10.1098/rsta.2001.0808Beyond simple depletion: phase behaviour ofcolloid{star polymer mixturesBy W. C. K. P o o n1, S. U. E ge l ha a f1, J. S te llb rin k1;2,J. A ll ga i er2, A. B. S cho fiel d1a n d P. N. P u s e y11Department of Physics and Astronomy, University of Edinburgh,May¯eld Road, Edinburgh EH9 3JZ, UK2IFF-Neutronenstreuung II, Forschungszentrum Julich GmbH,D-52425 Julich, GermanySigni cant progress has been made in the last decade in u nderstanding mixtures ofhard-sphere colloids and (smaller) non-adsorbing, ideal, linear polymers. We intro-duce extra complexity into this simple model system by replacing the linear polymerswith star-branched polymers with increasing functionality but constant radius ofgyration. The observed phase diagrams, interpreted in light of what is known abouthard-sphere colloid plus linear polymer and binary-hard-sphere mixtures, suggestthat 32-arm stars are close to be having hard-sphere-like in colloid{star mixtures atthis size ratio.Keywords: depletion; colloid; hard spheres; polym er; star polym er1. IntroductionColloids, polymers and surf actants almost always occur in the form of mixtures,whether in nature or as industrial products. One of the main tasks of soft con-densed matter physics is to give generic (i.e. chemical-details-independent) insightinto the structure, dynamics, phase behaviour and non-equilibrium proper ties of suchmixtures. In practice, this entails identifying and studying in detail model systemsstripped of as many extraneous features as possible.Phase transitions in `soft mixtures’ can be driven mainly by enthalpy or entropy.Demixing in mixtures of polymers is the outstanding example of enthalpy-drivenphenomena. In other cases, entropy dominates. Over the last decade, a system thathas emerged as a model for such entropy-driven phase transitions is a mixture ofhard-sphere colloids and (smaller) random-coil polymers in a near-theta solvent forthe latter. In this system, the only interaction is that of excluded volume betweenthe colloids and between the colloids and polymers; the polymer coils can be treated,to a rst approximation, as ideal, and therefore interpenetrate each other freely.Detailed studies by experiment, theory and simulation have led to substantialprogress in understanding phase transitions and metastability in this idealized model.The essential physics is captured by the `depletion’ picture rst proposed by Asakura& O osawa (1958) and later independently by Vrij (1976). The centres of mass of poly-mer molecules are excluded from the vicinity of each particle, creating a `depletionzone’. Overlap of the depletion zones from neighbouring particles creates extra vol-ume for the polymers, thus increasing their entropy and lowering the free energyPhil. Trans. R. Soc. Lond. A (2001) 359, 897{907897c® 2001 The Royal Society898 W. C. K. Poon and othersof the system. It turns out that the topology of the equilibrium phase diagramdepends on the relative sizes of the polymer and colloid. In addition, a rich `zoo’ ofnon-equilibrium behaviour has been identi ed and rationalized within an emerginggeneral framework.In this paper, we report expe riments that go systematically beyond the ideal-ized model: the nearly ideal linear polymer is replaced by star- branched polymersof increasing functionality (number of arms). To simplify the terminology, we willrefer to the model system and the more complex systems just introduced as thecolloid{polymer mixture and the colloid{star mixture, respectively. Moreover, when`polymer’ is used without quali cation, it re fers to a linear coil. Ou r generic aim isto see how far the emerging comprehensive u nderstanding of colloid{polymer mix-tures can aid the interpretation of phenomena in more complex systems. The speci cmotivation for choosing to study colloid{star mixtures is to observe the way star poly-mers of increasing functionality become progressively less like interpenetrable coilsand more like mutually excluding hard particles (Seghrouchni et al . 1998). Thus,studying colloid{star mixtures with di¬erent functionalities can tell us how phasebehaviour evolves between the extremes of a colloid{polymer mixture on the onehand, and a binary hard-sphere colloid on the other.Below, we rst review the phase behaviour and non-equilibrium properties ofcolloid{polymer mixtures in x2. In x3 we report the phase diagrams of colloid{star mixtures with stars of functionalities 2, 6, 16 and 32 but the same radii ofgyration (thus maintaining a constant star-to-colloid size ratio). The data are thendiscussed in x4 in terms of existing knowledge of colloid{polymer and binary hard-sphere mixtures. We conclude in x5 with some speculations on colloid{star mixtureswith stars of higher functionality, and suggestions of other areas of exploration thatgo systematically beyond simple depletion.2. Colloid{polymer mixtures : a brief r eviewThe theoretical prediction for the phase behaviour of a colloid{polymer mixture isby now well known (Gast et al. 1983; Lekkerkerker et al. 1992). The key parametercontrolling the topology of the phase diagram is the ratio of the size of the polymer,e.g. as measured by its radius of gyration (rg), to the radius of the colloid (R), ¹ =rg=R. When ¹ is less than a ce rtain critical value, ¹c, the addition of polymer merelyexpands the ®uid{crystal coexistence region of pure h ard spheres, which occurs at0:494 < ¿c< 0:545 (where ¿cis the colloid volume fraction). At ¹ > ¹c, a colloidalliquid phase becomes possible , and the phase diagram displays a colloidal gas{liquidcritical point and a region of three-phase coexistence of colloidal gas, liquid andcrystal. Mean- eld theories predict ¹cº 0:33. Computer simulations con rmed thispicture (Meijer & Frenkel 1994; Dijkstra et al . 1999). The phase diagrams for ¹ = 0:1and 0.5 calculated according to L ekkerkerker et al. (1992) are shown in gure 1.Experimentally, the most well-studied realization of this simple model system is amixture of sterically stabilized PMMA spheres and linear polystyrene (PS) dispersedin cis-decahydronaphthalene (cis -decalin) (Ilett et al . 1995). These PMMA particlesbehave as nearly perfect hard spheres (Underwood et al. 1994), while cis-decalin isa theta-solvent for PS at 13¯C (Berry 1966). The qualitative picture outlined abovewas con rmed, although there were quantitative di¬erences between experiment andtheory. Experimentally, ¹cº 0 :
View Full Document
Unlocking...