Relating Brownian motion to diffusion with superparamagnetic colloids

Darras, Alexis; Fiscina, Jorge; Vandewalle, Nicolas; Lumay, Geoffroy

doi:10.1119/1.4975382

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Relating Brownian motion to diffusion with superparamagnetic colloids

Darras, Alexis; Fiscina, Jorge; Vandewalle, Nicolas et al.

2017 • In American Journal of Physics, 85 (265)

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https://hdl.handle.net/2268/240413

DOI
10.1119/1.4975382

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Keywords :

colloids; diffusion; statistics

Abstract :

[en] An original experiment is introduced that allows students to relate the Brownian motion of a set of superparamagnetic colloidal particles to their macroscopic diffusion. An external and constant magnetic field is first applied to the colloidal suspension so that the particles self-organize into chains. When the magnetic field is removed, the particles then freely diffuse from their positions in the chain, starting from the same coordinate on the axis perpendicular to the initial chain. This configuration thus enables an observer to study the one dimensional diffusion process, while also observing the underlying Brownian motion of the microscopic particles. Moreover, by studying the evolution of the particle distribution, a measurement of the diffusion coefficient can be obtained. In addition, by repeating this measurement with fluids of various viscosities, the Stokes-Einstein relation may be illustrated.

Research center :

Group for Research and Applications on Statistical Physics-GRASP

Disciplines :

Physics

Author, co-author :

Darras, Alexis ; Université de Liège > Département de physique > Physique expér. de la matière molle et des syst. complexes

Fiscina, Jorge; Saarland University > Experimental physics > Christian Wagner AG

Vandewalle, Nicolas ; Université de Liège > Département de physique > Physique statistique

Lumay, Geoffroy ; Université de Liège > Département de physique > Physique expér. de la matière molle et des syst. complexes

Language :

English

Title :

Relating Brownian motion to diffusion with superparamagnetic colloids

Publication date :

March 2017

Journal title :

American Journal of Physics

ISSN :

0002-9505

Publisher :

American Association of Physics Teachers, Melville, United States - New York

Volume :

Issue :

265

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://aapt.scitation.org/doi/10.1119/1.4975382

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
ULiège - Université de Liège [BE]

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Bibliography

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, "Measuring Boltzmann's constant through holographic video microscopy of a single colloidal sphere, " Am. J. Phys. 82(1), 23-31 (2014).
S. Harris, "Diffusion coefficient for a Brownian particle, " Am. J. Phys. 44(3), 291-294 (1976).
P. Nakroshis, M. Amoroso, J. Legere, and C. Smith, "Measuring Boltzmann's constant using video microscopy of Brownian motion, " Am. J. Phys. 71(6), 568-573 (2003).
M. A. Catipovic, P. M. Tyler, J. G. Trapani, and A. R. Carter, "Improving the quantification of Brownian motion, " Am. J. Phys. 81(7), 485-491 (2013).
K. Ghosh, K. A. Dill, M. M. Inamdar, E. Seitaridou, and R. Phillips, "Teaching the principles of statistical dynamics, " Am. J. Phys. 74(2), 123-133 (2006).
B. Brazzle, "A random walk to stochastic diffusion through spreadsheet analysis, " Am. J. Phys. 81(11), 823-828 (2013).
J. Faraudo, J. S. Andreu, and J. Camacho, "Understanding diluted dispersions of superparamagnetic particles under strong magnetic fields: A review of concepts, theory and simulations, " Soft Matter 9(29), 6654-6664 (2013).
J. Faraudo and J. Camacho, "Cooperative magnetophoresis of superparamagnetic colloids: theoretical aspects, " Colloid Polym. Sci. 288(2), 207-215 (2010).
J. S. Andreu, J. Camacho, and J. Faraudo, "Aggregation of superparamagnetic colloids in magnetic fields: The quest for the equilibrium state, " Soft Matter 7(6), 2336-2339 (2011).
J. H. Promislow, A. P. Gast, and M. Fermigier, "Aggregation kinetics of paramagnetic colloidal particles, " J. Chem. Phys. 102(13), 5492-5498 (1995).
P. Domínguez-García, J. Pastor, and M. Rubio, "Aggregation and disaggregation dynamics of sedimented and charged superparamagnetic microparticles in water suspension, " Eur. Phys. J. E 34(4), 1-7 (2011).
P. Domínguez-García, S. Melle, J. Pastor, and M. Rubio, "Scaling in the aggregation dynamics of a magnetorheological fluid, " Phys. Rev. E 76(5), 051403 (2007).
M. Fermigier and A. P. Gast, "Structure evolution in a paramagnetic latex suspension, " J. Coll. Interf. Sci. 154(2), 522-539 (1992).
A. Darras, J. Fiscina, M. Pakpour, N. Vandewalle, and G. Lumay, "Ribbons of superparamagnetic colloids in magnetic field, " Eur. Phys. J. E 39(4), 1-6 (2016).
C. T. Yavuz, J. Mayo et al., "Low-field magnetic separation of monodisperse Fe3O4 nanocrystals, " Science 314(5801), 964-967 (2006).
K. M. Krishnan, "Biomedical nanomagnetics: A spin through possibilities in imaging, diagnostics, and therapy, " IEEE Trans. Magn. 46(7), 2523-2558 (2010).
J. L. Corchero and A. Villaverde, "Biomedical applications of distally controlled magnetic nanoparticles, " Trends Biotechnol. 27(8), 468-476 (2009).
U. Jeong, X. Teng, Y. Wang, H. Yang, and Y. Xia, "Superparamagnetic colloids: Controlled synthesis and niche applications, " Adv. Mater. 19(1), 33-60 (2007).
P. Liu, J. W. De Folter, A. V. Petukhov, and A. P. Philipse, "Reconfigurable assembly of superparamagnetic colloids confined in thermo-reversible microtubes, " Soft Matter 11(31), 6201-6211 (2015).
H. Carstensen, V. Kapaklis, and M. Wolff, "Phase formation in colloidal systems with tunable interaction, " Phys. Rev. E 92(1), 012303 (2015).
F. Martinez-Pedrero, A. Ortiz-Ambriz, I. Pagonabarraga, and P. Tierno, "Colloidal microworms propelling via a cooperative hydrodynamic conveyor belt, " Phys. Rev. Lett. 115(13), 138301 (2015).
F. Martinez-Pedrero and P. Tierno, "Magnetic propulsion of selfassembled colloidal carpets: Efficient cargo transport via a conveyor-belt effect, " Phys. Rev. Appl. 3(5), 051003 (2015).
R. M. Erb, H. S. Son, B. Samanta, V. M. Rotello, and B. B. Yellen, "Magnetic assembly of colloidal superstructures with multipole symmetry, " Nature 457(7232), 999-1002 (2009).
M. Llera, J. Codnia, and G. A. Jorge, "Aggregation dynamics and magnetic properties of magnetic micrometer-sized particles dispersed in a fluid under the action of rotating magnetic fields, " J. Magn. Magn. Mater. 384(93), 93-100 (2015).
K. Muller, N. Osterman, D. Babic, C. N. Likos, J. Dobnikar, and A. Nikoubashman, "Pattern formation and coarse-graining in twodimensional colloids driven by multiaxial magnetic fields, " Langmuir 30(18), 5088-5096 (2014).
J. W. Tavacoli, P. Baüer, M. Fermigier, D. Bartolo, J. Heuvingh, and O. du Roure, "The fabrication and directed self-assembly of micron-sized superparamagnetic non-spherical particles, " Soft Matter 9(38), 9103-9110 (2013).
G. Lumay, N. Obara, F. Weyer, and N. Vandewalle, "Self-assembled magnetocapillary swimmers, " Soft Matter 9(8), 2420-2425 (2013).
G. Grosjean, G. Lagubeau, A. Darras, M. Hubert, G. Lumay, and N. Vandewalle, "Remote control of self-assembled microswimmers, " Sci. Rep. 5, 1-8 (2015).
M. Pichumani and W. González-Viñas, "Spin-coating of dilute magnetic colloids in a magnetic field, " Magnetohydrodynamics 47(2), 191-199 (2011) available at http://mhd.sal.lv/Download/download.php?ed=rn&vol=47&nr= 2&an=11&p1=191&p2=191.
P. Pearle, B. Collett, K. Bart, D. Bilderback, D. Newman, and S. Samuels, "What Brown saw and you can too, " Am. J. Phys. 78(12), 1278-1289 (2010).
S. Fraden, A. J. Hurd, and R. B. Meyer, "Electric-field-induced association of colloidal particles, " Phys. Rev. Lett. 63(21), 2373-2376 (1989).
M. Kolb, "Unified description of static and dynamic scaling for kinetic cluster formation, " Phys. Rev. Lett. 53(17), 1653-1656 (1984).
F. Martínez-Pedrero, M. Tirado-Miranda, A. Schmitt, and J. Callejas-Fernández, "Formation of magnetic filaments: A kinetic study, " Phys. Rev. E 76(1), 011405 (2007).
S. Miyazima, P. Meakin, and F. Family, "Aggregation of oriented anisotropic particles, " Phys. Rev. A 36(3), 1421-1427 (1987).
G. P. Gajula, M. T. Neves-Petersen, and S. B. Petersen, "Visualization and quantification of four steps in magnetic field induced two-dimensional ordering of superparamagnetic submicron particles, " Appl. Phys. Lett. 97(10), 103103 (2010).
K. S. Khalil, A. Sagastegui, Y. Li, M. A. Tahir, J. E. Socolar, B. J. Wiley, and B. B. Yellen, "Binary colloidal structures assembled through ising interactions, " Nat. Commun. 3, 794-812 (2012).
Y. Gurevich, Y. Mankov, and R. Khlebopros, "Self-assembly of superparamagnetic ferrihydrite nanoparticles, " Dokl. Phys. 58(11), 478-481 (2013).
K. H. Taylor, "The influence of magnetic cohesion on the stability of granular slopes, " Ph.D. thesis, University of Nottingham, 2009. 39See supplementary material at http://dx.doi.org/10.1119/1.4975382, which includes a MATLAB script for image analysis, IMAGEJ macro and guidelines, and an illustrative video of the experimental protocol.
See supplementary material at http://dx.doi.org/10.1119/1.4975382, which includes a MATLAB script for image analysis, IMAGEJ macro and guidelines, and an illustrative video of the experimental protocol.
N. Otsu, "A threshold selection method from gray-level histograms, " Automat. 11(285-296), 23-27 (1975). 41Hint: This can be done in a single MATLAB command, provided the chain is parallel to one side of the picture. See line 37 of the MATLAB code in supplementary materials.
N.-S. Cheng, "Formula for the viscosity of a glycerol-water mixture, " Ind. Eng. Chem. Res. 47(98), 3285-3288 (2008).
T. Cosgrove, Colloid Science: Principles, Methods and Applications, 2nd ed. (John Wiley & Sons, United Kingdom, 2010), pp. 7-10.