chemistry journal of moldova

Ion Dranca/Chem.J. Mold. 2008, 3 (1), 31-43A necessary constraint of eq 2, is that the sample must be heated at a rate whose absolute value is equal to the rateof preceding cooling [6, 47]. The resulting dependence of ln versus T g-1are shown in Fig. 3. The plots are nonlinear,which is typically observed for the -relaxations [11, 48]. The effective activation energy decreases with temperature,which is consistent with the general tendency predicted by the WLF equation [15, 17]:Ec c T2 1 22.303R2( c2 T T g)(3)where c 1and c 2are the constants. Forcing data to an Arhenius plot yields averaged values of the effective activationenergy for PS100 and nPS90 that respectively are 201 and 305 kJ mol -1 . To determine a variation of E with the extent ofconversion from the glassy to rubbery state, , we have used an advanced isoconversional method [49, 50]. The methodoffers two major advantages over the frequently used methods of Flyn and Wall [51] and Ozawa [52]. First, it has beendesigned to treat the kinetics that occur under arbitrary variation in temperature, T(t),which allows one to account forself-heating/cooling detectable by the thermal sensor of the instrument. For a series of n experiments carried out underdifferent temperature programs, T(t),the activation energy is determined at any particular value of by finding E ,which minimizes the function(E)n n i i1 j1 J[E, Tj( t)]J[E, T ( t)](4)wheret EJ[ E , Ti ( t ) exp[ ] dttRT ( t)The second advantage is associated with performing integration over small time segments (eq 4), which allowsfor eliminating a systematic error [50] occurring in the Flynn and Wall and Ozawa methods when E varies significantlywith . In eq 5, is varied from to 1 – with a step =m -1 , where m is the number of intervals chosen for analysis.The integral, J in eq 4, is evaluated numerically by using the trapezoid rule. The minimization procedure is repeated foreach value of to find the dependence E on . Isoconversional methods determine the E values independently of thepreexponential factors, which a not produced directly by these methods. It allows one to eliminate the bias in the valueof the activation energy caused by its strong correlation with the exponential factor that is generally found when bothparameters are fit simultaneously [53]. The conversion, , can be evaluated from DSC data (Fig. 2) as the normalaizedheat capacity [54] as follows:( Cp Cpg)NCp (6)( C C )plpgTi(5)350300PS100nPS90E / kJ mol -12502001500.0 0.2 0.4 0.6 0.8 1.0Fig. 4. Variation of the activation energy for -relaxation with the extent of conversion35