Abstract

We describe a novel method of tracking the rotational motion of clusters of colloidal particles. Our method utilizes rigid body transformations to determine the rotations of a cluster and extends conventional proven particle tracking techniques in a simple way, thus facilitating the study of rotational dynamics in systems containing or composed of colloidal clusters. We test our method by measuring dynamical properties of simulated Brownian clusters under conditions relevant to microscopy experiments. We then use the technique to track and describe the motions of a real colloidal cluster imaged with confocal microscopy.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. C. A. Murray and D. H. Van Winkle, “Experimental observation of two-stage melting in a classical two-dimensional screened coulomb system,” Phys. Rev. Lett. 58, 1200–1203 (1987).
    [CrossRef] [PubMed]
  4. E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
    [CrossRef] [PubMed]
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  8. E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
    [CrossRef] [PubMed]
  9. J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  26. Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
    [CrossRef] [PubMed]
  27. D. Mukhija and M. J. Solomon, “Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy,” J. Colloid Interface Sci. 314, 98–106 (2007).
    [CrossRef] [PubMed]
  28. V. N. Manoharan, M. T. Elsesser, and D. J. Pine, “Dense packing and symmetry in small clusters of microspheres,” Science 301, 483–487 (2003).
    [CrossRef] [PubMed]
  29. M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
    [CrossRef]
  30. A. van Blaaderen, “Chemistry: colloidal molecules and beyond,” Science 301, 470–471 (2003).
    [CrossRef]
  31. A. van Blaaderen, “Materials science: colloids get complex,” Nature 439, 545–546 (2006).
    [CrossRef] [PubMed]
  32. S. C. Glotzer and M. J. Solomon, “Anisotropy of building blocks and their assembly into complex structures,” Nature Mater. 6, 557–562 (2007).
    [CrossRef]
  33. S. M. Anthony, M. Kim, and S. Granick, “Translation-rotation decoupling of colloidal clusters of various symmetries,” J. Chem. Phys. 129, 244701 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  37. M. G. Mazza, N. Giovambattista, H. E. Stanley, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
    [CrossRef]
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    [CrossRef]
  39. B. J. Berne, P. Pechukas, and G. D. Harp, “Molecular reorientation in liquids and gases,” J. Chem. Phys. 49, 3125–3129 (1968).
    [CrossRef]
  40. G. Williams, “Time-correlation functions and molecular motions,” Chem. Soc. Rev. 7, 89–131 (1978).
    [CrossRef]
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2011 (2)

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
[CrossRef]

2010 (1)

D. Chen, D. Semwogerere, J. Sato, V. Breedveld, and E. R. Weeks, “Microscopic structural relaxation in a sheared supercooled colloidal liquid,” Phys. Rev. E 81, 011403 (2010).
[CrossRef]

2009 (2)

J. Hernández-Guzmán and E. R. Weeks, “The equilibrium intrinsic crystal-liquid interface of colloids,” Proc. Natl. Acad. Sci. U.S.A. 106, 15198–15202 (2009).
[CrossRef] [PubMed]

M. Hoffmann, C. S. Wagner, L. Harnau, and A. Wittemann, “3D Brownian diffusion of submicron-sized particle clusters,” ACS Nano 3, 3326–3334 (2009).
[CrossRef] [PubMed]

2008 (1)

S. M. Anthony, M. Kim, and S. Granick, “Translation-rotation decoupling of colloidal clusters of various symmetries,” J. Chem. Phys. 129, 244701 (2008).
[CrossRef]

2007 (6)

S. C. Glotzer and M. J. Solomon, “Anisotropy of building blocks and their assembly into complex structures,” Nature Mater. 6, 557–562 (2007).
[CrossRef]

C. R. Nugent, K. V. Edmond, H. N. Patel, and E. R. Weeks, “Colloidal glass transition observed in confinement,” Phys. Rev. Lett. 99, 025702 (2007).
[CrossRef] [PubMed]

R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon, “Three-dimensional imaging of colloidal glasses under steady shear,” Phys. Rev. Lett. 99, 028301 (2007).
[CrossRef] [PubMed]

P. Schall, D. A. Weitz, and F. Spaepen, “Structural rearrangements that govern flow in colloidal glasses,” Science 318, 1895–1899 (2007).
[CrossRef] [PubMed]

D. Mukhija and M. J. Solomon, “Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy,” J. Colloid Interface Sci. 314, 98–106 (2007).
[CrossRef] [PubMed]

M. G. Mazza, N. Giovambattista, H. E. Stanley, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

2006 (7)

L. Hong, S. M. Anthony, and S. Granick, “Rotation in suspension of a rod-shaped colloid,” Langmuir 22, 7128–7131 (2006).
[CrossRef] [PubMed]

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

S. Martin, M. Reichert, H. Stark, and T. Gisler, “Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres,” Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

S. M. Anthony, L. Hong, M. Kim, and S. Granick, “Single-particle colloid tracking in four dimensions,” Langmuir 22, 9812–9815 (2006).
[CrossRef] [PubMed]

M. G. Mazza, N. Giovambattista, F. W. Starr, and H. E. Stanley, “Relation between rotational and translational dynamic heterogeneities in water,” Phys. Rev. Lett. 96, 057803 (2006).
[CrossRef] [PubMed]

A. van Blaaderen, “Materials science: colloids get complex,” Nature 439, 545–546 (2006).
[CrossRef] [PubMed]

J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
[CrossRef] [PubMed]

2003 (2)

A. van Blaaderen, “Chemistry: colloidal molecules and beyond,” Science 301, 470–471 (2003).
[CrossRef]

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, “Dense packing and symmetry in small clusters of microspheres,” Science 301, 483–487 (2003).
[CrossRef] [PubMed]

2001 (2)

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, “Real-space imaging of nucleation and growth in colloidal crystallization,” Science 292, 258–262 (2001).
[CrossRef] [PubMed]

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Opt. 40, 4152–4159 (2001).
[CrossRef]

2000 (2)

E. R. Dufresne, T. M. Squires, M. P. Brenner, and D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef] [PubMed]

1997 (1)

S. Kämmerer, W. Kob, and R. Schilling, “Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules,” Phys. Rev. E 56, 5450–5461 (1997).
[CrossRef]

1996 (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

1995 (1)

J. Challis, “A procedure for determining rigid body transformation parameters,” J. Biomech. 28, 733–737 (1995).
[CrossRef] [PubMed]

1994 (2)

D. G. Grier and C. A. Murray, “The microscopic dynamics of freezing in supercooled colloidal fluids,” J. Chem. Phys. 100, 9088–9095 (1994).
[CrossRef]

P. N. Pusey, W. C. K. Poon, S. M. Ilett, and P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

1990 (1)

C. A. Murray, W. O. Sprenger, and R. A. Wenk, “Comparison of melting in three and two dimensions: microscopy of colloidal spheres,” Phys. Rev. B 42, 688–703 (1990).
[CrossRef]

1989 (1)

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

1987 (2)

C. A. Murray and D. H. Van Winkle, “Experimental observation of two-stage melting in a classical two-dimensional screened coulomb system,” Phys. Rev. Lett. 58, 1200–1203 (1987).
[CrossRef] [PubMed]

P. N. Pusey and W. van Megen, “Observation of a glass transition in suspensions of spherical colloidal particles,” Phys. Rev. Lett. 59, 2083–2086 (1987).
[CrossRef] [PubMed]

1986 (3)

P. N. Pusey and W. van Megen, “Phase behaviour of concentrated suspensions of nearly hard colloidal spheres,” Nature 320, 340–342 (1986).
[CrossRef]

D. J. W. Aastuen, N. A. Clark, L. K. Cotter, and B. J. Ackerson, “Nucleation and growth of colloidal crystals,” Phys. Rev. Lett. 57, 1733–1736 (1986).
[CrossRef] [PubMed]

D. H. Van Winkle and C. A. Murray, “Layering transitions in colloidal crystals as observed by diffraction and direct-lattice imaging,” Phys. Rev. A 34, 562–573 (1986).
[CrossRef] [PubMed]

1978 (1)

G. Williams, “Time-correlation functions and molecular motions,” Chem. Soc. Rev. 7, 89–131 (1978).
[CrossRef]

1973 (1)

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

1968 (1)

B. J. Berne, P. Pechukas, and G. D. Harp, “Molecular reorientation in liquids and gases,” J. Chem. Phys. 49, 3125–3129 (1968).
[CrossRef]

1928 (1)

F. Perrin, “Étude mathématique du mouvement Brownien de rotation,” Ann. Sci. Ec. Normale Super. 45, 1–51 (1928).

Aastuen, D. J. W.

D. J. W. Aastuen, N. A. Clark, L. K. Cotter, and B. J. Ackerson, “Nucleation and growth of colloidal crystals,” Phys. Rev. Lett. 57, 1733–1736 (1986).
[CrossRef] [PubMed]

Ackerson, B. J.

D. J. W. Aastuen, N. A. Clark, L. K. Cotter, and B. J. Ackerson, “Nucleation and growth of colloidal crystals,” Phys. Rev. Lett. 57, 1733–1736 (1986).
[CrossRef] [PubMed]

Alsayed, A. M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

Anthony, S. M.

S. M. Anthony, M. Kim, and S. Granick, “Translation-rotation decoupling of colloidal clusters of various symmetries,” J. Chem. Phys. 129, 244701 (2008).
[CrossRef]

L. Hong, S. M. Anthony, and S. Granick, “Rotation in suspension of a rod-shaped colloid,” Langmuir 22, 7128–7131 (2006).
[CrossRef] [PubMed]

S. M. Anthony, L. Hong, M. Kim, and S. Granick, “Single-particle colloid tracking in four dimensions,” Langmuir 22, 9812–9815 (2006).
[CrossRef] [PubMed]

Axe, J. D.

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

Bartlett, P.

P. N. Pusey, W. C. K. Poon, S. M. Ilett, and P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Berne, B. J.

B. J. Berne, P. Pechukas, and G. D. Harp, “Molecular reorientation in liquids and gases,” J. Chem. Phys. 49, 3125–3129 (1968).
[CrossRef]

Besseling, R.

R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon, “Three-dimensional imaging of colloidal glasses under steady shear,” Phys. Rev. Lett. 99, 028301 (2007).
[CrossRef] [PubMed]

Blair, D. W.

J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
[CrossRef] [PubMed]

Breedveld, V.

D. Chen, D. Semwogerere, J. Sato, V. Breedveld, and E. R. Weeks, “Microscopic structural relaxation in a sheared supercooled colloidal liquid,” Phys. Rev. E 81, 011403 (2010).
[CrossRef]

Brenner, M. P.

E. R. Dufresne, T. M. Squires, M. P. Brenner, and D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Chaikin, P. M.

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

Challis, J.

J. Challis, “A procedure for determining rigid body transformation parameters,” J. Biomech. 28, 733–737 (1995).
[CrossRef] [PubMed]

Chen, D.

D. Chen, D. Semwogerere, J. Sato, V. Breedveld, and E. R. Weeks, “Microscopic structural relaxation in a sheared supercooled colloidal liquid,” Phys. Rev. E 81, 011403 (2010).
[CrossRef]

Chen, K.

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

Clark, N. A.

D. J. W. Aastuen, N. A. Clark, L. K. Cotter, and B. J. Ackerson, “Nucleation and growth of colloidal crystals,” Phys. Rev. Lett. 57, 1733–1736 (1986).
[CrossRef] [PubMed]

Cotter, L. K.

D. J. W. Aastuen, N. A. Clark, L. K. Cotter, and B. J. Ackerson, “Nucleation and growth of colloidal crystals,” Phys. Rev. Lett. 57, 1733–1736 (1986).
[CrossRef] [PubMed]

Crocker, J. C.

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef] [PubMed]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Dinsmore, A. D.

J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
[CrossRef] [PubMed]

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Opt. 40, 4152–4159 (2001).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne, T. M. Squires, M. P. Brenner, and D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Edmond, K. V.

M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
[CrossRef]

C. R. Nugent, K. V. Edmond, H. N. Patel, and E. R. Weeks, “Colloidal glass transition observed in confinement,” Phys. Rev. Lett. 99, 025702 (2007).
[CrossRef] [PubMed]

Ellenbroek, W. G.

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

Elsesser, M. T.

M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
[CrossRef]

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, “Dense packing and symmetry in small clusters of microspheres,” Science 301, 483–487 (2003).
[CrossRef] [PubMed]

Fujii, Y.

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

Gasser, U.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, “Real-space imaging of nucleation and growth in colloidal crystallization,” Science 292, 258–262 (2001).
[CrossRef] [PubMed]

Giovambattista, N.

M. G. Mazza, N. Giovambattista, H. E. Stanley, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

M. G. Mazza, N. Giovambattista, F. W. Starr, and H. E. Stanley, “Relation between rotational and translational dynamic heterogeneities in water,” Phys. Rev. Lett. 96, 057803 (2006).
[CrossRef] [PubMed]

Gisler, T.

S. Martin, M. Reichert, H. Stark, and T. Gisler, “Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres,” Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Glotzer, S. C.

S. C. Glotzer and M. J. Solomon, “Anisotropy of building blocks and their assembly into complex structures,” Nature Mater. 6, 557–562 (2007).
[CrossRef]

Granick, S.

S. M. Anthony, M. Kim, and S. Granick, “Translation-rotation decoupling of colloidal clusters of various symmetries,” J. Chem. Phys. 129, 244701 (2008).
[CrossRef]

S. M. Anthony, L. Hong, M. Kim, and S. Granick, “Single-particle colloid tracking in four dimensions,” Langmuir 22, 9812–9815 (2006).
[CrossRef] [PubMed]

L. Hong, S. M. Anthony, and S. Granick, “Rotation in suspension of a rod-shaped colloid,” Langmuir 22, 7128–7131 (2006).
[CrossRef] [PubMed]

Grier, D. G.

E. R. Dufresne, T. M. Squires, M. P. Brenner, and D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

D. G. Grier and C. A. Murray, “The microscopic dynamics of freezing in supercooled colloidal fluids,” J. Chem. Phys. 100, 9088–9095 (1994).
[CrossRef]

Guyer, R. A.

J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
[CrossRef] [PubMed]

Hachisu, S.

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

Han, Y.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

Harnau, L.

M. Hoffmann, C. S. Wagner, L. Harnau, and A. Wittemann, “3D Brownian diffusion of submicron-sized particle clusters,” ACS Nano 3, 3326–3334 (2009).
[CrossRef] [PubMed]

Harp, G. D.

B. J. Berne, P. Pechukas, and G. D. Harp, “Molecular reorientation in liquids and gases,” J. Chem. Phys. 49, 3125–3129 (1968).
[CrossRef]

Hernández-Guzmán, J.

J. Hernández-Guzmán and E. R. Weeks, “The equilibrium intrinsic crystal-liquid interface of colloids,” Proc. Natl. Acad. Sci. U.S.A. 106, 15198–15202 (2009).
[CrossRef] [PubMed]

Hoffmann, M.

M. Hoffmann, C. S. Wagner, L. Harnau, and A. Wittemann, “3D Brownian diffusion of submicron-sized particle clusters,” ACS Nano 3, 3326–3334 (2009).
[CrossRef] [PubMed]

Hollingsworth, A. D.

M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
[CrossRef]

Hong, L.

L. Hong, S. M. Anthony, and S. Granick, “Rotation in suspension of a rod-shaped colloid,” Langmuir 22, 7128–7131 (2006).
[CrossRef] [PubMed]

S. M. Anthony, L. Hong, M. Kim, and S. Granick, “Single-particle colloid tracking in four dimensions,” Langmuir 22, 9812–9815 (2006).
[CrossRef] [PubMed]

Ilett, S. M.

P. N. Pusey, W. C. K. Poon, S. M. Ilett, and P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Kämmerer, S.

S. Kämmerer, W. Kob, and R. Schilling, “Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules,” Phys. Rev. E 56, 5450–5461 (1997).
[CrossRef]

Kim, M.

S. M. Anthony, M. Kim, and S. Granick, “Translation-rotation decoupling of colloidal clusters of various symmetries,” J. Chem. Phys. 129, 244701 (2008).
[CrossRef]

S. M. Anthony, L. Hong, M. Kim, and S. Granick, “Single-particle colloid tracking in four dimensions,” Langmuir 22, 9812–9815 (2006).
[CrossRef] [PubMed]

Kob, W.

S. Kämmerer, W. Kob, and R. Schilling, “Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules,” Phys. Rev. E 56, 5450–5461 (1997).
[CrossRef]

Kobayashi, Y.

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

Kose, A.

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

Levine, A. J.

J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
[CrossRef] [PubMed]

Levitt, A. C.

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Opt. 40, 4152–4159 (2001).
[CrossRef]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef] [PubMed]

Liu, A. J.

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

Lubensky, T. C.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

Manoharan, V. N.

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, “Dense packing and symmetry in small clusters of microspheres,” Science 301, 483–487 (2003).
[CrossRef] [PubMed]

Martin, S.

S. Martin, M. Reichert, H. Stark, and T. Gisler, “Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres,” Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Mazza, M. G.

M. G. Mazza, N. Giovambattista, H. E. Stanley, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

M. G. Mazza, N. Giovambattista, F. W. Starr, and H. E. Stanley, “Relation between rotational and translational dynamic heterogeneities in water,” Phys. Rev. Lett. 96, 057803 (2006).
[CrossRef] [PubMed]

Mukhija, D.

D. Mukhija and M. J. Solomon, “Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy,” J. Colloid Interface Sci. 314, 98–106 (2007).
[CrossRef] [PubMed]

Murray, C. A.

D. G. Grier and C. A. Murray, “The microscopic dynamics of freezing in supercooled colloidal fluids,” J. Chem. Phys. 100, 9088–9095 (1994).
[CrossRef]

C. A. Murray, W. O. Sprenger, and R. A. Wenk, “Comparison of melting in three and two dimensions: microscopy of colloidal spheres,” Phys. Rev. B 42, 688–703 (1990).
[CrossRef]

C. A. Murray and D. H. Van Winkle, “Experimental observation of two-stage melting in a classical two-dimensional screened coulomb system,” Phys. Rev. Lett. 58, 1200–1203 (1987).
[CrossRef] [PubMed]

D. H. Van Winkle and C. A. Murray, “Layering transitions in colloidal crystals as observed by diffraction and direct-lattice imaging,” Phys. Rev. A 34, 562–573 (1986).
[CrossRef] [PubMed]

Nobili, M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

Nugent, C. R.

C. R. Nugent, K. V. Edmond, H. N. Patel, and E. R. Weeks, “Colloidal glass transition observed in confinement,” Phys. Rev. Lett. 99, 025702 (2007).
[CrossRef] [PubMed]

Ozaki, M.

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

Patel, H. N.

C. R. Nugent, K. V. Edmond, H. N. Patel, and E. R. Weeks, “Colloidal glass transition observed in confinement,” Phys. Rev. Lett. 99, 025702 (2007).
[CrossRef] [PubMed]

Pechukas, P.

B. J. Berne, P. Pechukas, and G. D. Harp, “Molecular reorientation in liquids and gases,” J. Chem. Phys. 49, 3125–3129 (1968).
[CrossRef]

Perrin, F.

F. Perrin, “Étude mathématique du mouvement Brownien de rotation,” Ann. Sci. Ec. Normale Super. 45, 1–51 (1928).

Pine, D. J.

M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
[CrossRef]

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, “Dense packing and symmetry in small clusters of microspheres,” Science 301, 483–487 (2003).
[CrossRef] [PubMed]

Poon, W. C. K.

R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon, “Three-dimensional imaging of colloidal glasses under steady shear,” Phys. Rev. Lett. 99, 028301 (2007).
[CrossRef] [PubMed]

P. N. Pusey, W. C. K. Poon, S. M. Ilett, and P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Prasad, V.

Pusey, P. N.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, “Real-space imaging of nucleation and growth in colloidal crystallization,” Science 292, 258–262 (2001).
[CrossRef] [PubMed]

P. N. Pusey, W. C. K. Poon, S. M. Ilett, and P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

P. N. Pusey and W. van Megen, “Observation of a glass transition in suspensions of spherical colloidal particles,” Phys. Rev. Lett. 59, 2083–2086 (1987).
[CrossRef] [PubMed]

P. N. Pusey and W. van Megen, “Phase behaviour of concentrated suspensions of nearly hard colloidal spheres,” Nature 320, 340–342 (1986).
[CrossRef]

Reichert, M.

S. Martin, M. Reichert, H. Stark, and T. Gisler, “Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres,” Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Sato, J.

D. Chen, D. Semwogerere, J. Sato, V. Breedveld, and E. R. Weeks, “Microscopic structural relaxation in a sheared supercooled colloidal liquid,” Phys. Rev. E 81, 011403 (2010).
[CrossRef]

Savage, J. R.

J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, and A. D. Dinsmore, “Imaging the sublimation dynamics of colloidal crystallites,” Science 314, 795–798 (2006).
[CrossRef] [PubMed]

Schall, P.

P. Schall, D. A. Weitz, and F. Spaepen, “Structural rearrangements that govern flow in colloidal glasses,” Science 318, 1895–1899 (2007).
[CrossRef] [PubMed]

Schilling, R.

S. Kämmerer, W. Kob, and R. Schilling, “Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules,” Phys. Rev. E 56, 5450–5461 (1997).
[CrossRef]

Schofield, A.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, “Real-space imaging of nucleation and growth in colloidal crystallization,” Science 292, 258–262 (2001).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef] [PubMed]

Schofield, A. B.

R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon, “Three-dimensional imaging of colloidal glasses under steady shear,” Phys. Rev. Lett. 99, 028301 (2007).
[CrossRef] [PubMed]

Semwogerere, D.

D. Chen, D. Semwogerere, J. Sato, V. Breedveld, and E. R. Weeks, “Microscopic structural relaxation in a sheared supercooled colloidal liquid,” Phys. Rev. E 81, 011403 (2010).
[CrossRef]

Sinha, S. K.

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

Sirota, E. B.

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

Solomon, M. J.

D. Mukhija and M. J. Solomon, “Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy,” J. Colloid Interface Sci. 314, 98–106 (2007).
[CrossRef] [PubMed]

S. C. Glotzer and M. J. Solomon, “Anisotropy of building blocks and their assembly into complex structures,” Nature Mater. 6, 557–562 (2007).
[CrossRef]

Spaepen, F.

P. Schall, D. A. Weitz, and F. Spaepen, “Structural rearrangements that govern flow in colloidal glasses,” Science 318, 1895–1899 (2007).
[CrossRef] [PubMed]

Sprenger, W. O.

C. A. Murray, W. O. Sprenger, and R. A. Wenk, “Comparison of melting in three and two dimensions: microscopy of colloidal spheres,” Phys. Rev. B 42, 688–703 (1990).
[CrossRef]

Squires, T. M.

E. R. Dufresne, T. M. Squires, M. P. Brenner, and D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Stanley, H. E.

M. G. Mazza, N. Giovambattista, H. E. Stanley, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

M. G. Mazza, N. Giovambattista, F. W. Starr, and H. E. Stanley, “Relation between rotational and translational dynamic heterogeneities in water,” Phys. Rev. Lett. 96, 057803 (2006).
[CrossRef] [PubMed]

Stark, H.

S. Martin, M. Reichert, H. Stark, and T. Gisler, “Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres,” Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Starr, F. W.

M. G. Mazza, N. Giovambattista, H. E. Stanley, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes–Einstein and Stokes–Einstein–Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

M. G. Mazza, N. Giovambattista, F. W. Starr, and H. E. Stanley, “Relation between rotational and translational dynamic heterogeneities in water,” Phys. Rev. Lett. 96, 057803 (2006).
[CrossRef] [PubMed]

Takano, K.

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

van Blaaderen, A.

A. van Blaaderen, “Materials science: colloids get complex,” Nature 439, 545–546 (2006).
[CrossRef] [PubMed]

A. van Blaaderen, “Chemistry: colloidal molecules and beyond,” Science 301, 470–471 (2003).
[CrossRef]

van Megen, W.

P. N. Pusey and W. van Megen, “Observation of a glass transition in suspensions of spherical colloidal particles,” Phys. Rev. Lett. 59, 2083–2086 (1987).
[CrossRef] [PubMed]

P. N. Pusey and W. van Megen, “Phase behaviour of concentrated suspensions of nearly hard colloidal spheres,” Nature 320, 340–342 (1986).
[CrossRef]

Van Winkle, D. H.

C. A. Murray and D. H. Van Winkle, “Experimental observation of two-stage melting in a classical two-dimensional screened coulomb system,” Phys. Rev. Lett. 58, 1200–1203 (1987).
[CrossRef] [PubMed]

D. H. Van Winkle and C. A. Murray, “Layering transitions in colloidal crystals as observed by diffraction and direct-lattice imaging,” Phys. Rev. A 34, 562–573 (1986).
[CrossRef] [PubMed]

Wagner, C. S.

M. Hoffmann, C. S. Wagner, L. Harnau, and A. Wittemann, “3D Brownian diffusion of submicron-sized particle clusters,” ACS Nano 3, 3326–3334 (2009).
[CrossRef] [PubMed]

Weeks, E. R.

D. Chen, D. Semwogerere, J. Sato, V. Breedveld, and E. R. Weeks, “Microscopic structural relaxation in a sheared supercooled colloidal liquid,” Phys. Rev. E 81, 011403 (2010).
[CrossRef]

J. Hernández-Guzmán and E. R. Weeks, “The equilibrium intrinsic crystal-liquid interface of colloids,” Proc. Natl. Acad. Sci. U.S.A. 106, 15198–15202 (2009).
[CrossRef] [PubMed]

C. R. Nugent, K. V. Edmond, H. N. Patel, and E. R. Weeks, “Colloidal glass transition observed in confinement,” Phys. Rev. Lett. 99, 025702 (2007).
[CrossRef] [PubMed]

R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon, “Three-dimensional imaging of colloidal glasses under steady shear,” Phys. Rev. Lett. 99, 028301 (2007).
[CrossRef] [PubMed]

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Opt. 40, 4152–4159 (2001).
[CrossRef]

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, “Real-space imaging of nucleation and growth in colloidal crystallization,” Science 292, 258–262 (2001).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef] [PubMed]

Weitz, D. A.

P. Schall, D. A. Weitz, and F. Spaepen, “Structural rearrangements that govern flow in colloidal glasses,” Science 318, 1895–1899 (2007).
[CrossRef] [PubMed]

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, “Three-dimensional confocal microscopy of colloids,” Appl. Opt. 40, 4152–4159 (2001).
[CrossRef]

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, “Real-space imaging of nucleation and growth in colloidal crystallization,” Science 292, 258–262 (2001).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef] [PubMed]

Wenk, R. A.

C. A. Murray, W. O. Sprenger, and R. A. Wenk, “Comparison of melting in three and two dimensions: microscopy of colloidal spheres,” Phys. Rev. B 42, 688–703 (1990).
[CrossRef]

Williams, G.

G. Williams, “Time-correlation functions and molecular motions,” Chem. Soc. Rev. 7, 89–131 (1978).
[CrossRef]

Wittemann, A.

M. Hoffmann, C. S. Wagner, L. Harnau, and A. Wittemann, “3D Brownian diffusion of submicron-sized particle clusters,” ACS Nano 3, 3326–3334 (2009).
[CrossRef] [PubMed]

Yang, H. D. O.

E. B. Sirota, H. D. O. Yang, S. K. Sinha, P. M. Chaikin, J. D. Axe, and Y. Fujii, “Complete phase diagram of a charged colloidal system: a synchrotron x-ray scattering study,” Phys. Rev. Lett. 62, 1524–1527 (1989).
[CrossRef] [PubMed]

Yodh, A. G.

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

Yunker, P. J.

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

Zhang, J.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[CrossRef] [PubMed]

Zhang, Z.

P. J. Yunker, K. Chen, Z. Zhang, W. G. Ellenbroek, A. J. Liu, and A. G. Yodh, “Rotational and translational phonon modes in glasses composed of ellipsoidal particles,” Phys. Rev. E 83, 011403 (2011).
[CrossRef]

ACS Nano (1)

M. Hoffmann, C. S. Wagner, L. Harnau, and A. Wittemann, “3D Brownian diffusion of submicron-sized particle clusters,” ACS Nano 3, 3326–3334 (2009).
[CrossRef] [PubMed]

Ann. Sci. Ec. Normale Super. (1)

F. Perrin, “Étude mathématique du mouvement Brownien de rotation,” Ann. Sci. Ec. Normale Super. 45, 1–51 (1928).

Appl. Opt. (1)

Chem. Soc. Rev. (1)

G. Williams, “Time-correlation functions and molecular motions,” Chem. Soc. Rev. 7, 89–131 (1978).
[CrossRef]

J. Biomech. (1)

J. Challis, “A procedure for determining rigid body transformation parameters,” J. Biomech. 28, 733–737 (1995).
[CrossRef] [PubMed]

J. Chem. Phys. (3)

D. G. Grier and C. A. Murray, “The microscopic dynamics of freezing in supercooled colloidal fluids,” J. Chem. Phys. 100, 9088–9095 (1994).
[CrossRef]

B. J. Berne, P. Pechukas, and G. D. Harp, “Molecular reorientation in liquids and gases,” J. Chem. Phys. 49, 3125–3129 (1968).
[CrossRef]

S. M. Anthony, M. Kim, and S. Granick, “Translation-rotation decoupling of colloidal clusters of various symmetries,” J. Chem. Phys. 129, 244701 (2008).
[CrossRef]

J. Colloid Interface Sci. (3)

A. Kose, M. Ozaki, K. Takano, Y. Kobayashi, and S. Hachisu, “Direct observation of ordered latex suspension by metallurgical microscope,” J. Colloid Interface Sci. 44, 330–338 (1973).
[CrossRef]

D. Mukhija and M. J. Solomon, “Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy,” J. Colloid Interface Sci. 314, 98–106 (2007).
[CrossRef] [PubMed]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

J. Phys. Condens. Matter (1)

P. N. Pusey, W. C. K. Poon, S. M. Ilett, and P. Bartlett, “Phase behaviour and structure of colloidal suspensions,” J. Phys. Condens. Matter 6, A29–A36 (1994).
[CrossRef]

Langmuir (3)

S. M. Anthony, L. Hong, M. Kim, and S. Granick, “Single-particle colloid tracking in four dimensions,” Langmuir 22, 9812–9815 (2006).
[CrossRef] [PubMed]

L. Hong, S. M. Anthony, and S. Granick, “Rotation in suspension of a rod-shaped colloid,” Langmuir 22, 7128–7131 (2006).
[CrossRef] [PubMed]

M. T. Elsesser, A. D. Hollingsworth, K. V. Edmond, and D. J. Pine, “Large core-shell poly(methyl methacrylate) colloidal clusters: synthesis, characterization, and tracking,” Langmuir 27, 917–927 (2011).
[CrossRef]

Nature (2)

A. van Blaaderen, “Materials science: colloids get complex,” Nature 439, 545–546 (2006).
[CrossRef] [PubMed]

P. N. Pusey and W. van Megen, “Phase behaviour of concentrated suspensions of nearly hard colloidal spheres,” Nature 320, 340–342 (1986).
[CrossRef]

Nature Mater. (1)

S. C. Glotzer and M. J. Solomon, “Anisotropy of building blocks and their assembly into complex structures,” Nature Mater. 6, 557–562 (2007).
[CrossRef]

Phys. Rev. A (1)

D. H. Van Winkle and C. A. Murray, “Layering transitions in colloidal crystals as observed by diffraction and direct-lattice imaging,” Phys. Rev. A 34, 562–573 (1986).
[CrossRef] [PubMed]

Phys. Rev. B (1)

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Other (1)

HYDRO++, http://leonardo.inf.um.es/macromol/programs/hydro++/hydro++.htm .

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Figures (6)

Fig. 1
Fig. 1

Top: Volumetric images of colloidal clusters with n = 4, 5, and 6 from 3D confocal micrographs. Images have been filtered and enhanced to allow easy visualization of the 3-dimensional structures. Individual particles are approximately 2 μm in diameter. Bottom: Ball-and-stick models of the clusters above. The cases n = 4 and n = 5 are accurate representations of the simulated tetrahedra and pentahedra discussed in the text.

Fig. 2
Fig. 2

(a) Trajectories of particles within a simulated Brownian tetrahedral cluster projected onto the surface of a unit sphere. Colors represent different particles, i.e. different choices for 0. (b) 2d projection of two trajectories through rotation space (φ x , φ y ). Colors correspond to the same particles in (a). Both trajectories in (b) begin at (0, 0) and end at open circles.

Fig. 3
Fig. 3

Mean square angular displacements of simulated tetrahedral clusters ( R = 3 μ m ) for different noise levels σx and diffusion coefficients of (a) 10−4 rad2/ts and (b) 10−3 rad2/ts. Open circles are the theoretical MSAD based on Eq. (20). Deviations from linearity at small Δt demonstrate the effect of noise when resolving small rotations. Deviations at large Δt, however, are the result of low statistics at these lag times.

Fig. 4
Fig. 4

(a) Measured values of Φ2 for non-diffusing tetrahedral (solid symbols) and pentahedral (open symbols) clusters. Colors indicate noise levels and symbols indicate cluster size. Solid lines are the prediction Φ 2 = 6 σ x 2 / n R 2 . (b) Same data in Fig. 3 with the appropriate Φ2 for each noise level subtracted.

Fig. 5
Fig. 5

Calculated MSD (blue squares) and MSAD (red circles) of a diffusing experimental tetrahedral cluster. Solid lines are best fit lines over range of data used to determine the respective diffusion coefficients.

Fig. 6
Fig. 6

The MSADs of simulated pentahedra ( R = 3 μ m ) with diffusion coefficients DR = 10−4 rad2/ts and DR = 10−2 rad2/ts and σx = 50 nm. Dashed lines show the uncorrected MSAD described below and solid lines are corrected data, obtained by multiplying the dashed lines by 2/3. Open circles are the theoretical MSAD from Eq. (20). We note that we have approximated diffusive motion by a single DR for each pentahedron, as described in section 3.

Tables (1)

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Table 1 Measurements from Tracking Tetrahedral Cluster

Equations (35)

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y i = s R x i + v ,
y i = R x i ,
R R 1 = R R T = R T R = E ,
det ( R ) = + 1 ,
1 n i = 1 n [ y i R x i ] T [ y i R x i ] .
i = 1 n ( y i ) T y i + ( x i ) T x i 2 ( y i ) T R x i .
i = 1 n ( y i ) T R x i = Tr ( R T i = 1 n y i ( x i ) T ) = Tr ( R T C ) ,
C = i = 1 n y i ( x i ) T .
C = UWV T ,
R = U [ 1 0 0 0 1 0 0 0 det ( U V T ) ] V T .
x i = x i x C M .
x i = R x i 0 .
x i ( t ) = R t Δ t R t 2 Δ t R 0 x i 0 = k R k x i 0 ,
( R / 3 ) ( 1 , ± 1 , ± 1 ) , ( R / 3 ) ( 1 , ± 1 , 1 ) ,
R ( 1 , 0 , 0 ) , ( R / 2 ) ( 1 , ± 3 , 0 ) , R ( 0 , 0 , ± 1 ) .
R x ( α ) = ( 1 0 0 0 cos α sin α 0 sin α cos α ) , R y ( β ) = ( cos β 0 sin β 0 1 0 sin β 0 cos β ) , R z ( γ ) = ( cos γ sin γ 0 sin γ cos γ 0 0 0 1 ) .
p ^ ( t ) = k R k p ^ 0 ,
φ ( t ) = 0 t ω ( t ) d t
Δ φ 2 ( Δ t ) = [ φ ( t + Δ t ) φ ( t ) ] 2 ,
Δ φ 2 ( Δ t ) = 4 D R Δ t ,
Δ φ 2 ( Δ t ) = Φ 2 ,
Δ φ 2 ( Δ t ) = 4 D R Δ t + Φ 2 ,
Φ 2 = 6 σ x 2 / n R 2 .
Δ r 2 = 6 D T Δ t ,
d tetra = 1.844 × d sphere ,
D T = k B T 3 π η d tetra
D R = k B T π η d tetra 3 ,
R u ^ = u ^ .
w ^ = u ^ × i ^ | u ^ × i ^ | .
R w ^ = w ^ .
sin ( Δ φ ) u ^ = w ^ × w ^ .
δ φ = cos 1 ( sin 2 θ cos δ φ u + cos 2 θ )
1 δ φ 2 sin 2 θ ( 1 δ φ u 2 ) + ( 1 sin 2 θ )
δ φ 2 sin 2 θ δ φ u 2 .
δ φ 2 = sin 2 θ δ φ u 2 = 2 3 δ φ u 2 ,

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