Ion Dranca/Chem.J. Mold. 2008, 3 (1), 31-43A necessary constraint <strong>of</strong> eq 2, is that the sample must be heated at a rate whose absolute value is equal to the rate<strong>of</strong> preceding cooling [6, 47]. The resulting dependence <strong>of</strong> 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 <strong>of</strong> the effective activationenergy for PS100 and nPS90 that respectively are 201 and 305 kJ mol -1 . To determine a variation <strong>of</strong> E with the extent <strong>of</strong>conversion from the glassy to rubbery state, , we have used an advanced isoconversional method [49, 50]. The method<strong>of</strong>fers two major advantages over the frequently used methods <strong>of</strong> 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 <strong>of</strong> the instrument. For a series <strong>of</strong> n experiments carried out underdifferent temperature programs, T(t),the activation energy is determined at any particular value <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> to find the dependence E on . Isoconversional methods determine the E values independently <strong>of</strong> thepreexponential factors, which a not produced directly by these methods. It allows one to eliminate the bias in the value<strong>of</strong> 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 <strong>of</strong> the activation energy for -relaxation with the extent <strong>of</strong> conversion35
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 derivative<strong>of</strong> the fictive temperature. The application <strong>of</strong> 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 <strong>of</strong> Cooperatively Rearranging Regions in PS100 and nPS90. On the basis <strong>of</strong> the result discussed inthe previous section, the polymer-clay system should have a larger region <strong>of</strong> cooperative rearrangement. Donth hasdemonstrated that the volume <strong>of</strong> 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 <strong>of</strong> (C ) is determined asv1vv(C ) ( C C(8)1vgwhere C g and C l are respective values <strong>of</strong> 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% <strong>of</strong> the total Cp at Tg [60 62].Figure 5, shows the results <strong>of</strong> our C measurements for PS100 and nPS90.ppThe values <strong>of</strong>C 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 <strong>of</strong> the heat capacity for PS100 and nPS90Cpfor PS are in very good agreement with earlier measurements [63, 64].36
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- Page 68 and 69: Chemistry Journal of Moldova. N. Ku
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- Page 122 and 123:
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- Page 124 and 125:
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- Page 126 and 127:
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