INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTERJ. Phys.: Condens. Matter 14 (2002) R859–R880 PII: S0953-8984(02)38822-2TOPICAL REVIEWThe physics of a model colloid–polymer mixtureWCKPoonDepartment of Physics and Astronomy, The University of Edinburgh, Mayfield Road,Edinburgh EH9 3JZ, UKReceived 1 July 2002Published 9 August 2002Online at stacks.iop.org/JPhysCM/14/R859AbstractThe addition of non-adsorbing polymer to a colloidal suspension inducesan interparticle ‘depletion’ attraction whose range and depth can be ‘tuned’independently by altering the polymer’s molecular weight and concentrationrespectively. Over the past decade, one particularly simple experimentalrealization of such a mixture has been studied in considerable detail:nearly-hard-sphere particles of poly(methyl methacrylate) and random-coilpolystyrene dispersed in simple hydrocarbon solvents (mainly cis-decalin). Thesimplicity of the system has enabled rather detailed comparison of experimentalfindings with theory and simulation. Here I review the current understandingof the equilibrium phase behaviour, structure, phase transition kinetics, andmetastability of this model colloid–polymer mixture. These findings form auseful reference point for understanding more complex mixtures. Moreover,in some cases, insights gained from studying this model system have relevancebeyond soft-condensed-matter physics, e.g. in understanding the liquid state,in controlling protein crystallization, and in elucidating the nature of glasses.(Some figures in this article are in colour only in the electronic version)Contents1. Introduction 8602. The system 8613. Equilibrium phase behaviour 8623.1. Hard spheres and near-ideal polymer: how to make a liquid 8623.2. Effect of temperature, polymer non-ideality, and polydispersity on phasebehaviour 8643.3. Equilibrium structure and particle dynamics 8663.4. Comparison with theory 8664. Phase transition kinetics 8705. Long-lived metastable states: gels and glasses 8725.1. The high-density limit: multiple glassy states 8725.2. Lower densities: clusters and gels 8740953-8984/02/330859+22$30.00 © 2002 IOP Publishing Ltd Printed in the UK R859R860 Topical Review6. Summary and outlook 877Acknowledgments 878References 8781. IntroductionThe work of Peter Pusey with his collaborators in the 1980s established that suspensions ofpoly(methyl methacrylate) (PMMA) particles sterically stabilized by chemically grafted poly-12-hydroxystearic acid (PHSA) behaved like almostperfect hard spheres. Their equilibriumphase behaviour in the test tube matched that predicted by computer simulations, showingcoexistence of colloidal fluid and crystal phases in the range 0.494 <φ<0.545 (where φis thevolume fraction) [1]. The colloidal crystals were found, using static light scattering, toconsist of hexagonally packed layers of particles stacked in a random sequence [2], consistentwith the simulation result that face-centred cubic and hexagonal close-packed arrangements ofhard spheres would have very similar free energies [3] (more accurate simulations have sincebeen achieved using novel methods; see, e.g., [4]). The diffusive dynamics of the particleswithin thefluid phase, probed by dynamic light scattering,were also consistent with them beinghard spheres [5]. A glass transition occurred at φg∼ 0.58, where the ‘caging’ of particles bytheir neighbours became essentially permanent and rearrangements leading to crystallizationdid not occur [1]. The non-decaying component of the density fluctuations in the glass phase,again probed by dynamic light scattering [6], showed significant agreement with some ofthe first calculations made on hard-sphere glasses using mode-coupling theory [7]. Finally,binary mixtures of PMMA particles with specific ratio of radii were found to give rise tovarious superlattice, or alloy, phases at high densities [8], consistent with simulations basedon packing considerations [9].Many of these achievements were ably reviewed by Peter himself in his Les Houchesnotes [10], published in the same year that he took up the Chair of Physics in Edinburgh. Inthese notes, Peter described the ‘colloids as atoms’ approach. Since colloids undergo Brownianmotion, they explore configurational space and will, given time, come to thermodynamicequilibrium. The tools of statistical mechanics, honed in the contextofatomic and molecularmaterials, can therefore be ‘borrowed’ to discuss the behaviour of colloids. This approach islikely to be particularly fruitful in cases where the particles have well-characterized size, shape,and interaction—‘model colloids’. Peter’s own work on hard-sphere PMMA particles has donemuch to establish this ‘paradigm’ for modern colloid physics. (For a historical perspective onthis approach, see the article by Haw in this Special Issue [11].)When, as a complete novice to colloids, I read Peter’s Les Houches review in 1991, thebrief section on colloid–polymer (CP) mixtures particularly held my attention. The exclusionof polymer from the region between two nearby particles leads to an unbalanced osmoticpressure pushing them together [12, 13], which can be modelled as an ‘effective attraction’;figure 1. The range and depth of this ‘depletion attraction’ are controlledbythepolymer’s sizeand concentration respectively. The simplest conceivable system of this kind (at least for aphysicist!) would be hard spheres mixed with a non-adsorbingpolymer, where the latter is itselfdissolved in a ‘theta solvent’ with the result that their mutual interaction is minimal (i.e. thepolymers are close to being ‘ideal’). In an important paper, Gast et al had already calculatedthe phase behaviour of just such a mixture [14], but the full range of their predictions hadnot been unequivocally confirmed in the early 1990s (e.g. there was no report of three-phasecoexistence); the experimental literature in fact contained a number of observations that didnot fit within the theoretical scheme (e.g. some of the optical micrographs published by Sperrysuggested various non-equilibrium aggregates [15]).Topical Review R861BCAFigure 1. Aschematic illustration of the depletion interaction. The centreof a polymer molecule (coil) is excluded from coming closer than a certaindistance, approximately its own radius of gyration, to the surface of acolloid (full circle) because of the high entropic cost of configurationaldistortion. Each colloid is
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