TopEM technology is used to separate the sensible and latent heat flows and determine the frequency dependence of the heat capacity

introduction

Clarifying the sensible heat and latent heat data of the material is of great significance

METTLER TOLEDO Differential Scanning Calorimeter DSC

Sensible heat and latent heat

The heat flow of a conventional DSC test for total heat flow consists of both an apparent heat flow (Cp, driven by an external temperature change) and an underlying heat flow (a part produced by physical conversion or chemical reaction, driven by changes in internal structure), which can be expressed as:

where β is the sample heating rate, Δhr is the enthalpy of the thermal reaction, and α is the degree of reaction (or degree of structural change).

During the heating or cooling process of an object, the temperature rises or decreases without changing the original phase state, and the heat flow that needs to be absorbed or released is called "sensible heat", and the first item in the corresponding equation (1) directly depends on the heating rate, where the scale factor is the heat capacity

Latent heat is the abbreviation of phase change latent heat, which refers to the heat

Basic principles of temperature modulation DSCs

The experimental method of modulating DSC (TMDSC) is to superimpose a small temperature oscillation (modulation) on top of a conventional temperature program (constant heating rate or cooling rate, or constant temperature condition

In DSC experiments, the sample is heat exchanged with the test instrument, and if heat is supplied to the sample, the temperature of the sample will increase; Conversely, if the heat is stopped, its temperature will decrease

In the formula, Cpf is the specific heat generated by fast internal degrees of freedom, independent of frequency; Cps are produced by slow internal degrees of

Sinusoidal Temperature Modulation DSC (ADSC)

One of the most widely used is the sinusoidal temperature modulation DSC technology (ADSC), which is based on the traditional DSC linear temperature control, superimposed on the modulation temperature of the sinusoidal waveform, so that the sample is under the composite temperature control of linear rise temperature and periodic fluctuation temperature, and the complex thermal effect is separated into reversible heat flow and total heat flow

Figure 1.

In all TMDSC techniques, three heat flows can be obtained from the test heat flow, which are: total heat flow ΦNon, reversible heat flow ΦRev and irreversible heat flow ΦNon

According to Formula (2), when the frequency is close to 0, it is similar to the quasi-steady state, at which time the reversible heat flow corresponds to the sensible heat, and the irreversible heat flow corresponds to the latent heat flow; When the frequency is infinite, the frequency-dependent specific heat capacitance change is entirely dependent on the kinetic process, which is partly reflected in the

However, due to experimental conditions, such as single-frequency conventional TMDSCs including sinusoidal temperature modulation ADSCs, the measured data may deviate significantly from the two heat flow components

Multi-frequency random temperature modulation TOPEM technology

TOPEM® is a multi-frequency temperature modulation DSC technique that differs from traditional temperature modulation techniques in terms of the type of modulation function and the method

Figure 2 TOPEM tests the signal over a wide frequency range with random temperature disturbances

In TOPEM®, data analysis is performed through correlation analysis of heat flow and heating rate

The TOPEM test process is a quasi-steady state test (when the frequency ω is close to 0, similar to the quasi-steady state), if the linear and steady state need to be within the range of test accuracy, the reversible heat flow and irreversible heat flow of the TOPEM® test can be attributed to the sensible heat flow and the latent heat flow, so that the sensible heat flow and the latent heat flow

Examples of TOPEM technology applications

In addition to isolating overlapping thermal effects like ADSCs, TOPEM technology can also obtain a quasi-steady specific heat capacity; Obtain multi-frequency data in one experiment to analyze frequency dependence; More accurate separation of sensible and latent heat; Reversible heat flow signal and irreversible heat flow signal based on quasi-steady state heat capacity are direct results of correlation analysis; It is suitable for the study of curing reactions, crystallization, melting, phase transition, etc

Figure 3 shows the curve of PET for TOPEM testing, and after analysis, the total heat flow curve, reversible and irreversible heat flow curves correspond to the sensible heat flow and latent heat flow, frequency correlation, and quasi-steady specific heat capacity
, respectively.
In the modulation heat flow curve, both the glass transition and the cold crystallization are clearly
visible.
In addition, it can be seen that during the glass transition process of about 80 °C, the heat capacity increases, but it decreases slightly during cold crystallization, which is more obvious
in the phase curve.
In addition to the quasi-static curve, the curve at a measurement frequency of 16.
7 Hz is also shown
.
During the glass transition, the transition of temperature to higher temperatures can be clearly seen as the frequency increases
.
Conversely, no displacement was observed during cold crystallization, indicating that this effect depends only on temperature, and frequency dependence can be studied in a single experimental test
.

Figure 3 TOPEM modulation analysis curve of PET material

conclusion

TOPEM is a multi-frequency random temperature modulation DSC technology developed by METTLER TOLEDO, which makes it possible to separate latent heat and sensible heat, under a sufficiently low base heating rate and small temperature perturbation, that is, to meet linear and steady-state conditions, as a result of which the reversible heat flow and irreversible heat flow are equal to the sensible heat flow and latent heat flow components at this base heating rate, that is, ΦRev = ΦSen and ΦNon = ΦLat, and have a high degree of accuracy
。 Frequency evaluation also allows complex (frequency-dependent) heat volumes to be determined over a wide frequency range with a single measurement, and the information obtained helps to explain thermal events as well as the study of
process dynamics.

References

[1] M.
Reading.
Trends Polym.
Sci.
1 (1993) 248.

[2] J.
E.
K.
Schawe.
Thermochim Acta 260 (1995) .

Lu Liming, Theory and application of TOPEM of stochastic temperature modulation DSC technology.

[4] J.
Schawe, UserCom 20, 11.

[5] J.
Schawe, UserCom 22, 11.