Radiation synthesis of low swelling acrylamide based hydrogels and determination of average molecular weight between cross-links Naim Mahmudi a , Murat S ß en b, * , Stojan Rendevski c , Olgun Gu ¨ven 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 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 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 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 cross- linking has some advantages over chemical cross-linking and 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 weight between 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 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 non- ionic polymeric networks known as Flory–Rehner equa- tion [1,2] M c ¼ ð1  2=/ÞV 1 m 2=3 2r m 1=3 2m m lnð1  m 2m Þþ m 2m þ vm 2 2m ð Þ : 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 swell- ing agent, v is the polymer–solvent interaction parameter, / is the functionality, m is the specific volume of the poly- mer, 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 experi- ments 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 * Corresponding author. Tel./fax: +90 312 2977989. E-mail address: msen@hacettepe.edu.tr (M. S ßen). www.elsevier.com/locate/nimb Available online at www.sciencedirect.com Nuclear Instruments and Methods in Physics Research B 265 (2007) 375–378 NIM B Beam Interactions with Materials & Atoms