Constant-heating-rate method

An equation and the procedure to calculate the value of de of a powdery ehemical of the TD type, including every gas-permeable oxidatively-heating substance, by applying the constant-heating-rate method is explained in detail in Section 6.4. 

The method to calculate the value of a or that of by substituting the individual values of and (zl T rajtiin, into Eqs. (84) or (85) is referred to as the constant-heating-rate method herein. 

These values of cr, except the ones measured herein and the ones, to which reference numbers are each attached, were measured predominantly by Kosaka et al. by applying the constant-heating-rate method, respectively [47, 51—53]. 

The value of of the sawdust of each wood species was measured herein by applying the constant-heating-rate method and is presented in Table 21 in (1) of Subsection 8.4.4,... 

On the other hand, the value of ate of powdery AIBN was calculated at 0.07 cm /min by applying the constant-heating-rate method in (3) of Subsection 6.4.3. 

M. Kosaka, T. Asahina and S. Ikuta, Measurement of Thermal Diffusivity by Applying the Constant-Heating-Rate Method ( I ), Application to Pyrophyllite and Stainless Steel (in Japanese), Research Reports of National Industrial Research Institute of Nagoya, 26, 11-14 (1977). 

Estimation from singie and muitipie constant heating rate methods... 

One reason for the higher values obtained using the single constant heating rate method (e.g., Eq. 9.3, [70]) is probably due to the different reactions proceeding in a mixed and complex manner. If this is true, it is difficult to evaluate the correct value of each elementary reaction, because the E value is calculated as an apparent value from the slope of the total plot made up of multiple reactions. 

This is a relatively fast and popular method that requires only a few milligrams of sample. AH is obtained from a measurement of the area under the melting peak obtained at a constant heating rate, in reference to the heat flow value of a standard. 

In the nonisothermal or dynamic mode, a sample is set into a calorimeter and the temperature is raised at a certain constant heating rate up to the operational temperature. The total heat of reaction is independent of the heating rate (recommended range is 2-20°C/min [1,140]). Three methods are possible ... 

Another group of methods for the analysis of data from temperature scans at constant heating rate is based on the integrated rate Eq. 

In a real system, the desorption energy (E is dependent on the coverage. Therefore, Gillis-D Hamers has evaluated the surface heterogeneity by the constant coverage, variable heating rate method, developed by Richards and Rees.30 This method estimates Ed as a function of coverage by the least-squares minimization of the experimental data. 

In Method 2, the reacting mixture was crystallized by raising the temperature from 160 to 210°C at a constant heating rate of 0.l6°C/min while stirring at 60 rpm. 

Direct heating aethod. In order to confirm the change in crystallization process, the gel mixture was heated directly to 200°C with a constant heating rate of 2.8°C min"1, and then it was maintained for 2 h. The resulting product contained sodalite with ZSM-34, and the morphology was completely different from the crystals prepared by the conventional method. 

In this study, the crystallization temperature and the heating rate were varied using the milled precursor, and ZSM-5 crystals could be synthesized. For example, the temperature was elevated from 160 to 210°C with a constant heating rate of 0.2°C/min (Method 2). The crystals prepared by Methods 1 4 had about same BET-surface area of 385 11 ma /g and the XRD patterns of ZSM-5. The average size of crystals reduced from 8 urn for Method 1 to 1 ym for Method 4. The concentration profiles of Si and A1 from outside to inside the crystals became uniform with reducing size. The activity of methanol conversion, the yield of gasoline fraction, and the content of aromatics in the gasoline clearly increased for the product of Method 4 (Fig. 6). 

Fig. 43. (a) Effect of order of reaction on plots of reaction rate against temperature for constant heating rate, frequency factor and activation energy. EjR = 20,000, lnA = 16.0. From ref. 350. (b) Method of measuring reaction order from the shape index of dta peak. Shape index S = alb. 

The most convenient (but also least accurate) method to derive information about the adsorption energy is based on the analysis of thermal desorption spectroscopy (TDS) data [5,20]. The temperature of the adsorbate covered surface is increased continuously with a constant heating rate p (so the momentary surface... 

AEM-u is able to evaluate the escape frequency factor v utilizing all the data of an object TSC spectrum. The advantageous property of this method is that both the v and i value could be determined. The equation used in AEM-y was derived from an equation of the TSC with constant heating rate under the condition of first-order slow retrapping is expressed as ... 

---