Reentrant equilibrium disordering in nanoparticle–polymer mixtures

Abstract

A large body of experimental work has established that athermal colloid/polymer mixtures undergo a sequence of transitions from a disordered fluid state to a colloidal crystal to a second disordered phase with increasing polymer concentration. These transitions are driven by polymer-mediated interparticle attraction, which is a function of both the polymer density and size. It has been posited that the disordered state at high polymer density is a consequence of strong interparticle attractions that kinetically inhibit the formation of the colloidal crystal, i.e., the formation of a non-equilibrium gel phase interferes with crystallization. Here we use molecular dynamics simulations and density functional theory on polymers and nanoparticles (NPs) of comparable size and show that the crystal-disordered phase coexistence at high polymer density for sufficiently long chains corresponds to an equilibrium thermodynamic phase transition. While the crystal is, indeed, stabilized at intermediate polymer density by polymer-induced intercolloid attractions, it is destabilized at higher densities because long chains lose significant configurational entropy when they are forced to occupy all of the crystal voids. Our results are in quantitative agreement with existing experimental data and show that, at least in the nanoparticle limit of sufficiently small colloidal particles, the crystal phase only has a modest range of thermodynamic stability.npj Computational Materials (2017) 3:3 ; doi:10.1038/s41524-016-0005-8 INTRODUCTIONOver five decades of experimental, theoretical and simulation work 1-13 have led to the knowledge that polymer-induced depletion attractions between colloids in solution can cause them to crystallize even at low polymer concentrations. For large colloids, both face centered cubic (FCC) and hexagonally closed packed (HCP) structures tend to form, since the free energy difference between these two polymorphs is very small. 14 In the nanoparticle limit, when the colloids and chains become comparable in size, we 13 recently showed that colloids preferentially crystallize into the HCP structure in the presence of a dilute concentration of long enough polymers, in preference to the FCC morphology. This preference is driven by the difference in the free energy cost of confining individual polymer chains within the voids of the two different colloidal crystal morphologies. Specifically, polymers prefer to occupy the octahedral voids (OV), which are~6 times larger in volume than the tetrahedral voids (TVs). The HCP structure features connected OVs, while in the FCC OVs are completely surrounded by TVs. Therefore, because a sufficiently long polymer chain must spread across multiple connected voids, it has significantly lower free energy in a HCP crystal than in the FCC analog. Further increasing the polymer density ϕ p , however, experimentally leads to disordered structures, and the formation of apparently kinetically arrested states (diffusion limited or reaction limited aggregations) that has generally been...

Entropic control over nanoscale colloidal crystals

“…However, if the polymer osmotic pressure is very large, it is expected that the crystal's interstices will eventually saturate and polymers may begin to interact; the polymorphic preference induced by 'dilutely' adsorbed polymers may begin to suffer as a result. Such investigations are the subject of ongoing work, which suggest that indeed, the resulting behaviour becomes significantly different [32]. Nonetheless, it is clear that often there exists a reasonable range of polymer densities which can both induce crystallisation of the colloids and lead to sufficient polymer partitioning to bias the formation of a desired polymorph, without incurring such complications.…”

“…This polymorphic selection mechanism represents a new addition to the 'engineering toolkit' with Downloaded by [University of Sussex Library] at 23:00 30 June 2016 which well-ordered colloidal crystals can be designed. Future work will continue to focus on extending the utility of this entropic control platform in order to stabilise arbitrarily chosen crystals, and establishing plausible experimental routes to these ends [32,33].…”

“…However, in what follows, I will review recent work that has revealed how to obtain a single chosen closepacked polymorph from a crystallising nanoscale binary mixture of colloids and polymers at will [29][30][31][32][33]. This can be accomplished by tuning the polymer's internal degrees of freedom, such as architecture and size, and so has been overlooked by previous investigations.…”

Direct Determination of the Phase Diagram of a Depletion-Mediated Colloidal System

“…By contrast, when attraction overwhelms the thermal energy, the particles are condensed to produce glassy structures or gels. 4,5 The origin of the depletion interaction and the principle behind the depletion-mediated colloidal assembly have been unveiled through various experimental and theoretical studies. The sole influence of depletion attraction on colloidal assembly and phase separation has been studied by introducing depletants into colloidal suspension, in particular for hard spheres.…”

“…In the particle-rich phases, monodisperse particles spontaneously form ordered crystals by rearranging beyond the nearest neighbors when the attraction potential is comparable with thermal energy. By contrast, when attraction overwhelms the thermal energy, the particles are condensed to produce glassy structures or gels. , The origin of the depletion interaction and the principle behind the depletion-mediated colloidal assembly have been unveiled through various experimental and theoretical studies. The sole influence of depletion attraction on colloidal assembly and phase separation has been studied by introducing depletants into colloidal suspension, in particular for hard spheres. ,− The depletion force or potential has been established with statistical kinetics , or direct measurement using an atomic force microscope. , …”