# 4 Thermomechanical Analysis (TMA)

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1 172 4 Thermomechanical Analysis 4 Thermomechanical Analysis (TMA) 4.1 Principles of TMA Introduction A dilatometer is used to determine the linear thermal expansion of a solid as a function of temperature. Unlike the classical methods in which the experimental setup is kept as free of forces as possible, in thermomechanical analysis, a constant, usually small load acts on the specimen [1]. The measured expansion of the specimen can be used to determine the coefficient of linear thermal expansion. The 1 st heating phase yields information about the actual state of the specimen, including its thermal and mechanical history. When thermoplastics soften, especially above the glass transition, orientations and stresses may relax, as a result of which postcrystallization and recrystallization processes may occur. On the other hand, the specimen may deform under the applied test load. To determine the coefficient of expansion as a material characteristic, the material must not undergo irreversible changes, such as postcrystallization, postpolymerization, relaxation of orientation or internal stress and so forth during a 2 nd heating phase that has followed controlled cooling. In addition, the anisotropy of the molded part must be taken into account; it is advisable to measure in the x-, y- and z-axes. The behavior of plastics on exposure to heat is described in detail in Section Coefficient of linear thermal expansion can serve as a material characteristic only where material behavior is reversible. The coefficient of linear thermal expansion may be recorded as the mean ( T) or differential (T) and is calculated in accordance with DIN [2], ISO Part 1 and 2 [3, 4]. The mean coefficient of linear thermal expansion ( T) is derived as follows: 1 l 2 l1 1 l th µm ( T) = = l 0 T2 T1 l 0 T m C ( T) is an experimental value that varies in each case over the individual temperature measurement range. It is therefore not suitable as a general characteristic or as a general value for calculations but pertains to a specific application. The temperature-dependent change of length is the progressive change of length expressed in terms of the initial length/reference length l 0. It is a relative measure of the linear

2 4.1 Principles of TMA 173 expansion, which always has a value of 0 at the start of the trial at the reference temperature T 0. The differential (or local) coefficient of linear thermal expansion (T) is derived as follows: 1 dl th µ m ( T) = l0 dt m C The values may assume the dimensions [10-6 C -1 ] or [K -1 ]. ISO [4] recommends [K -1 ], DIN [2] [10-4 C -1 ] or [K -1 ]. However, in this chapter, we shall use the unit [µm/(m C)] because, in our experience, this conveys a better impression of the magnitudes involved. Coefficients of linear thermal expansion as a function of temperature are shown in Fig. 4.1 for semicrystalline thermoplastics and in Fig. 4.2 for amorphous thermoplastics. The rise in the coefficient of linear thermal expansion in the glass transition range makes it clear that the values are not constant. For this reason, it is advisable to consider the whole curve when assessing the expansion behavior over a large temperature range. 400 macroprobe, 0.5 g load PE PBT [µm/m C] PP PA 46 (dry) Temperature [ C] Fig. 4.1 Coefficient of linear thermal expansion for PE, PP, PBT, and PA 46 Macroprobe, specimen crosssection approx. 6 x 6 mm, load 0.5 g, heating rate 3 C/min Characteristics are dependent on temperature range. The shape of the 1 st heating curve is governed by the direction of measurement (see Section ), the processing conditions, and the thermal and mechanical history (see Section

3 174 4 Thermomechanical Analysis ). Not only the measurement parameters (see Section ), but also additives affect the coefficient of linear thermal expansion. 400 macroprobe, 0.5 g load 300 PS ABS PC [µm/m C] PI Temperature [ C] Fig. 4.2 Coefficient of linear thermal expansion of PS, ABS, PC, and PI Macroprobe, specimen crosssection approx. 6 x 6 mm, load 0.5 g, heating rate 3 C/min Given reversible material behavior, linear expansion is roughly one third of volumetric expansion. Linear expansion = 1/3 x volumetric expansion Measuring Principle A cylindrical or oblong specimen measuring 2 6 mm in diameter or length and usually 2 10 mm in height is subjected to slight loading (0.1 5 g) via a vertically adjustable quartz glass probe. The probe is integrated into an inductive position sensor. The system is heated at a slow rate. If the specimen expands or contracts, it moves the probe. A thermocouple close to the specimen measures the temperature. Figure 4.3 shows schematic diagrams of the setup for different types of TMA apparatus. The diagram on the left shows the measuring system and the furnace above the specimen. The diagram on the right shows the measuring system located beneath the specimen; for heating, the furnace is lowered on the apparatus from above.

4 4.1 Principles of TMA 175 In TMA under load, the measured expansion curve always represents the sum of the different deformation components, such as linear thermal expansion and the load-dependent deformation (force, probe geometry, temperature-dependent modulus). load quartz glass probe inductive position sensor quartz glass probe sample thermocouple sample heater sample holder Fig. 4.3 Schematic diagrams of TMA apparatus Left: Apparatus above the specimen Right: Apparatus beneath the specimen Change of linear expansion is the result of linear thermal expansion and loaddependent compression. Probe shapes differ so as to accommodate various specimen geometries (films, fibers, varying cross-sections) and specific experimental goals (measurement of expansion behavior or of glass transition temperature) Normal probe 2. Macroprobe 3. Penetration probe 4. Setup for films or fibers in the tensile mode Fig. 4.4 Different shapes of probe used in TMA

5 176 4 Thermomechanical Analysis The choice of probe depends on the geometry of the specimen. To ensure maximum accuracy when determining the coefficient of linear thermal expansion, it is preferable to use probes with relatively large contact areas. Where the specimen is large enough, a macroprobe with a contact area of approx. 28 mm 2 is used. For smaller specimens, for example, with an edge length less than 6 mm, a normal probe with a contact area of approx. 5 mm 2 is suitable. Accurate coefficient of linear thermal expansion Large probe area low applied load Penetration probes with a small contact area of just about 0.8 mm 2 are suitable for determining the glass transition temperature. In the case of amorphous plastics especially, penetration by the probe as the specimen softens yields a signal that is readily evaluated. Owing to the small contact area, even a low applied load generates nonuniform, high compressive stress that does not permit correct sensing and evaluation of the expansion behavior. Therefore the coefficient of linear expansion cannot be determined with accuracy. Special holders allow thin films and fibers to be measured. For this, the specimen is held between two clamps and then suspended in the measuring device. To prevent the thin specimen from twisting or curling, it is loaded with a slight tensile force. Glass transition temperature determination Linear expansion large probe contact area low load Penetration small probe contact area high load Procedure and Influential Factors The stages involved in a TMA measurement are as follows: Prepare plane-parallel specimens. Measure initial length l 0. Load the specimen in the instrument. Choose applied load. Choose suitable experimental parameters. The influential factors and sources of error associated with the experiment are explained in detail in Section with the aid of experimental results from real-life examples. Factors exerting an influence on the apparatus and specimen are:

6 4.1 Principles of TMA 177 Type of load (shape of probe) Specimen preparation Influential factors Stress (load) Starting temperature Specimen geometry Eigenschaften Heating rate Evaluation Coefficient of Linear Expansion Change of length [µm/m] l l 0 0 T 0 T 1 T T 2 Temperature [ C] (T) ( T) Differential coefficient of linear thermal expansion: Mean coefficient of linear thermal expansion: Tangent at a temperature (T 2 ), slope at one point Slope over a temperature range ( T) l/l 0 Change of length: Change of length over a temperature range, expressed in terms of the initial length l 0 T Change of temperature: Difference between two temperatures (T 2 T 1 ) Fig. 4.5 Evaluation of the mean ( T) and differential (T) coefficients of linear thermal expansion

7 178 4 Thermomechanical Analysis The change of length of the specimen can be used to calculate both the mean coefficient of linear thermal expansion ( T) over a specific temperature range and the differential coefficient ( T) of linear thermal expansion (see Section 4.1.1). Figure 4.5 illustrates the difference between the two characteristics. While (T) is the respective slope of the tangent at a specific temperature, ( T) is the slope of a secant in a temperature range. For this reason, (T) can be meaningfully plotted as a function of temperature. Mean coefficient of linear thermal expansion: ( T) Differential coefficient of linear thermal expansion: (T) Glass Transition Temperature At the glass transition, many physical properties of amorphous plastics or of the amorphous domains of semicrystalline thermoplastics undergo stepwise changes in several orders of magnitude. The same applies to their coefficient of linear thermal expansion. Figure 4.6 shows how loading affects the linear expansion and the differential coefficient of linear expansion of plastics at the glass transition. Whether the expansion (rising curve) or penetration (falling curve) occur above the glass transition depends on the expansion, probe area, applied load, and the temperature-dependent modulus of elasticity. Generally, unreinforced plastics have a higher coefficient of linear thermal expansion above T g than below it because of greater segment mobility in the amorphous domains. Figure 4.6 (left) shows how, in the case of slight loading and a still relatively high modulus of elasticity even above T g (e.g. in semicrystalline thermoplastics or thermosets), the expansion curve is steeper above T g. At the same time, there is a step in -curve. If the modulus of elasticity changes extensively above T g, as in the case of thermoplastics and elastomers, the probe can penetrate into the specimen on even slight loading or at least superpose the expansion, Fig. 4.6, right. In such cases, the real expansion behavior can no longer be equivocally measured. In unreinforced plastics, (T) is greater above T g than below it.

8 4.1 Principles of TMA 179 Change of length [ µm/m] expansion T g T g [µm/m C] Change of length [ µm/m] penetration Tg T g (T ) P =0 [µm/m C] Temperature [ C] Temperature [ C] T g T g T P Glass transition temperature from linear expansion: Glass transition temperature from : Penetration temperature Expansion: The temperature at which the extrapolated tangents intersect before and after the glass transition (expansion curve) Penetration: The temperature at which the extrapolated tangents intersect; the maximum of the expansion curve Expansion: Inflection point of the step (-curve) Penetration: The maximum of the expansion curve can also be characterized by the temperature at which assumes the value 0. Penetration: The temperature at which the extrapolated tangents intersect; the maximum of the expansion curve [5] Fig. 4.6 Expansion behavior in the glass transition region Left: expansion Right: penetration Evaluating T g from the expansion curve In the literature [4, 6, 7], T g is evaluated from the expansion curve by determining the point where the extrapolated lines before and after the glass transition intersect. In [8], the intersection of the extrapolated lines on penetration is termed the softening temperature T s. Evaluating T g from the curve T g is calculated from the change of the differential coefficient of linear expansion. For expansion, the turning point of the step is used and, for penetration, the temperature at which = 0 µm/(m C) is used, as this reflects the maximum of the expansion curve.

9 180 4 Thermomechanical Analysis Test Report DIN contains useful information for compiling a complete test report that describes all experimental parameters and specimen details. Where appropriate, the test report should contain the following information [2]: Reference to the standards employed All details necessary for complete identification of the material analyzed Shape and dimensions of the specimens, where specimens are made of semifinished and finished products, the position of the specimens in the product and the direction of measurement must be stated. Pretreatment of specimens, recording any irreversible changes in length that may have occurred Number of specimens tested Experimental conditions Reference temperature and the pertinent length of the specimen Temperature range covered Coefficient of thermal expansion (T) in [10-4 C -1 ] to two decimal places as a function of temperature, on a plot Mean coefficient of linear thermal expansion ( T) in [10-4 C -1 ] to two decimal places where only one temperature interval was measured Diagram of the relative coefficient of linear thermal expansion as a function of temperature Details as to whether irreversible changes occurred during the measurements and how many repetitions of the test program were made until linear reversible changes in the length of the specimen occurred Date of the test Expansion curve Calibration The TMA apparatus must be calibrated in terms of length and temperature. If the loading force is applied electromagnetically, it may be calibrated with the aid of known weights. If the apparatus is in constant use, it should be calibrated every month. Because probes have different masses, a new calibration must be performed every time a probe is changed. Calibration and actual test measurements must be performed using the same probe geometry, applied load, heating rate, and temperature range (starting temperature). The specimen should be the same size as the calibration specimen. Calibration parameters = Experimental parameters

10 4.1 Principles of TMA Calibrating the Length The length is calibrated mostly with metallic specimens that have a known, reversible coefficient of linear thermal expansion. Aluminum specimens are frequently used. Their experimental coefficient of expansion in the temperature range of interest is compared with the standard literature value, see also ASTM E 2113 [11]. The calibration factor, F, is calculated as follows: literature F = experimental Calibrating the Temperature The temperature is calculated with pure metals (indium, zinc) that have known, reproducible melting points, Table 1.5. The metals should have melting points in the temperature range of interest. The metal is placed between two sheets (e.g., quartz glass or aluminum) in the apparatus and heated in accordance with the desired experimental parameters. When the melting point of the calibrating metal is reached, the probe compresses the discs, and a pronounced step shows up on the curve. The melting point is the intersection of the tangent to the resultant curve ranges. Several metals can be heated up simultaneously in a sandwich construction for measurement. Temperature calibration is performed with two metals using a penetration probe with an applied weight of 5 g. The temperature is quoted to +/- 1 C [9], see also ASTM E 1363 [12]. To measure the temperature as close to the specimen as possible, most devices feature a flexible thermocouple. Care must be taken not to hinder expansion of the specimen. After calibration, the position of the thermocouple must not be changed Overview of Practical Applications Table 4.1 shows which characteristics of TMA experiments can be used to assess quality deficiencies and processing flaws or to characterize materials. The scope of TMA is explained in more detail in Section using real-life examples and the pertinent characteristic curves. Application Characteristic Example Service temperatures for parts design, β Dimensional stability (constant expansion coefficient) Expansion behavior in different directions Anisotropy; along and across the direction of processing Orientation Shrinkage on deorientation > T g

11 182 4 Thermomechanical Analysis Application Characteristic Example Influence of reinforcing materials, β Change of expansion behavior Determination of glass transition temperatures T g Change of expansion curve Material composite 1 2 Adhesive film on support material; coinjection molding, plastic-metal hybrids Degree of curing in thermosets T g Determination of the glass transition temperature; superposition of shrinkage (through postcuring) and expansion Physical aging T g Shifting of T g to higher temperatures owing to reduced void volume in amorphous regions Table 4.1 Examples of practical applications of TMA in plastics

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