute suspensions [9], the formation of an arrested glass state in gibbsite platelets and silica sphere mixtures [10], and several sedimentation experiments in which a floating nematic layer sandwiched between two isotropic layers [11][12][13] was observed. From a theoretical point of view, the bulk properties of plate-sphere mixtures have been investigated via free-volume theory [14], density functional theory in the Onsager approximation with [15][16][17] and without [18] rescaling of the second virial coefficient as well as using fundamental measure density functional theory [15,[19][20][21], with explicit approximations to the configurational partition function [22], and via a density expansion on the work required to insert particles to the mixture [23].…”

Increasing entropy for colloidal stabilization

“…Although the entropically driven phase behaviours of binary colloidal dispersion systems have garnered considerable attention181920212223242526, these works have focused on phase demixing2627, and the function of entropy in the improvement of colloidal stability has been scarcely reported until now.…”