A Technique for the Rapid Acquisitionof Rheological Data, and its Application

to Fast Curing Systems

M. Grehlinger, TA Instruments

This paper describes a new method for rapid

data acquisition of rheological measurements,

and the ability to monitor waveforms in real-time

in separate motor and transducer (SMT)

rheometers. The waveform display is an invalu-

able tool for monitoring the quality of data being

generated. The new fast sampling capability

allows for data collection rates in

excess of 60 data points per

second. These data collection

rates are important for rapidly

changing systems, and for

materials that experience

very short relaxation

processes.

Modulated TMA � Measuring Expansion and

Contraction at the Same Time

Dr. R. Blaine, TA Instruments

Modulated TMA� (MTMA�)

is a useful technique for

resolving thermodynamic

events (e.g., coefficient of

thermal expansion) from

kinetic events (e.g, stress

relaxation, softening, and

heat shrinking) in materials

when they are subjected to a combined

linear and sinusoidal temperature program. Its

ability to simultaneously measure expansion

and contraction is demonstrated on both

thermoplastic and thermosetting materials.

Thermal Conductivity Measurements ofConductive Epoxy Additives by MDSC®

E. Verdonck, R. Blaine (TA Instruments) and

G. Dreezen (ICI, Belgium)

MDSC is one of a number of techniques for

measuring thermal conductivity of materials.

In this paper, a method is described using MDSC

with Tzero� technology to extend the upper limit

of accurate thermal conductivity measurement of

conductive epoxy based adhesives used in the

electronic industry.

DSC Method to Determine theKauzmann Temperature

Dr. B. Cassel, TA Instruments

This article details the use of specific heat

capacity data taken on a Q1000 DSC to

determine the temperature of zero mobility

in an amorphous system (the Kauzmann

temperature; Tk). At this temperature, reactive

or unstable materials can be safely stored in an

amorphous matrix, since the absence of

molecular mobility will prevent the interaction

of the reactive components.

S u m m e r 2 0 0 3

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Tech Talk

This section provides technical notes, application briefs, helpful hints, and specific information on the use of thermal analysis

and rheology instrumentation. The goal is to help you get the maximum value from your TA Instruments� equipment.

Click on the links below for additional information.

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Technical Documents & Hints Technical Information

Technical Documents & HintsThis section provides technical notes, application briefs, helpful hints, and specific information on the use of thermal analysis

and rheology instrumentation. The goal is to help you get the maximum value from your TA Instruments’ equipment.

Technical DocumentsAvailable for easy download are a series of technical notes and applications briefs relating to various topics in thermal

analysis and rheology.

Thermal Analysis1. Common PID Settings (TN049a)

2. ISO Thermal Methods (TN 46b)

3. ASTM International Thermal Methods (TN 21j) � A list of American Society for Testing and Materials International

(ASTM) standards that use thermal analysis or rheology

4. Weight Loss Determined from Mass Spectrometry Trend Data in a Thermogravimetric/

Mass Spectrometer System (TA306)

Rheology1. Using the DMA Q800 for ASTM International D 648 Deflection Temperature Under Load (RH086)

2. The Use of Low Shear-Stress Rheological Data in Settling of Particles in Paints (RH083)

HINTS

Have you ever been faced with loading a large data file onto a floppy disk? Of course, the size of a data file depends upon

the data acquisition rate and the number of signals collected. Reducing the number of signals and increasing the data

acquisition rate will reduce the size of a new file. But what about one that has already been collected.

A data file may be reduced in size through the use of the buffer in Universal Analysis. To adjust this buffer (with no data

files open), click on File and Options. The Data Buffer Size may now be set to a modest value of 4000 – 6000.

Now with the data file of interest open, click on File, Export Data File , and save to a binary file. A binary file can be

re-opened in UA. The new file will have a much smaller size and can easily be stored on a floppy disk. The resolution will

be fine.

Thanks to Don DiPietro and Ben Crowe (TA Instruments) for this hint

Thermal equilibrium of a sample and the measuring geometry or clamp are necessary before testing, especially during

isothermal experimentation in rheology testing. When using Rheology Advantage Instrument Control software, the

duration of the ‘equilibration’ section, within the conditioning step of any procedure, should be set to at least 2-3 minutes.

Thermal equilibration is also applicable to the Thermal Advantage procedures for DMA, where an ‘equilibrate at tempera-

ture’ segment, followed by ‘isothermal” segment (for at least 2-3 minutes), should always be included prior to testing.

Thanks to Fred Mazzeo (TA Instruments) for this hint.

MDSC‚ provides a tool for measuring heat capacity under isothermal conditions. But what amplitude and period should

one use? And how long should one wait to make a measurement? As there is no underlying heating rate, you do not have

to be concerned about getting enough cycles over a transitions. So you can pretty much choose any reasonable amplitude

and period. An amplitude of ± 1 ˚C with 100 s period is a common set of conditions. For most polymers, the glass

transition typically has a relaxation time on the order of tens of seconds so a 10-minute isothermal (5 minutes of data

“off” followed by 5 minutes of data “on”) is sufficient. Some melting relaxations take much longer. For this case, try a

20 minutes (5 minutes of data “off” followed by 15 minutes of data “on”).

Thanks to Steve Aubuchon of TA Instruments for this Hint.

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REWARDS FOR HINTSThis HINTS section, with its suggestions on how to do better or easier thermal analysis and rheology, has proven to

be very popular. So we are looking for even more HINTS to pass along. Do you have one that you would like to offer?

Send it to us and if we use it, we’ll send to you a FREE TA shirt and pen. Send your hints to rblaine@tainst.com.

Technical InformationThermal / Rheology Installation Requirements A new version of this valuable document has been prepared and is available for download on our website using the following

link. (http://www.tainst.com/support/library.cfm) The guide has been considerably revised and updated to include all the

Q Series™ thermal modules as well as our AR and ARES Series rheometers. It will be especially useful to customers

ordering new instruments, since it provides extensive information on weights, dimensions, electrical, gas, and laboratory

bench space requirements.

Rheology Advantage SoftwareA new release of Advantage Rheology software (V 4.1) offers not only significant enhancements to our AR 2000

Mobius Drive™ technology (see below), but also data presentation improvements for all AR Series instruments

(AR 2000, AR 1000, AR 550, AR 500). Updated versions of Rheology Advantage Navigator and Enhanced Polymer Library

software are also available. Rheology Advantage V 4.1 software is free of charge to all existing AR Series Advantage

software users, as are Navigator and the Enhanced Polymer Library if previously purchased. Download the form

(RA4.1email.doc), complete it, and return it by e-mail to TA Instruments. You will also have the opportunity to order the

Navigator and Polymer Library if you do not currently own them.

Note: The CD containing the above software also includes the current Advantage Thermal Analysis Software.

10th Anniversary of Modulated DSC®

This year marks the 10th anniversary of the introduction of Temperature Modulated

DSC invented by Dr. Michael Reading. It has been described by another eminent

practitioner, as the most significant advancement in thermal analysis since the

introduction of DSC. In the past decade, the technique, as pioneered by Dr. Reading

and TA Instruments, has progressed extensively, and currently over 50% of the

Q Series™ DSC systems shipped from our factory contain MDSC. As has been well documented, MDSC offers all the

performance features of standard DSC, overcomes its limitations, and in addition, provides the advanced capabilities for

separating the total heat flow signal into its heat capacity and kinetic related component signals. The latter capability offers

many significant advantages to the thermal analysts, including a way of measuring the initial crystallinity of polymers, and

the separation of overlapping thermal events (e.g., Tg and enthalpic events). An article highlighting the progress of MDSC in

the last decade by Dr. Reading will be included in the November issue of the TA Hotline.

Key Applications of the TA Instruments 2970 Dielectrics AnalyzerThe DEA 2970 has been successfully used to characterize a variety of materials by measuring their dielectric properties (e.g.,

permitivity, conductance, ionic conductivity) as a function of time or temperature. Using either parallel plate, or local / remote

single surface measurement sensors, the DEA can analyze materials from –150 to 500˚C. It is particularly valuable for

studying glass transitions, and lower energy β and γ transitions in thermoplastics (e.g., polyesters, polyacrylates), and curing

in thermosetting resins (e.g., epoxy). The latter capability is especially useful for studying the low energy curing reactions of

urethane / isocyanate mixtures that can be difficult to follow by DSC.

TA Instruments is now offering a complete DEA system (DEA, Controller, LNCA cooling device) at a very attractive price for

the remainder of 2003. Contact your TA Instruments Representative for further information.HOME

New Product Introductions

TA Instruments is committed to providing our customers with the latest technology. Highlighted below are new products

and accessories now available:

Advantage Integrity for AR Series RheometersTA Instruments is pleased to announce that in September, 2003, we will extend our Advantage Integrity

system to include the AR Series Rheometers (AR 2000, 1000, and 550). This will assist rheology

customers to comply with the requirements as expressed in the US FDA Electronic Records and

Electronic Signatures Rule (21-CFR-11) regulations. The Advantage Integrity System is offered with

a TA Instruments supplied secure server operating under Oracle V9i software, and in a second

configuration, which requires the customer to have or obtain the server independently. Integrity is

currently compatible with our Q Series DSC (Q1000, Q100, Q10) and TGA (Q500, Q50) thermal modules.

Multilingual Version of Thermal Advantage Software Also in September, 2003, TA Instruments will expand our Thermal Advantage Operating System Software to include both

German and Japanese languages. This will make our products increasingly useful to customers in these countries,

and further serves to demonstrate our commitment to the international community.

Real-Time Waveform Display and Rapid Data Acquisition for ARES Rheometers and RSA III Dynamic Mechanical AnalyzerComing in September, a new real-time waveform display and rapid data acquisition capability

available for all ARES Rheometers and RSA III DMA. The real-time waveform display enables

the user to view the stress and strain waveforms in TA Orchestrator software as they are being

generated. This function provides an invaluable tool for monitoring the quality of data being

generated and looking for distortions in the sine waves that may indicate non-linear viscoelastic

behavior. The new fast sampling capability allows for data collection rates in excess of 60 data

points per second. These data collection rates are important for rapidly changing systems, such

as UV Curable materials, and for materials that experience very short relaxation processes, such

as structured fluids. For more details see Featured Technical Article titled �A Technique for the

Rapid Acquisition of Rheological Data, and its Application to Fast Curing Systems�.

New Starch Pasting Rheometer and Starch Pasting CellTA Instruments introduces the Starch Pasting Rheometer (SPR) and Starch Pasting Cell (SPC);

two new products in the Rheomertrics Series of rheometers focused on improving the

characterization of starches. The cell is specifically designed for routine evaluation of the

gelatatinization process, or the �pasting curve�, which is accomplished by measuring the

viscosity of the starch suspension while heating and cooling under specific testing conditions.

Important starch performance parameters, including the pasting temperature, peak viscosity,

holding strength, and final viscosity are easily obtained. In addition, standard, highly sensitive,

rheological methods based on steady, transient and oscillatory measurements are available.

A cross-section of the pasting cell and impeller is shown. Heating is through resistive elements

placed concentrically to the cup. Cooling is through water carried in a helical conduit in close

proximity to the cup outer walls. Maximum temperature ramp heating rate is 15ûC per minute

and cooling rate is 30ûC per minute.

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Training Courses

TA Instruments conducts a wide variety of training courses around the world. For more information on courses in your area

click on the appropriate link below.

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North America International

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More Information: germany@tainst.com france@tainst.com info@taeurope.co.com

spain@tainst.com belgium@tainst.com sweden@tainst.com J-Marketing@tainstruments.com

2003 International Course Schedule

For International course schedules click the appropriate link below.

United Kingdom Germany France Spain

Benelux/Belgium Nordic Japan

Training Courses

Let Onsite training take you to a higher levelOur Onsite training courses are designed to give our customers the training they need, in the most efficient

manner possible. These courses take place in your facility where you are trained on your equipment with your samples.

We will customize a course for you that is lecture based, hands-on, or a combination of both. A typical agenda for DSC

might be as follows:

DSC Theory & Instrumentation (Lecture)

DSC Applications (Lecture)

DSC Calibration & Maintenance (Hands-on)

Running your samples (Hands-on)

Analyzing your data (Hands-on)

Usually we will cover one instrument per day, and the applications section will be geared towards your industry. The cost

is just $1500 per day plus travel expenses.

For more information contact training@tainstruments.com

Don�t forget to check out our other training opportunities

www.tainst.com/support/training.html

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A Higher Level

New Staff at TA Instruments

We are pleased to announce César del Río as our new technical salesman in the Madrid,

Spain office (he is in charge of the central part of Spain). César holds a degree in chemistry.

He has worked in Jülich Research Center in Germany and in the Central Research Department

of BAYER AG in Leverkusen (Germany), where he dealt with suspensions thermalstability using

rheology methods. Before joining TA Instruments he was working as a technical salesman for a

scientific materials distributor.

Charlie Mc Cue joined the TA Instruments UK Sales team on 4th August 2003 as the new Area

Sales Manager for UK North, Scotland and Northern Ireland, bringing to the team many years of

sales experience. Charlie has always had an excellent relationship with customers and his move

will certainly strengthen the UK team.

We are pleased to announce Jaime Vicioso as our new Service Engineer in our Barcelona

Office. Jaime holds a Technical Engineering degree in Industrial Electronics. As a Service

Engineer, he has 4 years of experience with analysis instruments and 2 years of experience

in amusement machines. He is used to dealing with laboratory customers, instruments and

applications.

Massimo Baiardo joins TA Instruments as a Service Engineer in Italy. Massimo holds a

degree in Industrial Chemistry - Macromolecular Chemistry and Ph.D. in Materials Engineering.

He brings over 9 years of experience to the business and has produced 10 publications in

interdisciplinary areas of materials science. Massimo is also the co-inventor of a US-EU patent

application.

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TA Instruments is pleased to introduce Ted Gresik as Sr. Technical Representative for the

New York and western CT territory. Ted has a degree in both electrical engineering and business.

He brings many years of thermal analysis experience to the business. Ted resides in Derby CT

where he will be based.

Conferences and Exhibitions

TA Instruments participates in a wide variety of exhibits, conferences, and seminars around the world. At many of these

functions, you have the opportunity to see our latest thermal analysis systems and rheometers. You also have a chance to

interface with our worldwide network of sales, service, and applications support professionals who can answer all your

questions. Click on the links below for additional information.

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North America International

North American Conferences and Exhibitions

Upcoming ConferencesA selected listing of conferences that should interest thermal analysis and rheology users is shown below. TA Instruments

will be participating as lecturers and / or exhibitors showing our latest thermal analysis and rheology products. For more

information on European conferences contact our specific country contacts.

Exhibits/ConferencesSAMPE - Society for the Advancement of Material and Process EngineeringConference:August 20, Ottawa, CA. For more information on the conference, or to register on-line,

visit: www.cancom.carleton.ca

ACS National ConferenceConference: September 8-10, 2003 � Jacob Javits Convention Center, New York, NY, USA. Please visit our booth #255,

if you plan to attend. For more information on the conference, or to register on-line, visit: www.acs.org

NATAS Conference on Thermal Analysis & ApplicationsConference / Short Course: September 20-24, 2003 � Albuquerque Hilton Hotel, Albuquerque, NM, USA. Please visit our

booth, if you plan to attend. For more information on the conference, or to register on-line, visit: www.natasinfo.org

AACC - American Association of Cereal ChemistsConference:September 28 - 30, Portland, OR. For more information on the conference, or to register on-line,

visit: www.aaccnet.org

Society of RheologyConference / Short Course: October 12-16, 2003 � Pittsburgh, PA, USA. Please visit our booth, if you plan to attend.

For more information on the conference, or to register on-line, visit: societyofrheology.org

NPIRI - National Printing Ink Research InstituteConference:October 15 - 17, Dana Point, CA. For more information on the conference, or to register on-line,

visit: www.napim.org

AAPS Annual MeetingConference: October 26-30, 2003 � Salt Palace Convention Center, Salt Lake City, UT, USA. Please visit our booth,

if you plan to attend. For more information on the conference, or to register on-line, visit: www.aaps.org

International Coatings ExpositionConference / Exhibition: November 12-14, 2003 � Pennsylvania Convention Center, Philadelphia, PA, USA.

Please visit our booth, if you plan to attend. For more information on the conference, or to register on-line,

visit: www.coatingstech.org

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More Information: germany@tainst.com france@tainst.com info@taeurope.co.com

spain@tainst.com belgium@tainst.com sweden@tainst.com J-Marketing@tainstruments.com

2003 International Conferences & Exhibitions

For International conference and exhibits click the appropriate link below.

United Kingdom Germany France Spain

Benelux/Belgium Nordic Japan

Which is the guy who said his equipment was as good as TA?

©Follman

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TA Instruments’ ExpansionTo accommodate our larger staff resulting from the Rheometrics acquisition,

TA Instruments has expanded its New Castle headquarters to include a second

building. This will house sales / marketing, service, and administration staff.

The original facility is being remodeled and will accommodate expanded

facilities for engineering, applications support, customer training, and thermal

and ARES rheometer manufacturing. By the end of August, the former

Rheometrics facility in Piscataway (NJ) will be closed, and all the new

TA Instruments employees will have been relocated to New Castle.

TA Engineer is awarded the Bronze Star in AfghanistanLieutenant Colonel Chris Carney was recently awarded the

Bronze Star for service in Afghanistan. Chris is a Principle

Manufacturing Engineer with TA Instruments and is serving with

his reserve unit as Chief Engineer for the Coalition/Joint Civil

Military Operations Task Force. In presenting the medal,

Lieutenant General Dan McNeil remarked �Carney�s leadership, selfless service and

commitment to mission accomplishment under the most extreme circumstances greatly

contributed to the success of Operation Enduring Freedom. His performance of duty in a

combat zone reflects great credit upon him, the Combined/Joint Task Force-180 and the

United States Central Command.� The efforts of Chris and his staff, in the rebuilding

of schools and hospitals, has surely left Afghanistan a much better place than it was when

they arrived.

Commenting on the presentation of the Bronze Star to Col. Carney, President Bob Hassel said, � TA Instruments is proud

of the service of Col. Carney and other TA Instruments employees in the National Guard and Reserves�. TA Instruments

was presented with the Pro Patria Award in 1997 as Delaware�s most supportive employer to the National Guard and

Reserves.

Web UpdatesAt TA Instruments, we are committed to keeping our website

up-to-date and useful for all of our customers. Our latest

enhancements include a complete recast of the Support Center

information. Details on our service packages, training courses,

technical support and a new page devoted to TA consumables

is now available. Be sure to visit our site and check out the

latest improvements.

TA News

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DSC Method to Determine the Kauzmann Temperature, The Temperature of Zero Mobility

in Amorphous Systems

R. Bruce CasselTA Instruments, 107 Lukens Drive, New Castle DE 19720

ABSTRACTPhysical properties such as viscosity vary with temperature in a roughly

exponential manner over the glass transition temperature (Tg) region. Hence, at sometemperature below Tg the molecular mobility will be essentially zero. At such a lowtemperature reactive or unstable materials can be safely stored in an amorphous matrix,and the absence of molecular mobility will prevent the interaction of the reactivecomponents. It has been proposed that the Kauzmann temperature (TK) demarks such apoint of zero mobility. (1) For materials for which the heat capacity data is available onboth the amorphous and crystalline phase, the Kauzmann temperature can be calculated.This paper delineates a method of determining the Kauzmann temperature using TAInstruments’ Universal Analysis Software and a spreadsheet. A following paper in thisseries describes methodology for determining the molecular relaxation time constant inthe temperature region between Tg and TK.

The material used to illustrate this technique is sucrose, which finds use inamorphous pharmaceutical formulations.

INTRODUCTIONPharmaceuticals that dissolve slowly in water pose a problem for both orally

administered solid dosage forms and parenterals injected from freshly prepared solutions.One approach to this problem has been that of using freeze-dried formulations, wherebythe active ingredient has been dissolved in an aqueous solution at higher temperature,then freeze-dried to remove the water. This traps the drug in an amorphous state, alongwith the amorphous excipient. Once in the amorphous form, the freeze-dried formulationreadily dissolves when taken orally or when it is reconstituted by adding water for aninjected dose. As long as the freeze-dried formulation is maintained sufficiently belowTg, the active drug remains in the amorphous state until it is ready for use. However, insome cases, these freeze-dried medications have been known to lose activity even whenheld several tens of degrees below the glass transition of the amorphous formulation. (2)The phenomena responsible for this are: first, the lowering of Tg by small amounts ofwater; and second, physical aging, whereby storage within the broad temperature regionof the glass transition allows long term mobility, as if the Tg were lowered. Because theTg is a kinetic phenomenon, properties in the Tg region are time dependent. Whenmeasured over a long time interval the Tg is found to be lower, commensurate to the longterm mobility.

In a previous publication (3) we explored the use of a Q Series DSC to measurethe extent of physical aging and to determine the enthalpic fragility parameter, which

quantifies the time dependence of the Tg parameter and the apparent shift in Tg inresponse to thermal aging. Here we extend the thermodynamic analysis of amorphoussucrose, which is a model system for pharmaceutical formulations containing a sugar(sucrose, glucose, maltose, etc.) as the primary excipient. In this treatment we calculatethe Kauzmann temperature by determining the point of intersection of the entropy plotsof the amorphous and crystalline phases of sucrose. That is, as an amorphous sample isannealed below Tg, the properties (e.g., molar volume, entropy and enthalpy) of thesuper-cooled liquid approach those of the material in the crystalline state. The Kauzmanntemperature is the temperature at which the entropy of the extrapolated equilibrium liquidstate equals that of the crystalline state. This theoretical limiting point for the liquid statealso agrees within experimental error with limiting temperature parameters used to fitviscoelastic data. (4)

The entropy plots of the amorphous and crystalline materials, whose intersectionis TK, are obtained by integration of Cp/T data taken by DSC.

∫=−2

1

)1()2(T

T

dTTCpTSTS Eq 1.

EXPERIMENTALA Q1000 DSC from TA Instruments was used to obtain specific heat data on

crystalline and amorphous sucrose. Because it uses proprietary Advanced TzeroTM

Technology, the instrument calibration provides an internal compensation for the effectsof DSC cell asymmetry. (5) The result is a baseline very close to zero milliwatts and adisplacement from that baseline that is due almost entirely to the specific heat of thesample specimen itself. Hence, the DSC output from a single run can be accuratelypresented directly in Cp units.

0

1

2

3

4

5

150 200 250 300 350 400 450 500

Temperature (K)

Cp

(J/g

K)

Cp(a)Cp(x)Cp(a,fit)

Figure 1.Specific Heat Capacity of Amorphous and Crystalline Sucrose

with a line fitted to the amorphous data above Tg

TmTg

The specific heat capacity of crystalline sucrose was obtained from deep subambient upthrough the melting point. The sample was then removed and cooled in seconds to roomtemperature, thus trapping the sucrose in the amorphous state. The sample was reloadedin the DSC, equilibrated at the same initial temperature, and heated over the sametemperature range to obtain Cp of sucrose in the amorphous state. Figure 1 shows the Cpdata of the crystalline form, Cp(x), the amorphous form Cp(a) and a linear construct fittedto Cp(a,fit) above Tg and extrapolated below Tg.

CALCULATIONSTo determine the Kauzmann Temperature, (TK) the relative entropy of sucrose is

calculated for both the crystalline and amorphous forms. This is accomplished byintegrating the Cp/T vs. T data. The two DSC Cp curves are exported into the ExcelTM

spreadsheet that is linked to TA Instruments’ Universal Analysis software. In Excel thedata above Tg from the amorphous sucrose, Cp(a), is fitted to a straight line and the threecurves are plotted as shown in Figure 1. Using Excel the entropy data corresponding tothese three curves are calculated using Equation 1. In carrying out the integrationindicated there is an integration constant which must be defined for each curve. In thecase of the S(x) data the entropy is taken as zero at the start of the DSC Cp scan; this thenis the reference point for the relative entropy curves plotted in Figure 2. For the othertwo curves, it is assumed that at any temperature above the crystalline melting point thatthe entropy is the same for all three curves. Hence, the entropy data is shifted to achievethat alignment. Having done this, the Kauzmann temperature is obtained as theintersection of S(x) and S(a,fit), the entropy of the supercooled liquid in its equilibriumstate. TK can be found graphically or by using interpolation between the spreadsheettable entries. For the sucrose data the value for TK was found to be 18°C. In otherwords, for this model amorphous system the temperature of zero molecular translationmobility is 18°C.

DISCUSSIONThe requirements for this method are that the material be sufficiently stable that

the specific heat can be measured from well below Tg to above the melt. Thus, amaterial that decomposes on melting would be a problem. This, in fact, was almost aproblem with the sucrose system, but the decomposition was adequately slow to initiatethat sufficient data above the melt could be obtained.

A second difficulty in using this method is that the crystalline Cpx data be that of100% crystalline material. If not, it is possible to make a correction, ∆Scor, for the errorin crystallinity when the heat of fusion of 100% crystalline material is known from othersources. Once a value for ∆Hm of 100% crystalline material has been established, thenthe relative entropy data can be corrected for the difference, ∆Hcor, between themeasured, and “true” heat of fusion:

TmHcorScor /∆=∆ Eq 2

Another apparent difficulty is that of the case where the amorphous phasecrystallizes just above Tg. In this case, the Cpa linear construct can be obtained by fittingdata just above Tg with data just above the melt. Alternatively, the use of a fast scanningrate may suppress the cold crystallization exotherm and allow more amorphous data to beused for the fit.

Another issue with this technique stems from the assumption that the specific heatof the amorphous phase is inherently linear and can be extrapolated linearly from abovethe glass transition down to the Kauzmann temperature. This is the same assumption

routinely used for determining the fictive temperature, but with a longer extrapolation. Arelated, possibly more serious experimental limitation is that the DSC instrumentalbaseline must be extremely reproducible so that the specific heat data does not haveinstrumentally produced curvature, since this, when extrapolated, would dramaticallyshift the calculated TK point.

Finally, the biggest drawback to this method may be that TK doesn’t indicate howlow in temperature to hold a material to prevent mobility-induced degradation over apractical shelf-life period. It may be that TK represents an unnecessarily low temperaturefor storage. The next paper in this series gives an alternative method to assess aparticular storage temperature between Tg and TK.

Despite the above objections, the DSC TK method is a relatively easy and quickmethod for identifying a safe storage temperature for materials to prevent either physicalaging or molecular mobility induced changes.

REFERENCES1. W. Kauzmann, Chemical Reviews, 1948, Vol. 43, 219-2562. B. C. Hancock, S. L. Shamblin, and G. Zografi, Molecular Mobility of Amorphous

Pharmaceutical Solids Below Their Glass Transition Temperature”, PharmaceuticalResearch, 1995, Vol 12, No. 6, 799-806

3. R. B. Cassel, “New DSC Technology in the Analysis of Physical Aging and Fragility ofAmorphous Sucrose”, TA Instruments Technical Publication, (2002) TA296, available attainst.com

4. I. M. Hodge and J. M. Reilly, “Nonlinear Kinetic and Thermodynamic Properties ofMonomric Organic Glasses”, J. Phys. Chem. B Vol. 103, No. 20 (1999)

5. R. L. Danley, “A New Technology to Improve DSC Performance”, Thermochim. Acta,Jan (2003)

KEY WORDSamorphous, DSC, entropy, excipients, Kauzmann, physical aging, sucrose

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

-50 0 50 100 150 200 250

Temperature (C)

Rel

ativ

e En

trop

y

S(x)S(a)S(a,fit)

Figure 2.Relative Entropy of Amorphous and Crystalline Sucrose

Showing the Crossover Point, TK, on Expanded Scale

Tg

15 16 17 18 19 20 21 22TK

TK

Tm

APPENDIX - SUGGESTIONS

To generate good heat capacity data:• Use the same sample for both amorphous and crystalline forms.• Pre-melt the sample in the pan for both amorphous and crystalline forms.• Ensure that the sample pan bottom is flat before and after all runs.• Use the same heating rate to obtain Cp data for both amorphous and crystalline forms.• Ensure adequate N2 purge-out of air to prevent oxidative decomposition.• Use the Zero Heat Flow step after equilibration at the first isotherm, then start

scanning.

Procedure to generate TK data after obtaining Cp data:Exporting the data. Overlay the crystalline and amorphous Cp data. The curves

should coincide above the melt. If not, use Rotate on the amorphous data to align the Cpdata above the melt while not shifting it at the low temperatures. (If more than a littleslope change is necessary, then the TK calculation may be compromised.) Export this datafrom UA. (Use data limits to recall and export only a single scanning cycle. File>ExportData File>Plot Signals Only>Binary Data File>[new file name]. Then recall this data filein UA, select the Cp signal, View>Data Table>Spreadsheet. Select a manageable datatable Increment (e.g., 2 degrees). Now you have columns of Cp and temperature data.

Calculating the Cp(a,fit) construct. Identify the regions in the Cp(a) plot whichyou wish to use to fit to the straight line: Cpa=AT+B. Copy the identified (Cp, T) datainto two continuous columns, and use the Slope and Intercept functions in ExcelTM tofind A and B for the line that statistically fits the data. Generate a column of data for thisline.

Calculating the entropy curves. Next, for the full T-range in the original datacalculate data columns of Cp/T for all three curves. Also calculate a data column forT(K), temperature in units of Kelvin. Calculate the entropy curves from each of the Cp/Tcolumns by integrating using Simpson’s rule. The formula to type into the firstintegration cell, G4 (which starts next to the second Cp/T entry, with zero being typedinto the first iintegral entry, G3) is:

36/)5443( GFFFT +++∆=Where ∆T=Temperature increment between table entries

F3 is the first Cp/T entryF4 is the second Cp/T entryF5 is the third Cp/T entryG3 is the first integral entry

Copy this formula into the cells next to each Cp/T column and multiply times theheating rate in ºC/sec to generate the entropy curves (since the integral performed wasover time).

Aligning the S(a,fit) data. Now look at the value of S(a,fit) at some temperatureabove the melt. It should be aligned to be the same as S(x) at that temperature. Socalculate the difference, and add the difference to each entry in the S(a,fit) columnproducing a new column of data. Now plot this data column, the S(x) column, and theT(K) column using a “scatter plot” with T(K) as the left-most (x-axis) column. The plotshould look like Figure 2 (without the S(a), curve, which is only displayed to show Tg. Ifyou have available a correction for the heat of fusion of the crystalline sample, then addthe ∆Hcor/T(K) correction to S(x) before subtracting to obtain the offset factor. TheExcel “scatter plot” of the two data sets S(x) and S(a,fit) versus T(K) will reveal theintersection point, TK. Plotting the region of the intersection on an expanded scale, orinterpolating between the column entries will allow determining TK.

Modulated Thermomechanical Analysis –Measuring Expansion and Contraction at the Same Time

Roger L. Blaine, TA Instruments 109 Lukens Drive, New Castle DE 19720 USA

rblaine@tainstruments.com

ABSTRACTIn modulated thermal analysis, a sinusoidally varying temperature program is added to an

underlying linearly changing or static temperature program. Fourier transformation of theoscillatory temperature “forcing function” and the result dependent variable provides thedeconvolution of these signals into reversing and nonreversing components. The reversingsignal is associated with properties dependent upon the temperature rate of change while thenonreversing signal defines kinetic events (that is, those associated with both time andtemperature). Thus for modulated thermomechanical analysis (MTMA), coefficient of thermalexpansion is observed in the reversing signal and stress relaxation, softening and heat shrinkingare observed in the nonreversing signal. The ability of MTMA to measure both expansion andcontraction simultaneously is demonstrated on samples including thermoset composite printedcircuit boards and heat-shrink packaging film.

INTRODUCTIONReading introduced modulated temperature thermal analysis in 1993 (1) with what has

become known as modulated differential scanning calorimetry (Modulated DSC, MDSC).This was followed a few years later by Blaine who reported on modulated thermogravimetry(MTGA) (2) and by Price with modulated thermomechanical analysis (MTMA) (3). All ofthese approaches are commercially available from TA Instruments (New Castle, DE).

The impact of modulated temperature measurements on thermal analysis can hardly beunderestimated. One leading observer has called modulated DSC “the greatest advance in DSCsince its inception” (4). Nearly half of the articles published in thermal analysis journals nowfeature one of the modulated temperature techniques.

In modulated temperature thermal analysis, a sinusoidal temperature “forcing function” isadded to the traditional linear (or isothermal) underlying heating rate. This forcing functioninduces in the sample a sinusoidal response that may be deconvoluted to yield reversing andnonreversing information.

When applied to thermomechanical analysis (TMA), the temperature modulationproduces a sinusoidal change in test specimen length. Figure 1, for example, shows themodulated temperature at the Figure bottom and the length change at the top both as their firstderivatives. Discrete Fourier transformation is applied in real time to continuously determine theaverage value and the amplitude value for each signal.

Figure 1. Modulated temperature and resultant modulated length

The governing equation for MTMA is given by (3):

dL/dt = A dT/dt + f (t, T) (1)

where L is length, T is temperature, t is time, A is expansivity, and f(x) is “some function of…”.The left hand term of equation 1, known as the total length change rate, is shown on the right tobe composed of two parts; a reversing contribution proportional to the time rate of change of theindependent parameter (temperature) and a nonreversing contribution from the absolute value ofthat independent parameter.

Since in TMA, the dependent parameter measured is length (not the time rate of changeof length) so the governing equation takes on the form of:

Ltotal =Lreversing + Lnonreversing (2)

where Ltotal is the average length from the Fourier deconvoltion, Lreversing is the (lengthamplitude / temperature amplitude) ∫ dT/dt K. The “average length”, “length amplitude” and“temperature amplitude” are the signals derived from the Fourier transformation process. ∫ dT/dtis the underlying heating rate averaged over a single period, while K is a calibration constantclose to unity. The nonreversing length is obtained from the difference between the total andreversing contributions.

Lnonreversing = Ltotal – Lreversing (3)

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There is always a “lag” between the applications of the forcing function and the resultantresponse. The use of sinusoidal forcing functions provides for the easy measurement andinterpretation of the magnitude of this lag through the use of a Lissajous plot such as the shownin Figure 2. Evaluation of the midpoint and extrema values of the Lissajous figure yields

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δ = arcsin a/b = arcsin 0.862/1.57 = 33 ° = 28 s

Figure 3. Length change and modulated length change at the glass transitionthe phase lag. In MTMA, this lag is rather large compared to other modulated temperaturetechniques, about 28 s, due to the large thermal mass and low thermal conductivity of the quartzsample stage and measuring probe. A practical rule-of-thumb is that the period of the appliedforcing function should be about ten times the time constant. So for MTMA, a period of about300 seconds is used. The applied temperature amplitude is selected based upon the value of theexpansivity value A in equation 1 but is typically ± 5 °C. And as with all modulated temperatureapproaches, at least 5 cycles is required across a transition in order to have reliable Fourierdeconvolution. This results in the typical underlying heating rate of 2 °C/min or less.

The value of the calibration coefficient is determined, as is the length change calibrationof the TMA (5), from the use of a reference material with a known CTE value. We used copperfor this purpose as it has no nonreversing or kinetic behavior in the region of interest between 50and 150 °C.

Figure 4. Glass transition with enthalpic recovery

RESULTS AND DISCUSSIONFigure 3 shows the dimension ( i.e., Ltotal) and modulated dimension signals for a cured

thermoset sample undergoing a change in coefficient of linear thermal expansion. Where there isno nonreversing phenomenon, the amplitude of the modulated dimension derivative isproportional to the coefficient of linear thermal expansion. The expansion is proportional to theamplitude of this signal. As the expansion increases so does the oscillatory dimension amplitudesignal.

A more complicated example is shown in Figure 4 where the oscillatory temperaturesignal is shown at the bottom (as its derivative) while the modulated length signal is shown at thetop. In this case both the amplitude and average value for the length change during the course of

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the experiment with a “peak” in the derivative curve appearing near 140 °C. The resultant total,reversing and nonreversing signals for this thermal curve are shown in Figure 5. The totaldimension, presented in the middle curve shows the masking effect on the glass transition by theenthalpic recover transition typical of aged thermoset material. The enthalpic recovery causesthe test specimen to shrink as it gains mobility upon passing through the glass transition. That is,the sample contracts (due to the enthalpic recovery) and expands (due to the glass transition) atthe same time with the total length change reflecting the sum of these two events. The uppertrace in Figure 5 shows the reversing expansion of the sample as a result of the increase in thecoefficient of linear thermal expansion. The bottom nonreversing curve contains the shrinkageinformation resulting from the enthalpic recovery.

Figure 5. Separation of the glass transition from the enthalpic recovery

Another example is shown in Figure 6 for a thin polymer film examined in tension. Asthe sample goes through the glass transition, the expansion of the material increases.Additionally, the sample softens in the region of the glass transition and the sample begins tostretch under tension. The expansion is separated out into the reversing length change while thestretching is resolved into the nonreversing dimension change. In this case, both thethermodynamic and kinetic components are in the same direction but are different in effect by anorder of magnitude.

In TMA, the glass transition temperature is identified by the extrapolation of the linearportions of the expansion curve before and after the transition to their intersection (6). Thisvalue taken from the reversing length change curve corresponds to 154 °C. In some cases, thesoftening temperature, either as the extrapolated onset (6) or at a specific modulus value (7), isused to estimate the glass transition temperature. Figure 7 shows that the extrapolated onset

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from the soften curve estimate the glass transition at 149 °C, some 5 °C lower that that obtainedfrom the change in linear expansion.

Figure 6. Separation of film stretching from expansivity

SUMMARYModulated thermomechanical analysis is shown to be a useful tool for determining

thermodynamic and kinetic, reversing and nonreversing length changes in materials when thesethermally induced events take place at the same time. This ability to separate thermodynamicfrom kinetic events aids in the interpretation of the thermal curve, measures expansion andcontraction taking place at the same time and provides a more accurate estimation of the glasstransition temperature than the softening temperature.

MTMA may have applications in other measurements where thermodynamic and kineticlength changes occur simultaneously. Such examples may include the softening of organic orinorganic glasses, heat set films and fibers, and shape memory alloys.

REFERENCES1. M. Reading, “Modulated Differential Scanning Calorimetry – A New Way Forward in Materials

Characterization“, Trends in Polymer Science, 1993, 1, pp. 248-253.2. R. L. Blaine and B. K. Hahn, “Obtaining Kinetic Parameters by Modulated Thermogravimetry“, Journal of

Thermal Analysis, 1998, 54, pp. 695-704.3. D. M. Price, “Novel Methods of Modulated Temperature Thermal Analysis“, Thermochimica Acta, 1998,

315, pp. 11-18.4. B. Wunderlich, Y. Jin and A. Bollar, “Mathematical Description of Differential Scanning Calorimetry

Based on Periodic Temperature Modulation”. Thermochimica Acta, 1994, 238, pp. 277-293.

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5. E 2113, “Length Change Calibration of Thermomechanical Analyzers”, ASTM International, WestConshohocken, PA

6. E 1545, “ Assignment of the Glass Transition Temperature by Thermomechanical Analysis”, ASTMInternational, West Conshohocken, PA.

7. E 2092, “Distortion Temperature in Three-Point Bending by Thermomechanical Analysis”, ASTMInternational, West Conshohocken, PA

Figure 7. Comparison of softening and glass transition temperatures.

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A Technique For The Rapid Acquisition Of Rheological Data,And Its Application To Fast Curing Systems

Mark Grehlinger, TA Instruments109 Lukens Drive, New Castle DE 19720

mgrehlinger@tainst.com

ABSTRACTCommercial rheometers typically rely on internal data acquisition and correlation systems

to generate dynamic mechanical test results. This approach has the advantage of beingintegrated with the rest of the instrument hardware and software control systems, but limits theoverall performance of the system to the capabilities of the internal electronics and processingfirmware. This limitation is not an issue at low test frequencies, where the time required toobtain a data point is related to the period of oscillation, but at higher tests frequencies data ratesgenerally top out at about 1-2 points per second regardless of measurement frequency.

For most materials this limitation is not a problem, since the rheological properties ofmost materials generally do not change that rapidly over time, and maximum temperatureramping rates tend to be limited by the thermal mass of the material and test fixtures rather thandata acquisition rates. There are, however, classes of reactive systems (for example UV cures)that undergo very large changes in viscoelastic properties in a relatively short period of time. Inthis case performance of most rheometers is not sufficient to accurately model the kinetics ofthese materials.

In this paper a new approach to fast rheological measurements will be discussed where anoff-the-shelf external Analog to Digital conversion system is integrated with rheometer controland analysis software, and used to obtain dynamic mechanical data at rates of over 60 points persecond. This technique is only applicable to rheometers using separate motor and transducers,where the analog voltages corresponding to measured torque and motor displacement are readilyaccessible.

INTRODUCTIONDynamic mechanical analysis (DMA) is a well-known method used to measure the

viscoelastic properties of materials such as polymers and structured fluid systems. Unlikeconventional viscometer measurements, DMA allows for the measurement of both the viscousand elastic properties of the materials being tested. This information can be used for such thingsas to gain insight in the processing behavior of molten polymers, and the end-use properties ofhigh-performance engineering plastics. DMA can also be used to look at structured fluids suchas paste and foodstuffs, and correlations can be made between these properties and factors suchas “mouth feel” in the case of foods, and flow and leveling in the case of paints.

In Dynamic Mechanical Analysis a sinusoidal stress or strain signal is imposed on asample confined to a well-defined geometry. Measurements can be made using either sheargeometries (e.g. parallel plate or cone and plate), or in linear geometries (e.g.rectangular/cylindrical tension-compression, or bending). In all cases however both the stress

and strain as a function of time must be either measured or deduced. Since the sample geometryis known, determining stress and strain on the sample is a matter of measuring or calculating themotor displacement and torque as a function of time, and then multiplying by the appropriategeometry constants.

The measurement of dynamic mechanical parameters from the transient stress and strainsignals involves the calculation of the magnitude of each of these sinusoidal signals and thephase shift between them. From these parameters it is possible to calculate all of theconventional DMA variables such as the complex viscosity (η*), elastic and loss moduli (G’,G”), and tan δ.

Cross Correlation

δ

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Stress / Strain Phasers

δγ(t)

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Figure1 Dynamic Mechanical Signals

Calculation of the amplitude of the stress and strain signals, and the phase shift betweenthem can be done using a variety of techniques, however most rheometers use either a DiscreteFourier Transform (DFT) or a cross-correlation algorithm. In the case of cross correlation, theincoming stress and strain signals are correlated against two reference sine waves of the samefrequency, that are shifted in phase by 90º from each other. This algorithm offers very goodnoise rejection, particularly if data are integrated over several cycles of oscillation (1).

The ARES rheometer used in this study uses two dedicated A/D converter to sample thetorque and displacement signals, with the number of cycles used for the correlation, and numberof points per cycle being a function of frequency, with the total number of raw samples used forthe data correlation generally fixed at 2048 (2). The actual time required to generate a singledynamic mechanical data point is of course tied to the measurement frequency, plus any timerequired by the instrument microprocessor and firmware to do the actual calculations. Atfrequencies below 2 rad/s, where a single cycle is used, the minimum measurement time isbetween 1 and 1 1/2 cycles of oscillation. At higher frequencies the limiting factor in the rate atwhich dynamic data can be obtained is not governed by the measurement period, but rather theinstrument firmware.

In most applications this limitation is not a factor, since the rheological properties beingmeasured are either relatively constant, or changing slowly enough that they can still beaccurately measured using conventional data acquisition and correlation systems. For materialswhere the rheology is rapidly changing (for example, curing materials or structured fluid systemswhich may break down under shear) this limitation may prevent accurate measurement of thesechanging properties over time.

With this in mind a system was developed for performing dynamic mechanical analysisexperiments at significantly higher data rates using an off-the-shelf external A/D converter andspecial software to perform the necessary calculations and automatically send the data stream tothe instrument data presentation software.

EXPERIMENTALDynamic mechanical analysis measurements were made using ARES rheometer (TA

Instruments). This instrument contains a rotational motor that applies a shear strain to sample,and a force rebalance transducer (FRT) that measures the resulting torque and normal force. Theoutput signals for both the motor and transducer are easily accessible via BNC connectors on theback of the instrument. The signals are scaled to ± 5 V full scale, corresponding to nominalvalues of ± 2000 gm-cm or ± 200 gm-cm torque (depending on transducer setting), and ± 0.5radians of angular displacement for the motor.

These signals were digitized using a National Instruments DAQPad-6020E USB-basedanalog to digital converter (DAQ), which features 8 dual-ended analog input channels with 12-bits of resolution, 8 digital I/O lines, and a maximum sampling rate of 100 kS/s. A specialsoftware module (RheoCorr) was written to interface this acquisitions system to the rheometercontrol software (TA Instruments Orchestrator), which allows Orchestrator to control theexternal DAQ hardware, send over the appropriate scaling constants (transducer calibrationfactors, geometry constants, etc.), and to receive the calculated dynamic mechanical properties.An ActiveX control provided by National Instruments (NI-DAQ) was used to interface the DAQto the RheoCorr software.

Viscoelastic parameters were calculated from the sampled data using the cross-correlation algorithm discussed above. There are, however, several additional factors that needto be considered in order to obtain accurate data. The first is the fact that the A/D hardware ismultiplexed in such a way that the individual torque and displacement samples do not occur atthe same point in time. This delay can be corrected by querying the driver software for the intrachannel delay time, and adjusting the calculated phase shift by the appropriate amount based onthe delay time and the measurement frequency. Another factor to consider is that the analogelectronics in the rheometer itself have a frequency-dependent phase shift (a correction that isnormally done in the instrument firmware), and this correction is taken into account in a similarfashion. Transducer compliance (3) was compensated for by modeling the transducer as a springwith a fixed compliance constant.

Rheological measurements were obtained on a sample of polydimethyl siloxane (PDMS,General Electric SE30), measured using a 25 mm diameter parallel plate geometry at roomtemperature in order to compare the accuracy of the external correlator to the data generated bythe conventional ARES electronics.

The ability of this measurement system to follow the rheological properties of fastreacting systems was tested by monitoring the change in complex viscosity (η*) of a urethanebased UV curing system. In this experiment the uncured polymer solution was tested using a38.1 mm diameter quartz parallel plate upper fixture, and a standard 50 mm diameter stainlesssteel bottom plate. A Novacure 2100 (Exfo) UV source was used to generate the ultravioletlight, which was passed through a 320 – 500 nm filter. The Novacure unit provides digital I/Olines for controlling the lamp shutter, and an analog output signal corresponding to the intensityof the UV signal. These signals where connected to the acquisition hardware, which allowed therheometer software to both control and monitor the UV intensity during measurements. Twinlight pipes, mounted above the quartz upper plate were used to illuminate the sample with the

UV radiation. Although this arrangement did not provide a uniform distribution of light over thearea of the quartz plate, it proved sufficient for testing purposes.

RESULTS AND DISCUSSION

Accuracy of Data Correlation SystemFigure 2 shows a comparison of frequency sweep data generated using the external

correlator software to the data generated by the ARES electronics using the PDMS sample. Datawere run using a series of frequencies from 0.1 to 100 rad/s and a strain amplitude of 5%, wellwithin the linear viscoelastic range of the material.

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Figure 2 Frequency Sweep PDMS

The actual data were generated using a series of time sweeps at each frequency, withmultiple data points collected at each rate in order to determine the repeatability of the data. Ascan be seen from the plot, the two sets of measurements are essentially equivalent to each otherover the frequency range examined.

The data generated by the ARES rheometer showed better repeatability frommeasurement to measurement within a single test frequency, which is most likely due to betterresolution in the ARES DAQ, which uses a 9-bit auto ranging algorithm coupled with a 16-bitDAQ to provide an effective resolution of 25 bits relative to the full-scale signal voltages. Theaverage relative standard deviation (RSD) in modulus values over the frequency range examinedwas found to be 0.04% for the ARES data, in contrast to 0.33% for the external correlationsystem. A similar trend was found in the phase angle measurements, where the ARES results

showed an average of 0.015% for the relative standard deviation at each frequency, and theexternal correlator data was found to have an average RSD of 0.315%.

In general, the difference between the modulus and phase angle values calculated by theARES and the results calculated by the external correlator system are generally within about0.5% of each other as shown in Figure 3. The errors tend to be larger at lower frequencies, aswould be expected since the torque levels measured are smaller. Also, no significant trend isseen in the errors at high frequencies, which indicates that the corrections used for compensatingfor transducer compliance, and phase errors work well, since these effects are much larger athigh frequencies.

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Measurements made using the external data acquisition system shows that it is possible toreliably generate dynamic mechanical data at a rate corresponding to a time period about 20%greater than the period of the measurement frequency. At a test frequency of 100 rad/s thiscorresponds to approximately 13 points per second, at 500 rad/s (the upper frequency limit forthe ARES) 66 points per second can be consistently obtained. The additional time provided ineach measurement cycles allows the software to marshal the raw data from DAQ driver to thedata calculation and presentation functions. Note that in cases where the maximum number ofpoints is not needed, the accuracy of the results can be improved by running the data correlationover several cycles of measurement.

Application to Fast Curing SystemsPrevious studies (4) have used similar experimental setups, and have relied on the fact

that the cross-linking reaction can be “stepped”, and then quenched by exposing the sample toshort bursts of UV light. The rheological properties can then be measured after each exposure, tomonitor the progress of the reaction. Our goal here was to see if it is possible to provide asystem for collecting data that is fast enough to be able to measure the rheology of such systemsin situ as the reaction progresses over time.

Figure 4 shows a plot of η* versus time for the UV-curing polymer system, during whichit was exposed to a 5 second pulse of UV radiation with an average intensity of approximately 50mW/cm2, occurring about 130 seconds into the test. The data were measured using a frequencyof 312 rad/s (50 Hz) and a strain amplitude of 5%. As previously noted, the UV exposure wasnot uniform across the area of the plate, so the degree of cure was not consistent in the same.

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Figure 4 Complex Viscosity (η*) versus Time for UV Curable polymer system

This plot shows good agreement between the values obtained using both correlationsystems. It is also apparent from the plot that the data generated by the external correlator allowsthe cure to be monitored with a much greater degree of accuracy due to the fact that the datacollection is occurring at a rate of approximately 20 points per second, versus 1 point per secondin the case of the ARES electronics.

Real-time Waveform MonitoringThis system also provides a means for monitoring the torque and strain waveforms

graphically in real time, which can be used to spot problems in measurements such as low signal

amplitudes, sample slippage, or material nonlinearity. Figure 5 shows a screen capture of theRheoCorr software showing a the torque signal used for correlation obtained on a sample oftoothpaste run at a frequency of 50 Hz, and a strain amplitude of 20% (outside of the linearregion for the sample).

Figure 5 Screen Capture showing Torque Waveform

The results show that at this strain level the torque waveform is noticeably asymmetricdue to a nonlinear response in the sample.

CONCLUSIONSA new system has been developed for obtaining dynamic mechanical analysis data in an

ARES rheometer at a much faster data rate than is possible using the standard instrumentelectronics and software. This system uses external data acquisition hardware to sample theanalog torque and strain data from the rheometer, and special software to analyze this data in

real-time, calculating rheological parameters from these signals. These parameters are thenpassed to the rheometer control and analysis software, where they can be displayed andmanipulated as standard data sets. The results show that data obtained with this system are ingood agreement with the data generated by the standard ARES firmware and software.

This system can be used to study the rheology of fast reactive materials (such as UV-curable polymers) where the rapid change in rheological properties is difficult to follow with thestandard data collection rates offered by the ARES and similar rheometers.

REFERENCES

1. C. W. Macosko, Rheology: Principles, Measurements, and Applications, 1994, VCHPublishers, Inc.

2. T.A. Instruments, Inc. ARES User Manual (2003).3. M. Gottlieb and C. W. Macosko, Rheologica Acta, 1982, 21, 90-94.4. S. A. Khan, et al. Rheologica Acta, 1992, 31, 151-160.

Thermal Conductivity Measurements of Conductive Epoxy Adhesives by MDSC®

Els Verdonck*, TA InstrumentsRaketstraat 60, 1130 Brussels, Belgium

Els_Verdonck@waters.com

Roger Blaine, TA Instruments, Inc.109 Lukens Drive, New Castle, DE19720

RBlaine@tainst.com

Gunther Dreezen, ICI Belgium / Emerson & CumingNijverheidstraat 7, 2260 Westerlo, Belgium

Gunther.Dreezen@nstarch.com

ABSTRACTDetermination of a material’s thermal conductivity is important in evaluating its utility

for a specific application. A variety of techniques are available to determine thermalconductivity, among them being Modulated DSC®. MDSC® has the advantage for measuringthermal conductivity of being readily available due to its application to the study of glasstransition, melting temperature, crystallization, etc. of materials. In this study it is shown that therange of MDSC for thermal conductivity measurements is extended up to 4.0 W/(K m) for theuse with conductive epoxy based adhesives.

INTRODUCTIONIn the electronics industry epoxy based adhesives or encapsulates are often used to mount

or protect electronic devices. Thermally conductive materials ensure heat transfer or heatremoval within the electronic device. The thermal conductivity of these adhesives is an importantcharacteristic, aiding device design so that premature failure is avoided. Often the desiredthermal conductivity is in the range 0.7 to 3.5 W/(K m).

ASTM Method E1952 (1) describes the measurement of thermal conductivity byModulated DSC. It is applicable to homogeneous, non-porous solid materials with a thermalconductivity in the limited range of 0.10 to 1.0 W/(K m). Thermal conductivity measurements inthe temperature range from 0 to 90°C are covered.

In this test the heat capacity of a thin and thick sample is measured with MDSC (2-4).When the thin sample is encapsulated in a pan of high thermal conductivity and subjected to atemperature modulation with long period, the sample is assumed to achieve a uniformtemperature distribution, and the measured specific heat capacity is the thermodynamic heatcapacity of the sample. When the thick sample is exposed to a temperature modulation at oneend, the measured apparent heat capacity is lower in comparison with the thin sample, because ofthe non uniform temperature distribution across the height of the sample. The apparent heat

capacity is proportional to the square root of the thermal conductivity of the sample, as shown byequation 1.

K = (8 L C2) / (Cp M d2 P) (1)

where:K = observed thermal conductivity in W/(K m)C = apparent heat capacity in mJ/K (thick sample)Cp = specific heat capacity in J/(g K) (thin sample)L = sample height in mm (thick sample)M = sample mass in mg (thick sample)d = sample diameter in mm (thick sample)P = period of modulation in sec

Using equation 1 the thermal conductivity of a sample is derived from the heat capacitymeasured on a thin and thick sample, and some geometric and experimental factors. If thethermal conductivity of the sample is low and approaches that of the surrounding purge gas, acorrection to the observed thermal conductivity is necessary to compensate for heat loss throughthe sample side (4).

In order to obtain a reliable measurement of the thermal conductivity with this ModulatedDSC method, the specimen thickness for the thick sample must be larger than the depth to whichheat from a modulated source penetrates the sample. So in order to augment the upper limit ofthermal conductivity that can be assessed, either the sample thickness must be increased or thepenetration depth decreased. Typically the sample thickness is limited by the size of the DSCfurnace to 3-4 mm (4). The penetration depth is given by equation 2 (5):

dp = (2 D / ω)1/2 (2)where:dp = penetration depthD = thermal diffusivity = K / (Cp ρ)ρ = densityω = angular frequency = 2 П / P

According to equation 2 the penetration depth can be decreased by decreasing the period of themodulated measurement. Typically a period of 60-100 sec is used (1). The upper thermalconductivity limit of about 1.0 W/(K m) is reached for a sample like Pyrex glass. For Pyrex theratio between apparent heat capacity and specific heat capacity, measured with an 80 secmodulation period, is about 0.80 (4). For lower thermal conductivity materials like e.g.polystyrene this ratio is only about 0.45 (4). This ratio is an indication of the ease with whichtemperature uniformity is achieved across the sample. Above a ratio of 0.80 the apparent heatcapacity approaches too close the specific heat capacity, resulting in an unreliable thermalconductivity determination. By reducing the period from 80 sec to 20 sec the limiting ratio of0.80 is expected to be reached only at conductivity higher than 1.0 W/(K m), and so most likelythe upper thermal conductivity limit that one can measure with MDSC will be extended.

Recently a new heat flow measurement technique has been developed, that greatlyimproves the modulated measurement (6-10). This approach is based on a new DSC sensor andthe use of a pan corrected four term heat flow equation; as one of the multiple consequences

modulation periods as short as 20 sec can readily be used. This DSC technique is explored toextend the range of thermal conductivity currently assessed by Modulated DSC, and to study thethermal conductivity of conductive epoxy based adhesives.

EXPERIMENTALThe two necessary heat capacity measurements are performed on a TA Instruments

Q1000 DSC, equipped with Modulated DSC® and using the four term heat flow equation (6).Nitrogen is used as a purge gas. The temperature and enthalpy calibration are performed usingindium. The heat capacity calibration is performed with sapphire.

The measurements are done at 25°C, with a modulation amplitude of 0.5°C.Measurements with a modulation period of 20, 30, 40, 70 and 100 sec are compared.

The specific heat capacity measurements are done on thin disks, with a thickness of 0.5-0.8 mm and a diameter of 5.20 mm ± 0.05 mm. These samples are placed directly on the DSCsensor, after wetting the sensor very lightly with silicone oil. The silicone oil is used to improvethe thermal contact between sensor and sample. The sensor on the reference side is wetted aswell with the silicone oil. This procedure differs from the original procedure described in (4),where the thin sample is encapsulated in a crimped sample pan from TA Instruments.

The apparent heat capacity measurements are performed on right circular cylinders, withsmooth and parallel faces. The thickness is between 3.0 and 4.0 mm and the diameter is 5.20 mm± 0.05 mm. These samples are placed directly on the DSC sensor, after wetting the samplesensor lightly with silicone oil. The reference sensor is equally wetted. This procedure differsfrom the procedure described in (4), where in between sample and wetted sensor, a thinaluminum disk is placed to ensure a uniform temperature distribution.

RESULTS AND DISCUSSIONFive different conductive epoxy resins are investigated. Heat capacity of a thin and thick

sample are measured with MDSC; the thermal conductivity is calculated using equation 1. Theresults are summarized in Table 1. The influence of different modulation periods is illustrated inFigures 1 and 2; performing measurements at various periods facilitates the data evaluation.

For the most conductive samples (1 and 2) good agreement is found between the MDSCmeasurement at 20 sec period and other techniques. For these samples at a period of 70-100 secthe ratio between apparent and specific heat capacity equals unity; only at 20 sec it is below 0.80,which seems to be the critical upper limit for reliable thermal conductivity determination.

For the intermediate conductive samples (3 and 4) the MDSC result at 20 sec period islower than expected. The ratio between apparent heat capacity and specific heat capacity is inthis case 0.43. Possibly this is below a critical lower limit, below which the modulation becomestoo fast for the sample to follow. The result at 100 sec period is also too low, however in thiscase C/Cp is far above 0.80 and the result no longer very accurate. 30 to 40 sec period(C/Cp=0.56 to 0.65) seems to be a good compromise, a thermal conductivity in good agreementwith the other techniques is found.

For the low conductivity material (sample 5) as expected from the ratio C/Cp a too lowvalue for the thermal conductivity is found at 20, 30 and 40 sec. At 70 and 100 sec the ratio C/Cpis respectively 0.49 and 0.60; consequently the thermal conductivity is expected to be reliable.However, it is higher than measured with other techniques. It should be noted in this respect thatthe correction for heat loss through the sample side, as described in (4), is not taken into accountin this study. For the high and intermediate conductive samples this correction is negligible,while for this low conductivity material it is necessary to take it into account.

Table 1 Thermal conductivity of various conductive epoxy resins measured with MDSC. Influence of modulation period on the result. Comparison with results obtained by other techniques (laser flash technique, hot disk method). Cp is the specific heat capacity measured on the thin sample, C is the apparent heat capacity measured on the thick sample.

Thermal conductivityin W/(K m)

Sample Period in sec Cp in J/(g K) Ratio C/Cp MDSC Othertechniques

1 20 0.42 0.77 4.0 3.8-3.930 0.87 3.440 0.92 2.970 1.0 1.8100 1.0 1.4

2 20 0.48 0.67 2.6 2.5-2.73 20 0.95 0.43 1.1 1.2-1.4

30 0.56 1.240 0.65 1.270 0.80 1.1100 0.86 0.88

4 20 0.92 0.42 0.98 1.2-1.440 0.65 1.2100 0.91 0.95

5 20 1.10 0.21 0.44 0.530 0.28 0.4540 0.33 0.4870 0.49 0.57100 0.60 0.60

For sample 5 the mean thermal conductivity result from 5 measurements is 3.96 W/(K m)with a standard deviation of 0.32 W/(K m) or 8 %. The relative standard deviation is in goodagreement with reference (11), where for lower conductivity materials like PS and PMMA awithin laboratory relative standard deviation of 12 % is found.

The thick samples are placed directly on the wetted sensor, without using an aluminumfoil in between. In reference (4) aluminum foil is recommended to distribute the heat moreevenly over the sample area, since the sample diameter is somewhat larger than the sensordiameter. In the present study, where better conducting samples are investigated, it is found thatthe use of the aluminum disk is superfluous. Moreover, omitting it increases the reproducibilityof the results. For the same reason of increased reproducibility, the heat capacity measurementson these better conducting samples are done without pan. The silicone oil contributes almostnothing to the specific heat capacity measurement of the thin samples: assuming an imbalance of0.1 mg silicone oil on sample versus reference side, would lead to a contribution to the sampleCp of less than 1 % (Cp of the silicone oil is 1.64 J/(g K)). Not using the silicone oil reduces the

reproducibility of the results far more. The specific heat capacity measured in this way is almostindependent of the modulation period. The largest difference on Cp found for the various samplesusing a modulation period of 100 sec versus 20 sec is less than 3 %.

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

modulation period (sec)

C/C

p

sample 1sample 3sample 5

Figure 1 Ratio of the apparent heat capacity C to the specific heat capacity Cp versus modulation period for differentsamples.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 20 40 60 80 100 120

modulation period (sec)

ther

mal

con

duct

ivity

in W

/(K m

)

sample 1sample 3sample 5

Figure 2 Thermal conductivity versus modulation period for different samples.

CONCLUSIONThis study shows that by decreasing the period of the modulation down to 20 sec, the

upper limit of thermal conductivity that can be measured by Modulated DSC is extended by afactor of 4 to 4 W/(K m). Using this method it is possible to measure accurately the thermalconductivity of conductive epoxy based adhesives for the electronic industry.

REFERENCES1. ASTM E 1952 – 98 Standard Test Method for Thermal Conductivity and Thermal Diffusivity by

Modulated Temperature Differential Scanning Calorimetry, Annual Book of ASTM Standards, vol. 14.02.2. S.M. Marcus and R.L. Blaine, Thermochimica Acta, 1994, 243, 231-239.3. R.L. Blaine and S.M. Marcus, Journal of Thermal Analysis, 1998, 54, 467-476.4. S.M. Marcus and R.L. Blaine, Thermal Conductivity of Polymers, Glasses and Ceramics by Modulated

DSC, TA Instruments application note TA086.5. Kittel and Kroemer, Thermal Physics, 2nd Edition, 424-427.6. R.L. Danley, Thermochimica Acta, 2003, 402/1-2, 91-98.7. R.L. Danley, Thermochimica Acta, 2003, 395, 201-208.8. R.L. Danley and P.A. Caulfield, Proceedings 29th Conf. N. Amer. Therm. Anal. Soc., 2001, 667.9. R.L. Danley and P.A. Caulfield, Proceedings 29th Conf. N. Amer. Therm. Anal. Soc., 2001, 673.10. L.C. Thomas, Proceedings 29th Conf. N. Amer. Therm. Anal. Soc., 2001, 818.11. R.L. Blaine and R.B. Cassel, Precision and Bias of the ASTM Test E1952 for Thermal Conductivity by

Modulated Temperature DSC, TA Instruments application note TA265.