2/2002

Information for users of METTLERTOLEDO thermal analysis systems

16Dear CustomerThe STARe system has once again found very many new users in 2002. The range of ap-plications has now been greatly expanded thanks to the introduction of the exciting newDMA/SDTA861e Dynamic Mechanical Analyzer and, more recently, the high pressureDSC827e module. The STARe System is extremely versatile and is nowadays used in prac-tically all industries for both quality assurance and research purposes.In UserCom we often publish articles from somewhat less well-known application areas.We hope that these applications will encourage you to try out one or the other in you fieldof work.

Interpreting DMA curves, Part 2Dr. Jürgen Schawe

IntroductionPart 1 of this series of articles (UserCom15) covers non-isothermal DMA measurementsand the dependence of the mechanical modulus on temperature. This second article dealswith the frequency dependence of the mechanical properties and quantities of stable sam-ples. Because of the enormous scope of this field, only the basic principles and generalrules that explain the behavior of materials are discussed.In practice, materials are subjected to stresses at many different frequencies. It is there-fore extremely important to have a detailed understanding of the effect of frequency onmechanical properties. In addition, it means that materials need to have different proper-ties under different conditions. For example, an adhesive should behave elastically with-out breaking when it suffers a blow (high frequencies), but should at the same time beable to “accommodate” stress arising from temperature fluctuations (low frequencies)like a liquid.

TA TipContents

TA Tip- Interpreting DMA curves, Part 2 1

New in our sales program- HP DSC827e 6- DSC and TGA crucible sets 7

Applications- Characterization of drugs

by DSC 8- Determination of the glass

temperature by dynamicmechanical analysis 10

- Drying and glass transitionusing IsoStep 13

Dates- Exhibitions 15- Courses and Seminars 15

UserCom 2/20022

Fig. 1. Models illustrating the mechanical behavior of materials. t1, t2 and t3 are the times before, during and after the load was applied, xo is the initial length and vis a constant rate.

Complex modulus and compliance

An ideal elastic solidIn shear mode, DMA measures the shearmodulus, G*, and the shear compliance,J*. An ideal elastic material stores the en-tire mechanical energy responsible for thedeformation. When the shear stress is re-moved, this energy is liberated. The modu-lus is independent of frequency; stress anddeformation (strain) are in phase. In thissituation, G* = G′, whereby G′ is known asthe storage modulus. An example that il-lustrates this behavior is that of a spring(Fig. 1a).

An ideal viscous liquidIn an ideal liquid, the applied stress andthe strain are phase-shifted by 90°. Be-cause the molecules are free to move, nomechanical energy is stored in the mate-rial - the energy is completely converted toheat. The corresponding model is thedamping device shown (Fig. 1b). Typically,a liquid is described with the frequency-in-dependent viscosity η0. In the case of theshear modulus, G*(ω) = iG″(ω). The im-aginary number, i = -1, is a mathemati-cal expression that represents the fact thatthe mechanical energy is dissipated, i.e.converted to heat. G″ is the loss modulus,where G″ = ωη0. In a liquid, the lossmodulus therefore increases linearly withthe frequency, f, where f = ω/2π.

Viscoelastic materialsIn real materials, the reaction to an exter-nal stress is accompanied by molecularrearrangements that take place over a widefrequency range. Examples of this are lat-

tice vibrations in solids at about 1014 Hzand cooperative rearrangements at theglass transition at about 10-2 Hz. Molecu-lar rearrangements are the reason for thedifferent relaxation processes. At highertemperatures, the frequency of the molecu-lar rearrangements increases. The result-ing temperature dependence of the relaxa-tion process is discussed in another articlein this publication (UserCom16, page 10).The properties of real materials lie betweenthose of an ideal liquid and an ideal solid.Due to the fact that they have both elasticand viscous properties, the materials aresaid to be viscoelastic. Their behavior isdescribed mathematically by the complex,frequency-dependent modulus

where G′ is the elastic part of the modulusand G″ the energy dissipation part (vis-cous component). Technical models thatillustrate viscoelastic behavior are combi-nations of springs and damping devices(Fig. 1c).

The complex complianceThe G* modulus describes the relaxationof the mechanical stress for a given strain.In everyday language, a material with alarger storage modulus is said to be“harder”.The DMA experiment can also be per-formed in such a way that the stress isgiven and the resulting strain is measured.One then talks of strain retardation. Theretardation time is a measure of the timedelay in the strain after imposition of thestress. In this case, the compliance, J*, isdetermined. This is also complex and fre-

quency dependent and is given by

where J′ and J″ are the storage and losscompliances. In simple terms, one can saythat a “softer” material has a greater (stor-age) compliance.The relationship between modulus andcompliance is given by the equation

This allows the following equations to bederived:J′ = G′/(G′2 + G″2) andJ″ = G″/(G′2 + G″2).The relationship between the modulus,compliance and loss factor (tan δ) for arelaxation process is illustrated in Figure 2.

The mechanical behavior of a material canbe expressed equally well using the modu-lus or the compliance. In practice, thequantity used depends on what you are ac-customed to, or to practical considerations.For example, the modulus is often usedwhen discussing mechanical behavior inthe rubbery plateau, whereas the compli-ance is used to separate different processes.

The frequency dependence ofmodulus and compliance

An overview of frequency depend-enceFigure 3 displays schematic curves of themoduli and compliances for an amor-phous polymer. The curves are displayed inlog-log presentation. At low frequenciesone can see the flow region, in which G′

√

3UserCom 2/2002

Fig. 2. Basic curve shapes of moduli, compliances and tan δ as a function of frequency.

Fig. 3. Schematic curves of moduli and compliances for a viscoelastic material.

and G″ increase with frequency and J′ andJ″ decrease. There then follows the regionof flow relaxation and the rubbery plateauin which G′ and J′ are almost constant. Alarge step in the storage part is character-istic for the main relaxation region. In thetransition region, the loss components ex-hibit peaks. At higher frequencies, second-ary relaxation (β-relaxation) occurs. Theresulting steps in G′ and J′ and peaks in G″and J″ are then relatively broad. A numberof different relaxation processes occur over

the entire frequency range. The frequencycorresponds to the characteristic length ofthe molecular rearrangement considered.The greater the frequency, the smaller isthe characteristic length. With secondaryrelaxation, the characteristic length isabout 0.5 nm, whereas at the main relaxa-tion (maximum of G″) it is about 2.5 nmand at the corresponding maximum of J″about 5 nm.The β-relaxation observed in polymers isoften attributed to the side chains. With

polymers that do not have movable sidechains, it is interpreted as a conforma-tional variation or fluctuation. The natureof these relaxation effects cannot howeverbe reduced to polymer specific processesbecause it is also observed in low molecu-lar weight glass formers.

Figure 4 displays the modulus of unvul-canized styrene-butadiene rubber (SBR) at-10 °C. The individual effects are discussedin the following sections.

Behavior in the glassy stateWe begin the discussion of the mechanicalbehavior at high frequencies. In Figure 4,the storage modulus, G′, is almost constantabove 105 Hz and the loss modulus is or-ders of magnitude (decades) less than G′.The frequency of the mechanical stressfluctuation is much greater than the char-acteristic frequency of the liquid-specificcooperative rearrangements. This meansthat these molecular processes, which arethe origin of the liquid properties, are notactivated. The material behaves just likean elastic solid. As shown in Figure 3, sec-ondary or β-relaxation occurs. With SBR,this process lies outside the actual rangemeasured. At frequencies below the β-re-laxation, the Andrade process is often ob-served. Here the frequency dependence ofJ″ is described by an exponential law,namely J″ ∝ ω-1/3. The loss compliancehas a slope of -1/3 in the log-log presenta-tion. With SBR, this region can be seen be-tween 105 and 108 Hz (see Fig. 5).

The glass processThe relaxation region in which the storagemodulus changes by several orders of mag-nitude is the glass transition (the main re-laxation or α-relaxation). This relaxationprocess is measured when the measuringfrequency lies in the frequency range ofthe cooperative rearrangements. If the fre-quency is lowered still further, the materialloses its solid-state properties. With SBR(Fig. 4), G′ changes from about 109 Pa to106 Pa with decreasing frequency. Themaximum of the corresponding G″ peak isat a frequency of 3⋅102 Hz at -10 °C. Thecompliance shows analogous behavior ex-cept that J′ increases with decreasing fre-quency (Fig. 5). The maximum of the J″peak is at 10-1 Hz (Fig. 5). Characteristic

UserCom 2/20024

Fig. 5. Storage and loss compliance of SBR at -10 °C. Fig. 6. Curve shape of the loss compliance in the re-tardation region in log-log presentation. The dashedline marks half the peak height.

Fig. 4. Storage and loss modulus of SBR at -10 °C.

quantities of the cooperative rearrange-ments are the relaxation time, τG, and theretardation time, τJ. At the maximum ofthe loss peak ω⋅τ ≈ 1. The retardation timeof SBR at -10 °C is therefore given by theequation τJ = 1/(2π⋅10-1) s, i.e. 1.6 s.Since the relaxation region is measured athigher frequencies in the modulus, therelaxation time, τG, is 5.3⋅10-4 s.

If one considers the simplest possible proc-ess for retardation, namely the Debye proc-ess (which describes a retardation processwith just one single retardation time), thenthe following equation applies

Here J0 and J∞ are the limiting values of

the compliance at low and high frequen-cies. The relationship between the retarda-tion and relaxation time is then given bythe equations τG = τJ (logJ0 - logJ∞) andτJ = τG (logG∞ - logG0). The logarithmicdistance, log ∆f, between the maxima ofthe J″ and G″ peaks can then be estimatedto be 3.0 (see Fig. 2). The experimental re-sult (3.5) shows that this simple estimateis also approximately valid for real proc-esses. The relatively large distance betweenthe J″ and G″ peaks therefore results fromthe large change in G′ and J′ at the glasstransition.The shape of the transition provides furtherinformation on the relaxation behavior.The curve shape of an isolated process isshown in Figure 6 using J″ as an example.In the log-log presentation, the Debye proc-ess has two linear limiting tangents withslopes of 1 and -1. The width at half heightof the peak is 1.14 frequency decades. Realprocesses show appreciably broader peaks -due to molecular interaction there is notjust one retardation time but a wide spec-trum of times. This results in a broader J″peak with the slopes of α and -αγ, where0 < α ≤ 1 and 0 < αγ ≤ 1. The quantitiesα and γ are known as Havriliak-Negami(HN) prameters and describe the width ofthe relaxation transition.

The location and width of the relaxationtransitions are very sensitive to changes inphysical and chemical structure (e.g. tocrystallization and changes in the polymerchain), and to fillers, plasticizers andcomposition in the case of polymer blendsor copolymers. Some examples are illus-trated in Figure 7.

5UserCom 2/2002

Fig. 8. Schematic curves showing the influence ofthe degree of cross-linking (a), and molecular weight(b) on the rubbery plateau (the arrow indicates thedirection of increase of the corresponding quantity).

Fig. 7. Schematic curves of different factors that influ-ence the glass process: a) influence of curve shape;b) shift of the frequency position (the arrow indicatesthe direction of increase of the corresponding quan-tity).

The rubbery plateauLow molecular weight substances begin toflow on decreasing the frequency immedi-ately after the glass transition. Polymershave a characteristic modulus, G0, of about1 Mpa in the rubbery plateau. The plateauis due to the entanglement of macromol-ecules to form a physical network. The

width of the plateau, log ∆f, depends on themolecular weight, M, where log ∆f ∝ M3.4

(Fig. 8). In the plateau, G″ is less than G′.In the middle of the plateau, G″ has aminimum (Fig. 4). At the end of the pla-teau, flow relaxation can be seen on the G″peak (with SBR in Fig. 4 at 10-6 Hz). Thisprocess cannot usually be seen directly inthe compliance curve because it is overlaidby flow.

With cross-linked materials such as vul-canized elastomers, the plateau modulus,G0, is proportional to the mean cross-link-ing density, κ, where κ ≈ G0/(2RT). Flowrelaxation can only be observed with verylightly cross-linked materials (Fig. 8).

Viscous flowAt very low frequencies, uncross-linkedpolymers flow. In the ideal case, the powerlaws G′∝ ω2 and G″∝ ω apply. Here theslopes of the modulus curves in log-logpresentation are 2 for G′ and 1 for G″. Atthe gel point, the G′ and G″ curves crossover one another.

ConclusionsKnowledge of the frequency dependence ofmechanical behavior is of great value forthe practical application of materials andfor material optimization. Information isobtained for material optimization becausethe frequencies at which the different proc-esses occur correlate with the characteristicvolumes of the corresponding molecularregions. At higher frequencies, smaller mo-lecular regions are observed.In comparison to temperature-dependentmeasurements, frequency-dependent meas-urements provide additional informationabout material properties in general andon molecular processes in particular.

UserCom 2/20026

New in our sales program

HP DSC827e

The new high pressure DSC module re-places the TC15/DSC27 combination. Thefollowing points have been improved in thenew pressure cell:• The maximum pressure now available

is 10 MPa (100 bar)• The cooling rate has been greatly in-

creased through an additional jacketcooling system.

• The latest DSC furnace technology hasbeen used

• New FRS5 sensor similar to that in theDSC822e

The same gas supply system and pressurevessel as before are used. STARe SW Ver-sion ≥ V7.xx is needed to control the HPDSC827e.The new HP DSC827e module offers excel-lent performance.

Specifications

Application possibilitiesWe foresee the following application possibilities for the high pressure DSC:

Pressure range 0 to 10 MPa(overpressure)

Temperature 22 - 600 °Crange

Temperature +/- 0.2 °Caccuracy

Temperature +/- 0.1 °Creproducibility

Sensor type FRS5 ceramic sensorwith 56 Au/AuPdthermopile

Signal time 2.3 sconstant

Measuring range 700 mW

Digital resolution 16 million points

Sampling rate Max. 10 points persecond (selectable)

Industry Applications

Chemical and pharma- - Reactions with reactive gases (e.g. O2, H2, CO2)ceutical industries - Reactions in pure, poisonous or fuel atmospheresand universities - Safety investigations

- Suppression of vaporization (through increase ofthe boiling point)

- Separation of chemical reactions and vaporizationthat overlap at normal pressure

- Investigation of reactions with volatile components- Catalytic reactions- Heterogeneous reactions- Adsorption and desorption- Measurement of the pressure dependence of the

boiling point- Determination of enthalpy of vaporization

Petrochemical - Oxidation stability (e.g. checking of oil additives inlubricants)

- Reactions with reactive gases

Plastics - Curing of polymers (e.g. polycondensations)- Oxidation stability

Paints/lacquers/adhesives - Cross-linking of adhesives- Suppression of vaporization (through increase of

the boiling point)

Electronics industry - Curing of resins (e.g. polycondensation)

Foodstuffs - Oxidation stability of fats and oils- Reactions with reactive gases

7UserCom 2/2002

Fig. 1. Comparison of the oxidation of a regular mineral oil with that of a synthetic oil at various oxygen pres-sures. The mineral oil oxidizes at significantly lower temperatures than the synthetic oil at the same oxygenpressure. In this example, the HP DSC827e module allows the lubricant oil to be analyzed under realisticconditions, i.e. such as occur at the operating temperature in an engine between the bearings and thecrankshaft.

DSC and TGA crucible sets

These two crucibles sets allow you to per-form measurements with different cruciblesbut without the need for you to purchase acomplete set of every type of crucible. Bothsets also contain the corresponding lids.

Choosing the right crucible is of utmostimportance in thermal analysis. The cruci-ble influences the• quality of the measurement and• the performance of the instrument.

• Low mass crucibles allow better separa-tion of overlapping effects➔ shorter signal time constants lead tobetter temperature resolution

• Crucibles with low wall heights facili-tate fast decomposition reactions➔ better gas exchange between sampleand atmosphere

• Crucibles with lids, or lids with a holeof µm-size retard vaporization➔ better separation of overlapping ef-fects

• The crucible material also influences

the measurement. A catalytic effect (e.g.platinum crucible) may, or may not bedesirable➔ samples are influenced, or not influ-

enced by the crucible material• Large volume crucibles allow larger

sample amounts to be measured➔ the sensitivity can be improved

TGA crucible set (ME 51 141 279)

Crucible type Volume (µl) Pieces

Aluminum standard 40 10

Platinum 30 1

Sapphire 70 1

Alumina 30 2

Aluminum 100 10

DSC crucible set (ME 51 141 278)

Crucible type Volume (µl) Pieces

Aluminum standard 40 10

Aluminum light 20 10

Crucible lid (with 50-µm hole) - 20

Gold 40 2

Aluminum 100 10

Application example

UserCom 2/20028

Applications

Characterization of drugs by DSCCamelia Nicolescu; Corina Arama (with the support of Prof. Dr. Pharm. Crina Maria Monciu) Department of Analytical Chemistry,“Carol Davila” School of Pharmacy, Traian Vuia Str. No.6, 70139 Bucharest, Rumania

IntroductionIt is well known that interactions betweenthe active substance and excipients caninfluence the pharmacological propertiesand behavior of drugs in biological sys-tems.In this study, mixtures of excipients andpiroxicam as the active substance wereground together and analyzed by DSC.The active substance, piroxicam (4-hy-droxy-2-methyl-N-pyridinyl-2H-1,2-benzo-thiazine-3-carboxamide 1,1-dioxide) is anon-steroidal drug that is often used forthe treatment of osteoarthritis and rheu-matoid arthritis. It shows a therapeutic ef-fect in very small doses and has few sideeffects. The drug’s mechanism has to dowith the disruption of prostaglandin forma-tion and inhibition of the enzyme cyclo-oxygenase.Besides the active substance itself, piroxicamtablets contain the following excipients:anhydrous lactose, lactose monohydrate,microcrystalline cellulose type 102 andmagnesium stearate.

Experimental detailsMeasuring cell: DSC821e,Crucible: aluminum 40 µl, lid with

50-µm hole to produce aself generated atmosphere

DSC program: heating from 75 to 200 °Cat 2 K/min

Atmosphere: stationary air

Measurements and resultsThe mixture of excipients and the activesubstance were first measured separately.The excipients curve shows a melting peakat 140 °C, while the active substance(piroxicam) melts at 202 °C (Fig. 1).

A series of mixtures was then prepared byfinely grinding the mixture of excipientswith increasing amounts of piroxicam. Fig-ure 2 displays the DSC curves of some ofthese samples.

Fig. 2. DSC curves of mixtures with different contents of piroxicam; heating rate 2 K/min, sample weight 8 to12 mg. Reactions of individual excipients occur below 160 °C. The piroxicam melting peak appears in therange 185 to 200 °C and is followed by immediate exothermic decomposition. The baseline type “horizontalfrom left” was therefore chosen to calculate the peak area (see example with 50% piroxicam).

Fig. 1. DSC curves of pure piroxicam and the mixture of excipients (anhydrous lactose, lactose monohydrate,microcrystalline cellulose type 102 and magnesium stearate). Heating rate 2 K/min. The pure piroxicam ex-hibits a sharp melting peak that appears well separated from the decomposition peak that follows. Theexcipients curve shows three effects: drying at 100 °C; melting/loss of water of crystallization of the lactosefrom 110 to 150 °C; decomposition of the lactose from 190 °C onward.

9UserCom 2/2002

The mixtures show an endothermic effectjust below 200 °C. This is attributed to themelting of the active substance. The factthat the melting temperature is lower (upto 10 K) can only be explained by assum-ing that there is a non-eutectic interactionbetween the substance and the excipients.The nonlinear increase in surface area isalso evidence supporting an interaction(Fig. 3).

The DSC curve of the piroxicam tablet(200 mg, manufactured by Terapia, Cluj,Rumania) is similar to that of the samplewith the same piroxicam content preparedby grinding piroxicam with the excipients(Fig. 4).

ConclusionsThe DSC curves show that interactions oc-cur between the different constituents, bothin the samples obtained by grinding theactive substance with the excipients and inthe piroxicam tablet itself. The interac-tions become less and less important withpiroxicam contents greater than 60%.Once the nonlinear relationship betweenthe enthalpy of melting and the content ofthe active substance has been established,the DSC piroxicam peak area can be usedto calculate the content of the active sub-stance for quality control purposes.

Literature[1] Thermal Analysis of a drug-polymeric

excipient solid systemF.Giordano, G.P. Bettinetti, A. La Manna,A. Marini, V. BerbenniJ. Thermal Anal. 34, 1988

[2] Effect of compressional forces onpiroxicam polymorphsG.A. Ghan, J.K. LallaJ. Pharm.Pharmacol. 1992, 44

[3] Bazele farmacologice ale practiciimedicaleV. StroescuEd. Medicala, ed. VII, 2001

Fig. 3. Up until a piroxicam content of 60%, the enthalpy of melting of samples with increasing piroxicamcontent remains appreciably less than that expected from the straight line drawn for no interaction.

Fig. 4. Below 160 °C, in the region of the excipients peak (moisture, water of crystallization), the DSC curveof the tablet (Comprimat 8.7 mg) is somewhat different to the curve of the sample with the same piroxicamcontent (10%) obtained by grinding piroxicam with the excipients. The curves are, however, very similar inthe region in which the piroxicam melts.

UserCom 2/200210

Fig. 1. Temperature-dependent modulus measurements of VSL5025-0 (L-SBR with contents of 25% styrene and 50% vinyl) at different frequencies.

Determination of the glass temperature by dynamic mechanicalanalysisDr. Claus Wrana, Bayer, Leverkusen, Germany

IntroductionThe glass transition temperature is a im-portant criterion for the technological useof polymeric materials. The applicationrange of elastomers is usually restricted totemperatures significantly above the glasstransition temperature to ensure that de-formation behavior is as far as possible en-tropy elastic.The glass transition temperature of a poly-mer is, however, strongly dependent on fre-quency, and the deformation of elastomersis usually time dependent (e.g. seals, sur-face of tires, etc.). This means that a glasstransition temperature measured underquasi static conditions (for example byDSC) is not a good criterion for the charac-terization of the low temperature behaviorof dynamically stressed materials.The temperature limits for dynamicallystressed elastomeric materials can be deter-mined by measuring the glass transitiontemperature using methods in which a pe-riodic stress is applied. The measurement

frequency should of course correspond tothe frequency at which the component isin practice stressed.If such a measurement is not possible, forexample at frequencies that are significantlyhigher or lower than the measurementrange of the instrument, then the glasstransition temperature can be obtained byextrapolation using the time-temperaturesuperposition principle. A quantitative re-lationship between the glass transition tem-perature and measuring frequency can beobtained through the semi-empirical WLFor analogous Vogel-Fulcher equation.In this article, the experimental relation-ship between frequency and time are deter-mined for a number of primary elastomers(NR, BR, SBR, NBR, IIR) from tempera-ture-dependent and frequency-dependentshear modulus measurements. The quanti-tative description of the time-temperaturesuperposition principle is performed usingthe semi-empirical WLF or analogousVogel-Fulcher equation.

Samples and sample preparationSamples for frequency and temperature-dependent measurements were prepared bycompressing the raw polymers to 2-mmthick sheets under a pressure of 2 MPa at80 °C. Two cylindrical disks of 6-mm di-ameter suitable for use with the doublesandwich sample holder of the DMA werepunched out from the sheets for eachmeasurement. The dynamic mechanicalmeasurements were performed on NR(natural rubber) and BR (polybutadiene)homopolymers, and on SBR, NBR, EPDMand IIR copolymers using a METTLERTOLEDO DMA/SDTA861e dynamic mechani-cal analyzer.

Measurements and resultsFirst of all, the complex shear modulus wasmeasured for each sample as a function oftemperature.To do this, the raw polymer was first cooledto well below its glass transition tempera-ture. The complex modulus was then meas-

11UserCom 2/2002

Fig. 2. The master curve of VSL5025-0 constructed from frequency-dependent measurements at a referencetemperature of -20 °C, and the shift diagram (upper left).

ured at five frequencies (1 Hz, 10 Hz, 100 Hz,300 Hz and 1000 Hz) at a heating rate of1K/min up to a temperature of 100 °C.Figure 1 shows the curves obtained fromthe temperature-dependent measurementof solution-polymerized styrene-butadienerubber (L-SBR) with contents of 25%styrene and 50% vinyl (polybutadiene in1,2 position). The glass transition tempera-tures can be determined from the tempera-ture maxima of the loss moduli. As expected,the glass transition temperature increaseswith increasing measuring frequency.

The samples that did not exhibit any crys-tallization effects in the temperature rangemeasured were then cooled again to a tem-perature below the glass transition temper-ature (usually about 20 K lower than theglass temperature determined at 1 Hz).Frequency-dependent measurements of thecomplex shear modulus were then per-formed at constant temperature at temper-ature intervals of 10 K. Above 0 °C the tem-perature interval was increased to 20 K.The final temperature for all measurementswas 160 °C.Master curves were then constructed fromthe individual measurements over frequen-cy at different temperatures by frequencyshifting. The result of master curve con-struction for L-SBR is displayed in Figure 2as an example. A reference temperature of-20 °C was chosen for this curve. The smalldiagram in the upper left part of Figure 2shows the shift factors, log(aT), of theindividual frequency-dependent measure-ments as a function of the measuring tem-perature.Relaxation frequency is temperature de-pendent. The quantitative relationship canbe determined by temperature- and fre-quency-dependent measurements of theshear modulus followed by master curveconstruction. The reference temperature ofthe master curve is usually chosen so thatthe maximum of the loss modulus, G″, isat a frequency of 1 Hz. With temperature-dependent measurements and a measuringfrequency of 1 Hz, this reference tempera-ture corresponds approximately to the tem-perature at which the maximum in the G″curve appears.

Figure 3 displays the shift factors of themaster curves (open symbols) and the tem-perature of the maxima of the loss moduliof the temperature-dependent measure-ments at the five measured frequencies(solid symbols) for all the polymers stud-ied (see Fig. 1). It was not possible to con-struct a master curve of polybutadiene -the crystallization that occurred due to thehigh cis 1,4 content and the associatedstereo-regularity of the polymer chains in-fluenced the kinetics of the glass relaxationprocess.For this reason, only the temperature max-ima of the loss moduli from the tempera-ture-dependent modulus measurementswere used for evaluation.

Temperature and frequency can be relatedquantitatively through the semi-empiri-cal WLF equation or the equivalent Vogel-Fulcher equation (see equations 1 and2).

c1, c2 : WLF constantsfR, TR : reference frequency or reference

temperature

f0 : limiting frequency for T → ∞∆E : activation energy for T → ∞TVF : Vogel-Fulcher temperatureR : universal gas constant

(= 8.3144⋅10-3 kJ/(K⋅mol))

The formal relationship between the WLFand Vogel-Fulcher equations is given by

the equations and

.

The continuous lines in Figure 3 corre-spond to fits of the shift data and the tem-perature maxima of the loss moduli to theVogel-Fulcher equation, whereby the pa-rameters f0, DE and the temperature, TVF,were used as fit parameters. The param-eters of the Vogel-Fulcher equation calcu-lated for each polymer are summarized inTable 1.

The Vogel-Fulcher equation provides agood description of the relationship be-tween frequency and temperature for allthe raw polymers studied. The parameter,f0, is identical within experimental accu-

UserCom 2/200212

Fig. 3. Shift factors (open symbols) and temperature maxima of the loss factors (solid symbols).

Table 1. Vogel-Fulcher parameters

Polymer ∆E [kJ/mol] fo [Hz] TVF [°C]

L-SBR (25% styrene, 50% vinyl) 9.8(±0,6) 9(±3)⋅1012 -60.5(±2)

NR (>98% cis1,4 polyisoprene) 12(±1,3) 2(±1)⋅1013 -109(±4)

E-SBR (23.5% styrene, 12% vinyl) 10.5(±0,8) 8(±3)⋅1012 -96(±2)

IIR (double bond content 0.9%) 22.2(±0,2) 1(±0.5)⋅1013 -153(±2)

NSBR (18% ACN) 10.4(±0,2) 6(±4)⋅1012 -104(±2)

BR (>98% cis1,4) 11.0(±0,4) 1.6(±1)⋅1013 -135(±2)

racy for all the polymers studied. In thedislocation concept, this parameter corre-sponds to the probability of a dislocation atinfinitely high temperature. The param-eter, DE, is comparable for all the polymersstudied with the exception of IIR. This pa-rameter characterizes the energy barrier ofthe dislocation process at temperatureswhere T >> TVF. The Vogel-Fulcher tem-perature, TVF, is polymer specific and givesthe temperature at which the relaxationtimes of the cooperative relaxations proc-esses taking place in the polymer convergeto infinity.

SummaryBoth temperature-dependent modulusmeasurements at different frequencies andfrequency-dependent measurements at dif-ferent temperatures were performed on allthe polymers studied . The combination ofthe two methods allowed the experimentalrelationship between the temperature andfrequency location of the glass process tobe determined and quantified by fitting theexperimental data to the empirical Vogel-Fulcher equation. With the exception ofpolyisobutylene (IIR), it was shown thatall the samples studied can be describedwithin measurement accuracy by identicalVogel-Fulcher parameters, f0 and DE.The glass transition temperature limits thepractical use of elastomeric materials atlow temperatures. Since the glass process isalso frequency dependent, the behavior ofthese materials at low temperatures alsodepends on the frequency of the dynamic

stress. The low-temperature behavior canbe characterized through a combinationof temperature- and frequency-dependentmeasurements of the shear modulus and

a quantitative description on the basis ofthe time-temperature superposition princi-ple using the empirical Vogel-Fulcherequation.

13UserCom 2/2002

Drying and glass transition using IsoStepDr. Jürgen Schawe, Dr. Uwe Hess

IntroductionIf several thermal events occur simultane-ously in a DSC measurement, the problemis then how to separate the different proc-esses involved. Often, a change in heatcapacity is overlapped by exothermic orendothermic peaks, e.g. through chemicalreactions, crystallization or vaporization.One possible way to separate the differentprocesses is to vary the measurement con-ditions in the conventional DSC. For ex-ample, heating and cooling measurementscan be performed at different rates and indifferent temperature ranges using differ-ent types of crucible. This is of course rela-tively time-consuming.IsoStep is a new technique that can beused to distinguish between such overlap-ping processes. It provides both the heatcapacity curve and the non-reversing curvesimultaneously.In this article, the separation of differentthermal events is demonstrated by measur-ing the glass transition of a spray-driedpharmaceutical substance. The measure-ment of a similar compound to determinethe change of heat capacity during the va-porization of water has been described in aprevious article [1, 2]. As an extension ofthis, the relationship between the watercontent and the glass transition tempera-ture is analyzed quantitatively usingIsoStep. Knowledge of this relationshipis important for processing the powder be-cause it can become sticky if the glasstransition temperature is below the process-ing temperature.

Experimental detailsThe DSC measurements were performedwith a DSC822e equipped with anIntraCooler. The STARe software with theIsoStep option was used for the evalua-tion.In the IsoStep method, a conventionalheat capacity measurement is combinedwith a quasi-isothermal kinetic evaluation.The temperature program consists of a se-ries of isothermal segments and heating

steps. The parameters (length of the iso-thermal segments, heating rate and stepheight in the heating step) are not re-stricted in any way. They can even be dif-ferent during a measurement dependingon the actual task or thermal event inves-tigated.The heat capacity as a function of tem-perature is obtained from the heat flowduring the heating step, and the non-re-versing curve from the heat flow duringthe isothermal step [3]. The measurementsdescribed here used temperature steps of1 K at 2 K/min. The isothermal period atthe beginning of the measurement was30 s. The measuring cell was purged withnitrogen.The sample used was a spray-dried phar-maceutical product consisting of twoamorphous components. The water con-tent of the starting material was analyzedby TGA/SDTA851e and found to be 6.08%.Samples of about 8 mg were sealed in40-µl aluminum crucibles with a 50-µmhole in the lid (ME-51140832). The sam-ples were dried each time in the DSC at80 °C for different periods of time before

measurement in order to obtain differentwater contents. The advantage of this pro-cedure was that the sample did not have tobe transported after drying. The small holein the lid restricts the evaporation of thewater so that drying proceeds in a definedway. The moisture content before the be-ginning the measurement, wini, was deter-mined by measuring the decrease of thewater content during the storage of thecrucibles with the TGA/SDTA851e [4]. Trialexperiments in the DSC and TGA showedthat the samples did not change chemi-cally during the predrying step.

Results and interpretationFigure 1 shows a typical IsoStep meas-urement curve as a function of the tem-perature. The upper limit of the curvecorresponds to the heat flow during theisothermal segments, from which the non-reversing curve is calculated.

Figure 2 shows the heat capacity and thenon-reversing curves of the material thathad been heated beforehand for 20 min-utes. In the heat capacity curve, two glass

Fig. 1. IsoStep measurement as a function of the temperature of a sample that had been preheated at 80 °Cfor 20 min.

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transitions can be seen at about 70 °C and125 °C. The broad vaporization peak ob-served in the non-reversing curve overlapsboth glass transitions. This peak is so largethat the glass transitions are not resolvedin a conventional DSC curve. The firstglass transition depends on the water con-tent and is responsible for the powdersticking. Its glass transition temperature,Tg, was therefore investigated as a functionof water content. In the heat capacitycurves (Fig. 3), one can see the shift of theglass transition temperature to higher tem-perature after longer drying times.

The water content before the measure-ment, wini, is of course not the same as thewater content at the glass transition tem-perature, wTg, because water escapes con-tinuously from the sample during themeasurement. This loss of water can be de-termined from the non-reversing curve byevaluating the partial peak area up to Tg.The relevant partial peak area, ∆hp, isshown by the hatched area in Figure 2. Ifthe specific heat of vaporization of water,∆hw, is known, the water content up to Tgcan be determined from the equation

∆hw can be determined from the total peakarea on vaporization, ∆H, and the loss ofmass during the measurement, ∆m, (de-termined by re-weighing): ∆hw = ∆H/∆m[4]. A value of 2500 J/g was obtained for∆hw [2]. This is somewhat greater thanthe value for free water (2400 J/g).

The glass transition temperatures deter-mined from the curves in Figure 3 are dis-played in Figure 4 as a function of the wa-ter content, wTg (Eq. (1)). This diagramcan be used to optimize the processingconditions for the material.

Fig. 2. Specific heat capacity and non-reversing (kinetic) curves as a function of the temperature or measurementtime, calculated from the measurement in Figure 1. The hatched area shows the amount of water vaporizedup to the glass transition temperature.

Fig. 3. Heat capacity curves measured after different drying times at 80 °C. The parameter is the drying time.The arrows point to the glass transition temperatures.

Fig. 4. Glass transition temperature as a function ofwater content at Tg.

Literature[1] M. Schubnell, J. Schawe,

UserCom 14 (2001) 5.[2] M. Schubnell, J.E.K. Schawe,

Int. J. Pharm., 192 (2001) 173.[3] U. Joerimann,

UserCom 15 (2002).[4] J.E.K. Schawe, U. Hess,

J. Thermal Anal. Cal., 68 / 2002 / 741.

SummaryWith IsoStep, the heat capacity and thenon-reversing curve can be determined si-multaneously in one measurement. This al-lows glass transition and vaporization proc-esses to be separated. With a spray-driedpharmaceutical substance, it has been shownthat the method can be used to quantitativelydetermine the effect of moisture on the glasstransition temperature. The measurementprocedure features easy sample preparation,direct measurement and high accuracy.

15UserCom 2/2002

Dates

Exhibitions, Conferences and Seminars - Veranstaltungen, Konferenzen und SeminareSIAT 2003, Symposium on International Automotive Technology in ass. with SAE Int. January 15-18, 2003 ARAI, Pune (India)15. Ulm-Freiberger Kalorimetrietage 19. bis 21. März 2003 Freiberg, Sachsen (Deutschland)INSTRURAMA April 2-4, 2003 Brussels (Belgium)TAC April 15-16, 2003 Huddersfield (UK)PLAST 06-10, Maggio 2003 Milano (Italy)AFCAT (Association de Calorimétrie et d’Analyse Thermique) May, 2003 Mulhouse (France)PhandTA 7 (Int. Conference/Workshop on Pharmacy and Applied Physical Chemistry) 7. bis 11. September, 2003 Innsbruck (Oesterreich)NATAS 2003 September 22-24, 2003 Albuquerque (USA)Het Instrument 2002 4-8 Novembre, 2003 Utrecht (Netherlands)RICH MAC 25-28 Novembre, 2003 Milano (Italy)

TA Customer Courses and Seminars in Switzerland - Information and Course Registration:TA-Kundenkurse und Seminare in der Schweiz - Auskunft und Anmeldung bei:Frau Esther Andreato, METTLER TOLEDO GmbH, Schwerzenbach, Tel: ++41 1 806 73 57, Fax: ++41 1 806 72 40, e-mail: esther.andreato@mt.comCourses/Kurse:TMA-DMA/SW Basic (Deutsch) 17. Februar 2003 TMA-DMA/SW Basic (English) February 24, 2003TGA (Deutsch) 18. Februar 2003 TGA (English) February 25, 2003DSC Basic (Deutsch) 19. Februar 2003 DSC Basic (English) February 26, 2003DSC Advanced (Deutsch) 20. Februar 2003 DSC Advanced (English) February 27, 2003SW Advanced (Deutsch) 21. Februar 2003 SW Advanced (English) February 28, 2003

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Editorial team

Dr. J. Schawe, Dr. R. Riesen, J. Widmann, Dr. M. Schubnell, C. Darribère, Dr. M. Wagner, Dr. D. P. May Ni Jing Urs JörimannPhysicist Chem. Engineer Chem. Engineer Physicist Chem. Engineer Chem. Engineer Chemist Chemist Electr. Engineer

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