Dispersion rheology of carbon nanotubes in a polymer matrix
Y. Y. Huang, S. V. Ahir, and E. M. Terentjev
Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom
Received 4 December 2005; revised manuscript received 30 January 2006; published 23 March 2006
We report on rheological properties of a dispersion of multiwalled carbon nanotubes in a viscous polymer
matrix. Particular attention is paid to the process of nanotubes mixing and dispersion, which we monitor by the
rheological signature of the composite. The response of the composite as a function of the dispersion mixing
time and conditions indicates that a critical mixing time t
*
needs to be exceeded to achieve satisfactory
dispersion of aggregates, this time being a function of nanotube concentration and the mixing shear stress. At
shorter times of shear mixing t t
*
, we find a number of nonequilibrium features characteristic of colloidal
glass and jamming of clusters. A thoroughly dispersed nanocomposite, at t t
*
, has several universal rheologi-
cal features; at nanotube concentration above a characteristic value n
c
2–3 wt. % the effective elastic gel
network is formed, while the low-concentration composite remains a viscous liquid. We use this rheological
approach to determine the effects of aging and reaggregation.
DOI: 10.1103/PhysRevB.73.125422 PACS numbers: 81.07.-b, 81.05.Qk, 83.80.Hj
I. INTRODUCTION
The pursuit of well dispersed nanotubes into a given ma-
trix is a fundamental problem that still hinders research and
development a long time since they were brought to global
attention.
1
Monitoring the quality of dispersion within a
given system gives rise to additional problems. While clus-
tering of spherical particles has been studied well, for both
spherical and highly asymmetrical platelets, rods, and
fibers,
2–6
there are no reliable direct techniques of observing
carbon nanotubes in the bulk of a composite suspension. All
optical methods cut off below a length scale of
0.2–0.5 m; all electron microscopy methods so promi-
nent in observations of individual nanotubes can only pro-
vide information about the sample surface, i.e., only repre-
sentative for the selected fields of view. This leaves
reciprocal space techniques and, more importantly, global in-
direct techniques of characterizing the dispersed nanocom-
posites. Each of these techniques suffers from the unavoid-
able difficulty in interpretation of results. A recent review
gives a summary of such approaches, their strong and weak
aspects, and prospects.
7
If efficient and economically viable bulk processing of
nanotube-polymer composites is to be realized, a well-
developed understanding of responses to simple steady-state
shear flow is required. In this paper we concentrate on the
analysis and interpretation of rheological characteristics of
nanocomposites at different stages of their dispersion and
subsequent aging tube reaggregation. Some rheological
data has appeared in the recent literature
8–11
but to our un-
derstanding, no work has yet been undertaken to apply rheo-
logical data to characterize the state of dispersion directly,
and moreover, to investigate the effect of conditions and
mixing time on the quality of nanotube dispersion.
In itself, dispersion is a spatial property whereby the in-
dividual components in this case nanotubes are spread with
the roughly uniform number density throughout the continu-
ous supporting matrix. The first challenge is to separate the
tubes from their initial aggregated assemblies, which is usu-
ally achieved by local shear forces. However, a homoge-
neous suspension ideally achieved after mixing is not neces-
sarily a stable state: the removal of a shearing force may
open the way to reaggregation. At very low concentrations,
the conditions of an ideal-gas occur, when the dispersed ob-
jects do not interact with each other. However, for nanotubes
with very high persistence length, the Onsager treatment of
anisotropic suspensions
12
suggests that the crossover concen-
tration when the rodlike objects start interacting and signifi-
cantly biasing their orientational pair correlation can be very
low indeed.
13,14
Experimental evidence suggests external hy-
drodynamic forces can also induce clustering in highly an-
isotropic suspensions.
15
There are several classical ways of
surface treatment, which improves the colloidal stability of
nanotubes;
7
in all cases it is more challenging than in usual
sterically stabilized colloids because of the unusual depth of
the primary van der Waals minimum due to the high polar-
izability of nanotubes. Many authors have suggested that
when the loading of nanotubes is above a critical value, a
network structure can form in the nanocomposite system dur-
ing mixing.
8,10,16
Elastic gel, arising from such an entangled
nanotube network,
17,18
may prevent individual tube motion
and thus serve as an alternative mechanism of stabilization.
In this work we choose to work with untreated tubes,
since our main goal is to examine the dispersion and reaggre-
gation mechanisms. We believe that the state of dispersion in
a given composite dispersion can be ascertained by measur-
ing the global rheological properties of the system. The vis-
cosity of the mixture has a direct correlation with the spatial
and orientational distribution of nanotubes in the matrix.
This can be used as a physical signal with which to monitor
the quality of dispersion, as long as the interpretation of the
rheological signal is calibrated. By studying the rheology of
a viscous polymer mixed with nanotubes at different stages
of dispersion and aging we aim to provide, for instance, an
answer to the question of how long one should shearmix
their nanotube-polymer sample to achieve a suitable level of
dispersion. Our conclusions are somewhat surprising: the re-
quired mixing time is so long and the required mixing shear
so high that one might question the quality of nanotube dis-
persion of many famous experiments in the last decade.
PHYSICAL REVIEW B 73, 125422 2006
1098-0121/2006/7312/1254229/$23.00 ©2006 The American Physical Society 125422-1