4 Thermal Analysis Tools ___________________________________________________________________ 406 Fig. 4.145 The present graph refers to a time scale of about 10 s for any one measurement and is to be compared, for example, to a DSC scan at 6 K min 1 . On the left-hand side of the graph, the high moduli of the glassy and semicrystalline solid are seen and can be compared to the table of bulk moduli in Fig. 4.144. At the glass transition, Young’s modulus for amorphous polystyrene starts dropping towards zero, as is expected for a liquid. The applied stress causes the molecules to flow, so that the strain increases without a limit when given enough time. Before very low values of E are reached, however, the untangling of the macromolecular chains requires more time than the 10 s the experiment permits. For a given time scale, the modulus reaches the so-called rubber-elastic plateau. Only at higher temperature (>450 K) is the molecular motion fast enough for the viscous flow to reduce the modulus to zero. Introducing permanent cross-links between the macromolecules by chemical bonds, the rubber- elastic plateau is followed with a gradual increase in E. The data for a semicrystalline sample of polystyrene are also shown in the graph of Fig. 4.145. They show a much higher E than the rubbery plateau. Here the crystals form a dense network between the parts of the molecules that become liquid at the glass transition temperature. This network prohibits flow beyond the rubber elastic extension of the liquid parts of the molecules. Unimpeded flow is possible only after the crystals melt in the vicinity of 500 K. 4.5.2 Instrumentation of TMA A schematic diagram illustrating a typical thermomechanical analyzer is shown in Fig. 4.146. This instrument was produced by the Perkin–Elmer Co. Temperature is controlled through a heater and the coolant at the bottom. Atmosphere control is possible through the sample tube. The heavy black probe measures the position of the 4.5 Thermomechanical Analysis, DMA and DETA ___________________________________________________________________ 407 Fig. 4.146 sample surface with a linearly variable differential transformer, LVDT (see Fig. 4.13). The floating suspension, combined with added weights at the top, controls the force on the sample. The measurement can be carried out in various modes of sample- configuration. The simplest application uses a negligible downward compression force to study the sample dimension. A wide foot in contact with the sample, applied with a minimal downward force, yields the linear expansivity and is an example of a one-dimensional dilatometer. By enclosing the sample in a dilatometer flask with fixed wall, one may also obtain data on volume expansion and compression. The problem in the volume dilatometer probe is, naturally, to find a filling medium which is a properly hydrostatic medium and is easily sealed without friction. More details on general dilatometry are discussed in Sect. 4.1. When the force on the sample is increased, the just described dilatometer becomes a thermomechanical analyzer, proper. The four types of probes at the top of A in Fig. 4.146 are being used to act in a penetration mode. A rod of well-defined cross section or geometry presses with a known force on the sample, and its penetration is measured as a function of temperature. The sharp, conical probe on the right is also used to characterize the sample by producing a plastic indentation. The setup at the bottom of A is designed to test the elastic modulus in a bending experiment. The deflection is followed at fixed loads with changing temperature. The two setups in B, finally, show special arrangements to put tension on a film or fiber sample. The measurement consists then of a record of force and length versus temperature. Measurements of shrinkage and expansion are important to analyze the performance of fibers and films. Thermomechanical analyzers are available for temperatures from as low as 100 K to as high as 2,500 K. Basic instruments may go from 100 to 1,000 K with one or two furnaces and special equipment for liquid N 2 cooling. For higher temperatures, 4 Thermal Analysis Tools ___________________________________________________________________ 408 Fig. 4.147 different designs with thermally stable materials are needed. The linear range of the LVDT may be several millimeters. The maximum sensitivity is as high as a few tenths of a micrometer. A typical mass on the weight tray or force on the spring may be as much as 200 g. The dimensions of the sample are typically 0.5 cm in diameter and up to a few centimeters in height. The data acquisition and treatment through electronics and computer is as varied as in DTA and calorimetry. Direct recording of length and derivative of length is most common. The heating rates range from perhaps 0.1 K min 1 to as high as 40 K min 1 . They depend on the sample size and holder configuration. Even faster heating and cooling rates are often used to accomplish quick, uncontrolled temperature changes. 4.5.3 Applications of TMA Data from a thermomechanical analysis are usually plotted as linear expansivity or length of the sample as a function of temperature. Figure 4.147 illustrates eight differentTMAexperiments. Thetopgraphsshow solid-solidtransitionsfor potassium ethylsulfate, K(C 2 H 5 )SO 4 , and dichlorodipyridylcobalt(II), Co(C 5 NH 5 ) 2 Cl 2 .The organic compound acetanilide, CH 3 CONHC 6 H 5 , which has a melting temperature of about 388 K, shows premelting shrinkage. The barium chloride, BaCl 2 $2H 2 O, decreases in volume when it loses its crystal water, but continues afterwards with a normal, positive expansivity. All these measurements were done in the compression or penetration mode. In this configuration melting registers as a decrease in length, despite an increase in volume of the sample, because the material starts flowing. The graphs at the bottom of Fig. 4.147 display results gained in the flexure mode under conditions that satisfy the ASTM (American Society forTestingand Materials). The deflection temperature is taken where the sample has been deformed by 0.010 in 4.5 Thermomechanical Analysis, DMA and DETA ___________________________________________________________________ 409 Fig. 4.148 (0.254 mm). For polycarbonate and poly(vinyl chloride) the deflections occur abruptly, close to the glass transition temperature, as is expected. For the two polyethylenes, the deflection is more gradual and can be related to the melting ranges of the semicrystalline polymers. In the next series of applications schematic TMA traces of polymeric fibers in the tension mode are compared to DTA traces. The analyzed fibers could, for example, be poly(ethylene terephthalate), PET (see Sects. 4.3, 4.4, and 5.2). As extruded, the fibers are largely amorphous with some orientation. The TMA in Fig. 4.148 shows the usual expansion below the glass transition, followed by shrinkage as soon as the glass transition is reached. The partially drawn molecules relax to smaller dimensions as soon as sufficient mobility is gained at the glass transition. When equilibrium is established in the liquid (rubbery) state, a gradual decrease in expansivity is observed as the sample crystallizes. The crystallization is clearly evident in the DTA experiment through its exotherm. On melting, the sample becomes liquid and starts flowing. The recording stops when the fiber ultimately breaks. The DTA trace illustrates the full melting process. Drawing causes higher orientation of the fiber, as is illustrated by Fig. 4.149. At the glass transition much larger shrinkage is observed than in Fig. 4.148. Subsequent crystallization occurs at lower temperature due to the better prior orientation. Since the DTA crystallization peak is smaller than the subsequent melting peak, one would conclude that the original drawn sample was already somewhat crystalline. Annealing the drawn fiber, as shown in Fig. 4.150, introduces sufficient crystal- linity to cause the shrinkage to occur continually between the glass and melting temperatures. One would interpret this behavior in terms of the existence of a rigid amorphous fraction that gradually becomes mobile at temperatures well above the 4 Thermal Analysis Tools ___________________________________________________________________ 410 Fig. 4.149 Fig. 4.150 glass transition. The TMA is thus a key tool in characterizing the various steps of fiber formation, particularly, if it is coupled with DSC and the analysis of molecular structure and mobility as discussed with Figs. 5.68–72 and 5.113–115. Even more detailed are the DTA traces reproduced in Fig. 4.151 for PET. The broken lines show the melting at constant length. The continuous lines show melting 4.5 Thermomechanical Analysis, DMA and DETA ___________________________________________________________________ 411 Fig. 4.151 of samples allowed to shrink freely. One can see from the changing of the melting peak with heating rates that equilibrium conditions were not fulfilled. The fact that the samples kept at fixed length, melt more sharply than the freely shrinking ones, is also in need of an explanation. The crystals are connected to the amorphous chains in the arrangement of the fibers. Any portion of the amorphous chains which is not fully relaxed after crystallization will increase the local melting temperature, as discussed in Chaps. 5 7. The degree of stretch is, however, determined by the crystals that set up a rigid network to maintain the strain in the amorphous chains. As the first crystals melt, the amorphous chains can start relaxing and thus decrease the melting temperature of the crystal portions to which they are attached, as shown in Fig. 4.151. There is, thus, a complicated sequence of melting and chain relaxation. In the PET case shown, there is a wide distribution of crystalline and intermediately ordered material (see Sect. 6.2), which causes the broad melting range of the samples. The fibers analyzed under the condition of fixed length, melt more sharply and increase in melting temperature with the heating rate. In the low-heating-rate samples, one can even detect a tilt of the peak toward low temperatures. This must mean that the collapse of the crystal network occurs so suddenly that it lowers the melting temperature faster than the heating rate increases the temperature. At a high heating rate, this decrease in melting temperature occurs less sudden, and the melting occurs at higher temperature and over a wider temperature range. In Figs. 4.148–150 the TMA and DTA curves don not show this decrease in temperature on melting because of the different experimental conditions and time scales. This discussion documents that various forms of thermal analyses have to be brought together, andcombined with knowledge fromthermodynamic theory, tobegin to understand the often complicated melting and crystallization behavior of polymeric materials (see Chaps. 5–7). 4 Thermal Analysis Tools ___________________________________________________________________ 412 Fig. 4.152 A final TMA example is shown in Fig. 4.152. It reproduces a penetration experiment with a rubbery material, cis-1,4-polybutadiene (CH 2 CH=CHCH 2 ) x . The glass transition occurs at 161 K. It softens the material to such a degree that the TMA probe penetrates abruptly. The quantitative degree of this penetration depends on the probe geometry, loading, and heating rate. At higher temperature the rate of penetration is then slowed somewhat by crystallization. At the melting temperature of the crystals grown during heating, the penetration is speeded up again. Thermomechanical analysis, thus, permits a quick comparison of different materials. As long as instrumental and measuring parameters are kept constant, quantitative comparisons are possible. 4.5.4 Principles and Instrumentation of DMA The study of elastic and viscoelastic materials under conditions of cyclic stress or strain is called dynamic mechanical analysis, DMA. The periodic changes in either stress or strain permits the analysis of the dynamic response of the sample in the other variable. The analysis has certain parallels to the temperature-modulated differential thermal analysis described in Sect. 4.4, where the dynamic response of the heat-flow rate is caused by the cyclic temperature change. In fact, much of the description of TMDSC was initially modeled on the more fully developed DMA. The instruments which measure stress versus strain as a function of frequency and temperature are called dynamic mechanical analyzers. The DMA is easily recognized as a further development of TMA. Its importance lies in the direct link of the experiment to the mechanical behavior of the samples. The difficulty of the technique lies in under- standing the macroscopic measurement in terms of the microscopic origin. The 4.5 Thermomechanical Analysis, DMA and DETA ___________________________________________________________________ 413 Fig. 4.153 technique and application of DMA has developed to such a degree that a separate textbook is necessary to cover it adequately. In this section only a brief introduction is given to show the ties to TMA and TMDSC. A detailed description of DMA can be found in the list of general references to this section. A major application lies in the analysis of flexible, linear polymers. Figure 4.153 shows a schematic drawing of a torsion pendulum. It was used for some of the first DMA experiments that were carried out as a function of temperature [43]. The pendulum is set into vibrations of small amplitude ( 3 o ) and continues to oscillate freely with a constant, characteristic resonant frequency of decreasing amplitude, recorded by a lamp and mirror arrangement. The viscoelastic properties are then computed from the frequency and the logarithmic decrement, ,ofthe amplitude. A typical torsional oscillation and a plot of the logarithm of the maximum amplitudes versus their ordinal numbers are shown in Fig. 4.154. The slopes of the curves A to D represent the logarithmic decrements. Dynamic mechanicalanalyzerscan be divided intoresonant and defined frequency instruments. The torsion pendulum just described is, for example, a resonant instrument. The schematic of a defined-frequency instrument is shown in Fig. 4.155. The basic elements are the force generator and the strain meter. Signals of both are collected by the module CPU, the central processing unit, and transmitted to the computer for data evaluation. The diagram is drawn after a commercial DMA which was produced by Seiko. At the bottom of Fig. 4.155, a typical sample behavior for a DMA experiment is sketched. An applied sinusoidal stress, ), is followed with a phase lag, ,bythestrain,J. The analysis of such data in terms of the dynamic moduli (stress-strain ratios, see Fig. 4.143) at different frequencies and temperature is the subject of DMA. 4 Thermal Analysis Tools ___________________________________________________________________ 414 Fig. 4.155 Fig. 4.154 Figure 4.156 illustrates the detailed technical drawing of a dynamic mechanical analyzer by TA Instruments. The sample is enclosed in a variable, constant- temperature environment, not shown,sothat the recorded parameters arestress, strain, time, frequency, and temperature. This instrument can be used for resonant and defined-frequency operation. Even creep and stress relaxation measurements can be performed. In creep experiments, a constant stress is applied at time zero and the 4.5 Thermomechanical Analysis, DMA and DETA ___________________________________________________________________ 415 Fig. 4.156 strain of the sample measured as a function of temperature. In stress-relaxation a constant strain is applied to the sample and the relaxation of the stress is followed. In the description of the basics of thermomechanical analysis in the first part of this section the mechanical properties were assumed to result from perfect elasticity, i.e., the stress is directly proportional to the strain and independent of the rate of strain. Hooke’s law expresses this relationship with a constant modulus as sketched at the top of Fig. 4.157 for the example of tensile stress and strain. The theory of hydrodynamics similarly describes an ideal liquid behavior making use of the viscosity (see Sect. 5.6). The viscosity is the property of a fluid (liquid or gas) by which it resists a change in shape. The word viscous derives from the Latin viscum, the term for the birdlime, the sticky substance made from mistletoe and used to catch birds. One calls the viscosity Newtonian, if the stress is directly proportional to the rate of strain and independent of the strain itself. The proportionality constant is the viscosity, , as indicated in the center of Fig. 4.157. The definitions and units are listed, and a sketch for the viscous shear-effect between a stationary, lower and an upper, mobile plate is also reproduced in the figure. Schematically, the Newtonian viscosity is represented by the dashpot drawn in the upper left corner, to contrast the Hookean elastic spring in the upper right. The idealized laws just reviewed can, however, not describe the behavior of matter if the ratios of stress to strain or of stress to rate of strain is not constant, known as stress anomalies. Plastic deformation is a common example of such non-ideal behavior. It occurs for solids if the elastic limit is exceeded and irreversible deformation takes place. Another deviation from ideal behavior occurs if the stress depends simultaneously on both, strain and rate of strain, a property called a time anomaly. In case of time anomaly the substance shows both solid and liquid behavior at the same time. If only time anomalies are present, the behavior is called linear [...]... Fig 4.1 58 The ratio of viscosity to modulus of one element of the Voigt model is called the retardation time Fig 4.1 58 4.5 Thermomechanical Analysis, DMA and DETA 417 _ and for the example of a shear experiment is a measure of the time needed to extend the spring to its equilibrium length, as shown in the graph The rise of the strain caused by the application of the... thermogravimetry For standard of time, see Fig 4.3 4.6.4 Decomposition An analysis of black praseodymium dioxide, PrO2, in a variety of atmospheres is shown in Fig 4. 187 as an example of decomposition reactions The measurements were carried out with a Mettler Thermoanalyzer as described in Figs 4.1 78 180 with a gas-flow rate of 10 L h 1 The TGA-curves are recalculated in terms of the chemical composition...4.5 Thermomechanical Analysis, DMA and DETA 415 _ Fig 4.156 strain of the sample measured as a function of temperature In stress-relaxation a constant strain is applied to the sample and the relaxation of the stress is followed In the description of the basics of thermomechanical analysis in the first part of this section the mechanical properties... sensor The change of current in the balance mechanism is used directly as the thermogravimetry signal The DTA setup consists of an additional reference holder with detection of the temperature difference by beam-mounted sensors The reliability of the balance is claimed to be ±100 g at Fig 4. 182 434 4 Thermal Analysis Tools _ a maximum sample mass of 200 mg The temperature... record the quasi-isothermal loss of mass After completion of the first step of the reaction, the normal heating is resumed The quasi-isobaric environment is created by a special labyrinth above the sample holder that maintains the self-generated atmosphere during the decomposition range With double holders, simultaneous DTA is possible as illustrated in Figs 4. 188 and 4.190 436 4 Thermal Analysis Tools... _ Fig 4. 185 A general variation of thermal analysis involves a feedback from the sample to control its heating or cooling rates, commonly known under the name samplecontrolled thermal analysis [50] (SCTA, ICTAC nomenclature, 1996) The SCTA can lead to an improved resolution of overlapping processes, more homogeneous transformations, and better data for the study of the kinetics A property... the rate of weight change in TGA, as pointed out in connection with the discussion of the Derivatograph of Fig 4. 185 Similarly, the evolved gas analysis, mentioned in Sect 2.1.3, can be controlled by coupling the pressure and temperature signals Another method of SCTA in TGA is the stepwise isothermal thermogravimetry During the first step, the heating rate is kept constant until the derivative of the... continuing change of mass decreases below a second threshold This triggers again the first step to continue the temperature program A third mode of SCTA applied to TGA is the HiRes™ method of TA Instruments Its main objective is to obtain a high resolution of overlapping processes in an experiment of short duration The method makes simultaneous use of the information on the rate of change of mass and temperature... the glassy state Semicrystalline 424 4 Thermal Analysis Tools _ Fig 4.170 polymers show a more complicated DMA picture (see Fig 4.145) because of the additional melting transition and a considerable broadening of the glass transition (see Chaps 6 and 7) 4.5.6 Dielectric Thermal Analysis, DETA The mechanism of dielectric effects of interest to DETA involves permanent... sample The crucibles are made of platinum or sintered aluminum oxide Typical sample masses may vary from a few to several hundred milligrams 432 4 Thermal Analysis Tools _ Fig 4.179 Fig 4. 180 Later developments include desktop thermogravimetry A typical apparatus is shown in Fig 4. 181 The readability of this balance is 1 g The electrical range of mass compensation is from . temperatures, 4 Thermal Analysis Tools ___________________________________________________________________ 4 08 Fig. 4.147 different designs with thermally stable materials are needed. The linear range of. is applied to the sample and the relaxation of the stress is followed. In the description of the basics of thermomechanical analysis in the first part of this section the mechanical properties. because of the additional melting transition and a considerable broadening of the glass transition (see Chaps. 6 and 7). 4.5.6 Dielectric Thermal Analysis, DETA The mechanism of dielectric effects of