Thermomechanical Analysis

One could argue that the standard type of thermomechanical analysis (TMA) tests, in which a very small load is applied to a sample, is really a subset of creep testing. Some vendors actually treat it as such in their dynamic mechanical analysis (DMA) software. However, TMA really needs to be addressed on its own for several reasons. First, the load applied for the classic TMA experiment, where we measure the unrestrained expansion of the sample, is really just enough to assure constant contact of the probe. Second, TMA looks not at the sample's response to the load in a expansion study but the material's response to changing temperature in terms of dimensional changes and the transitions that occur in the material.1 This is why fine force control is essential and dedicated TMAs often have load capacities of 1 N max. Also thermomechanical analyzers tend to be a different type of instrument, smaller and with better temperature control than the instruments used for measuring qualities like Young's modulus, viscosity, and creep, although the newer DMAs are now capable of these measurements although with a lesser degree of precision.2 Also, some new TMA permit limited DMA studies. Because of its convenient size and more precise temperature control associated with its smaller sample size, the TMA is a common instrument in many thermal laboratories and is the first mechanical analyzer used by many chemists. One could even suggest that all rheology and traditional mechanical tests should be included in this classification. In its purest form, TMA records changes in a material's dimensions under minimal, ideally zero, load and these are used as an indicator of the changes in the material's free volume. This data allows the calculation of a material's expansivity or coefficient of thermal expansion (CTE; sometimes written LCTE for linear coefficient of thermal expansion to differentiate it from the volumetric expansion) as well as detection of transitions in the material. TMA on inorganic glass was the first measurement of the glass transition and it still remains the preferred technique for that measurement in many applications. It is often said to be more sensitive to the glass transition than differential scanning calorimetry (DSC) by an order of magnitude. However, its greatest advantage is obtaining the CTE value as part of the data.

Theory of Thermomechanical Analysis

The basis of TMA is the change in the dimensions of a sample as a function of temperature. A simple way of looking at TMA is as a very sensitive micrometer. TMA is believed to have developed from hardness or penetration tests and was first reported as being used on polymers in 1948. Subsequently, it has been developed into a powerful tool in the analytical laboratory. TMA3 measurements record changes caused by changes in the free volume of a polymer.4 Changes in free volume, vf, can be monitored as the volumetric change in the polymer, the absorption or release of heat associated with that change, the loss of stiffness, increased flow, or the change in relaxation time.5 The free volume of a polymer, vf, is known to be related to viscoelasticity,6-7 aging,8-9 penetration by solvents,10 and impact properties.11-12 Defined as the space a molecule has for internal movement, it is schematically shown in Figure 4.1a. As the space available for the chains to move increases, larger and larger segments may move, giving rise to thermal transitions. This is often called the crankshaft model13 and is shown in Figure 4.1b.

The Tg in a polymer corresponds to the expansion of the free volume allowing greater chain mobility above this transition and in TMA this is what we measure by thermal expansion (see Figure 4.2). Real life does not show as sharp a Tg as shown here. Seen as an inflection or bend in the thermal expansion curve, this change in the TMA can be seen to cover a temperature range due to the distribution of molecular weights and relaxations times in a polymer. What we call a glass transition temperature or Tg is an indication of this range calculated by an agreed upon method (see Figure 4.3). This fact

FIGURE 4.1

Free volume, vf, in polymers: (a) the relationship of free volume to transitions, and (b) a schematic example of free volume and the crankshaft model. Below the Tg in (a) various paths with different free volumes exist depending on heat history and processing of the polymer, where the path with the least free volume is the most relaxed, (b) Shows the various motions of a polymer chain. Unless enough free volume exists, the motions cannot occur.

FIGURE 4.2

The increase in free volume is caused by increased energy absorbed in the chains and this increased free volume permits the various types of chain movement to occur.

FIGURE 4.3

The Tg is a region, shown here between the points where the tangents depart from the curve. The temperature of Tg, by convention, is taken as the intersection of those two tangents. This definition of the Tg as a single temperature can be problematic.

seems to be forgotten by inexperienced users, who often worry why perfect agreement isn't seen in the value of the Tg when comparing different methods. The width of the Tg can be as important an indicator of changes in the material as the actual temperature.

Experimental Considerations with TMA Samples

Experimentally, TMA consists of an analytical train that allows precise measurement of position and can be calibrated against known standards.

FIGURE 4.4

Testing geometries used for TMA measurements. Fixtures are often traditionally made in low expansion materials, like quartz glass or ceramics. Modern instruments and software allow correction for the fixture expansion and this permits the use of more robust materials like steel and titanium to also be used.

A temperature control system of a furnace, heat sink, and temperature measuring device (most commonly a thermocouple) surrounds the samples fixtures to hold the sample during the run are normally made out of quartz because of its low CTE, although ceramics and invar steels may also be used if appropriate factors are taken into account. Fixtures are commercially available for expansion, three-point bending or flexure, parallel plate, and penetration tests (see Figure 4.4), but specialized fixtures are common. Sample preparation varies with the method. Samples for CTE are the most difficult to prepare as ideally they are rectangular samples, with parallel and flat top and bottom sides. For anisotropic material, a cube is preferred with all sides parallel and squared. As large a sample as can be evenly heated should be prepared as this increases the accuracy of the CTE measurement. For glasses, samples of 2-5 inches in length are often used. Other geometries are more forgiving; in flexure tests of composites, a sliver of material taken off the edge of the sample with a blade is often used.

TMA applications are in many ways the simplest of the thermal techniques. We are just measuring the change in the size or position of a sample. However, they are also incredibly important in supplying information needed to design and process everything from chips to food products to engines. A sampling of American Society for Testing and Materials (ASTM) methods for TMA is shown in Table 4.1. Because of the sensitivity of the modern TMA, it is often used to measure Tgs that are difficult to obtain by DSC, such as those of highly crosslinked thermosets.

TABLE 4.1

ASTM Methods for TMA

D696-16 Standard Test Method for Coefficient of Linear Expansion

D4065-12 Standard Practice for Plastics: Dynamic Mechanical Properties: Determination and Report of Procedures

D4092-07 Standard Terminology: Plastics: Dynamic Mechanical Properties

E831-19 Standard Test Method for Linear Thermal Expansion of Solid Materials by TMA

E1363-18 Standard Test Method for Temperature Calibration of TMA

E1545-11 Standard Test Method for Assignment of the Glass Transition Temperature by TMA

E1824-18 Standard Test Method for Assignment of the Glass Transition Temperature by TMA in Tension

E1953-14 Standard Practice for Description of Thermal Analysis and Rheology Apparatus

E2092-18a Standard Test Method for Distortion Temperature in Three-Point Bending by TMA

E2113-18 Standard Test Method for Length Change Calibration of TMA

E2206-11 Standard Test Method for Force Calibration of TMA

E2347-16 Standard Test Method for Indentation Softening Temperature bv TMA

E2769-18 Standard Test Method for Elastic Modulus by TMA using 3 Point Bending

E2918-18 Standard Method for Performance Validation of TMAs

E3142-18 Standard Test Method for Thermal Lag of TMAs

Expansion and CTE

TMA allows the calculation of the thermal expansivity14 from the same data set used to calculate the Tg. Since many materials are used in contact with a dissimilar material in the final product, knowing the rate and amount of thermal expansion helps in designing around mismatches that can cause failure in the final product. This data is only available when the Tg is collected by thermal expansion, not by the flexure or penetration method. This is in many ways the simplest or most essential form of TMA measurement. A sample is prepared with parallel top and bottom surfaces and the sample is allowed to expand under minimal load (normally 5 mN or less, ideally it would be 0 mN) as it is slowly heated and cooled. Samples range down to micron-thick films but as thick a sample as possible should be used to minimize errors. For polymers, 5-mm tall blocks are common. Heating rates are normally kept low to allow equilibration of the sample to the furnace temperature. CTE is calculated by:

where oq is the linear CTE, 10 is the original length, 61 is the change in length, and 5T is the change in temperature. The F indicates this is done under constant force. Once this value is obtained, it can be used to compare the other materials used in the same produce. Large differences in the CTE can lead to motors binding, solder joints failing, composites splitting on bond lines, or internal stress build up. The Tg is obtained from the same data by measuring the inflection point in changes of slope of the baseline. As a material's CTE changes dramatically at Tg, one would expect this to be an easily detected transition. It can be but for highly crosslinked materials, the Tg can be so broad and the change in CTE so slight as to be undetectable. Other approaches, like flexure testing, are therefore used. Different Tg values will be seen for each mode of testing15 (see Figure 4.5) and it is necessary to report the method

FIGURE 4.5

Different methods of measuring the Tg in TMA give different values as shown in (a) the overlay of the penetration, flexure, and expansion runs; (b) the comparison of a polymer to a metal CTE run; (c) the baseline and uncorrected sample expansion for polystyrene. For an accurate CTE value, one must subtract the baseline from the data. Note that at the Tg, the material has softened enough that it collapses and begins to contract.

one used to get the Tg by TMA. Values on CTE vary greatly from quartz (~0.5 ppm) to stainless steel (11 ppm) to high polymers (-25 ppm). In tension, where metal fixtures are often used, it is common to subtract the baseline signal from the data (see Figure 4.5c).

If the material is heterogeneous or anisotropic, it will have different thermal expansions depending on the direction in which they have been measured. For example, a composite of graphite fibers and epoxy will show three distinct thermal expansions corresponding to the x, y, and z direction. Blends of liquid crystals and polyesters show a significant enough difference between directions that the orientation of the crystals can be determined by TMA.16 In fact, many other crystalline materials exhibit similar determination abilities.’^18 Similarly, oriented fibers and films have a different thermal expansivity in the direction of orientation than in the unoriented direction. This is normally addressed by recording the CTE in the x, y, and z directions (see Figure 4.6a). Bulk measurements or volumetric expansion can be made

FIGURE 4.6

Heterogeneous samples require the CTE to be determined in (a) the x, y, and z planes or (b) in bulk to obtain a volumetric expansion in the dilatometer. (c) A printed circuit board shows different behavior in three directions. Data redrawn from Hitachi App TA_021 and run on a Hitachi TMA-7100.

by dilatometry as shown in Figure 4.6b and this is discussed in detail in Section 4.5.

Expansion studies can also be run on samples immersed in solvents to measure the swelling of a polymer. This test is commonly used with rubbers to measure the crosslink density of the rubber.19-20 As crosslinking increases, the amount of swelling will decrease. Special fixtures are commercially available for this or standard fixtures may be used in a lined furnace. A sample is immersed in oil and the degree of swelling measured. Figure 4.7 shows results from a rubber swelling study as an instrument set up in an immersion bath to allow this type of testing.

 
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