Nanoparticle-organic hybrid materials consist of 10 nm diameter spherical inorganic core particles functionalized with oligomeric organic molecules. Although these systems contain no added solvent, they exhibit fluid behavior with the fluidity provided by the attached oligomers. We solve for the nonequilibrium probability density function for pairs of particles subject to a weak applied flow without hydrodynamic interactions. The intercore forces include hard-sphere repulsion and a many-body potential force resulting from the entropy of tethered oligomers filling the interstitial space. The latter potential is weak, O(a3/Rg3), when the oligomer radius of gyration Rg is much greater than the core radius a. While the long-time self-diffusivity of the cores and steady low shear viscosity of the system obtained from the analysis are similar to hard sphere suspensions at higher core volume fraction or with longer oligomeric chains, the material exhibits stronger resistance to the motion of core particles as the tethered hairs feel more entropic penalty to fill the space at low volume fractions and with shorter chains. This trend agrees qualitatively with experiments and molecular dynamics simulations and is a unique feature of the solvent-free nanoparticle fluid. The high frequency limit shear modulus is a linear function of ω1∕2 and the intercept provides information about many-body forces. Thus, the high frequency behavior shows characteristics of both hard and soft potentials.

1.
Agarwal
,
P.
, “
Self-suspended nanoparticle fluids
,” Ph.D. thesis,
Cornell University
,
2012
.
2.
Agarwal
,
P.
,
M.
Chopra
, and
L. A.
Archer
, “
Nanoparticle netpoints for shape-memory polymers
,”
Angew. Chem. Int. Ed.
50
,
8670
8673
(
2011a
).
3.
Agarwal
,
P.
,
S.
Srivastava
, and
L. A.
Archer
, “
Thermal jamming of a colloidal glass
,”
Phys. Rev. Lett.
107
,
268302
(
2011b
).
4.
Agarwal
,
P.
,
S. A.
Kim
, and
L. A.
Archer
, “
Crowded, confined, and frustrated: Dynamics of molecules tethered to nanoparticles
,”
Phys. Rev. Lett.
109
,
258301
(
2012
).
5.
Agarwal
,
P.
,
H.
Qi
, and
L. A.
Archer
, “
The ages in a self-suspended nanoparticle liquid
,”
Nano Lett.
10
,
111
115
(
2010
).
6.
Batchelor
,
G. K.
, “
Brownian diffusion of particles with hydrodynamic interactions
,”
J. Fluid Mech.
74
,
1
29
(
1976
).
7.
Batchelor
,
G. K.
, “
The effect of Brownian motion on the bulk stress in a suspension of spherical particles
,”
J. Fluid Mech.
83
,
97
117
(
1977
).
8.
Batchelor
,
G. K.
, “
Diffusion in a dilute polydisperse system of interacting spheres
,”
J. Fluid Mech.
131
,
155
175
(
1983
).
9.
Boon
,
J. P.
, and
S.
Yip
,
Molecular Hydrodynamics
(
McGraw-Hill
,
New York
,
1980
).
10.
Bourlinos
,
A. B.
,
E. P.
Giannelis
,
Q.
Zhang
,
L. A.
Archer
,
G.
Floudas
, and
G.
Fytas
, “
Surface-functionalized nanoparticles with liquid-like behavior: The role of the constituent components
,”
Eur. Phys. J. E
20
,
109
117
(
2006
).
11.
Brady
,
J. F.
, “
The rheological behavior of concentrated colloidal dispersions
,”
J. Chem. Phys.
99
,
567
581
(
1993
).
12.
Brady
,
J. F.
, “
The long-time self-diffusivity in concentrated colloidal dispersions
,”
J. Fluid Mech.
272
,
109
133
(
1994
).
13.
Briels
,
W. J.
,
D.
Vlassopoulos
,
K.
Kang
, and
J. K. G.
Dhont
, “
Constitutive equations for the flow behavior of entangled polymeric systems: Application to star polymers
,”
J. Chem. Phys.
134
,
124901
(
2011
).
14.
Chremos
,
A.
,
A. Z.
Panagiotopoulos
, and
D. L.
Koch
, “
Dynamics of solvent-free grafted nanoparticles
,”
J. Chem. Phys.
136
,
044902
(
2012
).
15.
Chremos
,
A.
,
A. Z.
Panagiotopoulos
,
H.-Y.
Yu
, and
D. L.
Koch
, “
Structure of solvent-free grafted nanoparticles: Molecular dynamics and density-functional theory
,”
J. Chem. Phys.
135
,
114901
(
2011
).
16.
Cohen
,
E. G. D.
,
R.
Verberg
, and
I. M.
de Schepper
, “
Viscosity and diffusion in hard-sphere-like colloidal suspensions
,”
Physica A
251
,
251
265
(
1998
).
17.
de Schepper
,
I. M.
,
H. E.
Smorenburg
, and
E. G. D.
Cohen
, “
Viscosity in dense hard sphere colloids
,”
Phys. Rev. Lett.
70
,
2178
2181
(
1993
).
18.
Fritz
,
G.
,
B. J.
Maranzano
,
N. J.
Wagner
, and
N.
Willenbacher
, “
High frequency rheology of hard sphere colloidal dispersions measured with a torsional resonator
,”
J. Non-Newtonian Fluid Mech.
102
,
149
156
(
2002
).
19.
Goyal
,
S.
, and
F. A.
Escobedo
, “
Structure and transport properties of polymer grafted nanoparticles
,”
J. Chem. Phys.
135
,
184902
(
2011
).
20.
Hansen
,
J.-P.
, and
I. R.
McDonald
,
Theory of Simple Liquids
, 3rd ed. (
Academic
,
London
,
2006
).
21.
Heyes
,
D. M.
, and
P. J.
Mitchell
, “
Self-diffusion and viscoelasticity of dense hard-sphere colloids
,”
J. Chem. Soc. Faraday Trans.
90
,
1931
1940
(
1994
).
22.
Kim
,
D.
, and
L. A.
Archer
, “
Nanoscale organic-inorganic hybrid lubricants
,”
Langmuir
27
,
3083
3094
(
2011
).
23.
Krekelberg
,
W. P.
,
T.
Kumar
,
J.
Mittal
,
J. R.
Errington
, and
T. M.
Truskett
, “
Anomalous structure and dynamics of the Gaussian-core fluid
,”
Phys. Rev. E
79
,
031203
(
2009
).
24.
Lekkerkerker
,
H. N. W.
, and
J. K. G.
Dhont
, “
On the calculation of the self-diffusion coefficient of interacting Brownian particles
,”
J. Chem. Phys.
80
,
5790
5792
(
1984
).
25.
Lin
,
K.-Y. A.
, and
A.-H. A.
Park
, “
Effects of bonding types and functional groups on co2 capture using novel multiphase systems of liquid-like nanoparticle organic hybrid materials
,”
Environ. Sci. Technol.
45
,
6633
6639
(
2011
).
26.
Lionberger
,
R. A.
, and
W. B.
Russel
, “
High frequency modulus of hard sphere colloids
,”
J. Rheol.
38
,
1885
1908
(
1994
).
27.
Lionberger
,
R. A.
, and
W. B.
Russel
, “
A smoluchowski theory with simple approximations for hydrodynamic interactions in concentrated dispersions
,”
J. Rheol.
41
,
399
425
(
1997a
).
28.
Lionberger
,
R. A.
, and
W. B.
Russel
, “
Effectiveness of nonequilibrium closures for the many body forces in concentrated colloidal dispersions
,”
J. Chem. Phys.
106
,
402
416
(
1997b
).
29.
Mason
,
T. G.
, and
D. A.
Weitz
, “
Linear viscoelasticity of colloidal hard sphere suspensions near the glass transition
,”
Phys. Rev. Lett.
75
,
2770
2773
(
1995
).
30.
Mausbach
,
P.
, and
H.-O.
May
, “
Static and dynamic anomalies in the Gaussian core model liquid
,”
Fluid Phase Equilib.
249
,
17
23
(
2006
).
31.
McLeish
,
T. C. B.
, and
S. T.
Milner
, “
Entangled dynamics and melt flow of branched polymers
,”
Adv. Polym. Sci.
143
,
195
256
(
1999
).
32.
McQuarrie
,
D. A.
,
Statistical Mechanics
(
University Science Books
,
Sausalito
,
2000
).
33.
Moganty
,
S. S.
,
N.
Jayaprakash
,
J. L.
Nugent
,
J.
Shen
, and
L. A.
Archer
, “
Ionic-liquid-tethered nanoparticles: Hybrid electrolytes
,”
Angew. Chem. Int. Ed.
49
,
9158
9161
(
2010
).
34.
Nugent
,
J. L.
,
S. S.
Moganty
, and
L. A.
Archer
, “
Nanoscale organic hybrid electrolytes
,”
Adv. Mater.
22
,
3677
3680
(
2010
).
35.
Park
,
Y.
,
J.
Decatur
,
K.-Y. A.
Lin
, and
A.-H. A.
Park
, “
Investigation of co2 capture mechanisms of liquid-like nanoparticle organic hybrid materials via structural characterization
,”
Phys. Chem. Chem. Phys.
13
,
18115
18122
(
2011
).
36.
Park
,
Y.
,
D.
Shin
,
Y. N.
Jang
, and
A.-H. A.
Park
, “
Co2 capture capacity and swelling measurements of liquid-like nanoparticle organic hybrid materials via attenuated total reflectance Fourier transform infrared spectroscopy
,”
J. Chem. Eng. Data
57
,
40
45
(
2012
).
37.
Petit
,
C.
,
Y.
Park
,
K.-Y. A.
Lin
, and
A.-H. A.
Park
, “
Spectroscopic investigation of the canopy configurations in nanoparticle organic hybrid materials of various grafting densities during co2 capture
,”
J. Phys. Chem. C
116
,
516
525
(
2012
).
38.
Rey
,
C.
,
L. J.
Gallego
, and
L. E.
González
, “
Properties of a hard-core fluid with a yukawa tail studied by molecular dynamics and the mean spherical approximation
,”
J. Chem. Phys.
96
,
6984
6988
(
1992
).
39.
Rodriguez
,
R.
,
R.
Herrera
,
L. A.
Archer
, and
E. P.
Giannelis
, “
Nanoscale ionic materials
,”
Adv. Mater.
20
,
4353
4358
(
2008
).
40.
Russel
,
W. B.
, and
A. P.
Gast
, “
Nonequilibrium statistical mechanics of concentrated colloidal dispersions: Hard spheres in weak flows
,”
J. Chem. Phys.
84
,
1815
1826
(
1986
).
41.
Stillinger
,
F. H.
, “
Phase transitions in the Gaussian core system
,”
J. Chem. Phys.
65
,
3968
3974
(
1976
).
42.
van der Werff
,
J. C.
,
C. G.
de Kruif
,
C.
Blom
, and
J.
Mellema
, “
Linear viscoelastic behavior of dense hard-sphere dispersions
,”
Phys. Rev. A
39
,
795
807
(
1989
).
43.
Verberg
,
R.
,
I. M.
de Schepper
, and
E. G. D.
Cohen
, “
Viscosity of colloidal suspensions
,”
Phys. Rev. E
55
,
3143
3158
(
1997
).
44.
Verberg
,
R.
,
I. M.
de Schepper
, and
E. G. D.
Cohen
, “
Diffusion of concentrated neutral hard-sphere colloidal suspensions
,”
Phys. Rev. E
61
,
2967
2976
(
2000
).
45.
Wagner
,
N. J.
, and
W. B.
Russel
, “
Nonequilibrium statistical mechanics of concentrated colloidal dispersions: Hard spheres in weak flows with many-body thermodynamic interactions
,”
Physica A
155
,
475
518
(
1989
).
46.
Yu
,
H.-Y.
, and
D. L.
Koch
, “
Structure of solvent-free nanoparticle–organic hybrid materials
,”
Langmuir
26
,
16801
16811
(
2010
).
You do not currently have access to this content.