Phase stability of colloidal mixtures of spheres and rods

Abstract

We determined the phase boundaries of aqueous mixtures containing colloidal rod-like fd-viruses and polystyrene spheres using diffusing-wave spectroscopy and compared the results with free volume theory predictions. Excluded volume interactions in mixtures of colloidal rods and spheres lead to mediated depletion interactions. The strength and range of this attractive interaction depend on the concentrations of the particles, the length L and diameter D of the rods and the radius R of the spheres. At strong enough attraction, this depletion interaction leads to phase separation. We experimentally determined the rod and sphere concentrations where these phase transitions occur by systematically varying the size ratios L/R and D/R and the aspect ratio L/D. This was done by using spheres with different radii and modifying the effective diameter of the rods through either the ionic strength of the buffer or anchoring a polymeric brush to the surface of the rods. The observed phase transitions were from a binary fluid to a colloidal gas/liquid phase coexistence which occurred already at very low concentrations due to the depletion efficiency of highly anisotropic rods. The experimentally measured phase transitions were compared to phase boundaries obtained using free volume theory (FVT), a well established theory for calculating the phase behaviour of colloidal particles mixed with depletants. We find good correspondence between the experimental phase transitions and the theoretical FVT model where the excluded volume of the rod-like depletants was explicitly accounted for in both the reservoir and the system.

Excluded volume interactions and phase stability in mixtures of hard spheres and hard rods

“…Here, we outline the FVT employed in this paper, which is based on previous work on binary HS mixtures 15 but extended to take the anisotropic shape of rod-like depletants into account. 27 In FVT the two compartments used are in osmotic equilibrium and the thermodynamic properties of the system can be described by the semi-grand potential Ω . The experimental system of interest here is the mixture of hard spheres (s) and hard rod-like depletants (r).…”

“…Comparison with the FVT by Vliegenthart and Lekkerkerker 17 showed that FVT predicts phase transitions at too low colloidal rod concentrations. 27 More recently, it was shown that experimentally observed phase boundaries in mixtures of fd-virus and polystyrene spheres can be described more accurately by FVT with excluded volume interactions already included at the level of the reservoir. 27 This novel FVT method is a relatively simple and quick method to predict the phase boundaries of colloidal mixtures.…”

“…27 More recently, it was shown that experimentally observed phase boundaries in mixtures of fd-virus and polystyrene spheres can be described more accurately by FVT with excluded volume interactions already included at the level of the reservoir. 27 This novel FVT method is a relatively simple and quick method to predict the phase boundaries of colloidal mixtures. An accurate description of the phase behaviour may also help to predict and understand nucleation and crystallisation in such complex mixtures.…”

“…27 More recently, it was shown that experimentally observed phase boundaries in mixtures of fd -virus and polystyrene spheres can be described more accurately by FVT with excluded volume interactions already included at the level of the reservoir. 27…”

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“…Slender rods are far more effective depletant than the commonly used polymers, as also the orientational entropy is strongly reduced when rods are confined between two cells [37][38][39]. As such the rod-like virus is a pure depletant that induces long-ranged attraction at very low volume fractions, inducing a depletion force that can be tuned by varying the concentration of these rods [40][41][42][43][44].…”