An Introduction to Dynamic Mechanical Analysis
Dynamic mechanical analysis (DMA) is becoming more and more commonly seen in the analytical laboratory as a tool rather than a research curiosity. This technique is still treated with reluctance and unease, probably due to its importation from the field of rheology. Rheology, the study of the deformation and flow of materials, has a reputation of requiring a fair degree of mathematical sophistication. Although many rheologists may disagree with this assessment,1 most chemists have neither the time nor the inclination to delve through enough literature to become fluent. Neither do they have an interest in developing the constituent equations that are a large part of the literature. DMA is a technique that does not require a lot of specialized training to use for material characterization. It supplies information about major transitions as well as secondary and tertiary transitions not readily identifiable by other methods. It also allows characterization of bulk properties directly affecting material performance.
Depending on whom you talk to, the same technique may be called dynamic mechanical analysis (DMA), forced oscillatory measurements, dynamic mechanical thermal analysis (DMTA), dynamic thermomechanical analysis, and even dynamic rheology. This is a function of the development of early instruments by different specialties (engineering, chemistry, polymer physics) and for different markets. In addition, the names of early manufacturers are often used to refer to the technique, the same way that Kleenex™ has come to mean tissues. In this book, DMA will be used to describe the technique of applying an oscillatory or pulsing force to a sample.
A Brief History of DMA
The first attempts that I found reported in the literature to use oscillatory experiments to measure the elasticity of a material were by Poynting2 in 1909. Other early works gave methods to apply oscillatory deformations by various means to study metals3 and many early experimental techniques were reviewed by te Nijenhuis in 1978.4 Miller's book on polymer properties referred to dynamic measurements in this early discussion of molecular structure and stiffness.5 Early commercial instruments included the Weissenberg rheogoniometer (approximately 1950) and the Rheovibron
(approximately 1958). The Weissenberg rheogoniometer, which dominated cone-and-plate measurements for over 20 years following 1955, was the commercial version of the first instrument to measure normal forces.6
By the time Ferry wrote Viscoelastic Properties of Polymers in 1961/ dynamic measurements were an integral part of polymer science and he gives the best development of the theory available. In 1967, McCrum et al. collected the current information on DMA and dielectric analysis (DEA) into their landmark textbook.8 The technique remained fairly specialized until the late sixties when commercial instruments became more user-friendly. About 1966, Gillham developed the torsional braid analyzer and started the modern period of DMA.
DMA can be simply described as applying an oscillating force to a sampleand analyzing the material's response to that force (see Figure 1.1). This is a In 1971, Macosko and Starita built a DMA that measured normal forces and from this came the Rheometrics Corporation.10 In 1976, Bohlin also developed a commercial DMA and started Bohlin Rheologia. Both instruments used torsional geometry. The early instruments were, regardless of manufacturer, difficult to use, slow, and limited in their ability to process data. In the late seventies, Murayani11 and Read12 wrote books on the uses of DMA for material characterization. Several thermal and rheological companies introduced DMAs in the same time period and currently most thermal and rheological vendors offer some type of DMA. Polymer Labs offered a dynamic mechanical thermal analyzer (DMTA) using an axial geometry in the early eighties. This was soon followed by an instrument from Du Pont. PerkinElmer developed a controlled stress analyzer based on its thermomechanical analyzer (TMA) technology, which was designed for increased low-end sensitivity. The competition between vendors has led to easier to use, faster, and less expensive instruments. The revolution in computer technology, which has significantly affected the laboratory, changed instrumentation in many ways and DMAs of all types became more user-friendly as computers and software evolved. In 2000, a small company named Triton Ltd made the next major change in moving away from a large, long throw core rod to limit mass and therefore increase responsiveness in the instrument. Triton sold this technology to PerkinElmer who uses it for their DMA. They were later acquired by Mettler-Toledo, who now offered two DMAs built on this approach. Along the way, a couple of specialized instruments developed for the rubber and other industries and the torsional model became considered rheometers while axial designs became a standard thermal analysis offering now known as DMA. We will look at instrumentation briefly in Chapter 5. Since the first edition of this book was published, several articles have appeared that review the state of the art.13 Many of these will be covered in later chapters.
How a DMA works. The DMA supplies an oscillatory force, causing a sinusoidal stress to be applied to the sample, which generates a sinusoidal strain. By measuring both the amplitude of the deformation at the peak of the sine wave and the lag between the stress and strain sine waves, quantities like the modulus, the viscosity, and the damping can be calculated. The schematic shows the arrangement of many DMAs where the motor is above the furnace. Other instruments place the sample above the motor. The LVDT could be a balance transducer or an optical encoder, depending on the brand.
simplification and we will discuss it in Chapter 5 in greater detail. From this, one calculates properties like the tendency to flow (called viscosity) from the phase lag and the stiffness (modulus) from the sample recovery. These properties are often described as the ability to lose energy as heat (damping) and the ability to recover from deformation (elasticity). One way to describe what we are studying is the relaxation of the polymer chains.14 Another description would be to discuss the changes in the free volume of the polymer that occur.15 Both descriptions allow one to visualize and describe the changes in the sample. We will discuss stress, strain, and viscosity in Chapter 2.
The applied force is called stress and is denoted by the Greek letter
The ratio of stress to strain is the modulus, which is a measurement of the material's stiffness. Young's modulus, the slope of the initial linear portion of the stress-strain curve (shown here as a dotted line), is commonly used as an indicator of material performance in many industries. Since stress-strain experiments are one of the simplest tests for stiffness, Young's modulus provides a useful evaluation of material performance.
will often drop several decades. (A decade is an order of magnitude based on a logarithmic scale.) This drop in stiffness can lead to serious problems if it occurs at a temperature different from expected. One advantage of DMA is that we can obtain a modulus each time a sine wave is applied, allowing us to sweep across a temperature or frequency range. So, if we were to run an experiment at 1 hertz (Hz) or 1 cycle/second, we would be able to record a modulus value every second. This can be done while varying temperature at some rate like 5°C-10°C/min so that the temperature change per cycle is not significant. We can then with a DMA record the modulus as a function of temperature over a 200°C range in 20-40 minutes. Similarly, we can scan a wide frequency or shear rate range of 0.01 to 1000 Hz in less than 2 hours assuming a rate of 2°C/min. In the traditional approach, we would have to run the experiment at each temperature or strain rate to get the same data. For mapping modulus or viscosity as a function of temperature, this would require heating the sample to a temperature, equilibrating, performing the experiment, loading a new sample, and repeating at a new temperature. To collect the same 200°C range this way would require several days of work.
The modulus measured in DMA is, however, not exactly the same as the Young's modulus of the classic stress-strain curve (see Figure 1.3). Young's modulus is the slope of a stress-strain curve in the initial linear region. In DMA, a complex modulus (E*), an elastic modulus (E'), and an imaginary
DMA uses the measured phase angle and amplitude of the signal to calculate damping, tan 6, and a spring constant, k. From these values, the storage and loss moduli are calculated. As the material becomes elastic, the phase angle, 6, becomes smaller and E* approaches E'.
(loss) modulus (E") are calculated from the material response to the sine wave. These different moduli allow better characterization of the material because we can now examine the ability of the material to return energy (E'), to lose energy (E"), and the ratio of these effects (tan delta), which is called damping. Chapter 5 discusses dynamic moduli along with how DMA works.