Modelling-aided development of a RheoDSC, an instrument Modelling-aided development of a RheoDSC, an instrument

for simultaneous rheological and calorimetric measurements

G. Van Assche, R. Verhelle, L. Van Lokeren, C. Block,

Vrije Universiteit Brussel, Physical Chemistry & Polymer Science, Pleinlaan 2, 1050 Brussels, Belgium, gvassche@vub.ac.beVrije Universiteit Brussel, Physical Chemistry & Polymer Science, Pleinlaan 2, 1050 Brussels, Belgium, gvassche@vub.ac.be

IntroductionIntroductionIntroductionIntroduction

Transformations in polymers, such as polymerisation,Transformations in polymers, such as polymerisation,

melting/crystallization, and phase separation/remixing, are

associated with changes in both rheological and thermal

properties. To permit simultaneous calorimetric andproperties. To permit simultaneous calorimetric and

rheometric measurements, the RheoDSC was developed.

The RheoDSC combines two commercial instruments, a TAThe RheoDSC combines two commercial instruments, a TA

Instruments Q2000 DSC and a TA Instruments AR-G2

dynamic rheometer. A rheological measurement is

FigFigFigFig.... 1111:::: RheoDSCRheoDSCRheoDSCRheoDSC setupsetupsetupsetup:::: (left)(left)(left)(left) rotorrotorrotorrotor assemblyassemblyassemblyassembly withwithwithwith connectionconnectionconnectionconnection

towardstowardstowardstowards thethethethe rheometerrheometerrheometerrheometer permittingpermittingpermittingpermitting rotorrotorrotorrotor alignment,alignment,alignment,alignment, (middle)(middle)(middle)(middle) DSCDSCDSCDSC

cellcellcellcell andandandand rotorrotorrotorrotor assemblyassemblyassemblyassembly showingshowingshowingshowing thethethethe offoffoffoff----centeredcenteredcenteredcentered positioningpositioningpositioningpositioning ofofofof

performed on a sample sitting on a sample plate that is on

top of the DSC sensor platform. This plate is fixed using

insulated screws on an aluminium insert that sits around the

thethethethe DSCDSCDSCDSC cellcellcellcell comparedcomparedcomparedcompared totototo thethethethe rotor,rotor,rotor,rotor, andandandand (right)(right)(right)(right) DSCDSCDSCDSC sensorsensorsensorsensor

platformplatformplatformplatform withwithwithwith statorstatorstatorstator assembly,assembly,assembly,assembly, sample,sample,sample,sample, andandandand rotorrotorrotorrotor (right)(right)(right)(right)....FigFigFigFig.... 2222:::: (left)(left)(left)(left) MeshedMeshedMeshedMeshed geometrygeometrygeometrygeometry withwithwithwith aboutaboutaboutabout 36000360003600036000 elements,elements,elements,elements,

(right)(right)(right)(right) MeshMeshMeshMesh qualityqualityqualityquality depicteddepicteddepicteddepicted forforforfor thethethethe 5555 %%%% worstworstworstworst

elementselementselementselements....

insulated screws on an aluminium insert that sits around the

base of the DSC sensor. The setup shown in Fig. 1.

Finite Element modellingFinite Element modellingFinite Element modellingFinite Element modelling

Through heat transfer modelling with COMSOL weThrough heat transfer modelling with COMSOL we

successfully optimized the design and the material selection.

All finite element simulations were performed using Comsol0.5

No RotorAll finite element simulations were performed using Comsol

Multiphysics v4.2 using the Heat transfer module and the

Chemical reaction engineering module. The transient

simulations were conducted with a direct PARDISO solver -1

-0.5

0

SR

/ K

8.0 mm tower

simulations were conducted with a direct PARDISO solver

and backward differentiation formula (BDF) on a Windows

XP 64 bit computer with an Intel® Core™ 2 Quad Q9550 @ -1.5

0

/ K PAI

PU-foam

-2

-1.5

-1

∆∆ ∆∆T

SR

XP 64 bit computer with an Intel® Core™ 2 Quad Q9550 @

2.83 GHz processor and 16 GB RAM memory. The total

assembly has approximately 36000 elements (Fig.2).-4.5

-3

∆∆ ∆∆T

SR

/ K PAI

-2.5

-2

0 1000 2000 3000time/s

no tower

For the optimization of the instrument design, DSC

ComsolComsolComsolComsol----aided design optimizationaided design optimizationaided design optimizationaided design optimization -6

-4.5

0 1000 2000 3000

Pyrex

FigFigFigFig.... 3333 ReductionReductionReductionReduction ofofofof thethethethe thermalthermalthermalthermal laglaglaglag inininin RheoDSCRheoDSCRheoDSCRheoDSC bybybyby placingplacingplacingplacing

aaaa cylindercylindercylindercylinder inininin PAI,PAI,PAI,PAI, thethethethe rotorrotorrotorrotor material,material,material,material, onononon thethethethe referencereferencereferencereference sidesidesideside totototo

equilibrateequilibrateequilibrateequilibrate thethethethe unbalanceunbalanceunbalanceunbalance....

For the optimization of the instrument design, DSC

experiments were simulated using Comsol. Simulations were

made for reacting or crystallizing samples by including

0 1000 2000 3000time/s

0.35

/K

PAIPU-foam

equilibrateequilibrateequilibrateequilibrate thethethethe unbalanceunbalanceunbalanceunbalance....

(top)(top)(top)(top) GeometricalGeometricalGeometricalGeometrical modelmodelmodelmodel depictingdepictingdepictingdepicting PAIPAIPAIPAI towerstowerstowerstowers ofofofof differentdifferentdifferentdifferent

heightsheightsheightsheights onononon thethethethe referencereferencereferencereference sensorsensorsensorsensor....

(bottom)(bottom)(bottom)(bottom) TemperatureTemperatureTemperatureTemperature differencedifferencedifferencedifference betweenbetweenbetweenbetween samplesamplesamplesample andandandand

referencereferencereferencereference sensor,sensor,sensor,sensor, ∆∆∆∆TTTTSRSRSRSR,,,, forforforfor thethethethe curecurecurecure ofofofof aaaa thermosettingthermosettingthermosettingthermosetting resinresinresinresinmade for reacting or crystallizing samples by including

suitable models for the transformation kinetics. In this way,

the simulated ‘measured heat flux’ can be compared to the0.15

0.25

Tn

o_re

acti

on

/K

Pyrex

PAI

Al203

referencereferencereferencereference sensor,sensor,sensor,sensor, ∆∆∆∆TTTTSRSRSRSR,,,, forforforfor thethethethe curecurecurecure ofofofof aaaa thermosettingthermosettingthermosettingthermosetting resinresinresinresin

forforforfor differentdifferentdifferentdifferent towertowertowertower heightsheightsheightsheights (no(no(no(no tower,tower,tower,tower, 0000....4444 mm,mm,mm,mm, 1111 mm,mm,mm,mm, 2222 mm,mm,mm,mm,

4444 mm,mm,mm,mm, 6666 mmmmmmmm andandandand 8888 mm)mm)mm)mm) ofofofof PAIPAIPAIPAI towerstowerstowerstowers onononon thethethethe referencereferencereferencereference

sensorsensorsensorsensor sidesidesideside andandandand forforforfor comparisoncomparisoncomparisoncomparison aaaa setupsetupsetupsetup withwithwithwith nononono rotorrotorrotorrotor onononon thethethethe

samplesamplesamplesample (heating(heating(heating(heating fromfromfromfrom 25252525 °CCCC totototo 250250250250 °CCCC atatatat 5555 KKKK minminminmin----1111 ))))....

heat release in the sample to evaluate thermal lag and peak

distortions.

- Thermal lag simulations (Fig. 3):

0.05

0.15

∆∆ ∆∆T

reacti

on -

∆∆ ∆∆T

2 3

Al

samplesamplesamplesample (heating(heating(heating(heating fromfromfromfrom 25252525 °CCCC totototo 250250250250 °CCCC atatatat 5555 KKKK minminminmin ))))....

- Thermal lag simulations (Fig. 3):

In a heat flux type DSC, the heat flow rate to the sample is

obtained by multiplying the temperature difference between

-0.05

0 1000 2000 3000time/s

∆∆ ∆∆

obtained by multiplying the temperature difference between

the sample and reference sensors with a calibration factor.

Thermal lag is observed when going from an isothermal to a

heating segment. It is due to a different time constant for heat

FigFigFigFig.... 4444 :::: SimulationsSimulationsSimulationsSimulations forforforfor selectingselectingselectingselecting thethethethe rotorrotorrotorrotor materialmaterialmaterialmaterial

(top)(top)(top)(top) TemperatureTemperatureTemperatureTemperature distributionsdistributionsdistributionsdistributions inininin thethethethe RheoDSCRheoDSCRheoDSCRheoDSC setupsetupsetupsetup forforforfor

differentdifferentdifferentdifferent rotorrotorrotorrotor materialsmaterialsmaterialsmaterials forforforfor anananan isothermalisothermalisothermalisothermal atatatat 100100100100 °CCCC....heating segment. It is due to a different time constant for heat

transfer on sample and reference side. The high heat

capacity and low thermal conductivity of the rotor cause a

differentdifferentdifferentdifferent rotorrotorrotorrotor materialsmaterialsmaterialsmaterials forforforfor anananan isothermalisothermalisothermalisothermal atatatat 100100100100 °CCCC....

(mid)(mid)(mid)(mid) TemperatureTemperatureTemperatureTemperature differencedifferencedifferencedifference betweenbetweenbetweenbetween samplesamplesamplesample andandandand

referencereferencereferencereference sensor,sensor,sensor,sensor, ∆∆∆∆TTTTSRSRSRSR,,,, forforforfor differentdifferentdifferentdifferent typestypestypestypes ofofofof rotorrotorrotorrotor materialsmaterialsmaterialsmaterials....

SimulationSimulationSimulationSimulation ofofofof nonnonnonnon----isothermalisothermalisothermalisothermal curecurecurecure experimentsexperimentsexperimentsexperiments ofofofof aaaa

thermosettingthermosettingthermosettingthermosetting epoxyepoxyepoxyepoxy amineamineamineamine ((((25252525 °CCCC totototo 250250250250 °CCCC atatatat 5555 KKKK minminminmin----1111))))....capacity and low thermal conductivity of the rotor cause a

slow equilibration and a considerable baseline shift upon

heating. Both can be reduced by balancing sample and

reference side by placing a PAI tower on it.

thermosettingthermosettingthermosettingthermosetting epoxyepoxyepoxyepoxy amineamineamineamine ((((25252525 °CCCC totototo 250250250250 °CCCC atatatat 5555 KKKK minminminmin ))))....

(below)(below)(below)(below) ContributionContributionContributionContribution ofofofof thethethethe reactionreactionreactionreaction exothermexothermexothermexotherm totototo ∆∆∆∆TTTTSRSRSRSR ....

-0.5

0

-1

120No Rotor

reference side by placing a PAI tower on it.

- Rotor material (Fig. 4)

Different rotor materials were evaluated for isothermal and -1.5

-1

-0.5

Heat

flo

w r

ate

/ W

.g-1

40

80

1.25 mm

CROSS

Different rotor materials were evaluated for isothermal and

nonisothermal conditions. For more conductive materials,

more heat will flow into the rotor, leading to an important

baseline in nonisothermal experiments. Subtracting the -0.5

0

0.5

1.75 mm

CROSS

no rotor

-3

-2.5

-2

Heat

flo

w r

ate

/ W

.g

-40

0

T /

°C

1.25 mm

baseline in nonisothermal experiments. Subtracting the

baseline shows that the reaction exotherm observed in ∆TSR

is only slightly deformed for PAI. -1.5

-1

-0.5

∆∆ ∆∆T

SR

/ K 0.75 mm

1.25 mm

CROSS

-3.5

-3

300 1300 2300time/s

Heat

flo

w r

ate

/ W

.g

-80

-40

T /

°C

No HolesEXO DOWN

is only slightly deformed for PAI.

- Rotor design (Fig. 5)

To further reduce the heat conduction from the sample to the-2.5

-2

-1.5

plain

time/s

-0.2

0

Heat

flo

w r

ate

/ W

.g-1

80

120

No RotorTo further reduce the heat conduction from the sample to the

rotor, small holes were drilled in the lower section of the rotor.

For crossed holes of 1.75 mm, the baseline offset is strongly

reduced, as less rotor material is heated up.

-2.5

0 1000 2000 3000time/s

-0.4

-0.2

Heat

flo

w r

ate

/ W

.g

0

40

No Holes

1.25 mm

No Rotor

CROSS

reduced, as less rotor material is heated up.

- Validation (Fig. 6)

Experiments with the different rotor designs for the

FigFigFigFig.... 5555:::: SimulationsSimulationsSimulationsSimulations forforforfor optimizingoptimizingoptimizingoptimizing thethethethe rotorrotorrotorrotor geometrygeometrygeometrygeometry....

(top)(top)(top)(top) GeometricalGeometricalGeometricalGeometrical representationrepresentationrepresentationrepresentation ofofofof modifiedmodifiedmodifiedmodified PAIPAIPAIPAI rotorsrotorsrotorsrotors....

(mid)(mid)(mid)(mid) SimulatedSimulatedSimulatedSimulated temperaturetemperaturetemperaturetemperature distributionsdistributionsdistributionsdistributions inininin thethethethe RheoDSCRheoDSCRheoDSCRheoDSC

setupsetupsetupsetup forforforfor aaaa PAIPAIPAIPAI rotorrotorrotorrotor withwithwithwith twotwotwotwo perpendicularperpendicularperpendicularperpendicular holesholesholesholes withwithwithwith aaaa-0.6

-0.4

Heat

flo

w r

ate

/ W

.g

-80

-40

T /

°C

1.25 mm

EXO DOWNExperiments with the different rotor designs for the

crystallization of an ethylene-vinyl acetate copolymer confirm

the strong reduction of the baseline offset using the crossed

holes rotor as well as the limited differences in peak

setupsetupsetupsetup forforforfor aaaa PAIPAIPAIPAI rotorrotorrotorrotor withwithwithwith twotwotwotwo perpendicularperpendicularperpendicularperpendicular holesholesholesholes withwithwithwith aaaa

radiusradiusradiusradius ofofofof 0000....75757575 mm,mm,mm,mm, 1111....25252525 mm,mm,mm,mm, andandandand 1111....75757575 mm,mm,mm,mm, andandandand aaaa rotorrotorrotorrotor withwithwithwith

twotwotwotwo levelslevelslevelslevels ofofofof holesholesholesholes inininin aaaa crosscrosscrosscross patternpatternpatternpattern (cross)(cross)(cross)(cross) indicatedindicatedindicatedindicated withwithwithwith thethethethe

pictogram,pictogram,pictogram,pictogram, simulatedsimulatedsimulatedsimulated forforforfor anananan isothermalisothermalisothermalisothermal atatatat 100100100100 °CCCC....

(below)(below)(below)(below) TemperatureTemperatureTemperatureTemperature differencedifferencedifferencedifference ∆∆∆∆TTTTSRSRSRSR forforforfor thethethethe differentdifferentdifferentdifferent rotorrotorrotorrotor

-0.6

300 1300 2300time/s

-80

FigFigFigFig.... 6666.:.:.:.: HeatHeatHeatHeat flowflowflowflow raterateraterate signalsignalsignalsignal forforforfor aaaa coolingcoolingcoolingcooling experimentexperimentexperimentexperiment ofofofof semisemisemisemiholes rotor as well as the limited differences in peak

distortion.

(below)(below)(below)(below) TemperatureTemperatureTemperatureTemperature differencedifferencedifferencedifference ∆∆∆∆TTTTSRSRSRSR forforforfor thethethethe differentdifferentdifferentdifferent rotorrotorrotorrotor

designsdesignsdesignsdesigns.... SimulationSimulationSimulationSimulation ofofofof nonnonnonnon----isothermalisothermalisothermalisothermal curecurecurecure experimentsexperimentsexperimentsexperiments ofofofof aaaa

thermosettingthermosettingthermosettingthermosetting epoxyepoxyepoxyepoxy amineamineamineamine ((((25252525 °CCCC totototo 250250250250 °CCCC atatatat 5555 KKKK minminminmin----1111))))....

FigFigFigFig.... 6666.:.:.:.: HeatHeatHeatHeat flowflowflowflow raterateraterate signalsignalsignalsignal forforforfor aaaa coolingcoolingcoolingcooling experimentexperimentexperimentexperiment ofofofof semisemisemisemi

crystallinecrystallinecrystallinecrystalline polymerpolymerpolymerpolymer (EVA(EVA(EVA(EVA 33333333)))) fromfromfromfrom 100100100100 °CCCC atatatat 5555 KKKK....minminminmin----1111 towardstowardstowardstowards

----60606060 °CCCC withwithwithwith thethethethe differentdifferentdifferentdifferent rotorrotorrotorrotor setupssetupssetupssetups withoutwithoutwithoutwithout (top)(top)(top)(top) andandandand withwithwithwith

(bottom)(bottom)(bottom)(bottom) subtractingsubtractingsubtractingsubtracting aaaa baselinebaselinebaselinebaseline....

This project was in collaboration with Prof. P. Van Puyvelde (KULeuven) and was

supported by TA Instruments, FWO (Vlaanderen) and IWT (Vlaanderen).

Excerpt from the proceedings of the 2015 COMSOL Conference in Grenoble