Post on 29-Mar-2020
High Pressure Investigations
of Liquid Crystals
– a Challenge to Experiment and Theory
Stanisław Urban
M. Smoluchowski Institute of Physics
Jagiellonian University
Krakow, Poland
27th Janik’s Friends Meeting
Zakopane, 10–17 July, 2011
Outline
Introduction
Phase transitions
Entropy separation at the clearing line
Molecular dynamics in different phases
Thermodynamic scaling of dynamical quantities
Summary
Remarks on the profits and difficulties of investigation
under elevated pressures
External pressure applied to a molecular system influences its physical
properties considerably. This is due to relatively weak intermolecular interactions.
Pressure (P) and temperature (T) are equivalent thermodynamic variables, but
they act on the molecular systems differently: T influences mainly excitations of the
rotational and vibrational energy levels whereas P changes mostly the
intermolecular distances.
In liquid crystals (LC) constituted of strongly anisotropic molecules the
interaction potential consists of a distant dependent and orientation dependent parts.
This causes that pressurization may change the phase diagrams, the molecular
ordering within a given LC phase as well as practically all physical properties of a
substance, quite easily. Moreover, a relatively low hydrostatic pressures (up to, say,
hundreds MPa) are sufficient to involve considerable changes of the properties of a
LC system.
The main advantage of the pressure studies of a molecular system arises from
the fact that a given property can be analysed at the isobaric, isothermal and
isochoric conditions which yields much more information than the usual ambient
pressure studies in function of temperature.
Especially important is a possibility of determining the parameters
characterising the interaction potentials in the LC phases.
Measurements under pressure - main difficulties
- Problems connected with the separation „sample - pressurizing medium”
- Measurements can hardly be automated
- Relatively big amounts of samples needed
- Frequent demaging of aparatus parts
- Measurements are time consuming
- Poor theoretical background
Albert Würflinger – Ruhr University Bochum
Mike Roland – Naval Research Laboratory, Washington
Strategy of hp investigations
Selection of samples
Determination of the T(P) phase diagram
Determination of the equation of state V(P,T)
Determination of the dynamical properties of molecules in particular
LC phases
Common analysis of the results with the aim to obtain information about
fundamental properties of the system studied (eg. interaction potential);
the theoretical models are needed.
Substances studied
Two-ring core
Ph-Ph
Cy-Ph
Cy-Cy
Dio-Ph
Pyr-Ph
Tail
Alkyl
Alkoxy
Strong polar group
CN
NCS
Variety of phase sequences
0 50 100 150 200 25040
60
80
100
120
140
Isotropic
Sm A
Crystal I
N
Crystal II
Tc = 77,75 + 0,237xp - 4.64x10
-5xp
2
TS-?
= 95,71 + 0,098xp + 1.58x10-4xp
2
Tm = 59,31 + 0,270xp - 2,49x10
-4xp
2
Tcr = 42.45 + 0,235xp - 2,39x10
-4xp
2
10DBT
T [oC]
P [MPa]
0 50 100 150 200 250320
340
360
380
400
H9C4 OC6H13
CN CN
C O
O
Cr
Sm A
Is
CNCN
T [K]
P [MPa]
S.Urban, A. Würflinger, Z. Naturforsch. 56a, 489 (2001)
A. Würflinger, S.Urban, PCCP 3, 3727 (2001)
0 50 100 150 20040
60
80
100
120O
O
H2n+1Cn NCS
Crystal II
Crystal I
Isotropic
Sm A
8DBT
T [oC]
P [MPa]
0 50 100 150 200300
320
340
360
380
400
(344K, 66MPa)
Cr
SA
N
Is
10CB
T / K
p / MPa
0 50 100 150 200 250300
320
340
360
380
400
11CB
T / K
Cr
SA
Is
N
(382K, 182MPa)
p / MPa
S. Urban, et al., Liq. Cryst., 30, 313-318 (2003).
0 50 100 150 20040
60
80
100
120
H11C5O C C NCS
F
TOLF5
Cr - 52.0o C - N - 65.4oC - Is
TNI
64.9 + 0.310xp -2.58x10-4
p2
Tm 52.4 + 0.263xp -2.59x10
-4p
2
Tfr 49.2 + 0.227xp -1.08x10
-4p
2
Cr
N
IsT / oC
P / MPa
0 20 40 60 80 100 120 140 160 180 20040
50
60
70
80
90
100
110 95oC
107MPa
9BT
Cr
E
I
T/ 0C
P / MPa
A?
9BT
CrE
100 MPa
N
0 20 40 60 80 100 120 140 160
30
40
50
60
70
80
90
100
110
10BTN?
A?
CrI
E
p [MPa]
T [oC]
55MPa
78oC
101MPa
91oC
I
E A
N
S.Urban, J. Czub, A. Würflinger
Phase Trans. 79, 331 (2006).
Y. Maeda, S.Urban,
Phase Trans. 83, 467 (2010).
88 92 96 100 104
20
24
20
24
20
24
20
24
20
24
20
24
T [oC]
148MPa
U[V]
138MPa
130MPa
122MPa
114MPa
106MPa10BT
70 80 90 10010
15
20
25
30
35
10
15
20
25
30
Cr
IsE
128.6MPa
T / oC
A?
100.2MPa
ECr
Is
9BT
0 20 40 60 80 100 120 140 160 180 20030
40
50
60
70
80
90
100
110
120
Sm E"
H13C6 C6H13
Sm E'
Cr
Sm ESm Bcr
Is
C6-C6
T [oC]
P [MPa]
S.Urban, M. Massalska-Arodz, A. Würflinger, K. Czuprynski,
Z. Naturforsch. 57a, 641 (2002)
• A common feature of smectogenic members is an appearance of splitting of the clearing lines at elevated pressures.
• With increasing the pressure at first the long-range molecular arrangement within the layer is canceled, and then the layer structure is canceled leading to the nematic or isotropic phase.
• The length of the alkyl tail(s) play important role in that effects.
nCB
nPCH
nCCH
nCHBT
nBT
The role of the length of terminal group(s) and a flexibility of the core
should be explained.
The slope of the clearing line
0,2
0,3
0,4
0,5
1011
12
nCB AI
Slo
pe
[K
/MP
a]
nBT EI
6C
HB
T N
I 8765
4 nPCH NI
5C
CH
NI
5P
CH
NI
5C
B N
I
3
6P
CH
NI
6O
CB
NI
6C
B N
I
87
65
4 14
n
The mean-field theories predict that
TNI (P)VΓNI (P) = const
Γ – material constant that reflects the volume dependence of the orientational
contribution to the internal energy, without a priori assumption about the
nature of anisotropic intermolecular potential; larger Γ implies stronger steric
repulsion relative to the attractive interactions.
Equation of state V(p,T) must be known!
)(log
)(log
PVd
PTd
NI
NI
The slope of the clearing line
vs. interaction potential
])()[()( 63
0rr
r
-0,015 -0,010 -0,005 0,000
2,50
2,52
2,54
2,56
2,58
log
( T
c /
K)
log(Vc [ml/g])
=5.03 0.02
log ( )
log ( )
c
c
d T P
d V P
6CHBT
-0.025 -0.020 -0.015 -0.010 -0.005 0.0000.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
6OPB8
log(VNI
/V0)
log
(TN
I/T0)
= 2.51 ± 0.2
-0,06 -0,04 -0,02 0,000,00
0,05
0,10
0,15
0,20
E - I
5BT = 2.2
6BT = 2.4
7BT = 2.2
5CB = 5.3
6CB = 6.3
7CB = 4.7
ln (V/Vo)
ln (
T/T
o)
N - I
nCB
nBT
N
N
O
The transition “LC phase – isotropic liquid” is a (usually weakly) first order phase
transition and is characterised by the entropy ΔStr constituting of two contributions:
a constant volume (or configurational) part ΔSconf and
a dilational part ΔSdil
ΔStr = ΔSconf + ΔSdil
PVT data enable us to separate both contributions:
ΔStr = ΔSconf + (∂S/∂V)TΔVtr
= ΔSconf + (∂P/∂T)VΔVtr.
Combining this expression with the Clausius-Clapeyron equation,
(∂P/∂T)tr = ΔStr/ΔVtr
one gets
ΔSconf = [(∂P/∂T)tr – (∂P/∂T)V ]ΔVtr
or ΔSconf /ΔStr = [(∂P/∂T)tr – (∂P/∂T)V ]/(∂P/∂T)tr.
Entropy separation at the clearing point
0
40
80
120
160
200
0 20 40 60 80 100 120 140
Crystal Nematic Isotropic
6CHBT
1.0150.995
0.980cm3/g0.950cm
3/g
T [oC]
P [
MP
a]
0 20 40 60 80 100 120 140
0,88
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
10MPa20
30 40
50 60
7080 90
100120 140
160
Vs
[cm
3/g
]
T [oC]
6CHBT - Isobars
ambient pressure
180MPa
0 50 100 150 200 2500,0
0,2
0,4
0,6
0,8
1,0
6CB N - I
6DBT A - I
6CHBT N - I
S
conf /S
tr
P [MPa]
6BT E - I
H13C6
NCS
ΔSconf /ΔStr = [(∂P/∂T)tr – (∂P/∂T)V ]/(∂P/∂T)tr.
Molecular dynamics in LC phases
Typical dielectric absorption spectra
103
104
105
106
107
0,00
0,05
0,10
0,15
0,20
0,25
0,30
6OPB8
T = 328 K
10MPa
18
25
33
40
63
70
93
116
130
145
"
f / Hz
104
105
106
107
0,0
0,1
0,2
0,3
0,4
a)
p = constant = 1 atm
62.9oC N
60.5
58.1
54.6 SA
51.0
47.3
43.7 SC
37.5
32.6 "
f / Hz
N
N
O
T = constant
τ|| = 1/(2πfmax), where fmax corresponds to ε”max
J. Czub, et al. Z. Naturforsch., 58a, 333 (2003)
10-5
10-4
10-3
10-2
10-1
100
101
102
103
10-3
10-2
10-1
100
10-3
10-2
10-1
100
"/" m
ax
f/fmax
T=64.0C
6BT
Debye
"/" m
ax
P=0.1MPa
Representative dielectric loss curves
for 6BT
C.M.Roland, et al. J. Chem. Phys., 128, 224506 (2008) 2,9 3,0 3,1 3,2 3,3 3,4
0,0
0,1
0,2
'
"Sm A
38.60C
6OPB8
105
106
107
0
1
2
3
4
5
6
307 K
309.7
312.2
315.2
f [Hz]
"
7PCH
1 atm
a
105
106
107
0
1
2
3
4
5
6b
20 MPa
60
100
120
7PCH
336 K
"
f [Hz]
2,7 2,8 2,9 3,0 3,1 3,2 3,310
-8
10-7
266 cm3/mol
1000/T [K-1]
1 atm
60 MPa
260 cm3/mol
|| [s]
7PCH
a)
0 50 100 150 200
255 260 265 2700
10
20
30
40
50
60
70
b)
#H
U
P [MPa]
U
,
H [
kJ/m
ol]
Vm [cm
3/mol]
7PCH
VT
pTUH
TRU
TRH
pRTV
V
V
p
T
###
1#
1#
#
)(
)/ln(
)/ln(
)/ln(
0 40 80 120 160 200 240
10-8
10-7
1.2410-7s 1.5810
-7s
384K
P / MPa
1.0710-8s
312K
7PCH
|| [s]
#H/#U 2
Thermodynamic scaling of the dynamical quantities
It was demonstrated by Roland and co-workers that the structural
relaxation times and viscosity measured as function of P, T and V can
be rescaled to one master curve with one adjusting parameter using
the simple exponential form
τ = A exp(B/TVγ) (A,B,C,D – constants)
η = C exp(D/TVγ)
The same was done by me for ~20 LC phases.
2,8 2,9 3,0 3,1 3,2 3,3 3,4-15,5
-15,0
-14,5
-14,0
-13,5
-13,0
-12,5
-12,0
1000/(TV)
6OPB8
c)
ln ( [s])
= 2.7 ± 0.1
N
N
O
Cr – SmC – SmA – N – I
S. Urban, C.M. Roland, J. Czub, K. Skrzypek, J. Chem. Phys, 127, 094901 (2007)
0 20 40 60 80 100 120 140 160 180 200-15,5
-15,0
-14,5
-14,0
-13,5
-13,0
-12,5
-12,0
2,85 2,90 2,95 3,00 3,05 3,10 3,15 3,20-15,5
-15,0
-14,5
-14,0
-13,5
-13,0
-12,5
-12,0
ln
p / MPa
313.3K
323.0K
332.2K
342.2K
346.2K
1000/T / K-1
ln
0.97
0.98
0.99
1.00
1.01 cm3/g
160 MPa
120
80
40 Δ #U /Δ # H ~53/78 ~0.68 SmA
~46/68 ~0.68 SmC
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.210
-8
10-7
10-6
10-5
10-4
6CHBT N
=5.07CB N
=3.3
7PCH N
=3.9
6OPB8 SA,C
=2.7
8BT SE
=4.1
T=const
p=const
V=const
1000/(TV)
[s]
4
8
12
4
8
12
1,02 1,04 1,06 1,08 1,10 1,12
4
8
12
333 K
343 K
353 K
363 K
373 K[
mP
a]
5PCH
2
7PCHIsotropic
3PCH
Vm [cm
3/g]
1,6 1,8 2,0 2,2 2,4 2,6
0,2
0,4
0,6
0,8
1
1000/TV
Isotropic
7PCH
*= 4.0
5PCH
*= 3.9
3PCH
* = 3.9
2,2 2,4 2,6 2,8 3,0 3,2
0,5
1
1,5
1000/TV
5PCH
*= 4.0
*
Nematic
3PCH
*= 4.2
7PCH
*= 3.8
1,6 1,8 2,0 2,2 2,4 2,6
5
10
15
20
333 K
343 K
353 K
363 K
373 K
[
mP
a]
1000/TV
3PCH
= 4.6
5PCH
= 4.57PCH
= 4.4
Isotropic
2,2 2,4 2,6 2,8 3,0 3,25
10
15
20
25
30
35
1000/TV
[
mP
a]
3PCH
= 4.8
5PCH
= 4.3
323 K
333 K
343 K
353 K
363 K
7PCH
= 4.1
Nematic
0,96 0,98 1,00 1,02 1,04 1,06 1,085
10
15
20
10
20
30
10
15
202530
3PCH
Vm [cm
3/g]
5PCH
CN
H15C7
7PCH
[
mP
a] 323 K
333 K
343 K
353 K
363 K
Nematic
2,2 2,3 2,4 2,5 2,6 2,7 2,810
-8
10-7
10-6
[s]
*
1000/TV
7PCH
= 3.9
* = 4.1
2.4 2.5 2.6 2.7 2.8 2.9 3.0
10-8
10-7
10-6
* = 3.8
= 3.6
1000/TV
5PCH
[s]
*
τ* = υ -1/3(kBT/m)1/2τ ~ Vm -1/3T 1/2 τ
* = υ 2/3(kBTm)-1/2 ~ Vm 2/3T -1/2
D. Fragiadakis and C.M. Roland, J. Chem. Phys.2011, 134, 044504.
S. Urban, Liq. Cryst., accepted
The question arises whether the three material constants, , τ and , can simply be compared.
The parameter characterises the thermodynamic phase transition
whereas the two others concern two different aspects of the dynamic
behaviour of molecules within the nematic phase. In fact, there is no a
theoretical basis for discussion a connection of the thermodynamic
conditions associated with the nematic – isotropic transition (or other
transitions) and the time scale of the flip-flop molecular motions in the
nematic phase.
The question arises whether the three material constants, , τ and , can simply be compared.
The parameter characterises the thermodynamic phase transition
whereas the two others concern two different aspects of the dynamic
behaviour of molecules within the nematic phase. In fact, there is no a
theoretical basis for discussion a connection of the thermodynamic
conditions associated with the nematic – isotropic transition (or other
transitions) and the time scale of the flip-flop molecular motions in the
nematic phase.
However, one can speculate about that taking into consideration some
experimental facts and well known relationships:
(i) and τ values were found to be identical or close for many LCs
hitherto studied.
Substance Nematic phase Isotropic phase
τ τ* * * 3PCH - - 4.8 4.2 5.0 4.6 3.9 5.0 5PCH 3.6 3.8 4.3 4.0 4.1 4.5 3.9 4.1 7PCH 3.9 4.1 4.1 3.8 3.8 4.4 4.0 3.8
Accuracy 0.15
The data determined from the calorimetric DTA, PVT and dielectric spectroscopy studies of liquid crystalline substances in
different phases. The activation parameters ΔH, ΔU and ΔV exhibit some changes within a given phase and were taken in a
mid part of the phase.
Substance Tc
[K]
∂Tc/∂P [K/MPa]
Phase ΔH [kJ/mol]
ΔU [kJ/mol]
ΔV [cm3/mol]
ΔU/ΔH Exper. Eq. (5) Eq. (12)
γ Г 104αP [1/K]
-104ατ [1/K]
-ατ/ αP
5CB 308.3 0.424 N 62 38 59 0.61 0.48 0.54 4.1 5.3 6.8 6.3 0.919
6CB 301.2 0.390 N 62 27 63 0.44 0.54 0.54 4.1 6.3 7.0 8.1 1.15
7CB 314.6 0.370 N 64 30 63 0.47 0.52 0.53 3.3 4.7 8.5 9.2 1.15
8CB 313.8 0.370 N, A 60/40 32/24 60/38 0.53/0.57 0.50 0.50 4.2 4.0 7.7 7.7 1.00
5PCH 328.1 0.440 N 69 39 70 0.57 0.59 0.58 3.5 5.2 6.3 9.0 1.42
7PCH 331.0 0.420 N 70 35 65 0.50 0.51 0.52 3.9 3.3 7.1 7.3 1.03
8PCH 328.3 0.412 N 70 36 60 0.51 0.58 0.56 3.6 3.4 6.7 9.2 1.37
6CHBT 316.7 0.419 N 63 33 65 0.52 0.54 0.52 5.0 5.0 5.8 6.8 1.174
6DBT 350.1 0.259 A 51 20 42 0.40 0.41 0.43 4.0 2.9 9.4 6.6 0.72
6OPB8 339.2 0.234 A, C 79/69 52/46 58/45 0.66/0.66 0.61 0.61 2.7 2.5 7.0 11.1 1.63
5BT 347.1 0.284 E 2.3 2.2
6BT 344.7 0.285 E 3.1 2.4
7BT 345.6 0.241 E 2.3 2.2
8BT 341.1 0.237 E 70 36 59 0.51 0.47 0.48 4.1 2.7 7.4 6.60 0.90
0 20 40 60 80 100 120 140 160
-8.0
-7.5
-7.0
-6.5
-6.0
8CB
7CB
60PB8
6CB
7PCH
60PB8
log
(
/s)
P [MPa]
0 50 100 150 200
0,6
0,8
1
1,2
1,4
1,6 Nematic
Isotropic
7PCH
[m
Pa]
P [MPa]
323 K
333
343
353
363
373
383
TNI
0 40 80 120 160 200 240
10-8
10-7
1.2410-7s 1.5810
-7s
384K
P / MPa
1.0710-8s
312K
7PCH
|| [s]
0 40 80 120 160 200 240300
320
340
360
380 7PCH
Cr
N
P / MPa
T [K]
I
It seems that the constancy of both
dynamical quantities at Tc is well fulfilled.
(ii) The relaxation time τ||(Tc) is independent of pressure and volume. {The same
concerns the structural relaxation times along the characteristic temperature-pressure
lines in glass-formers}.
(iii) The nematic order parameter S is constant along Tc(Pc).
(iv) The relaxation time τ|| is directly related to S via the so-called
retardation factor which in turn depends on the Maier-Saupe strength
parameter :
g = τ|| /τo ~ υ(V) S
Taking the above into consideration one can state
that , τ and should be the same if τ|| (and ) are
constant along the clearing line.
Conclusions
Pressure studies are indispensable for discussing the interaction potentials.
The thermodynamic potential parameter, Γ, measuring the variation of the interaction
energy with volume is associated with the stability limits of the ordered state.
The scaling parameter, γ, reflects the volume dependence of the dynamical quantities
within the whole range of a LC phase.
Equivalence of both parameters affirms the connection between the longitudinal
dynamics and the repulsive part of the interaction potential.
The fact that the thermodynamic conditions associated with the stability limits of the
ordered state bear a direct relationship to the time scale of molecular rotations is
unanticipated by any model and should guide theoretical progress in this class of
materials.
Large values of the scaling parameters (Γ and γ > 3, say) implies that the intermolecular
potential for LCs can be approximated as a repulsive inverse power law with the weaker
attractive forces treated as a spacially-uniform background,
U(r) ~ r -Γ + const
Thank you for
your attention
Predicted hp studies:
• substances with another phases (C, B, N*, …)
• substances forming the glassy state
• stimulation of theoretitions for developing appropriate models
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0 2 4 6 8
14
13
12
10
11
897
6 5
4
32
U
/H
1
1 5CB N
2 6CB N
3 7CB N
4 8CB N
5 8CB A
6 5PCH N
7 7PCH N
8 8PCH N
9 6CHBT N
10 6DBT A
11 6OPB8 A,C
12 6BT E
13 8BT E
14 5*CB Is
U/H=1/(1+0.18)
The parameter provides a measure of the
relative importance of V as opposed to T.
For strictly activated dynamics, in
which thermal energy dominates the
behavior, = 0, whereas for the hard
sphere limit .
Typical LC phases
Liq
uid
-like p
hase
s C
rysta
l-like p
hase
s