An original experiment is introduced that allows students to relate the of a set of particles to their macroscopic An external and constant is first applied to the so that the particles self-organize into chains. When the 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 process, while also observing the underlying of the microscopic particles. Moreover, by studying the evolution of the particle distribution, a of the coefficient can be obtained. In addition, by repeating this with fluids of various the Stokes-Einstein relation may be illustrated.
REFERENCES
1.
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
).2.
S.
Harris
, “ Diffusion coefficient for a Brownian
particle
,” Am. J. Phys.
44
(3
), 291
–294
(1976
).3.
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
).4.
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
).5.
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
).6.
B.
Brazzle
, “ A random walk to stochastic diffusion through spreadsheet
analysis
,” Am. J. Phys.
81
(11
), 823
–828
(2013
).7.
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
).8.
J.
Faraudo
and
J.
Camacho
, “ Cooperative magnetophoresis of superparamagnetic
colloids: theoretical aspects
,” Colloid Polym. Sci.
288
(2
), 207
–215
(2010
).9.
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
).10.
J. H.
Promislow
,
A. P.
Gast
, and
M.
Fermigier
, “ Aggregation kinetics of paramagnetic colloidal
particles
,” J. Chem. Phys.
102
(13
),
5492
–5498
(1995
).11.
P.
Domínguez-García
,
J.
Pastor
, and
M.
Rubio
, “ Aggregation and disaggregation dynamics of sedimented and
charged superparamagnetic micro-particles in water suspension
,”
Eur. Phys. J. E
34
(4
), 1
–7
(2011
).12.
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
).13.
M.
Fermigier
and
A. P.
Gast
, “ Structure evolution in a paramagnetic latex
suspension
,” J. Coll. Interf. Sci.
154
(2
), 522
–539
(1992
).14.
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
).15.
C. T.
Yavuz
,
J.
Mayo
et al, “ Low-field magnetic separation of
monodisperse Fe3O4 nanocrystals
,”
Science
314
(5801
),
964
–967
(2006
).16.
K. M.
Krishnan
, “ Biomedical nanomagnetics: A spin through possibilities in
imaging, diagnostics, and therapy
,” IEEE Trans. Magn.
46
(7
),
2523
–2558
(2010
).17.
J. L.
Corchero
and
A.
Villaverde
, “ Biomedical applications of distally controlled magnetic
nanoparticles
,” Trends Biotechnol.
27
(8
), 468
–476
(2009
).18.
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
).19.
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
).20.
H.
Carstensen
,
V.
Kapaklis
, and
M.
Wolff
, “ Phase formation in colloidal systems with tunable
interaction
,” Phys. Rev. E
92
(1
), 012303
(2015
).21.
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
).22.
F.
Martinez-Pedrero
and
P.
Tierno
, “ Magnetic propulsion of self-assembled colloidal carpets:
Efficient cargo transport via a conveyor-belt effect
,” Phys.
Rev. Appl.
3
(5
), 051003
(2015
).23.
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
).24.
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
).25.
K.
Muller
,
N.
Osterman
,
D.
Babic
,
C. N.
Likos
,
J.
Dobnikar
, and
A.
Nikoubashman
, “ Pattern formation and coarse-graining in two-dimensional
colloids driven by multiaxial magnetic fields
,”
Langmuir
30
(18
),
5088
–5096
(2014
).26.
J. W.
Tavacoli
,
P.
Bauër
,
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
).27.
G.
Lumay
,
N.
Obara
,
F.
Weyer
, and
N.
Vandewalle
, “ Self-assembled magnetocapillary
swimmers
,” Soft Matter
9
(8
), 2420
–2425
(2013
).28.
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
).29.
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=191.30.
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
).31.
S.
Fraden
,
A. J.
Hurd
, and
R. B.
Meyer
, “ Electric-field-induced association of colloidal
particles
,” Phys. Rev. Lett.
63
(21
),
2373
–2376
(1989
).32.
M.
Kolb
, “ Unified description of static and dynamic scaling for
kinetic cluster formation
,” Phys. Rev. Lett.
53
(17
),
1653
–1656
(1984
).33.
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
).34.
S.
Miyazima
,
P.
Meakin
, and
F.
Family
, “ Aggregation of oriented anisotropic
particles
,” Phys. Rev. A
36
(3
),
1421
–1427
(1987
).35.
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
).36.
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
).37.
Y.
Gurevich
,
Y.
Mankov
, and
R.
Khlebopros
, “ Self-assembly of superparamagnetic ferrihydrite
nanoparticles
,” Dokl. Phys.
58
(11
), 478
–481
(2013
).38.
K. H.
Taylor
, “ The influence of magnetic cohesion on the stability of
granular slopes
,” Ph.D. thesis, University of
Nottingham
, 2009
.39.
See supplementary material at
http://dx.doi.org/10.1119/1.4975382
E-AJPIAS-85-009703, which includes a matlab script for image
analysis, imagej macro and guidelines, and an illustrative video of the
experimental protocol.
40.
N.
Otsu
, “ A threshold selection method from gray-level
histograms
,” Automat.
11
(285–296
),
23
–27
(1975
).41.
Hint: 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.
42.
N.-S.
Cheng
, “ Formula for the viscosity of a glycerol-water
mixture
,” Ind. Eng. Chem. Res.
47
(98
),
3285
–3288
(2008
).43.
T.
Cosgrove
, Colloid Science: Principles, Methods and
Applications
, 2nd ed.
( John
Wiley & Sons
, United Kingdom, 2010
),
pp. 7
–10
.© 2017 American Association of Physics Teachers.
2017
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
