DMA or dynamic mechanical spectroscopy (DMS) is a means of measuring the viscoelastic properties of a material, the rheokinetics of a reacting material, or the rheology of a simple or complex fluid . DMA's versatility has made dynamic mechanical analyzer use in polyurethane science very widespread, and it is certainly one of the most useful pieces of equipment in characterizing poly-urethanes. Unlike a tensile test, the materials tested by DMA are rarely if ever tested intentionally to a failure condition. Instead, the sample is subjected to an oscillating or sinusoidal strain around a zero strain or a zero reference point. A so-called strain sweep is usually performed prior to a full analysis to make sure that the applied strain does not exceed the linear elastic limit of the material nor the force limits of the load cell. This is similar to maintaining the strain in the very-low-strain conditions found at the beginning of a tensile measurement. If the experimentalist were to exceed these linear viscoelastic conditions, the material would permanently deform, and the measurement would not have a clear reference condition. Strains are often on the order of 1% of the gauge length (distance between grips) or a few degrees relative to a full 360° twist of the material, depending in each case on the thickness and hardness of the material being tested. An experimentalist will likewise often perform a frequency sweep of the material prior to beginning a full material analysis. This is to assure that the material properties are not significantly sensitive to the frequency of the applied sinusoidal strain. A frequency-sensitive material, or a material near a rheological event like a glass transition, may show a frequency-dependent modulus, for instance. This frequency/temperature conflation is a process called time-temperature superposition and is well understood . Problems associated with this condition in a frequency experiment like DMA are easily avoided through good laboratory practice. A typical frequency is 1 Hz unless the point of the test is to explore the frequency dependence of the material (which is a common enough experiment). The conditions of the constant strain experiment apply to a rotational stress applied to a disk-shaped object in compression or a torsional stress applied to a rectangular object in tension. In both cases, a set of minimal force in compression or tension is applied to assure fixture contact or sample rigidity, respectively, and the sinusoidal strain and measured force measured against this initial "zero force" reference condition.
Alternatively, a constant sinusoidal stress can be applied to the sample and the resulting induced sample strain measured. This is a less common experiment than the constant strain experiment. In principle, the stress is defined by the strain and the strain defined by the stress; however, particularly, in the case of polyurethanes, this expectation is rarely if ever realized.
The mechanical analysis of viscoelastic materials is derived from the definition of mechanical properties in these experiments. As oscillation proceeds, the material stress (i) increases with strain, (ii) decreases as the material is returned to its zero strain state, and then (iii) increases again as the material is strained in the opposite direction from the first oscillation. For a perfectly elastic response, there is no energy lost within the material during the cycle, and the modulus of the material is given by
where E' is the so-called storage modulus of the material or the energy put into the material that is immediately available to be returned, "o" is the applied stress, and "г" is the applied strain (the use of Greek letters is conventional in this field). In a viscoelastic material, E represents the elastic component. Most nonideal materials such as polyurethanes will not be well represented by this equation as there are numerous molecular processes that can occur capable of dissipating some of the energy put into the sample during the stress phase of the experiment. In these oscillating experiments consisting of elastic energy storage E' and energy losses E" due to viscous processes, their moduli are defined by
The ratio of the loss modulus (E") to the storage modulus is termed the tan (8) (called the "tan delta"):
The tan 5 is the phase lag between applied strain and measured stress, a very sensitive function of phase transitions. Representative data obtained from a DMA experiment on a polyurethane elastomer is shown in Figure 5.25. Figure 5.25b is the
Figure 5.25 Representative DMA for a polyurethane elastomer: (a) storage and loss moduli and (b) tan delta spectrum—the ratio of loss divided by storage modulus.
tan 8 spectrum for this elastomer clearly showing the glass transition temperature (the peak with maximum at -25 °C in this case) and the onset of urethane reversion (see Chapter 3) beginning about 120 °C.
More than 70% of all polyurethane chemicals are processed into foams. The DMA spectra of these materials have been shown to be very similar if not identical to the underlying elastomer except exhibiting a much lower modulus reflecting the well-known squared dependence on density :
Experiments on foam samples are ordinarily done on disk-shaped samples. Examples of DMA fixtures for shear and torsional experiments are shown in Figure 5.26.
DMA experiments can also be employed to provide time- or temperature-dependent rheology for reacting systems. In this case, the components of the reaction are introduced into a cuplike fixture and a plate attached to the load cell submerged into the reacting components. The plate will oscillate through the reacting mixture measuring the growth of molecular weight as an increasing resistance to plate rotation. Since the forces are often low in the initial state, the plate usually must oscillate with relatively higher amplitude through the mixture. A typical DMA in use is shown in Figure 5.27 and the data obtainable from a rheokinetic experiment in Figure 5.28.
Figure 5.26 DMA fixtures: (a) parallel plate fixture for measurement of thin solid samples in shear or reacting liquids and (b) torsion fixture for measurement of solid sample viscoelastic properties. Fixtures are carefully engineered and machined to provide minimal compliance and minimum mass. Images courtesy of TA Instruments. © 2013.
Figure 5.27 A technician preparing a DMA for analysis using a cup and plate fixture.
Figure 5.28 Example of rheokinetic data obtainable with DMA for a 2-part reacting system like a polyurethane.