Kinetic arrest of crowded soft spheres in solvents of varying qualityE. Stiakakis,1D. Vlassopoulos,1,2B. Loppinet,1J. Roovers,1,3and G. Meier41FORTH, Institute of Electronic Structure and Laser, GR-71110 Heraklion, Crete, Greece2University of Crete, Department of Materials Science and Technology, GR-71003 Heraklion, Crete, Greece3NRC, Institute for Chemical Process and Environmental Technology, Ottawa, Ontario, Canada K1A 0R64Forschungszentrum Ju¨lich, Institut fu¨r Festko¨rperforschung, D-52425 Ju¨lich, Germany共Received 23 July 2002; published 13 November 2002兲Crowded solutions of multiarm star polymers, representing model colloidal spheres with ultrasoft repulsiveinteractions, undergo a reversible gelation transition upon heating in solvents of intermediate quality 共betweengood and ⌰). This unusual phenomenon is due to the kinetic arrest of the swollen interpenetrating spheres athigh temperatures, forming clusters, in analogy to the colloidal glass transition. In this work we demonstratethat the choice of the solvent has a dramatic effect on the gelation transition, because of the different degree ofstar swelling 共at the same temperature兲 associated with the solvent quality. We construct a generic kinetic phasediagram for the gelation of different stars in different solvents 共gelation temperature against effective volumefraction,) and propose a critical ‘‘soft sphere close packing’’ volume fractioncdistinguishing thetemperature-induced 共for⬍c) from the concentration-induced 共for⬎c) glass-like gelation. We con-clude that appropriate selection of the solvent allows for manipulation of the sol-gel transition in such ultrasoftcolloids.DOI: 10.1103/PhysRevE.66.051804 PACS number共s兲: 61.25.Hq, 82.70.Dd, 82.70.Gg, 83.80.HjI. INTRODUCTIONColloidal gelation and glass transition have fascinated sci-entists for many years 关1,2兴. These intriguing physical phe-nomena relate to the phase behavior of colloidal dispersions,and consequently to colloidal stabilization, which is of greatimportance for a variety of applications ranging from foodand biological products to oil recovery and coatings 关3兴.Whereas gelation and glass transition possess many commonfeatures, they also exhibit distinct differences originating atmolecular level. It is thus of prime interest to understandthoroughly gelation, glass transition and in more generalterms the physics of the transition from liquid to 共amor-phous兲 solid in colloidal suspensions. Till date, most of thework addressing these topics has been carried out with hardspheres 关1,3–6兴, which have been found to undergo a glasstransition to a disordered solid at a volume fraction⬃0.58; this transition is manifested as a nondecaying com-ponent of the dynamic structure factor and implies a struc-tural arrest of the crowded suspension 关4–6兴. More recently,soft colloids with weakly attractive interactions were inves-tigated 关2兴. Remarkably, glass transition and gelation werefound to be intrinsically related with the fluid to solid tran-sition, which is manifested as a kinetic arrest, and is drivenby the crowding of single particles 共caging due to steric hin-drance兲 or clusters of particles 共attraction-driven兲, respec-tively 关2,7兴. These observations corroborate the notion of ageneric jamming transition, a characteristic of a wide rangeof soft materials which lose their ability to flow at high vol-ume fractions 关1,8,9兴.Of particular interest in this class of materials, which be-come kinetically trapped when crowded, are polymericallystabilized colloids, such as colloidal particles with graftedpolymeric chains, the latter representing the stabilizing me-dium 关10,11兴. In these systems both colloidal 共core兲 andpolymeric 共chain兲 behavior contribute to the structure anddynamics of the suspension, and provide two groups of mo-lecular parameters for tuning such liquid-solid transitions.Multiarm star polymers constitute a limiting case of this typeof suspension, being characterized by a nonuniform mono-mer density profile, and yielding a very small deformablecore and corona of grafted chains with a typical size about 10times that of the core 共see Fig. 1兲关12,13兴. They are known torepresent model ultrasoft colloidal spheres with wide rangingweak repulsive potential 关14兴, which is monitored by thenumber and size of the star arms. In these systems the poly-meric and colloidal features have been identified and relateprimarily to arm 共or arm segment兲 collective relaxation andoverall star self-diffusion, respectively 关13兴. Their interplayreflects the relative polymeric and colloidal contributions onthe system’s dynamics, suggesting ways for molecular de-sign and control of such hybrid soft materials 关13,15,16兴.It was shown experimentally, that when suspended in sol-vents of intermediate quality between good 关17兴 and ⌰关18兴共characterized by excluded volume interactions only and ne-glecting the weak van der Waals attraction兲 at high volumefractions, these star polymers exhibited a dramatic increasein their mechanical moduli upon heating, eventually yieldinga solid-like response 关19兴. This phenomenon was character-ized by a slow kinetics of heating-induced gelation and aneven slower kinetics of liquification upon cooling 关20兴, andwas attributed to the formation of clusters causing a partialdynamic arrest of the swollen interpenetrating spheres athigh temperatures. A kinetic phase diagram was proposedand discussed in analogy to the phase diagram of charge-stabilized colloids; in the latter case colloids exhibited mac-rocrystalline order due to the increase of the number concen-tration, whereas the present ultrasoft systems gelled atconstant number of stars. Thus, achieving 共through differentmeans兲 a high enough volume fraction 共corresponding tooverlapping of the spheres兲 is the prerequisite for gelation.According to the proposed mechanism of the reversiblePHYSICAL REVIEW E 66, 051804 共2002兲1063-651X/2002/66共5兲/051804共9兲/$20.00 ©2002 The American Physical Society66 051804-1thermal gelation in intermediate solvents 关19,20兴, as the tem-perature increases the solvent quality improves and the pe-ripheral blobs of the interacting liquid-ordered soft spheresswell; consequently, the spheres enhance their arms’ overlap,but not to a large extent because of an increasingly strongexcluded volume repulsion.
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