Marian Paluch Co-workers: Ż. Wojnarowska K. Grzybowska A. Grzybowski K. Kamiński K. Adrjanowicz P....
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Transcript of Marian Paluch Co-workers: Ż. Wojnarowska K. Grzybowska A. Grzybowski K. Kamiński K. Adrjanowicz P....
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