Contribution of Slow Clusters to the Bulk Elasticity Near the Colloidal Glass Transition Jacinta C. Conrad, 1 Param P. Dhillon, 2 Eric R. Weeks, 3 David R. Reichman, 4 and David A. Weitz 1,5 1 Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 2 Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA 3 Department of Physics, Emory University, Atlanta, Georgia 30322, USA 4 Department of Chemistry, Columbia University, New York, New York 10027, USA 5 DEAS, Harvard University, Cambridge, Massachusetts 02138, USA (Received 18 July 2006; published 27 December 2006) We use confocal microscopy to visualize individual particles near the colloidal glass transition. We identify the most slowly-relaxing particles and show that they form spatially correlated clusters that percolate across the sample. In supercooled fluids, the largest cluster spans the system on short time scales but breaks up on longer time scales. In contrast, in glasses, a percolating cluster exists on all accessible time scales. Using molecular dynamics simulation, we show that these clusters make the dominant contribution to the bulk elasticity of the sample. DOI: 10.1103/PhysRevLett.97.265701 PACS numbers: 64.70.Pf, 82.70.Dd, 83.10.Rs Colloidal suspensions of hard-sphere-like particles are an excellent model system for the study of the glass tran- sition. Crowding of colloidal particles drives the glass transition [1,2]. The control parameter for hard spheres is the volume fraction, , rather than the temperature; col- loids undergo a glass transition as  is increased toward  g  0:58 [3]. New insight into the colloidal glass tran- sition has been obtained by imaging individual particles with confocal microscopy. The existence of spatial and temporal heterogeneities near the glass transition were confirmed by identifying the spatial correlations between structurally relaxing particles [1,2]. This allowed the direct observation of such heterogeneities [4,5], which had been inferred in other glasses [6 – 8]. It is the existence of such structural relaxations which distinguish a fluid from a glass. Ultimately, the glass is characterized by its solidlike behavior; even though it is disordered, it has a nonzero shear modulus at low frequencies [8]. The correlated clus- ters of mobile, relaxing particles, which have been the fo- cus of most prior studies, cannot bear a shear stress, and therefore cannot contribute to the development of the elas- tic modulus that typifies a glass. Instead, elasticity must re- sult from transiently immobilized regions, which percolate across the sample and can support a shear stress; while ear- lier studies have posited a relationship between the glass transition and rigidity percolation [9 –12], they do not con- sider the effects of dynamics. Regions of transiently immo- bilized particles would be directly analogous to the force chains that typify the jamming transition [13]. Such re- gions have not been identified in experiment, although their structure has been studied in simulation [14,15]. More- over, the implications of immobile regions on the macro- scopic mechanical properties have never been examined. In this Letter, we use confocal microscopy to image individual particles in colloidal suspensions near the glass transition. We identify the most slowly-rearranging parti- cles and show that they form spatially correlated clusters. On short time scales, the largest of these slow clusters spans the system, reflecting glasslike arrest, whereas on long time scales, the breakup of the spanning cluster reflects bulk, collective relaxation. The mechanical prop- erties of the slow clusters alone cannot be accessed experi- mentally; instead, we calculate rheological properties of these clusters using molecular dynamics simulation. We show that the slow dynamical clusters are responsible for the dominant contribution to the bulk elasticity of the sample; moreover, their break-up time is nontrivially cor- related with the time scale of the liquid-solid crossover identified from the frequency-dependent shear modulus. This provides the first direct evidence of the relationship between the solidlike behavior in a glass and the correlated regions of particles which are transiently immobile. We study a concentrated suspension of poly- (methylmethacrylate) colloids, sterically stabilized by poly-12-hydroxystearic acid [16], fluorescently dyed with rhodamine, and suspended in a mixture of cycloheptyl bromide and decahydronapthalene. The particles are nearly density- (  1:225 g=ml) and index-of-refraction- (n  1:50) matched, minimizing both sedimentation and scattering. The average radius is 1:18 m, with polydis- persity 5%. The particles are nearly hard-spheres but are slightly charged, crystallizing at a volume fraction   0:38 and melting at   0:42 [17], but the glass transition remains at  g  0:58 [2]. Prior to each experiment, we initialize the samples by stirring them [2,17]; no crystal- lization occurs in the samples during the experiment [17]. We image the particles in three dimensions using confocal microscopy, locating their centers to within 0:03 m in the horizontal plane and 0:05 m in the vertical plane [2,18]. We follow the time evolution of a 69 m  64 m  14 m section of the suspension, tracking the positions of 4000 particles during the experiment [19]. We identify slow particles by measuring NN, the number of changes in each particle’s nearest neighbors over a time difference  [15,20,21]. Nearest neighbors are identified as having separations less than that of the PRL 97, 265701 (2006) PHYSICAL REVIEW LETTERS week ending 31 DECEMBER 2006 0031-9007= 06=97(26)=265701(4) 265701-1  2006 The American Physical Society