Large attractive depletion interactions in soft repulsive–sphere binary mixtures

Abstract

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit, and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.

Depletion forces between particles immersed in nanofluids

“…Sanyal et al [24] and van Duijneveldt et al [25] were among the first to observe the fluid-solid phase transition in binary nearly-hard-sphere colloids with the size ratio 2R/ > 5, attributing it to the depletion of smaller spheres between larger spheres, an observation later extended to using polymer-coated spheres or pNIPAM nanogels as soft depletants [26,27]. A more recent theoretical study considering binary mixtures of soft repulsive spheres however predicted stronger depletion, as compared to hard spheres, and also a metastable fluid-fluid phase transition, which is yet to be verified experimentally [28]. Kaplan et al [29] and Dinsmore et al [30] reported that the fluid-solid transition for the larger spheres was promoted at a hard flat wall, due to the enhanced excluded volume effects at the wall, pointing to the importance of geometry consideration.…”

“…(4) is the correlation length between nanospheres, taking into consideration the range of interdepletant -soft‖ interactions of range [28]. In the presence of the electric double layer force, Zeng et al proposed that  =  -1 (the Debye length), and we suggest that could be generalised as the range of the soft inter-nanoparticle interaction, e.g.…”

How soft repulsion enhances the depletion mechanism

“…calculations [39][40][41][42][43][44][45]. Recent work has also been devoted to the effects induced by interactions between depletant molecules, such as the investigation of the phase behaviour of non-ideal mixtures of hard spheres with very short-range Yukawa tails [46] and a few studies on the effect of attractive interactions on depletion forces [47][48][49].…”

Depletion-driven four-phase coexistences in discotic systems

“…The first theory for the so-called depletion attraction originates from the work of Asakura and Oosawa in the 1950s [28,29]. For colloidal spheres mixed with non-adsorbing polymer chains, this depletion attraction has been widely studied [30], also for systems with direct colloid-colloid interactions beyond hard-core [31][32][33].…”