Polymer-enforced crystallization of a eutectic binary hard sphere mixture

Abstract

We prepared a buoyancy matched binary mixture of polydisperse polystyrene microgel spheres of size ratio Γ = 0.785 at a volume fraction of Φ = 0.567 just below the kinetic glass transition. In line with theoretical expectations, a eutectic phase behaviour was observed, but only a minor fraction of the samples crystallized at all. By adding a short non-adsorbing polymer we enforce interspecies fractionation into coexisting pure component crystals, which in turn also shows signs of intra-species fractionation. We show that in formerly inaccessible regions of the phase diagram binary hard sphere physics are made observable using attractive hard spheres.Binary colloidal mixtures are valuable model systems for fundamental studies of crystallization [1][2][3] . Detailed predictions of their phase behaviour exist for hard sphere (HS) systems of different size ratio Γ = R S /R L (where R i are the radii of small (S) and large (L) spheres, respectively). These show a sequence of spindle to azeotropic to eutectic phase diagram types with decreasing Γ, vanishing miscibility in the crystal phase for Γ < 0.85 and a huge variety of crystal structures for compounds [4][5][6][7][8][9] . For zero miscibility eutectics the inter-species fractionation is expected to cause a pronounced slowing of nucleation 8 . Polydispersities above 6% destabilize the crystal phases 11,12 (10% in 2D 10 ), hence additional intraspecies fractionation is expected for strongly polydisperse systems 13,14 1,2,7,18,19 and also the general sequence of phase diagram types was confirmed 20 , most parts of the phase diagram escape from a detailed experimental investigation; e.g., the exact locations of phase boundaries in compound forming systems have not yet been determined. Moreover, crystallization kinetics have not been obtained and, except for a recent 2D-study 21 , fractionation into coexisting Land S-crystals has not yet been observed. One main reason for this is the interference of crystallization with the glass transition (GT) at large volume fractions 22 . Furthermore, gravity seemingly enhances the trend to dynamically arrest the systems 23 . In addition, it may lead to differential sedimentation and inhomogeneities in composition 24,25 .In the present paper we avoid sedimentation using a binary mixture of buoyancy matched microgel particles. We further exploit earlier observations on a variety of systems, in which both vitrification can be suppressed [26][27][28] and crystallization be accelerated 29 by adding a short chained, non adsorbing polymer. Doing so, one moves from HS to attractive HS (AHS), which in principle may significantly alter both phase behaviour and crystallization kinetics [30][31][32][33][34][35][36][37] . However, using a binary AHS mixture at a size ratio of Γ = 0.785 we here give the first demonstration of the simultaneous precipitation of S-and L-crystals over the full range of compositions. Thus, we recover the zero miscibility eutectic solidification process expected for pure HS. Moreover, we provide experimental support...

Formation of Laves phases in buoyancy matched hard sphere suspensions

“…All static light scattering experiments were performed using a modified commercial instrument (SOFICA, France) described previously in some detail. 30,33 Here we only note that the angular resulution was 1° over a range of 25-145°, yielding scattering vector ranges of q = (5-30) µm -1 and q = (10-50) µm -1 for wave lengths of λ=633 nm or λ=403 nm, respectively. Taking the samples off the tumbler defines t W = 0.…”

“…In a previous study on a eutectic binary mixture of size ratio R S /R L = 0.74, we found that its eutectic phase behavior was retained upon addition of polymer. 30,31 Moreover, after suppressing the intervening glass transition the complete phase diagram, including the coexisting phases of pure L and S became accessible.…”

“…56 Moreover, sorting into L and S was also favored in the eutectic region of the same mixture. 30 In the experiments, we observe the crystallization of the pure S-component from the mixed ing. An interesting situation therefore emerges, where simultaneous sorting and local ordering compete.…”

Crystallization kinetics of colloidal binary mixtures with depletion attraction

“…Of course when we say 'slowed down', we compare it with the repulsive or attractive almost monodisperse colloids, because our analogous to A1 repulsive composition did not crystallize at all on a very long time scale. 44 In the case of slightly lower attraction (sample E6a), the stage of rapid conversion (up to 10 days) is accompanied by a slight crystal growth (up to 10 days in Fig. 5).…”

“…79 and f ¼ 0.567. 44 Upon increasing the volume fraction we instead observed vitrication. This observation is in line with earlier work [35][36][37] and has also been exploited to obtain a model system for studies of the hard sphere kinetic glass transition.…”