A mathematical model for Modulated Differential Scanning Calorimetry

Abstract

Reading and co-workers introduced a new technique a few years ago called Modulated Differential Scanning Calorimetry or MDSC. Here the first part of a theoretical analysis for this technique is given. A simple mathematical model for modulated differential scanning calorimetry in the form of an ordinary differential equation is derived. The model is analysed to find the effect of a kinetic event in the form of a chemical reaction. Some possible sources of error are discussed. A more sophisticated version of the model allowing for spatial variation in a calorimeter is developed and it is seen how it can be reduced to the earlier model. Some preliminary work on a phase change is also presented.

Theory and Practice of Modulated Temperature Differential Scanning Calorimetry

“…It can be seen that there is a strong frequency dependence of the results in the melt region. The simple model discussed above (from [12]) does not predict that this will occur. Fig.…”

“…In a simple case, this type of melting behaviour closely mimics heat capacity. This is discussed in more detail in [12] and the advanced section. It should be noted that this simple picture breaks down if cooling occurs during the modulation.…”

“…The heat flow modulation = ) cos( φ ω − t A HF (12) where φ = the phase difference between the modulation in the heat flow and the heating rate, also termed the "phase lag".…”

“…7 it can be seen that the effects of the thermal resistances are smaller when helium is used and a reasonable compromise is 40 seconds (again with a calibration factor). While it is true that considerable progress has been made by some workers in characterising and compensating for these nonideal experimental conditions [12,[21][22][23][24][25] for most experimentalists, the best approach it to use longer periods that avoid the complications engendered by these thermal resistances. It should be noted that, if helium is used, the concentration of helium in the actual cell will generally not be 100% and will vary with flow rate.…”

“…It is also intended to serve as a guide to understanding the remaining chapters that deal with the three principal classes of polymeric materials, thermosets, thermoplastic polymer blends and semi-crystalline polymers. The use of a modulated temperature profile with DSC, combined with a deconvolution procedure in order to obtain the same information as conventional DSC plus, at the same time, the response to the modulation, was first proposed by Reading and co-workers [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In this section we will describe the basic deconvolution procedure i.e.…”