Underlying heating rates

Modulation — amplitude, period, underlying heating rate, number of cycles under a transition... 

In standard TMDSC, an additional underlying heating rate complicates the analysis of Equation (6). It takes now die form (72) ... 

In the more recently developed temperature-modulated DSC (TMDSC, see Sect. 4.4 [11]), a sinusoidal or other periodic change in temperature is superimposed on the underlying heating rate. The heat capacity is now given by the bottom equation in Fig. 2.28, where and A are the maximum amplitudes of the modulation found in temperature difference and sample temperature, respectively, and co is the modulation frequency 27i/period. The equation represents the reversing heat capacity. In case there is a difference between the result of the last two equations, this is called a nonreversing heat capacity, and is connected to processes within the sample which are slower than the addition of the heat or which cannot be modulated at all (such as irreversible crystallization and reorganization, or heat losses). 

Adding an underlying heating rate to the measurement leads to a Lissajous figure as is shown in Fig. 4.121. The computation using the pseudo-isothermal method of Sect. 4.4.3 implies the plotting of HF(t) versus T t) - . A similar plot is obtained when plotting versus dT/dt. 

In Fig. 4.133 quasi-isothermal data of the filled circles are compared with standard TMDSC with the indicated underlying heating and cooling rates. As the underlying heating rate increases, the time scale of the modulation is approached, and the... 

TMDSC of lootactio Polypropylene with and Without Underlying Heating Rate... 

Next, a constant, irreversible thermal process with a latent heat is added to the modulation cycles, as is found on cold crystallization of PET (see Figs. 4.74 and 4.136-139). A latent heat does not change the temperatures of Fig. A. 13.1, so that the heat-flow rates need to be modified, as is shown in the upper graph of Fig. A. 13.2. The constant latent heat is indicated by the vertically shaded blocks and is chosen to compensate the effect of the underlying heating rate, so that the level of Ps is moved to zero. The reversing specific heat capacity is given by ... 

Metaer-Toledo DSC 820 Linear heating 7.24 K/min Linear cooling 5.24 K/min (Sawtooth modulation with an underlying heating rate of 1.0 K/min, and a modulation period p = 90 s)... 

Fig. 5.17 Temperature dependence of gas volume released during thermal decomposition of barium titanyl oxalate under heating rates (a) 50, (b) 100, (c) 300 °C/h, (d) rate controlled regime [283]...

Figure 1.1. Typical temperature-titne curve for an MTSC experiment (top) with resultant heating rate modulation and heat flow response (underlying heating rate 2°C/min, period 60 s, amplitude 0.32°C under nitrogen). 

If the results are to be expressed as heat capacities, then the average total heat flow is divided by the underlying heating rate fl. Thus,... 

It should be noted that the corrected heat flow phase is very small in most cases, so that the difference in value between C and Cp is negligible. For isothermal experiments, the reversing heat flow equals zero because of a zero underlying heating rate and consequently the non-reversing heat flow equals the total heat flow. 

In an MTDSC experiment, a repeated temperature modulation is superimposed on the normal linear temperature programme [1-5,74]. The modulation amplitude and frequency, and the underlying heating rate can be chosen independently. 

For non-isothermal experiments, heating only conditions, with the modulation amplitude chosen so that no cooling occurs over one complete cycle, are of no use in cure studies. On the contrary, for experiments with very low underlying heating rate, or when Cp should be measured as accurately as possible, it is advisable to use a larger modulation amplitude. Of course, the amplitude of the temperature modulation has to be limited, since its effect on the cure kinetics has to be negligible. Typical amplitudes are between 0.1 andl°C. 

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