Instant Notes: Analytical Chemistry

situation to become complex, and the measured modulus, E*,also becomes

complex:

E*=E’+iE′′

where E’is called the storage modulus, E′′the loss modulus, and their ratio is

the loss tangent with i = √|−1:

tan(d)=E′′/E′

Without concentrating on the involved nature of the mechanics and mathe-

matics, the measurement of the moduli and loss tangent allows the study of

many important commercial samples.

Instrumentation The term thermomechanical analysis (TMA) is usually used when the force
applied is constant, whereas if the force is made to oscillate, the technique is
dynamic mechanical analysis (DMA).
The furnace, computer, atmosphere control and temperature sensors are all
similar to those described in Topics G1 and G2. For mechanical measurements
the sample holders and sensors are very different.
For TMA, the length of the sample and the changes in length that occur
during heating are measured by a linear variable differential transformer
(LVDT). The movement of the transformer core produces an electrical signal,
sensitive to direction, and this signal is transmitted to the data system.
The sample is placed on a support within the furnace and contact made with
the LVDT through a rod. The force is applied either directly, by adding a weight
to the rod, or electrically using the LVDT. If a zero load is applied to the sample,
the expansion is measured. A schematic diagram of this system is shown in
Figure 1(a).
In a DMA, the system may operate in a number of different ways, to study
compression, shear, bending or torsion. The oscillatory force is applied by the
mechanism, and the sample behavior affects the response of the system. The
frequency of the oscillation may be altered, but is often about 1−10 Hz. From the
calibration of the apparatus, the data may be processed to give the storage and
loss moduli. One typical sample holder for DMA in the 3-point bending mode is
shown in Figure 1(b).

G3 – Thermomechanical analysis 317

Force control

LVDT

Furnace

(or cooler)

Sample

Support

(a)
Oscillator
Force signal

Displacement sensor

Push rod

Sample

Furnace

(b)

Fig. 1. (a) Schematic of a TMA system. (b) Schematic of a DMA system using 3-point bending.