Permeability, Diffusion and Solubility of Gases in Polyethylene, Polyamide 11 and Poly (Vinylidene Fluoride)
Oil & Gas Science and Technology - Rev. IFP, Vol.
Permeability, Diffusion and Solubility of Gases in Polyethylene, Polyamide 11 and Poly(vinylidene fluoride)
B. Flaconnèche 0 1
J. Martin 0 1
M.H. Klopffer 0 1
0 Mots-clés : perméabilité , diffusion, solubilité, gaz, PE, PA11, PVDF
1 et 4 , avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex - France
of PE, the influence of the volume fraction of the amorphous phase, ranging from 0.21 to 0.70, the
influence of temperature and the influence of the nature of the gas on the transport processes are
investigated. Also, the independence of these phenomena related to pressure and sample thickness,
between 0.5 and 6 mm, is shown. For PA11, after determining the influence of temperature and of the
nature of the gas used, the effect of the plasticizer incorporation in this polymer was studied. Regarding
PVF2, apart the classic parameters that are temperature and the kind of gas used, we compare the
coefficients of transport of CH4 and CO2 in PVF2 made up by extrusion or by compression moulding. For
each polymer, it is shown that permeability, diffusion and solubility depend on temperature following
Arrhenius’ laws. It also seems that diffusion is directly related to the gases molecule size and that the
solubility coefficient can be linked to the ε/K gases parameter. The comparison of the results obtained
with the available data in the literature seems satisfactory.
Keywords: permeability, diffusion, solubility, gases, PE, PA11, PVF2.
LIST OF THE USED NOTATIONS
Low density polyethylene Medium density polyethylene High density polyethylene Polyamide 11
Semicrystalline polymer density (g/cm3)
Melting point temperature (°C)
Enthalpy of fusion (J/g)
Degree of crystallinity (weight fraction) (%)
Volume fraction of the amorphous phase
Long period (Å)
Thickness of the amorphous zone (Å)
Thickness of the crystalline zone (Å)
Standard conditions of temperature (273 K) and
pressure (0.1013 MPa)
Permeability coefficient (cm3 (STP)/cm·s·MPa)
Diffusion coefficient (cm2/s)
Solubility coefficient (cm3 (STP)/cm3·MPa)
Time lag (s)
Gas Transport Coefficients
Characteristics of Gases
The gas transport coefficients in semicrystalline polymers
are generally complex to determine and to analyse, especially
in the field of high pressures and high temperatures.
Few literature data on this subject are available. Indeed, the
permeability (Pe), the diffusion (D) or the solubility
coefficients (S) vary generally with many parameters which
can be intrinsic to the polymer, such as the weight fraction
of crystallinity, the nature of the polymer or even the
thermal history of the sample [
]. The kind of gas used,
characterised by its molecule size or thermodynamical
parameters, is also a factor influencing these coefficients in
the same way as temperature [
In this work, the equipment of permeation and the time lag
method, described in , are used to obtain the transport
coefficients of gases in three semicrystalline polymers:
polyethylene (PE), polyamide 11 (PA11) and poly(vinylidene
fluoride) (PVF2). Some of the characteristics of these
polymers were determined before and after permeation
measurements. Five gases, helium, argon, nitrogen, methane
and carbon dioxide, were studied in a temperature range of
40° to 130°C and for pressures ranging from 4 to 12 MPa.
In the case of PE, the measurement repeatability was
verified. Then, it was established that the transport
coefficients are independent of the membrane thickness. For
each polymer, the effects of temperature and of the nature of
the gas are discussed and compared with the literature data.
In a more specific way, the influence of the plasticizer
incorporation in polyamide 11 and the effect of PVF2
processing conditions are shown.
1 EXPERIMENTAL PROCEDURE
1.1 Permeability Measurement
The determination of the transport coefficients of various
gases is made by a manometric method (pressure
accumulation in a closed volume). The precise description of
the “medium pressure” equipment used and its working
procedure are detailed in . Permeability, diffusion and
solubility are obtained from the experimental curves, by
using the “time lag” method. In the studied ranges of
pressure and temperature, the diffusion coefficient is
assumed to be independent of the gas concentration in the
polymer, and it is admitted that the solubility respects
Henry’s law. These restrictive assumptions allow to obtain
apparent values of D and S that are quite realistic when there
are few interactions between the gas and the polymer.
Then, the permeability coefficient, Pe, expressed in cm3
(STP)/cm·s·MPa, is directly proportional to the slope of the
straight line representing the gas flow rate versus the applied
pressure, in steady state, and is written as:
where Q is the amount of gas in cm3 (STP), l is the
membrane thickness in cm, A is the diffusion area in cm2, t is
the time in s, and p is the applied pressure in MPa. The
diffusion area was equal to 12.57 cm2 [2, 3]. The diffusion
coefficient, D, given in cm2/s, is obtained from the relation:
Θ, the “time lag” in s, corresponds to the intercept of the x
axis with the straight line in steady state.
The solubility coefficient S, expressed in cm3 (STP)/cm3 ·
MPa, is easily calculated as the ratio Pe/D.
1.2 Measurement Repeatability
A rigorous calibration of the permeation cell is very difficult
as far as the expected flow ranged from some tenths of cm3/h
to some cm3/h. Then, the potential drift of the equipment is
verified by testing regularly a standard polymer in average
The chosen polymer is an extruded, 30 m in length
and about 2 mm in thickness, band of medium density
polyethylene (MDPE) tested under CO2 at 4 MPa and 60°C.
The values of the transport coefficients obtained from several
tests are given in Table 1.
From these results, it can be concluded that the
measurement repeatability is correct in spite of some small
variations of temperature and pressure. The experimental
uncertainties on Pe, D and S, calculated in , are of the
order of some percents for permeability, from 10% to 15%
for the diffusion coefficient and about 20% for solubility.
Indeed, regarding permeability, the uncertainties depend
directly on the sensors used. On the other hand, a very small
variation of the slope in the steady state can entail important
variations of the time lag value, and, then, a strong
uncertainty on the diffusion coefficient. This will be the case
when the time lag is small as, for example, in the diffusion of
helium. The relative uncertainty on solubility, calculated by
the ratio Pe/D, is equal to the sum of the relative errors on
1.3 Processing Conditions and Polymer Characterisations
Six semicrystalline polymers were used during this study: a
low density polyethylene, noted LDPE, a medium density,
noted MDPE, two high density, referenced respectively
HDPE and HDPE-Rl, a polyamide 11, noted PA11 and a
poly(vinylidene fluoride), noted PVF2. All the polymer
samples necessary for the permeation tests were extracted from
plane sheets made up by compression moulding of pellets.
The processing conditions for each polymer are given below:
pressure: 10 MPa
cooling: air quenched (10°C/min)
– polyamide 11:
pressure: 10 MPa
cooling: air quenched (10°C/min)
– poly(vinylidene fluoride):
pressure: 10 MPa
cooling: air quenched (10°C/min).
The first three polyethylenes, LDPE, MDPE and HDPE,
were cooled in a standard way. To increase the degree of
crystallinity as more as possible, the last one, HDPE-Rl, was
cooled slowly at 1°C/min on a programmable press. Before
the permeation tests, the polyethylene and PVF2 samples
were maintained at ambient temperature (21°-23°C) in an
airconditioned room. For PA11, the membranes were annealed
under vacuum at 80°C during eight hours and, then, kept
under vacuum to avoid humidity absorption.
Some polymer characteristics were determined after
compression moulding. The density values of the polymer
samples were measured on a Mettler AE240 balance. This
measure is based on Archimedes’ principle. The fact that
polyethylenes and polyamide 11 have densities close to that
of water required the use of ethanol as solvent. For PVF2, the
measures were performed in water.
A differential scanning calorimeter (Perkin-Elmer DSC7)
was used to measure the melting temperature and the fusion
enthalpy of the studied polymers. DSC (Differential
Scanning Calorimetry) spectra, an example of which is given
in Figure 1, were obtained at a rate of 10°C/min, under a
continuous flow of argon and for a mass of sample of around
5 mg. The ratio of the fusion enthalpy of the semicrystalline
samples over the fusion enthalpy of the pure (100%)
crystalline polymer gives the degree of crystallinity, Xc, of
each polymer. The enthalpies of fusion of the pure crystalline
polymers were taken equal to 290 J/g for polyethylenes ,
to 226 J/g for polyamide 11  and to 100 J/g for PVF2 [
The values of Xc allowed the calculation of the volume
fraction of the amorphous phase, noted Φa, for every
polymer by the relation:
Φa = ( 1 − Xc )
ρ is the density of the semicrystalline polymer and ρa is the
density of the amorphous phase of the considered polymer.
The densities of the amorphous phase were taken equal to
0.855 g/cm3 for polyethylenes , to 1 g/cm3 for polyamide
11  and to 1.67 g/cm3 for poly(vinylidene fluoride) .
The “long period” of the polymers was determined by
tests of small angle X-ray diffusion (SAXS). The equipment
and the working procedure are described in . In this
system, the incidental bundle presents a surface of 2 mm2 and
the range of the observation angle can vary from 0.1° to 2°.
This represents the diffraction of regular structures, the
period of repetition of which varies from 40 to 700 Å. It
is the case of thin lamellae and interlamellae zones of
semicrystalline polymers. The spectrum obtained for this
type of polymer (Fig. 2) presents an interference peak
corresponding to the stack of the crystalline small lamellae
separated by the amorphous phase. The long period, Lp, is
calculated from the maximum qmax of the curve by:
2 sin θ
= 2 π
The degree of crystallinity measured by using DSC allows
to obtain the volume fraction of the crystalline phase (Φc)
contained in the polymers. Then, the thickness of the
crystalline zone, Lc, is calculated using the relation:
Lc = Lp Φc
The thickness of the amorphous zone, La, is calculated by
simple subtraction of Lc from Lp.
The polymers characteristics in their initial state,
determined by the techniques described above, are
recapitulated in Table 2.
Some characterisations were made after the permeation
tests in methane at 80° and 40°C, for two of the
polyethylenes, LDPE and HDPE-Rl. The comparison
between the DSC analysis performed at the initial state and
after the permeation tests at 80°C, allowed to note a slight
increase of the degree of crystallinity of LDPE (Fig. 3). At
the same time, the crystallinity of HDPE-Rl remained
constant. In the case of the measurements at 40°C, no
significant evolution of the permeability was identified.
Besides, DSC performed on samples annealed at 80°C,
during a time equivalent to the duration of the permeation
tests, gave identical thermograms (Fig. 4). In the case of
LDPE, the temperature of the permeation tests seemed to
increase slightly the degree of crystallinity. For all the
polymers, no effect of the gas was observed. Finally, the
“long period”, measured after the permeation tests, increased
slightly, for LDPE, from 124 Å initially to 131 Å, whatever
the kind of gas used (but it was not modified for HDPE-Rl).
This modification was due to the increase of the degree of
crystallinity of this polymer.
1.4 Gases Used
Table 3 recapitulates the main characteristics of the tested
gases that have a purity greater than 99%. For literature data,
like the Lennard-Jones’ parameter (ε/K) or the molecule
diameter, the amplitude of variation is rather wide.
OF GASES THROUGH POLYETHYLENE
This section is dedicated to the transport phenomena of
helium, argon, nitrogen, methane and carbon dioxide in
polyethylene . The influence of various parameters such as
the temperature, in a range of 40° to 80°C, the thickness of
membranes, the type of gas used and the crystallinity, was
studied. In some cases, the pressure varied from 4 to 10 MPa
to evaluate its effect on the transport coefficients.
Tables 4 to 8 respectively present the transport
coefficients of helium, argon, nitrogen, methane and carbon
dioxide in the four PE studied at various temperatures and
pressures. All the tests were performed on membranes of
2 mm in thickness. These different values will be analysed
and discussed in Sections 2.2 and 2.3 dedicated to the effects
of the temperature, PE crystallinity and kind of gas used.
2.1 Influence of the Sample Thickness
To verify that the thickness of the polymer membranes used
does not influence the transport coefficients in a significant
way, permeation tests were performed on MDPE in the
presence of CO2 at 80°C and a pressure of 4 MPa. The
sample thickness varied from 0.5 to 6 mm. Each test was
systematically repeated and the obtained results are given in
Considering the experimental uncertainties, the
permeability, diffusion and solubility values are not
influenced by the membrane thickness. Nevertheless, for the
tests on a sample of 0.5 mm thickness, D is a little smaller
than in the other cases. This can be explained considering that
the value of the time lag is less than 10 min. This implies
large uncertainties for the determination of D. As shown in
Figure 5, the duration of the tests was strongly dependent on
the membrane thickness. In this study, the time lag varied
from 10 min, for a thickness of 0.5 mm, to more than 8 h for
the highest thickness. A relation of proportionality between Θ
and l2 is obtained (Fig. 6). This implies a weak dependence of
the diffusion coefficient on the gas concentration in the
MDPE samples. Indeed, it is common to compare the speed
Permeation curves for MDPE at 80°C and 4 MPa of CO2.
Relationship between time lag and l2.
of the gas molecules to the relaxation speed of the polymer
chains. Then, the ratio of these speeds allows to separate the
various cases of diffusion. The main cases are:
– the relaxation rate of the polymer chains is very high
compared to the speed of gas molecules diffusion. Then,
the diffusion front propagates at the gas rate in the
polymer and the time lag is proportional to the square of
the membrane thickness;
– in a second case, the diffusion front moves much more
slowly than the gas. The time lag is equal to the time
necessary for this front to cross the membrane. This time
is directly proportional to the thickness.
By taking into account experimental uncertainties, it was
concluded that the transport coefficients seemed independent
of the sample thickness and that the diffusion coefficient
was apparently slightly dependent on the CO2 concentration
in MDPE. Considering these results, all the permeation
tests were made on membranes of 1 or 2 mm in thickness
depending on the polymers used.
2.2 Influence of the Temperature and Pressure
In the range of used pressures (4 to 10 MPa), no significant
effect was noticed on the gas transport coefficients in
polyethylene. The values of permeability, diffusion and
solubility, for helium and methane tests, rarely exhibited
variations greater than the experimental uncertainties. Then, it
was difficult to give a reliable conclusion for the pressure
effect on the transport coefficients. A similar study showed
that the CH4 and CO2 solubility in PE seemed independent of
pressure in a range from 0.1 to 4 MPa [
]. On the other hand,
the diffusion coefficient appeared to depend systematically on
concentration. Some other authors have noticed that, in
methane or nitrogen sorption tests in PE, S became dependent
on pressure from 15 MPa [
]. Regarding permeability,
a study dealt with ten gases from 0.1 to 13 MPa on
polyethylene and polypropylene [
]. The authors noted a
slight increase of permeability with the pressure of the most
soluble gases in PE, that are CO2 and CH .
The amorphous phase of the studied polymers consists in
entanglements of macromolecular chains. Increasing the
permeation tests temperature leads to a simultaneous increase of
Apparent activation energies for permeability, diffusion and heat of solutions of gases in polyethylenes
where EPe and ED are the activation energies of permeability
and diffusion and ∆ Hs the apparent heat of the solution [
As Figure 7 shows it, the temperature effect on the gas
transport in polymers is very important for permeability
(Fig. 7a) and diffusion (Fig. 7b) while solubility (Fig. 7c)
seems less sensitive to this parameter. The logarithmic
representation of Pe, D and S versus 1/T allows to obtain
straight lines, the slopes of which are proportional to the
activation energies of these phenomena. The obtained values
of EPe, ED and ∆ Hs for polyethylene and for each gas studied
are given in Table 10 and compared with the literature data.
The activation energies obtained during this study agree
well with the literature values, especially for permeability or
diffusion. On the other hand, the comparison is not suitable
for the solubility of some gases as helium, argon or methane.
In every case, the calculation of S remains based on
assumptions that can be restrictive: D depends on the gas
concentration and S respects Henry’s law. Furthermore, for
helium, as indicated above, a rather important error on the
diffusion coefficient may be done, entailing rather important
errors on the solubility and finally on ∆ Hs.
2.3 Crystallinity Effect and Influence of the Nature of Gas
The degree of crystallinity of semicrystalline polymers is a
parameter that modifies most of the properties of these
materials, in particular their transport coefficients [
]. To illustrate the crystallinity and the nature of the gas
effects, Figure 8 represents the permeability coefficients
the degree of chain mobility and of the gas molecule mobility.
It is current to express that the transport coefficients depend
on temperature according to Arrhenius’ laws of the type:
Pe = Pe 0 exp RT
D = D 0 exp RT
– ∆ Hs
S = S 0 exp RT
(Fig. 8a), the diffusion coefficients (Fig. 8b) and the
solubility (Fig. 8c) versus the volume fraction of the
amorphous phase contained in the four polyethylenes.
The obtained results (Tables 5-8) let appear a clear
influence of the PE crystallinity on the different coefficients.
The decrease of the amorphous phase content involves
systematically a decrease of Pe, D and S. These conclusions
are in good agreement with those of the literature where the
authors correlate the transport coefficients with the
crystallinity of polyethylene [
]. If the relations do not seem
explicit concerning permeability and, more particularly
diffusion, solubility seems to linearly depend on the volume
fraction of the amorphous phase in PE. In that case, the
crystalline phase acts as a barrier for gases, and the gases are only
soluble in the amorphous phase. It is then possible to write:
S = Sa Φa
where S is the solubility coefficient of the gas in
semicrystalline PE and Sa is the gas solubility in a totally
The values of Sa at 40°C in Table 11 have been obtained
from the slopes of the straight lines represented in Figure 8c
for only four of the gases used, namely, argon, nitrogen,
methane and carbon dioxide. Indeed, it seemed difficult to
take into account the values of the helium solubility as far
as the experimental errors in that case are very important.
The obtained results are very close to those of the literature
By representing ln (Sa) versus Lennard-Jones’ parameter
(ε/K) of gases, a straight line can be plotted (Fig. 9) whose
ln ( Sa ) = –4.80 + 0.021 ε / K
where the pressure unit for the expression of Sa is the bar
(1 bar = 0.1 MPa). This relation is close to those determined
by other authors [
] who found respectively for much
larger ranges of gases:
ln ( Sa ) = –5.07 + 0.022 ε / K
ln ( Sa ) = –4.80 + 0.022 ε / K
* Not determined.
Gases solubilities in amorphous polyethylene at 40°C
Sa (exp) (40°C)
Hence, in a first approximation, the solubility coefficient
of semicrystalline PE can be estimated in a simple way from
ε/K and from the volume fraction of the amorphous phase.
The relations between the crystallinity of PE and the
coefficients of permeability and diffusion are less evident.
Indeed, the polymers may be plasticized (in the case of high
solubility) or a difference of tortuosity due to the amount
of crystalline phase contained in PE [
] may occur.
Furthermore, PE is assumed to be a two-phase mixture of
crystallites and amorphous polymer. Now, the reality is quite
different and the intermediate phases between the amorphous
and the crystallites do not present the same behaviour than a
perfectly homogeneous amorphous environment. In order to
take correctly into account the quantity of amorphous phase
in the diffusion process, it would be necessary to know the
parameters of the crystalline morphology (distribution,
orientation, tortuosity, etc.) and of the amorphous phase
(entanglement density, etc.). In the case of permeability,
which results from both other phenomena, the difficulty is
identical. It is clear that Pe depends strongly on the
crystallinity but in a complex way [1, 2].
Considering the gas effect, it turns out that for a small gas
molecule (like helium), the diffusion coefficient governs
permeability, while, for larger molecules with similar size,
permeability is rather dependent on solubility. All the
available data allowed to classify the transport coefficients in
polyethylenes according to the nature of the gas and to
confirm the previous observation:
Pe ( CO 2 ) > Pe (He) > Pe ( CH 4 ) > Pe (Ar) > Pe ( N 2 )
D (He) >>> D ( CO 2 ) ≈ D (Ar) ≈ D ( CH 4 ) ≈ D ( N 2 )
3 PERMEATION OF GASES
THROUGH POLYAMIDE 11
Polyamide 11 was the second polymer studied during this
work. The measurements of the transport coefficients were
also performed for the five gases. The temperature ranged
from 40° to 100°C for He, and from 70° to 130°C for the
others. The applied pressure of CO2 was about 4 MPa while,
for the other gases, the pressure was fixed to 10 MPa. All the
obtained results are given in Table 12.
3.1 Temperature Influence
Figure 10 illustrates the temperature effect on the transport
coefficients in polyamide 11. As in the case of polyethylene,
the temperature influence on permeability, diffusion and
solubility can be described correctly by Arrhenius’ laws for
* Not determined.
Apparent activation energies for permeability, diffusion and heats of solution of gases in PA11
Temperature effect on transport coefficients for various gases
in polyamide 11 ( CO2, CH4, Ar, O N2, He).
(a) Permeability (cm3 (STP)/cm·s·bar) coefficients versus
(b) Diffusion coefficients versus reciprocal temperature.
(c) Solubility (cm3(STP)/cm3·bar) versus reciprocal temperature.
each gas. Then, the activation energies EPe, ED and ∆ Hs of
each transport phenomenon can be determined (Table 13).
The values of the permeability activation energy
determined during this study are in good agreement with
those found in the literature. On the other hand, the values of
ED and ∆ Hs agree well for argon, but are slightly different
from those obtained for the other gases [
3.2 Influence of the Gas Nature
Figure 10 shows the influence of the gas type on the transport
coefficients in polyamide 11. From Table 12, a summary of
the results is obtained by a classification of the gases with
regard to their transport coefficients in PA11:
Pe (He) > Pe ( CO 2 ) > Pe (Ar) > Pe ( CH 4 ) > Pe ( N 2 )
D (He) >>> D ( CO 2 ) ≈ D (Ar) > D ( N 2 ) ≈ D ( CH 4 )
3.3 Influence of the Weight Fraction of Plasticizer
Polyamide 11 has a glass transition temperature of about
40°C and is rather brittle at ambient temperature. In order to
decrease its Tg value, a plasticizer
(n-butyl-benzenesulfonamide (BBSA)) is incorporated into the polymer. For
example, in the case of flexible pipes for oil transport, this
avoids the risks of brittle fracture during the rolling-up of the
structures during storage. In [
], one can notice the plasticizer
influence on gas transport phenomena in polymers. Hence,
the coefficients of permeability, diffusion and solubility
in polyamide 11, containing five different fractions of
plasticizer, were measured with methane and carbon dioxide.
The plasticizer was incorporated into the polymer matrix
by using a Haake melting compounder [
necessary for the permeation tests were taken from plane
sheets processed by compression moulding. In the same way
as for polyethylene, some characteristics of these samples
were determined (Table 14). The determination of the
plasticizer content was performed by a gravimetric method
on a microbalance equipped with an infrared spectrometer.
Samples of about 10 mg were heated from 40° to 230°C at a
rate of 10°C/min, then maintained at 230°C during 80 min.
This technique allowed to know the exact plasticizer contents
of membranes before and after the permeation tests. At
the initial state, the weight fractions of plasticizer were
respectively 0%, 7.5%, 12.5%, 19% and 29.5%.
The permeability measurements were carried out at 120°C
and 4 MPa pressure, for membranes of 2 mm in thickness
(Table 15). At this temperature and whatever the kind of gas
used, no significant loss of plasticizer was noted. It can be
concluded that there was no extraction of plasticizer due to
temperature. It is necessary to underline that the tests
duration was systematically lower than 24 h and that, for
longer stays, the plasticizer could be extracted. The long
periods measured by SAXS remained also constant after the
permeation tests. However, these measurements indicated an
increase of the thickness of the crystalline zones. This result
was confirmed by the thermal analysis where it could be
noted a systematic increase of the PA11 crystallinity of about
4% to 5%.
Figure 11 represents the permeability (Fig. 11a), the
diffusion (Fig. 11b), and the solubility (Fig. 11c) of methane
and carbon dioxide in PA11 versus the plasticizer content.
These three curves confirm the influence of the plasticizer on
the gas transport coefficients in PA11. Indeed, the diffusion
rate of methane and carbon dioxide is five times slower
through the natural PA11 than through the same polymer
containing 30% of plasticizer. The solubility coefficient
(Fig. 11c) seems slightly modified by the plasticizer content
but relatively sensitive to the nature of the gas used: carbon
dioxide is about twice more soluble in PA11 than methane,
for all the contents of plasticizer. Hence, the increase of the
permeability can be attributed to the large variation of the
diffusion coefficient. The plasticizer incorporation in the
amorphous phase of PA11 gives more freedom to the
macromolecular chains and facilitates the diffusion of the gas
molecules. Furthermore, as the diffusion rates of the two
gases in PA11 are closed to each other, the difference of
permeability can be attributed, at constant plasticizer weight
fraction, to the high solubility of CO2 in this polymer.
4 PERMEATION OF GASES
THROUGH POLY(VINYLIDENE FLUORIDE)
The last polymer studied during this work was
poly(vinylidene fluoride). The coefficients of permeability,
diffusion and solubility were determined for He, Ar, N2, CH4
and CO2 for temperatures varying from 40° to 130°C, and
pressures of 4 MPa for CO2, 10 MPa for Ar, N2 and CH4 and
varying from 4 to 12 MPa for N2 (Table 16).
4.1 Influence of the Temperature and Pressure
No significant effect of the nitrogen pressure (in the range of
4 to 12 MPa) on the transport coefficients was noticed at
For PVF2, temperature is an important parameter
(Fig. 12). In a same way as for polyethylene and PA11, the
activation energies of the transport coefficients of gas in
PVF2 are supplied in Table 17.
Few studies concerning this polymer are available in the
literature. The values of the activation energies obtained
during this work can only be compared to those determined
] on the same polymer at a pressure varying from 0.1 to
2.5 MPa: in the case of helium, their EPe value is about of
36 kJ/mol, that is identical to the results of this study. In the
case of methane, the values are also close: EPe = 65 kJ/mol,
ED = 67 kJ/mol and ∆ Hs = –3.5 kJ/mol.
For gases of similar molecule size, like Ar, N2, CH4 and
CO2, the ED values are about identical. However, the
activation energy of permeability to CO2 is about half that of
the three other gases. This can be explained by the high
solubility of CO2 in PVF2.
4.2 Influence of the Samples Processing
The permeability measurements performed on PVF2
membranes taken from plane sheets moulded by compression
are compared to those made on samples taken from
singlescrew extruded bands (Table 18). The characteristics
determined on these two types of polymers are similar, in
particular the densities and the volume fractions of the
The comparison of the results obtained on the extruded
PVF2 with those of Table 12, performed in identical
operating conditions, lets appear only small differences. In
most of the cases, this slight difference is lower than the
experimental uncertainty, except for the permeation tests of
CO2 at 100°C. The lower temperature (97°C) at which the
permeation tests were made on the extruded sample can be a
good explanation of this variation. These observations are
confirmed in one study whose authors noticed that the
orientation of the polymer chains induced by the extrusion is
not sufficient to modify in a significant way the values of gas
transport coefficients in this PVF2 [
4.3 Effect of the Gas Nature
Figure 12 shows the importance of the type of gas used.
From all the available values, it was possible to establish a
gas classification for the different transport coefficients:
Pe (He) ≈ Pe ( CO 2 ) >> Pe (Ar) > Pe ( CH 4 ) > Pe ( N 2 )
D (He) >>> D ( CO 2 ) ≈ D (Ar) ≈ D ( CH 4 ) ≈ D ( N 2 )
As in the case of PE and PA11, D seems to depend
strongly on the gas molecule size. Indeed, gases with close
diameters have rather similar diffusion coefficients
(Fig. 12b). The very high solubility of CO2 in PVF2
(Fig. 12c) provides to this gas a permeability (Fig. 12a)
almost identical to the permeability to helium which has
nevertheless a 50-time higher diffusion coefficient.
The transport coefficients of five gases, He, Ar, N2, CH4 and
CO2, were determined from permeation tests analysed by
using the time lag method, for three semicrystalline
polymers, PE, PA11 and PVF2, in a range of temperature
from 40° to 80°C for PE and from 70° to 130°C for the
others. The applied pressures varied between 4 and 12 MPa.
For the diffusion and the solubility coefficients, the
polymer nature is obviously one of the most important
parameters. Whatever the tested gas, polyethylene is more
permeable than PA11 and PVF2, which present a very similar
behaviour. This result is attributed to the high diffusion
coefficients of gases in PE. One explanation could be that the
permeation tests temperature is closer to the melting point of
PE (130°C) than to that of PA11 (190°C) or PVF2 (170°C).
Then, the macromolecular chains of the amorphous phase of
PE have a greater mobility than those of the other materials.
PVF2 is twice as permeable to CO2 than PA11 and represents
a particular case. This phenomenon can be explained by the
strong interaction between CO2 and this polymer, resulting in
a very high solubility.
In the operating conditions used, the repeatability of
the tests is good and the membrane thickness (0.5 mm ≤
l ≤ 6 mm) does not modify in a significant way the
permeability, diffusion and solubility values.
Arrhenius’ laws can describe the temperature influence on
the gas transport coefficients in these polymers. The values
obtained for the activation energies of these phenomena are
in good agreement with those found in the literature.
For polyethylene, the degree of crystallinity is also an
important parameter and an increase of the volume fraction
of the amorphous phase (Φa) results in an increase of Pe, D
and S. By assuming the crystalline phase of PE totally
impenetrable to gases, an empirical correlation between Sa,
the gases solubility in the totally amorphous PE, and the
gases parameter, ε/K, was established. This relation is quite
similar to the others found in the literature.
For PA11, the addition of plasticizer in the polymer
matrix involves an important increase of the gas transport
Regarding PVF2, the macromolecular chains orientation
induced by extrusion is not sufficient to modify the
coefficients Pe, D and S.
Whatever the studied polymer, some complex relations
exist between D and the gas size. In the case of small
molecules such as helium, it seems that the diffusion
coefficient governs the permeation phenomenon. On the
other hand, for gases of quite similar sizes, having close
diffusion coefficients, it seems that permeability is then
strongly dependent on the gas-polymer interactions, which
are reflected by the solubility coefficient.
To have a better understanding of gas transport
phenomena in polymers, various domains should be
investigated. In order to quantify
more precisely the
competition between the effects of the polymer hydrostatic
compression and of material plasticizing, it would be
interesting to study the very high-pressure field. In the case
of mixed gases, it would be important to know if effects of
synergy between the gas molecules and a polymer matrix
might exist. All this would lead to perform realistic
predictions of polymer structures behaviour during the
contact of gas under pressure.
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