Isothermal heat flow rate measurements

The reaction calorimeter used in this study was a Mettler s RCl with a 1 L reactor vessel. Both heat flow and hydrogen uptake were measured. The heat flow rate measured under isothermal conditions is directly proportional to a summation of the rate of each reaction step weighted by heat of reaction A// of the corresponding step, i.e.,... 

As mentioned above, titration methods have also been adapted to calorimeters whose working principle relies on the detection of a heat flow to or from the calorimetric vessel, as a result of the phenomenon under study [195-196,206], Heat flow calorimetry was discussed in chapter 9, where two general modes of operation were presented. In some instruments, the heat flow rate between the calorimetric vessel and a heat sink is measured by use of thermopiles. Others, such as the calorimeter in figure 11.1, are based on a power compensation mechanism that enables operation under isothermal conditions. 

Enthalpy Measurements. A Perkin Elmer Differential Scanning Calorimeter Model DSC 1-B was used throughout. The instrument measures the heat flow rate (cal/s) by maintaining the sample and the reference isothermal to each other while they are heated or cooled with a linear known temperature rate (Scan speed, °C/min). (19)... 

The three types of isothermal heat flow calorimeters described above can be used to measure heat flow in semi-batch reactions, where one or more reactants are charged to the reactor and the other reactants are added at controlled rates throughout the reaction. With careful design the heat flow calorimeters can simulate process variables such as feed rate, stirring, distillation and reflux . 

The reversing heat capacity and the total heat-flow rate of an initially amorphous poly(3-hydroxybutyrate), PHB, are illustrated in Fig. 6.18 [21]. The quasi-isothermal study of the development of the crystallinity was made at 296 K, within the cold-crystallization range. The reversing specific heat capacity gives a measure of the crystallization kinetics by showing the drop of the heat capacity from the supercooled melt to the value of the solid as a function of time, while the total heat-Uow rate is a direct measure of the evolution of the latent heat of crystallization. From the heat of fusion, one expects a crystallinity of 64%, the total amount of solid material, however, when estimated from the specific heat capacity of PHB using the ATHAS Data Bank of Appendix 1, is 88%, an indication of a rigid-amorphous fraction of 24%. 

The term calorimetry denotes a variety of measurement methods which involve a measurement of the heat of physical or chemical changes in a sample. One of the most commonly used calorimetric methods is differential scanning calorimetry in which the difference in the heat flow rate to a primary sample and a reference sample is measured, when both are subjected to the similarly alternating temperature. Usually this is done in a specified, controlled atmosphere. In isothermal calorimetty the measurement temperature is kept as constant as possible, and, instead of temperature alternation, the other environmental parameters such as gas atmosphere, relative humidity, light exposure, etc., are alternated. 

The TMDSC enables another elegant possibility of Cp (magnitude) determination from the amplitude of the modulated part of the measured heat flow rate function both in the isothermal and. scanning modes of operation. This method is especially advantageous in cases of noisy signals with low sample masses or low heating rates. Precise calibration of the heat flow rate amplitude is a prerequisite for obtaining reliable results [43]. 

Figure 9.7 The measured functions from Figure 9.6 shifted and tilted for zero heat flow rate in isothermal equilibrium (power-compensated DSC heating rate lOKmin ).

After switching from fast cooling to isothermal conditions at time zero, the measured heat flow rate exponentially approaches a constant value (-10.3 mW) with a time constant of about 3 seconds for this DSC. The observed crystallization peak is often symmetric, and then the time of the peak maximum (nunimum) is a measure of crystallization half time. Integration of the peak yields the enthalpy change, which can be transformed into relative crystallinity by dividing by the limiting value at infinite time. To obtain development of absolute crystallinity (mass fraction) the curve has to be divided by the enthalpy difference between crystal and liquid at the crystallization temperature, which is available from ATHAS-DB [124], The commonly applied Kolmogorov-Johnson-Mehl-Avrami (KJMA) model for the kinetic analysis of isothermal crystallization data is based on volume fractions. Therefore, the mass fraction crystallinity, Wc, as always obtained from DSC, should be transformed into volume crystallinity. 

Besides the exothermal heat flow rate caused by the crystallization process, a decreasing heat capacity can be observed for most polymers during crystallization near the glass transition. Unfortunately, heat capacity cannot be measiued under isothermal conditions. But applying a small heating rate (temperature), perturbation during a quasi-isothermal measurement allows the determination of heat capacity as a function of time as discussed next. 

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 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... 

Usually, isothermal calorimeters are used to measure heat flow in batch and semi-batch reactions. They can also measure the total heat generated by the reaction. With careful design, the calorimeter can simulate process variables such as addition rate, agitation, distillation and reflux. They are particularly useful for measuring the accumulation of unreacted materials in semi-batch reactions. Reaction conditions can be selected to minimize such accumulations. 

Differential Scanning Calorimetry (DSC) This is by far the widest utilized technique to obtain the degree and reaction rate of cure as well as the specific heat of thermosetting resins. It is based on the measurement of the differential voltage (converted into heat flow) necessary to obtain the thermal equilibrium between a sample (resin) and an inert reference, both placed into a calorimeter [143,144], As a result, a thermogram, as shown in Figure 2.7, is obtained [145]. In this curve, the area under the whole curve represents the total heat of reaction, AHR, and the shadowed area represents the enthalpy at a specific time. From Equations 2.5 and 2.6, the degree and rate of cure can be calculated. The DSC can operate under isothermal or non-isothermal conditions [146]. In the former mode, two different methods can be used [1] ... 

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