USER COM 2/99 1

10Information for users ofMETTLER TOLEDO Thermal analysis systems 2/99

TA-TIP

TA-TIP- DSC purity determination

NEW in our sales program- TGA-FTIR Interface

Applications- TGA-FTIR combination for the investigation of sealing rings- Oxidative stability of petroleum oil

fractions- What can model free kinetics tell us

about reaction mechanisms?- Safety investigations with model

free kinetics- The glass transition from the point of

view of DSC measurements;Part 1: basic principles

- Determination of the expansioncoefficients of an injection moldedmachine part

- Two-component phase diagram- Crosslinking and degree of cure of

thermosetting materials

Contents

USER COM

DSC purity determination can be looked on as a super melting point determination thatis increasingly replacing classical melting point methods. The reason for this is that ityields both more information and more accurate results. Based on our 27 years of experi-ence of automatic purity determination, we would like to discuss the most important fac-tors that affect this method.

Validity of the Van't Hoff equationDSC purity determination is based on the fact that eutectic impurities lower the meltingpoint of a eutectic system. This effect is described by the Van’t Hoff equation:

The simplified equation is:

T TRT

Hx

Fff

= −002

2 0

1∆ .

where Tf is the melting temperature (which, during melting, follows the liquidus tem-perature), T0 is the melting point of the pure substance, R is the gas constant, ∆Hf is themolar heat of fusion (calculated from the peak area), x2.0 is the concentration (molefraction of impurity to be determined), Tfus is the clear melting point of the impure sub-stance, F is the fraction melted, ln is the natural logarithm, Apart is the partial area of theDSC peak, Atot is the total area of the peak and c is the linearization factor.In both cases, the reciprocal of the fraction melted (1/F) is given by the equation:

1

F

A c

A ctot

part

= ++

Non-eutectic impurities can also affect the melting point, and in the case of mixedcrystalls, even cause an increase. Impurities that form a an empty two-component system(mutual insolubility in the liquid phase, e.g. vanilline and iron oxide) have no effect at

DSC puritydetermination

T TR T T

Hx

Fffus

f

= − −00

2 011

∆ln( ).

Dear customerEven we are sometimes amazed at the vastnumber of new and existing applicationareas of thermal analysis. Thermal analy-sis can be used with great success to solveproblems in quality assurance through toresearch, and for both simple and com-plex investigations. Newcomers, however,often have difficulty interpreting thecurves. Last month we ran our first work-shop dealing specifically with this sub-ject. We received so many inquiries thatwe have decided to organize this workshopagain next year.

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Fig. 1. DSC curves of samples with increasing concentrations of impurity

all on the melting point of the main com-ponent. These types of impurity are there-fore not detected by DSC purity analysis(except via the lower heat of fusion).The first thing that has to be checked whenvalidating a method for purity determina-tion is whether the substance under investi-gation forms a eutectic system with the sup-posed main impurity. If the chemical proc-ess for the production of the substance isknown, then usually the by-products arealso known; otherwise the chemist mustmake some intelligent guesses. If necessary,the impurities can often be identified byHPLC. As soon as the main impurity hasbeen identified, samples containing specificamounts of impurity can be prepared andmeasured by DSC.This assumes that the main component isavailable with a degree of purity that isgreater than 99.5 mol%. As far as possible,the purity should be checked using differentmethods and not just by DSC purity analysisalone. The degree of purity can often beimproved by recrystallization and zonemelting or by drying. Not much substance isneeded - 100 mg are usually sufficient forthese investigations.A number of DSC purity determinations arenow performed on the main component andthe mean value calculated. It is better toprepare samples with increasing concentra-tions of impurity x2 directly in the DSC cru-cible using a microbalance. Samples pre-pared macroscopically are very often inho-

mogeneous. If the substances concernedare not already finely powdered, theyshould be ground and powdered in a mor-tar and possibly dried in a desiccator.Weigh several micrograms of the impurity(m2) into a tared DSC crucible, add severalmilligrams of the main component (m1)and note both weights. Seal the crucibleimmediately and place it in a cruciblestand so that its identity cannot be mis-taken. In this manner, prepare three to fivecrucibles with different concentrations ofimpurity x2. It is not necessary to mix thecomponents. The intimate contact of thefine powders is sufficient for the eutectic toform by diffusion.If the molecular masses of the two compo-

nents are similar, about 10, 20, 50 and 100micrograms of impurity are used for about4 mg of the main component. This givesimpurity concentrations of about 0.2%,

0.5%, 1% and 2% impurity. To calculate theconcentration of impurity in the samples,the molecular masses of the main compo-nent (M1) and of the impurity (M2) are en-tered in the following equation:x2

= m2/M2 / ((m1/M1) + (m2/M2))The mole fraction is then multiplied by100% to obtain numbers that are more con-venient to use.DSC purity determinations can now be per-formed on the artificially contaminatedsamples using a heating rate of 1 K/min. Ifthe sample melts without decomposition,and recrystallizes on cooling to room tem-perature, the same sample can be measuredagain. This improves the shape of the peakat the tip. Any slight decomposition orpolymorphism can of course change theshape of the peak.Try to detect the eutectic peak using themost impure sample. Since the eutecticmixture typically melts some 10 °C to50 °C lower than the pure component 1, itis a good idea to look for the eutectic peakby measuring a sample that is no longerrequired at a heating rate of 10 K/min(start temperature about 100 °C below themelting point of component 1). The eutec-tic peak (Figure 4, left) confirms the pres-ence of a eutectic system.Plot the error of x2 (x2 as determined byDSC minus x2 added). The ideal case is ahorizontal straight line with an error of0 mol% (Figure 2). If the error is distinctlypositive, then dissociation of the impurity isa possible explanation. Sodium chloride inwater, for example, gives an "error" of

Table 2. Added and measured impurities

m1 m2 Added Measured Errorimpurity impurity (measured - added)

[µg] [µg] [mol%] [mol%] [mol%]

3360 0 0.0 0.037 0.0373610 12 0.465 0.526 0.0615584 23 0.58 0.65 0.073224 36 1.55 1.45 -0.13868 94 3.30 2.77 -0.52

100% because of the complete dissociationof the Na+ and Cl- ions.

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Volatile impuritiesThe presence of moisture, i.e. water with itslow molecular mass has a large effect onthe results of DSC purity determinations.Organic solvents are also examples of vola-tile compounds that may typically bepresent. They are included in the evalua-tion if the measurements are performed inhermetically sealed crucibles.If only the nonvolatile impurities are of in-terest, which is normally the case for phar-maceutical active ingredients, then the cru-cible should be sealed with a pierced lid.Hole diameters of 0.3 mm to 1.0 mm areideal. The volatile impurities of substanceswith melting points above about 80 °C canthen evaporate and do not affect the re-sults. The endothermic vaporization peakcan, of course, give rise to baseline prob-lems which in turn affect the evaluation.This can be avoided by including an iso-thermal drying period at about 10 °C belowthe expected melting point. In this case it isimportant to purge the measuring cell withdry nitrogen (in general, gases from gasbottles are extremely dry).When using pierced lids, there is of coursethe danger that not only solvents but alsoother relatively volatile impurities are lostand thereby not measured.Small holes (< 0.3 mm) slow down diffu-sion and result in the formation of a self-

generated atmosphere that greatly retardsthe drying process. If the holes are toolarge (>1.0 mm) or if crucibles withoutlids are used, then quite often part of themain component is lost through sublima-tion.

Thermal stability of the substanceIf the main component undergoes partialdecomposition during the melting process,the decomposition products can immedi-ately depress the melting point. This effectdecreases noticeably with increasing heat-ing rate because at higher heating ratesthere is less time for the decomposition tooccur.There are also substances that do not de-compose at the beginning of the meltingprocess, but whose baselines after meltingare at a different level. In such cases, onemakes do with horizontal baselines begin-ning on the left (low temperature side) ofthe curve (Figure 4, right).In principle, the decomposition can beshifted to higher temperature using highpressure DSC at pressures of about 5 MPa.The melting behavior changes very littlecompared to that at normal pressure.

PolymorphismPolymorphism interferes with purity deter-mination especially when a polymorphictransition occurs in the middle of a melt-ing peak. With an optimum choice ofmeasurement parameters, the transitioncan be allowed to take place beforehand in

Fig. 2. Error of x2 as a function of the concentration of added impurity. Component 1 is high pu-rity dimethylterephthalate (M1 194.2 g/mol), component 2 is salicylic acid (M2 138.1 g/mol). Thesample weights and the results of the DSC purity determination are summarized in Table 1. Theerror in the DSC purity analysis of this system is less than 10% up to about 1.7% impurity.

Fig. 3. The upper diagram shows the melting curve of butylhydroxyanisole with the characteristicmelting of the metastable modification at about 60 °C, followed by crystallization of the stablemodification that finally melts at about 63 °C. Polymorphism interferes with both melting peaksand thereby prevents purity determination. In the lower diagram, the sample is first held at 60 °Cfor 10 minutes after which the transition to the stable modification is complete. The sample isthen cooled down to 35 °C and then heated at 2.5 K/min . Although the melting peak can beevaluated, the results are questionable because BHA contains isomers.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2 2.5 3 3.5

Error (impurity measured - added, mol%)

Impurity added, mol%

+ 10% Error

- 10% Error

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an isothermal segment. Afterwards the re-sulting stable modification melts in a dy-namic segment.The different modifications of a chemicalsubstance do not mutually depress their re-spective melting points.Certain substances exist in partially amor-phous form. This manifests itself in a no-ticeably smaller heat of fusion. A more seri-ous problem for DSC purity determinationis exothermic "premelting crystallization"at the beginning of the melting peak,which leads to completely erroneous re-sults. Here again, the crystallization can beallowed to take place isothermally beforemeasuring the melting curve.With hydrates, (or solvates), two meltingpoints can often be measured. In ahermetically sealed crucible the hydratemelts "in its own water of crystallization",quasi in a eutectic with maximum depres-sion of the melting point. In an open cruci-ble, the water of crystallization evaporatesoff on warming, and the peak of the result-ing anhydrous form occurs at correspond-ingly higher temperature.

Sample preparation and DSCmeasurement parametersSamples: The thermal resistance betweenthe sample and the crucible should be aslow as possible. In this respect, fine powdersare much more favorable than coarse ag-glomerates of particles. Furthermore, asample of fine powder is much more likelyto be representative of the substance as awhole.For these reasons, about 1 g of the sub-stance is ground in a clean agate mortarusing as little pressure as possible (thecrystal lattice of some substances can bedestroyed by excessive pressure). The pow-der is then stored for future use in a smallbottle.Samples that are liquid at room tem-perature are prepared by transferring adrop with a fine spatula to a tared stand-ard aluminum crucible. The crucible isthen hermetically sealed and weighed.The drop solidifies on cooling in the lowtemperature DSC.Sample weight: The heats of fusion ofmost organic substances are quite large(about 150 J/g), which is the reason whysmall sample weights can be used. Thisalso reduces the effect of temperature gra-dients within the sample. A sample weight

of 2 mg to 3 mg is optimum for very puresubstances, 3 mg to 5 mg for about 2 mol%impurity, and 5 mg to 10 mg for 5 mol% ormore impurity. It is good analytical prac-tice to weigh the crucible before and afterthe measurement in order to check for anylosses (this is also advisable for hermeti-cally sealed crucibles since dust or traces ofthe substance between the crucible and thelid prevent successful cold sealing).It is often preferable to perform three meas-urements in order to gain informationabout the homogeneity of the sample.Crucibles::::: The 40 µl standard aluminumcrucibles are normally used because theycan be hermetically sealed. From the pointof view of shape and low heat capacity, thelow mass 20 µl aluminum crucibles are

rate of 10 K/min can be used for substancesthat decompose. ASTM E928 lays down heat-ing rates of 0.3 to 0.7 K/min.Our experience with numerous stable sub-stances shows that the results are not very de-pendent on heating rates of up to 5 K/min. At10 K/min, the measured impurity concentra-tion tends to be lower (by about 10%).If the substance melts without decomposi-tion and crystallizes on cooling, the effectof the heating rate can be investigated bymeasuring the same sample at differentheating rates.Atmosphere::::: The DSC cell is usuallypurged with nitrogen at 50 ml/min in orderto prevent oxidative decomposition and toremove any volatile comonents that areformed.

Fig. 4. Schematic DSC melting curves (^exo) with suggested baselines. Left: since the eutectic isusually not measured, the horizontal baseline from the right is a good approximation. Middle: be-cause of anomalous cp effects, the right side of the baseline can for example be shifted in theendothermic direction. In this case use the Integral or possibly the Spline baselines. Right: thehorizontal line from the left is better for substances with marked decomposition after melting.

also very suitable. They cannot however behermetically sealed. Sometimes the moltensubstance is able to seep through thespace between the lid and the wall ofthe crucible (danger of contaminatingthe DSC sensor).Start temperature: This depends on thedegree of impurity expected and is usually10 °C to 30 °C below the melting point ofthe pure substance.End temperature: This is usually about5 °C above the melting point of the puresubstance.Heating rate: The optimum heating rateis 0.5 - 1 K/min for very pure substances,1 -2 K/min for samples with about 2 mol%impurity and 2 - 5 K/min for samples withimpurity levels above 5 mol%. A heating

Choice of the baselineA horizontal line drawn from the right (af-ter complete melting) is often preferred tothe usual line connecting both sides of thepeak. This is theoretically the correct base-line since after the eutectic peak smallquantities of the pure substance continu-ously melt. When slight decomposition oc-curs or with anomalous cp effects, it is betterto use one of the integral baselines, andwith more extensive decomposition to usethe horizontal line from the left. You willoften observe that the linearization correc-tion and to some extent the three confi-dence intervals are smallest when thebaseline is "right".

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TGA-FTIRInterface

With the new TGA-FTIR interface, Fouriertransform infrared spectrometers can beeasily interfaced to the TGA/SDTA851e/LF.A TGA-FTIR system consists of the follow-ing components:

The Mettler-Toledo TGA-FTIR Interface al-lows transfer lines with an outside diameter(including insulation) of 25.0 mm to45.0 mm and an internal diameter of3.0 mm to be attached.With the TGA-FTIR combination, you cananalyze the decomposition products of TGAsamples. Just as with the TGA-MS combina-tion, it provides you with a wealth of newinformation and makes a meaningful inter-pretation of the results possible.

Product Supplier Order No.SDTA851e (large furnace) 1100 °C orTGA/SDTA851e (large furnace) 1600 °C METTLER TOLEDO -

TGA-FTIR Interface METTLER TOLEDO 51 140 805

FTIR (e.g. Nexus) Nicolet -

Gas cell with heated transfer line Nicolet -

Tips for the evaluationThe evaluation itself is performed in aselected part of the melting curve, usuallyin the range 10% and 50% of the peakheight. The lower limits exclude excessivelyhigh concentrations of impurity in the liq-uid phase at the beginning of melting. Theupper limit eliminates data measured faraway from equilibrium conditions. In prin-ciple, you can change the limits, for exam-ple in order to avoid including an artifact.Another definition of the limits uses peakareas between 10% and 50%. This is ad-vantageous if the eutectic peak lies veryclose to the that of the pure melting sub-stance (the latter peak is of courseevaluated).In any case, you should check that thereare no artifacts of any consequence be-

tween the crosses (marked x) where theevaluation is performed.With higher concentrations of impurity, the"Purity Plus" (logarithmic form) evaluationprogram gives more accurate results. In addi-tion to this, the heat of fusion of the puremain component can be entered (if the valueis known accurately) so that any measure-ment error is excluded.Finally some comments on individual points:The linearization correction should bebetween –10% and +15% of the heat offusion.The calculated confidence intervals for95% probability tell you how good the fitis and hence whether the Van’t Hoffequation can be applied. The intervalsshould not be looked on as " error limits"for the results.

Normally the values for confidence inter-vals are as follows:• for the purity (and the concentration

of impurity), 0.01 to 0.2 mol%,whereby very pure substances oftengive relatively "poor" confidence inter-vals,

• for the extrapolated pure meltingpeak, 0.005 °C to 0.1 °C and

• for the linearization correction, 0.02%to 5%.

LiteratureFuther information and the results of inter-laboratory tests can be found in the publi-cation "Purity Determinations by ThermalMethods" (R. L. Blaine, C. K. Schoff, eds.)ASTM-PCN 04-838000-40 ASTM STP 838(1984).

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TGA-FTIR combination for the investigation ofsealing ringsDr. Frank P. Hoffmann; METTLER TOLEDO GmbH, Giessen

Thermogravimetric Analysis (TGA) is awell-established method that is used inquality assurance and quality control forthe characterization of the thermalbehavior of a very wide range of substances.With TGA alone, however, it is not possibleto learn anything about the composition ofthe volatile substances evolved from a sam-ple. The online combination of a TGA witha Fourier Transform Infrared Spectrometer(FTIR), however, enables both quantitative(TGA) and qualitative (FTIR) analysis tobe performed simultaneously. The tech-nique allows the substances evolved to beidentified and correlated with the weight-loss steps detected by the TGA.

The TGA-FTIR combinationThe METTLER TOLEDO TGA/SDTA851e

measuring module is interfaced to an FTIRspectrometer (Nicolet Analytical Instru-ments Nexus or Protege 460). The interfaceconsists of a thermostated gas transfer linethat connects the TGA to a thermostatedgas cell mounted in the spectrometer. TheTGA purge gas flushes the gases evolvedfrom the sample through the transfer lineinto the gas cell. The IR absorption of thegases is measured in the mid-infrared re-gion. Only a small volume of gas is re-quired for the measurement. This guaran-tees a high spectrometric detection sensitiv-ity and ensures that the TGA and IR signalscoincide.Apart from the entire IR spectrum, charac-teristic wavenumber regions can also be se-lected [1,2], and the changes in the spec-trum observed as a function of time or tem-perature. This method allows the gas mix-ture evolved to be examined selectively fordifferent components. In this way, relativeconcentration profiles of the individualcomponents (chemigrams) can be ob-tained.The TGA/SDTA851e module allows a largevariation of the purge gas flow rate. Thisenables the performance of the TGA-FTIRcombination to be optimized. With anotimum setting of the flow rate, a good

compromise between a sufficiently highproduct concentration and a short resi-dence time of the gases in the cell can beachieved.

Application example: the thermalstability of sealing ringsThe task was to investigate the thermaldegradation of sealing rings (elastomers)from two different manufacturers bothqualitatively and quantitatively, in order toobtain information about the onset tem-perature of the initial degradation and anyfurther degradation steps, and to identifythe volatile components evolved.The samples were measured in the tem-perature range 30 °C to 900 °C at a heat-ing rate of 10 K/min with a nitrogen purgegas flow rate of 40 ml/min. The sampleweights used were 27.52 mg and 37.41 mg.The gas cell and the transfer line werethermostated at 200 °C.

Figure 1 shows the results for sealingring 1. In this example, the derivative ofthe weight loss curve, the DTG curve, wasused to identify the individual TG steps.Each step in the TG curve gives rise to a

peak in the DTG curve. The TG curve wasfound to consist of six steps namely at130 °C, 320 °C, 460 °C, 510 °C, 650 °Cand 880 °C. The uppermost diagram showsthe chemigrams of H2O, HCN, CO2 andcyclohexane. The very small loss of weightat about 130 °C is due to the evaporationof water (0.06%). Afterwards, the decompo-sition of the nitrile groups leads to theelimination of HCN (0.6%). At the largestdecomposition step (53% at 460 °C) HCN,CO2 and above all cyclohexane are liber-ated. The latter is formed as a crackingproduct of the thermal degradation of thepolymer chain. The elimination of CO2 at650 °C and 890 °C is a result of the de-composition of the filler components(dolomite).The curves corresponding to the thermaldegradation of sealing ring 2 are shown inFigure 2 (the presentation is analogousthat in Figure 1). In this sample, only three

Fig. 1. TGA-FTIR measurement of elastomer sample 1

significant decomposition steps at 220 °C,330 °C and 470 °C are observed. Afterwardsthere is a continuous but very gradual lossof weight (1.2%). The chemigram of CS2 isshown instead of that of H2O. The very

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weak loss of weight detected in the TGAcurve at 220 °C (1.3%) corresponds to theformation of carbon disulfide. This resultsfrom the decomposition of sulfur com-pounds formed during vulkanization. HCNand CO2 are liberated during the second de-composition step (8.1% at 330 °C). Lateron, the liberation of cyclohexane begins atabout 390 °C in the third decompositionstep (53% at 470 °C).A comparison of the results of the two seal-ing rings shows differences with regard tothe composition of the elastomer and thefillers. The degradation of the polymerchain at about 480 °C is however almostidentical in both samples.Carbon disulfide does not occur as a de-composition product of sealing ring 1.

SummaryThe measurements show that a qualitativeand quantitative classification with regardto the thermochemical properties of thematerials is possible. The combination ofTGA and IR spectroscopy facilitates thecomparison of materials with given toler-ances in quality assurance and in the con-trol of incoming material. The interpreta-tion of the TGA curves is greatly enhanced

Fig. 2. TGA/FTIR measurement of elastomer sample 2

Oxidative stability of petroleum oil fractions

Introduction The determination of the oxidative induction temperature is a rapid method for assessing the stabilityof petroleum oil fractions. The same method can be used to measure the effectiveness of stabilizers.Besides this, aging processes can also be investigated. Standardized isothermal methods are oftenused instead of dynamic methods (e.g. ASTM D 5483 and ASTM E 1858). Analysis under high pres-sures of oxygen prevents the vaporization of volatile components and increases the rate of oxidation,thereby shortening the measurement time [1, 2].

Samples Diesel oils of the following petroleum fractions: Light (LGO), Light Cycle (LCGO), Light Vacuum(LVGO), Vacuum1 (VGO1), Vacuum2 (VGO2), Vacuum3 (VGO3) and Kerosine.

Information expected Comparison of the products with respect to their stability in oxygen.

Measurement parameters Measuring cell DSC27HP / TC15Crucible Aluminum 40 µl, with pierced lid (1 mm hole)DSC measurement Put the measuring cell under an atmosphere of oxygen and heat from 40 °C to

150 °C at 20 K/min (to save time), then continue up to 350 °C at 5 K/min.The measurement is automatically terminated when the value of the exothermicDSC signal reaches 10 mW (the combustion peak is not of interest).

Atmosphere Oxygen at 3 MPa, no purge gas.

by the (spectroscopic) separation of theevolved gases into individual components.In addition, this enables a separation ofoverlapping decomposition reactions to bemade, which in turn allows a better insightinto the mechanism and kinetics of the de-composition processes.

Literature[1] Rolf Schönherr: TGA-FTIR Atlas

"Elastomers"[2] Nicolet Vapor Phase Database

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Diagram

Interpretation The high pressure of oxygen prevents any premature vaporization so that, on heating, a deflection inthe DSC curve is caused only by a change in the specific heat of the sample and no other thermaleffects are observed before the beginning of oxidation. The full curve for light diesel oil (LGO) isshown in the upper diagram; the change in the heating rate at 150 °C is marked with a vertical line.The lower diagram shows the measurements of all the samples from 150 °C onwards. The curves arearranged so that they can be seen clearly. The tangents used for the evaluation are drawn for thesamples of lowest and highest stability. The abbreviations refer to the petroleum fractions mentionedabove.

Evaluation The oxidative stability is compared by determining the temperature at which oxidation begins (on-set). This value is considered to be characteristic of the sample. It is measured as the point of inter-section of the horizontal tangent of the baseline before oxidation and the tangent at the steepest partof the DSC curve:

Conclusions The stability of the various fractions is very different. The DSC curves also show differences at the be-ginning of oxidation. Similar fractions, however, show almost identical DSC curves with practicallythe same onset temperatures (e.g. VGO1 and VGO2). This makes it very easy to classify the fractionsaccording to their stability. Long-term stability at low temperatures can, however, only be predictedwith kinetic experiments.

Literature [1] A .T. Riga and G. H. Patterson, Eds., Oxidative Behavior of Materials by ThermoanalyticalTechniques, ASTM STP 1326, American Society for Testing and Materials, 1997

[2] H. Kopsch, Thermal Methods in Petroleum Analysis, VCH Verlagsgesellschaft, Weinheim,1995.

Petroleum Fraction Abbreviation Sample weight [mg] Onset [°C]

Light Cycle LCGO 4.805 173.3Kerosine 6.151 203.5Vacuum VGO1 6.391 210.4Vacuum VGO2 6.016 210.6Vacuum VGO3 6.635 214.6Light Vacuum LVGO 5.578 224.9

Light LGO 5.300 228.7

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What can model free kinetics tell us about reactionmechanisms?

Model free kinetics is based on anisoconversional computational techniquethat calculates the effective activation en-ergy (E) as a function of the conversion(α) of a chemical reaction, E = f(α).The variation of E = f(α), is not only ofimportance for reliable predictions, butalso allows one to draw important mecha-nistic conclusions [1, 2]. For instance, theshape of the activation energy curve indi-cates directly whether a reaction is simpleor more complex. For simple processes,E = f(α) is practically constant (horizon-tal line). Model free kinetics ofthermoanalytically measured reactions,however, rarely gives a constant activationenergy.The fact that a reaction is governed by aconstant activation energy does not neces-sarily mean, however, that it is a single stepreaction. Most probably it is a multi-stepprocess that is controlled by the rate of theslowest step.An example of a complex decompositionreaction with almost constant activationenergy is the thermal degradation ofpolypropylene under nitrogen. Figure 1shows E = f(α) obtained from the modelfree kinetics of a thermogravimetric study.From the almost constant activation energyof about 180 kJ mol-1, we can conclude thatrandom chain scission is the rate determin-ing step of the degradation reaction.If E = f(α) is not constant, the process iscomplex and consists of several reactionsteps. Certain complex reactions exhibit arather typical activation energy dependencyE = f(α). For instance, the decompositionreactions of many solid substances are re-versible:

AB s A s B g( ) ( ) ( )⇔ +

The effective activation energy is given byequation (1), [3]:

E E m HP

P P

m

m m= − +

−20

0

λ ∆ (1)

where E2 is the activation energy of the re-verse reaction, λ the heat of absorption, ma constant (0 < m ≤ 1), ∆H the heat of re-action, P0 the equilibrium pressure and Pthe partial pressure of the gaseous reactionproduct B. From equation 1 it is clear that,as long as the system is not far from equi-librium, the activation energy is tempera-ture dependent because of the temperaturedependence of the equilibrium pressure. If,at the starting temperature, the system isvirtually at equilibrium (i.e. P ≈ P0) thenboth the last term of equation 1 and the ac-tivation energy are large. With increasingtemperature, P0 increases and the systemdeparts from equilibrium, (i.e. P << P0),whereby the last term of equation becomessmaller and decreases to a constant valueclose to the heat of reaction. The loss ofwater of crystallization from calciumoxalate monohydrate under non-isother-mal conditions is a typical example of thistype of kinetic behavior (Figure 2).If a process involves two (or more) parallelreactions with different activation energies,the contribution of the reaction with thegreater activation energy increases with in-creasing temperature. This is the reasonwhy the experimentally observed activationenergy of such processes increases withtemperature and therefore also with conver-sion. An increasing activation energyE = f(α) indicates the occurrence of paral-lel reactions. An example of this is the ki-netics of curing of a DGEBA epoxy resin(diglycidylether of bisphenol A) withphthalic acid anhydride and a tertiaryamine as accelerator [4]. The experimen-tally observed E = f(α) is shown in Figure3. From this we can conclude that the cur-ing process consists of two parallel reac-tions with activation energies of about20 and 70 kJ mol-1. It is known from the

literature [5], that curing is initiated by thereaction of the amine with an epoxy groupvia the formation of a zwitterion. The latterreacts with the anhydride to form a car-boxyl anion that catalyses the polyaddition.In a competing reaction, the zwitterion re-acts with a hydroxyl group of the DGEBA toform an alkoxide anion which promotesthe homopolymerization of the DGEBA. Inorder to test this hypothesis, we measuredthe activation energy of the pure competingreaction (DGEBA with the amine but with-out the anhydride) with DSC. As Figure 3shows, the polymerization has a practicallyconstant activation energy of about20 kJ mol-1, which is thus consistent withthe value of the competing reaction previ-ously postulated. The low value of E indi-cates that the process is diffusion control-led. The other reaction with an activationof 70 kJ mol-1 is the polyaddition.Solid phase reactions of the type solid →solid + gas often begin under kinetic con-trol and then become more and more diffu-sion controlled. This is because the thick-ness of the surface layer already reacted in-creases, which results in the diffusion ofthe gaseous product becoming rate deter-mining. The activation energy of the diffu-sion of a gas in a solid is markedly lowerthan that for chemical reactions (a fewtens of kJ mol-1 compared with one to sev-eral hundred kJ mol-1). During the transi-tion from a kinetic to a diffusion controlledreaction, one therefore sees a decrease inE = f(α) from about one hundred to sev-eral tens of kJ mol-1. This type of depend-ence is also observed for the pyrolysis ofwood [6], (Figure 4).

In summary, it can be said that althoughthe shape of the curve of E = f(α) does notyield any detailled information about thereaction mechanisms, the information isnevertheless adequate for many practical

Sergey Vyazovkin, Center for Thermal Analysis, Department of Chemistry, University of Utah 315S. 1400 E., Salt Lake City, UT 84112,USA

10 USER COM 2/99

purposes. If, for example, the rate of a reac-tion that is initially kinetically controlledand then diffusion controlled is to be in-creased, then the contribution of slow dif-fusion must be diminished. This can bedone by modifying the starting material(e.g. more finely powdered) and optimizingthe reaction conditions.

Fig. 3. E = f(α) calculated using model free kinetics with DSCcurves. Above: the two parallel reactions of the polyaddition of anepoxy resin yield an activation energy that increases steeply.Below: the isolated homopolymerization reaction at a level of about20 kJ mol-1

Fig. 4. E = f(α) for the pyrolysis of various types of wood (pine, birchand oak)

Literature[1] S.Vyazovkin, Int. J. Chem. Kinet., 28,

95 (1996).[2] S.Vyazovkin, C. A. Wight, Annu. Rev.

Phys. Chem., 48, 125 (1997).[3] M. M. Pavlyuchenko, E. A. Prodan,

Doklady Akad. Nauk SSSR, 136, 651(1961).

[4] S. Vyazovkin, N. Sbirrazzuoli,Macromol. Rapid Commun. 20, 387(1999).

[5] L. Matejka, J. Lovy, S. Pokorhy, K.Bouchal, K. Dusek, J. Polym. Sci. A, 21,2873. (1983)

[6] S. Vyazovkin, Thermochim. Acta, 223,201, (1993).

Fig. 1. E = f(α) for the thermal degradation of PP in N2

E / k

J mol

-1E

/ kJ m

ol-1

E / k

J mol

-1

Fig. 2. E = f(α) for the elimination of water of crystallization fromcalcium oxalate monohydrate in N2 measured by model free kinetics

E / k

J mol

-1

αα

α α

USER COM 2/99 11

Safety investigations with model free kinetics

Hexel Composites is a company that manu-factures epoxy resin formulations at itsproduction site in Duxford, Cambridge, UK.In order to assure safety in the chemicalplant, a thorough understanding of the po-tential thermal hazards of these materialsis essential.Recently, we started a program to assess thecontribution that DSC kinetic data canmake. In particular, we wanted to comparethe results based on conventional nth orderkinetics and the new model free kinetics(MFK) with the data obtained by directmeasurement of the adiabatic behavior inhot storage tests (SPS6).

IntroductionSafety investigations frequently assumeadiabatic conditions (worst case), in whichan initial low level of exothermic energyslowly warms the reaction mass therebycausing the reaction rate to increase untilthe reaction finally "runs away". The tem-perature increases by an amount corre-sponding to the heat of reaction divided bythe average specific heat of the reactionmass. At this temperature, organic sub-stances can decompose and give rise togases and vapors. The time taken to reachthe maximum reaction rate (TMR, or as asymbol tmr) is of great importance. This isalso sometimes called the intervention timebecause up until this time an intervention(e.g. cooling) can still successfully preventan uncontrolled reaction. The TMR can beread off from the curve of the adiabatictemperature increase (point of inflection).The higher the adiabatic starting tempera-ture chosen for the measurement, theshorter the TMR.

FormulationsSix epoxy resins formulations with aminehardeners were chosen for our investiga-tions. In order to cover a larger tempera-ture range, three formulations with accel-erator systems were used (marked with an*), which lower the temperature of curefrom 175 °C to 120 °C.

Scott Barnett, Hexcel Composites, Cambridge, UK

Fig. 1. The measurement begins under adiabatic conditions as soon as the reaction has beenheated to the starting temperature T0. The time taken to reach the maximum reaction rate isknown as tmr.

Sample Hardener type Usual cure Adiabaticstarting number temperature temperature

[°C] [°C]

1 dicyandiamide * 120.0 70.0

2 dicyandiamide 175.0 100.0

3 dicyandiamide * 120.0 60.0

4 3,3'-Diamino-

diphenylsulfone 175.0 70.0

5 dicyandiamide * 120.0 62.5

6 dicyandiamide 175.0 70.0

Table 1. Usual cure temperatures and starting temperatures of some types of hardeners

Adiabatic hot storage testing is more diffi-cult and expensive to conduct than DSCmeasurements because it requires bothlarge amounts of sample (up to 1 kg) andspecially equipped laboratories to cope eco-logically with the fumes that are given off.An alternative to hot storage testing couldsave much time and expense.

tmr

T adiab

Time

Inflection point

12 USER COM 2/99

Nth order kineticsDSC measurements were performed at twodifferent temperatures, namely at the start-ing temperature of interest T0 for the calcu-lation of tmr and at a temperature that was20 °C higher (T1). (DSC measurements attemperatures below those of the hot storagetests are hardly possible because experi-mental times are too long and the DSC sig-nals too weak). The activation energy Eawas calculated from these curves usingEquation 1.

ET Ta =

−R ln( / )

( / ) ( / )

φ φ0 1

0 11 1

R is the gas constant 8.314 J mol-1 K-1 andφ is the peak height (in W/g) of the DSCcurve at the temperature T, the isothermaltemperature in degrees Kelvin.The activation energy could also be calcu-lated directly using the nth order kineticssoftware option.The time required to reach the maximumreaction rate under adiabatic conditions,tmr, is then given by Equation 2.

tc T

Emrp

a

=R 0

2

0φ

cp is the specific heat of the reaction mix-ture, T0 the adiabatic starting temperaturein degrees K and φ0 the maximum heatoutput in W/g at T0.

As can be seen in Table 2, the results ob-tained from the nth order kinetics do notagree with those from SPS6 measurements.This was in fact expected because the iso-thermal DSC curves do not take the usualcourse described by nth order kinetics (theformulations exhibit a delayed increase(formal autocatalysis)) instead of immedi-ately reaching a maximum rate and thensteadily decreasing.

Model free kineticsFor these experiments, we performed dy-namic DSC measurements at three differentheating rates. The model free kinetics soft-ware calculates the activation energy as afunction of reaction conversion. Model freekinetics allows predictions to be made ofthe reaction course at almost any tempera-ture (conversion plot). The maximum re-action rate can be read off from each ofthese conversion curves (most easily from

Equation 1

Equation 2

Table 2. Summary of the values of tmr obtained by different methods. The results from nth orderkinetics are clearly unreliable. The results from MFK are however much nearer the truth.

Sample Adiabatic starting tmr from nth tmr from model tmr fromnumber temperature order kinetics free kinetics SPS6

[°C] [h] [h] [h]

1 70.0 0.33 5.7 2.3

2 100.0 2.31 63.0 80.0

3 60.0 1.05 15.2 15.0

4 70.0 2.28 11.3 11.5

5 62.5 0.97 5.2 3.7

6 70.0 2.76 80.0 127.0

sample was heated quickly beforehand witha small immersion heater so that it reachedthe the temperature T0 in a reasonable pe-riod of time. This experimental setup infact corresponds to a large- scale adiabaticDTA! A pen recorder plots the voltage as afunction of time. The time required toreach the maximum reaction rate tmr at thepoint of inflection of the "DTA curve" isread off from the graph.

ConclusionsThe time required to reach the maximumreaction rate under adiabatic conditions tmris an important safety criterion of exother-mic chemical reactions.DSC measurements of the curing reactionof epoxy resin systems can be used to calcu-late tmr values if they are based on predic-tions of model free kinetics. Nth order ki-netics are not at all suitable for this pur-pose. For safety reasons, the expensive hotstorage tests still cannot be completelyeliminated. They are indispensable for newformulations. The effect of small changesin the formulation can, however, be esti-mated quite well using model free kinetics.

the first derivative). This is multiplied bythe heat of reaction (in J/g), in order to ob-tain φ0 for Equation 2.The value for tmr from model free kineticscorrelates well that from SPS6. This has todo with the fact that model free kineticscan also describe complex reactions with agood degree of accuracy.

Hot storage tests (SPS6)About 300 g of the freshly prepared formu-lation were weighed into the Dewar vesseland a thermocouple mounted in the middleof the sample. A graphite block with a holefor the other thermocouple was used as areference. The Dewar vessel and the graph-ite reference were placed in an oven at theisothermal temperature of interest T0. The

USER COM 2/99 13

The glass transition from the point of view of DSCmeasurements; Part 1: basic principles

IntroductionThe glass transition is a phenomenon thatcan in principle occur in all noncrystallineor semicrystalline materials. The require-ment is a sufficiently large degree of mo-lecular disorder at least in one direction. Toexplain the processes that take place duringa glass transition we assume for simplicitythat we are dealing with a homogeneousliquid.In a liquid, in addition to the molecularvibrations and rotations (of atoms orgroups of atoms) that also occur in solids,there are cooperative movements orrearrangements in which several moleculesor segments of molecular chains partici-pate. The cooperative units can be regardedas tempory clusters that fluctuate with re-gard to both space and time. The size ofthese cooperative units is typically a fewnanometers. This characteristic length de-creases with increasing temperature. An-other characteristic quantity is the time re-quired for the cooperative rearrangementsto take place. It can be described by an in-ternal relaxation time τ.The glass transition is very sensitive tochanges in molecular interactions. Meas-urement of the glass transition can be usedto determine and characterize structuraldifferences between samples or changes ina sample. The glass transition is thereforean important source of information thatcan be obtained from the thermal analysisof materials. This first article discusses anumber of basic principles that aid the in-terpretation of results. Practical aspects ofthe glass transition will be dealt with inPart 2 in the next edition of UserCom.

Description of the effectThe thermal glass transition is observedwhen a melt that is not able to crystallizeundergoes supercooling. This phenomenoncan be explained by assuming that duringcooling, the characteristic time for the co-operative rearrangements approaches thesame order of magnitude as the time deter-mined by the measurement conditions (i.e.by the cooling rate). The movements spe-

cific to the liquid state "freeze" (vitrifica-tion). This results in a reduction of theheat capacity. The temperature at whichthis effect is observed shifts to lower valueswith decreasing cooling rate. The glasstransition is a dynamic transition of the su-percooled melt from a state of metastableequilibrium to a nonequilibrium state(glass).On heating, the molecular processes "thaw"(devitrification), but at a temperature thatis a little higher than that at which they"froze" on cooling. This leads to overheat-ing or enthalpy relaxation peaks in theheating curve.Figure 1 shows the theoretical change of

again, then the same glass transition tem-perature is measured. Any differences thatarise between the glass transition tempera-ture measured in this way on heating orcooling are due to effects of thermal con-ductivity within the sample. If the sampleis held for some time at a temperature Ta,then it ages and the enthalpy becomessmaller. It attains the state designated bythe point D. On heating again, the enthalpyintersects the liquid line at the temperatureTg2 (point E). The glass temperature haschanged through aging.The glass transition temperature Tg2 canalso be attained by cooling from the melt ata lower cooling rate. On cooling, the coop-

Fig. 1. Theoretical enthalpy curve at the thermal glass transition

the enthalpy (the integral of the heat ca-pacity curve) during a thermal glass transi-tion.The sample is cooled from A to C at a con-stant rate. Around B it passes through theregion of the glass transition with the glasstransition temperature Tg1. If the sample isthen immediately heated up to the point A

erative units then have more time for theirrearrangements to take place, which resultsin them freezing later. The slower the cool-ing rate, the lower the glass transition.As can be seen in Figure 2, hysteresis occursbetween the cooling curve and the heatingcurve even under the same conditions. Thiseffect can be explained by assuming that

Enth

alpy

Liquid

Glass

Temperature

14 USER COM 2/99

Fig. 2. Specific heat capacity of polystyrene in the region of the glass transition (curve 1 shows thecooling measurement at 2 K/min, curve 2 is the heating measurement immediately after at2 K/min).

ing effects occur. The glass transitiontemperature Tg1 is the point of intersec-tion of the extrapolated curves of the liq-uid and the glass. Curve 2 is the corre-sponding heating curve when the heat-ing and cooling rates are the same. In

this curve, relatively small overheatingeffects occur. The glass transition tem-perature is Tg1. Curve 3 differs fromcurve 2 only in a more rapid heatingrate. This leads to larger overheating ef-fects but the glass transition tempera-ture remains the same. If the heatingrate is lower than the cooling rate, theglass transition temperature does notchange, but the overheating effect is re-duced. Curve 4 represents the measure-ment of a sample that was heated at thesame rate as in curve 2, but which wasstored for some time at a temperature Tabelow the glass transition temperature.Two effects occur: the glass transitiontemperature is lower (Tg2) and the over-heating peak is larger by an amountequal to the value of the enthalpy re-laxation ∆H. The process of storage be-low the glass transition temperature isalso known as physical aging.Figure 4 shows the measurement curves ofsamples of polyethylene terephthalate(PET) that have been subjected to differentperiods of physical aging. The shift and theincrease in size of the overheating peak canbe clearly seen.

the frozen movements do not thaw untila higher tememperature is reached.Figure 3 shows the differences betweenthe heating and cooling curves in theenthalpy versus temperature diagram.Curve 1 is a cooling curve. No overheat-

Fig. 3. Theoretical enthalpy curves at the glass transition toillustrate the differences between cooling and heating curves.The curves are described in the text.

Tg1Tg2Ta

Temperature

Enth

alpy

1 2

3

4

∆H

Fig. 4. Heating curves of PET after different periods of physical aging at 65 °C.Heating rate: 10 K/min; Cooling from the melt to room temperature within a fewseconds using the sample changer.

USER COM 2/99 15

Visualization of the glass transitionThe glass transition is a kinetic effect thatoccurs at the transition from a supercooledliquid to a glassy solid state. The processesthat occur will be explained with the helpof a model.On cooling a sample that forms a glass, thecharacteristic relaxation time τ increaseswith decreasing temperature. This meansthat the cooperative rearrangements be-come slower. As can be seen in Figure 5,one can think of the continuous coolingprocess as being divided up into a series ofsmall steps. At high temperatures (pointmarked 1 in Figure 5), the relaxation time

Determination of the glasstransition temperatureVarious quantities can be used to character-ize the glass transition. Besides the glasstransition temperature (Tg), the height ofthe cp step (∆cp) and the width of the glasstransition (∆T) are often determined.Other quantities that are used are theheight of the overheating peak and itsmaximum temperature. In Figure 6, anumber of characteristic quantities areshown.

Various methods are used to determine theglass transition temperature. Each method

c Tc T c T

c Tp gl g g g

g g( )( ) ( )

( )=−

+2

• Richardson method: Determination ofthe fictive temperature of the glass as theglass transition temperature. This tem-perature corresponds to the intersectionof the extrapolated enthalpy curves of theglass and the liquid in the enthalpy tem-perature diagram shown in Figure 1. Inthe previous section, only this glass tran-sition temperature was discussed. The de-termination is done by means of an areacalculation (see Figure 7).At Tg, A1+A3=A2.

If no overheating peak occurs, the glasstemperatures determined by all four meth-ods are almost the same. Larger differencesarise between the different glass transitiontemperatures with curves that exhibit over-heating peaks (see Figure 8).

The fictive temperature describes the actualstate of the glass. The glass transition tem-perature determined in this way thereby in-cludes information about the history of thematerial and its structure. All other meth-ods for determining Tg are not only affectedby the state of the glass but also by the ac-tual experimental parameters. They arehowever useful to identify a sample by itsTg or to evaluate comparative measurements.

gives a somewhat different result, which iswhy both the evaluation method and themeasurement parameters should always bestated. The following is a short summary ofthe evaluation methods:• Bisector method: Tg is the temperature at

which the bisector of the angle betweenthe two tangents intersects the measure-ment curve.

• Point of inflection: Tg is the temperatureof the point of inflection of the DSCcurve.

• Half step height: A straight line extrapo-lation is performed on the cp curves ofthe liquid (cl) and the glass (cg). Tg isthe temperature at which the measure-ment curve attains a height equal to halfthe value of the step height:

τ is so short that the sample can com-pletely relax to equilibrium during such astep. The sample is then in equilibrium(liquid). At point 2, the the relaxation timeis already appreciably larger. Molecularrearrangements are, however, still rapidenough for the sample to just reach equi-librium during a step. At point 3, the coop-erative rearrangements have become soslow that there is not sufficient time for thesample to relax to equilibrium. The mo-lecular rearrangements "freeze". The heatcapacity is thereby reduced by an amountcorresponding to these rearrangements (cpstep). Only the types of movement specificto solids remain. From this point of view, aglass behaves as a solid although its struc-ture corresponds to that of a liquid.

Fig. 6. The figure shows a number of characteristic quantities at the glass transi-tion. Tg: glass transition temperature; ∆T=T2-T2, the width of the glass transi-tion, Delta Cp, the step height ; Tm ,the maximum temperature of the relaxationpeak; h, the peak height and A the peak area)

Fig. 5. Illustration of the thermal relaxation with stepwise cool-ing in the region of the glass transition.

Tem

pera

ture

Time

16 USER COM 2/99

Fig. 7. Determination of the glass transition temperature as a fictive temperature by means of amethod based on area caculations.

Fig. 8. The figure shows the glass transition temperature determined by different methods (Tf, asthe fictive temperature, Th, by the bisector method, Ti, by the point of inflection method).

Fig. 9. Determination of the enthalpy relaxation (3.34 J g-1) using a sample that had not beenphysically aged (second run) using PET as an example (1: first heating run, 2: second heating runof the same sample. 3: difference of the curves of the first and second runs).

TemperatureTg

Heat

capa

city

A3

A2

A1

Enthalpy relaxationEnthalpy relaxation in a glass depends onthe mechanical and thermal conditionsduring manufacture and storage. It affectsthe overheating peak of heating curves.A method that is frequently used to deter-mine the enthalpy relaxation is to first heatthe sample up, then cool it down at thesame rate and afterwards immediately heatit a second time. The subtraction of the sec-ond heating curve from the first yields theenthalpy relaxation.

∆H c T c T dTT

T

= −∫ ( ( ) ( ))1 2

1

2

This method is illustrated in Figure 9. A di-rect determination of the enthalpy relaxa-tion from the area of the overheating peakcan lead to large errors.

USER COM 2/99 17

IntroductionParts that are made by the injectionmolding of fiberglass reinforced polymersusually have expansion coefficients thatare direction dependent. The sample inves-tigated here was a machine component(shaft) made of fiberglass filledpolyphenylene sulfide (PPS). For the con-struction of the machine, it was importantto know the the expansion coefficients ofthe shaft in the axial and radial directions.The information was quickly and easily ob-tained by TMA measurements.

Sample preparationMeasurements of expansion coefficients areperformed using the least possible sampleloading. To improve accuracy, it is advan-tageous to use samples that are thick in thedirection of measurement. The upper andlower surfaces of the sample should be flat,smooth and parallel. In this investigation,one sample in the radial direction and twosamples in the axial direction were pre-pared from the shaft. Paticular care wastaken to minimize any thermal strainswhen cutting and polishing the samples.The dimensions of the samples were as fol-lows:Sample A (axial), diameter 9.3 mm, height4.9 mm,Sample B (axial, from the other end of theshaft), diameter 5 mm, height 8.7 mm,Sample C (radial, same end as sample B),height 6.8 mm, area 5 mm x 5 mm.

Measurement parametersModule: TMA/SDTA840 with a 3.0 mm ballpoint probeLoad: 0.02 N. A 0.5 mm thick quartz glassdisk was placed between the probe and thesample in order to distribute the load uni-formly over the surface of the sample.Temperature program: 30 °C to 200 °C at1 K/minAtmosphere: Air, stationary atmosphere.

ResultsFigure 1 shows the results of the dilatationmeasurements on sample A with and with-out thermal pretreatment. In the first heat-ing run at 1 K/min, a glass transition canbe seen which starts at about 78.3 °C. Theeffect is rather unclear because of enthalpyrelaxation. The second heating run, whichwas also measured at 1 K/min, shows a

much clearer glass transition at 91.2 °C.Figure 2 shows the mean values for the co-efficients of expansion and the glass transi-

tion temperatures of samples B and C(axial and radial direction of the shaft)measured using the second heating run.The results are summarized in Table 1. It isapparent that the glass transition tempera-tures for the two directions differ by about3 °C. In addition, the expansion coeffi-cients in the axial and the radial directionsdiffer by about a factor 2 above the glass

transition temperature Tg, and by about30% below Tg. This shows that the orienta-tion (mentioned at the beginning) that oc-

Determination of the expansion coefficients of aninjection molded polyphenylene sulfide machinepart above and below the glass transitiontemperature

Fig. 1. The first and second TMA heating heating curves of sample A (axial). The mean linear co-efficients of expansion have been evaluated.

Axial direction Radial direction

Glass transition temperature, Tg 91.1 °C 94.0 °C

Expansion coefficient below Tg 25.1 ppm/K 35.8 ppm/K

Expansion coefficient above Tg 50.5 ppm/K 88.73 ppm/K

Table 1. Glass transition temperatures and the mean coefficients of linear expansion in the axialand radial directions.

18 USER COM 2/99

curs in injection molded parts during theproduction process has a considerable ef-fect on the mechanically determined glasstransition temperature and on the coeffi-cients of thermal expansion.A comparison of the mean coefficients ofexpansion of the two samples in the axialdirection (sample A and sample B) showssmall but neverless significant differences.This indicates that the different flow pathsalso have an effect on the thermal proper-ties of the injection molded part. In otherwords, one can detect not only direction de-pendent anisotropic behavior, but also lo-cation dependent effects (which are courseappreciably smaller).

Two-component phase diagram and the deter-mination of the eutectic composition of dimethylterephthalate (DMT) and benzoic acid

IntroductionThe regions in which the various phases ofa binary mixture are in equilibrium can bedescribed by a so-called two-componentphase diagram in which the temperature isplotted as a function of composition. Theterm eutectic melting diagram is also usedif we are dealing with solid-liquid transi-tions.There are in fact 12 different basic types oftwo-component melting diagrams (see forexample [1]). In practice, however, we of-ten encounter euctectic systems whose two-component phase diagrams are of the typeshown schematically in Figure 1.

Two-component phase diagramsfrom DSC measurementsThese types of two-component phase dia-grams can be determined by DSC measure-ments. To do this, samples containing mix-tures of the two substances in different ra-tios are prepared and measured by DSC.Points on the liquidus line are determined

Fig. 2. TMA curves showing the glass transition and the mean coefficients of linear expansion inthe axial and radial directions of the PPS injection molded part (samples B and C).

T

A B

E

S+A S+B

S

A+B

liquidus line

solidus line

xB

T1

TE

Figure 1: Below the solidus line both substances exist in separate crystalline forms in the solidstate. If the temperature of a mixture of the two components is slowly raised, a portion of the sam-ple melts at the melting point of the eutectic. In this liquid mixture phase, either pure A or pure Bin the solid state is also present depending on whether one is on the left or the right side of the eu-tectic composition. On further heating, the remainder of the solid phase melts until finally thewhole sample has completely melted at a temperature corresponding to the initial composition ofthe mixture xB. Above the liquidus line there is only one phase (homogeneous melt).

USER COM 2/99 19

Fig. 3. Determination of the eutectic composition of DMT and benzoic acid.

Fig. 4. Two-component phase diagram of DMT and benzoic acid.

by measuring the clear melting points ofthe different samples and plotting these asa function of the composition of the sam-ple. The clear melting point (the tempera-ture at which melting is complete) corre-sponds approximately to the temperature ofthe maximum of the second peak, i.e. themelting peak of the pure (main) compo-nent.These types of measurements can also beused to determine the eutectic composition:the heat of fusion of the eutectic meltingpeak is plotted against composition and theeutectic composition obtained by extrapo-lation. This is appreciably more accuratethan extrapolating the nonlinear liquidustemperatures. In this way, the meltingpoint of the eutectic (solidus line) and anadditional point of the two-componentphase diagram have been determined.

ResultsThis method is illustrated in Figures 2 to 4using the system dimethyl terephthalate(DMT) and benzoic acid as an example.Figure 2 shows the DSC curves for variousmixtures with different ratios of DMT andbenzoic acid. As expected, the eutectic al-ways melts at the the same temperature.The heat of fusion of the eutectic peak ishowever different in each case because ofthe different sample compositions. The plotof the heats of fusion of the eutectic peaksagainst sample composition (Fig. 3) yieldsa value of 72 mol% for the eutectic compo-sition. The two-component phase diagramof DMT and benzoic acid can then be plot-ted from the melting points of the peaks(see Fig. 4).

Measurement parametersModule:DSC821e, stationary air atmosphereTemperature program: 70 °C to 160 °C at 5 K/minSample weights:between 4 mg and 8 mg

References[1] Landolt-Börnstein,

Schmelzgleichgewichte , 6th Edition,Volume II/ Part 3, page 1

Fig. 2. DSC curves of different mixtures of DMT and benzoic acid. The benzoic acid content isgiven in units of mole percent.

0.0 0.2 0.4 0.6 0.8 1.0

90

100

110

120

130

140

Solidus

Liquidus

Tem

pe

ratu

re [

°C]

Mole Fraction of Benzoic Acid

0,0 0,2 0,4 0,6 0,8 1,00

30

60

90

120

150

Ent

halp

y of

Eut

ectic

Pea

k [J

/g]

Mole Fraction of Benzoic Acid

20 USER COM 2/99

Crosslinking and degree of cure of thermosettingmaterials by Differential Scanning Calorimetry(DSC)

Fig. 1. This shows a typical DSC heating curve (heating rate 10 K/min) of a thermosetting resin ,in this case an epoxy resin such as is used for the production of printed circuit boards in the elec-tronics industry.

Dr. Bernhard Benzler; METTLER TOLEDO GmbH, Giessen

Thermosets (or thermosetting plastics) isthe term used to describe a group of hardand amorphous plastics that remain rigidup until their degradation temperatures.They consist of close-meshed cross-linkedmacromolecules and cannot therefore meltor be dissolved.

Phenolics and aminoplastics, epoxy resins(EP resins) and unsaturated polyester res-ins (UP resins) are examples of thermoset-ting materials. The former arepolycondensation products whereas the lat-ter are made by polyaddition and polymeri-zation. The precursor products are knownas thermosetting resins. Following the ad-dition of additives (hardeners, accelerators,fillers, etc.), they react or cure to formthermosets.In practice, thermosets can be found invery many different forms: with fillers inmoldings such as drinking cups, unreactedas powder coatings, and fiberglass rein-forced as composites and constructionalmaterials for printed circuit boards in theelectronics industry. Typical for these ther-mosetting materials is that the polymeriza-tion normally takes place during themolding process because they cannot beshaped thermoplastically.The properties of the products depend to alarge extent on the degree of the polymeri-zation. As part of a quality assurance pro-gram, tests are essential to check the prop-erties of the products for their intended use.A suitable control method should be easy toperform and give a high degree of repro-ducibility, and the sample preparationshould be relatively simple. Spectroscopicmethods, for example, cannot normally beused because of the insolubility of thecrosslinked product. In practice, twothermoanalytical methods, namelyThermomechanical Analysis (TMA) and inparticular Differential Scanning

Calorimetry (DSC), have been very success-ful and have in fact become standardmethods.

The measurement curve first shows anendothermic step at about 60 °C due to aglass transition. The resin is transformedfrom a glassy brittle state to a rubbery state.The glass transition is clearly overlapped bya so-called enthalpy relaxation effect thatwould no longer be observed if the samplewere immediately measured again aftercooling. The small endothermic peak witha maximum at about 100 °C is caused bythe melting of additives (e.g. catalyst, ac-celerator, etc).Under the conditions used for this experi-ment, the curing reaction begins at about130 °C and is observed as a largeexothermic peak in the temperature rangeup to about 270 °C. The peak maximum,

i.e. the temperature at which the greatestformation of heat or the greatest reactionrate occurs, is at about 185 °C. A secondmaximum at about 250 °C shows that thereaction consists of different steps. The to-tal heat of reaction is determined by inte-gration. This quantity can serve as a refer-ence value to evaluate the completeness ofthe reaction, for example when thepostcuring reactions of a series of produc-tion samples are measured under the sameconditions. Such postcuring effects are,however, difficult to detect if the degree ofcure is already more than 95%.

The parameters of the glass transition,however, provide a more sensitive measureof the degree of cure, in particular the glasstransition temperature Tg and the size ofthe accompanying change of the specificheat capacity cp. With increasing

USER COM 2/99 21

Tg [°C] ∆cp [J/(g K)]

Epoxy resin (first heating run) 66 0.40

after isothermal curing 106 0.29

second heating run 120 0.27

crosslinking, the freedom of movement inthe polymer decreases, resulting in a shiftof Tg to higher temperature and a decreasein ∆cp.Distinct differences in the shape of thecurves are already clearly visible aboveabout 130 °C - the curve of the postcuredsample has the smallest exothermic effect,i.e. the least amount of postcuring.The glass transition temperature Tg of the

finished product is of vital importance forits use because many important propertieschange at the glass transition (e.g. themodulus of elasticity, the coefficient ofthermal expansion and the dielectric lossfactor). Neglecting the control of the glasstransition can, for example, result inprinted circuit boards that are incompletelycured, which in turn results in damage onflow soldering.

ConclusionsThe examples described show that differen-tial scanning calorimetry (DSC) is able toprovide information about the reactivityand the crosslinking or degree of cure of aresin or resin system. The sample prepara-tion is easy and the measurement straight-forward and rapid. This is not only true forthe epoxy system described above but alsofor other resin systems. Condensation resinsgive rise to volatile by-products and shouldbe measured in sealed and pressure-tightcrucibles. The same is true if volatile com-ponents are present, e.g. solvents.The measured heat of reaction is the sumof all the thermally induced processes. Asimple comparison of samples can providepractical and meaningful information evenif the user has no real knowledge of the in-dividual effects. These results are comple-mented by important data on the glasstransition which are obtained in the samemeasurement.

The parameters of the glass transition differ greatly:

Fig. 2. This shows three DSC heating curves that were measured at a heating rate of 20 K/min.One of the samples is identical to the resin measured in Figure 1, so that the curve obtained (con-tinuous line) is practically the same despite the more rapid heating rate. The second sample wasallowed to react by maintaining it isothermally at 170 °C for 10 minutes , cooled and afterwardsexamined by heating up to 220 °C (dashed line). The third curve (dotted line) is the repeat meas-urement of this sample. The DSC measurements led to the complete postcuring of the isother-mally cured sample.

22 USER COM 2/99

Tips for databases

Customers often ask us about the most effi-cient method to manage their data. InUserCom 4 we gave a number of tips aboutorganizing data in such a way as to facili-tate a search later on (e.g. organizationaccording to method group, project ortask). In UserCom 8 we suggested how onecan create meaningful filenames which areinfact codes that indicate the content of thefile.Software Version V5.1x onwards allows youto choose between 5 different databases.The idea behind these databases is the fol-lowing:

Each database should cover a certain pe-riod. We recommend, for example, a year,which would then give you one data baseper year. Thanks to easy switching from onedatabase to the other, you always haverapid access to the data from the last 5years. Older data should be stored on anexternal device.

The optimum way of maintaining and us-ing such a database is as follows:• Weekly backup of data on an external de-

vice (e.g. DAT, ZIP or CD) or on a net-work server.

Only the database actually selected isbacked-up.

• Annual backup of the data on an exter-nal device.

• At the end of the year, the current data-base should be copied to the database ofthe new year (export it and import it intothe new database on the hard disk). Inthis new database, all the data exceptthat concerning methods, crucibles,gases, customers and the modules withtheir adjustment dates can be deleted.Customers who have the "Install Plus"software option can do this very simplywith the following tip:

Stored on an external device

DB2000 DB99 DB98 DB97 DB96 DB95 DB94 DB93 DB92 DB91

Stored on the hard disk

Exhibitions, Conferences and Seminars - Veranstaltungen, Konferenzen und SeminarePittcon March 13-16, 2000 New Orleans (USA)ANALYTICA 11.-14. April, 2000 München (Deutschland)INSTRURAMA April 25-28 , 2000 Brussels (Belgium)PLAST 2000 08-13 Maggio, 2000 Milano (Italy)GEFTA-Tagung 17.-19. Mai, 2000 Dresden (Deutschland)ACHEMA 22.-27.Mai, 2000 Frankfurt (Deutschland)ASTM Symposium on Modulated Techniques May 25-26, 2000 Toronto (Canada)6th Laehnwitzseminar on Calorimetry June 13-17, 2000 Kuehlungsborn (Germany)ICTAC 2000 August 14-18, 2000 Copenhagen (Denmark)NATAS October 4-8, 2000 Orlando (USA)

- always create methods under the"neutral" user name Mettler. If, lateron, you want to delete these methodsvia the user, you should define a dif-ferent "neutral" user name because

the user name Mettler can not be de-leted.

- Users should always work under theirown user names.You therefore only have to delete all theusers with their corresponding data inthe database of the new year (deleteall), and define new users and your newdatabase is immediately ready for thenew year.

Assuming your data has to be accessible forten years, your database concept is similarto that described in the diagram below:

Your data are then clearly structured and itis very easy to remove any data no longerrequired from the database.

USER COM 2/99 23

TA Customer Courses and Seminars in Switzerland-Information and Course Registration:TA Kundenkurse und Seminare in der Schweiz-Auskunft und Anmeldung bei:Helga Judex, Mettler-Toledo GmbH, Schwerzenbach,Tel.: ++41-1 806 72 65, Fax: ++41-1 806 72 40, e-mail: helga.judex@mt.comTMA (Deutsch) 13. März 2000 Greifensee TMA/DMA (Deutsch) 11. September 2000 GreifenseeSTARe SW Workshop Basic (D)13. März 2000 Greifensee STARe SW Workshop Basic (D) 11. September 2000 GreifenseeTGA (Deutsch) 14. März 2000 Greifensee TGA (Deutsch) 12. September 2000 GreifenseeDSC Basic (Deutsch) 15. März 2000 Greifensee DSC Basic (Deutsch) 13. September 2000 GreifenseeDSC Advanced (Deutsch) 16. März 2000 Greifensee DSC Advanced (Deutsch) 14. September 2000 GreifenseeSTARe SW Workshop Adv. (D) 17. März 2000 Greifensee STARe SW Workshop Adv. (D) 15. September 2000 GreifenseeTMA (English) March 20, 2000 Greifensee TMA/DMA (English) September 18, 2000 GreifenseeSTARe SW Workshop Basic (E) March 20, 2000 Greifensee STARe SW Workshop Basic (E) September 18, 2000 GreifenseeTGA (English) March 21, 2000 Greifensee TGA (English) September 19, 2000 GreifenseeDSC Basic (English) March 22, 2000 Greifensee DSC Basic (English) September 20, 2000 GreifenseeDSC Advanced (English) March 23, 2000 Greifensee DSC Advanced (English) September 21, 2000 GreifenseeSTARe SW Workshop Adv. (E) March 24, 2000 Greifensee STARe SW Workshop Adv. (E) September 22, 2000 Greifensee

Workshop Tips und Hinweise für gute Messungen 20.11.99 GreifenseeWorkshop Kurveninterpretation 21.11.99 GreifenseeSeminar Kopplungstechniken 22.11.99 GreifenseeSeminar Dynamisch Mechanische Analyse (DMA) 23.11.99 Greifensee

TA-Kundenkurse und Seminare (Deutschland)Für nähere Informationen wenden Sie sich bitte an METTLER TOLEDO GmbH, Giessen: Frau Ina Wolf, Tel.: ++49-641 507 404.DSC-Kundenkurs 29.2./1.3. 2000 Giessen/DSTARe SW Workshop 2.3. 2000 Giessen/DDSC-Kundenkurs 7./8.11. 2000 Giessen/DTG-Kundenkurs 9./10.11. 2000 Giessen/DThermogravimetrische Bodenanalyse – Grundlagen und 22.03.2000 Giessen/DAnwendungsmöglichkeiten eines neuen AnalysenverfahrensFachseminar: Thermische Analyse an polymeren Werkstoffen in der Automobilindustrie 28.9. 2000 Giessen/DDMA-Messtechnik – die Methode und ihre Anwendungen 29.9. 2000 Giessen/D

Cours et séminaires d’Analyse Thermique en France et en BelgiqueFrance: Renseignements et inscriptions par Christine Fauvarque, Mettler-Toledo S.A., Viroflay,Tél.: ++33-1 30 97 16 89, Fax: ++33-1 30 97 16 60.Belgique: Renseignements et inscriptions par Pat Hoogeras, N.V. Mettler-Toledo S.A., Lot,Tél.: ++32-2 334 02 09, Fax: ++32 2 334 02 10.TMA (français) 2 Mai 2000 Viroflay (France) Jour d’information 3 Mars 2000 Rouen (France)TGA (français) 3 Mai 2000 Viroflay (France) Jour d’information 21 Mars 2000 Paris (France)DSC Basic (français) 4 Mai 2000 Viroflay (France) Jour d’information 23 Mai 2000 Dijon (France)DSC Advanced (français) 5 Mai 2000 Viroflay (France) Jour d’information 20 Juin 2000 Grenoble (France)TMA (français) 2 Octobre 2000 Viroflay (France) Jour d’information 26 Septembre 2000 Mulhouse (France)TGA (français) 3 Octobre 2000 Viroflay (France) Jour d’information 6 Octobre 2000 Paris (France)DSC Basic (français) 4 Octobre 2000 Viroflay (France) Jour d’information 24 Octobre 2000 Paris (France)DSC Advanced (français) 5 Octobre 2000 Viroflay (France) Jour d’information 14 Octobre 2000 Montpellier (France)Jour d’information 11 Janvier 2000 Nice (France) Jour d’information 28 Novembre 2000 Poitiers (France)Jour d’information 25 Janvier 2000 Clermont-Ferrand (F) STARe user forum 4 Octobre 2000 Bruxelles (France)Jour d’information 2 Février 2000 Metz (France)

TA Customer Courses and Seminars in the NetherlandsFor further information please contact: Hay Berden at Mettler-Toledo B.V., Tiel, Tel.: ++31 344 63 83 63.Thermische Analyse seminar, basistraining 22.02.2000 Tiel/NLThermische Analyse seminar, gevorderde training 23.02.2000 Tiel/NLSTARe-Software seminar 24.02.2000 Tiel/NL

Corsi e Seminari di Analisi Termica per Clienti in ItaliaPer ulteriori informazioni prego contattare: Simona FerrariMettler-Toledo S.p.A., Novate Milanese, Tel.: ++39-2 333 321, Fax: ++39-2 356 2973.Corsi per Clienti: 08-09 Marzo 2000 Novate Milanese

07-08 Giugno 2000 Novate Milanese20-21 Settembre 2000 Novate Milanese

Giornate di informazione: 03 Marzo 2000 Milano 29 Marzo 2000 Torino21 Marzo 2000 Napoli 30 Maggio 2000 Bologna22 Marzo 2000 Roma 31 Maggio 2000 Venezia23 Marzo 2000 Firenze

TA Customer Courses and Seminars for Sweden and Nordic countriesFor details of training courses ans seminars please contact:Catharina Hasselgren at Mettler Toledo AB, Tel: ++46 8 702 50 24, Fax: ++46 8 642 45 62E-mail: catharina.hasselgren@mt.com

TA Customer Courses and Seminars in USA and CanadaBasic Thermal Analysis Training based upon the STARe System version 6 is being offered April 21-22 and October 12-13 at our Columbus, OhioHeadquarters. Training will include lectures and hands-on workshops.For information contact Jon Foreman at 1-800-638-8537 extension 4687 or by e-mail jon.foreman@mt.comTA course February 9 – 11, 2000 California TA course October 10 – 11, 2000 Columbus (OH)TA course June 21 – 22, 2000 Columbus (OH) TA information day February 8, 2000 California

TA Customer Courses and Seminars in UKFor details of training courses and seminars please contact:Rod Bottom at Mettler-Toledo Ltd., Leicester, Tel.: ++44-116 234 50 25, Fax: ++44-116 234 50 25.15 March 2000 Winchester 31 May 2000 Wakefield22 March 2000 Glasgow 7 June 2000 Warrington19 April 2000 Burton upon Trent 14 June 2000 Bristol26 April 2000 Maidstone

TA Customer training Course in South East Asia regional office, Kuala LumpurFor information on dates please contact:Malaysia: Jackie Tan/Ann Owe at ++ 603-7032773, fax: 603-7038773Singapore: Lim Li/Clive Choo at ++ 65-7786779, fax: 65-7786639Thailand: Warangkana/Ajjima Sartra at ++ 662-7196480, fax: 662-7196479Or SEA regional office: Soosay P. at ++ 603-7041773, fax: 603-7031772For further information regarding meetings, products or applications please contact your local METTLER TOLEDO representative.Bei Fragen zu weiteren Tagungen, den Produkten oder Applikationen wenden Sie sich bitte an Ihre lokale METTLER TOLEDO Vertretung.Internet: http:/www.mt.com

RedaktionMettler-Toledo GmbH, AnalyticalSonnenbergstrasse 74CH-8603 Schwerzenbach, Schweiz

Dr. J. Schawe, Dr. R. Riesen, J. Widmann, Dr. M. Schubnell, U. Jörimann

e-mail: urs.joerimann@mt.comTel.: ++41 1 806 73 87, Fax: ++41 1 806 72 60

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