Abstract

We discuss a new method for simultaneously probing translational, rotational, and vibrational dynamics in dilute colloidal suspensions using digital holographic microscopy (DHM). We record digital holograms of clusters of 1-μm-diameter colloidal spheres interacting through short-range attractions, and we fit the holograms to an exact model of the scattering from multiple spheres. The model, based on the T-matrix formulation, accounts for multiple scattering and near-field coupling. We also explicitly account for the non-asymptotic radial decay of the scattered fields, allowing us to accurately fit holograms recorded with the focal plane located as little as 15 μm from the particle. Applying the fitting technique to a time-series of holograms of Brownian dimers allows simultaneous measurement of six dynamical modes — three translational, two rotational, and one vibrational — on timescales ranging from 10−3 to 1 s. We measure the translational and rotational diffusion constants to a precision of 0.6%, and we use the vibrational data to measure the interaction potential between the spheres to a precision of ∼50 nm in separation distance. Finally, we show that the fitting technique can be used to measure dynamics of clusters containing three or more spheres.

© 2011 OSA

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    [CrossRef] [PubMed]
  4. A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
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2010 (3)

2009 (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]

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 (1)

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]

2006 (2)

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]

M. Andersson and S. L. Maunu, “Structural studies of poly(N-isopropylacrylamide) microgels: Effect of SDS surfactant concentration in the microgel synthesis,” J. Polym. Sci., Part B: Polym. Phys . 44, 3305–3314 (2006).
[CrossRef]

2005 (3)

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

E. Andablo-Reyes, P. Díaz-Leyva, and J. L. Arauz-Lara, “Microrheology from rotational diffusion of colloidal particles,” Phys. Rev. Lett. 94, 106001 (2005).
[CrossRef] [PubMed]

J. Baumgartl and C. Bechinger, “On the limits of digital video microscopy,” Europhys. Lett. 71, 487493 (2005).
[CrossRef]

2003 (2)

Y. Pu and H. Meng, “Intrinsic aberrations due to mie scattering in particle holography,” J. Opt. Soc. Am. A 20, 1920–1932 (2003).
[CrossRef]

M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

2002 (2)

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

2001 (1)

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[CrossRef]

2000 (1)

1999 (1)

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82, 4352–4355 (1999).
[CrossRef]

1996 (3)

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

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by non-spherical particles: a review,” J. Quant. Spectrosc. Radiative Transfer 55, 535–575 (1996).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the t matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

1981 (1)

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).

1980 (1)

1978 (2)

M. Doi and S. F. Edwards, “Dynamics of rod-like macromolecules in concentrated solution. Part 1,” J. Chem. Soc. Faraday Trans. 2 74, 560–570 (1978).
[CrossRef]

C. M. Sorensen, R. C. Mockler, and W. J. O’Sullivan, “Multiple scattering from a system of brownian particles,” Phys. Rev. A 17, 2030–2035 (1978).
[CrossRef]

1976 (1)

A. Vrij, “Polymers at interfaces and the interactions in colloidal dispersions,” Pure Appl. Chem. 48, 471–483 (1976).
[CrossRef]

1958 (1)

S. Asakura and F. Oosawa, “Interaction between particles suspended in solutions of macromolecules,” J. Polym. Sci. 33, 183–192 (1958).
[CrossRef]

1934 (1)

F. Perrin, “Mouvement brownien d’un ellipsoide-I. Dispersion diélectrique pour des molécules ellipsoidales,” J. Phys. Radium 7, 497–511 (1934).
[CrossRef]

1909 (1)

J. Perrin, “Mouvement brownien et réalité moléculaire,” Ann. Chim. Phys. 18, 1–114 (1909).

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]

Andablo-Reyes, E.

E. Andablo-Reyes, P. Díaz-Leyva, and J. L. Arauz-Lara, “Microrheology from rotational diffusion of colloidal particles,” Phys. Rev. Lett. 94, 106001 (2005).
[CrossRef] [PubMed]

Andersson, M.

M. Andersson and S. L. Maunu, “Structural studies of poly(N-isopropylacrylamide) microgels: Effect of SDS surfactant concentration in the microgel synthesis,” J. Polym. Sci., Part B: Polym. Phys . 44, 3305–3314 (2006).
[CrossRef]

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]

Arauz-Lara, J. L.

E. Andablo-Reyes, P. Díaz-Leyva, and J. L. Arauz-Lara, “Microrheology from rotational diffusion of colloidal particles,” Phys. Rev. Lett. 94, 106001 (2005).
[CrossRef] [PubMed]

Arkus, N.

G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan, “The free-energy landscape of clusters of attractive hard spheres,” Science 327, 560–563 (2010).
[CrossRef] [PubMed]

Asakura, S.

S. Asakura and F. Oosawa, “Interaction between particles suspended in solutions of macromolecules,” J. Polym. Sci. 33, 183–192 (1958).
[CrossRef]

Baumgartl, J.

J. Baumgartl and C. Bechinger, “On the limits of digital video microscopy,” Europhys. Lett. 71, 487493 (2005).
[CrossRef]

Bausch, A. R.

M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

Bechinger, C.

J. Baumgartl and C. Bechinger, “On the limits of digital video microscopy,” Europhys. Lett. 71, 487493 (2005).
[CrossRef]

Beck, M.

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[CrossRef]

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Plenum Press, 1985).

Bishop, A. I.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Brenner, M. P.

G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan, “The free-energy landscape of clusters of attractive hard spheres,” Science 327, 560–563 (2010).
[CrossRef] [PubMed]

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

Cheong, F. C.

Crocker, J. C.

M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[CrossRef]

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82, 4352–4355 (1999).
[CrossRef]

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

Dhont, J. K.

J. K. Dhont, An Introduction to Dynamics of Colloids (Elsevier, 2003).

Díaz-Leyva, P.

E. Andablo-Reyes, P. Díaz-Leyva, and J. L. Arauz-Lara, “Microrheology from rotational diffusion of colloidal particles,” Phys. Rev. Lett. 94, 106001 (2005).
[CrossRef] [PubMed]

Dinsmore, A. D.

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82, 4352–4355 (1999).
[CrossRef]

Doi, M.

M. Doi and S. F. Edwards, “Dynamics of rod-like macromolecules in concentrated solution. Part 1,” J. Chem. Soc. Faraday Trans. 2 74, 560–570 (1978).
[CrossRef]

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

Edwards, S. F.

M. Doi and S. F. Edwards, “Dynamics of rod-like macromolecules in concentrated solution. Part 1,” J. Chem. Soc. Faraday Trans. 2 74, 560–570 (1978).
[CrossRef]

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

Gardel, M. L.

M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

Gay, C.

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

Gisler, T.

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[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]

Grier, D. G.

F. C. Cheong and D. G. Grier, “Rotational and translational diffusion of copper oxide nanorods measured with holographic video microscopy,” Opt. Express 18, 6555–6562 (2010).
[CrossRef] [PubMed]

F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
[CrossRef] [PubMed]

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

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

Heckenberg, N. R.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).

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]

Hsu, M. F.

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Kaplan, P. D.

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[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]

Kim, S. H.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

Kreis, T. M.

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

Krishnatreya, B. J.

Lee, S. H.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

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]

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by non-spherical particles: a review,” J. Quant. Spectrosc. Radiative Transfer 55, 535–575 (1996).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the t matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

Manoharan, V. N.

G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan, “The free-energy landscape of clusters of attractive hard spheres,” Science 327, 560–563 (2010).
[CrossRef] [PubMed]

Matteo, J. A.

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82, 4352–4355 (1999).
[CrossRef]

Maunu, S. L.

M. Andersson and S. L. Maunu, “Structural studies of poly(N-isopropylacrylamide) microgels: Effect of SDS surfactant concentration in the microgel synthesis,” J. Polym. Sci., Part B: Polym. Phys . 44, 3305–3314 (2006).
[CrossRef]

Meng, G.

G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan, “The free-energy landscape of clusters of attractive hard spheres,” Science 327, 560–563 (2010).
[CrossRef] [PubMed]

Meng, H.

Mishchenko, M. I.

Mockler, R. C.

C. M. Sorensen, R. C. Mockler, and W. J. O’Sullivan, “Multiple scattering from a system of brownian particles,” Phys. Rev. A 17, 2030–2035 (1978).
[CrossRef]

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]

Nieminen, T. A.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).

Nikolaides, M. G.

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

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]

O’Sullivan, W. J.

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[CrossRef]

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J. Perrin, “Mouvement brownien et réalité moléculaire,” Ann. Chim. Phys. 18, 1–114 (1909).

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[CrossRef]

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S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

Rubinsztein-Dunlop, H.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).

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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).
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C. M. Sorensen, R. C. Mockler, and W. J. O’Sullivan, “Multiple scattering from a system of brownian particles,” Phys. Rev. A 17, 2030–2035 (1978).
[CrossRef]

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M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
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M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[CrossRef]

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S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

van Oostrum, P.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

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M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
[CrossRef]

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
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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]

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S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

Yi, G. R.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 71, 18275–18282 (2005).

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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).
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[CrossRef]

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[CrossRef] [PubMed]

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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. Opt. Soc. Am. A (2)

J. Phys. Radium (1)

F. Perrin, “Mouvement brownien d’un ellipsoide-I. Dispersion diélectrique pour des molécules ellipsoidales,” J. Phys. Radium 7, 497–511 (1934).
[CrossRef]

J. Polym. Sci. (1)

S. Asakura and F. Oosawa, “Interaction between particles suspended in solutions of macromolecules,” J. Polym. Sci. 33, 183–192 (1958).
[CrossRef]

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M. Andersson and S. L. Maunu, “Structural studies of poly(N-isopropylacrylamide) microgels: Effect of SDS surfactant concentration in the microgel synthesis,” J. Polym. Sci., Part B: Polym. Phys . 44, 3305–3314 (2006).
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M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by non-spherical particles: a review,” J. Quant. Spectrosc. Radiative Transfer 55, 535–575 (1996).
[CrossRef]

Nature (London) (1)

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, and D. A. Weitz, “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces,” Nature (London) 420, 299–301 (2002).
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Opt. Eng. (1)

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (1)

C. M. Sorensen, R. C. Mockler, and W. J. O’Sullivan, “Multiple scattering from a system of brownian particles,” Phys. Rev. A 17, 2030–2035 (1978).
[CrossRef]

Phys. Rev. E (1)

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud’homme, M. Beck, and D. A. Weitz, “Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking,” Phys. Rev. E 64, 061506 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

M. L. Gardel, M. T. Valentine, J. C. Crocker, A. R. Bausch, and D. A. Weitz, “Microrheology of entangled f-actin solutions,” Phys. Rev. Lett. 91, 158302 (2003).
[CrossRef] [PubMed]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).

E. Andablo-Reyes, P. Díaz-Leyva, and J. L. Arauz-Lara, “Microrheology from rotational diffusion of colloidal particles,” Phys. Rev. Lett. 94, 106001 (2005).
[CrossRef] [PubMed]

J. C. Crocker, J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82, 4352–4355 (1999).
[CrossRef]

Pure Appl. Chem. (1)

A. Vrij, “Polymers at interfaces and the interactions in colloidal dispersions,” Pure Appl. Chem. 48, 471–483 (1976).
[CrossRef]

Science (2)

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]

G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan, “The free-energy landscape of clusters of attractive hard spheres,” Science 327, 560–563 (2010).
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J. K. Dhont, An Introduction to Dynamics of Colloids (Elsevier, 2003).

B. J. Berne and R. Pecora, Dynamic Light Scattering (Plenum Press, 1985).

C. B. Markwardt, “Non-linear least squares fitting in IDL with MPFIT,” http://arxiv.org/abs/0902.2850 (2009).

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (10)

Fig. 1
Fig. 1

Diagram of experimental apparatus for in-line digital holographic microscopy.

Fig. 2
Fig. 2

Cartoon of experimental system and of the depletion interaction. Shaded area around each polystyrene sphere shows the excluded volume around each sphere, set by the radius of the depletant particles. The centers of the depletant particles cannot enter the shaded areas. We simultaneously measure the translation, rotation, and vibrational dynamics of pairs of particles interacting through a depletion attraction with several kBT well depth.

Fig. 3
Fig. 3

Simulated holograms, calculated using the algorithms described in Sections 4.2 and 4.3, for colloidal clusters made of 1-μm-diameter polystyrene spheres in water. Blue diagrams are renderings of the particles in real space; they are oriented so that the incident light propagates into the page. (a) Single sphere. (b) Dimer, spheres in contact. (c) Dimer, spheres separated by 200 nm. The magnitude of the separation is larger than typically observed experimentally and has been chosen for clarity. (d) Dimer, spheres in contact, rotated 30° into the page and 45° axially. (e) Trimer, parallel to the detector plane.

Fig. 4
Fig. 4

Comparison between simulated hologram calculated using T-matrix method and simulated hologram computed from Lorenz-Mie superposition, for a dimer composed of 1.57 μm spheres. As shown in the blue rendering, the upper particle is rotated 45° into the page. The rendering is oriented so that the incident light direction is into the page. (a) Hologram intensity along red dashed lines in (b) and (c). The hologram calculated from a T-matrix solution (blue) differs qualitatively from the hologram calculated by superposing the Lorenz-Mie solution for two spheres (green) due to near-field coupling. (b) Simulated hologram computed from T-matrix code. (c) Simulated hologram calculated by Lorenz-Mie superposition.

Fig. 5
Fig. 5

Hologram of a dimer composed of 1 micron spheres, held together by a depletion interaction. (a) Comparison of the recorded hologram (solid black lines) to the best fit, as calculated from the T-matrix scattering model (red symbols), along the three dashed lines indicated. (b) Recorded hologram. (c) Best fit. The blue diagram above the holograms shows a rendering of the particle positions from the fit. The upper sphere is rotated 34.9° into the page. The rendering is oriented so that the incident light direction is into the page.

Fig. 6
Fig. 6

Translations of dimer center-of-mass in the laboratory frame. Left: histograms of the distributions of cluster center-of-mass displacements in the x direction at 20, 100, and 500 ms. Solid lines are fits to a Gaussian. Right: Laboratory-frame mean-square displacements. Solid line represents linear (diffusive) behavior. Error bars are at most comparable in size to the plot symbols.

Fig. 7
Fig. 7

Measured translational mean-square displacements parallel and perpendicular to dimer axis. The solid lines are linear fits from which we determine D and D . Left: linear plot; our errorbars are shown by the dashed lines. Right: same data shown on a log-log plot.

Fig. 8
Fig. 8

Left: Mean-square displacement of dimer axis vector u. The red line is a fit to Eq. (3), and the dashed lines are errorbars. Right: Same data plotted to show linear relationship.

Fig. 9
Fig. 9

Measured pair potential for a colloidal dimer. Only differences in U(r) are relevant; the actual values are arbitrary. The measured potential is qualitatively consistent with an attractive depletion force and an electrostatic repulsion. The bin width of the histogram of particle center-to-center separations, from which we determine the distribution of separations and the potential, is 11.7 nm.

Fig. 10
Fig. 10

Hologram of a trimer of 1.3 micron spheres. a) Comparison between the recorded hologram (solid black line) and the best fit, as calculated from the T-matrix scattering model (red symbols), along the three dashed lines indicated. b) Recorded hologram. c) Best fit. The blue diagram above the holograms shows a rendering of the particle positions from the fit. The leftmost sphere is rotated 38.3° into the page. The rendering is oriented so that the incident light direction is into the page.

Equations (18)

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Δ x 2 ( τ ) = 2 D | | τ
Δ x 2 ( τ ) = 4 D τ
Δ u 2 ( τ ) = 2 ( 1 exp [ 2 D r τ ] ) .
D = k B T 16 π η a r [ ( 2 r 2 1 ) S 2 r ] r 2 1
D = k B T 32 π η a r [ ( 2 r 2 3 ) S + 2 r ] r 2 1
S = 2 r 2 1 log [ r + ( r 2 1 ) 1 / 2 ] .
D r = 3 k B T 32 π η a 3 r 3 [ ( 2 r 2 1 ) S 2 r ] r 4 1 .
P ( r ) exp [ U ( r ) / k B T ] .
E s c a t E s c a t , 1 + E s c a t , 2 .
I = 1 + 2 α [ E s c a t e ^ ] + α 2 | E s c a t | 2
( E s c a t , E s c a t , ) = i ( S 2 S 3 S 4 S 1 ) ( E i n c , E i n c , ) .
S 1 = i l = 1 k = l l p = 1 2 R l p ( n m e d k 0 r ) a k l p , τ k l ( 3 p ) ( θ ) e i k φ
S 2 = l = 1 k = l l p = 1 2 R l p ( n m e d k 0 r ) a k l p , τ k l p ( θ ) e i k φ
S 3 = l = 1 k = l l p = 1 2 R l p ( n m e d k 0 r ) a k l p , τ k l p ( θ ) e i k φ
S 4 = i l = 1 k = l l p = 1 2 R l p ( n m e d k 0 r ) a k l p , τ k l ( 3 p ) ( θ ) e i k φ .
R l , 1 ( r ) = i r d dr ( r h l ( 1 ) ( r ) )
R l , 2 ( r ) = h l ( 1 ) ( r )
G = i ( H n o r m , i H mod , i ) 2 ( i 1 ) n p a r a m s

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