Marian PaluchCo-workers:

Ż. WojnarowskaK. GrzybowskaA. GrzybowskiK. KamińskiK. AdrjanowiczP. WłodarczykJ. Pionteck (Christian-Albrechts University of Kiel, Germany)

Univerity of Silesia, Poland

Entropic models

Thermodynamic scaling

VH is a popular pharmaceuticalmaterial correcting irregular heart beat and reducing blood pressure problems

Tg = 325 KTg = 325 K

Protic ionic liquid

10-1 100 101 102 103 104 105

10-2

10-1

Modulu

s''

frequency [Hz]

Isobar at 150 MPa

decreasing temperature

T = 2.5 K

T = 353.15 K

T = 383.15 K

10-2 10-1 100 101 102 103 104 105 106

10-3

10-2

10-1

Modulu

s''

frequency [Hz]

Isotherm at 383.15 K p = 25 MPa

increasing pressure

p = 0.2 MPa

p = 375 MPa

the structural(α-) relaxationthe structural(α-) relaxation

Dielectric measurements

20 40 60 80 100 120 140 160 180

0,82

0,84

0,86

0,88

0,90

0,92

T [°C]

Vsp

[cm

3 /g]

20 MPa

30 MPa

50 MPa

100 MPa

150 MPa

200 MPa

200 220 240 260 280 300 320 340 360 380 400 420 440 460

100

200

300

400

500

600

700

spec

ific

heat

(J/

K/m

ol)

Temp [K]

heating

Tg(P)

PVT measurements DSC measurements

Tτ = T(τ=5s)ΔCg(Tg) =0.52 J/gK

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

-3,2

-3,0

-2,8

-2,6

-2,4

-2,2

-2,0

-1,8

-1,6

-1,4

-1,2

-1,0

-0,8

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

-2,6

-2,4

-2,2

-2,0

-1,8

-1,6

-1,4

-1,2

-1,0

-0,8

log

M"

log frequency [Hz]

p=0.1MPa,T=325.15K

p=50MPa,T=332.15K

p=100MPa,T=343.15K

p=150MPa,T=353.15K

p=200MPa,T=363.15K

p=250MPa,T=365.65K

p=300MPa,T=373.15K

log frequency [Hz]

p = 0.1 MPa, T=325.15K p = 300 MPa, T=373.15K

log

M"

kww = 0.68

kww=0.61

The Kohlraush-Williams-Watts function

Time –Temperature – Pressure principle is not valid in case of VH

The α-loss peak becomes narrower with

compression !

320 330 340 350 360 370 380 390

-7

-6

-5

-4

-3

-2

-1

0

1

2

log

10[

(s)]

Isobars: p = 0,1 MPa

p = 50 MPa

p = 100 MPa

p = 150 MPa

p = 200 MPa

p = 250 MPa

p = 300 MPa

T [K]

= 1s

Effect of pressure on fragility

VFT equation: Isobaric fragility:

T=322.15K T=343.15K T=353.15K T=363.15K T=373.15K T=383.13K

-50 0 50 100 150 200 250 300 350 400

-7

-6

-5

-4

-3

-2

-1

0

1

log

10 [

(s)

]

p [MPa]

Activation volume:

Activation equation:

0 50 100 150 200 250 300 350320

330

340

350

360

370

380

0 50 100 150 200 250 300320

330

340

350

360

370

380

Tg

[K]

Pg [MPa]

= 5s

Tg from PVT

Tg [K

]

Pg [MPa]

T = const p = const

0 50 100 150 200 250 300 350

0,12

0,14

0,16

0,18

0,20

dT

g/d

P (

K/M

Pa)

Pressure (MPa)

2,6 2,7 2,8 2,9 3,0 3,1

-6

-4

-2

0

2

V=0,865 cm3/g

V=0,8675 cm3/g

V=0,87 cm3/g

V=0,8725 cm3/g

V=0,875 cm3/g

V=0,8775 cm3/g

log 1

0[(

s)]

1000/T [K-1]

Isobar at 0,1 MPa

322,80 K

328,41 K

333,22 K

338,52 K

344,23 K

348,13 K

Volume Temperature

0 EV/EP 1

1

logV

V

ET

1

logP

P

ET

activation energy at constant volume:

activation energy at constant pressure:

320 325 330 335 340 345 350 355 360 3650,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

E

V/E

p, T

gp

Tgp

Ev/Ep

T [K]

>>1

~ 1 comparable

0P

T dominate

V dominate

0 20 40 60 80 100 120 140 160 180 200 2201.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

p [MPa]

/

pThermal effects become more importent with increasing pressure

330 340 350 360 370 380 390

104

106

108

110

112

114

116

118

mT

T [K]

Isotherms: T=332.15K T=343.15K T=353.15K T=363.15K T=373.15K T=383.15K

0,90 0,92 0,94 0,96 0,98 1,00 1,02

-7

-6

-5

-4

-3

-2

-1

0

1

log

10(

s)]

Vg/V

Isothermal fragility decreases with the increase in temperature

0,82 0,83 0,84 0,85 0,86 0,87 0,88320

330

340

350

360

370

380

390

-9,0x10-2 -8,0x10-2 -7,0x10-2 -6,0x10-22,51

2,52

2,53

2,54

2,55

2,56

2,57

2,58

2,59

linear fit

Tg= aV

g

Tg [K

]V

g [cm3/g]

log

10[T

g/(K

)]

log10[Vg/(cm3/g)]

Isotherms: T=332.15K T=343.15K T=353.15K T=363.15K T=373.15K T=383.15K

3,4x10-3 3,6x10-3 3,8x10-3 4,0x10-3 4,2x10-3 4,4x10-3 4,6x10-3

-7

-6

-5

-4

-3

-2

-1

0

1

2

log

10[(

s)]

T-1V-

scaling exponent = 2.45

= 1s

Isobar at 0.1 MPa

0 20 40 60 80 100 120 140 160 180 200 2202,40

2,45

2,50

2,55

2,60

2,65

2,70

2,75

2,80

2,85

2,90

2,95

p [MPa]

I method

II method

The exponent γ is slightly dependent on pressure

m=3γ

γes = 11.09γ = 2.45

A. Grzybowski, M. Paluch, and K. Gryzbowski J. Phys. Chem. (2009)

0 50 100 150 200

0,86

0,88

0,90

0,92

Volu

me (cm

3/m

ol)

Pressure (MPa)

Isotherm at T=130 oC

0 50 100 150 200

2000

2500

3000

3500

4000

bulk

mod

ulus

Pressure (MPa)

Bulk modulus

γ = 10.7

A.N. Papathanassiou, Phys. Rev. E (2009)

The Avramov model is an entropic model

320

340

360

380

-6

-4

-2

0

2

4

6

0

100

200300

400

log 1

0[(s

)]

logτ0 = -9.9 ± 0.1

F0 = 6.9 ± 0.1

Π = 207 ± 6

C/cP = 0.172 ± 0.1

β = 0.91 ± 0.22

The fitting parameters:

Calculated:

From experiment:

0,82 0,84 0,86 0,88 0,90-7

-6

-5

-4

-3

-2

-1

0

1

2

332K 343K 353K 363K 373K 383K

log 10

[]

Volume (cm3/g)

1 bar

γG = 2.47 ± 0.1

D = 4.65 ± 0.2γG = 1.3

The fitting function:

where:

(a)

(b)

The fitting parameters:

Calculated from eq. (a)

R. Casalini, et. al. J. Chem. Phys (2006)

1. Taking into account the behavior of some properties like: the shape of relaxation function of the α-relaxation, isothermal fragility or pressure dependence of γ, VH (and probably other glass-forming liquids which belong to the same class of materials as VH) cannot be counted among strongly correlating systems.

2. The relationship between dynamic and thermodynamic properties established within entropy Avramov model is not supported by experimental data of VH