Analysis of Melting Processes Using TOPEM

Introduction 

The measurement and interpretation of melting processes using temperature modulated DSC (TMDSC) is one of the more demanding tasks in thermal analysis.

This is possibly the reason why a number of ideas and proposals can be found in the scientific literature that do not stand up to a critical analysis. Despite this, TMDSC can provide interesting and important information about melting behavior that would otherwise be difficult to obtain.

Starting out from the basic principles of melting behavior discussed in reference [1], we want to show with the aid of suitable examples how melting behavior can be investigated using TOPEM^®.

Basic Principles of Temperature Modulated DSC

Measurement principles and requirements

In TMDSC, a conventional temperature program (heating or cooling at a constant rate, or isothermal conditions) is overlaid with a small temperature perturbation (modulation). In the evaluation algorithm, it is assumed that the reaction of the sample to the conventional temperature program and the modulation do not influence each other. The underlying part (from the conventional temperature program) and the part from the modulation can then be separated. While just as in conventional DSC the underlying part of the heat flow (total heat flow) contains the entire information, the part that is generated by the modulation, only contains information about processes that can more or less follow the modulation. 

In all modulation techniques, the measurement conditions must be chosen so that measurement and evaluation take place under linear and almost stationary conditions. This means that the result is independent of the intensity (amplitude) of the modulation and that the total heat flow during a relevant evaluation window (period) does not change much. The quality of the measurement improves as the underlying heating rate is reduced.

Especially in the analysis of melting processes, small modulations must be used because otherwise artifacts are measured that lead to the misinterpretation of results.

TOPEM^® is a modern TMDSC technique that differs from conventional TMDSC with regard to the type of modulation function and evaluation. In TOPEM^®, a stochastic function is used for modulation. The intensity of the modulation function is the height of the pulse. The evaluation consists of a correlation analysis of the measured heat flow and heating rate in a selectable evaluation window. [2, 3]. 

Total, reversing and non-reversing heat flow

In all TMDSC techniques, three heat flow components are determined from the measured heat flow. These are the total heat flow, Φ_tot, the reversing heat flow, Φ_rev, and the non-reversing heat flow, Φ_non.

In conventional TMDSC, the total heat flow is obtained from the measured heat flow by averaging over at least one period. The reversing heat flow is determined from the modulated component. The non-reversing heat flow is given by the difference:

Φ_non =  Φ_tot – Φ_rev

In TOPEM^® the evaluation is carried out by means of a correlation analysis of the heat flow and the heating rate.

This yields the component of the measured heat flow that correlates with the heating rate and another component that does not correlate with the heating rate. The non-correlating component is the non-reversing heat flow, Φ_non. The reversing heat flow is determined from the correlating heat flow part [3]. The total heat flow is calculated from the sum of the two quantities: At first sight, this difference in approach seems relatively unimportant. In TOPEM^®, however, it allows a consistency test of the measurement to be performed as described below. 

Sensible and latent heat flow

In principle, the heat flow consists of two components namely the sensible heat flow, Φ_s, and the latent heat flow, Φ_l, [3, 4]. 

The latent heat flow does not explicitly depend on the temperature but on the kinetics of the thermal event. An example is the curing reaction of an adhesive. A temperature change during the reaction cannot cause the sample to return to its initial state. It will only change the reaction rate. The sensible heat flow depends explicitly on the heating rate. An example is the heat flow into an inert sample, which is directly proportional to the heating rate. Here, the proportionality factor is the heat capacity.

Basic principles

The starting point is the description of melting and crystallization processes by means of free enthalpy given in reference [1]. A diagram summarizing this is shown in Figure 1. The red, black and green curves are the free enthalpies of the melt, the crystal and the glass. The dashed curves represent intermediate states. The curve with the smallest free enthalpy characterizes the stable state. All other states are metastable. The system tries to achieve the stable state but is hindered by kinetic processes (e.g. nucleation).

Conclusions

When TOPEM^® is used to investigate melting processes, attention must be paid to the linearity of the measurement. The linear region is determined beforehand in preliminary experiments.

The range in which TOPEM^® curves are valid can be established by comparing the total heat flow and the mean value of the measured heat flow. Processes that take place under conditions of local equilibrium can be detected in the reversing heat flow because they more or less follow the temperature modulation.

Processes that take place far from equilibrium do not follow the temperature modulation and thus contribute to the non-reversing heat flow.

_{Analysis of Melting Processes using TOPEM^® | Thermal Analysis Application No. UC 254 | Application published in METTLER TOLEDO Thermal Analysis UserCom 25}