chemistry journal of moldova

Chemistry Journal of Moldova. Ion Dranca/Chem.J. General, Industrial Mold. and 2008, Ecological 3 (1), 31-43 Chemistry. 2008, 3 (1), 31-43VARIATION IN ACTIVATION ENERGY AND NANOSCALECHARACTERISTIC LENGTH AT THE GLASS TRANSITIONIon DrancaChemistry Institute, Moldova Academy of Sciences3 Academiei Str., Chisinau MD2028, Moldovadrancai@yahoo.com; Tel. 37322 72 54 90 Fax.37322 73 98 54Current address: Department of Pharmaceutics, University of Minnesota, 55455, USAAbstract: Differential scanning calorimetry has been used to study the -relaxation (glass transition) in virginpolystyrene (PS), PS-clay nanocomposite, amorphous indomethacin (IM), maltitol (Mt) and glucose (Gl). Variationof the effective activation energy (E) throughout the glass transition has been determined by applying an advancedisoconversional method to DSC data on the glass transition. The relaxations have been characterized by determiningthe effective activation energies (E) and evaluating the sizes of cooperatively rearranging regions at the glasstransition (V g). The values of V ghave been determined from the heat capacity data. The -relaxation demonstratesmarkedly larger values of E (~340 vs ~270 kJ mol -1 ) for the PS-clay system than for virgin PS. For IM in the glasstransition region, the effective activation energy of relaxation decreases with increasing temperature from 320 to160 kJ mol -1 . In the T gregion E decreases (from~250 to ~150 kJ mol -1 in maltitol and from~220 to ~170 kJ mol -1in glucose) with increasing T as typically found for the -relaxation. It has been found that in the sub-T gregion Edecreases with decreasing T reaching the values ~60 (glucose) and ~70 (maltitol) kJ -1 that are comparable to theliterature values of the activation energies for the -relaxation. Heat capacity measurements have allowed for theevaluation of the cooperatively rearranging region in terms of the linear size The PS-clay system has also been foundto have a significantly larger value of V g, 36.7 nm 3 as compared to 20.9 nm 3 for PS. Heat capacity measurements ofIM have allowed for the evaluation of the cooperatively rearranging region (CRR) in term of linear size (3.4 nm) andthe number of molecules (90). The size of CRR have been determined as 3.1 (maltitol) and 3.3 (glucose) nm.Keywords: activation energy; differential scanning calorimetry (DSC); - and -relaxation; advanced isoconversionalmethod; kinetics (polym. and pharm.).IntroductionDifferential scanning calorimetry (DSC) is a major tool for measuring the glass transition or, so-called,-relaxations in polymer systems [1]. In particular, it has been successfully employed to explore glass transition invarious nanostructured polymer systems, including thin films [2,3] and polymers confined to nanopores [4,5]. In DSC,the glass transition shows up as a heat capacity step. An increase in the heating rate q causes this step to shift to a highertemperature. This effect is used in the popular method by Moynihan et al [6], for evaluating the effective activation-1energy, E, from the slope of the q versus T gplots.The glass transition kinetics are commonly treated in the frameworks of the Tool [7]-Narayanaswamy [8]-Moynihan[9] (TNM) model that assumes the activation energy of the process to be constant. As fairly noted [10,11], the assumedArrhenius temperature dependence disagrees with the typically observed Vogel [12]-Tamman [13]-Fulcher [14] (VTF) and/or Williams-Landel-Ferry [15] (WLF) dependencies. In particular, Kovacs et al. [10], stressed that the applications of theTNM model should be limited “to systems in which viscosity obeys an Arrhenius dependence within and above the glasstransition range”. According to Angell [16], such systems are termed as strong glass-forming liquids, whereas the systemsthat obey the VTF/WLF behavior are called fragile liquids. The departure from the Arrhenius behavior is characterized bythe dynamic fragility, m. In general, this parameter is the smallest for inorganic oxide glasses and the largest for polymericglasses. Needles to say, the VTF/WLF behavior typically observed for polymers gives rise to an effective activationenergy that varies with temperature [17]. In our previous communication [18], we proposed to use an isoconversionalmethod to detect the variation in the activation energy throughout the glass transition. The application of the methodwas demonstrated for two polymers: polystyrene (PS) and poly(ethylene terephthalate) (PET). Why variation? Constantactivation energy is usually the anticipated outcome of kinetic evaluations. This expectation appears to be supported bytheoretical reasoning. The Arrhenius equation, eq (1),k Aexp(E/ RT)(1)where E is the activation energy (the heat of activation), A the preexponential factor, T the temperature, R the gasconstant, materializes Arrhenius hypothesis [19] that normal (i.e. inactive) molecules are in an endothermic equilibriumwith active ones, which take part in the reaction. According to Arrhenius, E is the heat absorbed in the process of31