Gas transport properties of poly(2-ethoxyethyl methacrylate-co-2- hydroxyethyl methacrylamide)

Article abstract of DOI:10.1021/ma049945h

A series of methacrylic copolymers was prepared by radical polymerization of the monomers 2-ethoxyethyl methacrylate and 2-hydroxyethyl methacrylamide and a small quantity of a cross-linking agent ethylene glycol dimethacrylate. Water swelling of the membranes, mechanodynamical analysis, density measurements, and ATR-FTIR studies were performed on the copolymers. High vacuum pressure techniques were used to evaluate the flow of He, O₂, N₂, CO₂, CH₄, CH₃CH₃, and CH ₂CH₂ through these membranes, and solubility, diffusivity, and permeability coefficients were determined. The effect of the increase of the amount of methacrylamide in the copolymer on transport properties, glass transition, fractional free volume, cohesive energy density, and specific interactions has been studied and is reported in this work.

Full text of DOI:10.1021/ma049945h

4
156
Macromolecules 2004, 37, 4156-4163
Gas Transport Properties of Poly(2-ethoxyethyl
methacrylate-co-2-hydroxyethyl methacrylamide)
,
†
†
‡
‡
†
†
P . Tiem blo,* M. F . La gu n a , F . Ga r c ı´ a , J . M. Ga r c ı´ a , E. Ria n d e, a n d J . Gu zm a´ n
Instituto de Ciencia y Tecnolog ´ı a de Pol ´ı meros (CSIC), Calle J uan de la Cierva 3, 28006 Madrid,
Spain, and Universidad de Burgos, Plaza Misael Ba n˜ uelos s/ n, 09001 Burgos, Spain
Received J anuary 8, 2004; Revised Manuscript Received March 12, 2004
ABSTRACT: A series of methacrylic copolymers was prepared by radical polymerization of the monomers
-ethoxyethyl methacrylate and 2-hydroxyethyl methacrylamide and a small quantity of a cross-linking
2
agent ethylene glycol dimethacrylate. Water swelling of the membranes, mechanodynamical analysis,
density measurements, and ATR-FTIR studies were performed on the copolymers. High vacuum pressure
techniques were used to evaluate the flow of He, O , N , CO , CH , CH CH , and CH CH through these
2 2 2 4 3 3 2 2
membranes, and solubility, diffusivity, and permeability coefficients were determined. The effect of the
increase of the amount of methacrylamide in the copolymer on transport properties, glass transition,
fractional free volume, cohesive energy density, and specific interactions has been studied and is reported
in this work.
In tr od u ction
of the resulting polymer. Thus, in the case of aliphatic
side chains, increasing the length of the chain from 3
to 9 bonds lowers the Tg by almost 80 °C; similarly,
when the number of bonds in the oxyethylenic side chain
increases from 3 to 9, the Tg is lowered by almost 100
The development of polymeric materials with tailored
properties requires both accurate knowledge on prop-
erty-structure correlations and proficiency at synthe-
sizing polymers with predetermined structures. In the
field of species separation using polymeric membranes,
a lot of work has been done during the last three decades
in the synthesis of polymers with improved selectivity
°
C. In both cases, then, at room temperature, polymers
with long side chains are softer and more flexible and,
in accordance, their diffusion coefficients higher than
similar methacrylates with shorter pendant groups. An
important finding on the structure-property relation-
ship was that copolymers with units of different side
chain length behaved in the same way as the corre-
sponding homopolymer with the same average side
chain length regarding both transport properties and
1
-4
for given gases and vapors,
in the development of
and in the opening of
better membrane technology,3
,5-9
new research fields, such as facilitated transport for the
separation of very similar species (O2/N2, paraffin/
olefin), application of pervaporation for the separation
of azeotropic mixtures, polymer gels containing ionic
1
2
Tg values.
salts for ionic transport, etc.1
0,11
At this moment, areas
On the other hand, if the pendant group is not an
oxyethylenic linear chain but a crown ether with the
same number of oxyethylenic units, then flexibility is
not attained and consequently Tg is not lowered and
of interest in membrane technology include, for in-
stance, the ability of future membranes to operate in
chemical, thermal, or pressure conditions under which
they are unable now or the ability to separate very
similar species. Polymeric based new materials in which
inorganic or metallic components lead to the generation
of new properties is one of the fields recently developing.
In this context, a few years ago we began systematic
research on the synthesis and gas transport properties
of solid methacrylic polymers or copolymers in which
the structure is varied in order to (i) obtain basic
knowledge on the dependence of gas transport on the
structure of the methacrylate and (ii) synthesize meth-
acrylic polymers with tailored properties which can
constitute the matrix of new membrane materials.
As we showed in previous work, the transport proper-
ties are strongly dependent on the side groups present
in the methacrylate structure. To date we have studied
1
4
diffusion coefficients are not increased. We compared,
in particular, the behavior of poly(1,4,7,10-tetraoxacy-
clododecan-2-yl)methacrylate and its linear chain ana-
logue poly(2-[2-(2-ethoxyethoxy)ethoxy]ethyl methacryl-
ate). These crown ether methacrylic polymers have the
added interest of being able to coordinate metal ions in
hydrophobic solvents, originating the separation from
their associated anions and making their salts soluble
in these solvents. The use of such compounds for species
1
5-18
separation has been investigated recently.
Particu-
larly important is the possibility to develop membranes
in which facilitated transport of oxygen takes place.1
As we have seen, the mechanical properties of these
crown ether methacrylates are reasonable; they are not
fragile, and easy to handle in the solid state, and
therefore interesting in different transport fields.
9-22
1
2
13
the effect of introducing aliphatic or oxyethylenic side
chains of increasing length; the polarity of these chains
is very low, and the main effect of introducing these
chains as side groups is the possibility to enhance
flexibility and mobility and to lower the glass transition
One of the application fields in which methacrylate
membranes can be successfully used is the development
of water-swelled membranes able to diffuse oxygen
readily. None of the methacrylic polymers studied by
us to date could be used in such applications, as the
apolarity of the structure does not allow the swelling
in water to take place. The development of methacrylic
polymers with polar side chains which absorb water was
*
To whom correspondence should be addressed. E-mail:
ptiemblo@ictp.csic.es.
†
‡
Instituto de Ciencia y Tecnolog ´ı a de Pol ´ı meros (CSIC.
Universidad de Burgos.
1
0.1021/ma049945h CCC: $27.50 © 2004 American Chemical Society
Published on Web 04/24/2004

Macromolecules, Vol. 37, No. 11, 2004
Gas Transport Properties 4157
therefore envisaged. However, highly polar structures
are also very often rigid, fragile, and difficult to handle
in the solid state because of their poor mechanical
properties. The copolymerization of monomers with long
apolar side chains and monomers with highly polar
pendant groups seems to be a solution to obtain meth-
acrylic membranes which are both easy to handle in the
solid state and readily form gels when swelled with
water. In the following paper we present the results of
two such copolymers, one prepared with 2,3-dihydroxy-
propyl methacrylate (MAG) and 2-ethoxyethyl meth-
acrylate (EEMA) and the other with 2-hydroxyethyl
methacrylamide (HEMAM) and 2-ethoxethyl methacryl-
ate. As will be shown, not all polar monomers are useful
for our purposes and not all compositions of useful
copolymers are of interest.
F igu r e 1. Density of copolymers as a function of their
composition in membranes dried at 68 °C for 3 days.
Ta ble 1. P h ysicoch em ica l Ch a r a cter iza tion of th e
Cop olym er s
Exp er im en ta l Section
1
. P r ep a r a tion a n d Ch a r a cter iza tion of th e Mem -
EEMA
T (°C)
swelling %
g
br a n es. Ma ter ia ls. Methacryloyl chloride, 2-aminoethanol,
ethanedioldimethacrylate, 1,2-isopropylideneglycerol (IPG),
and triethylamine (Fluka) were used as received. The com-
mercial monomer 2-ethoxyethyl methacrylate (EEMA) (Ald-
rich, 99%) was purified by distillation under high vacuum. 2,2′-
Azobisisobutyronitrile (AIBN, Fluka, 98%) was recrystallized
from methanol and dried under high vacuum at room tem-
perature.
sample
molar % DMTA F (g/cm3) FFV H2O uptake
PEEMA
100
90
80
70
60
50
-16
47
75
99
139
189
1.114
1.116
1.107
1.101
1.095
1.091
0.158
0.162
0.174
0.180
0.191
0.195
0.8
2.7
20.4
52.4
71.8
152.7
MM-90/10
MM-80/20
MM-70/30
MM-60/40
MM-50/50
Syn th esis of th e Mon om er s HEMAM a n d MAG. The
monomer 2-hydroxyethyl methacrylamide (HEMAM) was
prepared by adding dropwise methacryloyl chloride to 2-ami-
noethanol dissolved in an aqueous sodium hydroxide solution.
The reaction was carried out at 0 °C under nitrogen atmo-
sphere. The monomer was purified by means of several
extractions with dichloromethane, obtaining a product with
purity higher than 99%, as determined by high-performance
liquid chromatography (HPLC) and gas chromatography.23
pyl methacrylate will be called hereafter MG-X/Y, where X
stands for the molar fraction of ethoxy ethyl and Y stands for
the molar fraction of 2,3-dihydroxypropyl methacrylate.
2. Mem br a n e Ch a r a cter iza tion . 2.1. F r a ction a l F r ee
Volu m e Estim a tion : Den sity Mea su r em en ts. The density
of the membranes derived was accomplished with a 5 mL Weld
pycnometer device at 25 °C. A 200 mg amount of the proper
membrane was introduced in the dried pycnometer, and the
solvent was added to the device. The density, which appears
in Figure 1 and Table 1, was obtained from the different
weights of pure solvent and the solvent-membrane system.
The density values were used to estimate the fractional free
volume (FFV) at 25 °C by applying
The monomer 2,3-dihydroxypropyl methacrylate (MAG) was
obtained by acid hydrolysis of their intermediate compound,
isopropylidene methacrylate, which was previously prepared
by reaction between methacryloyl chloride with 1,2-isopropyl-
ideneglycerol (IPG) in chloroform under nitrogen atmosphere
and using triethylamine to neutralize hydrogen chloride
evolved during the reaction. Methacryloyl chloride was added
dropwise into the solution of IPG over a period of 30 min, and
the reaction medium was kept cold with an ice-water bath.
The triethylamine salt was removed by filtration, and the
reaction mixture was washed several times with distilled
water. Finally, the crude product was distilled under vacuum
to give the monomer. The purity of all the compounds was
checked by high-performance liquid chromatography (HPLC)
V - 1.3Vw
FFV )
(1)
V
where V is the polymer specific volume and V
w
is the specific
van der Waals volume, which was estimated by using the
25
Hyperchem computer program, version 5.01.
2
.2. Rela xa tion s a n d Tr a n sition s: Mech a n od yn a m ica l
An a lysis. The mechanodynamical spectra of the copolymers
were obtained with a Thermal Instrument DMA 983 analyzer
in flexion mode from rectangular strips, typical dimension
being 8 × 4 × 0.6 mm. The temperature dependence of the
2
4
and NMR.
Syn th esis of th e Cop olym er s (Mem br a n es). The mem-
branes were prepared by radical polymerization of a mixture
of EEMA (ranging from 50 to 100 wt %) and MAG or HEMAM
using 1,2-ethanedioldimethacrylate as cross-linking agent and
AIBN (2.5 wt %) as initiator. The nominal cross-linking ratio,
i.e., the ratio between the number of moles of monomer to the
cross-linking agent, was 600 for MAG/EEMA membranes and
loss modulus was determined at 0.1 Hz, between -150 and
250 °C, at a heating rate of 5 °C min-1, and using a
deformation amplitude of 1 mm. Some selected spectra appear
in Figure 2. Figure 3 shows the glass-transition temperature
as a function of the weight percentage of EEMA.
2.3. Sp ecific In ter a ction s: ATR-F TIR. The composition
and specific interactions in these copolymers have been studied
by ATR-FTIR. The spectra were recorded on the membranes
3
20 for HEMAM/EEMA membranes. The addition of a cross-
linking agent is necessary in order to obtain membranes with
adequate mechanical properties. The reaction was carried out
in a silanized glass mould of 100 µm thickness in oxygen-free
atmosphere at 70 °C for 5 h. The network was extracted three
times in acetone/water (1/1) for a period of 72 h. Finally, the
network was dried at room temperature for 1 week, and the
residual solvent was eliminated under high vacuum at room
temperature.
Copolymers made of 2-ethoxyethyl methacrylate and 2-hy-
droxyethyl methacrylamide will be called hereafter MM-X/Y,
where X stands for the molar fraction of ethoxyethyl and Y
stands for the molar fraction of methacrylamide. Copolymers
made from 2-ethoxyethyl methacrylate and 2,3-dihydroxypro-
using a FTIR Perkin-Elmer Spectrum-One, 10 scans, and 2
cm-1 resolution. The carbonyl region (1600-1800 cm-1) and
the 3000-4000 cm-1 region are depicted in Figures 4 and 5,
and will be discussed in the following sections.
3. P er m ea tion Mea su r em en ts. The same lab-made per-
meator as in former work26 has been used. It consists of a gas
cell in the middle of which the polymer membrane is placed.
This membrane separates the upstream and downstream
chambers. For simplified equations relating the gas flow
through the membrane to the transport coefficients to be valid,
the downstream pressure has to be kept very low, negligible
as compared to the upstream. This is accomplished by thor-

4
158 Tiemblo et al.
Macromolecules, Vol. 37, No. 11, 2004
F igu r e 2. Mechanodynamical analysis of copolymers MM-
0/50 (O), MM-70/30 (4), and MM-90/10 (0) showing the glass
5
transition.
-
1
F igu r e 4. ATR-FTIR in the region 1600-1800 cm of the
MM copolymers.
F igu r e 3. Glass-transition temperature as a function of the
composition of the MM copolymers.
ough evacuation of the downstream pressure, prior to any
measurement, by means of a Edwards turbomolecular pump.
At the low-pressure side, a MKS Baratron type 627B absolute
pressure transducer measures the pressure increase, while
upstream a Gometrics pressure detector is used to control the
gas pressure at which the experiment is performed. The
Baratron 627B can be used in the pressure range 1-10-4 Torr.
The Baratron is connected via a MKS power supply/readout
unit to the PC, which records the pressure increase at given
time intervals. The whole setup is temperature controlled in
the range 5-80 °C by means of a water bath.
-
1
F igu r e 5. ATR-FTIR in the region 3000-3800 cm of the
Before measurements are performed, a vacuum is kept
overnight in order to remove any residual solvent from the
membrane and to attain a downstream pressure as low as
possible. Prior to the permeation experiment, measurement
of the pressure increase due to imperfect vacuum isolation of
the downstream chamber is recorded. This blank experiment
is then subtracted from the permeation experiment performed
immediately afterward in order to calculate the gas transport
coefficients from the corrected pressure curves. In this way
the pressure increase is related solely to the gas diffusing
across the membrane.
MM copolymers.
∞
Q(t) Dt
1
6
2
(-1) (
2
2
2
-Dn π t/l )
)
-
-
e
(2)
∑
2
2
2
lC1
l
π
n)1
n
The diffusion coefficient is directly obtained from the fitting,
and the solubility coefficient is directly proportional to C . The
permeability P is obtained as S‚D ) P. Calculation of the
uncertainties in the diffusion coefficients has been performed
in the following way
1
The permeability and diffusivity coefficients have been
calculated from the curves measuring the pressure increase
at the downstream. Equation 2, derived from integration of
Fick’s laws, relates the amount of diffusant per unit of area,
Q(t), traversing the membrane to the thickness of the mem-
brane, l, to the concentration of diffusant at the upstream side
of the membrane C and to the diffusion coefficient D. In fact,
1
only four terms of this equation are enough to correctly fit our
flow curves.
2
lꢀ(l)
l ꢀ(θ)
+
[ 3
|
| |
2
|
]
θ
6
θ
σ ) 100
(3)
D
where θ is the time lag. Uncertainties in permeability and
diffusivity are about 20% and 15%, respectively.

Macromolecules, Vol. 37, No. 11, 2004
Gas Transport Properties 4159
Ta ble 3. Hea t of Solu tion of th e Ga ses in P EEMA a n d
MM-70/30
gas
∆H
s
(kJ mol-1) PEEMA
∆H
s
(kJ mol-1) MM-70/30
O
N
CO
CH
CH
CH
2
2
2.1
1.2
-6.7
-6.7
-3
2
4
2
3
-24
-11.5
-8.4
-19.4
CH
CH
2
3
F igu r e 6. Diffusion coefficients of MM-70/30 in Arrhenius
coordinates. The actual activation energies appear in Table
2
. The code for gases is oxygen (9), nitrogen (O), methane (]),
carbon dioxide (1), ethane (b), and ethylene (4).
F igu r e 8. Diffusion coefficients as a function of the molar
percentage of EEMA in each MM copolymer. The code for gases
is oxygen (9), nitrogen (O), methane (]), carbon dioxide (1),
ethane (b), and ethylene (4).
F igu r e 7. Solubility coefficients of MM-70/30 in Arrhenius
coordinates. The actual heats of solution appear in Table 3.
The code for gases is oxygen (9), nitrogen (O), methane (]),
carbon dioxide (1), ethane (b), and ethylene (4).
Ta ble 2. P EEMA a n d MM-70/30 Diffu sion Activa tion
En er gies
gas
E
d
(kJ mol-1) PEEMA
E
d
(kJ mol-1) MM-70/30
O
N
CO
CH
CH
CH
2
2
15
18
19
33
39
18
46
52
43
F igu r e 9. Solubility of gases as a function on the molar
percentage of EEMA in each MM copolymer. The code for gases
is oxygen (9), nitrogen (O), methane (]), carbon dioxide (1),
ethane (b), and ethylene (4).
2
4
2
3
CH
CH
2
3
a permanent dipole and thus strongly interacts with
polar matrixes.
Resu lts
. Tem p er a t u r e Dep en d en ce of t h e Tr a n sp or t
1
2. Tr a n sp or t Coefficien ts a t 35 °C a n d 1 Ba r . The
flow of He, O2, N2, CO2, CH4, CH3CH3, and CH2CH2
through our five copolymers has been measured at 35
°C and 1 bar, and the diffusivity, permeability, and
solubility of each of the gases have been determined as
explained in the Experimental Section. The results are
shown in Figures 8-10 as a function of the molar
percentage of 2-ethoxyethyl methacrylate in each co-
polymer. In all five copolymers at 35 °C, D(He) > D(O2)
> D(N2) ≈ D(CO2) > D(CH4) > D(CH2CH2) > D(CH3-
CH3), an expected trend which is in accordance with the
size of the gases. Figure 11 shows the diffusion coef-
ficients in the five copolymers and in PEEMA as a
function of the critical volume of the gas. The correlation
between gas size and diffusivity is very good; the
membrane with the lowest diffusion coefficients is MM-
50/50, followed by MM-60/40, MM-70/30, and MM-80/
20 and PEEMA, which have almost exactly the same
diffusion values, and finally the highest diffusivity for
all gases is that of MM-90/10. This is also seen in Figure
8: as the molar percentage of 2-ethoxyethyl methacryl-
ate increases, so do diffusion coefficients, up to 80/20,
Coefficien ts. The temperature dependence of the trans-
port coefficients has been studied only in poly(2-ethoxy
ethyl methacrylate) and in copolymer MM-70/30. The
diffusion and solubility coefficients have been deter-
mined in the range 0-40 °C as our device does not
permit much higher temperature increases. As shown
in Figures 6 and 7, no unexpected behavior is presented
by the membranes: diffusivity increases with temper-
ature in a roughly Arrhenius fashion, and the temper-
ature dependence of the coefficient is stronger the larger
the diffusing gas (Figure 6 and Table 3). Solubility
increases on lowering the temperature and more so the
larger the interaction of the gas with the matrix (Figure
7
, Table 3). Comparison of the data from PEEMA and
copolymer MM-70/30 is in agreement with what we
know about their structure: the heats of solution in the
more apolar PEEMA matrix are endothermic for oxygen
and nitrogen, which are not strongly interacting gases,
and small and exothermic for carbon dioxide. In the case
of MM-70/30, all heats of solution are exothermic in
particular in the case of carbon dioxide, which possess

4
160 Tiemblo et al.
Macromolecules, Vol. 37, No. 11, 2004
F igu r e 12. Diffusion coefficients as a function of the fractional
free volume of each MM copolymer and of PEEMA. The code
for gases is oxygen (9), nitrogen (O), methane (]), carbon
dioxide (1), ethane (b), ethylene (4), and helium (*).
F igu r e 10. Permeability of the gases as a function of the
molar percentage of EEMA in each MM copolymer. The code
for gases is oxygen (9), nitrogen (O), methane (]), carbon
dioxide (1), ethane (b), ethylene (4), and helium (*).
MG when unswelled were very poor, which makes the
handling of the samples difficult because of their fragil-
ity as the amount of 2,3-hydroxypropyl methacrylate
increased. From a practical point of view it is very
desirable that membranes show both good mechanical
properties in the solid state and high swelling ratio, and
therefore, series MG has been for the moment disre-
garded. On the other hand, the series MM, even with
methacrylamide molar ratios as high as 50%, has very
good mechanical properties in the solid state and is
readily water swelled, which is very important as
diffusion coefficients in hydrogels are mostly dependent
on the swelling ratio.
F igu r e 11. Diffusion coefficients of the gases in the five
copolymers and in PEEMA as a function of their critical
volume. The symbol code for the copolymers is MM-50/50 (3),
MM-60/40 (0), MM-70/30 (3), MM-80/20 (]), MM-90/10 (O),
and PEEMA (*).
Discu ssion
Diffu sion a n d F r ee Volu m e. Routine characteriza-
tion of membranes aimed at gas transport involves
mainly determination of the free volume and chain
mobility in the bulk, two structural features related to
diffusivity, and determination of specific interactions,
which are related to solubility. As free volume and chain
mobility increase, so does diffusivity, for this property
is determined by the rate at which holes of adequate
size are generated in the matrix. Figure 12 shows the
diffusion coefficients of all the studied gases in the six
membranes as a function of the fractional free volume.
Surprisingly, on going from MM-50/50 to MM-80/20, as
FFV decreases, diffusivity increases strongly; this is
certainly not the usual behavior. On the other hand, the
dependency shown by the diffusion coefficients of all the
gases as a function of the glass-transition temperature
of the membrane (Figure 13) follows the trend usually
found in amorphous materials.
Ta ble 4. Tr a n sp or t Coefficien ts of EEMA/MAG a n d
EEMA/HEMAM a t 35 °C a n d 1 ba r
8
4
D × 10
S × 10
-3
P
2
-1
(cm3 (STP) cm cmHg-1
(
cm
s
)
)
(barrer)
sample
O
2
N
2
CO
2
O
2
N
2
CO
2
O
2
N
2
CO
2
MM-50/50 2.7 1.4 1.2
MG-50/50 4.5 1.2 1.9
11.2
5.4
10.8
10
130
89
0.3 0.15 1.56
0.24 0.12 1.74
then diffusivity does not change much with a further
increase of 2-ethoxyethyl methacrylate content.
Figure 9 shows the solubility of the studied gases in
the six membranes. Solubility decreases gradually as
the content of 2-ethoxyethyl methacrylate increases, the
only noteworthy feature being the fact that, except for
carbon dioxide, in poly(2-ethoxyethyl methacrylate)
gases have a higher solubility than in any of the
copolymers. It is not surprising that the presence of a
polar monomer such as 2-hydroxy ethyl methacrylamide
should increase the solubility of the gases in the matrix.
The order of solubility coefficients is also as expected:
S(CO2) > S(CH2CH2) ≈ S(CH3CH3) > S(CH4) > S(O2)
Figure 14 shows the diffusion coefficient of oxygen as
a function of FFV for a number of polymers studied by
2
7-32
us or others.
Though scatter of the data exists, there
is an inverse correlation between fractional free volume
and diffusivity given by the well-known Fujita equa-
3
3
tion
>
S(N2). Permeability, the product of diffusivity and
solubility, varies as shown in Figure 10.
-Hydroxyethyl methacrylamide has not been the only
-
B/FFV
2
D ) Ae
(4)
polar monomer tested. In fact, we began by synthesizing
a series of copolymers of EEMA and 2,3-hydroxypropyl
methacrylate (series MG). The swelling ratios of copoly-
mers MM-50/50 and MG-50/50 are, respectively, 153%
and 54%, and their transport coefficients in the solid
state are compared in Table 4. Both copolymers are
water swelled, more so MM-50/50, and the transport
coefficients in the solid state are very similar in both of
them. However, the mechanical properties of the series
According to free-volume theories, B ) γv*/ vm, where
γ accounts for the overlap in free volume and varies
from 0.5 to 1, v* is the minimum critical volume needed
to accommodate a diffusing molecule, and vm is the
average free volume. As a matter of fact, our five
copolymers and PEEMA do not show especially anoma-
lous diffusion coefficients when compared to other
polymers. It is not the values in themselves but the

Macromolecules, Vol. 37, No. 11, 2004
Gas Transport Properties 4161
F igu r e 16. Diffusivity of oxygen in a set of polymers as a
function of the ratio between their glass transition and
fractional free volume at 25 °C. Membranes measured under
the glass transition are represented with open symbols,
membranes measured over their glass transition are repre-
sented with solid symbols, and membranes studied in this
work are represented with a star.
F igu r e 13. Diffusion coefficients as a function of the glass-
transition temperature of each of the MM copolymers and of
PEEMA. The code for gases is oxygen (9), nitrogen (O),
methane (]), carbon dioxide (1), ethane (b), ethylene (4), and
helium (*).
As shown in the mechanodynamical spectra of Figure
, there is only one Tg in the copolymers and no block
2
structures or phase separation seems to exist; the
structure of the membranes is homogeneous. PEEMA
and MM-90/10 are measured over, and at their Tg and
therefore their rubbery state could explain their high
diffusivity. However, MM-80/20 has a Tg of 75 °C, and
the rest of the copolymers show even higher Tg; thus,
MM-70/30 to MM-50/50 are glasses at the measuring
temperature.
Diffu sion a n d Molecu la r In ter a ction s. A look at
the FTIR spectra (Figures 4 and 5) shows that as the
ratio between HEMAM and EEMA increases, the IR
band corresponding to the CdO stretching of the amide
group shifts to lower wavenumber and the band due to
the stretching of the associated NH group increases with
respect to the free NH group. In fact, the shift to lower
wavenumber of νamide(CdO) is due to the increase in a
F igu r e 14. Diffusivity of oxygen in a set of polymers as a
function of their fractional free volume at 25 °C. Membranes
measured under the glass transition are represented with open
symbols, membranes measured over their glass transition are
represented with solid symbols, and membranes studied in this
work are represented with a star.
-
1
band at 1634 cm of associated νamide(CdO) and pro-
-1
gressive disappearance of the band at 1650 cm , related
to free or less associated νamide(CdO). In addition, a
-
1
shoulder appears at ca. 1708 cm due to the existence
of EEMA carbonyls involved in hydrogen bonding, and
this shoulder is more intense the higher the amount of
HEMAM in the copolymer. Then, as the amount of polar
methacrylamide increases, the inter- or intramolecular
interactions between the copolymer units, via hydrogen
bonding between NH and CO groups, increases, leading
to a stiffer molecular structure. This is the origin of the
strongly positive deviation of Tg shown in Figure 3 and
most probably also of the decrease in diffusivity shown
in the glassy copolymers MM-80/20 to MM-50/50. That
MM-90/10 shows the normal trend in the correlation
between FFV and D with respect to PEEMA is probably
due to the fact that when considerable cooperative chain
motions exist, the intermolecular interactions must be
partly or totally released; in fact, the IR spectrum of
MM-90/10 is very different from that of the other
copolymers, both in the position of the ν(CdO)amide and
in the very low intensity of the band due to interacting
NH groups. Therefore, as the amount of HEMAM in the
copolymer increases, the structure changes from flexible
and apolar to stiff and polar and as a result diffusivity
decreases even if FFV increases.
F igu r e 15. Diffusivity of oxygen in a set of polymers as a
function of their glass transition. Membranes measured under
the glass transition are represented with open symbols,
membranes measured over their glass transition are repre-
sented with solid symbols, and membranes studied in this
work are represented with a star.
trend with FFV shown in Figure 12, which will be
explained. It seems that as the composition of the
copolymer changes and the amount of polar monomer
increases, some other structural changes apart from
FFV take place, which causes the decrease of diffusivity
even if FFV is increasing.
Diffu sion a n d Gla ss Tr a n sition . Figure 15 shows
the evolution of diffusivity with glass-transition tem-
peratures in the same polymers as in Figure 13. In this
case, the trend followed by our copolymers is the same
as that followed by polymers as a whole: as Tg in-
creases, the diffusivity at a given measuring tempera-
ture decreases, and this effect is more conspicuous when
Tg is under the measuring temperature than when it is
over. Finally, Figure 16 shows the correlation between
D and Tg/FFV, and again the five copolymers lie in the
normal range of values.
Diffu sion a n d Coh esive En er gy Den sity. In 1954
Meares proposed that the diffusion of a penetrant
through a glassy matrix could be viewed as a jump
motion between neighboring holes through channels
large enough to constitute an adequate passageway.33
This is also the picture derived from MD simulation of

4
162 Tiemblo et al.
Macromolecules, Vol. 37, No. 11, 2004
F igu r e 18. Logarithmic deviation between the oxygen diffu-
sion coefficients as a function of the CED of each MM
copolymer. Open symbols correspond to copolymers measured
F igu r e 17. Diffusion coefficients as a function of cohesive
energy density of each of the MM copolymers and of PEEMA.
The code for gases is oxygen (9), nitrogen (O), methane (]),
carbon dioxide (1), ethane (b), and ethylene (4).
under their T
g
; solid symbols correspond to copolymers mea-
sured over their T
g
.
the diffusional process. Thus, the diffusional process is
governed by both the number and size of the holes and
the energy required to open a passageway between
them. The number and size of the “holes” in the
materials is quantified by determining the free volume
in the matrix, while the activation energy of the channel
opening was equated by Meares to the product of the
passageway volume and the polymer cohesive energy
density CED
coefficient and the logarithm diffussion coefficient of the
corresponding fit) vs CED of the different polymers
yielded very reasonable straight lines for a number of
gases. The same data treatment has been performed
with our data, representing the logarithmic deviation
of the oxygen diffusion coefficient as obtained from
Figure 14. This is represented in Figure 18. As in the
37
work cited before, the good correlation shown in Figure
1
8 strongly supports that the scatter of the data when
representing log D as a function of the inverse of FFV
is clearly related to the different CEDs of the polymeric
matrixes studied. This scatter due to CED does not
mean that free volume theories have to be abandoned
in the interpretation of transport data; as explained by
Nagel et al., the dependence on CED can be contained
in the prefactor of the Fujita equation.
1
4
2
E ) πd R‚CED‚N
(5)
D
A
In this equation the passageway is taken as a cylinder
of the same diameter d as the penetrant and of length
R, which is the length of the diffusional step. Cohesive
energy density is, together with the fractional free
volume, a parameter strongly related to the diffusional
process.3
Figure 17 shows the diffusion coefficient of the gases
studied in this work as a function of the CED of each of
our polymers. Equation 5 proposes a relationship be-
tween ED and CED and not between D and CED;
however, there is experimental evidence33 that D0 and
ED are directly related, and therefore, the correlation
between ED and CED should also qualitatively hold for
D and CED. The CED of our polymers has been
3
7
As for applications, all the methacrylic copolymers
from MM-80/20 to MM-50/50 have good mechanical
properties in the solid state, are not fragile at room
temperature, show moderately high glass-transition
temperatures, form transparent membranes, and have
high swelling ratio. These solid methacrylic matrixes
are appropriate to be used in the development of soft
0,34,35
38
contact lenses; thus, it is envisaged to measure oxygen
permeability in the corresponding hydrogels.
Con clu sion s
3
6
estimated by a group contribution method. The diffu-
sion coefficients of the five copolymers decrease as their
CED increases (Figure 17); the progressive incorpora-
tion of 2-hydroxyethyl methacrylamide in the copolymer
makes the intermolecular interactions stronger and thus
the structure stiffer and characterized by higher CED
values. Under these conditions the creation of a channel
between microcavities becomes progressively more dif-
ficult. By stiffer it is meant both that the glass transition
shifts to higher temperatures and that less sub-Tg
relaxations are found. These local sub-Tg motions are
known to contribute largely to the molecular diffusion
in glasses, as, for example, they make the creation of a
channel or passageway easier. It is noteworthy that as
for the effect of the matrix CED on the diffusion
coefficients of the gases, the homopolymer PEEMA does
The transport properties of a series of methacrylic
copolymers prepared by radical polymerization of the
monomers 2-ethoxyethyl methacrylate and 2-hydroxy-
ethyl methacrylamide and a small quantity of a cross-
linking agent, ethylene glycol dimethacrylate, have been
studied. Water swelling of the membranes, mechano-
dynamical analysis, density measurements, and ATR-
FTIR studies have been performed on the copolymers.
The cohesive energy density has also been estimated.
As the amount of monomer 2-[(methacryloyloxy)amino]-
ethanol increases, FFV, CED, swelling ratio, and Tg
increase while diffusivity and permeability decrease
strongly. A linear relationship exists between the
logarithmic deviation of the diffusion coefficients and
CED. The development of strong specific intermolecular
interactions involving the amide groups and accordingly
a stiffer chain structure are responsible for the decrease
in diffusivity and the large positive deviation from the
Fox equation of the studied copolymers.
not seem to belong to the same series as the other five
coplymers. In recent work,37 it has been proposed that
the scatter in the correlation between diffusion coef-
ficients and fractional free volume is related to the CED
of each polymeric matrix. In fact, a representation of
the logarithmic deviation (defined as the difference
between the logarithm of the experimental diffusion
Even if the structure becomes stiffer, copolymers with
a large amount of 2-hydroxyethyl methacrylamide show
good mechanical properties in the solid state together

Macromolecules, Vol. 37, No. 11, 2004
Gas Transport Properties 4163
with a high swelling ratio, which makes them adequate
for the development of contact lenses.
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Polymer 2001, 42, 7395.
(
(
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