chemistry journal of moldova

Ion Dranca/Chem.J. Mold. 2008, 3 (1), 31-43where C pis the observed heat capacity, and C pgand C plare respectively the glassy and equilibrium (liquid) heat capacity.Because the values C pgand C plare temperature dependent, they must be extrapoled into the glass transition region.According to Hodge, [54] the C pNvalue provides a precise a precise approximation to the temperature derivativeof the fictive temperature. The application of the isoconversional method to the resulting versus T data obtained atdifferent heating rates yields the E dependencies shown in Figure 4. The activation energies decrease from 280 to 140kJ mol -1 for PS100 and from 350 to 160 kJ mol -1 for nPS90. Note that the values obtained for PS100 fall within the largeinterval, 160-900 kJ mol -1 , reported in the literature [54-59].Volume of Cooperatively Rearranging Regions in PS100 and nPS90. On the basis of the result discussed inthe previous section, the polymer-clay system should have a larger region of cooperative rearrangement. Donth hasdemonstrated that the volume of the cooperatively rearranging region at the glass transition can be estimated fromcalorimetric data by using the following equation [48, 60]:kB is the Boltzman constant, gVg2 1kBTg(v) (7)2(T)T is an apparent glass transition temperature, is the density (1.05 g cm -3 for PS [61]),1and C is the isohoric heat capacity. The value of (C ) is determined asv1vv(C ) ( C C(8)1vgwhere C g and C l are respective values of the glassy and liquid heat capacity extrapoled to Tg . The difference betweenisohoric and isobaric heat capacities is usually neglected [60] so that Cv can be replaced with Cpwhich is readilyobtainable from calorimetric measurements. More recently, Hempel et al. [62] demonstrated that the difference can beaccounted via the following correction:1vl1 1(C ) (0.74 0.22) (C )(9)vTIf the glass transition is measured on heating, the mean temperature fluctuation, T (10)2.5where T is the temperature interval within which Cp varies between 16 and 84% of the total Cp at Tg [60 62].Figure 5, shows the results of our C measurements for PS100 and nPS90.ppThe values ofC p/ J K -1 g -12.01.91.81.71.61.51.41.3nPS90PS100C p=0.34C p=0.241.240 60 80 100 120 140T / o CFig. 5. Temperature dependence of the heat capacity for PS100 and nPS90Cpfor PS are in very good agreement with earlier measurements [63, 64].36