Abstract
We studied the diffusion of ellipsoidal colloids by using a combination of single-particle tracking (SPT) and differential dynamic microscopy (DDM). The micrometer-sized polystyrene particles have an aspect ratio of ≈ 4.3. SPT provides the particle trajectories and translation diffusion coefficient of the particles. DDM analyses appropriate for anisotropic particles were then used to extract the rotational diffusion coefficient of the particles. The results matched well with the theoretical prediction of translational and rotational diffusion coefficients for ellipsoids in the bulk. We extended our method to surface bound particles, which shows that rotation slowed by a larger amount compared to translation. This can be explained qualitatively by assuming heterogeneity of viscous and hydrodynamic forces experienced by surface bound particles. The research will be useful to study the viscous friction experienced by anisotropic colloids in complex fluids and surface friction at chemically or topologically modified substrates.
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References
Matsuoka H, Morikawa H, Yamaoka H (1996) Rotational diffusion of ellipsoidal latex particles in dispersion as studied by depolarized dynamic light scattering. Colloids Surfaces A: Physicochem Eng Aspects 109:137–145
Lehner D, Lindner H, Glatter O (2000) Determination of the translational and rotational diffusion coefficients of rodlike particles using depolarized dynamic light scattering. Langmuir 16:1689–1695
Cush R, Dorman D, Russo PS (2004) Rotational and translational diffusion of tobacco mosaic virus in extended and globular polymer solutions. Macromolecules 37:9577–9584
Han Y, Alsayed AM, Nobili M, Zhang J, Lubensky TC, Yodh AG (2006) Brownian motion of an ellipsoid. Science 314:624–630
Tsay JM, Doose S, Weiss S (2006) Rotational and translational diffusion of peptide-coated CdSe/CdS/ZnS nanorods studied by fluorescence correlation spectroscopy. J Am Chem Soc 128:1639–1647
Kuipers BW, Van de Ven MC, Baars RJ, Philipse AP (2012) Simultaneous measurement of rotational and translational diffusion of anisotropic colloids with a new integrated setup for fluorescence recovery after photobleaching. J Phys Condens Matter 24:245101
Wilcoxon J, Schurr JM (1983) Dynamic Light scattering from thin rigid rods: anisotropy of translational diffusion of tobacco mosaic virus. Biopolymers 22:849–867
Alam S, Mukhopadhyay A (2014) Translational and rotational diffusions of nanorods within semidilute and entangled polymer solutions. Macromolecules 47:6919–6924
Anthony SM, Kim M, Granick S (2008) Translation-rotation decoupling of colloidal clusters of various symmetries. J Chem Phys 129:244701
Stuckert R, Plüisch CS, Wittemann A (2018) Experimental assessment and model validation on how shape determines sedimentation and diffusion of colloidal particles. Langmuir 34:13339–13351
Chakrabarty A, Konya A, Wang F, Selinger JV, Sun K, Wei Q-H (2013) Brownian motion of boomerang colloidal particles. Phys Rev Lett 111:160603
Cerbino R, Trappe V (2008) Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Phys Rev Lett 100:188102
Berne BJ, Pecora R (2000) Dynamic Light Scattering New York: Dover
Shokeen N, Issa C, Mukhopadhyay A (2017) Comparison of nanoparticle diffusion using fluorescence correlation spectroscopy and differential dynamic microscopy within concentrated polymer solutions. Appl Phys Lett 111:263703
Edera P, Bergamini D, Trappe V, Giavazzi F, Cerbino R (2017) Differential dynamic microscopy microrheology of soft materials: a tracking-free determination of the frequency-dependent loss and storage moduli. Phys Rev Materials 1:073804
Brenner H (1961) The slow motion of a sphere through a viscous fluid towards a plane surface. Chem Eng Sci 16:242–251
Bayles AV, Squires TM, Helgeson ME (2016) Dark-field differential dynamic microscopy. Soft Matter 12:2440–2452
Reufer M, Martinez VA, Schurtenberger P, Poon WCK (2012) Differential dynamic microscopy for anisotropic colloidal dynamics. Langmuir 28:4618–4624
Wittmeier A, Holterhoff AL, Johnson J, Gibbs JG (2015) Rotational analysis of spherical, optically anisotropic janus particles by dynamic microscopy. Langmuir 31:10402–10410
Pal A, Martinez VA, Ito TH, Arlt J, Crassous JJ, Poon WCK, Schurtenberger P (2020) Anisotropic dynamics and kinetic arrest of dense colloidal ellipsoids in the presence of an external field studied by differential dynamic microscopy. Sci Adv 6:eaaw9733
Ho CC, Keller A, Odell JA, Ottewill RH (1993) Preparation of monodisperse ellipsoidal polystyrene particles. Colloid Polym Sci 271:469–479
Jaqaman K, Loerke D, Mettlen M, Kuwata H, Grinstein S, Schmid SL, Danuser G (2008) Robust single particle tracking in live cell time-lapse sequences. Nat Methods 5:695–702
Happel J, Brenner H (1991) Low Reynolds number hydrodynamics. Springer, Dordrecht
Giavazzi F, Edera P, Lu PJ, Cerbino R (2017) Image windowing mitigates edge effects in Differential Dynamic Microscopy. Eur Phys J E 40:97
Cerbino R, Piotti D, Buscaglia M, Giavazzi F (2018) Dark field differential dynamic microscopy enables accurate characterization of the roto-translational dynamics of bacteria and colloidal clusters. J Phys: Condens Matter 30:025901
Giavazzi F, Haro-Pérez C, Cerbino R (2016) Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy. J Phys: Condens Matter 28:195201
Piazza R, Degiorgio V (1996) Rotational diffusion of hard spheres: forward depolarized light-scattering measurements and comparison to theory and simulation. J Phys: Condens Matter 8:9497–9502
Shimizu H (1962) Effect of molecular shape on nuclear magnetic relaxation. J Chem Phys 37:765–778
Tirado MM, Torre JGdl (1979) Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders. J Chem Phys 71:2581–2587
Broersma S (1960) Viscous force constant for a closed cylinder. J Chem Phys 32:1632–1635
Brenner H (1974) Rheology of a dilute suspension of axisymmetric Brownian particles. Int J Multiphase Flow 1:195–341
Vasanthi R, Bhattacharyya S, Bagchi B (2001) Anisotropic diffusion of spheroids in liquids: slow orientational relaxation of the oblates. J Chem Phys 116
Cichocki B, Jones RB (1998) Image representation of a spherical particle near a hard wall. Phys A 273:273–302
Rogers SA, Lisicki M, Cichocki B, Dhont JKG, Lang PR (2012) Rotational diffusion of spherical colloids close to a wall. Phys Rev Lett 109:098305
Cicerone MT, Ediger MD (1996) Enhanced translation of probe molecules in supercooled o-terphenyl: signature of spatially heterogeneous dynamics? J Chem Phys 104:7210–7218
Acknowledgements
The authors thank Prof. Michael Solomon for access to confocal set-up and useful discussion. The confocal setup is a part of the Biointerfaces Institute, University of Michigan.
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Acknowledgements are made to the National Science Foundation through Grant CBET-2115827.
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Shokeen, N., Mukhopadhyay, A. Rotational and translational diffusion of colloidal ellipsoids in bulk and at surfaces. Colloid Polym Sci 299, 1595–1603 (2021). https://doi.org/10.1007/s00396-021-04893-8
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DOI: https://doi.org/10.1007/s00396-021-04893-8