Термомеханический анализ (ТМА): принципы и области применения
Вебинар в записи

Термомеханический анализ (ТМА): принципы и области применения

Вебинар в записи
TMA technique
TMA technique

ТМА – один из важнейших методов термического анализа, дополняющий методы ДСК, ТГА и ДМА. Термомеханический анализ используется для регистрации изменений размеров различных материалов в зависимости от температуры: термопластов, реактопластов, эластомеров, адгезивов и покрытий, плёнок и волокон, металлов, керамики и композитов. Термомеханический анализ (ТМА) – высокочувствительный метод, поэтому с его помощью можно определять слабо выраженные физические переходы, связанные с изменениями модуля, отверждением и расслоением.

Эффекты и свойства, которые можно изучать с использованием ТМА: тепловое расширение и усадка волокон и пленок, размягчение, стеклование, кристаллизация, плавление, реакции отверждения и сшивки.

Принцип измерения в методе ТМА
Прибор ТМА регистрирует изменение длины образца в зависимости от температуры и приложенной нагрузки.
В ТМА эксперименте образец помещают в держатель, после чего к нему через измерительный датчик прикладывается постоянная нагрузка. Соприкасаясь с образцом, датчик перемещается вверх или вниз, по мере того как длина или толщина образца изменяется в зависимости от температуры. Смещение датчика измеряется с помощью линейного дифференциального
трансформатора (датчик LVDT), подключенного к другому концу датчика. Способ размещения образца в держателе
и прилагаемая нагрузка зависят от режима измерения и цели анализа.

English , 日本語 , Русский

Thermomechanical Analysis

Slide 0: Thermomechanical Analysis

Ladies and Gentlemen
Welcome to this seminar on thermomechanical analysis – or TMA as it is usually called.
TMA is an important technique in thermal analysis.

A TMA instrument is used to study the dimensional changes of a material as a function of temperature or time.

Slide 1: Contents

In this seminar, I would like to explain the basic principles of thermomechanical analysis and at the same time introduce two high-performance TMA instruments.

I also want to point out a number of important design features and benefits and discuss the different sample measurement modes.

Finally, I will present examples to illustrate the different application possibilities of TMA in various industries.

Slide 2: What is TMA?

The picture on the left of the slide shows a section of railway track. Between winter and summer, or even night and day in some places, the temperature can change by as much as 80 degrees Celsius. A temperature increase of this magnitude will cause a 50 meter section of steel track to expand by 6.5 centimeters. Sufficient space must therefore be left between the sections of railway track in order to prevent buckling.

In practice, many modern materials are subject to a wide temperature range during use. This means that expansion and contraction always has to be taken into account, for example in the design of composite materials.

Thermomechanical analysis is used to characterize expansion and contraction behavior and to determine the coefficient of thermal expansion – or CTE as it is called for short.

Depending on the measurement mode used, TMA allows you to measure:
thermal expansion and shrinkage behavior,
softening, and
changes in mechanical properties of materials induced by physical or chemical transitions such as the glass transition, crystallization, melting and curing.

The TMA curves in the diagram on the right show the measurement of a polyethylene terephthalate or PET disk in the dilatometry mode. The upper curve shows the thickness of the sample as a function of temperature, and the lower curve the calculated CTE curve.


Slide 3: Basic Principles of TMA

This upper diagram illustrates the basic measuring principle of a TMA instrument.

The sample is placed on the sample support and a constant load is applied to it via the measuring probe. The probe remains in contact with the sample and moves upward or downward as the sample length, in this case the sample thickness, changes with temperature. The displacement of the probe is measured by means of a linear variable differential transformer or LVDT sensor connected to the other end of the probe. The sample setup and applied load vary depending on the measurement mode and the information required. This will be discussed in more detail later in the seminar.

The bottom right diagram shows a typical TMA dilatometry curve. In this mode, a very low force is applied to the probe and the sample length is measured as a function of temperature. The length gradually increases with increasing temperature. When the glass transition temperature, Tg, (tee gee) is reached, there is a significant increase in the rate of expansion and slope of the curve.
The Tg is evaluated as the point of intersection of the extrapolated slopes. The curve of the instantaneous CTE is calculated from the length curve. The step corresponds to the glass transition.


Slide 4: TMA/SDTA840 and 841e

This slide shows a schematic diagram of two modern thermomechanical analyzers, the METTLER TOLEDO TMA/SDTA840 and TMA/SDTA841e.

The sample support and probe are made of quartz glass. This has a very low coefficient of linear thermal expansion in the temperature range up to 1100 degrees Celsius.

The probe is parallel-guided and moves freely on frictionless bearings in a vertical direction and precisely follows the dimensional changes of the sample. The desired load on the probe is produced by the force generator. An electromagnetic linear motor counteracts the weight of the moving parts and ensures that the probe transfers the desired force to the sample. The force used is typically in the range 0 to 1 newton.

The displacement sensor is a linear variable differential transformer or LVDT. The ferromagnetic core inside the coil system is connected to the measuring probe and generates an electrical signal proportional to the displacement. The position of the probe is measured with nanometer resolution.

A protective gas such as nitrogen is normally used to protect the mechanical and electronic parts from the effects of corrosive decomposition products. The LVDT and other parts are also protected against temperature changes through the use of thermostating and reflector baffles.

There are two temperature sensors. One sensor measures the furnace temperature and controls the temperature program. The other sensor is situated in the sample support directly below the sample and measures its temperature, from which the SDTA signal is derived. The SDTA sensor measures the calorimetric effects of the sample.

Slide 5: Measurement Modes

I would now like to discuss the different TMA measurement modes. The choice of the measurement mode is determined by the shape and properties of the sample and the information required.

The upper left diagram in the slide illustrates the dilatometry or compression mode. In the dilatometry mode, the parallel-sided sample is covered with a quartz glass disk to distribute the force uniformly over the contact area. A low force is applied that is just sufficient to ensure that the probe remains in contact with the sample. The CTE of bulk materials can be measured in this way. Compression behavior is measured by applying larger forces. This mode is used to study the mechanical properties of soft materials such as foams, gels and elastomers.  

The next mode is penetration. The aim of a penetration measurement is to determine the temperature at which the sample begins to soften or deform under an applied load. A ball-point probe is often used for such measurements in order to apply a high initial stress or force per unit area. Initially, the ball-point probe is only in contact with a very small area of the sample. As the sample softens on warming, the probe penetrates more and more into it. Alternatively, a probe with a contact surface area of 1 square millimeter can be used in order to apply a constant stress.

The tension mode is often used to investigate the expansion and shrinkage behavior of films and fibers. The samples are prepared externally using the appropriate accessories. Plastic films and metal foils are installed in the film attachment device using two clips. Fibers, threads and wires are fixed in place in the fiber attachment device by means of copper clips. Usually a low force is applied that is just sufficient to ensure that the film or fiber remains slightly taut between the clips and does not buckle.

Special accessories for investigating the swelling behavior of materials in solvents are also available. A parallel-sided sample is placed in a glass vial and covered with a quartz glass disk. A lid is then placed on the vessel to prevent evaporation of solvent. The probe enters through a hole in the lid and rests on the sample with a low force. Solvent is injected using a syringe at the beginning of an isothermal measurement and the change in sample thickness resulting from the absorption of solvent is measured as a function of time.

Finally, there is three-point bending. This mode is ideal for stiff samples such as fiber-reinforced plastics or other polymers and composites that do not show any measurable deformation in the compression mode. Bending measurements are often made in the so-called dynamic load TMA mode, or DLTMA mode, in which the force applied to the sample alternates periodically. This mode is very sensitive to changes in Young’s modulus caused by the thermal effects of the sample such as the glass transition, curing, and melting.

The following slides show typical measurement curves to illustrate each particular measurement mode.   

Slide 6: Measurement Modes                      Dilatometry

The first slide shows the TMA measurement of a 0.5-millimeter disk of amorphous PET in the dilatometry mode.

The curve in the upper diagram records the thickness of the sample with increasing temperature. The sample first expands slowly up to the glass transition. The expansion rate then increases significantly on further heating due to the increased mobility of the molecules in the liquid state. Afterward, softening and cold crystallization processes occur and the sample shrinks. After crystallite formation, the sample expands again above 150 degrees before it finally melts. Melting is accompanied by a drastic decrease in viscosity and thickness.

The lower curve shows the coefficient of thermal expansion, CTE, as a function of temperature. This is calculated from the thickness curve and the initial sample thickness. The CTE curve typically exhibits a step increase at the glass transition. The information can also be presented in the form of a table.

Slide 7: Measurement Modes                              Penetration

The penetration measurements were performed with the same PET disk used in the previous slide.
The results yield information about softening behavior and softening temperatures. The two curves were measured using loads of 0.1 and 0.5 newtons. The depth of penetration is influenced by the applied force and the sample geometry.

At low temperatures, the probe penetrates very slowly into the sample until the glass transition is reached, which is indicated by a step-like decrease in the ordinate signal. The ordinate signal decreases during cold crystallization and afterward remains more or less constant. A further penetration step occurs at higher temperature when the sample melts.

Slide 8: Measurement Modes                                    Tension

This slide shows the measurement of a PET fiber in tension.

Below about 75 degrees Celsius, the fiber is in the glassy state and is dimensionally stable.
Afterward, the sample starts to shrink due to the increased mobility of the molecules. The orientation of the molecules produced in the stretching process during the manufacture of the fiber is gradually destroyed.
The rate of shrinkage increases as the melting temperature is approached. The minimum length is reached at about 255 degrees. Afterward, the viscosity of the sample decreases dramatically and the sample starts to flow.

Slide 9: Measurement Modes                            Swelling

The curve in the diagram shows the swelling of an elastomer in toluene.

The sample was allowed to equilibrate for two minutes at 30 degrees Celsius and the initial thickness measured. The furnace was then opened briefly and the glass vessel filled with toluene at the same temperature using a syringe.
The probe measures the increase in thickness of the sample on swelling due to the absorption of the solvent. As can be seen, it swells by about 30% in the first ten minutes.

Slide 10: Measurement Modes     Dynamic Load TMA (DLTMA)

As mentioned previously, bending measurements are often performed in the Dynamic Load TMA, or DLTMA, mode.

In this mode, the load applied to the sample alternates periodically between a small force, F1, and a large force, F2, as shown in the upper diagram. In practice, a period of about 12 seconds is often used. This is in contrast to a normal TMA measurement in which the load remains constant.
The displacement or bending of the sample varies as the force changes. The blue curve in the lower diagram shows the response of an ideal elastic sample such as a steel spring, which deforms without delay under changing load. In contrast, viscoelastic materials such as polymers exhibit a significant time dependence due to molecular rearrangement during the relaxation processes.

DLTMA measurements allow the Young’s Modulus of the sample to be determined, which is basically the ratio of stress to strain. In the compression mode, stress is the difference between the two forces, F, (delta eff) divided by the area under stress. The strain is L, (delta ell) the deformation caused by F, divided by the initial sample thickness. After rearrangement, we see that the modulus can be determined from the applied force and the measured displacement amplitudes and sample geometry.

The DLTMA mode can be applied to all measurement modes, that is, to compression, tension and bending. It is very sensitive to changes in the modulus of materials and is therefore an excellent technique for studying weak chemical and physical transitions. DLTMA is in fact ideal for the determination of the modulus of soft materials. However, for the measurement of a wide stiffness range, we recommend dynamic mechanical analysis using the METTLER TOLEDO DMA/SDTA861e.

Slide 11: Measurement Modes                       Bending/DLTMA

The upper diagram shows the bending measurement of a laminate consisting of two thin metal sheets bonded together by an epoxy adhesive. The upper and lower envelopes of the DLTMA curve show the deformation measured using forces of 0.5 and 1.0 newton. The difference between the envelopes is a measure of the elasticity or compliance of the sample. The mean curve is about equivalent to the deformation under a static force of 0.75 newtons.  

The lower diagram shows the modulus of bending of the sandwich structure calculated from the DLTMA curve. Since the elastic modulus of the metal sheets hardly changes, the step decrease in the modulus curve at about 100 degrees Celsius is attributed to the glass transition of the epoxy adhesive.
Bending measurements using DLTMA are very sensitive and are ideal for deter¬mining the curing, softening or glass transition temperature of coatings, adhesive bonding layers, and filled thermosets. Sample prepara¬tion is usually a matter of adapting the sample geometry to the bending accessory.

Slide 12: Why Use TMA?

I would now like to summarize the main reasons for using TMA.

As we discussed earlier, TMA can be used to determine the coefficient of thermal expansion and to characterize the expansion and shrinkage behavior of materials. A good understanding of such behavior is important, particularly for materials that undergo stretching or orientation processes during manufacturing, such as films and fibers.

The softening temperature of materials can be also measured by TMA in penetration experiments. Materials soften at the glass transition temperature or on melting.

DLTMA measurements are very sensitive to changes in Young’s modulus of a sample. The method can be used to detect weak glass transitions that cannot be detected by differential scanning calorimetry as well as curing processes of highly filled thermosetting composites.

Creep and recovery behavior as well as swelling behavior in solvents are important properties of elastomers. TMA can be used to characterize such behavior under isothermal conditions.

In principle, any chemical or physical transitions that cause dimensional changes can be measured by TMA, for example the delamination and decomposition of printed circuit boards is a typical TMA application.

The next slide presents an overview of the possible applications of TMA in various industries.  

Slide 13: Industries and Applications

As we can see from the table, a key application of TMA is the determination of the coefficient of thermal expansion of a wide range of materials such as polymers, metals and alloys and composites in various industries. For example, in the electronics industry the determination of the CTE, glass transition temperature and delamination of printed circuit boards by TMA is a standard test.

TMA can be also used to determine the softening temperatures of coatings, lacquers and adhesives to check that curing is sufficient. In the textile and packaging industries, TMA is often used to characterize the expansion and shrinkage behavior of films and fibers. Creep and recovery of elastomers for sealing applications is also an important application.

In universities and academia, dimensional changes of materials are investigated under the most varied experimental conditions.

In the following slides, I would like to present several different application examples that demonstrate the analytical power and versatility of the TMA technique.

Slide 14: Application 1                       Determination of CTE

Materials expand or contract as a result of an increase or decrease in temperature. They exhibit different expansion and contraction behavior in different temperature ranges. The possibility of dimensional changes due to temperature change must be taken into account when designing composites from different materials, and in many engineering applications. Otherwise, cracks and damage can occur and lead to product failure.
The diagram shows the determination of the coefficient of thermal expansion, CTE, of several different inorganic materials by TMA.
The prerequisites for accurate CTE results are low signal noise, a low heating rate and blank subtraction. Materials with non-uniform thermal expansion are of special interest:
These include Invar, a nickel steel alloy with 36% nickel, which has practically zero thermal expansion at ambient temperature. Duran glass, like most mineral glasses, has very low coefficient of expansion below the glass transition temperature. Crystalline quartz, measured here in the c-axis direction, expands steadily up to the solid-solid transition at about 575 degrees Celsius after which it begins to contract.

Slide 15: Application 2             Characterization of a PCB board

This slide shows a typical application of TMA in the electronics industry.

A printed circuit board (or for short a PCB) is a laminate consisting of several layers of support material bound together by a thermosetting matrix resin. A high performance PCB exhibits several important properties:
First, structural rigidity and dimensional accuracy;
Second, a sufficiently high softening or glass transition temperature of the matrix resin to prevent the deterioration of mechanical and dielectric properties;
Third, adequate thermal durability and stability of the matrix resin to withstand the soldering bath temperature and possible heat accumulation in later operation.
Any degradation of the matrix resin is accompanied by outgassing, which can force the layers apart, that is cause delamination, thereby destroying the laminate.
This slide demonstrates how these properties can be characterized using TMA.

The sample was measured in the dilatometry mode. It expands gradually on heating up to the glass transition temperature at about 94 degrees Celsius. Above this temperature, the slope of the expansion curve becomes steeper. The curve exhibits a typical glass transition, which can be evaluated as the point of intersection of the two slopes of the TMA curve.

The CTE curve shows a step increase from approximately 80 ppm per degree to 320 ppm per degree. It is important to note that printed circuit boards are anisotropic and exhibit quite different CTE values for length, width and thickness. To obtain complete information, the CTE should therefore be measured in all three directions.

Delamination is observed as spikes and jumps in the TMA curve, starting at about 320 degrees and becoming more serious above 360 degrees.

Slide 16: Application 3                        Softening of coatings

Coatings are applied to substrates in many industrial applications to improve the surface properties of the substrates. The thermal and mechanical stability of such coatings and their thickness are characteristics that play an important role in product quality, process control, and cost control.

In this application, two copper wires, A and B, with different enamel insulation coatings were measured in the TMA penetration mode.
In both cases, the resulting TMA curves exhibit two steps. The first step of each curve at about 150 degrees Celsius is due to softening of the individual insulation coatings. The second step above about 200 degrees corresponds to the decomposition of the coatings. In sample A, both effects occur about 20 degrees to higher temperature compared with the effects in sample B. This demonstrates that the thermal and mechanical stability of the insulation of wire A is superior.

The TMA penetration mode is often the most sensitive method for measuring the softening or glass transition of thin coatings.
The thickness of the coatings can be also estimated by adding the heights of the two steps together and dividing by two because both the lower and the upper layers contribute to the steps.
The results show that the coatings are 12 to 15 microns thick.  

Slide 17: Application 4                  Shrinkage of polymer films

Stretched films often have a preferred orientation and hence exhibit anisotropic mechanical properties. These properties can be characterized by measuring the expansion or shrinkage behavior using TMA.

The slide shows the TMA curves of two polyethersulfone-based film samples.
The red curves show the results obtained from the stretched film measured in and across the stretching direction, and the blue curves the results from the unstretched film.

The unstretched sample is isotropic and shows the same behavior in both measurement directions.
The behavior of the stretched sample is very different in the stretched direction compared with at right angles. In the stretched direction, the film shrinks from about 100 degrees Celsius onward, whereas across the stretched direction, the length of the film increases with increasing temperature.

Slide 18: Application 5                  Curing of an epoxy coating

Several thermal analysis techniques can be used to characterize the curing behavior of thermosets.
Differential scanning calorimetry (or DSC) is the technique normally used to follow the crosslinking process by measuring the heat evolved in the reaction. The DSC method cannot, however, determine the increase of the viscosity or the modulus of elasticity during curing.
A TMA bending measurement is a good choice to correlate both effects. This application shows how TMA and the simultaneous DTA function, SDTA, have been combined in the TMA/SDTA840.

The sample used in this application was a razor blade with a 0.3-mm layer of freshly mixed epoxy adhesive coated on its underside. The measurement was performed at a heating rate of 5 degrees per minute using an alternating load of 0.02 and 0.04 newtons. The upper diagram shows the DLTMA and the SDTA measurement curves.

At temperatures below 90 degrees Celsius, the liquid adhesive has little influence on the deformation of the razor blade. As the adhesive cures and hardens, deformation of the razor blade becomes more restricted and decreases significantly. The Young’s modulus curve in the lower diagram shows clearly how the modulus increases during the curing process.
The curing reaction produces an exothermic peak between 50 and 150 degrees Celsius on the SDTA curve. Integration of the peak results in the conversion curve shown in blue. The vertical black dotted line at 65% conversion corresponds roughly to the gelation of the adhesive. It also intersects the green Young’s modulus curve at two thirds of its change.

The same instrumental setup also allows the glass transition temperature of the cured resin to be determined in a second heating run.

Slide 19: Application 6                   Gelation of an adhesive

An adhesive is initially in the liquid state. During isothermal curing, the viscosity of the thermosetting resin increases with increasing conversion, and the resin undergoes crosslinking to form a solid. From the technical point of view, the gel point during the curing process is of major interest because it is the point at which the adhesive becomes attached to the structure involved.

The sample was inserted into a pre-equilibrated measuring cell and measured by DLTMA using alternating forces of ±0.1 newton. Initially, while the sample is still liquid, the probe switches between the highest and lowest position under the changing load, as seen from the large deformation amplitude. With further curing, the sample cures and hardens and eventually the probe becomes stuck in the sample. The reaction time at which the probe can no longer be raised from the sample corresponds to the gel point. The measurement results show that the gel point at 10 degrees Celsius is approximately 26 minutes.

Dynamic mechanical analysis is however the best technique for measuring the gel point. In this technique, the gel point is measured as the point of intersection of the storage and loss modulus.

Slide 20: Application 7          Creep of differently vulcanized SBR samples

The most important properties of elastomers used for sealing applications are the elastic modulus and the creep and viscous flow behavior. Creep refers to the time- and temperature-dependent elastic and plastic deformation of a material when it is subjected to a load or stress. Creep deformation consists of two components, reversible creep relaxation and irreversible viscous flow. The former deformation is restored over time when the stress is reduced or removed. Viscous flow however causes permanent deformation and geometry change and often leads to product failure.

The time-independent elastic deformation of a material under load is determined by its Young’s modulus. It indicates the deformation capacity of the material under an applied stress.

All these properties can be readily investigated by TMA in isothermal creep and recovery experiments. In such experiments, the sample is maintained isothermally at a specified temperature, a force is applied and held constant for a certain period, and then quickly removed. The strain, that is, the relative change in thickness of the sample, is recorded as a function of time.

In this application, styrene butadiene rubbers with different degrees of vulcanization were investigated at 30 degrees Celsius.
The unvulcanized SBR0 sample shows the largest elastic deformation as marked by the black arrow on the left of the diagram. With increasing degree of vulcanization, the deformation of the vulcanized SBR samples 1 to 3 gradually decreases and the elastic modulus increases.
SBR0 also exhibits the largest degree of viscoelastic relaxation while, in contrast, the relaxation of the crosslinked SBR samples is much less pronounced.
Furthermore, the SBR0 sample has the largest irreversible deformation component. This is shown by the black arrow on the right of the diagram. The creep recovery segment would however have to be appreciably longer to observe the complete recovery. The SBR1 and SBR2 samples still show a certain amount of viscous flow whereas in the SBR3 sample this deformation component is practically no longer observed due to the high degree of crosslinking.

The results show that increasing the degree of crosslinking of elastomers by vulcanization is an effective way to increase the elastic modulus and reduce the undesired viscous flow for sealing applications.

Slide 21: Application 8                       Swelling of polymers

The swelling behavior of elastomers in different solvents is often of interest for their practical use later on.
In this application, the swelling behavior of four technical elastomers in toluene was studied at room temperature:
MQ is a methyl-silicone elastomer,
EPDM an ethylene-propylene-diene terpolymer,
NBR an acrylonitrile-butadiene elastomer, and
FPM a fluoroelastomer.
The diagram displays the normalized TMA curves as a function of time. FPM swells only by about 2% in toluene. The material is clearly very resistant to toluene. It can for example be used as a sealing ring in this solvent. The situation is very different with the other elastomers, in particular, the silicone rubber, which swells by more than 35%.
Swelling measurements allow elastomers and sealing rings to be specifically selected for particular applica¬tions.

Slide 22: Summary:                    TMA/SDTA 840 and 841e

This slide summarizes the features and benefits of the TMA/SDTA840 and 841e.

Thermomechanical analysis is an excellent technique for studying the expansion behavior and softening temperature of various materials such as thermoplastics, thermosets, elastomers, adhesives and coatings, films and fibers, metals, ceramics and composites. TMA is also very sensitive method and can be used to determine weak physical transitions that are associated with changes in modulus, curing, and delamination.

A key feature and advantage of the METTLER TOLEDO TMA instruments is the parallel-guided measuring sensor. Thanks to this patented mechanical design, the measuring probe moves up and down without friction, ensuring that the results are of high quality. The nanometer resolution enables the instruments to detect very small dimensional changes. The wide measurement range of ±5 millimeters allows both small and large changes to be measured.

Dynamic load TMA is available for all modes of operation. It is a powerful technique for measuring weak transitions such as the glass transition of a highly filled composite through the change in Young’s modulus.

The simultaneous DTA signal yields additional calorimetric information about thermal effects such as curing and melting. It provides accurate temperature calibration using reference materials with well-defined melting points.

Furthermore, the gas-tight cell ensures that measurements can be performed in a defined atmosphere. The TMA/SDTA840 can be coupled to a mass spectrometer or an FTIR spectrometer to analyze and identify gaseous products evolved from samples.  

Slide 23: For more information on TMA

Finally, I would like to draw your attention to information about thermomechanical 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 of thermal analysis UserCom can be downloaded as PDFs from www.mt.com/usercoms.

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 24: Thank you

This concludes my presentation on thermomechanical analysis. Thank you very much for your interest and attention.

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