Принципы метода ДМА
Динамический механический анализ (ДМА) применяеся для исследований зависимости механических и вязкоупругих свойств материалов от температуры, времени и частоты при воздействии периодических нагрузок. Метод позволяет анализировать термопластичные и термореактивные полимеры, композитные материалы, эластомеры, керамику, металлы, адгезивы, краски и лаки, пленки и волокна, композиты, пищевые продукты, фармацевтические продукты, жиры и масла, конструкционные материалы.
Метод ДМА позволяет получать как качественную, так и колличественую информацию, например:
- модуль Юнга и модуль сдвига
- характеристики демпфирования и вязкоупругие свойства
- данные о структуре и морфологии полимеров
- текучесть и релаксационные характеристики
- процессы кристаллизации
- влияние наполнителей в полимерах
Данная информация является очень важной для инженеров и технологов, ученых-материаловедов и химиков.
Slide 0: Dynamic Mechanical Analysis
Ladies and Gentlemen
Welcome to this seminar on dynamic mechanical analysis – or DMA dee emm ay as it is usually called.
DMA dee emm ay is one of the most important techniques in thermal analysis. It can be used to study the viscoelastic properties and behavior of a wide range of materials as a function of temperature or frequency.
Slide 1: Contents
In this seminar, I would like to explain the basic principles of dynamic mechanical analysis and at the same time introduce a high-performance DMA dee emm ay instrument. I also want to point out a number of important design features and explain their functionality. Finally, I will present several examples to illustrate the different application possibilities of the DMA dee emm ay technique.
Slide 2: Basic Principles of DMA
The picture on the left of the slide shows the wing of an airplane undergoing a quality test. The wing is subjected to strong deformational stresses such as occur at take-off and landing. The red sensors record the measurement data. Large-scale tests of this nature are however very time-consuming and expensive.
Most modern constructional components are in fact subject to a wide range of stresses at different frequencies. DMA dee emm ay measurements can be used to characterize the viscoelastic behavior of materials and measure modulus values. This helps to ensure that suitable materials with the right mechanical properties are used. Depending on the measurement mode, DMA dee emm ay determines either the shear modulus (G) gee, or the Young’s modulus (E) ee.
The diagram on the right shows the results of a DMA dee emm a measurement of PET pee ee tee in the shear mode. The curves display the storage modulus (G′) gee prime , loss modulus (G″) gee double-prime, and tan delta as a function of temperature.
Slide 3: Basic Principles of DMA
This slide shows idealized DMA dee emm ay curves such as would be obtained from the measurement of an amorphous thermoplastic polymer. The blue curve (G′) gee prime is the storage modulus, the red curve (G″) gee double-prime is the loss modulus, and the black dashed curve is tan delta or the loss factor. Tan delta is the loss modulus divided by the storage modulus. The three quantities are displayed as a function of temperature. They describe the elastic behavior of the material in this temperature range. The elastic modulus is measured in units of Pa, MPa or GPa pascal, mega-pascal, or giga-pascal. One pascal is equal to a force of one newton per square meter.
In the glassy state, the polymer is almost ideally elastic and the value of the storage modulus (G′) gee prime is very high. As we move from left to right along the temperature axis, we first enter the glass transition range. The material becomes leathery and soft and the storage modulus decreases by about three orders of magnitude. The loss modulus (G″) gee double-prime and tan delta exhibit peaks. After the glass transition, we move into the so-called rubbery plateau in which the loss modulus and tan delta are small. In this region, thermoplastic materials exhibit rubbery-like properties and can be plastically deformed. The width of the rubbery plateau increases with increasing molar mass. At higher temperatures, the material starts to flow – assuming of course that it does not begin to decompose. The storage modulus decreases while the loss modulus and tan delta become larger and the material behaves like a liquid.
Slide 4: Basic Principles of DMA
Now let me explain the shear measurement mode. The sample holder is shown schematically in the red and green diagram in the upper right-hand corner of the slide. In this mode, two identical test specimens are held between three disks that are clamped together to form a sample holder. The middle disk is moved up and down under instrument control. The sample is subjected to a periodically changing force and undergoes deformation at the same frequency. The magnitude of the deformation is small and is within the linear elastic range of the sample. Typical of viscoelastic behavior is that the deformation lags behind the applied force. This produces a so-called phase shift.
The left part of the diagram shows the curves of the force and displacement amplitude and illustrates the phase shift. The in-phase component corresponds to the storage modulus (M′) emm prime and the out-of-phase component to the loss modulus (M″) emm double-prime. The storage modulus relates to the energy stored in the material and the loss modulus to the energy dissipated in the form of heat. Tan delta is often referred to as the loss factor or damping factor. It is a measure of how well a material dissipates energy.
Slide 5: Basic Principles of DMA
The concept of storage modulus and loss modulus can be illustrated by considering what happens when a tennis ball bounces on the ground. On impact, the ball undergoes deformation and does not bounce back up to the height from which it was dropped. Part of the energy supplied for the deformation has been lost. The height that the ball reaches after the deformation corresponds to the energy the ball was able to store elastically and reversibly. This corresponds to the storage modulus whereas the loss modulus corresponds to the energy that has been dissipated as heat. The term tan delta is the loss factor.
If a material is completely elastic, it stores the entire mechanical energy involved in the deformation. The energy is released without loss when the deformation force no longer acts. This is for example the case when a steel ball bounces on a hard surface – it bounces back up to the original height. In contrast, in an ideal viscous liquid in which the molecules are free to move, no energy is stored and the energy is converted to heat. The behavior of viscoelastic materials is characterized by loss and storage components. These and other quantities can be determined by DMA dee emm ay measurements.
Slide 6: DMA/SDTA861e
This slide shows a modern dynamic mechanical analyzer, the METTLER TOLEDO DMA/SDTA861e dee emm ay ess dee tee ay eight sixty-one ee. The instrument is built on a very strong and rigid stand. This enables measurements to be performed over large ranges of force and frequency. The instrument weighs about 120 kg kilograms and is about 80 cm centimeters in height. The furnace consists of two symmetrical halves that can be moved in and out horizontally to close or open the furnace. The excellent accessibility makes it easy to install the sample holders for the different measurement modes.
The measurement system is shown schematically in the diagram on the left. It consists of a motor that generates a dynamic force in the frequency range 1 mHz 1 milli-hertz to 1 kHz 1 kilo-hertz. The force is applied to the sample loaded in the clamp or sample holder by means of a drive shaft. The force sensor measures the force applied to the sample, and the displacement sensor the deformation of the sample.
The METTLER TOLEDO DMA dee emm ay differs from many conventional instruments in that the applied force is measured and that the sample can be prepared externally. A further important feature is that there is temperature sensor close to the sample. This allows thermal effects to be simultaneously measured by means of SDTA ess dee tee ay.
Slide 7: DMA/SDTA861e
This slide shows schematic diagrams of the different DMA dee emm ay measurement modes. The mode used for the experiment is determined by the shape and nature of the sample and the information required. Diagram 1 illustrates the shear mode. This mode allows a very wide range of samples to be measured, for example solids or even viscous liquids using the modified sample holder. This mode is especially suitable for measuring polymers – the sample can be measured from the glassy state through to the melt in one single measurement.
Diagram 2 shows the 3-point bending mode. This mode is ideal for very stiff samples with a modulus greater than 1 GPa 1 giga-pascal. If the sample softens during the measurement, the dual cantilever or single cantilever modes shown in diagrams 3 and 4 can be used. In these two modes, the samples are clamped either at both ends or just at one end.
Diagram 5 shows the tension measurement mode, which is excellent for thin bars, films and fibers. Besides this, there is also the compression mode, which is particularly good for measuring foams.
The shear mode measures the shear modulus (G) gee. All the other modes measure Young’s modulus (E) ee.
Slide 8: DMA/SDTA861e
Sample preparation and sample clamping or loading is crucial for achieving good quality measurements. METTLER TOLEDO has paid a great deal of attention to this aspect and has developed the technique of external sample preparation for the different modes of measurement.
The slide illustrates how a sample is loaded into the shear sample holder. Image 1 shows its individual parts. It consists of three disks and two guide pins that initially hold the disks together. The method requires two sample specimens of equal size. Image 2 shows the first step of assembly. The first disk is placed over the guide pins. One of the sample specimens is then positioned on it and held in place by means of the second disk as shown in Image 3. In Images 4 and 5, the second sample specimen is mounted and held in place by the end disk. The guide pins are then slightly tightened. Image 6 shows the sample holder ready for installation in the instrument. After installation, the temperature sensor is attached to the end disk and secured with the central screw. Finally, the two guide pins are removed and the measurement can begin.
Slide 9: Measurement Possibilities
DMA dee emm ay measurements can be performed as a function of temperature, frequency or amplitude. This slide gives an overview of the different applications associated with each parameter. Temperature scans are mainly used to investigate processes such as the glass transition, crystallization, and curing reactions, or to study damping behavior. Frequency scans provide information on relaxation behavior, molecular interactions, and damping behavior. Finally, amplitude scans are used for studying possible non-linear behavior of materials or the effects of fillers.
Slide 10: Measurement Possibilities: Temperature scan
This slide shows a temperature scan of a sample of a polylactide or PLA pee ell ay in the range −60 to +110 °C minus 60 to plus 110 degrees Celsius. The sample was measured in the tension mode. The diagram shows the storage modulus (E') ee prime, the loss modulus (E") ee double prime and tan delta. The glass transition can be clearly identified in all three curves. At low temperatures, the sample is hard and the modulus is very high. At the glass transition, the sample becomes soft and the modulus decreases.
Slide 11: Measurement Possibilities: Frequency scan
In practice, materials undergo stress over a wide frequency range. Since the mechanical properties of materials change with frequency, information on the frequency dependence is extremely important. Depending on the application, a material usually has to exhibit different properties. For example, an adhesive should be able to absorb stresses due to temperature fluctuations (low frequencies) like a liquid. At the same, however, the adhesive must react elastically to a blow (high frequencies) without breaking.
The slide shows a frequency sweep of the main relaxation range of an SBR elastomer. SBR is short for styrene-butadiene rubber. The measurement was performed isothermally at −10 °C minus 10 degrees Celsius. It demonstrates that DMA can cover a wide frequency range. Between 1 mHz and 1 kHz 1 milli-hertz and 1 kilo-hertz, G′ gee prime changes by about three decades. The maximum value of tan delta of 2.29 is reached at about 32 Hz hertz. At higher frequencies, the material is harder and the storage modulus is greater. Measurements at frequencies below 0.1 Hz hertz are very time-consuming.
Slide 12: Measurement Possibilities: Master curve construction
As I have just mentioned, measurements at low frequencies can be quite time-consuming. Besides this, at the other end of the scale, very high frequencies cannot be directly measured. There is however a solution to this problem, namely the method known as master-curve construction. The aim is to be able to make predictions in frequency ranges that are not readily accessible to direct measurements. One makes use of the fact that at high frequencies a material behaves the same as at low temperatures. This is known as the time-temperature-superposition principle, or TTS principle. Master-curves can be quickly constructed using the DMA861 to the excellent temperature stability and accuracy of the instrument as well as the high frequencies that can be reached. This allows information to be gained about the dynamic behavior, and the molecular structure and crosslinking network of materials.
The first step in master curve construction is to perform several frequency scans at different isothermal temperatures, in the example shown here at –60 °C, –50 °C and –26 °C minus 60, minus 50 and minus 26 degrees Celsius.
Slide 13: Measurement Possibilities: Master curve construction
This slide shows how master curves are constructed. The individual isothermal frequency sweep curves are shifted horizontally until the end sections overlap. This is shown by the arrows in the diagram using the three measurements from the previous slide. The master-curve increases the accessible frequency range to frequencies that cannot be directly measured. In this example, the reference temperature was −26 °C minus 26 degrees Celsius.
Slide 14: Measurement Possibilities: Master curves of SBR
This slide shows the storage and loss modulus master curves of an unvulcanized SBR elastomer. The two master curves were constructed from several individual isothermal frequency scans performed at different temperatures. The curves exhibit different processes such as flow, flow relaxation, the rubbery plateau, and the glassy process.
Slide 15: Measurement Possibilities: Amplitude scans
This slide shows amplitude scans of samples of natural rubber with different contents of carbon-black filler. Here, phr means parts by weight of carbon-black per hundred parts of rubber. The measurements were performed at shear amplitudes of 30 nm 30 nano-meters to 1 mm 1 millimeter. The measurement curves provide information about the linear elastic range and the interaction between the polymer and the filler. Whenever possible, measurements should be performed within the linear range. Otherwise, the modulus determined depends on the experimental conditions.
As this example shows, the modulus of filled polymers increases with increasing filler content, but decreases with increasing displacement amplitude.
Slide 16: Why Use DMA?
This slide summarizes the main reasons for using DMA.
As we have seen, DMA can be used to study the viscoelastic properties of materials in the relevant frequency and temperature range under different conditions. Furthermore, it enables us to determine modulus values.
The investigation of relaxation behavior is also very important - in particular, relaxation in the main relaxation region, that is in the glass transition region, or in secondary relaxation regions. The latter relaxation has to do with the mobility of short segments in polymers. No other technique of classical thermal analysis can provide such sensitive information about the glass transition as DMA.
Curing processes and the effect of fillers such as nanofillers in polymers can also be studied. Products with different nano-filler contents exhibit different properties due to interaction between the matrix and the filler. The information gained can be used to optimize the formulation used for manufacturing the products.
Slide 17: Why Use DMA?
DMA has numerous potential applications and can be used in practically all industries.
The summary in this slide shows that DMA studies are mainly used for the measurement of glass transitions, for investigating the curing reactions of thermosets and elastomers with regard to process optimization, or for studying damping behavior. Furthermore, modulus values can be determined.
I would now like to present several different application examples that demonstrate the analytical power and versatility of the DMA technique.
Slide 18: Application 1: PET in shear mode
This application presents the results of a shear measurement of a sample of PET pee ee tee that had been heated and then cooled very quickly beforehand. It shows that the instrument can measure the mechanical behavior of the thermoplastic material from the hard sample through to the molten state in just one single measurement. The first effect is beta-relaxation with a maximum at about −70 °C minus 70 degrees Celsius. The glass transition occurs at approximately +80 °C plus 80 degrees and is accompanied by a decrease in the storage modulus. At about 110 °C 110 degrees, cold crystallization takes place and the modulus increases again. On further heating, the crystallites undergo recrystallization. From about 240 °C 240 degrees onward, the crystallites begin to melt. The storage modulus (G′) gee prime decreases and the material becomes liquid. During the course of the measurement, the storage modulus changes from about 109 to 102 Pa ten to the power of nine to ten to the power of two pascals.
Slide 19: Application 2: PTFE film: phase and glass transitions
This application presents DMA dee emm ay and DSC measurements of a sample of polytetrafluorethylene, PTFE. The blue curve is the DMA measurement in tension and the red curve the measurement in the shear mode. These two curves are compared with the DSC measurement curve in black recorded in the same temperature range. The DSC curve shows the phase transitions of PTFE at about –100 °C and +30 °C minus 100 and plus 30 degrees as well as melting at 327 °C 327 degrees. The same transitions can also be easily measured by DMA. The transition at –100 °C minus 100 degrees is much clearer. In addition, the shear and tension measurements show the glass transition at 130 °C 130 degrees. This cannot be detected in the DSC curve due to the low intensity of the transition.
Slide 20: Application 3: DMA of silicone oil, liquid shear clamp
This slide displays the results obtained from silicone oil measured in a shear sample holder specially designed for liquids. The sample holder containing the sample was installed in an instrument which had already been cooled to –150 °C minus 150 degrees. Under these conditions, the sample was not able to crystallize and was in an amorphous state at the beginning of the measurement. The measurement curves show the decrease in the storage modulus (G′) gee prime at the glass transition at about –115 °C minus 115 degrees. This is followed by an increase at −100 °C minus 100 degrees due to crystallization and then melting at –40 °C minus 40 degrees where the storage modulus again decreases. The sample is then liquid and the red curve of the loss modulus (G″) gee double-prime lies above the black curve of the storage modulus. The storage modulus changes by 7.5 seven and a half decades.
Slide 21: Application 4: Coating in shear mode
This application shows how the glass transition temperature of a thin coating on a substrate can be measured. This is often difficult to do with DSC because the coating has to be separated from the substrate. In the DMA method, the complete sample, that is substrate and coating, are loaded into the shear sample holder and measured directly. Direct measurements of coatings are only possible in shear and not in bending or tension. In this application, the coating was 0.1 mm millimeters thick and covered an area of 2 by 2 mm millimeters.
Slide 22: Application 5: PCB in 3-point bending
This application shows the measurement of a printed circuit board in the 3-point bending mode. The matrix materials used for such composites consist of filled crosslinked polymers. The storage modulus of such materials must be sufficiently high at the application temperature. The determination is best performed using 3-point bending. The value obtained for the Young’s modulus of this printed circuit board was 24.2 GPa giga-pascal. At the glass transition, the material softens and the modulus decreases to 8.3 GPa giga-pascal. The step in the storage modulus is associated with peaks in the loss modulus and tan delta.
Slide 23: Application 6: Curing of EVA in shear
This slide shows the first and second heating runs of an EVA copolymer measured in the shear mode between −60 °C and +200 °C minus 60 and plus 200 degrees Celsius. EVA is used as an adhesive in the manufacture of photovoltaic modules. During the lamination process, EVA undergoes a curing reaction. This process can be easily studied by DMA.
In DMA, one makes use of the fact that the shear modulus (G′) is proportional to the crosslinking density. The higher the value of G′, the greater the crosslinking density. The first heating run shows the decrease in the modulus at the glass transition and on melting, and finally the curing reaction where the modulus increases. The same sample was then cooled and measured a second time. The second heating run shows the glass transition and melting but no postcuring. The modulus reaches the same value as at end of the first heating run.
Slide 24: Summary: DMA/SDTA861e
This slide summarizes the features and benefits of the DMA/SDTA861e Dynamic mechanical analysis is an excellent technique for characterizing the mechanical properties of materials such as thermoplastics, thermosets, elastomers, adhesives, paints and lacquers, films and fibers, composites, foodstuffs, pharmaceuticals, fats and oils, ceramics, constructional materials and metals.
The METTLER TOLEDO DMA instrument measures both force and displacement. The advantage of this is that the instruments records the force actually applied to the sample. The large force range allows both very soft and very hard materials to be analyzed. Furthermore, temperature adjustment is accurate because the sample temperature is measured. The possibility of measuring over a wide frequency range is another important advantage. It means that measurements can be performed under realistic conditions. The extraordinary wide stiffness range allows accurate measurements to be made from the glassy to the viscoelastic state without having to change the sample geometry or the deformation mode. External sample preparation is very practical and greatly simplifies the loading of samples into the sample holder.
Furthermore, measurements can be performed as a function of temperature, frequency or amplitude. This allows effects such as primary and secondary relaxation, crystallization, damping behavior, and the influence of fillers in polymers to be studied.
Slide 25: For More information on DMA
Finally, I would like to draw your attention to information about dynamic mechanical analysis that you can download from the Internet. METTLER TOLEDO publishes articles on thermal analysis and applications from different fields twice a year in UserCom, the well-known METTLER TOLEDO biannual technical customer magazine. Back issues can be downloaded as PDFs from www.mt.com/usercoms as shown at the bottom of the slide.
Slide 26: For more information on DMA
In addition, you can download information about webinars, application handbooks or information of a more general nature from the Internet addresses given on this slide.
Slide 27: Thank you
This concludes my presentation on dynamic mechanical analysis. Thank you very much for your interest and attention.