Control of transport processes in composite microstructures is critical to the development of high-performance functional materials for a variety of energy storage applications. The fundamental process of conduction and its control through the manipulation of granular composite attributes (e.g., grain shape) are the subject of this work. We show that athermally jammed packings of tetrahedra with ultrashort range order exhibit fundamentally different pathways for conduction than those in dense sphere packings. Highly resistive granular constrictions and few face–face contacts between grains result in short-range distortions from the mean temperature field. As a consequence, ‘granular’ or differential effective medium theory predicts the conductivity of this media within 10% at the jamming point; in contrast, strong enhancement of transport near interparticle contacts in packed-sphere composites results in conductivity divergence at the jamming onset. The results are expected to be particularly relevant to the development of nanomaterials, where nanoparticle building blocks can exhibit a variety of faceted shapes.

References

References
1.
Shakouri
,
A.
,
2011
, “
Recent Developments in Semiconductor Thermoelectric Physics and Materials
,”
Annu. Rev. Mater. Res.
,
41
, pp.
399
431
.10.1146/annurev-matsci-062910-100445
2.
Smith
,
K. C.
,
Mukherjee
,
P. P.
, and
Fisher
,
T. S.
,
2012
, “
Columnar Order in Jammed LiFePO4 Cathodes: Ion Transport Catastrophe and Its Mitigation
,”
Phys. Chem. Chem. Phys.
,
14
, pp.
7040
7050
.10.1039/c2cp40135e
3.
Schlapbach
,
L.
, and
Züttel
,
A.
,
2001
, “
Hydrogen-Storage Materials for Mobile Applications
,”
Nature
,
414
, pp.
353
358
.10.1038/35104634
4.
Smith
,
K. C.
, and
Fisher
,
T. S.
,
2012
, “
Models for Metal Hydride Particle Shape, Packing, and Heat Transfer
,”
Int. J. Hydrogen Energy
.,
37
(
18
), pp.
13417
13428
.10.1016/j.ijhydene.2012.06.087
5.
Baxter
,
J.
,
Bian
,
Z.
,
Chen
,
G.
,
Danielson
,
D.
,
Dresselhaus
,
M. S.
,
Fedorov
,
A. G.
,
Fisher
,
T. S.
,
Jones
,
C. W.
,
Maginn
,
E.
,
Kortshagen
,
U.
,
Manthiram
,
A.
,
Nozik
,
A.
,
Rolison
,
D. R.
,
Sands
,
T.
,
Shi
,
L.
,
Sholl
,
D.
, and
Wu
,
Y.
,
2009
, “
Nanoscale Design to Enable the Revolution in Renewable Energy
,”
Energy Environ. Sci.
,
2
, pp.
559
588
.10.1039/b821698c
6.
Maxwell
,
J. C.
,
1873
,
Treatise on Electricity and Magnetism
,
Clarendon Press
,
Oxford
.
7.
Rayleigh
,
L.
,
1892
, “
On the Influence of Obstacles Arranged in a Rectangular Order Upon the Properties of a Medium
,”
Philos. Mag.
,
34
, pp.
481
502
.
8.
Torquato
,
S.
,
2002
,
Random Heterogeneous Materials
,
Spring-Verlag
,
New York
, pp.
467
468
.
9.
Bruggeman
,
D. A. G.
,
1935
, “
Calculation of Various Physics Constants in Heterogenous Substances I. Dielectricity Constants and Conductivity of Mixed Bodies From Isotropic Substances
,”
Ann. Phys.
,
24
(
7
), pp.
636
664
.10.1002/andp.19354160705
10.
Yonezawa
,
F.
, and
Cohen
,
M. H.
,
1983
, “
Granular Effective Medium Approximation
,”
J. Appl. Phys.
,
54
, p.
2895
.10.1063/1.332490
11.
Sen
,
P. N.
,
Scala
,
C.
, and
Cohen
,
M. H.
,
1981
, “
A Self-Similar Model for Sedimentary-Rocks With Application to the Dielectric-Constant of Fused Glass-Beads
,”
Geophysics
,
46
(
5
), pp.
781
795
.10.1190/1.1441215
12.
Hasselman
,
D. P. H.
, and
Johnson
,
L. F.
,
1987
, “
Effective Thermal-Conductivity of Composites With Interfacial Thermal Barrier Resistance
,”
J. Compos. Mater.
,
21
(
6
), pp.
508
515
.10.1177/002199838702100602
13.
Nan
,
C.-W.
,
Birringer
,
R.
,
Clarke
,
D. R.
, and
Gleiter
,
H.
,
1997
, “
Effective Thermal Conductivity of Particulate Composites With Interfacial Thermal Resistance
,”
J. Appl. Phys.
,
81
(
10
), pp.
6692
6699
.10.1063/1.365209
14.
Every
,
A. G.
,
Tzou
,
Y.
,
Hasselman
,
D. P. H.
, and
Raj
,
R.
,
1992
, “
The Effect of Particle-Size on the Thermal-Conductivity of ZnS Diamond Composites
,”
Acta Metall. Mater.
,
40
(
1
), pp.
123
129
.10.1016/0956-7151(92)90205-S
15.
Tsotsas
,
E.
, and
Martin
,
H.
,
1987
, “
Thermal Conductivity of Packed Beds: A Review
,”
Chem. Eng. Process.
,
22
, pp.
19
37
.10.1016/0255-2701(87)80025-9
16.
Bauer
,
R.
, and
Schlünder
,
E. U.
,
1978
, “
Effective Radial Thermal Conductivity of Packings in Gas Flow—Part II: Thermal Conductivity of Packing Fraction Without Gas Flow
,”
Int. Chem. Eng.
,
18
, pp.
189
204
.
17.
Cates
,
M. E.
,
Wittmer
,
J. P.
,
Bouchaud
,
J.-P.
, and
Claudin
,
P.
,
1998
, “
Jamming, Force Chains, and Fragile Matter
,”
Phys. Rev. Lett.
,
81
(
9
), pp.
1841
1844
.10.1103/PhysRevLett.81.1841
18.
Haji-Akbari
,
A.
,
Engel
,
M.
,
Keys
,
A. S.
,
Zheng
,
X.
,
Petschek
,
R. G.
,
Palffy-Muhoray
,
P.
, and
Glotzer
,
S. C.
,
2009
, “
Disordered, Quasicrystalline and Crystalline Phases of Densely Packed Tetrahedra
,”
Nature
,
462
, pp.
773
777
.10.1038/nature08641
19.
Smith
,
K. C.
,
Alam
,
M.
, and
Fisher
,
T. S.
,
2010
, “
Athermal Jamming of Soft Frictionless Platonic Solids
,”
Phys. Rev. E
,
82
(
5
), p.
051304
.10.1103/PhysRevE.82.051304
20.
Smith
,
K. C.
,
Fisher
,
T. S.
, and
Alam
,
M.
,
2011
, “
Isostaticity of Constraints in Amorphous Jammed Systems of Soft Frictionless Platonic Solids
,”
Phys. Rev. E
,
84
, p.
030301
.10.1103/PhysRevE.84.030301
21.
Ma
,
Y.
,
Hao
,
Q.
,
Poudel
,
B.
,
Lan
,
Y.
,
Yu
,
B.
,
Wang
,
D.
,
Chen
,
G.
, and
Ren
,
Z.
,
2008
, “
Enhanced Thermoelectric Figure-of-Merit in p-Type Nanostructured Bismuth Antimony Tellurium Alloys Made From Elemental Chunks
,”
Nano Lett.
,
8
(
8
), pp.
2580
2584
.10.1021/nl8009928
22.
Zebarjadi
,
M.
,
Esfarjani
,
K.
,
Bian
,
Z.
, and
Shakouri
,
A.
,
2011
, “
Low-Temperature Thermoelectric Power Factor Enhancement by Controlling Nanoparticle Size Distribution
,”
Nano Lett.
,
11
(
1
), pp.
225
230
.10.1021/nl103581z
23.
Jeng
,
M.-S.
,
Yang
,
R.
,
Song
,
D.
, and
Chen
,
G.
,
2008
, “
Modeling the Thermal Conductivity and Phonon Transport in Nanoparticle Composites Using Monte Carlo Simulation
,”
ASME J. Heat Transfer
,
130
(
4
), p.
042410
.10.1115/1.2818765
24.
Wang
,
X.
,
Yang
,
Y.
, and
Zhu
,
L.
,
2011
, “
Effect of Grain Sizes and Shapes on Phonon Thermal Conductivity of Bulk Thermoelectric Materials
,”
J. Appl. Phys.
,
110
(
2
), p.
024312
.10.1063/1.3611421
25.
Hsieh
,
T.-Y.
,
Yang
,
J.-Y.
, and
Hong
,
Z.-C.
,
2009
, “
Thermal Conductivity Modeling of Compacted Type Nanocomposites
,”
J. Appl. Phys.
,
106
(
2
), p.
023528
.10.1063/1.3182803
26.
Zhou
,
J.
,
Li
,
X.
,
Chen
,
G.
, and
Yang
,
R.
,
2010
, “
Semiclassical Model for Thermoelectric Transport in Nanocomposites
,”
Phys. Rev. B
,
82
, p.
115308
.10.1103/PhysRevB.82.115308
27.
Jaoshvili
,
A.
,
Esakia
,
A.
,
Porrati
,
M.
, and
Chaikin
,
P. M.
,
2010
, “
Experiments on the Random Packing of Tetrahedral Dice
,”
Phys. Rev. Lett.
,
104
(
18
), p.
185501
.10.1103/PhysRevLett.104.185501
28.
Keller
,
J. B.
,
1963
, “
Conductivity of a Medium Containing a Dense Array of Perfectly Conducting Spheres or Cylinders or Nonconducting Cylinders
,”
J. Appl. Phys.
,
34
, pp.
991
993
.10.1063/1.1729580
29.
Jacobson
,
M.
, and
Völker
,
M.
,
2011
, “N-Dimensional Sparse Arrays,” MATLAB Central File Exchange, http://www.mathworks.com/matlabcentral/fileexchange/29832, Retrieved April 29, 2013.
30.
McPhedran
,
R. C.
, and
McKenzie
,
D. R.
,
1978
, “
The Conductivity of Lattices of Spheres. I. The Simple Cubic Lattice
,”
Proc. R. Soc. London, Ser. A
,
359
, pp.
45
63
.10.1098/rspa.1978.0031
31.
Jaluria
,
Y.
, and
Torrance
,
K.
,
2003
,
Computational Heat Transfer (Series in Computational Methods in Mechanics and Thermal Sciences)
,
Taylor & Francis
,
London
.
32.
Johansen
,
H.
, and
Colella
,
P.
,
1998
, “
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
,”
J. Comp. Phys.
,
147
, pp.
60
85
.10.1006/jcph.1998.5965
33.
Notay
,
Y.
,
2010
, “
An Aggregation-Based Algebraic Multigrid Method
,”
Electron. Trans. Numer. Anal.
,
37
, pp.
123
146
.
34.
Napov
,
A.
, and
Notay
,
Y.
,
2010
, “
An Algebraic Multigrid Method With Guarranteed Convergence Rate
,” Technical Report No. GANMN 10-03.
35.
Notay
,
Y.
,
2011
, “
Aggregation-Based Algebraic Multigrid for Convection-Diffusion Equations
,” Technical Report No. GANMN 11-01.
36.
O'Hern
,
C. S.
,
Silbert
,
L. E.
,
Liu
,
A. J.
, and
Nagel
,
S. R.
,
2003
, “
Jamming at Zero Temperature and Zero Applied Stress: The Epitome of Disorder
,”
Phys. Rev. E
,
68
, p.
011306
.10.1103/PhysRevE.68.011306
37.
Neudecker
,
M.
,
Ulrich
,
S.
,
Herminghaus
,
S.
, and
Schröter
,
M.
,
2012
, “
Jammed Frictional Tetrahedra are Hyperstatic
,” e-print arXiv:1202.6272.
38.
Jiao
,
Y.
, and
Torquato
,
S.
,
2011
, “
Maximally Random Jammed Packings of Platonic Solids: Hyperuniform Long-Range Correlations and Isostaticity
,”
Phys. Rev. E
,
84
, p.
041309
.10.1103/PhysRevE.84.041309
39.
Choy
,
T. C.
,
1999
,
Effective Medium Theory: Principles and Applications
,
Clarendon Press
,
Oxford
.
You do not currently have access to this content.