Korea-Australia Rheology Journal, 29(1), 9-15 (February 2017)
DOI: 10.1007/s13367-017-0002-6
www.springer.com/13367
Non-Newtonian behavior observed via dynamic rheology for various particle types
in energetic materials and simulant composites
Jong Han Choi1, Sangmook Lee2,* and Jae Wook Lee1,*
Applied Rheology Center, Department of Chemical and Biomolecular Engineering, Sogang University,
Seoul 04107, Republic of Korea
2
Division of Chemical Engineering, Dankook University, Yongin 16890, Republic of Korea
(Received August 4, 2016; final revision received November 25, 2016; accepted December 8, 2016)
1
The rheological properties of polymer composites highly filled with different filler materials were examined
using a stress-controlled rheometer with a parallel-plate configuration, for particle characterization of the
filler materials in plastic (polymer) bonded explosive (PBX). Ethylene vinyl acetate (EVA) with dioctyl adipate (DOA) was used as the matrix phase, which was shown to exhibit Newtonian-like behavior. The dispersed phase consisted of one of two energetic materials, i.e., explosive cyclotrimethylene trinitramine
(RDX) or cyclotetramethylene tetranitramine (HMX), or a simulant (Dechlorane) in a bimodal size distribution. Before the test, preshearing was conducted to identify the initial condition of each sample. All examined filled polymer specimens exhibited yield stress and shear-thinning behavior over the investigated
frequency range. The complex viscosity dependence on the dynamic oscillation frequency was also fitted
using an appropriate rheological model, suggesting the model parameters. Furthermore, the temperature
dependency of the different filler particle types was determined for different filler volume fractions. These
comparative studies revealed the influence of the particle characteristics on the rheological properties of the
filled polymer.
Keywords: dynamic rheology, PBX, simulant, highly filled, bimodal
1. Introduction
Plastic (polymer) bonded explosive, called PBX, primarily consists of a large amount of secondary explosives,
such as cyclotrimethylene trinitramine (RDX), cyclotetramethylene tetranitramine (HMX), along with a polymer
binder to enhance the PBX properties. Such improvements
have made it possible for PBX to become widely employed
in industry and in various applications, ranging from
sports signal flares and fireworks to rocket and armament
field (Patenaude, 2001; Thiboutot et al., 2015). The PBX
performance is principally dependent on the explosive
particle contents (Lin et al., 2015). Therefore, it is important to control and characterize the contents and dispersion
conditions of the particles contained within the PBX polymer matrix.
One of the most important factors affecting PBX formulation is the need to obtain an appropriate interaction
between the polymer binder and explosive filler, so as to
provide advantages such as thermal stability, desirable
mechanical properties, and better safety (Jyoti and Baek,
2014; Sarangapani et al., 2015; Teipel and Förter-Barth,
2001). The poor dispersion often causes bad influences on
the material properties, performances, and sensitivity of
the PBX. Therefore, the effective interactions involving
*Corresponding authors; J.W. Lee ([email protected]) and
S. Lee ([email protected])
© 2017 The Korean Society of Rheology and Springer
particles that are well dispersed in the polymer matrix are
essential to obtain superior properties. Some previous
studies have determined the appropriate polymer-particle
interaction through calculation of the material surface
energy using a particular method. Specifically, in those
studies, the viscoelastic behavior of the PBX was investigated in order to analyze the surface interaction between
the polymer binders and explosives, i.e., the RDX and
HMX (Shim, 2001; Shim et al., 2004).
The rheology can also provide helpful information on
the above highly filled composites, which can exhibit
complex behavior. The multiple particles dispersed in the
polymer matrix organize to form interparticle network
structure, which relies not only on the particle characteristics, but also on external conditions, such as the material
deformation induced by the shear stress (σ) or shear rate
( γ· ) and the temperature. Structural changes are revealed
by the rheological properties, in terms of the complex viscosity (|η*|) and the storage (G') and loss (G'') moduli
under a given dynamic oscillation frequency. Therefore,
examination of the characteristics of the highly filled
materials under various conditions is important for determining the processing parameters, and this approach can
be utilized in norm-referenced assessment for product
evaluation (Rahimi et al., 2007).
In previous reports, rheological characterization has
been used to examine various types of propellant, and
notable behaviors have been detected using a rotational
pISSN 1226-119X eISSN 2093-7660
9
Jong Han Choi, Sangmook Lee and Jae Wook Lee
rheometer (Jyoti and Baek, 2014; Miller et al., 1991;
Rahimi et al., 2007; Sarangapani et al., 2015; Teipel and
Förter-Barth, 2001). Moreover, for safety reasons, several
rheological studies of PBX simulants have also been conducted (Lee et al., 2014a; Lee et al., 2014b). However, no
studies on comparisons of the characteristics of the various filler materials in PBX can be found in the literature.
The purpose of this work is to study the effects of different types of filler particles, both explosives and simulant, on the rheological properties under oscillatory shear
conditions. In order to verify them, we employed appropriate viscosity models to fit the data curve (Saini and
Shenoy, 1986), evaluated the yield stress (σyield; Dzuy and
Boger, 1983), and demonstrated the temperature dependency (Sarangapani et al., 2015).
2. Experimental
2.1. Materials
Ethylene vinyl acetate (EVA) with 28 wt.% vinyl acetate
content, which is a commercial elastomeric polymer, and
dioctyl adipate (DOA) as a plasticizer were obtained from
Hanwha Chemicals Co., (Korea; EVA1528, DOA). Both
materials were used in equivalent proportions to form the
polymer matrix employed in this study. The explosives,
RDX and HMX, were supplied by Hanwha Corporation
(Korea) in a two different sizes to compose bimodal filler
system for maximum packing. As an explosive simulant,
an aliphatic chlorine-containing crystalline organic compound named Dechlorane (DEC) was purchased from
OxyChem (USA). It was selected because it had the similar physical properties to those of the explosives such as
particle size and density (1.8 g/cm3). The filler system
consisted of two different size distributions, coarse (20-30
μm) and fine (3-4 μm), in a ratio of 8:2 by weight.
2.2. Composite Preparation
Because of the safety and manufacturing-method consistency regulations regarding explosive materials, the
PBX and simulant sample preparation was supported by
Hanwha Corporation and the Agency of Defense Development (Korea). Each particle type was mixed with an
EVA/DOA matrix in a kneader and occupied a 0.5-L volume at 90oC. Two specimens were produced with 39 vol.%
of either HMX or DEC. Additional six specimens were
comprised of HMX, DEC, or RDX at 49 or 61 vol.%.
After melt mixing, the samples were compression-molded
to disc shape so that the rheological properties could be
measured under at the same temperatures.
2.3. Measurements
The rheological measurements were conducted using a
stress-controlled rotational rheometer (Physica MCR500;
Anton Paar), to examine the viscoelastic properties in
10
terms of the |η*|, G', and G''. A 25-mm diameter parallel
plate was mounted with a gap size of 1.5 mm during the
experiments. A frequency sweep test ranging from 0.1 to
100 rad/s was employed in order to characterize the rheological parameters by frequency. The applied strain was
1%. Before the main frequency sweep test, preprocessing
step, i.e., pre-shearing, was performed under constant frequency of 10 rad/s for 50 min. The purpose of this step is
to make initial condition of each specimen identically.
Measurements were conducted at 90, 100, and 110oC for
all specimens (Schmidt and Münstedt, 2002).
3. Results and Discussion
Figure 1 shows the rheological properties as a function
of the angular frequency at 90oC for the polymeric matrix,
which consisted of EVA and DOA at a weight ratio of 1:1.
The dynamic rheological data are represented by symbols
indicating the experimental results. The |η*| exhibits slight
shear-thinning behavior in the given frequency range. In
particular, plateau-like region is observed at high frequency.
Furthermore, the G'' response dominates the G' over the
entire frequency range, indicating that the polymer matrix
has fluid-like behavior in this frequency region.
Compared to the unfilled polymer matrix, the samples
with the various particle contents exhibit higher values for
the |η*| and shear thinning, as shown in Figs. 2-4. Regardless of the particle concentration, the |η*| values of the
RDX- and HMX-filled composites are higher than those
of the DEC-filled composites. This difference can primarily be attributed to promoted interactions due to the specific filler properties, such as the polarity and hydrogen
bonding, because the same polymer matrix is used in each
specimen. The interactions occur between the particles or
the particles and matrix. From the markedly high viscosity
at lower frequencies, the existence of σyield in the filled
polymer systems can be confirmed, which is due to the
particle tendency to agglomerate into network structures
Fig. 1. (Color online) Rheological properties of EVA/DOA
matrix at 90oC (|η*|: complex viscosity; G': storage modulus; G'':
loss modulus).
Korea-Australia Rheology J., 29(1), 2017
Non-Newtonian behavior observed via dynamic rheology for various particle types in energetic materials and simulant composites
Fig. 2. (Color online) Complex viscosity versus frequency for
the specimens 39 vol.% filled with HMX or DEC particles at
90oC. (The solid lines behind the symbols indicate the theoretical
model fitting via the experimental data.)
in the polymer matrix. The presence of particle network
structures prevents mobility of the polymer melt in the
low-frequency region, where the shear is insufficient to
break the particle structure. This trend is also observed in
the case of particle loading. Moreover, at 61 vol.% particle
content, the results for both the RDX- and HMX-filled
system exhibit significant deviation from the DEC-filled
system results in the low-frequency range. This behavior
suggests that critical particle loading level has been reached,
leading to more effective interactions with smaller interparticle distances. The stronger interparticle forces of the
RDX and HMX in the polymer, compared to the relatively
weak force for the DEC particles, seem to facilitate this
difference in behavior. In fact, the |η*| increases exponentially under unimodal particle conditions with a significantly lower particle concentration (Farris, 1968; Kaully et
al., 2007). However, for a bimodal system, smaller-sized
particles are located in interstitial sites between the larger
particles; therefore, the critical particle volume also
increases. Once the filled materials begin to flow, however, the filler networks are degraded and the dispersed
particles are also oriented along the flow direction. Therefore, shear thinning is apparent in such filled polymer
samples (Genovese, 2012).
In this study, the |η*| was also examined using an appropriate theoretical model, which was suggested by Saini
Fig. 3. (Color online) Complex viscosity versus frequency for
the specimens 49 vol.% filled with RDX, HMX, or DEC particles at 90oC. (The solid lines behind the symbols indicate the theoretical model fitting via the experimental data.)
Fig. 4. (Color online) Complex viscosity versus frequency at
90oC for the specimens 61 vol.% filled with RDX, HMX, or
DEC particles at 90oC. (The solid lines behind the symbols indicate the theoretical model fitting via the experimental data.)
and Shenoy (1986). The experimental results were well
fitted according to
n–1
Kω
*
η = ------------------------------2 ( n – m )/2
(1 + ω )
(1)
where K is the complex viscosity at a frequency of 1 rad/
s and at n = m, ω is the angular frequency, and n and m
Table 1. Theoretical model parameters fitting to complex viscosity for highly filled composites.
vol.%
39
49
61
RDX
HMX
DEC
K
n
m
K
n
m
K
n
m
21,000
65,900
0.56
0.16
0.18
0.25
12,800
30,400
97,600
0.54
0.48
0.20
0.29
0.26
0.17
2,300
5,400
23,900
0.36
0.59
0.73
0.38
0.30
0.29
Korea-Australia Rheology J., 29(1), 2017
11
Jong Han Choi, Sangmook Lee and Jae Wook Lee
Table 2. Yield stress values for each particle system.
vol.%
RDX, σyield
HMX, σyield
DEC, σyield
39
49
61
183.3
1,241.9
86.68
196.6
970.9
15.05
35.64
291.4
Fig. 5. (Color online) Complex viscosity versus shear stress for
the specimens filled with RDX, HMX, or DEC particles at 90oC.
(The numbers on the graph mean filler content (vol.%)).
are the slopes of the |η*| versus ω curve for 0.1 ≤ ω ≤ 1
and 1 ≤ ω ≤ 100 regions, respectively. The fitting curves
obtained from Eq. (1) are indicated by the solid lines in
Figs. 2-4. The results for the K, n, and m parameters are
also shown in Table 1. This theoretical model was adopted
because the curves obtained in Figs. 2-4 are well fit using
this approach, which is based on application of the conventional power-law fluid model to two distinct regions in
the low- and high-frequencies, divided by a reference
point at 1 rad/s (Saini and Shenoy, 1986).
The yield behavior mentioned with regard to Figs. 2-4 is
depicted in Fig. 5, in the form of rather demonstrative
flow curves of the relationship between the |η*| and σ. All
specimens with the various particle types exhibit marked
reductions in viscosity for each specific stress value. This
value can be considered to be σyield. For stress values greater
than σyield , particle movement begins to occur; this corresponds to structural transformation leading to changes in
the particle interactions (Malkin, 2013).
A Casson model fit was conducted for each composition
in order to determine σyield of the non-Newtonian behavior,
according to
σ
0.5
0.5
0.5 0.5
= σyield + ηy γ·
(2)
where ηy is a constant. This method calculates σyield via
extrapolation of γ· versus σ data to the γ· o in order to
determine the intersection with the σ axis. A straight-line
fit is then obtained; the results for the examined specimens
are shown in Figs. 6-8. A non-zero positive crossover
point is obtained in all cases, which can be used to prove
the existence of σyield. Note that the addition of particles
increases the possibility for a network to form restricting
the polymer melt motion and resulting in a stronger σyield.
Note that the critical loading level of 61 vol.%, which corresponds to the rheological data mentioned above, has
been shown to increase considerably for the same reason
12
Fig. 6. (Color online) Casson plot of RDX-filled composites.
Fig. 7. (Color online) Casson plot of HMX-filled composites.
(Bae et al., 2012; Kim et al., 2016).
However, there is some deviation from the extrapolation
line in the initial γ· range. This phenomenon, which has
also been reported in a previous paper presenting a similar
result (Dzuy and Boger, 1983), has been explained as
originating from a slip effect between the material and the
rheometry configuration. In the present report, in order to
prove the presence of the slip, two different kinds of tube
having identical dimensions but different surface roughness values were used. The tube with the rougher surface
collected data that fit the extrapolation straight line significantly more closely than those of the smooth tube. Further, the slip effect is prominent with increasing particle
concentration. This suggests that there is some relationship between the slip effect and σyield. Table 2 contains
Korea-Australia Rheology J., 29(1), 2017
Non-Newtonian behavior observed via dynamic rheology for various particle types in energetic materials and simulant composites
Fig. 8. (Color online) Casson plot of DEC-filled composites.
Fig. 10. Storage (G') and loss (G'') moduli versus frequency for
RDX-filled composites (○ : 49 vol.%; □ : 61 vol.%).
Fig. 9. (Color online) Yield stress as a function of filler content.
Fig. 11. Storage (G') and loss (G'') moduli versus frequency for
HMX-filled composites (△ : 39 vol.%; ○ : 49 vol.%; □ : 61 vol.%).
concrete σyield values for the different particle types as a
function of the particle volume fraction, which was evaluated from Figs. 6-8. For 61 vol.% particle content, it is
clearly apparent that the σyield of RDX-filled composite is
higher than HMX-filled composite, despite the reduced
possibility for hydrogen bonding in the latter case. This
behavior may be attributed to lower steric hindrance,
which can encourage more efficient interparticle bonding.
Therefore, although HMX has a greater number of hydrogen bonding sites, the RDX-filled polymer exhibits a
stronger σyield than the HMX under these conditions.
Figures 10-12 show the G' and G'' results as functions of
angular frequency for each composite with different particle content values at 90oC. Both properties increased
with increased particle volume contents, indicating lower
dependency on the angular frequency than that exhibited
by the |η*|. For lower filler contents, G'' is dominant over
G' throughout the entire frequency range. However, for
the higher filler content value of 61 vol.%, the crossover
point between the two moduli in the frequency region
occurs at a point for which G' is greater than G'', regardless of filler type. The crossover point indicates the material state transition, from solid to liquid-like behavior or
Korea-Australia Rheology J., 29(1), 2017
Fig. 12. Storage (G') and loss (G'') moduli versus frequency for
DEC-filled composite (△ : 39 vol.%; ○ : 49 vol.%; □ : 61 vol.%).
from liquid to solid-like behavior. This transition of the viscoelastic properties may be induced by changes in the
microstructure forming the particle network structure,
which can be encouraged towards solid-like behavior
(Hwang et al., 2012; Sungsanit et al., 2010).
The σyield dependency on the temperature is shown in
three-dimensional charts in Figs. 13-15. Generally, a change
in temperature induces a change in the viscosity of the
13
Jong Han Choi, Sangmook Lee and Jae Wook Lee
Fig. 13. (Color online) Yield-stress dependency on temperature
for each filler type at 39 vol.%.
variations in σyield in response to increasing temperature,
from 90 to 110oC, are shown. The trends tend to change
according to the reaggregate with further increase in temperature, thereby improving the flowability of the polymer
matrix (Yu et al., 1999). The σyield values of the RDX- and
HMX-filled composites at 90oC are similar; however, the
HMX-filled composite seems to exhibit higher σyield values than the RDX-filled composite at other temperatures.
In spite of the strong hydrogen bonding in the RDX which
results from the steric hindrance (Brodman et al., 1976),
the additional effect of the morphology is critical under
higher-temperature conditions (Sarangapani et al., 2015).
Although the DEC has lower particle interaction than the
other two examined energetic materials, the same trend is
also exhibited with regard to the temperature. This behavior can be explained using the same rationale as for the
HMX. Therefore, it can be concluded that the particle
morphology has a significant effect on the particle structure of a highly filled polymer system.
4. Conclusions
Fig. 14. (Color online) Yield-stress dependency on temperature
for each filler types at 49 vol.%.
Fig. 15. (Color online) Yield-stress dependency on temperature
for each filler types at 61 vol.%.
Highly concentrated polymer composites were prepared
using three different types of filler particle (RDX, HMX,
and DEC) in bimodal compositions with a polymer matrix.
These materials were then studied in order to confirm the
effect of each particle type on the viscoelastic properties
of the polymer matrix. All samples were subjected to
preshearing before the primary experiment in order to
identify the initial states of the highly filled polymer composites. The |η*| was then determined via dynamic rheometry at a process temperature of 90oC and, exhibited
non-Newtonian flow with yield behavior. An appropriate
model was employed in order to fit the data curve to facilitate prediction of further complex behavior. The viscosity
was found to increase with increased particle content. A
significant increase in viscosity was observed up to 61
vol.% particle content, indicating a critical content level at
which the particles were positioned sufficiently close to
interact with each other and to form a network structure.
For the same reason, the σyield values determined from
Casson plots for the various specimens exhibited the same
trend with regard to the particle concentrations. Moreover,
the difference in σyield values of the RDX and HMX could
be explained in terms of the influence of the molecular
steric hindrance on the hydrogen bonding. The temperature dependence of the particle structure in the polymer
was also examined, and it was found that the particle network structure was influenced by both the particle interaction (force) and the particle morphology.
Acknowledgments
continuous-phase, polymer matrix. However, the particle
interaction also changes with increased temperature. The
14
This work was supported by Hanwha Corporation and
Korea-Australia Rheology J., 29(1), 2017
Non-Newtonian behavior observed via dynamic rheology for various particle types in energetic materials and simulant composites
Agency of Defense Development, Korea (No. UC120019GD).
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