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Caractérisa)onparDSC:défautsintrinsèqueset

apportsdelamodélisa)on

ErwinFRANQUET(erwin.franquet@univ-pau.fr)LaTEP–IPRA/UniversitédePauetdespaysdel’Adour Jeudi16Mars2017

E.Franquet,J.-PBédécarrats,J.-P.Dumas,S.Gibout,D.Haillot

1Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)on 16/03/2017

Généralités§ Analysethermique 3§ DSC 4Interpréta)on§ GrandeursidenSfiables 9§ Erreur(très)courante 13§ Inconnuessurcertainsparamètres 16Modélisa)on§ Analysethéorique 18§ ModélisaSon/SimulaSon 19§ Résultats 21Caractérisa)on§ IdenSficaSon:méthodesinverses 28§ Processusd’inversion 29§ Résultats 35ConclusionAnnexes§ Bibliographie 41§ Discussionssupplémentaires... 44

Sommaire

2

Généralités

16/03/2017

3

Analysethermique

Différentsappareils/mesures§ Calorimètre:mesurechaleur§ DifferenSalthermalanalysis(DTA):mesuretempérature§ AdiabaScscanningcalorimetry(ASC):mesuretempérature§ DifferenSalscanningcalorimetry(DSC):mesurevariaSondeflux

§ méthodeT–history...

§ Thermo-gravimétrie§ Analysethermo-mécanique…

Différentsmodesd’u)lisa)on§ dynamique§ isotherme(step)

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités

16/03/2017

4

DSC§ Deuxtypes:

§  Heatflux(ex:DSC131deSetaram)§  PowercompensaSon(ex:PyrisDiamonddePerkin–Elmer)

§ ImposiSond’unesollicitaSonthermique§ Mesured’unfluxdechaleur

§ ObtenSond’unthermogramme(courbeDSC)§  Modedynamique§  Modeisotherme(step)

16/03/2017

1. Introduction1

The calorimetry is an usual technique which permits to analyze a physical or chemical2

phenomena by the release or the absorption of thermal energy. This paper is restrictive to3

the transformation solid ! liquid and more particularly to the melting. We will present4

different cases as those of pure substances and binary solutions.5

We intend, first, to recall the classical procedure to determine the temperature range of6

transformation of the energy involved. The main principle is to consider the temperature7

inside the sample as homogeneous and at a value practically equal to the programmed tem-8

perature. The difference between these two temperatures being, for a given heating rate, a9

constant and small correction justified by only the thermal resistance between the metallic10

pan and the plate [1].11

For many years [2, 3, 4, 5], we have explained that, at the time of the melting, the tem-12

perature inside the sample is not at all homogeneous. We will recall also our model. It13

will be particularly highlighted that the thermograms, even they are expressed versus the14

programmed temperature, they are curves versus time. n.b. : dire quelque part que l’on va15

comparer avec les droites, pentes. . .16

2. Homogeneous model17

In such a case, schematically depicted in figure 1, it is supposed that the whole sample18

and the reference, and the corresponding metallic cells, may be represented by an unique19

temperature, being respectively TS and TR [1, 6, 8].20

Tplt

RS RR

TS TR

Figure 1: Schematic representation of the calorimeter with the homogeneous model (n.b. : the gap betweenthe cells and the plates is only here to highlight the existence of thermal resistances and is obviously notphysical).

.

Within this assumption, the heat flux measured corresponds to [1]:21

�(t) =Tplt � TS

RS| {z }�S

� Tplt � TR

RR| {z }�R

(1)

4

0pltT t Tβ= + ( )tφ

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités

40

peak

/ ~ t a n g e n t

"(~ l \ ~ l ~ \ l k extrQpatoted finol baseline I-~ samp[e meosuremen! curve , ~ ~ ' ~ . ' ~ _ ~ q , ~ / r

c_C~ ~ , n ; ~ , b a s e l i ~ b ' ~ finolis~ 7"c Tfin ~CI : I extropolofed inifiol J f I t . . . . c_

l isothermol i bosetine I L ,--. ~ J-- - - ~fropoloted isother. Tp oJ .__., I::1_ o linifiol b o s e - J _ _ . - p " - I " - 7 - 'inferpolol'ed isofherlnul hoseline tool fin.l boseline F:::

I~ I isothermol ~ __ ~ ~ jnferpolnfed isofh . . . . I . . . . line isel'hermul Tini ~iso sl. 0 itnitiot zero ~ - - [- - - I - - - " - - ' +

= " + i + ++o,+n+ ine zero line ~:x'fropototed isofher-

�9 ' ~ /st tool fmol zero line

tsf tini te tp tc /'fin fend

t ime t

Figure 14 a.Zerms to describe a measured curve and its characteristic times, illustrated by the example of a DSC curve with peak. Corresponding characteristic temperatures are assigned to the characteristic times. (Subscripts: st start, end end of temperature program).

step

('~ tangent ~ l / - - " l ~ a s u r e m e n t cur ve

extrapotofed finnl

--4---- CJ f-.-

�9 - " f ~ i ~ i n ilia[ bnseline o ...._.,

+ \ D r--

]"sf ~ni re TI/;P ~ ~in Tend

femperofure 7-

Figure 14b. Terms to describe a measured curve and its characteristic temperatures, illustrated by the example of a DSC curve with step. Corre- sponding characteristic times are assigned to the characteristic temperature. (Subscripts" st start, end end of temperature program).

5

DSC

Modedynamique

16/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités

6

DSC

Modeisotherme

16/03/2017

-5

-4

-3

-2

-1

0

1

hea

tfl

ow(m

W)

20

30

40

50

60

70

80

90

100

110

120

Tp

(C

)

10000 20000 30000 40000 50000 60000 70000 80000

time (s)

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités

7

DSC

Informa)onsliminaires§ Signaltemporel§ MéthoderelaSve:

§  ForteinfluenceéchanSllon(s)calibraSon§  DéfiniSonlignesdebase/zéro

§ Résultatsdépendants:

§  Masse§  Vitessedechauffe/refroidissement

16/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités

816/03/2017

Interpréta)on

916/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

Grandeursiden)fiables§ Températures

§  TransiSonsdepremipremièreèreespèce:Tonset§  TransiSonsdesecondeespèce:Tsolidus

§ GrandeursénergéSques

§  Capacitéscalorifiques(i.e.dansleszonessensibles)§  Chaleurlatente(i.e.variaSonsd’enthalpie)§  Enthalpie(enmodeisotherme)

§ Donnéescourante:latempératuredefusionetlachaleurlatenteImplicitement,onconsidèredoncuncorpspur...

1016/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

E. Franquet et al. / Thermochimica Acta 546 (2012) 61– 80 63

0.0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

[W]

-5 0 5 10 15Tp [ C]

Fig. 1. Experimental thermogram of a pure substance (water).

0

50

100

150

200

250

300

350

400

h(T)

[kJ/kg]

-2 -1 0 1 2 3 4 5 6 7 8T [ C]

0

50

100

150

200

250

300

350

400

-2 -1 0 1 2 3 4 5 6 7 8

Fig. 2. Comparison of the enthalpy profile obtained by a direct integration of thethermogram for a heating rate of 5 K min−1 (dotted red) and 2 K min−1 (dashed blue)with the exact enthalpy (black line) for a pure substance (water). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)

the enthalpy should be discontinuous for a pure substance1 butis instead smeared on several degrees (implicitly implying thanwater melts between 0 ◦C and 7 ◦C for the higher rate and between0 ◦C and 2 ◦C for the lower one). It is worth highlighting herethat this error will always be present, even at low heating rates,since the thermogram has always a non-zero width and there-fore cannot correctly describe a Dirac function. Usually, one seemsto accept such an approximation as long as the error is below0.5 K [10].

1 It also means than the derivative of the enthalpy is here a Dirac function, whichwas not present in the DSC curve.

0

5

10

15

20

25

30

35

40

[mW]

-20 -15 -10 -5 0 5 10Tp [ C]

Fig. 3. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 0.48%).

0

5

10

15

20

25

30

35

[mW]

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Tp [ C]

Fig. 4. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 9.02%).

Let us now deal with a binary solution, e.g. a H2O/NH4Cl samplewith a solute mass fraction x = 2.98%. This test is performed witha 11.9 mg sample still heated at a heating rate = 5 K min−1. Theexperimental thermogram is shown in Fig. 3. Usually, the eutec-tic temperature is obtained thanks to the onset temperature ofthe first peak, as for a pure substance. Then, an analog method,based on graphical projections on the baseline, is applied to thesecond peak in order to obtain the so-called liquidus temperature.Yet, this method leads to wrong estimations when the two peaksare closed together, as in the case of Fig. 4 where a greater massfraction was considered. Moreover, the raw determination of theenthalpy from the experimental thermogram still lead to spuriousresults [8], as shown in Figs. 5 and 6. In the first case, of a lowconcentration, the integrated profile is much more spread than theexact enthalpy and an offset of the liquidus temperature (i.e. endof the melting) of 2–5 ◦C is observed. Generally, the corresponding

1116/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

-5

0

5

10

15

20

25

30

35

'[m

W]

0 2 4 6 8 10

Tp [�C]

T ?/ TM

Limit ?

Area / LM

E. Franquet et al. / Thermochimica Acta 546 (2012) 61– 80 63

0.0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

[W]

-5 0 5 10 15Tp [ C]

Fig. 1. Experimental thermogram of a pure substance (water).

0

50

100

150

200

250

300

350

400

h(T)

[kJ/kg]

-2 -1 0 1 2 3 4 5 6 7 8T [ C]

0

50

100

150

200

250

300

350

400

-2 -1 0 1 2 3 4 5 6 7 8

Fig. 2. Comparison of the enthalpy profile obtained by a direct integration of thethermogram for a heating rate of 5 K min−1 (dotted red) and 2 K min−1 (dashed blue)with the exact enthalpy (black line) for a pure substance (water). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)

the enthalpy should be discontinuous for a pure substance1 butis instead smeared on several degrees (implicitly implying thanwater melts between 0 ◦C and 7 ◦C for the higher rate and between0 ◦C and 2 ◦C for the lower one). It is worth highlighting herethat this error will always be present, even at low heating rates,since the thermogram has always a non-zero width and there-fore cannot correctly describe a Dirac function. Usually, one seemsto accept such an approximation as long as the error is below0.5 K [10].

1 It also means than the derivative of the enthalpy is here a Dirac function, whichwas not present in the DSC curve.

0

5

10

15

20

25

30

35

40

[mW]

-20 -15 -10 -5 0 5 10Tp [ C]

Fig. 3. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 0.48%).

0

5

10

15

20

25

30

35

[mW]

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Tp [ C]

Fig. 4. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 9.02%).

Let us now deal with a binary solution, e.g. a H2O/NH4Cl samplewith a solute mass fraction x = 2.98%. This test is performed witha 11.9 mg sample still heated at a heating rate = 5 K min−1. Theexperimental thermogram is shown in Fig. 3. Usually, the eutec-tic temperature is obtained thanks to the onset temperature ofthe first peak, as for a pure substance. Then, an analog method,based on graphical projections on the baseline, is applied to thesecond peak in order to obtain the so-called liquidus temperature.Yet, this method leads to wrong estimations when the two peaksare closed together, as in the case of Fig. 4 where a greater massfraction was considered. Moreover, the raw determination of theenthalpy from the experimental thermogram still lead to spuriousresults [8], as shown in Figs. 5 and 6. In the first case, of a lowconcentration, the integrated profile is much more spread than theexact enthalpy and an offset of the liquidus temperature (i.e. endof the melting) of 2–5 ◦C is observed. Generally, the corresponding

E. Franquet et al. / Thermochimica Acta 546 (2012) 61– 80 63

0.0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

[W]

-5 0 5 10 15Tp [ C]

Fig. 1. Experimental thermogram of a pure substance (water).

0

50

100

150

200

250

300

350

400

h(T)

[kJ/kg]

-2 -1 0 1 2 3 4 5 6 7 8T [ C]

0

50

100

150

200

250

300

350

400

-2 -1 0 1 2 3 4 5 6 7 8

Fig. 2. Comparison of the enthalpy profile obtained by a direct integration of thethermogram for a heating rate of 5 K min−1 (dotted red) and 2 K min−1 (dashed blue)with the exact enthalpy (black line) for a pure substance (water). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)

the enthalpy should be discontinuous for a pure substance1 butis instead smeared on several degrees (implicitly implying thanwater melts between 0 ◦C and 7 ◦C for the higher rate and between0 ◦C and 2 ◦C for the lower one). It is worth highlighting herethat this error will always be present, even at low heating rates,since the thermogram has always a non-zero width and there-fore cannot correctly describe a Dirac function. Usually, one seemsto accept such an approximation as long as the error is below0.5 K [10].

1 It also means than the derivative of the enthalpy is here a Dirac function, whichwas not present in the DSC curve.

0

5

10

15

20

25

30

35

40

[mW]

-20 -15 -10 -5 0 5 10Tp [ C]

Fig. 3. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 0.48%).

0

5

10

15

20

25

30

35

[mW]

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Tp [ C]

Fig. 4. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 9.02%).

Let us now deal with a binary solution, e.g. a H2O/NH4Cl samplewith a solute mass fraction x = 2.98%. This test is performed witha 11.9 mg sample still heated at a heating rate = 5 K min−1. Theexperimental thermogram is shown in Fig. 3. Usually, the eutec-tic temperature is obtained thanks to the onset temperature ofthe first peak, as for a pure substance. Then, an analog method,based on graphical projections on the baseline, is applied to thesecond peak in order to obtain the so-called liquidus temperature.Yet, this method leads to wrong estimations when the two peaksare closed together, as in the case of Fig. 4 where a greater massfraction was considered. Moreover, the raw determination of theenthalpy from the experimental thermogram still lead to spuriousresults [8], as shown in Figs. 5 and 6. In the first case, of a lowconcentration, the integrated profile is much more spread than theexact enthalpy and an offset of the liquidus temperature (i.e. endof the melting) of 2–5 ◦C is observed. Generally, the corresponding

1216/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

0

50

100

150

200

250

300

enth

alpy

(Jk

g-1

)

40 50 60 70 80 90 100 110 120

temperature ( C)

0

50

100

150

200

250

300

enth

alpy

(Jk

g-1

)

40 50 60 70 80 90 100 110 120

temperature ( C)

1316/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

Erreur(très)courante

Enthalpies:h=h(β)§ Incohérencethermodynamique…§ Variabled’étatindépendanteducheminsuivi§ spécialistesobSennentdesvaleurséloignéesdecellesavancéesparlesfournisseurs(#10–47%)[Lazaro2006,Barreneche2013,Lazaro2016]

1416/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

0

50

100

150

200

250

300

350

400

h(T

)[k

J/k

g]

-2 -1 0 1 2 3 4 5 6 7 8

T [ C]

0

50

100

150

200

250

300

350

400

-2 -1 0 1 2 3 4 5 6 7 8

-50

0

50

100

150

200

250

300

350

400

h(T

)[k

J/k

g]

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0

T [ C]

1516/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

1616/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on

Inconnuessurcertainsparamètres

Modestep§ Paramétrageetinfluencedesdifférentssteps:

§  Intervalledetempérature§  Vitessedechauffe

§ Influencedubruitsurlesignal§ StabilitédescondiSonsopératoires(cyclecomplet#jour)

17

Modélisa)on

16/03/2017

18

Analysethéorique

Comportementdelacellule§ Présencedetransfertsthermiquespendantlechangementdephase

Erreurcommise§ Hypothèsedesuited’étatàl’équilibrefausselorsdelatransiSon

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

FT

plt FT T>

φ(t) ≅ φ(TP ) ≠dhdT

19

Modélisa)on/Simula)on

Solu)on§ Prendreencomptelesphénomènesdetransfertsthermiques§ Biland’énergiecompletdusystèmeenrégimeinstaSonnaire

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

Z zR

r

1α

2α2α2α

pltT

TP

r

z@⌦3

@⌦1

@⌦2

↵3

↵2

↵1

( ).h Ttρ

λ∂

= ∇ ∇∂

( )i i plt ii

S T Tφ α= −∑

20

Modélisa)on/Simula)on

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

21

Résultats

Influencedesparamètresdebase§ masse§ vitesse

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

-50000

0

50000

100000

150000

200000

250000

-5 0 5 10 15 20

0.5K/min 1K/min 2K/min 5K/min

10K/min 15K/min 20K/min

J/kg.K

Tplt

22

Résultats

Challengedesméthodesusuelles

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

-20

0

20

40

60

80

-20 -15 -10 -5 0 5 10

mW

TpltTonset

TMTE

-20

0

20

40

60

80

-20 -15 -10 -5 0 5 10

mW

Tplt

TE TM

(a)(b)

(c)

23

Résultats

Challengedesméthodesusuelles

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

�2 0 2 4 6 80

0.5

1

1.5

2·10�2

A

B

C

D

E

F

Tplt(�C)

�(W

)

Figure 8: Thermogram (red) and baseline (blue) for the water–L case.

23

24

Résultats

Challengedesméthodesusuelles

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

100

150

200

250

300

350

400

h(T

)[kJ/k

g]

260 270 280 290 300 310 320

T [�C]href (T ){Ti, hi}

106

107

"[�

]

1

2

5

10

2

⌧[hrs]

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

�T [K]

"⌧

5

106

"[�

]

2

5

10

⌧[hrs]

0 1 2 3 4 5 6 7 8 9 10� [K/min]

"⌧

25

Résultats

Analysedelafermeturethermodynamique

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

-100

0

100

200

300

400

500

h[kJ/kg]

255 260 265 270 275 280 285 290 295 300

T [K]

TMSolid

Melting

Liquid

LM

-50

0

50

100

150

200

250

300

350

h[k

J/kg]

-20 -15 -10 -5 0

T [ C]

TE

TM

26

Résultats

Analysedelafermeturethermodynamique

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on

16/03/2017

2716/03/2017

Caractérisa)on

2816/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Iden)fica)on:méthodesinverses

Combinaisonexp./num.§ MesuredufluxdechaleurenfoncSondutemps§ ModélisaSonetsimulaSondelacellulesollicitée

Couplage§ DéfiniSond’uncritèredecomparaison(foncSonobjecSf)§ ModificaSondesparamètresd’entrée,dontlesparamètresthermodynamiques,pourminimiserlafoncSonobjecSf

§  Simplex...§  AlgorithmesgénéSques

Mesure

ModèleDirect

Thermo

Réponse

Systèmeréel

Algorithmed’inversion

2916/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Processusd’inversion

3016/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Processusd’inversion

3116/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Processusd’inversion

3216/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Processusd’inversion

3316/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Processusd’inversion

3416/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Processusd’inversion

3516/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Résultats

Corpspurs

3616/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on

Résultats

Mélanges

-50

0

50

100

150

200

250

300

350

h(T

)[k

J/k

g]

-20 -15 -10 -5 0

T [ C]

x=10.0%

x=9.02%

x=5.0%

x=0.48%

37

Conclusion

16/03/2017

38

Conclusion

Méthodepra)que§ InformaSonsparcellaires§ Biaisdemesurecourant§ InterprétaSonerronée(très)répandue

Numériqueindispensable§ Meilleurecompréhensiondesphénomènesimpliqués,etdeleursconséquences§ ChallengeetamélioraSondesméthodesusuelles§ Aideàlamiseenplacedenouvellesméthodeset/ouprotocoles§ CaractérisaSonpluspoussée

§  Thermodynamiqueconsistante§  Touttypedeloid’état

Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onConclusion

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That’sallfolks

CONTACT

ErwinFRANQUET

LaTEP–IPRA/ENSGTI

erwin.franquet@univ-pau.fr

40

Annexes

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41Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onBibliographie

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[Albright2010]G.Albright,M.Farid,andS.Al-Hallaj.DevelopmentofamodelforcompensaSngtheinfluenceoftemperaturegradientswithinthesampleonDSC-resultsonphasechangematerials.JournalofThermalAnalysisandCalorimetry,101:1155–1160,2010[Barreneche2013]C.Barreneche,A.Solé,L.Miró,I.Martorell,A.I.Fernández,L.F.Cabeza.StudyondifferenSalscanningcalorimetryanalysiswithtwooperaSonmodesandorganicandinorganicphasechangematerial(PCM).ThermochimicaActa,553(0):23–26,2013[Brown1998]M.E.Brown,editor.Handbookofthermalanalysisandcalorimetry,volume1.PrinciplesandPracSce.Elsevier,1998.[Hohne2003]G.W.H.Höhne,W.F.Hemminger,andH.-J.Flammersheim.DifferenSalscanningcalorimetry.Springer,2ndediSon,2003[Lazaro2006]A.Lázaro,EvaGünther,H.Mehling,StefanHiebler,J.M.Marin,andB.Zalba.VerificaSonofaT-historyinstallaSontomeasureenthalpyversustemperaturecurvesofphasechangematerials.MeasurementScienceandTechnology,17(8):2168–2174,2006

42Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onBibliographie

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[Lazaro2013]A.Lázaro,C.Peñalosa,A.Solé,G.Diarce,T.Haussmann,M.Fois,B.Zalba,S.Gshwander,andL.F.Cabeza.IntercomparaSvetestsonphasechangematerialscharacterisaSonwithdifferenSalscanningcalorimeter.AppliedEnergy,109:415–420,2013[Richardson1997]M.J.Richardson.QuanStaSveaspectsofdifferenSalscanningcalorimetry.ThermochimicaActa,300(1-2):15–28,1997[Rudtsch2002]S.Rudtsch.UncertaintyofheatcapacitymeasurementswithdifferenSalscanningcalorimeters.ThermochimicaActa,382(1-2):17–25,2002[Sarge1994]S.M.Sarge,E.Gmelin,G.W.H.Höhne,H.K.Cammenga,W.Hemminger,W.Eysel.ThecaloriccalibraSonofscanningcalorimeters.ThermochimicaActa,247(2):129–168,1994[Sarge1999]StefanM.Sarge,EberhardGmelin,GuntherW.H.Hohne,HeikoK.Cammenga,WolfgangHemminger,andWalterEysel.ThecaloriccalibraSonofscanningcalorimeters.ThermochimicaActa,247(2):129–168,1994.

43Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onBibliographie

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[Utschick1988]H.Utschick,B.Gobrecht,C.Fleischhauer,A.Treffurth,andH.Müller.OnthecomplexinfluenceoftheexperimentalparametersandtheproperSesofthesubstancesontherepresentaitonofsolid-liquidtransiSonsstudiedwithadifferenSalscanningcalorimeter.J.ThermalAnalysis,33:297–304,1988

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