MTDSC experiments

Heat Capacity = Heat Flow/Heating Rate or for MTDSC experiments... 

An additional calibration constant is required for accurate MTDSC experiments this is the heat capacity calibration. The heat capacity constant is calculated as the ratio of the theoretical heat capacity of a known standard to the measured heat capacity of the material. The heat capacity constant is sensitive to changes in the modulation conditions, especially the frequency of modulation. 

The chapter is arranged in three sections. First, we outline the principles of MTDSC, including a discussion of the practicalities of running MTDSC experiments. Second, we outline the typical thermal events and systems for which MTDSC is well suited, and finally we review some of the applications of MTDSC within the pharmaceutical sciences to date. 

The basis of the separation or deconvolution procedure can be illustrated by a few simple equations. When used with a sinusoidal perturbation, the temperature program for an MTDSC experiment is given by ... 

FIGURE 4.7 Results for MTDSC experiments on polystyrene annealed for different lengths of time up to 45 min. The inset bars are a guide to the scale for each signal. 

Figure 1.2. Raw data from an MTDSC experiment for quenehed PET plus one signal resulting from the Fourier transform, the phase lag (underlying heating rate 2°C/min, period 60 s, amphtude 0.32°C under nitrogen).

Where a multiplexed sine wave or saw-tooth modulation is used the deconvolution procedure can be used to extract the response at a series of frequencies [4,10,19,20]. However, current commercial products restrict themselves to using the first component of the Fourier series, which is then, with the assumption of linearity, equivalent to using a single sinusoidal modulation. It is true that looking at the whole Fourier series, rather than just the first component, offers scope for increasing the amount of information that can be obtained from an MTDSC experiment. This applies even to single sinusoidal modulations (because non-linearities produce harmonics) as well as multiple simultaneous sine waves or saw-tooth modulations. This will be considered in greater detail below in the section on advanced MTDSC. 

In this chapter, the major benefits of MTDSC to characterise reacting polymer systems are highlighted, with a special focus on polymer network formation. All MTDSC experiments shown are performed on TA Instruments 2920 DSC equipment with the MDSC accessory. Dynamic rheom-etry measurements were made with a TA Instruments ARIOOO-N rheometer in parallel plates mode using disposable aluminium plates. 

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. 

The range of frequencies that can be used in practice is limited to about one decade, so that no strong frequency effects are expected, as opposed to the conditions of DETA where frequencies can easily be changed from 1 to 10 Hz. The modulation frequency in all MTDSC experiments shown is... 

For the cure studies in this work, this deviation is not so important. Firstly, because most of the MTDSC experiments are performed above —50°C, and secondly, because for quantitative analyses a mobility factor is calculated by normalising the heat capacity between reference heat capacities determined at the same temperature. Thus, changes in Kc with temperature have no effect on this result (section 5.8). 

Melamine-formaldehyde (MF) resins of a molar ratio F/M = 1.70 were prepared at 95°C by dissolving 505 g melamine in 592 g formalin (34.5 wt% aqueous formaldehyde with a pH of 9.2). The reaction was stopped when the reaction mixture reached the cloud point [75]. At 25°C, the pH of the MF resin was adjusted to 7.5 and 9.5. These resins were spray-dried using a Buchi spray dryer and further dried for half an hour in a vacuum oven at 60° C before each MTDSC experiment. Liquid C-NMR spectra showed that more methylene bridges and ether bridges and fewer residual methylol groups (see section 2.2.1 were present in MF pH 7.5 compared to MF pH 9.5. 

The total heat flow obtained in quasi-isothermal MTDSC experiments agrees very well with the heat flow evolution obtained in a conventional DSC experiment, performed under the same conditions without of the modulation (Figure 2.2a). Neither changing the modulation amplitude nor the period had an effect on the reaction exotherm seen in the non-reversing heat flow. This illustrates the negligible effect of the perturbation on the cure reaction. 

Figure 4.15. Temperatures in an MTDSC experiment with sinusoidal modulation.

Figure 4.16. Temperatures in the beginning of MTDSC experiments modulated with a quasi-isothermal sawtooth.

Figure 4.26. Temperature profiles for MTDSC experiments involving sinusoidal and stepwise...

Figure 4.40 illustrates the change of sample temperature (dashed line) and heat flow rate (heavy solid line) for a quasi-isothermal MTDSC experiment, as suggested by the bottom heating rate program of Figure 4.28 = 0). This analysis should be compared to Figure 4.34, which was... 

As mentioned above, an MTDSC experiment usually involves the application of a sinusoidal perturbation to the linear heating program of a conven-... 

An MTDSC experiment can not only generate the total heat flow similar to the heat flow obtained in conventional DSC but also separate the total heat flow into its reversing and nonreversing components. The total heat flow is the sum of the thermal events and is generally equivalent to the heat flow seen in conventional DSC. The reversing heat flow is the heat capacity component (plus other terms in some cases see text below) of the total heat flow Cp dT/dt as noted in Eq. (2.91)]. 

For an MTDSC experiment additional run parameters must be selected when compared with conventional DSC. For TAI modules, these parameters are... 

Figure 2.94. Different modulation selections are available for an MTDSC experiment. Seven choices are available heat or cool only, heat with some cooling or conversely cooling with some heating, heat with an associated zero ramp or conversely cool with an associated zero ramp, and finally a modulation around a particular temperature, namely, quasi-isothermal [from Wunderlich (1997b) reprinted with permission from B. Wunderlich].

Figure 2.98. Construction of Lissajous figures from the modulated heat flow. The Lissajous figures can be used to evaluate whether steady state is achieved in an MTDSC experiment. Where the loops overlap, the system is in steady state. The above mentioned quasi-isothermal run was performed on a sample of poly(propylene terephthal-ate) (PPT). [From Pyda and Wunderlich (2000) reprinted with permission from John Wiley Sons, Inc.]...

When attempting to use MTDSC, it should be kept in mind that it is a supplementary technique to traditional DSC and should be considered an extension of conventional DSC. It does not replace it. Before attempting an MTDSC experiment, conventional DSC measurements should first be done to evaluate the need for a modulated run. Care must be taken in a modulated experiment, since the use of modulation adds an additional complication, and any MTDSC experiment, like any DSC experiment, should be verified by other means whenever possible. There are several disadvantages associated with MTDSC. The choice of experimental parameters is difficult, and the use of incorrect parameters could lead to erroneous results. Additionally, interpretation of the heat flow components can be difficult. Finally, speed—MTDSC is usually run at a slower ramp than conventional DSC because of the need to obtain a sufficient number of modulation cycles over a transition region. 

Figure 2.113. Glass transition temperature-conversion relation for stoichiometric DGEBA + MDA mixtures as obtained from MTDSC experiments the cure temperature range (Tcuie) is also shown (Swier, unpublished results).

MTDSC Experiments. The selection of experimental parameters is especially important when running MTDSC experiments the underlying... 

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