Thermal Analysis of Polymeric Materials
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4.5 Thermomechanical Analysis, DMA and DETA |
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curve at the bottom of Fig. 4.173 shows its change with frequency. At both, high and low frequencies approaches zero, in the dispersion region it reaches a maximum.
Debye derived the classical equations for the complex permittivity:
(3)
where is the relaxation time. The loss reaches its maximum at . At this point
= ( zero + )/2 and = ( zero )/2. Analogous to DMA a loss tangent can be defined (tan = / ). Actually measured dispersion curves are, however, flattened
and extend over wider frequency ranges, as shown by the solid curves in Fig. 4.173. As in the DMA case, this can be accounted for by assuming a relaxation-time spectrum. If several distinct relaxation mechanisms occur with sufficiently widely separated relaxation times, Eqs. (1) and (3) need to be expanded by additional terms describing the added processes. As with DMA, temperature and frequency are related, permitting a similar time-temperature superposition of the data.
A convenient way to represent the experimental data at constant temperature is in a Cole-Cole plot shown in Fig. 4.174, making use of the following equation:
(4)
where o is the most probable relaxation time at which shows the maximum. The empirical fitting parameter is zero if the relaxation process follows simple Debye behavior as described by Eq. (3) and tends toward one for broader relaxation time spectra. On plotting of versus , a circle is obtained with and zero as
Fig. 4.174
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intercepts with the abscissa. For = 0 the center of the circle lies on the abscissa at
( + zero )/2. With increasing , the center moves below the abscissa and a diameter from zero encloses the angle /2 with the abscissa. The data in Fig. 4.174 were drawn with an of about 0.25.
4.6 Thermogravimetry
4.6.1 Principle and History
The additional variable of state for thermal analysis by thermogravimetry is mass, as suggested in Fig. 4.175. The SI unit of mass is the kilogram [kg], which is the mass of an international prototype in form of a platinum cylinder and is kept at the International Bureau of Weights and Measures near Paris, France (see also Fig. 2.3). The last adjustment was made for the 1990 SI scale. Originally, that is in 1795, the gram was chosen as mass standard. It was to represent the mass of 1 cm3 of H2O at its freezing temperature. In 1799 the mass standard was changed to 1,000 cm3 of water at its maximum of density at 277.13 K, since the larger mass could be measured more precisely. At present, this connection is only approximate, but the difference from the old size is hardly noticeable for practical applications. Today the mass standard is independent of the volume of water.
The basic mass determination is simple. It consists in a comparison of the force exerted by gravity on the two masses to be compared, using for example a beam balance as is shown schematically in Fig. 4.175. For practically all thermal analyses, changes in temperature, pressure, volume, or chemical bonding do not change the total mass. The main calculation from a direct measurement of mass is to establish the number of moles of the compound or element in question. This is achieved by division through the molar mass, MW. With the general use of SI units, one must remember that the molar masses must be entered in kg, not g! The mole is defined as the number of atoms in exactly 12 g (0.012 kg) of the isotope 12 of carbon. The number of particles per mole is 6.02214×1023, Avogadro’s number.
The principles of thermogravimetry are also illustrated in Fig. 4.175. The sample, indicated by number 3, is kept in a controlled furnace, 2, whose temperature is monitored by the thermocouple, 4, via the millivoltmeter, 5. The balance, 1, allows continuous mass determination. A plot of mass as a function of temperature, T, or time, t, represents the essential thermogravimetry result. The definitions of the temperature units [K] and time units [s] are given in Sect. 4.1 with Fig. 4.2.
In gravimetry the sample represents, according to the definition of Sect. 2.1, an open system. The mass-flow across the boundaries of the sample holder is continuously monitored by the balance. One can suggest immediately two logical extensions of thermogravimetry. In order to identify the mass flux, an analysis technique, such as mass spectrometry or exclusion chromatography can be coupled to the furnace. The other extension involves the simultaneous measurement of the heat flux by calorimetry. Instruments that couple all three techniques have been built and can fully characterize an open system. Since one should, however, always be able to precisely repeat scientific experiments, it should be possible to separately measure mass change,
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Fig. 4.175
composition of the evolved gases, and heat flux. Frequently the dedicated instruments that focus on one measurement are more precise and easier to handle than the combination thermal analysis.
The wood-block print reproduced in Figs. 4.176 suggests that thermogravimetry was already possible a long time ago. Mass, temperature, and time determinations are among the oldest measurements of general interest. Looking into the alchemist’s
Fig. 4.176
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laboratory of the fifteenth century in Fig. 4.176, one can see that respectable balances and furnaces were available already at that time. Accurate temperature determination would have been somewhat more difficult then, as was discussed in Sect. 4.1.
It took considerable time until what one might call modern thermogravimetry was developed. Early analyses by Hannay and Ramsey in 1877 may have been the first of the more modern thermogravimetry experiments. They studied the rate of loss of volatile constituents of salts and minerals during drying. Most definitive, however, was the thermobalance designed by Honda in 1915. An interesting review of thermogravimetry was published by Duval [46]. A note about nomenclature, although the ICTAC suggests the name thermogravimetry in favor of the older term thermogravimetric analysis, it permits the old abbreviation TGA since TG would lead to confusion with the abbreviation of the glass transition temperature, Tg.
4.6.2 Instrumentation
The schematic of a typical thermogravimetric system is illustrated based on the classical, high-precision instrument, the Mettler Thermoanalyzer [47]. The block diagram of Fig. 4.177 gives a general overview of the instrumentation and control, and Fig. 4.178 is a sketch of a basic thermoanalyzer installation. The center table provides space for the high temperature furnace, the balance, and the basic vacuum equipment. The cabinet on the right houses the control electronics and computer. On the left is the work bench and gas-cleaning setup.
The weighing principle is shown in the upper right diagram in Fig. 4.178. At the center is the beam balance with a sapphire wedge support. The operation is based on the substitution principle. As a sample is added to the balance pan, an equivalent mass is lifted off above the pan to keep the balance in equilibrium. In this classical balance
Fig. 4.177
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Fig. 4.178
the main weights still are moved manually, as in standard analytical balances (15.99 g). For continuous recording, there is compensation by an electromagnetic force that acts on the right balance beam. A photoelectric scanning system detects any imbalance and adds an electromagnetic force to compensate the pull of gravity. This electromagnetic force can correct imbalances between 0 and 1,000 mg, and is recorded with an accuracy of 50 g over the whole 16 g weighing range. Modern instruments cover more, or all of the weighing range electromagnetically.
The gas flow diagram is illustrated in the bottom diagram of Fig. 4.178. The pumping system produces a vacuum of about 10 3 Pa ( 10 5 mm Hg). After evacuation of the balance, a chosen inert gas can be added through the left inlet. A flow rate as high as 30 L h 1 is possible without affecting weighing precision. Corrosive gases are entered separately through the top inlet. This second gas flow is arranged so that corrosive gases added to or developed by the sample cannot diffuse back into the balance compartment. A cold trap and a manometer are added on the right side, located at a point just before the gas outlet. At this position one can add further analysis equipment to identify the gases evolved from the sample.
Figures 4.179 and 4.180 illustrate two furnaces for TGA for different temperature ranges. The figures are self-explanatory. Several different sample holders are shown in the bottom portions of the figures. The multiple holders can be used for simultaneous thermogravimetry and DTA, the single crucibles are used for simple thermogravimetry. The major problem for the combined thermogravimetry and DTA technique is to bring the thermocouple wires out of the balance without interference with the weighing process. Even the temperature control of the sample holder may be a major problem in vacuum experiments since the thermocouple does not touch the sample. The crucibles are made of platinum or sintered aluminum oxide. Typical sample masses may vary from a few to several hundred milligrams.
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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 0 to 150 mg, and the overall capacity of the balance is 3,050 mg. The temperature range is room temperature to 1,250 K with heating rates from 0 to 100 K min 1.
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Fig. 4.181
Figure 4.182 illustrates the Seiko TG/DTA300 combined thermogravimetry and differential thermal analyzer. The mass compensation is governed completely electromagnetically by the optical deflection 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
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a maximum sample mass of 200 mg. The temperature range is room temperature to 1,750 K.
Figure 4.183 reproduces the schematic of the TA Instruments 951 Thermogravimetric Analyzer, a table-top instrument first described in 1968 in connection with mass-spectrometric product analysis [48]. The balance is fully electromagnetic, with photoelectric detection of the null position. The sample, E, is suspended from a quartz beam, D, connected to the balance beam. A taut-band electric meter movement, B, balances the forces. Position F allows for a tare. The left-hand envelope is a quartz tube and fits into a horizontal, moveable furnace, outlined in the diagram. The righthand envelope, K, is cold. The center-housing of the balance, A, is of aluminum. The O-rings, M, make the instrument vacuum-tight. Gases can be led over the sample via the connection on the left which can be connected to standard glassware. The sample temperature, finally, is measured by a floating thermocouple, J, in the vicinity of the sample. The accuracy of the balance is ±5 g with a sample capacity of 1 g. The temperature range is from room temperature up to 1,500 K.
Fig. 4.183
In Figs. 4.184 an infrared image furnace by Sinku Riko is illustrated. For fast heating of the furnace one uses radiation from two 150-mm-long infrared heaters, focused by the two elliptical surfaces onto the sample. The sample is in a platinum/rhodium cell (5×5 mm), which is surrounded by a transparent, protective quartz tube. A thermocouple for temperature measurement and control touches the sample cell. The weighing system consists of a quartz-beam torsion balance that is kept at equilibrium by an electromagnetic force. Equilibrium is, as usual, detected photoelectrically. The infrared furnaces can provide heat almost instantaneously, so that heating can be done at rates as fast as 1,200 K min 1. Control of temperature is achieved by regulating the current through the furnace according to the output of the
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Fig. 4.184
sample thermocouple. With such a fast temperature rise, accurate isothermal thermogravimetry can be performed. The constancy of temperature is claimed to be ±0.5 K. The temperature range goes up to about 1,500 K. Besides single sample cells, double cells capable of giving simultaneously DTA signals can be used in this instrument. Outside of the sample cell, little heating occurs throughout the apparatus, so that cooling from 1,000 K to room temperature is quick.
Other specialized heating methods include microwave heating, which has been suggested for uniform heating of larger samples, laser heating for in situ analysis of bulk materials, and heating with high-frequency electromagnetic fields to reach high temperatures.
The Derivatograph Q 1500 D is shown in Fig. 4.185. Its principle was first described in 1958 [49]. The two furnaces are operable from 300 to 1300 K. They permit fast sample changes without the need to wait for a furnace to cool. The balance is an analytical beam-balance with automatic weight changes and continuous weight recording through an LVDT that detects the deviation of the balance beam (see Sect. 4.1). In addition, the instrument measures the derivative of the mass change by sensing the movement of an induction coil suspended from the balance arm inside a magnet. Today derivatives are routinely available by external computation. This derivative is used for quasi-isothermal and quasi-isobaric measurements. The sample is in this case heated with a constant heating rate until a non-zero derivative in sample weight is sensed. Then, heating is switched to a very small temperature increase to 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
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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 that can most easily be used for SCTA is 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 mass reaches a pre-set threshold. The second step is then run at constant temperature until 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. Between transitions the heating rate is increased, within a transition it slows, allowing any desired resolution by changing the coupling between the rates of mass and temperature change.
Besides the standard weighing methods, it has also been proposed to use the piezoelectric properties of quartz for mass determination. Change in the weight of a sample that has been deposited directly on the quartz surface, causes a change in the oscillation frequency of the quartz crystal. Mass changes as small as 10 12 g can be determined by this method. The changes in frequency with temperature must be established by calibration, or the experimentation must be done isothermally.