The Separation of Sensible and Latent Heat Flow using TOPEM

TOPEM^® is a new temperature-modulated DSC technique. Latent and sensible heat flows can be separated and the frequency-dependent heat capacity determined in one single measurement.

Introduction

In TOPEM^®, a temperature program is used in which an underlying temperature ramp or an isothermal segment is modulated with a series of small temperature pulses of random pulse width. Using this technique, it is possible to separate sensible and latent heat flows from one another. In addition, the frequency-dependent heat capacity can be determined, which allows conclusions to be drawn about the dynamics of processes. In this article, we will present several applications that demonstrate the power of this new technique.

Sensible and Latent Heat Flow

In a DSC experiment, heat is continuously exchanged between the sample and the measuring instrument. If heat is supplied to the sample, its temperature increases, and conversely if heat is removed, its temperature decreases. The term sensible relates to the part of the heat exchanged between the measuring instrument and the sample that results in a change in temperature of the sample. After the supply or removal of heat, the temperature change takes place either immediately or, due to dynamic processes in the sample, after a certain time delay.

If the total sensible heat is to be measured, it follows that a sufficiently long period of time must elapse after the heat has been supplied or removed. In other words, measurement of sensible heat is only possible under quasi-static conditions. An important characteristic feature of sensible heat is that the processes associated with the uptake or loss of heat can be reversed. Thermodynamically we are dealing with reversible processes that occur close to a local metastable state.

Examples are

Temperature change outside a thermal event
Heat capacity changes in second order phase transitions
Heat capacity changes during chemical reactions
Glass transitions
Reversible melting (e.g. of polymers)

The latent heat is the non-sensible part of the total heat flow. It can be endothermic or exothermic and is associated with irreversible changes in structure.

Such processes begin in a thermodynamically non-equilibrium state and end in a (metastable) equilibrium state. They can take place time-dependently or be kinetically controlled and therefore be time-dependent.

Examples are:

Non-reversible chemical reactions.
Crystallization in supercooled liquids
Melting with supercooled crystallization
Vaporization of volatile components

A conventional DSC measurement always measures the sum of the latent and sensible heat. Temperature-modulated DSC (TMDSC) attempts to separate the total heat flow into a sensible heat flow component (often called reversing) and a latent heat flow component (often called non-reversing). If the reversing heat flow is measured dynamically, it is in general less than the sensible heat flow because all time-dependent processes that take longer than the characteristic measuring time (e.g. 60 s) are not measured. In quasi-static measurements, the difference between the sensible and reversing heat becomes minimal. For this reason, using TOPEM^® , it is possible to obtain an excellent separation of sensible and latent heat flows.

Applications

Second order transitions

In second order phase transitions, the heat capacity first increases up to a critical temperature and then decreases suddenly. It is a phenomenon in which effects due to latent heat do not occur. Correspondingly no measurement effects are to be expected in the non-reversing heat flow curve.

The solid-solid transition of sodium nitrate at 275 °C was measured as an example. Since the heat capacity change following the critical temperature is expected to take place over a very small temperature range (about 0.1 K), a measurement can only be successful if it is performed at a very low heating rate using a very small temperature modulation. In this case an underlying heating rate of 20 mK/min and a pulse height of 5 mK were used.

The resulting heat flow curves are presented in Figure 1. As expected only the reversing and total heat flow curves show a transition peak. The non-reversing heat flow curve does not show any effect despite the sharp change after the critical temperature. This proves that TOPEM^® is clearly able to differentiate between effects that exhibit sensible and latent heat flows.

Change in the heat capacity during an isothermal chemical reaction

In a chemical reaction, a change in heat capacity can occur for several reasons:

Difference in the heat capacities of starting materials and reaction products
Phase separations
Vaporization of volatile reaction participants
Vitrification

In polymerization reactions, the glass transition temperature of the reaction products increases with increasing degree of polymerization. If the glass transition temperature of the reaction product is greater than the reaction temperature, vitrification can occur during the reaction. The viscosity of the reaction mixture then increases markedly and the reaction practically stops. Vitrification is observed as a step in the heat capacity (sensible heat flow) curve. In conventional DSC this step is overlapped by the contribution from the reaction enthalpy (latent heat flow).

Conclusions

The contents of calcium sulfate dihydrate and calcium sulfate hemihydrate can be determined in cement with good accuracy by thermogravimetry. A quantitative determination is only possible if the samples are measured in an almost hermetically sealed crucible. This is most easily done using aluminum crucibles sealed with a lid with a 50-µm hole. If a pierced lid is not available, the same effect can be achieved by placing a grain of sand (about 20 µm in diameter) on the rim of the crucible before sealing it.

_{The Separation of Sensible and Latent Heat Flow using TOPEM^® | Thermal Analysis Application No. UC 225 | Application published in METTLER TOLEDO Thermal Analysis UserCom 22}