This letter describes the formation of two-dimensional (2D) crystals of dipolar particles (TN) made of electrostatically charged, joined, millimeter-scale Teflon (T) and nylon-6,6 (N) spheres, and the separation of these crystals, as a distinct phase, from a mixture of TN and similar, capacitively charged particles that were coated with gold (Au2). The extent of separation increased with increasing amplitude of agitation, and with decreasing density of particles. Above a threshold in the amplitude of agitation, the crystals broke apart and the particles remixed. This system is a 2D model of the nucleation of crystals of polar molecules in a polarizable liquid.

1.
W. R.
Harper
,
Contact and Frictional Electrification
(
Laplacian
,
Morgan Hill, CA
,
1998
);
J.
Lowell
and
A. C.
Roseinnes
,
Adv. Phys.
29
,
947
(
1980
).
2.
B. A.
Grzybowski
,
A.
Winkleman
,
J. A.
Wiles
,
Y.
Brumer
, and
G. M.
Whitesides
,
Nature Mater.
2
,
241
(
2003
).
3.
G. K.
Kaufman
,
S. W.
Thomas
, III
,
M.
Reches
,
B. F.
Shaw
,
J.
Feng
, and
G. M.
Whitesides
, “
Phase separation of 2D meso-scale Coulombic crystals from meso-scale polarizable “solvent”
,”
Soft Matter
(in press).
4.
A. F.
Diaz
and
R. M.
Felix-Navarro
,
J. Electrost.
62
,
277
(
2004
).
5.
A.
Kudrolli
,
Rep. Prog. Phys.
67
,
209
(
2004
);
J. C.
Williams
,
Powder Technol.
15
,
245
(
1976
).
6.
See EPAPS Document No. E-APPLAB-93-045851 for experimental details, measurement of charges, calculation of density (ρ), calculation and limiting behavior of separation (Φ) and scaled separation (Φ*), and separation as a function of the number fraction of TN (χTN) and the angle of agitation with respect to gravity (α). For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
7.
J.
Stambaugh
,
Z.
Smith
,
E.
Ott
, and
W.
Losert
,
Phys. Rev. E
70
,
031304
(
2004
).
8.

To avoid any dependence of Φ on the density of spheres on the plate, we defined the “neighbors” of sphere n as the six spheres closest to sphere n, regardless of their actual distance from sphere n. For all the calculations in this paper, we set ntot=6 (i.e., we considered only the six nearest neighbors of each sphere). Other values of ntot did not yield qualitatively different results from those reported here.

9.

Previous work showed that at this frequency and amplitude, 30s was long enough for the charge on each sphere to become constant.

10.
H. A.
Makse
,
J.
Brujic
, and
S. F.
Edwards
,
Los Alamos Natl. Lab., Prepr. Arch., Condens. Matter, 1
(
2005
), p.
1
53
, arXiv:cond-mat/0503081;
C.
Song
,
P.
Wang
, and
H. A.
Makse
,
Nature (London)
453
,
629
(
2008
).
11.

We calculated ΦmaxC-S for each density (Fig. S6),6 and divided the values of Φ by ΦmaxC-S to obtain Φ*; this normalization allowed us to compare directly the values of Φ for different densities of particles.

12.

We agitated the particles at the combination of A(0.25mm) and ω(60Hz) for which Φ(t) increased monotonically and most rapidly at ρ=8.8spherescm2 (Fig. 2).

13.
D. W.
Mayo
,
R. M.
Pike
, and
P. K.
Trumper
,
Microscale Organic Laboratory
, 3rd ed. (
Wiley
,
New York
,
1994
), p.
403
.
14.
G. R.
Desiraju
,
Angew. Chem., Int. Ed.
46
,
8342
(
2007
).
15.
V. M.
Krishnamurthy
,
G. K.
Kaufman
,
A. R.
Urbach
,
I.
Gitlin
,
K. L.
Gudiksen
,
D. B.
Weibel
, and
G. M.
Whitesides
,
Chem. Rev. (Washington, D.C.)
108
,
946
(
2008
).

Supplementary Material

You do not currently have access to this content.