Refers to a change of state induced by changing temperature or pressure (or volume) from one thermodynamic equilibrium to another

Refers to the time required to respond to the time required to respondTo a change in temperature or pressure (or volume). It also implies Some measure of the molecular motion, especially near a transition Condition. Frequently, an external stress is present permitting the re-Laxation to be measured

Refers to the emission or absorption of energy – that is a loss peak – at a transition

heat fluxorcp

poly(dimethyl siloxane) (PDMS)

•glass transition•enthalpy relaxation•cold crystallization•melting

i

i

in

c

c

Hd

n

HdH

ddnnn

dTT

HdH

dnn

Hdp

p

HdT

T

HdH

i

i

i

p

p

n

iii

pT

n

i nTpiipT

iiiii

c

npnp

n

ii

nTpinTnp

i

ij

p

i

i

ijii

componenttheofpotentialchemical

reactionofextend

reactionaincomponenttheoftcoefficientricstoichiome

component substanceofamount

capacityheatmolar

capacityheatspecific~

1

reaction ofenthalpy aldifferenti

,1 ,,

,

0

,,

1 ,,,,

TdcHT

Hc p

pp

~~

Qt

Q

t

H

t

Tc

dHdTc

iii npnpnpp

p

,,,

~

~

T

t

T(t)slope:

*~

~1

*

:abovefromand

*

m

QcQ

ct

Tm

t

Tm

ppp

p

Cp can be calculated from the heat fluxQ

Q is determined by the exactness of the signalM*is determined by the exactness of the program rates

Consequently, a correction is needed that is independent ofthe parameters of the instrument:

samplesapphire

samplesample

sapphire

sample~

~

mQ

mQ

Q

Q

c

c

p

p

M. J. O`Neill, Anal. Chem. 38 (1966) 1331

transtransppp

HTTcT

H

t

Q

~

Tg, Tm, Tcr, TS-N, TSA-SC,…TN-I…

Classification of the thermodynamic transitions according to Paul Ehrenfest*):

Discontinuity the derivative (1st, 2nd,…) of the Gibbs function G

*)Ehrenfest P Proc Kon Akad Wetensch Amsterdam (1933) 36, 153

dHdG

dnn

Gdp

p

GdT

T

GdG

SdTTdSdHdGTSHG

ST

n

i

i

npi

V

nT

S

np

i

ijii

,

1 ,,,

First Order Transitions

In a real experiment heat transfer requires time and a temperature gradient

and this is what we actually see:a (endothermal) melting peak

cmmm TTTT 00

thermodynamic equilibrium melting temperature

experimental melting temperature

isothermal crystallization temperature

stability parameter

1cm

TT0

mmTT

cmmTTT

intercept

01

slope

0

mT

mT

cT

unstableTcT

stablemostTT

m

mm

1

0 0

case commonmost theis5.0

J. D. Hoffman, J. J. Weeks, J. Res. Bureau Standards 66A (1962) 13 *(solution crystl.)

Hoffman & Weeks Plot*Hoffman & Weeks Plot*

Volume

Enthalpy

Storage modulus

At the glass transitionExpansivity

Heat capacity

Loss modulus

T

Vspec

Hspec

(dV/dT)~ (dH/dT)p= cp

TcrTg1

Tg2

high cooling rate CR1

low cooling rate CR2

Ti2 Tg2 Te2

Tg1

Calculation of Tg according toM. J. Richardson, N. G. Savill, Brit. Polym. J. 11 (1979) 123

Tg determined independent of the heating rate

integration

time