31.2: Differential Thermal Analysis and Differential Scanning Calorimetry

Differential thermal analysis (DTA) and differential scanning calorimetry (DSC) are similar methods in which the response of a sample and a reference to a change in temperature. In DTA the temperature applied to the sample is increased linearly and the difference between the temperature of the reference material, \(T_{ref}\), and the temperature of the sample, \(T_{samp}\), is recorded as function of the sample's temperature

\[\Delta T = T_{ref} - T_{samp} \nonumber \]When the sample undergoes an exothermic process, such as a crystallization or a chemical reaction, the temperature of the sample increases more than does the temperature of the reference, resulting in a more negative value for \(\Delta T\). For an endothermic process, such as melting of a crystalline material or the loss of waters of hydration, the sample's temperature lags behind that for the reference materials, resulting in a more positive value for \(\Delta T\). Figure \(\PageIndex{1}\) shows the general shape of DTA curve with negative peaks signaling an endothermic process and positive peaks signaling an exothermic process. Changes in \(\Delta T\) that are not peaks, but shifts in the baseline—as seen at the far left of the curve in Figure \(\PageIndex{1}\)—are the result of a simple phase transition for which \(\Delta H = 0\).In DSC the temperature applied to the sample is increased linearly and the relative amount of heat needed to maintain the sample and the reference at the same temperature is measured. For an endothermic process, more heat flows into the sample and for an exothermic process, less heat flows into the sample. The result is a DSC curve that looks similar to that for DTA (see Figure \(\PageIndex{1}\)).

Figure \(\PageIndex{1}\): Illustration showing typical experimental curves for a differential thermal analysis (DTA) or a differential scanning calorimetry analysis (DSC) for a polymeric material. For a DTA analysis, the difference in temperature, \(\Delta T\), is measured and for a DSC analysis, the flow of heat is measured. The three responses seen here are, from left-to-right, a phase transition, an exothermic crystallization, and an endothermic melting.

Instrumentation

Figure \(\PageIndex{2}\) shows the basic components of a heat-flux differential scanning calorimeter. The sample and the reference materials are sealed within small aluminum pans and placed on separate platforms within the sample chamber. The two platforms are connected by a metal disk that provides a low resistance path for moving heat between the sample and the reference to maintain a \(\Delta T\) of zero between the two. Another instrumental design for differential scanning calorimetry, which is called power compensation DSC, places the sample and the reference in separated heating chambers and measures the difference in the power applied to the two chambers needed to maintain a \(\Delta T\) of zero.

Figure \(\PageIndex{2}\): Components of instrument for a differential scanning calorimetry (DSC) experiment. The sample and the reference material are (a) placed in small aluminum pans, each with a separate lid, and then (b) the lid and the pan are crimped together. The sample chamber in (c) allows for applying heat to the sample and the reference, which are place in the center of the chamber. A close-up of the sample chamber (d) shows two—well-used—platforms on which the sample and the reference are placed. An insulated cap sits on top of the sample chamber. Although the basic set-up shown here is for DSC, it is similar to the instrumentation for a differential thermal analysis. For a sense of scale, the pan in (a) is approximately 5 mm across and has a depth of 1 mm, and the platforms in (d) also are 5 mm across.

Applications

Integrating a peak in DSC or DTA to determine its its area, \(A\), gives a signal that is proportional to \(\Delta H\)

\[\Delta H = K \times A \nonumber \]

where the calibration constant, \(k\), is determined using an established reference material. Both DSC and DTA find applications in the study of polymers, liquid crystals, and pharmaceutical compounds.