Rheological Analysis of nanofiber reinforced polyethylene composites
Qiang Zeng and Karen Lozano
Department of Mechanical Engineering, University of Texas Pan American, Edinburg, TX 78539 USA
Abstract
The melt rheological analysis of high-density polyethylene reinforced with vapor grown carbon
nanofibers was performed using an oscillatory rheometer. The influence of frequency,
temperature and nanofiber concentration (ranging from 0 to 30wt%) on the viscoelastic variables
was investigated. The selected nanofibers had an average diameter of 50 nm and lengths of
10μm. These nanofibers were purified to remove amorphous carbon and to provide for an open
network of nanofibers. High shear working conditions were used to disperse the nanofibers
uniformly within the matrix. Rheological analysis was carried out in the temperature range of
160 to 210°C and frequency range of 0.062 to 628.3 rad/s. The rheological measurements show
an accentuation of the shear-thinning behavior for the composites. An enhancement in the
viscoelastic properties is observed as nanofiber concentration increases. The modulus and
viscosity of the system increased significantly at low frequencies given the high aspect ratio of
the nanofibers. A dual increase effect on storage and loss modulus was observed being
significantly higher on storage modulus. The increased modulus was due to stiffness imparted by
the fiber and efficient stress transfer at the interface between nanofiber and the polyethylene
matrix. The viscosity difference between the composites and pure polyethylene at frequencies
higher than 600rad/s such as those used in extrusion and injection was negligible. This shows
that the difficulty of processing these composites is not an issue at high shear rates such as those
used in conventional polymer processing technologies such as injection or extrusion molding.
Introduction
This research focus on assessing the practical possibility of using nanofibers to produce
thermoplastic composites, their processability and reinforcing effect is analyzed through a
comprehensive rheological analysis. Vapor grown carbon fibers (VGCFs), have circular cross
sections, with outer diameters varying from 40nm to 10m (depending on the production
method), and central hollow cores with diameters of a few nanometers. The graphitic networks
are arranged in concentric cylinders. This structure brings the fibers extraordinary mechanical,
electrical, and thermal properties. Given the interesting properties of the carbon nanofibers, their
combination with polymers offers a composite material with promising scientific enhancement
[XX]. Nanofiber reinforced composites can yield smaller and lighter weight components that can
provide greater flexibility in application field. The thermal conductivity of VGCNF composites
makes them attractive for electronic heat sinks, radiator fins etc. Recent studies on thermal
conductivity conducted by Lozano showed significant improvement [3]. In the electronic
industry, nanofiber composites could be used as electrostatic dissipative (ESD) materials as well
as electromagnetic interference (EMI) attenuators depending on the electrical resistivity value.
ESD and EMI properties are obtained given the high aspect ratio of the fibers which facilitate the
formation of an interconnecting network within the polymer matrix. Recent studies on
nanofiber/nanotube reinforced polymers have reported resistivity values on the ESD range []. To
further decrease the resistivity values into the EMI range, manipulation of the nanofibers needs
to be conducted such as alignment or metallization of the nanofibers []. Structural enhancements
will provide for ……………..
When reinforcements are introduced in a plastic matrix, it is known that a compromise is
usually made between the improved properties in the solid state and the increased difficulty in
processing. Usually it is a barrier that needs to be overcome for mass development. Rheological
analysis is considered an effective tool to predict the processing behavior as well as to study the
microstructure of the composite. The response of complex viscosity, storage modulus, loss
modulus and tan delta obtained in a rheological analysis provides for a better understanding of
structural features such as dispersion of the filler in the matrix, filler concentration, filler size
distribution, wettability of the filler and matrix/fiber interactions.
Several studies have been conducted in the area of development and characterization of
nanofiber/nanotube reinforced polymers but as Potschke et al. recently stated, rheological studies
of this type of systems have not received much attention []. Rheology of molten plastics is by
itself a complex subject since the plastics exhibit viscous flow and elastic recoil. Introducing
nanofiber/nanotubes into this rheological complex material make it even more challenging and
interesting, since it is known that this kind of reinforcements will alter molecular mobility and
crystallinity of the matrix [XX]. The present study focus on the melt rheological analysis of a
nanofiber reinforced semicrystalline polymer composite. The objective is to further understand
the relationships between rheological properties, composition, temperature and time to provide
for a better understanding of matrix-fiber interactions as well as to relate the composite structure
with process optimization and performance.
BACKGROUND
Rheological analysis has been conducted for other type of fiber reinforced polymer matrix
composites using primarily capillary and rotational rheometers. D. Roy et al. studied short
carbon fiber filled thermoplastic elastomeric blends of natural rubber and high-density
polyethylene composites. Nontreated carbon fibers having lengths 6 mm were used and the
rheological measurements were conducted by using a capillary rheometer. D. Roy et al. observed
that at temperatures lower than 160oC, viscosity increased with increasing fiber loading. It was
observed that the use of a capillary rheometer changed the original viscoelastic behavior of the
composites due to wall slip effects and fiber alignment. Jayamol George et al. also applied a
capillary rheometer to study surface treated short pineapple fiber reinforced low-density
polyethylene composites. The melt viscosity was found to increase with fiber loading due to an
improved fiber-matrix interfacial adhesion. On the other side, S.A.R. Hashmi et al. used an
oscillatory rotational rheometer to understand the rheological behavior of the poly (phenylene
sulphide)-tubular-fiber-reinforced polypropylene composites. The viscoelastic properties such as
the dynamic viscosity, complex viscosity, storage modulus and loss modulus increased with
addition of fiber loading. They also observed that at low frequencies the effect of composition
was pronounced and viscosity increased significantly but the difference was reduced as the
frequency was increased. Pötschke et al. study the rheology of multiwalled carbon nanotubes
(MWNT) reinforced polycarbonate composites. They observed that a rheological percolation
threshold was achieved at a MWNT concentration of 2wt%. This percolation threshold refers to
the formation of an interconnected network of MWNT’s and coincided with the electrical
percolation threshold. They also observed a dual effect increase in G’ and G” being predominant
G” in concentration of less than 5wt% and G’ at higher concentrations [9].
In the past several decades, few rheological models have been proposed to
mathematically model and predict the viscoelastic behavior of composites. Various parameters
have been applied in different constitutive equations in order to model the viscoelastic behavior
of different composite systems. The two parameters power-law model has been used to fit the
medium to high shear rate range. The four parameters Carreau model has been used in the low to
medium shear rate range and the Herschel-Bulkley model has been successful at predicting shear
thin behavior at all shear rates [10]. Most of the modeled composites were filled by micro or
larger scale fillers which differ considerably from nano-scale fillers. Nanofilled composites have
a thermo-rheological complex behavior affected by large relaxation processes. The development
of models that can be applied to nanocomposites presents a challenging area of study.
In the present study, it was needed to preserve the initial fiber orientation to understand
the properties of the isotropic system. The selected testing method was a rotational rheometer
where the fiber orientation was not changed dramatically. Folkes et al. explained that an
appropriate way of assessing rheological properties, eliminating the effect of aligning the fibers,
is to characterize flow using a dynamic mechanical approach. In this case, the initial fiber
orientation is only slightly perturbed during each cycle of deformation and hence the rheological
data can be correlated with known fiber orientation distributions [11]. For this reason, a smallamplitude dynamic oscillation test was selected as the testing method.
Experimental
Materials and Sample Preparation
The VGCNFs (Pyrograph IIITM) used in this study were supplied by Applied Science, Inc. These
were produced by a catalytic process of hydrocarbons in the vapor-state. VGCNF have circular
cross-sections (with average diameter 50nm) and central hollow cores commonly called
filaments. The as-received VGCF were observed by scanning electron microscopy to be highly
entangled having dispersed amorphous carbon and metal catalysts. De-agglomeration and high
dispersion of the nanofibers into the polymer matrix was needed therefore, the VGCNF were
purified to remove unwanted products, providing opening of the highly tangled nests of
nanofibers without shortening them. Purification was conducted as developed by Lozano et al.
[12].
A high density polyethylene (HDPE) from Philips Chemical Company was chosen as the
matrix. Polyethylene was chosen since it is a linear polymer that can contribute to the
development of highly aligned nanofiber systems that are now being developed by the group.
VGCNF and the HDPE were mixed in a HAAKE Rheomix using two cam type rotors. The
mixing sequence was that developed by Lozano et al. [13]. The mixing temperature was 190°C.
Due to the high shear processing conditions, a homogeneous dispersion and distribution of the
nanofibers was obtained. The composites were then hot pressed at 200°C, and at the pressure 7
tons. Samples were cut into coupons of 2cm in diameter and 1mm thickness for the rheological
tests.
Rheological testing
A Haake RheoStress® RS 150 rheometer with the high temperature measuring system TC501,
ceramic rotors and electric heating system was used. The rotational measurements were
performed using a parallel-plate sensor PP20 (Ø=20mm) with an initial gap of 1mm. The
samples were set between the parallel plates preheated to 190°C. The linear viscoelastic range
(where the properties are independent of strain) was determined by a strain sweep before testing
the viscoelasticity of the composites under a frequency sweep. This strain sweep test was
conducted under different frequency conditions (0.1, 1, 10, and 100 Hz). The frequency sweep
was then conducted to obtain the corresponding curves for storage modulus (G’), loss modulus
(G”), damping (tan ) and complex viscosity (η*). These tests were conducted in dynamic
(oscillation) mode with a frequency range of 628.3 down to 0.062 rad/s collecting 6 data points
per decade.
Results and Discussion
Storage Modulus and Loss Modulus
The strain sweep results are presented in Figure 1. It is observed that the storage modulus
increased with the increasing of the frequency. A strain value of 0.001 was selected for the
frequency sweep experiment. This strain value falls in the linear viscoelastic range for all
samples.
The variation of the dynamic storage (G’) and loss (G”) modulus with frequency (f), for
VGCNF-reinforced polyethylene at 190°C are shown in Fig 2 and 3, respectively. Both storage
modulus and loss modulus increased with increase in frequency and with increase in
concentration of VGCF. However, Fig 2 and 3 show that the effect of VGCNF concentrations in
polyethylene composites is much lower at high frequencies than at low frequencies which
eventually lead to decrease the modulus curves slope of composites with the increase of the fiber
concentration as it can be observed in these two curves. In Fig 2, The storage modulus was
increased from 0.003MPa (pure PE) to 0.72MPa (30wt% VGCNF) at 0.0628 rad/s. As frequency
increased, the storage modulus difference decreased between composites with various VGCNF
loading compared with that in the low frequency. The storage modulus behavior indicates that
the ability to store the energy of external forces in these composites was increased. The same
phenomena are also observed in Figure 3 for loss modulus, which indicated that the ability of
impact absorption was improved. It is another factor that we should not oversee in order to
fabricate a better composite material although the increasing of mechanical properties is the main
point we usually want to achieve. In order to improve the modulus significantly certain filler
concentration is required in these composites, as we can see in these two curves below 5wt%
fiber loading only a small increase can be observed. At 10wt% VGCNF concentration, the
modulus starts showing a large increase at lower frequencies. This can be interpreted by the
threshold theory. Below 10wt% concentration in composites, the storage modulus enhancement
occurs due to stiffness imparted by the fiber that allows efficient stress transfer, whereas this
property is controlled mainly by the matrix/fiber-matrix interface rather than by the reinforcing
fibers when the concentration is higher than 10wt%. Beyond 20wt% nanofiber loading, G’ curve
even almost turns to independent of frequency due to the fact that the modulus curves slope of
composites are decreasing with the increase of the fiber concentration. In most cases it results in
the formation of a plateau at very low applied frequencies, which indicates that relaxation of the
polymer composites is concentrated in the low-frequency region and an apparent yield stress was
exhibited because of the forming of a nanofiber network structure within the matrix. This
behavior is generally observed in fiber-filled polymeric melt [14]. It is interesting to note in
figure 2 that due to the nanofiber network existence at 30wt% fiber loading, the storage modulus
increases considerably at low frequencies and no yield stress was observed. In order to fabricate
a better composites material, we usually expect that the mechanical properties increase as well as
toughness. In figure 5, the loss modulus increases with the increase of the fiber concentration at
all frequencies, which indicated that the ability of absorbing more applied impact was improved.
The value of storage modulus (G’) and loss modulus (G”) for the composite did not
change very much until the fiber loading over 10wt% at which a significantly increasing of the
modulus was observed. In the former case, the modulus enhancement occurs due to stiffness
imparted by the fiber that allows efficient stress transfer, whereas this property is controlled
mainly by the matrix/fiber-matrix interface rather than by the reinforcing fibers in the latter. At
all the frequencies, the storage modulus G’ increase is much higher than the corresponding
increase in loss modulus G”. The presence of a shift position of the crossover point of the
different fiber concentrations is interesting when two curves G’ (f) and G”(f) are superimposed
on the same graph (Fig 4). It is found to be the characteristics of the how soon the composites
transfer to solid like behavior from liquid behavior. From the superimposed curve we can see
that the cross-point is moving to the left with the increasing of fiber concentration. It indicates
that with the percentage of VGCF increasing the composite polymer exhibits elastic-like
behavior at lower frequency.
Complex Viscosity (η*)
The complex viscosity is important for determining rheological properties. The real part of the
complex viscosity is an energy-dissipation term similar to the imaginary part of the complex
modulus. The dependence of VGCNF volume fractions and frequency (f) on melt complex
viscosity (η*) of VGCNF reinforced PE at 190 °C is shown in Figure. A typical pseudoplastic
behavior for the pure PE and its VGCNF reinforced composites can be observed. In general, the
pseudoplastic behavior of fiber reinforced polymer composites can be explained in two ways; (a)
The impact of high frequency will try to weaker the interfacial bonding existing between fiber
and matrix. (b) In molten polymeric system, when chemical interaction among polymer particles
exists, with increase of shear rate, the layers may be sheared away resulting in decreased
viscosity.
In filled polymer system, the presence of fibers perturbs the normal flow of polymer and
hinders the mobility of chain segments in flow therefore the viscosity of the filled polymer
system increases [3,9]. It is evident from the Figure 5 that the viscosity of the VGCNF filled PE
composites decreases monotonically with the increasing frequency but increases with the
increase of fiber loading, which is associated with the increase in the storage modulus. In filled
polymer system, the present of fibers will perturb the normal flow of polymer and hinder the
mobility of chain segments in flow []. It is also interesting to note that the composition of less
than 10 wt% fibers tends to produce a small increase in viscosity and follow closely with the
unfilled PE with increasing frequency matching the properties obtained in the G’ curve. At
concentrations lower than 5wt% the viscosity curve exhibits an obvious Newtonian plateau at
low frequencies. This plateau appeared for the 10wt% and 20wt% samples; the viscosity curves
drop steeply at these concentrations. But However, due to the network formation and strong
interactions of the nanofibers, a similar zero shear plateau can be observedfor the 30wt% sample.
Loading of 10wt% VGCNF might can also be considered as the threshold for the composite
viscosity behavior. It might may relate with the threshold value of thermal and electrical
conductivity. a test trying to prove this is on the way. High VGCNF loading composites Higher
VGCNF loading show significant viscosity increases as high as two orders magnitude where the
observed increase in viscosity can be attributed to the interaction of VGCNF-PE matrix and
VGCNF-VGCNF. It is also observed that at low frequencies the effect of composition is
pronounced and η* increased significantly with increased concentration of VGCNF. As the
frequency increasing this difference is reduced, even for the loading as high as 30wt%, the
difference of the viscosity is reduced. It is showed that the nanofiber composite materials exhibit
a stronger shear thinning effect than pure polyethylene. This behavior is due to the fact that at
low oscillatory frequencies, disoriented fibers collisions dominate the flow compared with the
situation at high frequencies where matrix behavior becomes the dominant factor.
As it happens, when fiber reinforced polymer composites are processed under high shear
forces condition such as those used in injection molding or extrusion processes when the
injection molding, extrusion processing etc. are applied to process the fiber reinforced polymer
composites, the viscosity will continue to decrease due to wall slip effect caused by the
alignment of fibers in the direction of flow. The viscosity values at high frequencies, for filled
and unfilled thermoplastics, will tend to be closer under the real process condition. It is an
important factor in explaining the successful exploitation of these materials in injection molding
technology, since differences in energy requirements will be negligible to mold the filled
composites.
Due to the substantial temperature changes occur at various stages during molding, flow
curves were obtained at 160,190 and 210 °C. Figure 8 shows the variation of viscosity with
temperature at different fiber loading at two shear rates. It is clear that viscosity decreases with
increase of temperature for the filled and unfilled systems. At higher temperature, the molecular
motion is accelerated due to the availability of greater free volume and also due to the decrease
in entanglement density and weaker intermolecular interactions. The decrease in viscosity is
more predominant at low shear rate frequencies than at high shear rate frequencies. This is due to
the reduction of VGCNF limitation effect on polymer chain moving at low frequency.
Theoretical modeling
Earlier investigations of the rheological properties of polymer melts have shown that the data
under dynamic conditions can be related to that obtained under steady shear within certain ranges
of shear rates and frequencies [10]. From all the methods of correlating dynamic and steady-state
data based on theoretical models available in the literature, the empirical method suggested by
Cox and Merz [10] for relating steady-shear viscosity with the absolute value of complex
viscosity * is even to this date the most attractive of all. According to the Cox-Merz method
.
 ( )   * ( )
.
(   )
where η = viscosity, η *=complex viscosity,
.
 =shear rate and ω =frequency(rad/s) the
relationship simply indicates that for prediction purposes, the magnitude of complex viscosity is
comparable with that of shear viscosity at equal values of frequency and shear rate. The
relationship has been found to hold well for flexible chain thermoplastic melts, particularly in the
lower and intermediate ranges of frequency and shear rate [13]. In reference to the filled polymer
system, care has to be taken in applying this rule due to the change of melt flow introduced by
the fillers. Even though, literature still can be found which reported the application of this rule on
filled polymer system, such as the work conduced by P.R. hornsby et al. They used magnesium
hydroxide as filler for PP and found that for all the samples there is a very close correlation
between the complex viscosity angular frequency curves and the capillary viscosity shear rate
data, in accordance with the Cox-Merz rule [13].
Based on the Cox-Merz rule, there have been several rheological models developed to predict the
viscoelasiticity of filled polymer system such as the Carreau model.
The Carreau model, has been widely applied in pure and filled polymer system, such as
wollastonite-filled polypropylene[]. This model is given by
.
     ( 0    ) /(1    ) n
2
Whereη0 =zero shear rate viscosity,λ= characteristic time,η∞ =infinity shear rate viscoisity
and n=shear-shinning characteristic. Figure 9 shows how the Carreau model fits the obtained
experimental data when the fiber loading is as low as 5 wt% in the VGCNF filled PE system.
However, when the Cox-Merz rule is tested for higher fiber loading system, it fails. The
difference between the steady-state and dynamic data increases with increasing loading
especially at high frequency range. This is because high aspect ratio fiber-fiber interaction.
Therefore, the viscosity curves were broken into two regions and fit separate equations in each
region. The Carreau model was applied for first region of frequency lower than 1 rad/s due to the
fact that the zero shear rate viscosity 0 was well considered in this model. For the high
frequency range higher than 1 rad/s, it was found out that Herschel-Bulkley model [] was a better
fit for the high fiber loading melt system. However, a significant deviation was still observed at
extremely high frequency range in which the injection molding will be conducted, This deviation
can be explained by the fact that the uncontrolled fiber interaction and disorder flow. For this
reason, it was realized that a new model for this nanofibers reinforced polymer system needs to
develop.
Damping
In order to obtain the information of how efficient the nano-composites lose energy to
molecular rearrangements and internal friction, the relation between frequency and tan delta
( Tan δ=G”/G’) was obtained and it is showed in Fig 10, In this composite system, the tan delta
(tan) decreases with the incorporation of fiber, which is due mainly to the existence of effective
interfacial bonding between VGCNF and PE matrix so that the viscoelastic energy dissipation in
the composite was limited. Otherwise, if lack of the interfacial bonding, applied energy will be
dissipated in the form of heat due to the interaction between the fiber and matrix. For example, in
P.K.Sengupta’s research paper, the reversed behavior has been observed by testing damping in
both transverse and parallel directions on unidirectional carbon fiber-reinforced PP composites
[]. They indicated that due to improper wetting of the high concentration fibers (35vf%) by the
matrix, the fiber-fiber friction increases rapidly therefore the damping of the composite reach
even higher value than the low fiber concentration composites. In our study, the VGCNFs were
properly purified and disentangled so that the contact surface area was increased extensively
therefore the polymer matrix can have a better wetting on them. and therefore provided more
active chemical site to form bonds with the polymer matrix. It is also observed that with an
increase in the volume fraction of the fibers, the tan δ becomes flat as the fiber restricts the
relaxation of the polymer when measurement force is applied.
Conclusions
In this research, a banbury type mixer was used to mix purified VGCNF in high density
polyethylene. Melt rheological properties of these system have been studied as a function of fiber
loading, shear rate and temperature. In general the viscosity of the system increased with fiber
loading due to an increased hindrance to the melt flow. However, The composites show stronger
pseudoplastic behavior with increase fiber concentration, especially in the high frequency region
where the rheological properties of the composites were dominated by the PE matrix therefore
the addition of VGCNF to the polyethylene does not bring a change in processing behavior. The
influence of surface treatment on the melt flow properties was studied. It is found that addition of
bonding increases the viscosity of composite due to increased fiber-matrix interaction. The melt
flow studies were carried out in the temperature 160,190, 210°C. It was found that viscosity of
the melt decreases with increase of temperature. This is associated with the molecular motion
due to the availability of greater free volume and weaker intermolecular interactions. However,
the effect is less significant at high frequency due to the breakage of the bonding between
matrix/fibers and matrix. A comparison between theoretical and experimental values was
conducted and observed excellent fits at low and medium frequency, however, a significant
deviation from theoretical value was observed at high frequency due to fiber behavior. It is
suggested that a multiple parameter rheology model is required to predict the melt flow behavior
of nanofiber reinforced polymer matrices.