The dielectric virial expansion is developed for composite systems with embedded interacting dielectric dipolar spheres. Introducing a multiple-scattering expansion for the polarization energy in the presence of an external field enables the derivation of a virial expansion for the polarizability. Substituting the polarizability into the Clausius-Mossotti relation yields the virial series for the effective medium permittivity. When the dipole moment of the particles or inclusions vanishes, the leading-order term in the series reduces to the Maxwell-Garnett mixing rule, whereas the higher-order terms provide corrections that become important at higher densities. The dielectric virial coefficients are readily evaluated by replacing the surface charge contributions with image lines. Numerical data are presented for the second virial coefficients to illustrate the effects of polarization.

1.
L. D.
Landau
,
E. M.
Lifshitz
, and
L. P.
Pitaevskii
,
Electrostatics of Continuous Media
, 2nd ed. (
Butterworth-Heinemann
,
1984
).
2.
E.
Allahyarov
,
H.
Löwen
, and
L.
Zhu
,
Phys. Chem. Chem. Phys.
18
,
19103
(
2016
).
3.
J.
Tang
and
E. H.
Sargent
,
Adv. Mater.
23
,
12
(
2011
).
4.
E. I.
Izgorodina
,
M.
Forsyth
, and
D. R.
MacFarlane
,
Phys. Chem. Chem. Phys.
11
,
2452
(
2009
).
5.
P.
Sheng
and
W.
Wen
,
Annu. Rev. Fluid Mech.
44
,
143
(
2012
).
6.
J. C.
Maxwell Garnett
,
Philos. Trans. R. Soc., A
205
,
237
(
1906
).
7.
L.
Rayleigh
,
Philos. Mag.
34
,
481
(
1892
).
8.
T. C.
Choy
,
Effective Medium Theory: Principles and Applications
(
Oxford University Press
,
2016
).
9.
D.
McLachlan
,
A.
Priou
,
I.
Chenerie
,
E.
Issac
, and
F.
Henry
,
J. Electromagnet. Wave.
6
,
1099
(
1992
).
10.
V. D.
Bruggeman
,
Ann. Phys.
416
,
636
(
1935
).
11.
P.
Debye
,
Phys. Z.
13
,
97
(
1912
).
12.
F.
Claro
and
R.
Rojas
,
Phys. Rev. B
43
,
6369
(
1991
).
13.
M.
Scheller
,
S.
Wietzke
,
C.
Jansen
, and
M.
Koch
,
J. Phys. D: Appl. Phys.
42
,
065415
(
2009
).
14.
F.
Wu
and
K. W.
Whites
,
IEEE Trans. Antennas Propag.
49
,
1174
(
2001
).
15.
J. G.
Kirkwood
,
J. Chem. Phys.
4
,
592
(
1936
).
16.
L.
Onsager
,
J. Am. Chem. Soc.
58
,
1486
(
1936
).
17.
J. G.
Kirkwood
,
J. Chem. Phys.
7
,
911
(
1939
).
18.
A. D.
Buckingham
and
J. A.
Pople
,
J. Chem. Soc. Faraday Trans.
51
,
1029
(
1955
).
19.
A. D.
Buckingham
and
C. G.
Joslin
,
Mol. Phys.
40
,
1513
(
1980
).
20.
C. G.
Joslin
,
Mol. Phys.
42
,
1507
(
1981
).
21.
S.
Yang
,
A. J.
Schultz
, and
D. A.
Kofke
,
Mol. Phys.
115
,
991
(
2017
).
22.
J.
Qin
,
J. J.
de Pablo
, and
K. F.
Freed
,
J. Chem. Phys.
145
,
124903
(
2016
).
23.
K. S.
Gustafson
,
G.
Xu
,
K. F.
Freed
, and
J.
Qin
,
J. Chem. Phys.
147
,
064908
(
2017
).
24.
K.
Barros
and
E.
Luijten
,
Phys. Rev. Lett.
113
,
017801
(
2014
).
25.
K.
Barros
,
D.
Sinkovits
, and
E.
Luijten
,
J. Chem. Phys.
140
,
064903
(
2014
).
26.
Z.
Gan
,
S.
Jiang
,
E.
Luijten
, and
Z.
Xu
,
SIAM J. Sci. Comput.
38
,
B375
(
2016
).
27.
M.
Shen
,
H.
Li
, and
M.
Olvera de la Cruz
,
Phys. Rev. Lett.
119
,
138002
(
2016
).
28.
D. W.
Jepsen
,
J. Chem. Phys.
44
,
774
(
1966
).
29.
J. D.
Jackson
,
Classical Electrodynamics
, 3rd ed. (
Wiley
,
1998
).
30.
J. C.
Maxwell Garnett
,
Philos. Trans. R. Soc., A
203
,
385
(
1904
).
31.
K.
Huang
,
Statistical Mechanics
, 2nd ed. (
Wiley
,
1987
).
32.
D.
McQuarrie
,
Statistical Mechanics
(
University Science Books
,
2000
).
33.
V. A.
Markel
,
J. Opt. Soc. Am. A
33
,
1244
(
2016
).
34.
K.
Yang
,
X.
Huang
,
Y.
Huang
,
L.
Xie
, and
P.
Jiang
,
Chem. Mater.
25
,
2327
(
2013
).
35.
R.
Sekar
,
A.
Tripathi
, and
P.
Pillai
,
Mater. Sci. Eng. B
5
,
33
(
1989
).
36.
I.
Webman
,
J.
Jortner
, and
M. H.
Cohen
,
Phys. Rev. B
15
,
5712
(
1977
).
37.
B. E.
Springett
,
Phys. Rev. Lett.
31
,
1463
(
1973
).
38.
Y.
Rao
,
J.
Qu
,
T.
Marinis
, and
C.
Wong
,
IEEE Trans. Compon. Packag. Technol.
23
,
680
(
2000
).
39.
P.
Thomas
,
K.
Varughese
,
K.
Dwarakanath
, and
K.
Varma
,
Compos. Sci. Technol.
70
,
539
(
2010
).
40.
T.
Yamada
,
T.
Ueda
, and
T.
Kitayama
,
J. Appl. Phys.
53
,
4328
(
1982
).
41.
G.
Garner
,
N.
Shorrocks
,
R.
Whatmore
,
M.
Goosey
,
P.
Seth
, and
F.
Ainger
,
Ferroelectrics
93
,
169
(
1989
).
42.
P.
Kim
,
N. M.
Doss
,
J. P.
Tillotson
,
P. J.
Hotchkiss
,
M.-J.
Pan
,
S. R.
Marder
,
J.
Li
,
J. P.
Calame
, and
J. W.
Perry
,
ACS Nano
3
,
2581
(
2009
).
43.
M. C.
Araújo
,
C.
Costa
, and
S.
Lanceros-Méndez
,
J. Non-Cryst. Solids
387
,
6
(
2014
).
44.
I.
Fisher
,
W.
Kaplan
, and
M.
Eizenberg
,
J. Appl. Phys.
95
,
5762
(
2004
).
You do not currently have access to this content.