Oxygen Permeability Coefficient of High Density Polyethylene/Cu Nanofibers Nanocomposites below Percolation

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The main objective of this study was to relate the elastic modulus of a polymer nanocomposite to its permeability coefficient. The materials studied included high density polyethylene (HDPE) filled with copper nanofibers (Cu-nanofibers). Both of the experimental values of the elastic modulus and the gas permeability coefficient of the HDPE/Cu-nanofibers films were obtained from Grigoriadou et al. and Bikiaris & Triantafyllidis studies. In this study, the Halpin-Tsai model was modified and then used to fit the elastic modulus experimental data. It was found that the modified shape factor (ω′) of the Cu fibers as a function of the composite volume fraction is125exp(−41∅). Then, the model was used to predict the oxygen permeability coefficient of the HDPE/Cu-nanofibers films below the percolation point. It was found that the tensile modulus of the nanocomposites increased by 24% whereas the permeability to oxygen coefficients decreased by 65% compared to pristine HDPE. Also, the results from the models match the experimental data.

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DOI: http://dx.doi.org/10.1590/1516-1439.035415

Oxygen Permeability Coefficient of High Density Polyethylene/Cu

Nanofibers Nanocomposites below Percolation

_Atheer Mohammad Almasri_ _a_ _*_

_aDepartment of Chemical Engineering, College of Engineering, Al Imam Mohammad Ibn Saud Islamic_

_University – IMSIU, Kingdom of Saudi Arabia_

Received: August 10, 2015; Revised: August 29, 2015

The main objective of this study was to relate the elastic modulus of a polymer nanocomposite to
its permeability coefficient. The materials studied included high density polyethylene (HDPE) filled
with copper nanofibers (Cu-nanofibers). Both of the experimental values of the elastic modulus and the
gas permeability coefficient of the HDPE/Cu-nanofibers films were obtained from Grigoriadou et al.
and Bikiaris & Triantafyllidis studies. In this study, the Halpin-Tsai model was modified and then used
to fit the elastic modulus experimental data. It was found that the modified shape factor ( ω′ ) of the Cu
fibers as a function of the composite volume fraction is _125exp_ (− _41_ ∅) . Then, the model was used to
predict the oxygen permeability coefficient of the HDPE/Cu-nanofibers films below the percolation
point. It was found that the tensile modulus of the nanocomposites increased by 24% whereas the
permeability to oxygen coefficients decreased by 65% compared to pristine HDPE. Also, the results
from the models match the experimental data.

Keywords: _Cu-nanofiber, polyethylene, Halpin-Tsai model, permeability coefficient, percolation_

1. Introduction

In the past few decades, polymers have replaced many
conventional materials in different applications due to the
cost and manufacturability advantages. Polyethylene (PE),
for example, is one of the most important, most popular, and
cheapest polymers, hence PE is produced in large quantities
and is used in many different applications, in particular food
packaging wrapping films, pipes, bottles, etc. 1 . PE is widely
used because of the many attractive properties such as low
density, low cost, low toxicity, and high processability 2 .
According to ASTM standards, PE can be low density
polyethylene (LDPE), medium density polyethylene (MDPE),
or high density polyethylene (HDPE) 3 . PE density range
allows a wide range of mechanical and processing behavior;
molecular weight, branching, and degree of crystallinity also
influence how the PE behaves 4 .

Polymer nanocomposites can be produced by adding
fillers. Fillers can be natural fibers such as hemp, rice‑husk,
textile, chitosan, curauá etc. or inorganic fibers made from
materials such as clay, alumina, glass, boron, silicon carbide,
carbon etc. It was found that mechanical properties of polymer
composites can be enhanced with increasing nanofiller
content-as documented in literature 5-16 . It was also found
that barrier to gas properties of the polymer composites
can be enhanced (i.e. the values of the permeability to gas
coefficient reduce as percentage of fiber contents increases)
as documented in the literature 17-27 . One important key
factor that enhances mechanical properties of the polymer
is the aspect ratio of the fillers (i.e. the ratio between the
length of the fiber to its diameter). It was found that as the
aspect ratio increases, less percentage of the filler is needed.

Thus, better mechanical properties with few amounts of
fillers. For example, improvements in mechanical properties
have been observed by adding the weight percentages of
carbon nanotubes (CNT) 28 . In addition, permeability to gas
coefficient is improved by dispersing nanofillers. For instance,
reductions in permeability coefficient have been detected
by increasing the weight percentages of clay 29 .

This study considers the experimental data from
Grigoriadou et al. 30 on mechanical properties of HDPE/Cu
nanofiber nanocomposite films and the experimental data
from Bikiaris & Triantafyllidis 31 on oxygen barrier properties
of HDPE/Cu nanofiber nanocomposite films. The tensile
modulus of elasticity (elastic modulus) and the barrier to
oxygen permeability were measured as a function of filler
content. The studies are based on the percolation theory 32
that the materials properties show either a small increase or
decrease below the percolation concentration of the filler 33 .
When percolation concentration is above threshold, the
material properties show a power law increase with filler
content 34,35 .

The main objective of this study was to correlate
the permeability to oxygen coefficient decrease for
HDPE/Cu‑nanofiber composite to the mechanical increase
of the modulus of elasticity based on a model developed
using Halpin-Tsai equation below the percolation point.
In addition to the correlation between the permeability and
modulus of elasticity of HDPE/Cu nanocomposite, it is
worthy to study the effect of copper nanofibers when added
to PE matrix. For example, Cu nanofibers are attractive as
copper is 100 times cheaper than silver and 1000 times more

b d l i h h lli fib 36

2. Experimental

This study is based on the elastic modulus experiment
findings of the HDPE/Cu-nanofibers films and used as obtained
by Grigoriadou et al. 30, also this study is based on the oxygen
permeability coefficients data of the HDPE/Cu‑nanofibers films
obtained by Bikiaris & Triantafyllidis 31 . Some modifications
were made and will be explained in the Results and Discussion
section. . Thus, all materials and samples preparations were
taken from the above two references 30,31 .

_2.1. Materials_

High density polyethylene (HDPE) was supplied by
Total Petrochemicals (Feluy, Belgium) under the trade name
Lumicene mPE M5510 EP. It has a melt flow rate (MFR)
of 0.28 g/10 min at 2.19 kg/190 °C and density 0.955 g/cm 3
and Tm 133 °C. Copper nanofibers were synthesized via the
reduction of a copper–amine complex in an aqueous-non polar
bilayer system consisted of CTAB/TMEDA/H2O/Cyclohexane
(for more details look at Cho & Huh 37 ).

_2.2. Nanocomposites preparation_

In Grigoriadou et al. 30 study; HDPE nanocomposites
containing 0.5, 1 and 2.5 wt% of Cu-nanofibers were prepared
by melt mixing in a Haake-Buchler Reomixer (model 600)
at 220 °C and 30 rpm for 15 min with roller blades and a
mixing head with a volumetric capacity of 69 cm 3 .

_2.3. Mechanical properties_

Measurements of tensile mechanical properties of the
prepared nanocomposites in Grigoriadou et al. 30 study were
performed on an Instron 3344 dynamometer, in accordance
with ASTM D638 [38], using a crosshead speed of 50 mm/min.
Thin films (100±25 μm) prepared by a PW 30 hydraulic
press at a temperature of 220±3 °C. The thin films were
prepared in order to measure the mechanical properties
of these sheets, dumb-bell-shaped tensile test specimens
(central portions 5 × 0.5 mm thick, 22 mm gauge length)
were cut in a Wallace cutting press. Then, the values of
Young’s modulus were determined.

_2.4. Oxygen permeability_

Oxygen permeability was studied based on Bikiaris and
Triantafyllidis 31 study on relatively thin films (50±5 μm) of
HDPE/Cu-nanofiber samples also prepared by a PW 30 hydraulic
press at a temperature of 220±3 °C. Permeability rates of
O2 through these films were measured using a Davenport
Apparatus (London).

3. Results and Discussion

This study is based on the experimental findings of
Grigoriadou et al. 30 and Bikiaris & Triantafyllidis 31 for the
elastic modulus and oxygen permeability coefficients of
the HDPE/Cu-nanofibers films. Grigoriadou et al. 30 in their
HDPE/copper nanofiber nanocomposites study measured the
tensile modulus of elasticity (elastic modulus) in accordance
with ASTM D638 [38] using a crosshead speed of 50 mm/min.
The values of the elastic modulus for plain HDPE is 652

i d 3 0 d 80 h 0 % C

Moreover, the effective elastic modulus of Cu-nanofibers
can be deduced from Equation 2 as follows:

_E_ _f_ = (ω+ ∅) _Ec_ −ω( _1_ −∅) _Em_ _Em_ (4)
β(ω∅+ _1_ ) _Em_ - ( _1_ −∅) _Ec_ 

Linear fitting for Cu-nanofibers/HDPE composites shows
an effective elastic modulus of 18 GPa. Figure 1 shows the
experimental elastic modulus along with the fitted elastic

d l f l i i d l ( i 1) d f h

nanofibers, 1.0 wt% Cu nanofiber, and 2.5 wt% Cu nanofiber
were added, respectively.

In this study, among all of the models used to predict
the elastic modulus of composite materials, the Halpin-Tsai
model 39,40 was used to fit the experimental data.

_1_ + ~~ω~~ ( _E_ _f_ / _Em_ ) - _1_ ∅
_Ec_ = _1_ - (( _EEff_ // _EEmm_ )) −+ _1_ ω∅ _E_

( _E_ _f_ / _Em_ ) +ω

( _E_ _f_ / _Em_ )

_1_ + ~~ω~~ ( _E_ _f_ / _Em_ ) - _1_ ∅

= ( _E_ _f_ / _Em_ ) +ω

_1_ - ( _E_ _f_ / _Em_ ) − _1_ ∅

( _E_ _f_ / _Em_ ) +ω

_f_ / _Em_

~~ω~~ _f_ _m_ ∅

( _E_ _f_ / _Em_ ) +ω

(1)

( _E_ _f_ / _Em_ )
( _E_ _f_ / _Em_ ) −

_c_ = _1_ - (( _EEff_ // _EEmm_ )) −+ _1_ ω∅ _Em_

( _E_ _f_ / _Em_ )

_f_ / _Em_

Where _EC_, _EF_, and _EM_ are the moduli of composite, fiber, and
matrix, respectively, (ω) is the shape factor, and ∅ is the
volume fraction of the filler. The shape factor (ω) is related
to the aspect ratio of reinforcement length ( _l_ ) and diameter
( _d_ ) and defined as ( _2l/d_ ). Cu-nanofibers used in this study
have an average diameter between 200 and 400 nm and
length in the range of 15 to 25 μm. Thus, the calculated shape
factor (ω) based on the aforementioned data lies between
125 and 150. The filler volume fraction (∅) is a function of
the Cu-nanofibers weight fraction and the densities of both
the filler and the matrix as follows

_w_ _f_

_f_

ρ _f_
_w_ _f_ ( _1_ − _w_ _f_

∅= _f_

_w_ _f_ + ( _1_ − _w_ _f_ )

(2)

_f_ + ( _1_ − _w_ _f_

ρ _f_ ρ _m_

_f_ ρ _m_

Where _wF_, _wM_, ρ _F_ and ρ _M_ are Cu-nanofibers weight fraction,
matrix weight fraction, Cu-nanofibers density, and matrix
density, respectively.

Halpin-Tsai equation was originally used for composites
with unidirectional reinforcement, but Cox 41 modified and
improved it to account for the randomness of discontinuous
fibers by introducing an orientation factor (β) 42 . If the fiber
length is greater than the thickness of specimen, the fibers
are assumed to be randomly oriented in two dimensions;
and the orientation factor (β) is 1/3, while if the fiber length
is smaller than the thickness of the specimen, the fibers are
assumed to be randomly oriented in three dimensions; and
the orientation factor (β) is 1/6. In this study, the length range
of Cu-nanofibers is shorter than the specimen thickness,
100 μm, thus β is considered to be 1/6 and the Halpin-Tsai
equation can be modified to become:

_1_ + β ( _E_ _f_ / _Em_ ) - _1_ ∅
_Ec_ = _1_ - ~~ω~~ ββ (( _EEff_ // _EEmm_ )) −+ _1_ ω∅ _E_

β ( _E_ _f_ / _Em_ ) +ω

( _E_ _f_ / _Em_ )

_1_ + β ( _E_ _f_ / _Em_ ) - _1_ ∅

= ~~ω~~ β ( _E_ _f_ / _Em_ ) +ω

_1_ - β ( _E_ _f_ / _Em_ ) − _1_ ∅

β ( _E_ _f_ / _Em_ ) +ω

β ( _E_ _f_ / _Em_ ) - _1_
~~ω~~ β ( _E_ _f_ / _Em_ ) +ω
β ( _E_ _f_ / _Em_ ) − _1_

_f_ / _Em_

( _E_ _f_ / _Em_ )

β ( _E_ _f_ / _Em_ )

_c_ = _1_ - β (( _EEff_ // _EEmm_ )) −+ _1_ ω∅ _Em_

(3)

( _E_ _f_ / _Em_ )

β ( _E_ _f_ / _Em_ ) +ω

_f_ / _Em_

(ω+ ∅) _Ec_ −ω( _1_ −∅) _E_

β(ω∅+ _1_ ) _Em_ - ( _1_ −∅)

= (ω+ ∅) _Ec_ −ω( _1_ −∅) _Em_

β(ω∅+ _1_ ) _Em_ - ( _1_ −∅) _Ec_ 

_f_ = β(ω(ω+ ∅∅+) _E1_ ) _cE_ − _m_ ω−( _1_ ( _1_ −∅−∅)) _EEmc_  _Em_

Linear fitting for Cu-nanofibers/HDPE composites shows
an effective elastic modulus of 18 GPa. Figure 1 shows the
experimental elastic modulus along with the fitted elastic

modified Halpin-Tsai model (Equation 3). The shape factor (ω)
was 125 for both equations, as a function of Cu-nanofibers.

It is very important to investigate the influence of the
shape factor (ω) on the elastic modulus of the composite
( _EC_ ) to account for the randomness of discontinuous Cu
nanofibers. The effect of the shape factor (ω) on the model
curve for elastic modulus of HDPE/Cu composites is shown
in Figure 2. Accordingly, the shape factor ( ω ) values were
taken to be between the minimum of 125 and 150.

It is evident from Figure 2 that the experimental data
need further modification to fit the nonlinear region for the
Cu-nanofibers content over 1wt%. Yeh et al. 43 have modified
the exponential shape factor ( ω ) to have the following form

ω′ =ω _e_ −∅− _a_ _b_ (5)

Where ( ω′ ). is the modified shape factor, (ω) is the shape
factor, _a_ and _b_ are constants related to the degree of fillers
clusters and agglomerations, which are responsible for the

Figure 1. Experimental elastic modulus along with elastic modulus
fitted by Halpin-Tsai equation (Equation 1) and the modified HalpinTsai equation (Equation 3).

nonlinear behavior of the Halpin-Tsai equation. Therefore,
the larger _a_ nd _b_ values indicate more aggregation of
the Cu‑nanofiber in the polymeric matrix. Hce, this
aggregation of the Cu-nanofibers leads to reduction of the
elastic modulus of the composites. Therefore, the modified
Halpin‑Tsai (Equation 3) can be further modified to become

_1_ +ω′ β ( _E_ _f_ / _Em_ ) - _1_ ∅
_Ec_ = _1_ - ββ (( _EEff_ // _EEmm_ )) −+ _1_ ω∅′ _E_

β ( _E_ _f_ / _Em_ ) +ω′

_f_ / _Em_

_1_ +ω′ β ( _E_ _f_ / _Em_ ) - _1_ ∅

= β ( _E_ _f_ / _Em_ ) +ω′

_1_ - β ( _E_ _f_ / _Em_ ) − _1_ ∅

′

β (

β ( _E_ _f_ / _Em_ )

( _E_ _f_ / _Em_ ) −

( _E_ _f_ / _Em_ )

ω′ _f_ _m_

β ( _E_ _f_ / _Em_ ) +ω′

′

ββ (( _EEff_ // _EEmm_ )) −+ _1_ ω′ _Em_ (6)

_c_ = _1_ - ββ (( _EEff_ // _EEmm_ )) −+ _1_ ω∅′ _Em_

( _E_ _f_ / _Em_ )

β ( _E_ _f_ / _Em_ ) +ω′

ω′

_f_ / _Em_

Equation 6 is the nonlinear form of the Halpin-Tsai equation,
so it fits the Cu-nanofibers over 1wt% better. As indicated in
Figure 3, large _a_ value tends to reduce the stiffness (Elastic
Modulus) of the composite at high Cu-nanofiber loadings.
After systematic variation of _a_ in the modified shape factor
( ω′ ), the results in Figure 3 show that the best value of _a_ to
fit the model is 41 with a minimum percentage error between
the fit and the experimental Elastic modulus. Also, Figure 3
shows that there is no need to find a fit value of _b_ in the
modified shape factor ω, thus ′ _b_ value equals zero.
Both, the small value of _a_ and the zero value of _b_ indicate
a little to no aggregations of the Cu-nanofiber in the HDPE
matrix. The experiment showed 30 that no aggregates formed
in any Cu-nanofiber content using different characterization
techniques, even at high fiber content. This discovery was
an advantage because most fillers aggregate and difficult to
disperse such as carbon nanotubes.

However, the final form of the Halpin-Tsai model that
fits the relative elastic modulus of our experimental data is
given by Equation 7.

 _1_ + _125exp_ (− _41_ ∅) _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_ ∅ 
  _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_ ∅)  
=  
  _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_  
 _1_ -  _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_ ∅)  ∅ 

 _1_ + _125exp_ (− _41_ ∅) _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_

_Ec_ =   _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_
_Em_   _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_ 

 _1_ -  _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_ ∅)  ∅

/ _6_ ( _E_ _f_ / _Em_ )

_f_ / _Em_

(− _41_ ∅) _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_

 _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_ ∅)

(7)

/ _6_ ( _E_ _f_ / _Em_ )

/ _6_ ( _E_ _f_ / _Em_ )

_c_ =   _1_ / _6_ ( _E_ _f_ / _Em_

_m_   _1_ / _6_ ( _E_ _f_ / _Em_

_1_      - 

(− _41_ ∅)

/ _6_ ( _E_ _f_ / _Em_ )

_f_ / _Em_

The experimental results in Grigoriadou study 30 show
no significant increase in elastic modulus in line with the
percolation theory. The increase was up to 24% between

Figure 2. Experimental elastic modulus along with the effect of Figure 3. Effect of the aggregation-related constant ( _a_ ) on Elastic

the pristine HDPE and the maximum Cu-nanofiber contents
(2.5wt%Cu-nanofiber). Moreover, there were no results
beyond this content, and were no dramatic increase in
the modulus, this confirmed the fact that the mechanical
percolation threshold was not reached.

Elastic modulus increases as the Cu-nanofiber loadings
increases. In addition, this increase in elastic modulus is also
accompanied by a reduction of gas permeability coefficient
as the loadings of Cu-nanofiber increased 31 . At the deduction
of Equation 7, some assumptions were applied such as the
percolation concentration of the nanofiller was not reached,
and lower nanofiller permeability to oxygen coefficient in
comparison with matrix permeability coefficient, which are
true in gas transport process case as well. Thus, Equation 7
can be used to describe relative permeability to oxygen
coefficient in the following form 27

=  _0 75_ .  _1_ + _125_ exp (− _41_ ∅) _1_ / _6_ ( _E_ _f1_ // _6E_ ( _mE_ ) _f_ + / _125expEm_ ) - _1_ (− _41_ ∅)  ∅  + _0 18_ . 
  _1_ -  _1_ / _6_ ( _E_ _f1_ // _6E_ ( _mE_ ) _f_ + / _125expEm_ ) - _1_ (− _41_ ∅) ∅  

_Pm_ =  _0 75_ .  _1_ + _125_ exp _1_ - (− _141_ / _6_ ∅ ( _E_ ) _f11_ /// _6E6_ ( _m_ ( _EE_ ) _f_ + _f1_ / _125exp_ // _E6Em_ ( _mE_ )) - _f_ + _1_ ( / _125exp_ - _E41m_ ) ∅−) _1_ (−∅ _41_ ∅)  ∅  + _0 18_ .  _Pc_

_0 75_ .  _1_ + _125_ exp (− _41_ ∅) _1_ / _6_ ( _E_ _f1_ // _6E_ ( _mE_ ) _f_ + / _125expEm_ ) - _1_ (− _41_ ∅)  ∅  + .

  _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_  

_f_ / _Em_

(− _41_ ∅) _1_ / _6_ ( _E_ _f1_ // _6E_ ( _mE_ ) _f_ + / _125expEm_ ) - _1_ (− _41_ ∅)

(9)

_m_ =  _0 75_ .  _1_ -   _11_ // _66_ (( _EEf_ _f_ // _EEmm_ )) −+ _1125exp_ (−∅ _41_ ∅)   + _0 18_ .  _Pc_

/ _6_ ( _E_ _f_ / _Em_ )

_f_ / _Em_ )

(− _41_ ∅)

 _1_ + _125exp_ (− _41_ ∅) _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_

_Pm_   _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_

/ _6_ ( _E_ _f_ / _Em_ )

_f_ / _Em_

(− _41_ ∅) _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_

 _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_ ∅)

(8)

/ _6_ ( _E_ _f_ / _Em_ )

/ _6_ ( _E_ _f_ / _Em_ )

_Pm_ =   _1_ / _6_ ( _E_ _f_ / _Em_

In addition to that, the experimental Oxygen Transmission
Rate (OTR) from Bikiaris & Triantafyllidis 31 study through
each film was converted to permeability coefficient using
the following equation

_P_ = _OTR xl_ (10)

Where _l_ is the thickness of the film.

Figure 5 shows the comparison of the experimental
permeability to oxygen coefficient from Bikiaris & Triantafyllidis 31
study and the calculated values of the permeability to oxygen
coefficient from Equation 9 as a function of weight fraction
of Cu-nanofibers. As shown in Figure 5, the modified model
(Equation 9) correlates well for the composite samples and
gives very precise permeability to oxygen coefficient up to
1wt% of Cu-nanofiber. The maximum discrepancy between
the experimental and the theoretical values was up to 2%.

Figure 4. The comparison of relative coefficient of gas permeability and
relative elastic modulus for nanocomposites of HDPE/Cu-nanofibers.

Figure 5. Experimental permeability to oxygen coefficient along

i h h d i d d l (E i 9)

_Pc_   _1_ / _6_ ( _E_ _f_ / _Em_ ) - _1_

 _1_ -  _1_ / _6_ ( _E_ _f_ / _Em_ ) + _125exp_ (− _41_

_c_   _1_ / _6_ ( _E_ _f_ / _Em_

_1_      - 

(− _41_ ∅)

/ _6_ ( _E_ _f_ / _Em_ )

_f_ / _Em_

Where _PM_ and _PC_ are the permeability coefficient of
the polymeric matrix and of the composite material,
respectively.

The experimental results show a slightly decrease
in oxygen permeability up to 1wt%Cu-nanofiber, then a
significant decrease in oxygen permeability at 2.5wt%
Cu-nanofiber up to 65% relative to the HDPE matrix.
This makes one believe that 2.5wt% filler content is beyond
the permeability percolation because of expected dramatic
decrease. Also, if Equations 7 and 8 are compared, they
show enhancement in the composite modulus relative to the
pure HDPE matrix, and this enhancement is accompanied
by reduction in permeability to oxygen of the nanofilms
as the Cu-nanofiber content increases. Therefore, elastic
modulus and permeability to gas coefficient are inversely
proportional.

In Figure 4, the relationship between the relative
permeability to oxygen coefficient (Pm/Pc) and the relative
modulus of the nanocomposite (Ec/Em) is presented. Because
there are only two experimental points available from both
studies by Grigoriadou et al. 30 Bikiaris & Triantafyllidis 31
below percolation, we expect that the relationship between
the relative permeability coefficients and the relative
elastic moduli is linear with a slope of 0.75. It is worthy
to mention that even we have a third point in the relative
permeability at 2.5wt%, this point was not included in
Figure 4 because it is believed that this concentration is
beyond the percolation. The reduction between the 1wt%
and 2.5wt% is large (almost 65% reduction). However,
the relationship in Figure 4 does not pass through the
origin and as seen in Figure 4 at Ec/Em=1.09 the value
of Pm/Pc=1, which means that at small contents of Cunanofiber the value of Pc is close to the permeability to
oxygen coefficient for HDPE matrix. The above mentioned
circumstances make necessary to modify Equation 8 to
b f ll

4. Conclusion

Cu-nanofibers are effective fillers for enhancing mechanical
and oxygen barrier properties of HDPE. The enhancements
of these properties depend on the Cu-nanofiber content.
The reduction in oxygen permeability with Cu-nanofiber
below percolation increase was due to the decrease of HDPE
fraction accessible for the gas transport process. However, the
reduction was not significant because HDPE has relatively
low fraction of amorphousity (crystallinity is high) thus the
diffusive motion of oxygen between the molecular chains of
PE is very low. Often, oxygen transfers easily without any
obstacles. Also, it was noticed that mechanical percolation
is independent of permeability percolation and they happen
at different filler contents. Also, this permeability model can
be used to predict the permeability coefficient for composite

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