Radiation synthesis of low swelling acrylamide based hydrogels and ...

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Nuclear Instruments and Methods in Physics Research B 265 (2007) 375–378
NIM B
Beam Interactions
with Materials & Atoms
www.elsevier.com/locate/nimb
Radiation synthesis of low swelling acrylamide based hydrogels
and determination of average molecular weight between cross-links
Naim Mahmudi a , Murat Sßen b, *, Stojan Rendevski c , Olgun Güven b
a State University of Tetovo, Faculty of Natural Science and Mathematics, 1200 Tetovo, Former Yugolav Republic of Macedonia
b Hacettepe University, Department of Chemistry, Beytepe, 06532 Ankara, Turkey
c Institute of Physics, Faculty of Natural Sciences and Mathematics, University ‘‘Ss. Cyril and Methodius’’, Gazi Baba, bb., Skopje, Republic of Macedonia
Available online 8 September 2007
Abstract
A comparative analysis of determination of cross-link density (m e ) of hydrogels by using swelling tests and mechanical measurements
has been made. Poly(acrylamide/methacrylamide) P(AAm/MAAm) and poly(acrylamide/hydroxyethyl methacrylate) P(AAm/HEMA)
hydrogels were prepared by using gamma rays and used as model hydrogel systems. The uniaxial compression test was applied to cylindrical
gel samples in the swollen state at pH 7. Stress–strain curves of hydrogels were evaluated to calculate the shear modulus values.
The average molecular weight between cross-links ðM c Þ and m e obtained from mechanical measurements were significantly different than
the values obtained from swelling experiments. Large differences were attributed to the uncertainty on the value of the v parameter used
in the Flory–Rehner equation. ±1% change in this parameter doubled or reduced the M c value of hydrogel to half value.
Ó 2007 Elsevier B.V. All rights reserved.
PACS: 61.25.Hq; 82.35.Lr; 81.40.Wx
1. Introduction
* Corresponding author. Tel./fax: +90 312 2977989.
E-mail address: msen@hacettepe.edu.tr (M. Sßen).
Highly cross-linked polymers are generally chemically
prepared from their monomers or polymers in the presence
of cross-linking agents. It is also well known that ionizing
radiation induced simultaneous polymerization and crosslinking
has some advantages over chemical cross-linking
and it is widely used in recent years for the synthesis of various
hydrogels for biomedical applications.
One of the basic parameters that describe the structure
of a hydrogel network is the average molecular weight
between cross-links or cross-link density of the network.
Several theories have been proposed to calculate the average
molecular weight between cross-links. In the highly
swollen state, the constrained junction theory indicates that
a real network exhibits properties closer to those of the
phantom network model. The following equation derived
from the phantom network model has been used for nonionic
polymeric networks known as Flory–Rehner equation
[1,2]
ð1 2=/ÞV 1 m 2=3
2r
M c ¼
m1=3 2m
mðlnð1
m 2m Þþm 2m þ vm 2 2mÞ : ð1Þ
Here, M c is the average molecular weight of network
chains, m 2m is the polymer volume fraction of cross-linked
polymer in swollen gel, V 1 is the molar volume of the swelling
agent, v is the polymer–solvent interaction parameter,
/ is the functionality, m is the specific volume of the polymer,
and m 2r is the polymer volume fraction in the relaxed
state, i.e. after cross-linking but before swelling.
Rubberlike elasticity and uniaxial deformation experiments
have been used for the characterization of various
types of cross-linked polymeric systems. For uniaxial
deformation, the statistical theories of rubber elasticity
yield Eq. (2) for gaussian chains.
f ¼ Gðk k 2 Þ; ð2Þ
where f is the force acting per unit cross-sectional area of
the undeformed gel specimen, G is the elastic modulus of
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.nimb.2007.09.007

376 N. Mahmudi et al. / Nucl. Instr. and Meth. in Phys. Res. B 265 (2007) 375–378
the sample, and k is the deformation ratio (deformed
length/initial length). For a homogenous network of
gaussian chains, the elastic modulus of gel swollen to
equilibrium, G, is related to the network cross-link density
by Eq. (3) [3].
G ¼ A q M c
RT m 2=3
2r m1=3 2m ;
where q is the polymer density. The prefactor A, equals 1
for an affine network and (1 2//) for a phantom
network.
The effective cross-link density, m e , of a cross-linked
structure can be obtained from the results of compressive
strain measurements using Eqs. (2)–(4):
M c ¼ q m e
:
In our previous studies we have shown that simple compression
analyses and equations derived from phantom
network theory can be used for the determination of effective
cross-link density of highly swollen hydrogels without
needing some polymer-solvent based parameters as in the
case of swelling [4].
In this study we compared swelling and mechanical
analyses for the determination of cross-link density of
hydrogels prepared by ionizing radiation with relatively
low degree of swelling.
2. Experimental
Four components were used in the preparation of acrylamide–methacrylamide–methylenebisacrylamide
(AAm/
MAAm/MBA/water) and acrylamide–2-hydroxyethyl
methacrylate–methylenebisacrylamide (AAm/HEMA/
MBA/water) hydrogels, namely acrylamide, methacrylamide,
and 2-hydroxyethyl methacrylate as monomers and
methylenebisacrylamide as the cross-linking agents and
water as dispersing medium. The mass proportion of the
monomers in the initial mixtures is summarized in Table 1.
The AAm/MAAm/MBA/water and AAm/HEMA/
MBA/water solutions were placed in PVC straws of
3 mm diameter and irradiated at 15 kGy and 6.6 kGy
doses, respectively. They have been determined to be minimum
doses corresponding to complete conversion. Fresh
ð3Þ
ð4Þ
hydrogels obtained in long cylindrical shapes were cut into
pieces 3–4 mm in length. Unreacted monomer and uncrosslinked
polymers were removed by washing the gels for two
days in distilled water. They were dried in vacuum oven in
315 K. Percentage gelation i.e. percentage conversion of
monomers and cross-linking agent into insoluble networks,
was based on the total weight of the cross-linking agent
and monomers in the initial mixture. Washed and dried
hydrogels were left to swell in distilled water at room temperature
to determine the parameters of swelling. Swollen
gels removed from the water bath at regular intervals were
dried superficially with filter paper, weighed and immediately
placed in the same bath still in equilibrium swelling
state. Elastic properties and shear modulus of hydrogels
were determined by using a Zwick Z010 model Universal
Testing Instrument and uniaxial compression module.
The crosshead speed was 5 mm/min.
3. Results and discussion
3.1. Swelling behavior of hydrogels
For the characterization of the network structure and
determination of effective cross-link density of prepared
hydrogels their swelling behavior at pH 7 was first investigated.
The percentage swelling of hydrogels was calculated
by the following equation;
S%ðmÞ ¼½ðm t m o Þ=m o Š100;
where m t and m o are the weights of the swollen and dry gels
respectively.
Representative swelling curves for AAm/MAAm/MBA
systems are given in Fig. 1. Very similar curves were
obtained for the other hydrogel systems. The % equilibrium
swelling values of all prepared hydrogels were collected
in Table 2. As can be seen from this table %
swelling of hydrogels is lower than 550%. The equilibrium
value of swelling was used in each case to calculate the volume
fraction of polymer (m 2m ) by using Eq. (5) given below
where q and q w are the densities of dry gel and water. W is
the weight fraction of polymer in swollen gel.
1=m 2m ¼ 1 þ q=q w ðw 1 1Þ : ð5Þ
Table 1
Mass composition of monomers and cross-linking agent in the feed solutions and corresponding abbreviations used for the hydrogels
Gel code
Mass of monomers, cross-linking agent and water
AAm (g) MAAm (g) HEMA (ml) MBA (%) a Water (ml)
0.2AAm0.2MAAm2MBA 0.2 0.2 – 0.5 1
0.2AAm0.2MAAm4MBA 0.2 0.2 – 1.0 1
0.2AAm0.2MAAm6MBA 0.2 0.2 – 1.5 1
1AAm1HEMA0.05MBA 1.0 – 1.0 0.05 2
1AAm1HEMA0.1MBA 1.0 – 1.0 0.1 2
1AAm1HEMA0.2MBA 1.0 – 1.0 0.2 2
1AAm1HEMA0.4MBA 1.0 – 1.0 0.4 2
1AAm1HEMA0.8MBA 1.0 – 1.0 0.8 2
a MBA(%) equal to (mass of MBA/mass of AAm + mass of MAAm or HEMA) * 100.

N. Mahmudi et al. / Nucl. Instr. and Meth. in Phys. Res. B 265 (2007) 375–378 377
% S
600
500
400
300
200
100
1: 0.2AAm0.2MAAm2MBA
2: 0.2AAm0.2MAAm4MBA
3: 0.2AAm0.2MAAm6MBA
0
0 500 1000 1500 2000 2500
Time (min)
Fig. 1. Swelling degree versus time for AAm/MAAm/MBA hydrogels.
The v parameter of hydrogels is generally calculated by
using the following equation [5].
v ffi 1=2 þ m 2m =3;
ð6Þ
which is the result of an assumption as M c goes to infinity
which makes the denominator in Eq. (1) equal to zero i.e.
lnð1 m 2m Þþm 2m þ vm 2 2m
¼ 0: ð7Þ
Serial expansion of the logarithmic term lnð1 m 2m Þ¼
ð m 2m þ m 2 2m =2 m3 2m =3 Þ for small m 2m values gives
the following equation;
m 2 2m =2 m3 2m =3 þ vm2 2m
¼ 0; ð8Þ
upon rearrangement is converted into Eq. (6). This equation
shows that v parameter approaches to 0.5 for small
m 2m values.
In this study, we have calculated M c ðM cðsÞ Þ values of
hydrogels by using m 2m and v obtained from Eq. (6) and
other relevant parameters from swelling experiments and
collected the results in Table 2. To account for calculations
of these parameters from swelling experiments the subscript
‘‘s’’ was used throughout in the abbreviations.
3.2. Mechanical properties of hydrogels and determination of
M c
For the investigation of the effect of MBA on the
mechanical properties of AAm/MAAm and AAm/HEMA
1
2
3
hydrogels and for the determination of true M c ðM cðmÞ Þ and
v parameter, uniaxial compression was applied by using the
Universal Testing Instrument. The subscript ‘‘m’’ was used
to indicate that these parameters are calculated from
mechanical measurements. Typical stress–strain curves of
hydrogels were given in Fig. 2. As can be seen from the figure,
the magnitude of stress increased with increasing MBA
content in the hydrogel for a given strain. Shear modulus
values of hydrogels were calculated by using elastic deformation
theory and Eq. (2). [1]. When the equation is
applied to the initial stages of deformation, plots of f versus
k k 2 yield straight lines, Fig. 3 where k is the deformation
ratio and equal to L/L o . L o and L are the lengths of
the undeformed and deformed hydrogels during compression,
respectively. The G value was calculated from the
slope of the lines and listed in Table 2. By using G values
and other relevant experimental parameters, M c and m e
were calculated from Eqs. (3) and (4) and collected in Table
2. As can be seen from Table 2. the magnitudes of M c calculated
from mechanical properties are different from those
obtained by using swelling experiments. Large difference
was attributed to using incorrect v parameter in the modified
Flory–Rehner equation. The actual v parameters were
calculated by using M cðmÞ values and Eq. (1). Recalculated
v parameters (v m ) and the differences between v s and v m are
also given in Table 2. For the investigation of the effect of v
parameter on the M c values the theoretical M c values were
Stress, kPa
150
125
100
75
50
25
1: 0.2AAm0.2MAAm2MBA
2: 0.2AAm0.2MAAm4MBA
3: 0.2AAm0.2MAAm6MBA
0
0 5 10 15 20 25 30
Strain, %
Fig. 2. Strain versus stress curves of AAm/MAAm/MBA hydrogels.
3
2
1
Table 2
Network properties and cross-link densities of hydrogels
Sample %S v s M cðsÞ (g/mol) M cðmÞ (g/mol) v m m e(s) (mol/cm 3 ) m e(m) (mol/cm 3 ) v s v m G (kPa)
0.2AAm/0.2MAAm/2MBA 540 0.54 39,600 6790 0.52 3.29E 05 1.92E 04 0.02 29.0
0.2AAm/0.2MAAm/4MBA 360 0.55 9750 2970 0.54 1.32E 04 4.35E 04 0.01 77.1
0.2AAm/0.2MAAm/6MBA 300 0.56 6230 2880 0.55 2.09E 04 4.51E 04 0.01 87.3
1AAm/1HEMA/0.05MBA 410 0.55 14,385 7745 0.55 9.02E 05 1.68E 04 0.00 46.7
1AAm/1HEMA/0.1MBA 380 0.56 11,915 6780 0.55 1.08 E 04 1.91E 04 0.01 53.9
1AAm/1HEMA/0.2MBA 370 0.56 10,020 6030 0.55 1.29 E 04 2.15E 04 0.01 62.4
1AAm/1HEMA/0.4MBA 330 0.56 8805 4780 0.55 1.46 E 04 2.68E 04 0.01 79.4
1AAm/1HEMA/0.8MBA 280 0.57 5450 3660 0.56 0.000237 3.52E 04 0.01 108.0

378 N. Mahmudi et al. / Nucl. Instr. and Meth. in Phys. Res. B 265 (2007) 375–378
Stress, kPa
150
125
100
75
50
25
1: 0.2AAm0.2MAAm2MBA
2: 0.2AAm0.2MAAm4MBA
3: 0.2AAm0.2MAAm6MBA
3
2
1
and Table 2 for the sample of (0.2AAm/0.2MAAm/
2MBA) composition, only a difference of 0.02 in v parameter
caused 4.8-fold increase in the M c value. For the
second (0.2AAm/0.2MAAm/4MBA) and third (0.2AAm/
0.2MAAm/6MBA) samples a change in v parameter by
0.01 caused 2.3 and 1.2 fold increase in M c , respectively.
Also, for the (1AAm/1HEMA/0.05MBA), (1AAm/
1HEMA/0.1MBA), (1AAm/1HEMA/0.2MBA), 0.01 difference
in v parameter caused for 0.85; 0.75; 0.66 fold
increase in M c :
Fig. 3. k
M c
x 10 3
40
30
20
10
0
0.00 0.25 0.50 0.75 1.00 1.25
-(λ-λ -2 )
k 2 versus stress curves of AAm/MAAm/MBA hydrogels.
1: 0.2AAm0.2MAAm2MBA
2: 0.2AAm0.2MAAm4MBA
3: 0.2AAm0.2MAAm6MBA
1
2
3
4. Conclusions
The aim of this study was to determine molecular weight
between cross-links and effective cross-link density of radiation
synthesized AAm/MAAm/MBA and AAm/HEMA/
MBA hydrogels by using data from swelling analyses and
compression tests. Values calculated from mechanical tests
were found to be quite different from those obtained by
using swelling experiments. Large difference was attributed
to the incorrect value of the v parameter used in the modified
Flory–Rehner equation. These results clearly show
that for reliable determination of cross-link density of
hydrogels by swelling experiments the v parameter must
be known reliably or determined experimentally.
References
0
0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57
χ
Fig. 4. The change of M c with v value of AAm/MAAm/MBA hydrogels.
obtained, Fig. 4 by using v and experimentally obtained
polymer based parameter. As can be seen from Fig. 4
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