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Radiation synthesis of low swelling acrylamide based hydrogelsand determination of average molecular weight between cross-links

Naim Mahmudi a, Murat Sen b,*, Stojan Rendevski c, Olgun Guven b

a State University of Tetovo, Faculty of Natural Science and Mathematics, 1200 Tetovo, Former Yugolav Republic of Macedoniab 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 (me) of hydrogels by using swelling tests and mechanical measurementshas 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 cylin-drical 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 ð M cÞ and me obtained from mechanical measurements were significantly different thanthe values obtained from swelling experiments. Large differences were attributed to the uncertainty on the value of the v parameter usedin the Flory–Rehner equation. ±1% change in this parameter doubled or reduced the M c value of hydrogel to half value. 2007 Elsevier B.V. All rights reserved.

PACS : 61.25.Hq; 82.35.Lr; 81.40.Wx

1. Introduction

Highly cross-linked polymers are generally chemicallyprepared from their monomers or polymers in the presenceof cross-linking agents. It is also well known that ionizingradiation induced simultaneous polymerization and cross-linking has some advantages over chemical cross-linkingand it is widely used in recent years for the synthesis of var-ious hydrogels for biomedical applications.

One of the basic parameters that describe the structure

of a hydrogel network is the average molecular weightbetween cross-links or cross-link density of the network.Several theories have been proposed to calculate the aver-age molecular weight between cross-links. In the highlyswollen state, the constrained junction theory indicates thata real network exhibits properties closer to those of thephantom network model. The following equation derivedfrom the phantom network model has been used for non-

ionic polymeric networks known as Flory–Rehner equa-tion [1,2]

M c ¼ ð1 2=/ÞV 1m

2=32r m

1=32m

m lnð1 m2mÞ þ m2m þ vm22mð Þ

: ð1Þ

Here, M c is the average molecular weight of networkchains, m2m is the polymer volume fraction of cross-linkedpolymer in swollen gel, V 1 is the molar volume of the swell-ing agent, v is the polymer–solvent interaction parameter,/ is the functionality, m is the specific volume of the poly-

mer, and m2r is the polymer volume fraction in the relaxedstate, i.e. after cross-linking but before swelling.Rubberlike elasticity and uniaxial deformation experi-

ments have been used for the characterization of varioustypes of cross-linked polymeric systems. For uniaxialdeformation, the statistical theories of rubber elasticityyield Eq. (2) for gaussian chains.

f ¼ G ðk k2Þ; 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 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.nimb.2007.09.007

* Corresponding author. Tel./fax: +90 312 2977989.E-mail address: [email protected] (M. Sen).

www.elsevier.com/locate/nimb

Available online at www.sciencedirect.com

Nuclear Instruments and Methods in Physics Research B 265 (2007) 375–378

N BBeam Interactions

with Materials & Atoms

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the sample, and k is the deformation ratio (deformedlength/initial length). For a homogenous network of gaussian chains, the elastic modulus of gel swollen toequilibrium, G , is related to the network cross-link densityby Eq. (3) [3].

G ¼ A q

M c RT m

2=3

2r m

1=3

2m ; ð3Þ

where q is the polymer density. The prefactor A, equals 1for an affine network and (1 2//) for a phantomnetwork.

The effective cross-link density, me, of a cross-linkedstructure can be obtained from the results of compressivestrain measurements using Eqs. (2)–(4):

M c ¼ q

me

: ð4Þ

In our previous studies we have shown that simple com-pression analyses and equations derived from phantom

network theory can be used for the determination of effec-tive cross-link density of highly swollen hydrogels withoutneeding some polymer-solvent based parameters as in thecase of swelling [4].

In this study we compared swelling and mechanicalanalyses for the determination of cross-link density of hydrogels prepared by ionizing radiation with relativelylow degree of swelling.

2. Experimental

Four components were used in the preparation of acryl-amide–methacrylamide–methylenebisacrylamide (AAm/MAAm/MBA/water) and acrylamide–2-hydroxyethylmethacrylate–methylenebisacrylamide (AAm/HEMA/MBA/water) hydrogels, namely acrylamide, methacryla-mide, and 2-hydroxyethyl methacrylate as monomers andmethylenebisacrylamide as the cross-linking agents andwater as dispersing medium. The mass proportion of themonomers 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 kGydoses, respectively. They have been determined to be min-imum doses corresponding to complete conversion. Fresh

hydrogels obtained in long cylindrical shapes were cut intopieces 3–4 mm in length. Unreacted monomer and uncross-linked polymers were removed by washing the gels for twodays in distilled water. They were dried in vacuum oven in315 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 agentand monomers in the initial mixture. Washed and driedhydrogels were left to swell in distilled water at room tem-perature to determine the parameters of swelling. Swollengels removed from the water bath at regular intervals weredried superficially with filter paper, weighed and immedi-ately placed in the same bath still in equilibrium swellingstate. Elastic properties and shear modulus of hydrogelswere determined by using a Zwick Z010 model UniversalTesting 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 anddetermination of effective cross-link density of preparedhydrogels their swelling behavior at pH 7 was first investi-gated. The percentage swelling of hydrogels was calculatedby the following equation;

S %ðmÞ ¼ ½ðmt moÞ=mo100;

where mt and mo are the weights of the swollen and dry gels

respectively.Representative swelling curves for AAm/MAAm/MBAsystems are given in Fig. 1. Very similar curves wereobtained for the other hydrogel systems. The % equilib-rium swelling values of all prepared hydrogels were col-lected in Table 2. As can be seen from this table %swelling of hydrogels is lower than 550%. The equilibriumvalue of swelling was used in each case to calculate the vol-ume fraction of polymer (m2m) by using Eq. (5) given belowwhere q and q

w are the densities of dry gel and water. W is

the weight fraction of polymer in swollen gel.

1=m2m ¼ 1 þ q=qwðw1 1Þ

: ð5Þ

Table 1Mass 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 10.2AAm0.2MAAm4MBA 0.2 0.2 – 1.0 10.2AAm0.2MAAm6MBA 0.2 0.2 – 1.5 11AAm1HEMA0.05MBA 1.0 – 1.0 0.05 21AAm1HEMA0.1MBA 1.0 – 1.0 0.1 21AAm1HEMA0.2MBA 1.0 – 1.0 0.2 21AAm1HEMA0.4MBA 1.0 – 1.0 0.4 21AAm1HEMA0.8MBA 1.0 – 1.0 0.8 2

a MBA(%) equal to (mass of MBA/mass of AAm + mass of MAAm or HEMA) * 100.

376 N. Mahmudi et al. / Nucl. Instr. and Meth. in Phys. Res. B 265 (2007) 375–378

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The v parameter of hydrogels is generally calculated byusing the following equation [5].

v ffi 1=2 þ m2m=3; ð6Þ

which is the result of an assumption as M c goes to infinitywhich makes the denominator in Eq. (1) equal to zero i.e.

lnð1 m2mÞ þ m2m þ vm22m ¼ 0: ð7Þ

Serial expansion of the logarithmic term lnð1 m2mÞ ¼ðm2m þ m2

2m=2 m32m=3 Þ for small m2m values gives

the following equation;

m22m=2 m3

2m=3 þ vm22m ¼ 0; ð8Þ

upon rearrangement is converted into Eq. (6). This equa-

tion shows that v parameter approaches to 0.5 for smallm2m values.

In this study, we have calculated M cð M cðsÞÞ values of hydrogels by using m2m and v obtained from Eq. (6) andother relevant parameters from swelling experiments andcollected the results in Table 2. To account for calculationsof these parameters from swelling experiments the sub-script ‘‘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 themechanical properties of AAm/MAAm and AAm/HEMA

hydrogels and for the determination of true M cð M cðmÞÞ andv parameter, uniaxial compression was applied by using theUniversal Testing Instrument. The subscript ‘‘m’’ was usedto indicate that these parameters are calculated frommechanical measurements. Typical stress–strain curves of hydrogels were given in Fig. 2. As can be seen from the fig-

ure, the magnitude of stress increased with increasing MBAcontent in the hydrogel for a given strain. Shear modulusvalues of hydrogels were calculated by using elastic defor-mation theory and Eq. (2). [1]. When the equation isapplied to the initial stages of deformation, plots of f versusk k2 yield straight lines, Fig. 3 where k is the deforma-tion ratio and equal to L/Lo. Lo and L are the lengths of the undeformed and deformed hydrogels during compres-sion, respectively. The G value was calculated from theslope of the lines and listed in Table 2. By using G valuesand other relevant experimental parameters, M c and mewere calculated from Eqs. (3) and (4) and collected in Table2. As can be seen from Table 2. the magnitudes of M c cal-

culated from mechanical properties are different from thoseobtained by using swelling experiments. Large differencewas attributed to using incorrect v parameter in the modi-fied Flory–Rehner equation. The actual v parameters werecalculated by using M cðmÞ values and Eq. (1). Recalculatedv parameters (vm) and the differences between vs and vm arealso given in Table 2. For the investigation of the effect of vparameter on the M c values the theoretical M c values were

0 500 1000 1500 2000 25000

100

200

300

400

500

600

1: 0.2AAm0.2MAAm2MBA



%

S

Time (min)

1

2

3

Fig. 1. Swelling degree versus time for AAm/MAAm/MBA hydrogels.

Table 2Network properties and cross-link densities of hydrogels

Sample %S vs M cðsÞ (g/mol) M cðmÞ (g/mol) vm me(s) (mol/cm3) me(m) (mol/cm3) vs vm G (kPa)

0.2AAm/0.2MAAm/2MBA 540 0.54 39,600 6790 0.52 3.29E05 1.92E04 0.02 29.00.2AAm/0.2MAAm/4MBA 360 0.55 9750 2970 0.54 1.32E04 4.35E04 0.01 77.10.2AAm/0.2MAAm/6MBA 300 0.56 6230 2880 0.55 2.09E04 4.51E04 0.01 87.31AAm/1HEMA/0.05MBA 410 0.55 14,385 7745 0.55 9.02E05 1.68E04 0.00 46.71AAm/1HEMA/0.1MBA 380 0.56 11,915 6780 0.55 1.08 E04 1.91E04 0.01 53.91AAm/1HEMA/0.2MBA 370 0.56 10,020 6030 0.55 1.29 E04 2.15E04 0.01 62.41AAm/1HEMA/0.4MBA 330 0.56 8805 4780 0.55 1.46 E04 2.68E04 0.01 79.4

1AAm/1HEMA/0.8MBA 280 0.57 5450 3660 0.56 0.000237 3.52E04 0.01 108.0

0 5 10 15 20 25 30

0

25

50

75

100

125

150

3

2

1


2: 0.2AAm0.2MAAm4MBA3: 0.2AAm0.2MAAm6MBA

S t r e s s ,

k P a

Strain, %

Fig. 2. Strain versus stress curves of AAm/MAAm/MBA hydrogels.

N. Mahmudi et al. / Nucl. Instr. and Meth. in Phys. Res. B 265 (2007) 375–378 377

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obtained, Fig. 4 by using v and experimentally obtainedpolymer based parameter. As can be seen from Fig. 4

and Table 2 for the sample of (0.2AAm/0.2MAAm/2MBA) composition, only a difference of 0.02 in v param-eter caused 4.8-fold increase in the M c value. For thesecond (0.2AAm/0.2MAAm/4MBA) and third (0.2AAm/0.2MAAm/6MBA) samples a change in v parameter by0.01 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 dif-ference in v parameter caused for 0.85; 0.75; 0.66 foldincrease in M c:

4. Conclusions

The aim of this study was to determine molecular weightbetween cross-links and effective cross-link density of radi-ation synthesized AAm/MAAm/MBA and AAm/HEMA/MBA hydrogels by using data from swelling analyses andcompression tests. Values calculated from mechanical tests

were found to be quite different from those obtained byusing swelling experiments. Large difference was attributedto the incorrect value of the v parameter used in the mod-ified Flory–Rehner equation. These results clearly showthat for reliable determination of cross-link density of hydrogels by swelling experiments the v parameter mustbe known reliably or determined experimentally.

References

[1] J.E. Mark, B. Erman (Eds.), Rubberlike Elasticity a Molecular Primer,Wiley, NewYork, 1988.

[2] M. Sen, N. Pekel, O. Guven, Angew. Macromol. Chem. 251 (1998) 1.

[3] O. Okay, S. Durmaz, Polymer 43 (2002) 1215.[4] O. Uzun, M. Hassnisaber, M. Sen, O. Guven, Nucl. Instr. and Meth. B

208 (2003) 242.[5] W. Xue, S. Champ, M.B. Huglin, Polymer 42 (2001) 3665.

0.00 0.25 0.50 0.75 1.00 1.25

0

25

50

75

100

125

150



3: 0.2AAm0.2MAAm6MBA3

2

1

S t r e s s ,

k P a

-(λ -λ -2)

Fig. 3. k k2 versus stress curves of AAm/MAAm/MBA hydrogels.

0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.570

10

20

30

40

32

1




M c

x 1 0 3

χ

Fig. 4. The change of M c with v value of AAm/MAAm/MBA hydrogels.

378 N. Mahmudi et al. / Nucl. Instr. and Meth. in Phys. Res. B 265 (2007) 375–378

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