Direct observation of a local structural mechanism for dynamic arrest

Transcription

1 Direct observation of a local structural mechanism for dynamic arrest C. PATRICK ROYALL 1,2 *, STEPHEN R. WILLIAMS 3, TAKEHIRO OHTSUKA 2 AND HAJIME TANAKA 2 * 1 School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK 2 Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo , Japan 3 Research School of Chemistry, The Australian National University, Canberra, ACT 2, Australia * paddy.royall@bristol.ac.uk; tanaka@iis.u-tokyo.ac.jp Published online: 22 June 28; doi:1.138/nmat2219 The mechanism by which a liquid may become arrested, forming a glass or gel, is a long-standing problem of materials science. In particular, long-lived (energetically) locally favoured structures (LFSs), the geometry of which may prevent the system relaxing to its equilibrium state, have long been thought to play a key role in dynamical arrest. Here, we propose a definition of LFSs which we identify with a novel topological method and directly measure with experiments on a colloidal liquid gel transition. The population of LFSs is a strong function of (effective) temperature in the ergodic liquid phase, rising sharply approaching dynamical arrest, and indeed forms a percolating network that becomes the arms of the gel. Owing to the LFSs, the gel is unable to reach equilibrium, crystal gas coexistence. Our results provide direct experimental observation of a link between local structure and dynamical arrest, and open a new perspective on a wide range of metastable materials. When a liquid is cooled sufficiently, and is unable to access the thermodynamic equilibrium state, it may undergo dynamical arrest, which broadly occurs in two forms, glasses and gels 1,2. The former are associated with supercooling a liquid below its freezing temperature, whereas the latter are identified with arrested phase separation 3 5. Although possible dynamic mechanisms have received considerable attention, direct experimental evidence of structural mechanisms 6, has proved elusive 8 1. In the case of the colloidal gels of interest here, it has been suggested that spinodallike phase separation leads to the formation of a colloid-rich percolating network 4. Furthermore, dynamic asymmetry between large colloidal particles and small solvent molecules is expected to promote the formation of a network structure of the slow (colloidrich) component: viscoelastic phase separation 11. We expect that local arrest leads to rigidity in the arms of the network and are thus motivated to seek some local structural signature that underlies the overall arrest. In the case of the colloidal gels of interest here, the underlying thermodynamic ground state is crystal gas coexistence. Thus, in addressing the question of why gelation occurs, that is, why phase separation is arrested and the locally dense arms are geometrically frustrated from crystallizing, some parallels may be drawn with those glasses in which the thermodynamic ground state is a crystal. Colloidal gels are governed by their potential-energy landscape 12, where the thermodynamic equilibrium state is located in a deep valley, the global energy minimum (crystal gas coexistence). However, many other local energy minima exist, corresponding to gels. In this picture, dynamical arrest occurs when the system is quenched sufficiently that it can only explore a limited number of (local) potential-energy minima on the experimental timescale. In other words, on cooling, the minima become separated by energy barriers too high to surmount easily. The system is then trapped in a local minimum in the potential-energy landscape, unable to escape and reach equilibrium unless a very rare event occurs, and is non-ergodic on any reasonable timescale 13. This description is intuitively appealing and relevant for many processes such as protein folding 12, but direct interpretation of the potential-energy landscape in an experimental system remains very challenging. The key lies in identifying these local minima in the potential-energy landscape, and connecting them with dynamical arrest. Such a mechanism was proposed by Frank 6, who, by considering groups of 13 atoms of the Lennard-Jones model of noble gases, noted that five-fold symmetric icosahedral structures are energetically favoured compared with face-centred-cubic (f.c.c.) structures and are therefore local potential-energy minima. Icosahedra are expected in the liquid phase, with the population increasing on cooling, and their five-fold symmetry may impede crystallization 6,. Although isolated 13-atom structures were considered, immersion in a bulk liquid has little effect on the potential-energy considerations 14. Attempts to verify this link between (icosahedral) locally favoured structures (LFSs) and dynamical arrest took a significant step forward using the bond-order parameter W 6 (see the Supplementary Information), which is associated with five-fold symmetry in computer simulations of the Lennard-Jones model 15. Indeed, on approaching dynamical arrest, domains consistent with five-fold symmetry have been found 16. Some evidence of fivefold symmetry in liquids has also been found in experiments 1,18, along with indirect measurements of five-fold symmetry on cooling below the glass-transition temperature 19. However, unambiguous, direct, experimental evidence of an increase of five-fold symmetry on dynamical arrest seems to be lacking. In any case, bulk scattering measurements that average over many particles seem unlikely to yield direct identification of LFSs. Colloidal suspensions, which, owing to their well-defined thermodynamic temperature 2, may 556 nature materials VOL JULY Macmillan Publishers Limited. All rights reserved.

2 a b c d.15 e 2. f Gel L X W 6 φ P (W 6 ) c P ( 1 4 ) r.r /σ t/ τ B Figure 1 Structural and dynamic characterization of the colloidal liquid gel transition. a c, Confocal microscopy images of a hard-sphere-like colloidal suspension c P = (a), a colloid polymer mixture c P =. 1 5 (ergodic liquid) (b) and a dynamically arrested gel c P = (c). Polymers are not shown in a c. Scale bars = 1 µm. d, W 6 bond-order parameter distribution. Colours correspond to polymer weight fractions 1 4. Here, gelation occurred at c PG =.± e, Phase diagram, in the φ c P plane, where φ is the colloid volume fraction. Red data points denote ergodic liquids; blue data points denote colloidal gels. The solid line is taken from free-volume theory, which considers the equilibrium case where the gel undergoes phase separation to gas crystal coexistence 3. Dotted lines are tie lines of equal chemical potential; L and X are colloidal liquids and crystals, respectively. f, MSDs at various. The straight dashed line has a slope of 1 (ergodic liquid). Polymer concentrations are quoted as. τ B is the time to diffuse one radius at infinite dilution, 19 s. Here, we assume isotropic motion and track the colloids in two dimensions and time. be treated as mesoscopic atoms, provide one promising means to identify LFSs experimentally, as it is possible to determine the coordinates of every particle with microscopy 21. Despite some evidence for five-fold symmetry in dilute gels 22 and hard-sphere glasses 21, supercooled hard-sphere liquids show little change in W 6 approaching dynamical arrest 23. We propose that simply making a measurement such as W 6, which averages over many particles, is insufficient to unambiguously identify LFSs. Here, we argue that the icosahedron is just one example of an LFS, appropriate for Lennard-Jones-like materials. We shall define LFSs as being the global potential-energy minimum of a group of m particles in isolation 24, noting that m is not fixed. Even for spherically symmetric potentials at fixed m, various structures are found, depending on the interaction range 12,24. The global minimum structures we consider are shown in Supplementary Information, Fig. S1. Although other energy minima exist for these isolated clusters 24, here we shall consider only the global minimum for each m. Significantly, a number of these structures are not five-fold symmetric. We directly identify these LFSs by the use of a novel algorithm, the topological cluster classification (TCC). We consider a colloidal gel because it has a well-defined attractive interaction 25,26 (see Supplementary Information, Fig. S2), such that under our definition LFSs are clearly and unambiguously defined, unlike, for example, athermal hard-sphere glasses. Our analysis reveals a massive rise in LFSs, forming a percolating network on dynamical arrest; in fact, the arms of the gel predominantly comprise LFSs. Adding polymer to a colloidal suspension can induce effective attractions widely accepted as a larger scale analogue of simple atomic systems. Colloid polymer mixtures exhibit different phases including colloidal gases, liquids and solids, along with dynamically arrested states such as glasses and gels 3,2. The phase diagram of the system studied here is shown in Fig. 1e. The depletion attraction between the colloids, which drives the phase behaviour, results from the polymer entropy, because the polymer-free volume is maximized when the colloids approach one another (see Supplementary Information, Fig. S2) 25. Controlling the state point by adding polymer in this way allows the system to be quenched from the high-temperature-like, hard-sphere limit, to dynamical arrest, which at moderate colloid concentrations results in a gel. We observe the system with confocal microscopy, Fig. 1a c, and fix the colloid volume fraction to φ =.35, comfortably below φ =.494, the equilibrium freezing point for hard spheres (our system with no polymer). Similar results were obtained in a more dilute system (φ =.5). By adding salt 26, we avoid long-ranged electrostatic repulsions 22. We determine the colloid coordinates 21 and calculate the bond-orientational order parameter W 6 (ref. 15), before analysing the LFSs. Our experiments are supplemented by brownian dynamics computer simulations. We now consider how to identify the LFSs. We seek structures that constitute the ground state for each m. We have carefully characterized the interaction potential in our model colloidal system 26 and found it to be almost identical to the attractive Morse potential (see Supplementary Information, Fig. S2 and equation (S2)). We therefore take those structures that constitute nature materials VOL JULY Macmillan Publishers Limited. All rights reserved.

3 a b c d Free h.c.p. f.c.c. Figure 2 Coordinates identified as belonging to different LFSs. a, Liquid, =.3±.4. b, (Ergodic) liquid close to gelation, =.92±.4. c, Colloidal gel, = 1.8±.4. d, Dilute gel, φ =.5, c P = , showing percolating LFSs. Particles are colour-coded as follows: grey, free (not in any cluster), shown.4 actual size; white, m = 5, shown.6 actual size; yellow, crystalline, shown.8 actual size. Other particles are members of LFSs of size m given by the colours, shown.8 actual size. global potential-energy minima for clusters interacting via the Morse potential (with range parameter ρ = 3) to be LFSs 24. Furthermore, we use the Morse potential in our brownian dynamics simulations, and find a very similar behaviour (see the Supplementary Information). To identify these structures in the bulk system, we have developed a novel topological method, TCC, that identifies LFSs in terms of their bond network. We begin with the bond network between all of the particles. The bond length is equated with the interaction range, that is, the polymer size,.18σ, where σ = 2.4 µm is the colloid diameter 25,26, leading to percolation in both the colloidal gel and the liquid for φ =.35. All of the shortest path three-, four- and five-membered rings in the bond network are identified. These rings are then classified in terms of those with an extra particle bonded to all of the particles in the ring and those that have two or no such extra particles. We term these the basic LFSs, into which many of the larger LFSs can be decomposed. A given particle may be a member of more than one basic LFS, that is, basic LFSs may overlap. We use this strategy to identify all of the LFSs with 13 or less particles. The LFSs we consider are shown in Supplementary Information, Fig. S1. In addition, we identify the f.c.c. and hexagonal close-packed (h.c.p.) 13-particle structures in terms of a central particle and its 12 nearest neighbours. If a particle was found to be part of more than one LFS size, it was labelled as part of the larger size, and the association with the smaller ignored. For more details, see ref. 28. Having outlined our method, we proceed to the results. Real-space confocal microscope images are shown in Fig. 1a c. At low polymer concentrations, a colloidal liquid is seen (Fig. 1a,b); higher concentrations lead to a dynamically arrested network, or gel, (Fig. 1c), with large-scale structure consistent with arrested spinodal decomposition 4. The radial distribution function illustrates the change in structure resulting from the increasing levels of attraction, with a rise in the first-, and higher order maxima, accompanied by a shift to smaller separations, shown in Supplementary Information, Fig. S3. The mean squared displacement (MSD) is shown in Fig. 1f. This shows typical characteristics of dynamical arrest, and leads us to a definition of the polymer concentration c P required for gelation c PG. At low polymer concentration, < 1, we find a diffusive liquid; higher polymer concentration, > 1, leads to dynamical arrest, where only very local displacements are observed. Figure 1d shows the distribution of the bond-orientational order parameter W 6. These exhibit little change, only a fractional shift to negative values, consistent with a slight increase in five-fold symmetry, for moderate polymer concentrations. Our data are in line with that of ref. 23 in that W 6 may not change greatly on arrest. However, dynamical arrest certainly occurs (Fig. 1f). We now consider direct measurement of LFSs using the topological cluster classification. Figure 2a shows LFSs in a liquid, =.3 ±.4. The LFSs are readily identified, but, at 558 nature materials VOL JULY Macmillan Publishers Limited. All rights reserved.

4 N LFS /N Ergodic liquid N LFS /N Dynamically arrested h.c.p. f.c.c N B /N Total Figure 3 Proportion of particles in LFSs as a function of polymer concentration. Total bonds per particle N B /N shown as black crosses. Black diamonds are the total fraction of particles identified as being a member of an LFS or within a local crystalline environment. Coloured lines trace the proportion of particles identified with a given LFS size m (right side of figure). Colours denote m. Black squares and triangles correspond to particles in a local crystalline environment. Inset: Expanded view of the outlined area. Shaded areas are guides to the eye. this state point, with weaker interactions than those required for gelation (higher effective temperature), they are clearly isolated. Increasing the polymer concentration to =.92 ±.4 (Fig. 2b), while still in the ergodic liquid phase, the population of LFSs increases significantly, but they remain isolated. This is not the case in the gel, where a percolating network comprising LFSs is seen, Fig. 2c, = 1.8±.4. Thus, it seems that dynamical arrest may be associated with the formation of a percolated network of LFSs. In Fig. 2, LFSs with different sizes and different structures are seen, underlining the importance of considering more than one species. The growth in LFS population is illustrated in Fig. 3. The most striking feature is the strong increase approaching dynamical arrest, as suggested by Fig. 2. In general, smaller LFSs are more populous. We have shown that the LFSs become much more numerous on dynamical arrest. We recall that the equilibrium state is gas f.c.c. crystal coexistence, and that the arms of the gel are mostly LFSs that are geometrically incompatible with f.c.c. crystals (Fig. 2c,d, see Supplementary Information, Fig. S1), and therefore crystallize very slowly. The high incidence of octahedral LFSs of size m = 6 (W 6 =.12, see Supplementary Information, Fig. S1) may help to explain the lack of change in the W 6 distribution on quenching. Although octahedra form part of the f.c.c. lattice, crystal growth will be suppressed by the proximity of other popular clusters with more negative W 6 values such as m = 5 (triangular bipyramid) (W 6 =.121), m = 9 (C2 v ) (W 6 =.148) and m = 8 (C s ) (W 6 =.144). Noting that, under our definition, icosahedra are not LFSs for this system, we stress that the nature of the LFSs, and hence the degree of five-fold symmetry, is a materialspecific property. Our results suggest that the LFSs form faster than large crystals can nucleate and impede crystallization, see the inset of Fig. 3. At higher polymer concentrations, this kinetic trapping is expected to be more severe and indeed on deep quenching the small population of crystalline particles falls drastically (Fig. 3, inset), hints of which have been seen in computer simulation 29. Thus, kinetic selection may win over global energetic considerations. Note that the number of bonds per particle N b /N rises much more slowly than does the LFS population, so the population increase is not merely due to the local densification associated with gelation. In the high-temperature-like hard-sphere limit, where there are no attractions between the particles, we still find LFSs. This might seem surprising, because LFSs are energetically favoured states. However, many LFSs result in efficient local packing 3 and provide an important avenue by which a dense system may lower its free energy. We now consider our earlier assertion that LFSs correspond to local energy minima, by comparing the coordination number of the particles in clusters with the free particles not identified with any cluster. Figure 4a shows that particles in LFSs have substantially more neighbours than free particles. For this shortranged attractive interaction, the number of neighbours provides a good measure of the potential energy of each particle. We thus conclude that the structures we define as LFSs represent lowenergy states. We have shown that dynamical arrest is correlated with the growth in the proportion of particles in LFSs, but a clear link implies a connected LFS network. We note that by considering a range of LFSs, and allowing them to interpenetrate, our TCC method permits the formation of a percolating network, but, given the variety of structures considered, filling space with LFSs is likely to be geometrically frustrated. Percolation is confirmed in Fig. 2d, where the structure of a dilute gel φ =.5, = 1.45±.14, is shown. Here, the arms of the gel clearly comprise LFSs, forming a network. In the more dense system φ =.35, we test for LFS percolation by measuring the dimension of the largest connected region of LFSs l c, and plotting this as a fraction of image size L in Fig. 4b. Here, l c /L = 1 corresponds to percolation, and indeed we see that the LFSs percolate around c PG. We furthermore examine the dynamics of the LFSs. We expect that, on gelation, as the particles become trapped in LFSs, then the LFS lifetime should increase strongly. We illustrate this with movies, which show short-lived LFSs in the colloidal liquid (see Supplementary Information, Movie S1, =.3 ±.4); approaching the gel state (see Supplementary Information, Movie S2, =.86±.4) the LFSs last longer, which strongly contrasts with the gel state (see Supplementary Information, Movie S3, = 1.8 ±.1), in which we find a largely arrested network of LFSs, with some mobility (and subsequent LFS breakup) due to the more mobile surface particles. We note that this is consistent with computer simulations where dynamical heterogeneity was connected to surface ( fast ) particles and slower particles in the core of the arms 31. We now present evidence that the arrest is directly related to the LFSs. By tracking the colloidal particles in time, similarly to ref. 32, we measure the effect of the clusters on the MSD for an ergodic liquid just above gelation =.9 ±.6 and.88 ±. (Fig. 4c). We see that the particles that remain in LFSs for a prolonged time diffuse considerably more slowly than those that do not. As the effective temperature is lowered further, this effect becomes more pronounced. We also recall that the population of particles in LFSs increases markedly around these state points. This shows how the formation of long-lived clusters, on gelation, is the mechanism responsible for the dynamic slowing. Whereas coordinate tracking errors complicate accurate measurements of displacement in the experimental data, brownian dynamics simulation data in the gel state show a similar trend to the ergodic liquid (Fig. 4d). The faster particles not in LFSs may be connected to the fast surface population noted by Puertas et al. 31. The lifetime of the LFSs is expected to increase in the ergodic liquid, but to diverge on arrest. We measure LFS lifetime as the correlation of the residency of individual particles in an LFS, nature materials VOL JULY Macmillan Publishers Limited. All rights reserved.

5 a 8 b 1. LFS 6 All.8 5 Free.6 N N /N Ergodic liquid 1 2 Dynamically arrested 3 I C /L.4.2 Ergodic liquid Dynamically arrested c 1..9 d e 1.14 δr. δr /σ δr. δr /σ τlfs τ τ LFS /τ t/ τ B c LFS (t )c LFS () Figure 4 Static and dynamic characteristics of gelation. a, Coordination numbers N N /N as a function of polymer concentration. The average coordination number of all particles is shown by the black line; the blue line denotes particles within LFSs and the red line denotes free particles that do not form part of an LFS. b, The length of the largest connected low-energy region as a fraction of the image length l c /L as defined in the text. The low-potential-energy regions are defined as connected groups of particles identified as part of an LFS. The largest low-energy region is thus the largest group of connected particles in an LFS. Shaded areas are a guide to the eye. c, MSD as a function of time spent in an LFS for the ergodic fluid =.9 and.88. The measuring time here was τ =.3τ B. d, MSD calculated from brownian dynamics simulations as a function of time spent in an LFS for a gel, ɛ/ɛ G = 1.43 (see the Supplementary Information), here τ = 1.2τ B. e. LFS lifetime as characterized by c LFS ()c LFS (t ) (see text for definition). Legend denotes. c LFS ()c LFS (t), where c LFS (t) = 1 if a particle in an LFS at time is still in an LFS at a later time t, and otherwise. Plotting c LFS ()c LFS (t) in Fig. 4d reveals a very considerable increase in the LFS lifetime on gelation. However, at long times, coordinate tracking errors lead to LFSs being identified as breaking up. Note, however, that all state points for > 1 collapse onto the same curve, indicating little change in the dynamics and that the decay is probably due to the tracking errors. This is supported by brownian dynamics simulations without such tracking errors, which show a clear divergence in the lifetime on gelation (see Supplementary Information, Fig. S6). Combining our observations, we may present a mechanism for arrest. In the ergodic liquid, isolated LFSs have a short lifetime, but at some polymer concentration, percolation of LFSs occurs. Connecting LFSs results in a significant lowering in potential energy. The dilute gel in Fig. 2d, for example, in which the LFSs are bonded to one another, should have a lower energy than an equivalent number of isolated LFSs. This formation of a percolating network of LFSs therefore, represents a deep local minimum in the energy landscape, in which the system is kinetically trapped for some time. We note that this mechanism is compatible with the connection between arrest and phase separation 4 rather than a cluster glass transition 33. In summary, we have presented clear experimental evidence of a local structural mechanism for colloidal gelation. By carefully identifying relevant LFSs, we reveal that dynamical arrest is associated with the formation of a percolating network of LFSs. In other words, dynamical arrest is driven by a network of particles, each in a local energy minimum, unable to reach the equilibrium state, gas crystal coexistence. We have also shown that a high population of LFSs, expected in a dynamically arrested system, is not necessarily correlated with a strongly negative W nature materials VOL JULY Macmillan Publishers Limited. All rights reserved.

6 We have considered a colloidal gel, but because we focused on local structure, in particular the suppression of crystallization, our approach has very clear implications for a great many metastable materials, from colloidal glasses, even to molecular and metallic glasses. We emphasize the importance of considering many different LFSs, and that in general these are material specific. Finally, we believe that our TCC method offers significant potential to advance our understanding of the structure in amorphous materials, and may for example provide a useful means to study crystallization pathways. METHODS EXPERIMENTAL DETAILS We used polymethylmethacrylate colloids sterically stabilized with polyhydroxyl steric acid. The colloids were labelled with the fluorescent dye 4-chloro- -nitrobenzo-2-oxa-1,3-diazol and had a diameter σ = 2.4 µm with 3% polydispersity. The polymer used was polystyrene, with a molecular weight of 3.1 1, here M w /M n = 1.3 (ref. 26). To closely match the colloid density and refractive index, we used a solvent mixture of cis-decalin and cyclohexyl bromide. Owing to the refractive index matching, the van der Waals interactions are reduced to a fraction of the thermal energy k B T and neglected. To screen any electrostatic interactions, we dissolved tetra-butyl ammonium bromide salt, to a concentration of 4 mm, so the Debye screening length is well below the characteristic depletion interaction range 26. In detailed studies of the same system, we found excellent agreement with the depletion interaction 25, assuming some polymer swelling, due to the good solvent used, resulting in a polymer colloid size ratio of.18 (ref. 26). We conducted a number of experiments, in the case of φ =.35, in which the gel point c PG = 1.± We attribute this difference to weak charging effects, but stress that no further change in behaviour was detected. Received 3 September 2; accepted 19 May 28; published 22 June 28. References 1. Trappe, V., Prasad, V., Cipelletti, P., L., Segre, N. & Weitz, D. A. Jamming phase diagram for attractive particles. Nature 411, 2 5 (21). 2. Sciortino, F. & Tartaglia, P. Glassy colloidal systems. Adv. Phys. 54, (25). 3. Poon, W. C. K. The physics of a model colloid-polymer mixture. J. Phys. Condens. Matter. 14, R859 R88 (22). 4. Manley, S. et al. Glasslike arrest in spinodal decomposition as a route to colloidal gelation. Phys. Rev. Lett. 95, (25). 5. Zaccarelli, E. Colloidal gels: Equilibrium and non-equilibrium routes. J. Phys. Condens. Matter 19, (2). 6. Frank, F. C. Supercooling of liquids. Proc. R. Soc. Lond. A 215, (1952).. Tanaka, H. Two-order-parameter description of liquids. 1. A general model of glass transition covering its strong to fragile limit. J. Chem. Phys. 111, (1999). 8. Ediger, M. Spatially heterogeneous dynamics in supercooled liquids. Annu. Rev. Phys. Chem. 51, (2). 9. Widmer-Cooper, A. & Harrowell, P. On the relationship between structure and dynamics in a supercooled liquid. J. Phys. Condens. Matter 1, S425 S434 (25). 1. Widmer-Cooper, A. & Harrowell, P. Free volume cannot explain the spatial heterogeneity of Debye Waller factors in a glass-forming binary alloy. J. Non-Cryst. Solids 352, (26). 11. Tanaka, H. Viscoelastic phase separation. J. Phys. Condens. Matter 12, R2 R264 (2). 12. Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses (Cambridge Univ. Press, Cambridge, 24). 13. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 41, (21). 14. Mossa, S. & Tarjus, G. Locally preferred structure in simple atomic liquids. J. Chem. Phys. 119, (23). 15. Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and gases. Phys. Rev. B 28, (1983). 16. Jonsson, H. & Andersen, H. Icosahedral ordering in the Lennard-Jones liquid and glass. Phys. Rev. Lett. 6, (1988). 1. Reichert, H. et al. Observation of five-fold local symmetry in liquid lead. Nature 48, (2). 18. Di Cicco, A., Trapananti, A., Faggioni, S. & Filipponi, A. Is there icosahedral ordering in liquid and undercooled metals? Phys. Rev. Lett. 91, (23). 19. Schenk, T., Holland-Moritz, D., Simonet, V., Bellissent, R. & Herlach, D. M. Icosahedral short-range order in deeply undercooled metallic melts. Phys. Rev. Lett. 89, 55 (22). 2. Pusey, P. N. in Liquids, Freezing and the Glass Transition (eds Hansen, J. P., Levesque, D. & Zinn-Justin, J.) (North-Holland, Amsterdam, 1991). 21. van Blaaderen, A. & Wiltzius, P. Real-space structure of colloidal hard-sphere glasses. Science 2, (1995). 22. Campbell, A. I., Anderson, V. J., van Duijneveldt, J. S. & Bartlett, P. Dynamical arrest in attractive colloids: The effect of long-range repulsion. Phys. Rev. Lett. 94, 2831 (25). 23. Gasser, U., Schofield, A. & Weitz, D. Local order in a supercooled colloidal fluid observed by confocal microscopy. J. Phys. Condens. Matter 15, S35 S38 (23). 24. Doye, J. P. K., Wales, D. J. & Berry, R. S. The effect of the range of the potential on the structures of clusters. J. Chem. Phys. 13, (1995). 25. Asakura, S. & Oosawa, F. On interaction between 2 bodies immersed in a solution of macromolecules. J. Chem. Phys. 22, (1954). 26. Royall, C. P., Louis, A. & Tanaka, H. Measuring colloidal interactions with confocal microscopy. J. Chem. Phys. 12, 445 (2). 2. Pham, K. N. et al. Multiple glassy states in a simple model system. Science 296, (22). 28. Williams, S. R. Topological classification of clusters in condensed phases. Preprint at < (2). 29. Charbonneau, P. & Reichman, D. Systematic characteristation of thermodynamic and dynamical phase behaviour in systems with short-ranged attraction. Phys. Rev. E 5, 115 (2). 3. Manoharan, V. N., Elesser, M. T. & Pine, D. J. Dense packing and symmetry in small clusters of microspheres. Science 31, (23). 31. Puertas, A. M., Fuchs, M. & Cates, M. E. Dynamical heterogeneities close to a colloidal gel. J. Chem. Phys. 121, (24). 32. Weeks, E., Crocker, J., Levitt, A., Schofield, A. & Weitz, D. Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 28, (21). 33. Kroy, K., Cates, M. & Poon, W. Cluster mode-coupling approach to weak gelation in attractive colloids. Phys. Rev. Lett. 92, (24). Supplementary Information accompanies this paper on Acknowledgements The authors are grateful to A. van Blaaderen and D. Derks for particle synthesis help and gifts. We wish to thank P. Bartlett, D. Derks, D. Head and R. Jack for critical reading of the manuscript, and T. Ichikawa for kind instrumentation support. This work was partially supported by a grant-in-aid from the Ministry of Education, Culture, Sports, Science and Technology, Japan. C.P.R. is grateful to the Royal Society for financial support. Author contributions C.P.R., S.R.W. and H.T. conceived the project and wrote the manuscript, C.P.R. carried out the experiments, simulation and analysis, S.R.W. wrote the TCC code and T.O. wrote the W 6 analysis code. Author information Reprints and permission information is available online at Correspondence and requests for materials should be addressed to C.P.R. or H.T. nature materials VOL JULY Macmillan Publishers Limited. All rights reserved.