Ozawa plot

YAGA-OZAWA PLOT YONETANI-THEORELL PLOT INDUCED FIT MODEL... 

METAL IONS IN NUCLEOTIDE-DEPENDENT REACTIONS YAGA-OZAWA PLOT... 

Fig. 23. The Ozawa plot for determining n associated with the first exotherm of the 0.90Te02-0.10WCh sample (Celikbilek et al., 2011)...

Figure 10. Ozawa plots of (a) PEN and (b) the PEN/CNT 0.5 nanocomposites during non-isothermal crystallization.

It must be mentioned that there are many reports on deviation of the Ozawa plots from linearity and also on M values that are different from those predicted theoretically. The analysis of nonisothermal crystallization encounters even more difficulties than that of isothermal crystallization. Additional problems result from the requirement to combine the results of several crystallization experiments performed at different cooling rates. The Ozawa theory is based on the assumption that the nucleation rate dependence on temperature f(T) is unaffected by a cooling rate. As a consequence, the validity of the Ozawa approach is limited to a narrow range of cooling rates that results in the crystallization in similar temperature intervals. Markedly different cooling rates cause variation of M, for instance as shown in Reference [64]. The same applies to other simplified approaches, for example, the Nakamura isokinetic model, in which nonisothermal crystallization is treated as a succession of isothermal processes. The results are reasonable as long as the nucleation process is not infiu-... 

Figure 7.10 The Ozawa plot for iPP crystallized at different cooling rates in the range from 0.62 to 40 C/min (a) ln -ln [1 - a(T)] versus Inivl plots, (b) H(T) versus T master curve. Reprinted from Piorkowska, E., et al. Critical assessment of overall crystallization kinetics theories and predictions. Prog. Polym. Sci. 2006,31, 549-575. Copyright 2006, with kind permission from Elsevier.

Ozawa analysis was also applied to analyze the talc effect on crystallization. Ozawa plots were constructed at the crystallization temperature, T, for each cooling rate to understand the behavior at the maximum crystallization rate. Fig-6 shows the plots of ln[-ln(l-X)] versus In (cooling rate) for samples of 1% talc. It is clear that the relationship is not linear suggesting a simple Ozawa relationship was not followed, which is not unusual for polypropylene [4, 22]. Ozawa exponent, or the slope of the plot for each temperature, was determined at the cooling rate that generated the corresponding T,.. The results are summarized in Fig-7. The Ozawa exponent, m, ranged approximately from 1.6 to 3 for the neat material and blends of various talc contents. 

Fig-6 Ozawa plots at Tc obtained from different cooling rates... 

Electrophysiological studies on rat hippocampal neurons show two types of KAR with different current responses to KA. In the KA1 response, KA causes little increase in membrane Ca2+ permeability and an outward rectification in the current-voltage plots. The KA2 response is characterized by prominent Ca2+ permeability and an inward rectification in the current voltage plots (Ozawa et al., 1991). 

The dependence of gas adsorption on the pore structure of the sorbent has been extensively studied by Ozawa, Kusumi, and Ogino (34) and theoretically correlated by application of the Pickett equation. Data obtained from this study has been plotted... 

DSC ts widely used to predict the potential explosive hazard of materials in an ASTM method. The basis of the method, developed by Committee E 27, is the determination of the reaction kinetics using Ozawa s procedure (206). Ozawa employs a ploi of the logarithm of the DSC heating rate versus the peak maxima temperatures E. Z, k. and t can be calculated from this plot. The ASTM method has been used to evaluate the thermal stability of irinitrotoluene (207). nitrocellulose (208). and many other substances. 

A plot of In (j) against l/T, at a given fractional mass, yields a straight line from whose slope E can be calculated. Further, if the TG curves are plotted as fractional mass against VT at various heating rates the curves may be superimposed on each other by a lateral shift which is proportional to ln0. A master curve is thereby obtained. If the TG curves cannot be superimposed in this manner, the Ozawa method is not applicable. In practice, the degree of conversion at the DTG peak temperature varies with... 

Here, q is called the Ozawa index. Corresponding to one-dimensional growth, q = 2 two-dimensional growth, q = 3 and three-dimensional growth, = 4. In practical measurements, one may determine the values of crystallinity XJa) at a constant temperature from a series of DSC crystallization curve with various cooling rates a, and then plot lg[—ln(l—X )] versus lg(a), to obtain the Ozawa index directly from the slope, as illustrated in Fig. 10.31a-c. 

To characterize the spherulitic nucleation during nonisothermal crystallization, the Ozawa equation is applied, which could be obtained by integrating twice by parts the Avrami equation and assuming cooling at the constant rate, a. The slope of the plot ln -ln[l - a(T)] versus In(fl) equals two or three for instantaneous nucleation, three or four for nucleation prolonged in time, in two- and three-dimensional crystallization, respectively. The values from three to four, depending on temperature range were obtained for iPP from DSC nonisothermal crystallization [4],... 

Ozawa and Kissinger plots are the most commonly used equations to calculate non-isothermal kinetic data, such as Avrami constant, n and crystallization activation energy, Ea, respectively (Celikbilek et al., 2011 Kissinger, 1956 Ozawa, 1971 Prasad Varma, 2005). 

The activation energy can be therefore obtained from the slope, by plotting the iln( /Tm2) vs 1/Tm. Ozawa also proposed that the activation energy may be estimated from the shifting of DSC curve as the heating rate is changed, it is based on the general equation (5),... 

Figure 2.2 (a) Thermogravimetric curves of PTFE (b) Arrhenius plots for thermogravimetric analysis of PTFE (c) rate constant versus temperature curves of PTEE (d) half life temperatures curve of PTEE and (e) conversion versus time at 500 °C curves of PTFE. Reproduced with permission from T. Ozawa, Bulletin of Chemical Society of Japan. 1965 Chemical Society of Japan [3]... 

The Flynn-Wall-Ozawa method [142, 143] has been used to determine the activation energy from dynamic tests by plotting the logarithm of heating rate as a function of the inverse of the temperature, at different conversions. Being integrated with the initial condition of a = 0 at r= To, the equation (24) can be arranged as follows ... 

The thermal degradation mechanisms of poly(styrene-co-methacrylonitrile) (P(S-co-MAN)) is reported in terms of the competition between the depolymerisation and backbiting reaction on the basis of the bond dissociation energies of the C-C and C-H bonds in the polymer chains [a.l88j. The activation energy of pyrolysis obtained by Ozawa s plot increased with the content of methacrylonitrile units in the copolymer chain, although the onset temperatures of loss of sample mass in the TG curves shifted to the lower temperature region. Yields of each monomer, dimer and trimer, and also those of hybrid dimers and... 

Similarly, as in the case of the Avrami analysis of isothermal crystallization, the discrepancies between experimentally determined curves and predictions of the Ozawa equation originate mainly from oversimplified assumptions concerning the polymer crystallization. Those discrepancies inspired some authors to search for other equations enabling a better description and analysis of nonisothermal crystallization. For instance, the classic isothermal Avrami analysis based on Equation (7.5) with E expressed by Equation (7.10) was applied to nonisothermal crystallization [65, 66]. Such an approach has no theoretical justification. Even if a straight line Avrami plot is obtained, the parameters k and n are, at best, two adjustable parameters without a clear physical meaning. The Jeziomy method [67] deserves similar criticism. Jeziomy proposed using Equation (7.5) and Equation (7.10) and characterizing the process with the parameter kc defined as ... 

A plot of log V against log t should give a straight line with the intercept of log F T) = log[H(T)/k] and the slope of equal to -n/M. In fact, the Ozawa equation and the isothermal Avrami equation (Eq. 7.10) are derived from the same general Equation (7.6a) and Equation (7.6b) but with different assumptions in the Ozawa equation a constant cooling rate is assumed, while in the Avrami Equation (7.10) the growth rate G is a constant. Therefore, the combination of the equations proposed in References [68] and used by many authors has no justification and is erroneous. 

A similar plot for poly(butylene naphthalene 2,6-dicarboxylate) is given in Fig. 9.25.(96) In contrast to the previous figure, these plots are only linear at the lower portion and curvature is observed at the higher levels of crystallinity. These results indicate that in this case the crystallization has not been limited to Region I. Curvature in the Ozawa type plot has also been observed with poly(aryl ether ether ketone) (40), poly(aryl ether ether ketone ketone) (97) and poly(aryl ether ether sulfide).(97a) Curvature and deviation from the theory will be observed, if crystallization occurs beyond Region I, because the derived Avrami equation is no longer vaUd. 

---