Of non-isothermal data

Although there are experimental and interpretative limitations [189, 526] in the kinetic analysis of non-isothermal data, DTA or DSC observations are particularly useful in determining the temperature range of occurrence of one or perhaps a sequence of reactions and also of phase changes including melting. This experimental approach provides, in addition, a useful route to measurements of a in the study of reactions where there is no gas evolution or mass loss. The reliability of conclusions based on non-isothermal data can be increased by quantitatively determining the... 

A very fast testing of polymer stability is based on non-isothermal experiments (DSC, chemiluminescence) where the whole plot of the parameter followed may be visualized over a large temperature interval. The transfer of non-isothermal data to isothermal induction times involves a variety of more or less sophisticated approaches such as published in Ref. [8] or discussed later. 

The usual starting point for the kinetic analysis of non-isothermal data is ... 

The activation energies for the decomposition of sodium n-propoxide and sodium iso-propoxide derived from the isothermal data are slightly higher than those of non-isothermal data. There could be two possible reasons (1) the temperature ranges of the isothermal and non-isothermal measurements are not the same and (2) the initial stage of decomposition under isothermal conditions includes a retardation period and also the specimen experiences a non-isothermal condition till the isothermal temperature is reached. Similar observations are reported in the literature [58,67]. 

Sampling of a two-fluid phase system containing powdered catalyst can be problematic and should be considered in the reactor design. In the case of complex reacting systems with multiple reaction paths, it is important that isothermal data are obtained. Also, different activation energies for the various reaction paths will make it difficult to evaluate the rate constants from non-isothermal data. 

The techniques referred to above (Sects. 1—3) may be operated for a sample heated in a constant temperature environment or under conditions of programmed temperature change. Very similar equipment can often be used differences normally reside in the temperature control of the reactant cell. Non-isothermal measurements of mass loss are termed thermogravimetry (TG), absorption or evolution of heat is differential scanning calorimetry (DSC), and measurement of the temperature difference between the sample and an inert reference substance is termed differential thermal analysis (DTA). These techniques can be used singly [33,76,174] or in combination and may include provision for EGA. Applications of non-isothermal measurements have ranged from the rapid qualitative estimation of reaction temperature to the quantitative determination of kinetic parameters [175—177]. The evaluation of kinetic parameters from non-isothermal data is dealt with in detail in Chap. 3.6. 

Despite the aforementioned shortcomings the experimental data obtained using commercial autoclaves can be kinetically inteipreted in spite of non-isothermal operation, as shown further on in this chapter. Kinetic expressions obtained in this manner will rather be interpolation equations than equations reflecting real reaction mechanisms. 

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

The kinetics of the CTMAB thermal decomposition has been studied by the non-parametric kinetics (NPK) method [6-8], The kinetic analysis has been performed separately for process I and process II in the appropriate a regions. The NPK method for the analysis of non-isothermal TG data is based on the usual assumption that the reaction rate can be expressed as a product of two independent functions,/ and h(T), where f(a) accounts for the kinetic model while the temperature-dependent function, h(T), is usually the Arrhenius equation h(T) = k = A exp(-Ea / RT). The reaction rates, da/dt, measured from several experiments at different heating rates, can be expressed as a three-dimensional surface determined by the temperature and the conversion degree. This is a model-free method since it yields the temperature dependence of the reaction rate without having to make any prior assumptions about the kinetic model. 

Analysis of the non-isothermal polymerization of E-caprolactam is based on the equations for isothermal polymerization discussed above. At the same time, it is also important to estimate the effect of non-isothermal phenomena on polymerization, because in any real situation, it is impossible to avoid exothermal effects. First of all, let us estimate what temperature increase can be expected and how it influences the kinetics of reaction. It is reasonable to assume that the reaction proceeds under adiabatic conditions as is true for many large articles produced by chemical processing. The total energy produced in transforming e-caprolactam into polyamide-6 is well known. According to the experimental data of many authors, it is close to 125 -130 J/cm3. If the reaction takes place under adiabatic conditions, the result is an increase in temperature of up to 50 - 52°C this is the maximum possible temperature increase Tmax- In order to estimate the kinetic effect of this increase... 

Figure 2.34. Comparison of theoretical predictions (curve, calculated from Eq. (2.8S) according to the dissipative model of non-isothermal curing) with experimental data on the decrease of the induction period at high shear rates for phenolic-based compounds (vertical bars) and silicon-based composites at different initial temperatures 150°C (1) 170°C (2) and 190°C (3).

Dielectric relaxation of complex materials over wide frequency and temperature ranges in general may be described in terms of several non-Debye relaxation processes. A quantitative analysis of the dielectric spectra begins with the construction of a fitting function in selected frequency and temperature intervals, which corresponds to the relaxation processes in the spectra. This fitting function is a linear superposition of the model functions (such as HN, Jonscher, dc-conductivity terms see Section II.B.l) that describes the frequency dependence of the isothermal data of the complex dielectric permittivity. The temperature behavior of the fitting parameters reflects the structural and dynamic properties of the material. 

The methods used in the analysis of non-isothermal kinetic data can be classified as derivative, also referred to as differential methods, based on the use of equation... 

Comparison of methods of analysis of isothermal and non-isothermal data... 

The decompositions of compounds containing the ions [Cr(NHj)5(H20)] or [Cr(NH3)4(H20)2] were studied by Wendlandt et al. [30,31]. In subsequent investigations of the thermal deaquation and anation reactions of [Cr(NH3)5(H20)]X3 (X = Cl", Br, T and NO3 ), Nagase and Yokobayashi [32] supplemented TG and thermochemical studies with isothermal measurements of evolved gas pressure, a-time curves were sigmoid and values of EJkJ mol, based on first-order rate constants, increased slightly in the sequence NOj" (102) < Cl" (110) < Br (124) < r (128). These values differ fi om earher values estimated from non-isothermal data. 

Zsako et al. [56] found that values of (obtained from non-isothermal data) for the reactions ... 

Simple salt reactants (131 entries). Articles concerned with decompositions of simple salts were often concerned with kinetic characteristics, many used non-isothermal data, and stoichiometric information was provided for some of these chemical changes. Several of these studies were concerned with determining trends of behaviour through comparisons between related salts. Detailed descriptions of the chemical steps and identifications of the rate-controlling processes in the mechanisms were less frequently provided. A small proportion of the papers was concerned with previously well-studied reactions such as the dissociations of carbonates (13 entries), including the effects of procedural variables on the decompositions of CaCOj (4 entries) and of dolomite (5 entries). 

None of this insight is available from empirical rate equations. It should also be pointed out that all the conclusions reported here are based on a rate expression fitted to non-isothermal data obtained using a TSR. This is the essence of satisfactory data correlations one can examine reaction conditions that were not accessible by direct experimentation. Such procedures are an uncertain business in the case of empirical rate expressions. On the other hand, behaviour simulated using appropriate mechanistic rate expressions can be safely examined under any reaction condition. 

Studies of thermal and fiie resistant properties of the polypropylene/multi-walled carbon nanotube composites (PP/MWCNT) prepared by means of melt intercalation are discussed. The sets of the data acquired with the aid of non-isothermal thermogravi-metric (TG) experiments have been treated by the model kinetic analysis. The thermal-oxidative degradation behavior of PP/MWCNT and stabilizing effect caused by addition of multi-walled carbon nanotube (MWCNT) has been investigated by means of thermogravimetric analysis (TGA) and election paramagnetic resonance (EPR) spectroscopy. 

Fundamental kinetic studies are by preference performed in isothermal rather than in non-isothermal reaction conditions because frequently, as cure proceeds, parallel reactions with different activation energies occur, changing the relative rates of reactions with temperature. In theory, one non-isothermal experiment comprises all the kinetic information normally enclosed in a series of isothermal experiments, which makes the kinetic analysis of non-isothermal DSC data very attractive. The criteria forjudging the kinetic parameters derived from non-isothermal experiments must be its... 

Modifications of Eq. (25) have been derived for other growth situations, but are not reliable, or not sound mathematically. Similarly, non-isothermal kinetics analyses are rather uncertain unless they are supported by structural data and isothermal thermal analysis. If the latter is available, however, non-isothermal data are not needed, except, perhaps, for quality control. 

Several investigators discuss the determination of the overall decomposition kinetics of hydrocarbons on the basis of non-isothermal experimental data. Kershenbaum and Martin[10], Kunzru et al.[ll], and Leftin and Cortes[12], studied the pyrolysis pro-... 

In thermal analysis, the reactions studied are almost invariably heterogeneous and the reaction temperature is usually being continuously increased or decreased according to some set (usually linear) program. Many methods for the analysis of the non-isothermal kinetic data have been developed and numerous papers have appeared and are still appearing on this topic. On the other hand, it is a field of considerable controversy. All controversies regarding the versatility or otherwise of non-isothermal kinetics stem from the applicability of the Arrhenius... 

While a number of established characterization methods exist for mesopores and macropores, the assessment of microporosity is much less advanced, due to experimental difficulties and the lack of a suitable model for the interpretation of the isotherm data. Obtaining accurate experimental isotherms is hampered by the long equilibration times required at the low liquid nitrogen temperatures. In order to overcome this limitation the micropore structure evaluation can be based on isotherms of carbon dioxide or other vapors obtained at higher temperatures, provided that a suitable equilibrium model for the sorption of non spherical molecules is available. 

Rotaru, A. Gosa, M. (2009). Computational thermal and kinetic analysis Complete standard procedure to evaluate the kinetic triplet form non-isothermal data. Journal of Thermal Analysis and Calorimetry, Vol. 97, pp. 421 26 ISSN 1388-6150 (Print), 1572-894 (electronic version)... 

Table 2. Different methods for interpretation of non-isothermal kinetic data...

Even if the above problems can be resolved, batch reactors can measure with accuracy the intrinsic rates of slow pyrolysis reactions. For faster reactions, the time required to heat the sample up to reaction temperature and then cool it down becomes an appreciable fraction of the total, and thus the accuracy with which data can be obtained becomes progressively poorer. If, however, the temperature history is well-defined, the non-isothermal data can be corrected using the "equivalent reaction time" concept (Hougen and Watson, 1947), which can provide, in some cases, a reasonable accuracy. The equivalent reaction time is the time required at a reference temperature to produce the same conversion as that obtained in the actual non-isothermal operation. 

Figure 15.32 Plot of In [P] vs 1/T for decomposition fraction (a = 0.1-0.9) of sodium methoxide under non-isothermal data.

---