Thermokinetic method

If a reliable kinetic model and data on cooling capacity are at hand, runaway scenarios can be examined by computer simulations and only final findings have to be tested experimentally. Such an approach has been presented, e.g. by Zaldivar et al. (1992). However, the detailed reaction mechanism and reaction kinetics are rarely known. Therefore, thermokinetic methods with gross (macro-)kinetics dominate among methods for data... 

The thermokinetic method [107,108] uses the measurement of the forward rate constant of the equilibrium... 

The thermokinetic method takes advantage of the correlation observed between... 

Fig. 2.23. Determination of the proton affinity of cyclohexanecarboxamide (a) by the kinetic method, and (b) by the thermokinetic method. The horizontal lines show the indicative values ln[AH]V[BrefH] = 0 in (a) and REs according to different authors in (b). [101] Adapted from Ref. [109] by permission. IM Publications, 2003.

Proton transfer is one of the prominent representatives of an ion-molecule reaction in the gas phase. It is employed for the determination of GBs and PAs (Chap. 2.11.2) by either method the kinetic method makes use of the dissociation of proton-bound heterodimers, and the thermokinetic method determines the equilibrium constant of the acid-base reaction of gaseous ions. In general, proton transfer plays a crucial role in the formation of protonated molecules, e.g., in positive-ion chemical ionization mass spectrometry (Chap. 7). 

For the determination of reaction parameters, as well as for the assessment of thermal safety, several thermokinetic methods have been developed such as differential scanning calorimetry (DSC), differential thermal analysis (DTA), accelerating rate calorimetry (ARC) and reaction calorimetry. Here, the discussion will be restricted to reaction calorimeters which resemble the later production-scale reactors of the corresponding industrial processes (batch or semi-batch reactors). We shall not discuss thermal analysis devices such as DSC or other micro-calorimetric devices which differ significantly from the production-scale reactor. 

Acrylamide polymerization initiated by the H202-hydroxylamine system also has been described 59). The polymerization rate is proporti onal to the square root of H202 and hydroxylamine concentrations, and first order with respect to the monomer concentration. If traces of Fe (a few ppm) are added, the order with respect to the hydroxylamine concentration has been found to depend on the Fe concentration. A thermokinetic method has been applied in determining the overall activation energy... 

Treatment with Methyl Iodide. Samples of Illinois No. 6 were treated with methyl iodide, CH3I, and the products were analyzed by using two methods the method of Postovski and Harlampovich (10) for thiols and aliphatic sulfides, and our thermokinetic method. The results of the groups analyses are described in Table VI. The results show that only a very small fraction of the organic sulfur is indeed accounted for by the CH3I method, and therefore the value of this method as an analytical tool is questionable. 

Hence, the main aim of the technological process in obtaining fibres from flexible-chain polymers is to extend flexible-chain molecules and to fix their oriented state by subsequent crystallization. The filaments obtained by this method exhibit a fibrillar structure and high tenacity, because the structure of the filament is similar to that of fibres prepared from rigid-chain polymers (for a detailed thermodynamic treatment of orientation processes in polymer solutions and the thermokinetic analysis of jet-fibre transition in longitudinal solution flow see monograph3. ... 

Thermal methods in kinetic modelling. Methods for the estimation of thermokinetic parameters based on experiments in a reaction calorimeter will be discussed below. As mentioned in section 5.4.4.3, instantaneous heat evolved due to a single reaction is directly proportional to the reaction rate. Assume that the reaction is of first order. Then for isothermal operation ... 

In this case, although the reported enthalpy of reaction refers to the difference 7/yh (B) —//ja (A), where Ta and 7], represent the selected temperatures of the peak onset and offset, respectively, an approach based on the thermokinetic analysis of the measured curve was used to compute the peak baseline, and a very detailed description of the method used to derive the thermodynamic and kinetic data is given by the authors. Finally, a general and very important application of... 

Zhan, S., Lin, J., Qin, Z. and Deng, Y. (1996) Studies of thermokinetics in an adiabatic calorimeter. 11 Calorimetric curve analysis methods for ireversible and reversible reactions. Journal of Thermal Analysis, 46,1391—401. 

City gas combustion on Cu is somewhat more complicated than the general mechanism (786). In the high-temperature state, the copper oxide was assumed to adsorb CO2 strongly so that the surface was blocked. Thus this model is a hybrid between thermokinetic blocking/reactivation models and thermokinetic bulk transition models. This mechanism was modeled mathematically, although the parameters for the simulations were not obtained by independent methods but rather by a curve fit procedure. 

The thermokinetic parameter as defined above provides semiquantitative information on the kinetics of the processes occurring in a calorimeter. The rigorous mathematical modeling of the thermokinetics for heat-flow calorimeters (2,34,42,130-132) and isoperibol calorimeters (133) has been recently discussed. Using these methods it is possible to obtain quantitatively the energetic as well as the kinetic parameters describing a number of important processes such as adsorption, desorption, consecutive processes involving the formation of adsorption intermediates, and chemical reactions. 

Further limitations and rules for the application of thermokinetic conver imi data are given in Section 4,3.3.3 in the context of thermokinetic evaluation methods. 

A reasonable thermokinetic evaluation is possible only if it has been ensured with the help of other techniques that reactions running parallel to the desired one are of absolutely mirwr importance only. In practical terms this requirements means that it has to be ensured with the aid of e.g. classical analytical methods that within the evaluated interval the process of interest can be described in terms of a mass balance with sufficient accuracy with a single gross conversion equation. 

Multiple Steady States and Local Stability in CSTR.—In the two decades since the seminal work of van Heerden and Amimdson, there has been vast output of papers conoemed with the dynamic behaviour of stirred-tank reactors. Bilous and Amundson put the van He den analysis of local stability of the equilibrium state on a rigorous basis by use of linear stability theory. Their method is similar to the phase-plane treatments of thermokinetic ignitions and oscillations discussed here in Sections 4 and 3 (and preceded them dironologically). The mass and energy balance for the CSTR having a single reactant as feedstock may be expressed as ... 

Thus, the construction of predictive models of photobioreactors requires careful formulation of radiative transfer within the reaction volume, in order to obtain the radiation field (cf step 1 in the earlier procedure). Such analysis is developed this chapter, starting in Section 2 with determination of the light scattering and absorption properties of photosynthetic-microorganism suspensions. Next, these properties are used in Section 3 for analysis of radiative transfer and in Section 4 for rigorous solution of the radiative transfer equation by the Monte Carlo method. Finally, the thermokinetic coupling between radiative transfer and photosynthesis is addressed in Section 5. It should be noted that Sections 2 and 4 mainly summarize works that have been already published elsewhere, whereas Sections 3 and 5 include extensive original work and results. 

Faraz et al. obtained new composites from carbon nanofibres (CNFs) and bismaleimide, using a thermokinetic mixing method [97]. The addition of CNFs slightly improved the thermal stability of the nanocomposites. The presence of CNFs caused the formation of more char residue, hut this char was fliermally unstable and it degraded faster compared to the char formed in the case of pure resin. 

To apply each of the methods presented below, a knowledge of the physical properties of the investigated object is not necessary. These methods have been qualified as useful in calorimetry to identify the dynamic parameters and to study thermokinetics. 

Many methods are used to determine heat effects. Some of them allow the determination of the total heat effect Q studied, while others permit the determination not only of the total heat effects, but also of the course of thermal power P in time t (function P(t), called the thermokinetics or thermogenesis). 

In the dynamic method ( 3.2.6), the calorimeter is treated as a simple body of uniform temperature. The detailed form of Eq. (1.148) is then a heat balance equation of a sint5)le body. The dynamic method is a one of the most frequently used in the determination of total heat effects and thermokinetics. 

The multibody (domain) method [67, 209, 210] allows the determination of thermokinetics as well as the total heat effects of the process examined. The method is based on the general heat balance equation [Eq. (1.148)]. The mathematical model of the calorimeter is described by the following set of equations ... 

The method of state variables for the determination of thermokinetics was proposed by Brie et al. [239]. The method was applied in the following works [239, 243, 244]. 

When the time constants r and r" and T(t) are known, it is possible to determine the T (t) and T"(t) values consecutively, and thus P(t). The numerical differential correction method has also been applied to reproduce the thermokinetics in these calorimetric systems, in which time constant vary in time [258-264], such as the TAM 2977 titration microcalorimeter produced by Thermometric. These works extended the applications of the inverse filter method to linear systems with variable coefficients. In many cases [258-262], as in the multidomains method, as a basis of consideration the mathematical models used were particular forms of the general heat balance equation. 

From the methods in which the set of heat balance equations was used, the multidomains method ( 3.2.3) and the finite elements method ( 3.2.4) were elaborated. Numerical methods for the determination of thermokinetics in n-n calorimeters ( 3.2.11.1 - 3.2.11.6) were also developed. 

---