Thermal Analysis of Polymeric Materials Part 8 pdf

4.5.3 Applications of TMA Data from a thermomechanical analysis are usually plotted as linear expansivity orlength of the sample as a function of temperature.. Thefibers analyzed under t

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 min1 On the left-hand side of thegraph, the high moduli of the glassy and semicrystalline solid are seen and can becompared to the table of bulk moduli in Fig 4.144 At the glass transition, Young’smodulus 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 increaseswithout 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-calledrubber-elastic plateau Only at higher temperature (>450 K) is the molecular motionfast enough for the viscous flow to reduce the modulus to zero Introducingpermanent 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 crystalsform a dense network between the parts of the molecules that become liquid at theglass transition temperature This network prohibits flow beyond the rubber elasticextension of the liquid parts of the molecules Unimpeded flow is possible only afterthe crystals melt in the vicinity of 500 K

4.5.2 Instrumentation of TMA

A schematic diagram illustrating a typical thermomechanical analyzer is shown inFig 4.146 This instrument was produced by the Perkin–Elmer Co Temperature iscontrolled through a heater and the coolant at the bottom Atmosphere control ispossible through the sample tube The heavy black probe measures the position of the

4.5 Thermomechanical Analysis, DMA and DETA _407

sample-is a properly hydrostatic medium and sample-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 inFig 4.146 are being used to act in a penetration mode A rod of well-defined crosssection or geometry presses with a known force on the sample, and its penetration ismeasured as a function of temperature The sharp, conical probe on the right is alsoused to characterize the sample by producing a plastic indentation The setup at thebottom of A is designed to test the elastic modulus in a bending experiment Thedeflection 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 Themeasurement 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 twofurnaces and special equipment for liquid N cooling For higher temperatures,

4 Thermal Analysis Tools _408

Fig 4.147

different designs with thermally stable materials are needed The linear range of theLVDT may be several millimeters The maximum sensitivity is as high as a fewtenths 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 diameterand up to a few centimeters in height The data acquisition and treatment throughelectronics and computer is as varied as in DTA and calorimetry Direct recording oflength and derivative of length is most common The heating rates range from perhaps0.1 K min1to as high as 40 K min1 They depend on the sample size and holderconfiguration Even faster heating and cooling rates are often used to accomplishquick, uncontrolled temperature changes

4.5.3 Applications of TMA

Data from a thermomechanical analysis are usually plotted as linear expansivity orlength of the sample as a function of temperature Figure 4.147 illustrates eightdifferent TMA experiments The top graphs show solid-solid transitions for potassiumethylsulfate, K(C2H5)SO4, and dichlorodipyridylcobalt(II), Co(C5NH5)2Cl2 Theorganic compound acetanilide, CH3CONHC6H5, which has a melting temperature ofabout 388 K, shows premelting shrinkage The barium chloride, BaCl2$2H2O,decreases in volume when it loses its crystal water, but continues afterwards with anormal, 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 modeunder conditions that satisfy the ASTM (American Society for Testing and 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 occurabruptly, close to the glass transition temperature, as is expected For the twopolyethylenes, 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 thetension 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, thefibers are largely amorphous with some orientation The TMA in Fig 4.148 showsthe usual expansion below the glass transition, followed by shrinkage as soon as theglass transition is reached The partially drawn molecules relax to smaller dimensions

as soon as sufficient mobility is gained at the glass transition When equilibrium isestablished in the liquid (rubbery) state, a gradual decrease in expansivity is observed

as the sample crystallizes The crystallization is clearly evident in the DTAexperiment through its exotherm On melting, the sample becomes liquid and startsflowing The recording stops when the fiber ultimately breaks The DTA traceillustrates the full melting process

Drawing causes higher orientation of the fiber, as is illustrated by Fig 4.149 Atthe glass transition much larger shrinkage is observed than in Fig 4.148 Subsequentcrystallization occurs at lower temperature due to the better prior orientation Sincethe DTA crystallization peak is smaller than the subsequent melting peak, one wouldconclude that the original drawn sample was already somewhat crystalline

Annealing the drawn fiber, as shown in Fig 4.150, introduces sufficient linity to cause the shrinkage to occur continually between the glass and meltingtemperatures One would interpret this behavior in terms of the existence of a rigidamorphous fraction that gradually becomes mobile at temperatures well above the

crystal-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 offiber formation, particularly, if it is coupled with DSC and the analysis of molecularstructure 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 Thebroken 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 meltingpeak with heating rates that equilibrium conditions were not fulfilled The fact thatthe samples kept at fixed length, melt more sharply than the freely shrinking ones, isalso 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 notfully relaxed after crystallization will increase the local melting temperature, asdiscussed in Chaps 57 The degree of stretch is, however, determined by the crystalsthat set up a rigid network to maintain the strain in the amorphous chains As the firstcrystals melt, the amorphous chains can start relaxing and thus decrease the meltingtemperature 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 PETcase shown, there is a wide distribution of crystalline and intermediately orderedmaterial (see Sect 6.2), which causes the broad melting range of the samples Thefibers analyzed under the condition of fixed length, melt more sharply and increase inmelting temperature with the heating rate In the low-heating-rate samples, one caneven detect a tilt of the peak toward low temperatures This must mean that thecollapse of the crystal network occurs so suddenly that it lowers the meltingtemperature faster than the heating rate increases the temperature At a high heatingrate, 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 theTMA 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 bebrought together, and combined with knowledge from thermodynamic theory, to begin

to understand the often complicated melting and crystallization behavior of polymericmaterials (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 (CH2CH=CHCH2)x.

The glass transition occurs at 161 K It softens the material to such a degree that theTMA probe penetrates abruptly The quantitative degree of this penetration depends

on the probe geometry, loading, and heating rate At higher temperature the rate ofpenetration is then slowed somewhat by crystallization At the melting temperature ofthe crystals grown during heating, the penetration is speeded up again

Thermomechanical analysis, thus, permits a quick comparison of differentmaterials 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 orstrain is called dynamic mechanical analysis, DMA The periodic changes in eitherstress or strain permits the analysis of the dynamic response of the sample in the othervariable The analysis has certain parallels to the temperature-modulated differentialthermal analysis described in Sect 4.4, where the dynamic response of the heat-flowrate is caused by the cyclic temperature change In fact, much of the description ofTMDSC was initially modeled on the more fully developed DMA The instrumentswhich measure stress versus strain as a function of frequency and temperature arecalled dynamic mechanical analyzers The DMA is easily recognized as a furtherdevelopment of TMA Its importance lies in the direct link of the experiment to themechanical 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 separatetextbook 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 inthe analysis of flexible, linear polymers

Figure 4.153 shows a schematic drawing of a torsion pendulum It was used forsome of the first DMA experiments that were carried out as a function of temperature[43] The pendulum is set into vibrations of small amplitude (3o

) and continues to

oscillate freely with a constant, characteristic resonant frequency of decreasingamplitude, recorded by a lamp and mirror arrangement The viscoelastic propertiesare then computed from the frequency and the logarithmic decrement, , of theamplitude A typical torsional oscillation and a plot of the logarithm of the maximumamplitudes versus their ordinal numbers are shown in Fig 4.154 The slopes of thecurves A to D represent the logarithmic decrements

Dynamic mechanical analyzers can be divided into resonant and defined frequencyinstruments The torsion pendulum just described is, for example, a resonantinstrument 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 arecollected by the module CPU, the central processing unit, and transmitted to thecomputer for data evaluation The diagram is drawn after a commercial DMA whichwas produced by Seiko At the bottom of Fig 4.155, a typical sample behavior for aDMA experiment is sketched An applied sinusoidal stress,), is followed with aphase lag,

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 mechanicalanalyzer by TA Instruments The sample is enclosed in a variable, constant-temperature environment, not shown, so that the recorded parameters are stress, strain,time, frequency, and temperature This instrument can be used for resonant anddefined-frequency operation Even creep and stress relaxation measurements can beperformed In creep experiments, a constant stress is applied at time zero and the

4.5 Thermomechanical Analysis, DMA and DETA _415

of Fig 4.157 for the example of tensile stress and strain

The theory of hydrodynamics similarly describes an ideal liquid behavior makinguse of the viscosity (see Sect 5.6) The viscosity is the property of a fluid (liquid orgas) 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 unitsare listed, and a sketch for the viscous shear-effect between a stationary, lower and anupper, mobile plate is also reproduced in the figure Schematically, the Newtonianviscosity is represented by the dashpot drawn in the upper left corner, to contrast theHookean 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 asstress anomalies Plastic deformation is a common example of such non-idealbehavior It occurs for solids if the elastic limit is exceeded and irreversibledeformation takes place Another deviation from ideal behavior occurs if the stressdepends simultaneously on both, strain and rate of strain, a property called a timeanomaly 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

4 Thermal Analysis Tools _416

4.5 Thermomechanical Analysis, DMA and DETA _417

Fig 4.159

and for the example of a shear experiment is a measure of the time needed to extendthe spring to its equilibrium length, as shown in the graph The rise of the straincaused by the application of the stress to the parallel spring and dashpot is retarded,but ultimately the full equilibrium extension is reached For the Maxwell model thesame ratio is called its relaxation time and is a measure of the time needed for theinitially applied stress to drop to zero, as shown on the right of Fig 4.158 Description

of the macroscopic behavior of a material would be simple if the spring in the Voigt

or Maxwell models could be identified with a microscopic origin, such as a bondextension or a conformational change in an entropy elastic extension, and the dash potwith a definite molecular friction One can imagine, however, that there must be manydifferent molecular configurations contributing to the viscoelastic behavior of thesample For this reason the simple models are expanded to combinations of manyelements “i” as shown in Fig 4.159 These combinations of the elements of the modelare linked to retardation and relaxation time spectra Naturally, there may also becombinations of both models needed for the description

For most polymeric materials, viscoelastic behavior can be found for sufficientlysmall amplitudes of deformation Rigid macromolecules and solids, in general, showrelatively little deviation from elasticity and behave approximately as indicated inFig 4.144 The major application of DMA is to flexible, linear macromolecules fromthe glass transition to the rubbery state

The analysis of DMA data is illustrated in Fig 4.160 with the example of sheardeformation The periodicity of the experiment is expressed in frequency, either inhertz, , (dimension: s1), or in 7 (dimension: radians per second) Periodicexperiments at frequency 7 in DMA, as also in TMDSC, are comparable to anonperiodic, transient experiment with a time scale of t 1/7 = 0.159 s

4 Thermal Analysis Tools _418

Fig 4.160

To describe the stress and strain caused by the modulation, as given by theinstrument of Fig 4.155, one defines a complex modulus G* as shown in Fig 4.160.Analogous expressions can be written for Young’s modulus and the bulk modulus.The real component G1 represents the in-phase component, and G2 is the out-of-phasecomponent The letter i represent, as usual, the square roots of1 In order toevaluate G*, the measured stress is separated into its two components, one in-phasewith the strain, and one out-of-phase The simple addition theorem of trigonometrylinks) to the complex terms of the modulus Also given are the equations for G1, G2,and the tangent of the phase difference

only a part of the measured total stress, there is a loss in the recovered mechanicalenergy in every cycle This energy, dissipated as heat over one cycle, W2, is given

at the bottom of Fig 4.160

A strain-modulated DMA parallels the temperature-modulated DSC discussed inSect 4.4 Figure 4.161 shows a comparison to the results in Figs 4.90, written for acommon phase lag Note that the measured heat-flow rate HF(t) lags behind themodulated temperature, while the measured shear stress advances ahead of themodulated strain Besides modulation of strain, it is also easily possible to modulatethe stress, and even temperature-modulation is possible and of interest for comparison

of DMA to TMDSC, as was established recently [44]

The data are further analyzed mathematically In particular, it is of interest toestablish retardation and relaxation time spectra that fit the measured data using Voigt

or Maxwell models Adding the temperature dependence of the data leads to theinteresting observation that time and temperature effects are often coupled by the time-temperature superposition principle Effects caused by an increase in temperature canalso be produced by an increase in time scale of the experiment The ratio of modulus

to temperature, when plotted versus the logarithm of time for different temperatures,

4.5 Thermomechanical Analysis, DMA and DETA _419

Fig 4.161

can be shifted along the time axis by aTand brought to superposition The shift factor

aT, is the ratio of corresponding time values of the modulus divided by the respectivetemperatures T and To A great variety of amorphous polymers have in the vicinity

of the glass transition a shift factor aTthat is described by the approximately universalWilliams-Landel-Ferry equation (WLF equation):

log aT= [17.44(TTg)] / [51.6 + (T Tg)]

The mechanical spectra and temperature dependencies derived from DMA provide,

as such, no immediate insight to their molecular origin Qualitatively the variousviscoelastic phenomena are linked to the energy-elastic deformation of bonds and theviscous effects due to large-amplitude movement of the molecular segments Thelatter are based on internal rotation causing conformational motion to achieve theequilibrium entropy-elastic response

4.5.5 Applications of DMA

The application of DMA to the study of the glass transition of poly(methylmethacrylate) is shown in Fig 4.162 The graph illustrates the change in Young’sstorage modulus E1 as a function of frequency Measurements were made on aninstrument as in Fig 4.155 with frequencies between 0.03 and 90 Hz The low-temperature data (below 370 K) show the high modulus of a glass-like substance Athigher temperature this is followed by the glass transition region, and the last trace,

at 413 K, is that of a typically rubber-elastic material (see also Fig 4.145) With theproper shift aT, as described in Sect 4.4.4, the master curve at the bottom of Fig 4.163can be produced The shift factors a are plotted in the upper right graph in a form

4 Thermal Analysis Tools _420

Fig 4.162

Fig 4.163

which indicates a logarithmic dependence on the inverse of temperature as expectedfrom the WLF equation An activation energy of 352 kJ mol1can be derived fromthe plot Figures 4.164 and 4.165 show the same treatment for tan

transition is marked by the maximum in the plot of tan

temperature The reference temperature chosen for the shift is 393 K

4.5 Thermomechanical Analysis, DMA and DETA _421

Fig 4.164

Fig 4.165

Figure 4.166 shows a DMA analysis of an amorphous polycarbonate, isopropylidenediphenylene carbonate) These data were taken with an instrument likethat seen in Fig 4.156 Measurements were made at seven frequencies between 0.01and 1 Hz at varying temperatures Again, the glass transition is obvious from thechange in flexural storage modulus, as well as from the maximum of the loss modulus

poly(4,4'-4 Thermal Analysis Tools _422

Fig 4.166

Fig 4.167

Figure 4.167 illustrates the analysis of the shift factors using the WLF equation asgiven in Fig 4.163 with of the constants fitted for the polycarbonate Finally, inFigs 4.168 and 169 the master curves are generated by shifting the data for the lossand storage moduli, as given in Fig 4.166 The master curves represent the full dataset of Fig 4.166

4.5 Thermomechanical Analysis, DMA and DETA _423

4 Thermal Analysis Tools _424

1 In SI-units the dimension of the dipole moment, is C m (C = coulomb or A s, see Fig 2.3)

4.5.6 Dielectric Thermal Analysis, DETA

The mechanism of dielectric effects of interest to DETA involves permanent dipoles1which exist within the sample and try to follow an alternating electric field, but may

be hindered to do so when attached to segments of molecules with limited mobility.The fundamental analogy of dielectric and mechanical relaxation has been pointed outalready in 1953 [45]

An electric field in a material causes polarization,2as summarized in Fig 4.171.The polarization may have different origins: (1) Electron polarization, an interactionthat shifts the electrons with respect to the center of the atom (2) Atom polarization,caused by shift of relative positions of bonded atoms (3) Dipole or orientationpolarization, the effect to be discussed The first two types of polarization involve fastdisplacement of positive and negative charges relative to each other within a time-scale of about 1015s Both are usually treated together as induced polarization andare related to the refractive index, n, by the equation of Maxwell (see also thediscussions of light scattering, Sect 1.4.2 and Appendix 3) The time scale of dipolepolarization is 1012to 1010s for mobile dipoles, but may become seconds and longer

4.5 Thermomechanical Analysis, DMA and DETA _425

Fig 4.171

Fig 4.172

for less mobile dipoles In case the sample contains freely migrating charges, such assmall ions, a space-charge or ion polarization exists which interferes with themeasurement of dipole polarization and must be avoided

The polarization of a material is measured via its relative permittivity (dielectricconstant),r, by placing it between the plates of a condenser as shown schematically

in Fig 4.172 The three-electrode arrangement has the goal to confine the field in the

4 Thermal Analysis Tools _426

as indicated in the figure

The Debye equation gives the link to the molar polarizability:

where M is the molecular mass,' the density, NAthe number of molecules per mole(Avogadro's number),othe induced molecular polarizability, and the permanentdipole moment Changing now from a stationary electric field to one that changessinusoidally, the time scale of the experiment becomes important as in DMA.Figure 4.173 shows in its dotted upper curve the change in relative permittivity as afunction of frequency of a simple polar material that shows only one dispersion region

At high frequency, the permanent dipoles cannot follow the changing alternatingelectric field, i.e., they do not contribute to the polarization and Eq (1) consists of onlythe first part of the right-hand side As the frequency approaches a time scale thatpermits the permanent dipoles to align, one reaches the dispersion region and thepermittivity (dielectric constant) increases, until a low frequency limit is reached forthe assumed single relaxation mechanism

The time-dependent behavior of the permittivity is treated analogously to the DMAdata in Sect 4.5.4 A complex permittivity,*

, is written as:

where1 and 2 are the in-phase and the out-of-phase components of the permittivity,respectively As in DMA,2 represents the loss factor or dielectric loss The dotted

4.5 Thermomechanical Analysis, DMA and DETA _427

where- is the relaxation time The loss reaches its maximum at -7 At this point

1 = (1zero+1)/2 and2 = (1zero 1)/2 Analogous to DMA a loss tangent can bedefined (tan

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-timespectrum If several distinct relaxation mechanisms occur with sufficiently widelyseparated relaxation times, Eqs (1) and (3) need to be expanded by additional termsdescribing 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:

where-ois the most probable relaxation time at which2 shows the maximum Theempirical fitting parameter is zero if the relaxation process follows simple Debyebehavior as described by Eq (3) and tends toward one for broader relaxation timespectra On plotting of 2 versus 1, a circle is obtained with 1 and zero1 as

4 Thermal Analysis Tools _428

intercepts with the abscissa For = 0 the center of the circle lies on the abscissa at(1 + zero1)/2 With increasing , the center moves below the abscissa and a diameterfromzeroencloses the angle%/2 with the abscissa The data in Fig 4.174 weredrawn 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, assuggested 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 theInternational 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, thegram was chosen as mass standard It was to represent the mass of 1 cm3

of H2O atits freezing temperature In 1799 the mass standard was changed to 1,000 cm3

ofwater at its maximum of density at 277.13 K, since the larger mass could be measuredmore precisely At present, this connection is only approximate, but the differencefrom the old size is hardly noticeable for practical applications Today the massstandard is independent of the volume of water

The basic mass determination is simple It consists in a comparison of the forceexerted by gravity on the two masses to be compared, using for example a beambalance 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 totalmass The main calculation from a direct measurement of mass is to establish thenumber of moles of the compound or element in question This is achieved bydivision through the molar mass, MW With the general use of SI units, one mustremember that the molar masses must be entered in kg, not g! The mole is defined asthe number of atoms in exactly 12 g (0.012 kg) of the isotope 12 of carbon Thenumber 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, ortime, t, represents the essential thermogravimetry result The definitions of thetemperature 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, anopen system The mass-flow across the boundaries of the sample holder is continu-ously 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 Theother extension involves the simultaneous measurement of the heat flux by calorime-try Instruments that couple all three techniques have been built and can fullycharacterize an open system Since one should, however, always be able to preciselyrepeat scientific experiments, it should be possible to separately measure mass change,

The wood-block print reproduced in Figs 4.176 suggests that thermogravimetrywas already possible a long time ago Mass, temperature, and time determinations areamong the oldest measurements of general interest Looking into the alchemist’s

4 Thermal Analysis Tools _430

Fig 4.177

laboratory of the fifteenth century in Fig 4.176, one can see that respectable balancesand furnaces were available already at that time Accurate temperature determinationwould have been somewhat more difficult then, as was discussed in Sect 4.1

It took considerable time until what one might call modern thermogravimetry wasdeveloped 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 ofvolatile constituents of salts and minerals during drying Most definitive, however,was the thermobalance designed by Honda in 1915 An interesting review ofthermogravimetry was published by Duval [46] A note about nomenclature, althoughthe ICTAC suggests the name thermogravimetry in favor of the older term thermo-gravimetric analysis, it permits the old abbreviation TGA since TG would lead toconfusion with the abbreviation of the glass transition temperature, Tg

4.6.2 Instrumentation

The schematic of a typical thermogravimetric system is illustrated based on theclassical, high-precision instrument, the Mettler Thermoanalyzer [47] The blockdiagram of Fig 4.177 gives a general overview of the instrumentation and control, andFig 4.178 is a sketch of a basic thermoanalyzer installation The center table providesspace 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 isthe work bench and gas-cleaning setup

The weighing principle is shown in the upper right diagram in Fig 4.178 At thecenter is the beam balance with a sapphire wedge support The operation is based onthe 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

4.6 Thermogravimetry _431

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 electromagneticforce that acts on the right balance beam A photoelectric scanning system detects anyimbalance and adds an electromagnetic force to compensate the pull of gravity Thiselectromagnetic force can correct imbalances between 0 and 1,000 mg, and is recordedwith an accuracy of 50g over the whole 16 g weighing range Modern instrumentscover more, or all of the weighing range electromagnetically

The gas flow diagram is illustrated in the bottom diagram of Fig 4.178 Thepumping system produces a vacuum of about 103 Pa (105 mm Hg) Afterevacuation of the balance, a chosen inert gas can be added through the left inlet Aflow rate as high as 30 L h1 is possible without affecting weighing precision.Corrosive gases are entered separately through the top inlet This second gas flow isarranged so that corrosive gases added to or developed by the sample cannot diffuseback into the balance compartment A cold trap and a manometer are added on theright side, located at a point just before the gas outlet At this position one can addfurther analysis equipment to identify the gases evolved from the sample

Figures 4.179 and 4.180 illustrate two furnaces for TGA for different temperatureranges 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 neous thermogravimetry and DTA, the single crucibles are used for simple thermo-gravimetry The major problem for the combined thermogravimetry and DTAtechnique is to bring the thermocouple wires out of the balance without interferencewith the weighing process Even the temperature control of the sample holder may be

simulta-a msimulta-ajor problem in vsimulta-acuum experiments since the thermocouple does not touch thesample The crucibles are made of platinum or sintered aluminum oxide Typicalsample masses may vary from a few to several hundred milligrams

4 Thermal Analysis Tools _432

Fig 4.179

Fig 4.180

Later developments include desktop thermogravimetry A typical apparatus isshown in Fig 4.181 The readability of this balance is 1g The electrical range ofmass compensation is from 0 to 150 mg, and the overall capacity of the balance is3,050 mg The temperature range is room temperature to 1,250 K with heating ratesfrom 0 to 100 K min1

by beam-mounted sensors The reliability of the balance is claimed to be ±100g at

4 Thermal Analysis Tools _434

Thermo-In Figs 4.184 an infrared image furnace by Sinku Riko is illustrated For fastheating 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 plati-num/rhodium cell (5×5 mm), which is surrounded by a transparent, protective quartztube A thermocouple for temperature measurement and control touches the samplecell The weighing system consists of a quartz-beam torsion balance that is kept atequilibrium by an electromagnetic force Equilibrium is, as usual, detectedphotoelectrically The infrared furnaces can provide heat almost instantaneously, sothat heating can be done at rates as fast as 1,200 K min1 Control of temperature isachieved by regulating the current through the furnace according to the output of the

so that cooling from 1,000 K to room temperature is quick.

Other specialized heating methods include microwave heating, which has beensuggested for uniform heating of larger samples, laser heating for in situ analysis ofbulk materials, and heating with high-frequency electromagnetic fields to reach hightemperatures

The Derivatograph Q1500 D is shown in Fig 4.185 Its principle was firstdescribed in 1958 [49] The two furnaces are operable from 300 to 1300 K Theypermit 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 weightrecording 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 bysensing the movement of an induction coil suspended from the balance arm inside amagnet Today derivatives are routinely available by external computation Thisderivative 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 sampleweight is sensed Then, heating is switched to a very small temperature increase torecord the quasi-isothermal loss of mass After completion of the first step of thereaction, the normal heating is resumed The quasi-isobaric environment is created

by a special labyrinth above the sample holder that maintains the self-generatedatmosphere during the decomposition range With double holders, simultaneous DTA

is possible as illustrated in Figs 4.188 and 4.190

, Avogadro’s number

The principles of thermogravimetry... time and is a measure of the time needed for theinitially applied stress to drop to zero, as shown on the right of Fig 4.1 58 Description

of the macroscopic behavior of a material would be... out -of- phase The simple addition theorem of trigonometrylinks) to the complex terms of the modulus Also given are the equations for G1, G2,and the tangent of the phase difference

only a part