268 Propellants, Explosives, Pyrotechnics 26, 268 272 (2001)
Rheology of Nano-Scale Aluminum Suspensions
Ulrich Teipel and Ulrich Förter-Barth
Fraunhofer-Institut für Chemische Technologie (ICT), Joseph-von-Fraunhofer-Straße 7, D-76327 Pfinztal (Germany)
Dedicated to Dr. Axel Homburg on the Occasion of his 65th Birthday
Summary fixtures included a modified coaxial cylinder (Mooney-
Ewart-System) and a cone and plate.
Nano-scale aluminum particles are innovative materials which are
Under steady state shear flow, the characteristic material
used increasingly in energetic formulations. In this contribution, the
function can be described as follows:
rheological behavior of suspensions with either paraffin oil or HTPB as
the matrix fluid and nano-scale aluminum (ALEX) as the dispersed
_ _ _
tðgÞ ÅºZðgÞ g ð1Þ
g g g
phase is described and discussed. The paraffin oil=aluminum suspen-
sions exhibit non-Newtonian flow behavior over a wide range of
_
Here, ZðgÞ is a characteristic material function that
g
concentrations, whereas the HTPB=aluminum suspensions exhibit
describes the flow properties when the fluid is subjected to
Newtonian behavior (i.e. the viscosity is independent of shear stress)
up to a concentration of 50 vol.% aluminum. Both systems have a rheometric flow.
unusual viscoelastic properties in that their elastic moduli are inde-
In oscillatory shear flow, the fluid is subjected to a periodic
pendent of the solids concentration.
^
(e.g., sinusoidal) deformation g(t) with an amplitude g at a
g
(5)
radial frequency o ź 2 p f (Fig. 1):
^
gðtÞ Åº g siotÞð2Þ
g
1. Introduction
Subjecting the material to an oscillatory (sinusoidal) shear
deformation at sufficiently small amplitudes, i.e. in the linear
Aluminum particles are well known as an ingredient in
viscoelastic range, results in a sinusoidal shear stress t(t)
energetic materials. The typical diameter of aluminum used
output (Fig. 2). Viscoelastic material behavior is character-
in explosives and propellants is in the order of 30 mm(1). To
ized by the existence of a phase shift d between the shear
enhance aluminum s reactivity, for instance during combus-
stress output t(t) and the deformation input g(t):
tion of solid rocket propellants, it is advantageous to use
particles with the largest possible specific surface area, i.e.,
^
tðtÞ Åº t siot þ dÞð3Þ
t
particles with a smaller mean particle size are desirable. By
By definition, the phase shift, d, of a perfectly elastic solid
vaporizing and subsequently condensing aluminum in argon,
is zero and that of a purely viscous fluid is p=2, whereas for
or by electric explosion of an aluminum wire, it is possible to
viscoelastic fluids 0 d p=2.
produce aluminum particles in the nanometer size range(2,3).
The shear stress function can be described in terms of the
Particles in this size range exhibit physical properties very
frequency dependent complex shear modulus G*(o),
different than those in the micrometer range. At such small
sizes, interparticle interactions become significantly more
^
tðtÞ Åº gjG ðoÞj siot þ dðoÞÞ ð4Þ
g
important and, as a result, nano-scale particles have a higher
tendency to agglomerate(4). In addition, the changed material
The complex shear modulus can also be expressed as
behavior of nano-scale particles can lead to processing
^
t
tðoÞ
difficulties when they are mixed with a fluid polymer
jG ðoÞj ź ð5Þ
^
g
g
matrix. This work examines and discusses the rheological
properties of suspensions containing nano-scale aluminum
The complex shear modulus G*(o) of a viscoelastic
particles in steady state and oscillatory shear flows.
material is composed of two material functions, a real and
an imaginary component, called the storage modulus, G0(o),
and the loss modulus, G00(o), respectively. The storage
modulus G0(o) is proportional to the deformation energy
2. Measurement Methods
stored by the material (the elastic component), while the loss
modulus G00(o) is proportional to the amount of energy
The rheological behavior of suspensions filled with nano-
dissipated by the material (the viscous component).
scale aluminum was examined in steady state and oscillatory
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
shear flow using a UDS 200 rotational rheometer manufac-
jG ðoÞj ź G0ðoÞ2 þ G00ðoÞ2 ð6Þ
tured by Physica Meßtechnik GmbH. The measurement
# WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2001 0721-3115/01/0612 0268 $17.50þ:50=0
Propellants, Explosives, Pyrotechnics 26, 268 272 (2001) Rheology of Nano-Scale Aluminum Suspensions 269
Figure 3. Nano-scale aluminum powder.
Figure 1. Deformation and shear rate profiles in oscillatory shear
flow.
terminated polybutadiene (HTPB). The paraffin oil exhibited
Newtonian flow behavior with a dynamic viscosity of
Z(20 C) ź 198 mPas. It had a density r ź 874.7 kg=m3 and
a surface tension s ź 30.5 mN=m. The hydroxy-terminated
polybutadiene (designated HTPB R 45-M) also exhibited
Newtonian flow behavior with a dynamic viscosity of
Z(20 C) ź 9300 mPas.
The nano-scale aluminum (ALEX) was obtained from
Argonide Corporation, Stanford, Florida=USA. The density
of the aluminum particles was determined by gas pycnometry
to be r ź 2.4 g=m3 and the specific surface area determined
by gas adsorption was S ź 11.2 m2=g. A SEM image of the
aluminum powder is shown in Figure 3.
4. Results
Figure 2. Shear stress profile of a viscoelastic fluid resulting from an
4.1 Flow Behavior of the Paraffin Oil=Aluminum
oscillatory shear deformation.
Suspensions
Oscillatory shear experiments must be conducted at
Prior to the rheological characterization, the paraffin oil=
deformations within the material s linear viscoelastic
aluminum suspensions were stirred for a number of hours and
range. In this range, at a constant radial frequency o, the
the aluminum was well dispersed using an ultrasound homo-
^
deformation amplitude g is proportional to the resulting shear
g
genizer. This process ensured that aluminum agglomerates
^ ^ ^
stress amplitude t, i.e., t g: This is only the case at
t t g
were broken down and the suspension was adequately
sufficiently small oscillatory deformations. Within the
homogenized. After mixing, the flow behavior was charac-
linear viscoelastic region, the moduli G0(o), G00(o) and
terized under steady shear flow. The relative viscosity as a
G*(o) are independent of the oscillatory amplitude in tests
function of shear rate is shown in Figure 4 for the suspen-
conducted at a constant frequency.
sions, which ranged in solids concentration from 2 to
The mean particle size and particle size distribution of the
45 vol.%, as well as for the pure paraffin oil.
aluminum were determined via laser diffraction spectro-
The relative viscosity Zrel is defined as the ratio of the
metry or photon correlation spectroscopy. Scanning electron
viscosity of the suspension to that of the matrix fluid at a
micrographs were also accomplished to further characterize
_
constant shear rate g :
g
the material.
_
ZSuspension j g
g
Zrel ź ð7Þ
ZParaffinoel
3. Materials With increasing aluminum concentration the suspensions
exhibit more amd more distinct shear thinning behavior.
The suspensions investigated consisted of nano-scale This non-Newtonian response can be attributed to particle
aluminum particles dispersed in paraffin oil or hydroxy- particle interactions and the changed hydrodynamics of the
270 Ulrich Teipel and Ulrich Förter-Barth Propellants, Explosives, Pyrotechnics 26, 268 272 (2001)
Figure 4. Relative viscosity of the paraffin oil=aluminum suspensions as a function of shear rate; W ź 20 C.
suspension compared to the single phase fluid. At small shear observed, up to a concentration CV 25 vol.%. At very low
rates, the viscosity increase as a function of concentration is concentrations, there is almost no difference in the relative
particularly pronounced. In this shear rate range, the inter- viscosity determined at the minimum and maximum shear
particulate forces dominate over the relatively weak hydro- rate. In this range of concentration, sufficient distance
dynamic forces, so that the rheological response of the between the particles contributes to small particle particle
suspension is strongly dependent on the solids concentration interactions, and likewise flow induced orientation of the
and the resulting structural interactions. As the shear rate is particles has a relatively minor effect on the viscosity.
increased, the hydrodynamic forces also increase, leading to Increasing the concentration leads to an increased contribu-
flow induced structuring of the nano-scale particles and a tion of the viscosity from particle particle interactions. The
corresponding decrease in the viscosity at a given solids quiescent particle structure formed with increasing concen-
concentration. The effect of solids concentration on the tration at low shear rates is one of the reasons for the strong
suspension viscosity is much less pronounced at higher dependence on concentration of the limiting viscosity at zero
shear rates because of the flow induced structuring of the shear rate, as shown in Figure 5. At higher shear rates a flow
system. induced structure is formed leading to a reduction in the
Figure 5 shows the relative viscosity of the suspension as a relative viscosity at a given solids concentration. The differ-
_
function of solids concentration for the limiting viscosity at ence of the viscosity function at the two shear rates g ! 0
g
_ _
zero shear rate (g ! 0) and at a relatively high shear rate, and g ź 1000 s 1, which increases with increasing solids
g g
_
g
g ź 1000 s 1. concentration, can be attributed primarily to the behavior
At the highest shear rate examined, a linear increase in the of the particles in the Couette flow. At a concentration of
relative viscosity as a function of solids concentration is 45 vol.%, the viscosity difference is nearly on the order of 104.
Figure 5. Relative viscosity of paraffin oil=aluminum suspensions as a function of solids concentration.
Propellants, Explosives, Pyrotechnics 26, 268 272 (2001) Rheology of Nano-Scale Aluminum Suspensions 271
Figure 6. Relative viscosity of HTPB=aluminum suspensions as a function of shear rate, W ź 20 C.
ZSuspension
4.2 Flow Behavior of HTPB=Aluminum Suspensions
Zrel;S ź ź 1 þ 5:5 CV 31:4 C2 þ 74:5 C3
V V
ZHTPB
Figure 6 shows the relative viscosity of the HTPB=
ð8Þ
aluminum suspensions as a function of shear rate for solids
Eq. (8) is valid for solid volume concentrations CV up to
concentrations from 0 CV 47 vol.%.
50 vol.%.
Hydroxy-terminated polybutadiene, HTPB R 45-M,
without additives exhibits Newtonian flow behavior (see
Fig. 6 or Refs. 6 and 7). In contrast to the paraffin oil=
aluminum suspensions, the HTPB suspensions exhibited 4.3 Viscoelastic Properties of the Suspensions
Newtonian behavior over a wide shear rate range up to a
solids concentration of 50 vol.%. With increasing concen- Viscoelastic material properties can be determined by
tration, the relative viscosity of the suspensions increased; oscillatory shear experiments. The complex shear modulus
however, the behavior remained linear. Figure 7 shows the determined by dynamic experiments in the linear viscoelastic
relative viscosity of the suspensions as a function of solids region can be expressed in terms of two material functions (as
concentration. shown in Eq. (6)), the storage modulus G0ðoÞ and the loss
The rheological characterization of the HTPB-based sus- modulus G00ðoÞ:
pensions filled with nano-scale aluminum yielded the follow- The storage and loss modulus functions of the paraffin
ing relationship for the relative viscosity as a function of solid oil=aluminum suspensions are shown in Figure 8 for various
volume concentration: solids concentrations. At low frequencies the storage
modulus is smaller than the loss modulus, meaning that the
viscous properties are dominant in this frequency range. Both
functions increase steadily with frequency; however, the
slope of the storage modulus function is greater than that of
the loss modulus and, as a result, the two functions intersect
at a characteristic frequency oi, which differs depending on
the solid volume concentration. Above this frequency, the
elastic properties are dominant. The structural relaxation
time l is equal to the reciprocal of the frequency at which
the storage and loss moduli intersect:
oi l ź 1 ð9Þ
For the paraffin oil=aluminum suspensions up to solids
concentrations CV 40 vol.%, the structural relaxation
time range from 0.24 s l 0.37 s. It was also observed
that the storage modulus G0ðoÞ was essentially independent
Figure 7. Relative viscosity of the HTPB=aluminium suspensions as a
function of solids concentration. of the aluminum concentration. One concludes that for
272 Ulrich Teipel and Ulrich Förter-Barth Propellants, Explosives, Pyrotechnics 26, 268 272 (2001)
Figure 8. Storage and loss modulus functions of the paraffin oil=aluminum suspensions.
Figure 9. Storage and loss modulus functions of the HTPB=aluminum suspensions.
Propellants and Combustion, 100 Years after Nobel  , Begell
these suspensions, filled with nano-scale particles, the
House, 1997, pp. 636 645.
stored (elastic) deformation energy is independent of the
(3) F. Tepper, G. V. Ivanov, M. Lerner, and V. Davidovich,   Ener-
particle concentration.
getic Formulations from Nanosize Metal Powders  , 24th Inter-
The storage and loss modulus functions of the HTPB= national Pyrotechnics Seminar, Monterey, California, USA, July
27 31, 1998, pp. 519 530.
aluminum suspensions are shown in Figure 9 for various
(4) O. G. Glotov, V. E. Zarko, and M. W. Beckstead,   Agglomerate
solids concentrations. As in the previous case, the storage
and Oxide Particles Generated in Combustion of Alex contain-
modulus G0ðoÞ is independent of solids concentration.
ing Solid Propellants  , 31st Int. Annual Conference of ICT,
However, the structural relaxation times for the HTPB- Karlsruhe, Germany, June 27 30, 2000, pp. 130=1 130=15.
(5) U. Teipel,   Rheologisches Verhalten von Emulsionen und
based suspensions are significantly smaller than those of
Tensidlösungen  , Dissertation, Universität Bayreuth, 1999;
the paraffin oil-based suspensions, falling in the millisecond
Wissenschaftliche Schriftenreihe des Fraunhofer ICT, Band 22.
range (0.0021 s l 0.0062 s).
(6) A. C. Hordijk, H. W. R. Sabel, L. Schonewille, and J. J. Meulen-
brugge,   The Application of Rheological Equipment for Improved
Processing of HTPB based PBXs  , 27th Int. Annual Conference of
ICT, Karlsruhe, Germany, June 25 28, 1996, pp. 3=1 3=11.
(7) R. Muthiah, V. N. Krishnamurthy, and B. R. Gupta,   Rheology of
5. References
HTPB Propellant: Development of Generalized Correlation and
Evaluation of Pot Life  , Propellants, Explosives, Pyrotechnics 21,
(1) R. R. Miller, E. Lee, and R. L. Powell,   Rheology of Solid Pro-
186 192 (1996).
pellant Dispersions  , Journal of Rheology 35=5, 901 920 (1991).
(2) G. V. Ivanov and F. Tepper,   Activated Aluminum as a Stored
Energy Source for Propellants", in: K. K. Kuo (ed.)   Challenges in (Received July 17, 2001; Ms 2001=044)