Isothermal heating methods, thermal

Another reason that isothermal heating methods are used in the initial screen is to identify materials that have time dependent thermal stability. These materials have a thermal decomposition that does not follow a simple Arrhenius relationship in which the reaction rate increases exponentially with an increase in temperature. Instead an extended induction period is required before the decomposition becomes detectable. An example of this behavior is shown in Figure 2. The DTA isothermal test recorder traces of methane sulfonic acid, 3,7-dimethyloctyl ester at different test temperatures are shown. The induction time varies from less than 1 hr. at 180 C to 46 hr. at 130 C. As with this compound, it is not unusual that once decomposition is detected it proceeds very rapidly, releasing all of the heat in a short period of time. Dynamic heating methods do not indicate if this type of thermal instability is present if it is, the initial detection temperature from dynamic tests will be grossly misleading as to the thermal stability of the material. 

Studies connected with the analysis of cooled samples allow to obtain thermal dependencies of oxide solubilities by analysis of the saturated melt heated to the definite temperature. Main disadvantages of isothermal saturation method are ... 

The crystallization kinetics of amorphous materials can be investigated either isothermally or non-isothermally by using thermal analysis techniques. In the isothermal method, the sample is heated above the glass transition temperature and the heat absorbed during the crystallization process is measured as a function of time. On the other hand, in the non-isothermal method, the sample is heated at a fixed rate and then the change in enthalpy is recorded as a function of temperature. Thermal analysis techniques such as differential thermal analysis (DTA) and differential scanning calorimetry (DSC) are quite popular for kinetic analysis of crystallization processes in amorphous solids (Araujo Idalgo, 2009 Malek, 2000 Prasad Varma, 2005). 

Basically, the methods consist of a variety of calorimetric methods and a few non-calorimetric methods. In calorimetry the following methods are nsed adiabatic, isoperibol, isothermal, heat condnction, drop and differential scanning calorimeters, and differential thermal analysis. Cryoscopic, vapor pressure, and enthalpy of solution methods are considered to be non-calorimetric methods. 

Isothermal calorimeters measure thermal power (heat production rate), while (semi)adiabatic calorimeters measure temperature (change). It is possible to calculate one of these from the other, but to do so we need to take the derivative (to go from semiadiabatic to isothermal) or integrate (to go from isothermal to semiadiabatic) and in both cases we need the heat capacity of the sample. The thermal power signal from an isothermal calorimeter shows more details than the temperature signal from an adiabatic calorimeter as the former directly assesses the rate of the process, while an adiabatic calorimeter measures the integral of the rate. Isothermal calorimetry is thus a more generally useful analytical method than semiadiabatic calorimetry. 

Two alternative methods have been used in kinetic investigations of thermal decomposition and, indeed, other reactions of solids in one, yield—time measurements are made while the reactant is maintained at a constant (known) temperature [28] while, in the second, the sample is subjected to a controlled rising temperature [76]. Measurements using both techniques have been widely and variously exploited in the determination of kinetic characteristics and parameters. In the more traditional approach, isothermal studies, the maintenance of a precisely constant temperature throughout the reaction period represents an ideal which cannot be achieved in practice, since a finite time is required to heat the material to reaction temperature. Consequently, the initial segment of the a (fractional decomposition)—time plot cannot refer to isothermal conditions, though the effect of such deviation can be minimized by careful design of equipment. 

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 ... 

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. 

Nitrogen adsorption was performed at -196 °C in a Micromeritics ASAP 2010 volumetric instrument. The samples were outgassed at 80 °C prior to the adsorption measurement until a 3.10 3 Torr static vacuum was reached. The surface area was calculated by the Brunauer-Emmett-Teller (BET) method. Micropore volume and external surface area were evaluated by the alpha-S method using a standard isotherm measured on Aerosil 200 fumed silica [8]. Powder X-ray diffraction (XRD) patterns of samples dried at 80 °C were collected at room temperature on a Broker AXS D-8 diffractometer with Cu Ka radiation. Thermogravimetric analysis was carried out in air flow with heating rate 10 °C min"1 up to 900 °C in a Netzsch TG 209 C thermal balance. SEM micrographs were recorded on a Hitachi S4500 microscope. 

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