Isothermal heat rate measurements

The studies of Criddle et al. [17] on carrot and tomato cell cultures outlined basic procedures for isothermal heat rate measurements of plant tissues. Samples are placed in an ampule, sealed to prevent any water vapor loss, placed in the calorimeter at the desired temperature and the heat rates recorded directly. Figure la shows the type of thermogram obtained. There is an initial rapid change in recorded heat rate while sample and ampules are thermally equilibrated. Following equilibration, (about 45 min in this example) the amplitude of the thermal signal is corrected for baseline values obtained with empty ampules to yield the sample metabolic heat rate. Temperature may then be adjusted to new values to establish temperature coefficients of heat rate or the ampules may be opened and the sample environment modified before the ampule is resealed and re-equilibrated for evaluation of effects of the modification on plant activities. Because plants are ectotherms that live in a variable temperature environment, temperature dependence studies using sequential i.sothermal mea.surements are essential for characterization of plant physiological properties. 

Batch studies. Methods and equipment have been described for isothermal measurement of metabolic heat rates and determination of the flux rates of both O2 and CO2 [21, 22, 39]. Isothermal heat rates are determined as in section 1.8.1. O2 rates are determined by pressure change. CO2 rates are determined by two methods, one measuring heat rate increases in the presence of a CO2 trap and the other by measuring pressure change. 

One method of CO2 determination measures isothermal heat rate of a tis.sue sample first in the presence of a small container of water, then in the presence of the container with 0.4 M NaOH. With NaOH present, CO2 is trapped as carbonate with concomitant production of heat. The increased heat rate in the presence of base can be related to Rcoi through the known enthalpy change for carbonate formation, -108.5 kJ mof CO2 140] Thus, the difference in heat rates measured for tissue in the presence and absence of NaOH divided by 108.5 yields / ( 02 23]. 

In this method, data are obtained for reaction proceeding at a series of different heating rates [539,560,561]. This reduces the advantage of the non-isothermal method and one might just as well perform a series of isothermal measurements for which the subsequent analysis will be both more accurate and much simpler. Use of the technique can be illustrated by reference to the work of Ozawa [561] which is quoted as typical. The Doyle equation [eqn. (25)] above can be written... 

Thermal decomposition was performed using a SDT Q-600 simultaneous DSC-TGA instrument (TA Instruments). The samples (mass app. 10 mg) were heated in a standard alumina 90 il sample pan. All experiments were carried out under air with a flow rate of 0.1 dm3/min. Non-isothermal measurements were conducted at heating rates of 3, 6, 9, 12, and 16 K/min. Five experiments were done at each heating rate. 

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. 

The measurement of an enthalpy change is based either on the law of conservation of energy or on the Newton and Stefan-Boltzmann laws for the rate of heat transfer. In the latter case, the heat flow between a sample and a heat sink maintained at isothermal conditions is measured. Most of these isoperibol heat flux calorimeters are of the twin type with two sample chambers, each surrounded by a thermopile linking it to a constant temperature metal block or another type of heat reservoir. A reaction is initiated in one sample chamber after obtaining a stable stationary state defining the baseline from the thermopiles. The other sample chamber acts as a reference. As the reaction proceeds, the thermopile measures the temperature difference between the sample chamber and the reference cell. The rate of heat flow between the calorimeter and its surroundings is proportional to the temperature difference between the sample and the heat sink and the total heat effect is proportional to the integrated area under the calorimetric peak. A calibration is thus... 

Reproducibility of the used heating rate for comparison with other investigations. Selection of small and large heating rates depending on the type of investigation. Equilibrium measurements (e.g. 0.2 °C7min) or stepwise isothermal. Exploratory runs (standard rate 4-6 °C/min). 

The adsorption isotherms of xenon were measured at 34°C using a classical volumetric apparatus. The 29xe-NMR measurements were performed at the same temperature on a Bruker CXP-200 spectrometer operating at 55.3 MHz. The n-hexane adsorptions were conducted at 90°C on a Stanton Redcroft STA-780 thermoanalyzer. The samples were submitted to a preliminary calcination under dry air up to 650°C with a heating rate of 10°C/min. 

A known amount of zeolite was loaded into a 10 mm NMR tube with an attached vacuum valve. The sample was evacuated to about 2xl0 < torr for 3 days at room temperature, then it was heated to 350 C with a heating rate of 0.2 C/min, the sample was allowed to maintain at this temperature for about 30 hours (2x10 torr). After cooling to room temperature, a known amount of xenon gas was introduced into the sample tube and was sealed by the vacuum valve. All the xenon adsorption isotherms were measured by volumetric method at room temperature. 

The stabilized temperature platform furnace (STPF) concept was first devised by Slavin et al. It is a collection of recommendations to be followed to enable determinations to be as free from interferences as possible. These recommendations include (i) isothermal operation (ii) the use of a matrix modifier (iii) an integrated absorbance signal rather than peak height measurements (iv) a rapid heating rate during atomization (v) fast electronic circuits to follow the transient signal and (vi) the use of a powerful background correction system such as the Zeeman effect. Most or all of these recommendations are incorporated into virtually all analytical protocols nowadays and this, in conjunction with the transversely heated tubes, has decreased the interference effects observed considerably. 

XRD patterns were obtained with a Rigaku D/MAX-IIA diffractometer system equipped with Ni-filtered Cu-Ka radiation. N2 adsorption/desorption isotherms were measured with a Micromeritics ASAP 2010 system. NH3-TPD was conducted under He flow of 30 ml/min and a heating rate of 20 °C/min. 

Fig. 7. Comparison of cure curves at various temperatures, obtained from isothermal measurements (solid curves), and calculated from DSC scans at different heating rates (dashed curves) (From Ref. 65 Fig. 4)...

Reaction characterisation by calorimetry generally involves construction of a model complete with kinetic and thermodynamic parameters (e.g. rate constants and reaction enthalpies) for the steps which together comprise the overall process. Experimental calorimetric measurements are then compared with those simulated on the basis of the reaction model and particular values for the various parameters. The measurements could be of heat evolution measured as a function of time for the reaction carried out isothermally under specified conditions. Congruence between the experimental measurements and simulated values is taken as the support for the model and the reliability of the parameters, which may then be used for the design of a manufacturing process, for example. A reaction modelin this sense should not be confused with a mechanism in the sense used by most organic chemists-they are different but equally valid descriptions of the reaction. The model is empirical and comprises a set of chemical equations and associated kinetic and thermodynamic parameters. The mechanism comprises a description of how at the molecular level reactants become products. Whilst there is no necessary connection between a useful model and the mechanism (known or otherwise), the application of sound mechanistic principles is likely to provide the most effective route to a good model. 

The kinetic constant can be calculated from the maximum heat release rate measured under isothermal conditions ... 

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