Post on 15-Dec-2015
Soft bend elastic constant and transition to a modulated nematic phase
Alenka Mertelj,1 Martin Čopič,1,* Geoffrey R. Luckhurst2, R. P. Tuffin3, and Owain Parri3
1Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
2School of Chemistry, University of Southampton, Southampton SO17 1BJ, UK 3Merck Chemicals Ltd, Chilworth Technical Centre, University Parkway, Southampton SO16
7QD, UK
Outline
• Observation of modulated phase in nematic phase of flexible dimers
• Nematic fluctuations and dynamic light scattering
• Temperature and order parameter dependence of elastic constants
• Conclusions
Modulated nematic phase
• Observed in flexible dimers of biphenyls like 1,7-bis(4-cyanobiphenyl-4-yl)heptane (CB7CB) and CB9CB [1], or CB11CB[2]
• I.Dozov [3] proposed that a softening of the bend elastic constant could lead to a modulated nematic phase with nematic director forming a twist-bend helix
• In [2] it was suggested that in CB11CB the modulation is due to soft splay elastic constant
• Numerical modeling of A. Ferrarini indicates that bend elastic constant in dimers can become negative
[1] M. Cestari et al., Phys. Rev. E 84, 031704 (2011)
[2] V. P. Panov et al., Phys. Rev. Lett.105, 167801 (2010).
[3] I. Dozov, Europhys. Lett. 56, 24 (2001).
Observed modulation under polarized microscope
Structures proposed by Dozov
Dozov’s model
2
2
2
2
3
2
2
2
2
2
2
2
12
32
22
1 4
1
2
1zjzji n
dz
dCnn
dz
dCnn
dz
dCKKKF bts
1
3332
1
320 27
,3
,3
4
CK
KF
C
Kk
K
Ksb
Splay-bend phase:
2
3332
2
320 54
,3
,2 CK
KF
C
Kk
K
Ksb
Twist-bend phase:
If 21 2KK
then twist-bend is the stable phase
Microscope observation - thin cell (8 m)
n
Microscope observation – thick cell (20 m)
n
Light scattering
• Elastic constants can be measured by observation of thermal director flucutations
• Relaxation rates give ratios Ki/ηi
• Scattering intensity gives (ε)2/Ki
• As ε is proportional to S, we get Ki /S2
• Ki /S2 are lowest order “bare” elastic coefficients in Landau-deGennes free energy
Bend
Splay
Twist
n/ ti ee rqn0
nqn
n q0( )nB
n
2
2k T
K q
Nematic fluctuations
Relaxation rates
2,1,1 2
32
iqKqK
i
zi
i
czzb
z
qqqq
45431
224
22
23
2
11 )(
)(
cza
z
q
222
2
12
Two modes: bend-splay and bend-twist, for q along n – pure bendRelaxation rates:
Effective viscosities:
Usually α2 >> α3, so that bend viscosity is smaller due to backflow
• The direction and polarization of the incoming and scattered light and n determine which mode is observed
Samples
NC (CH2)x CN X=7,9 - CB7CB and CB9CB
• CB7CB : TNI = 116 oC, TNX = 103 oC
• CB9CB : TNI = 124 oC, TNX = 109 oC
• Planar orientation
CB7CB diffusivities (K/η)
102 104 106 108 110 112 114 1160.0
2.0x10-11
4.0x10-11
6.0x10-11
8.0x10-11
1.0x10-10
Bend Twist Splay
Ki/
i(m2 /s
)
Temperature
CB7CB
Note increase in the splay diffusivity below TNX
CB9CB diffusivities (K/η)
106 108 110 112 114 116 118 120 122 124 1260.0
2.0x10-11
4.0x10-11
6.0x10-11
8.0x10-11
1.0x10-10
1.2x10-10 Bend Splay Twist
File: DLS_CB9CBcorT.org, 11-Aug-12 Window: Diff
Ki/
i(m2 /s
)
Temperature (oC)
Note increase in the splay diffusivity below TNX
Normalized “bare” elastic constants
102 104 106 108 110 112 114 116
1
Bend Bend Twist Splay
Ki/S
2
Temperature
CB7CB
T=116oC:K
1>K
2>K
3,
K1/K
2 2.8
K2/K
3 2.3
106 108 110 112 114 116 118 120 122 124 1260.1
1
10 Twist Bend Splay
Ki/S
2
Temperature
CB7CB CB9CB
• Absolute scattering cross-sections is difficult to measure, so we obtain only T dependence of Ki relative to the value at TNI
• The bend constant softens, but increases just above TNX
• The splay constant increases below TNX , also seen in diffusivity
“Bare” elastic constants – linear scale
102 104 106 108 110 112 114 1160.0
0.5
1.0
1.5
2.0
Bend Bend Twist Splay
Ki/S
2
Temperature
CB7CB
106 108 110 112 114 116 118 120 122 124 126
0.5
1.0
1.5
2.0 Twist Bend Splay
Ki/S
2
Temperature
CB7CB CB9CB
Ki are normalized to 1 at TNI.
CB9CB: True K3
• The increase close to TNI is due to S2
104 106 108 110 112 114 116 118 120 122 1240.12
0.15
0.18
n
T
108 110 112 114 116 118 120 122 124 126
0.4
0.6
0.8
1.0
1.2
K3/K
3(TN
I)
Temperature• Δn measured by
polarization interference• Δn is proportional to S
True elastic constants of CB9CB.
-16 -14 -12 -10 -8 -6 -4 -2 00
1
2
3
4
5
Ki
T-Tc [K]
Values are relative to the values at TNI. Black squares - splay, green triangles – twist, red circles – bend.
Mixture of dimers
The phase diagram for a mixture of KA and the liquid crystal dimer, CBF9CBF
Elastic constants of mixture
Elastic constants of mixture by Frederiks transition
Minimum K3 =0.63 pN – by light scattering 0.3 pN
Relation to cubic invariants
jkliklij QQQC ,,1 ljlkikij QQQC ,,2 ljklikij QQQC ,,3
)22(3/1 321)3(
1 CCCK
)2(3/1 31)3(
2 CCK
)4(3/1 321)3(
3 CCCK
•To quadratic order in gradient of Q splay and bend constants are equal.
•Cubic invariants that contribute to the elastic constants are
Values of third order coefficients
0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.160.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Ki/
n2
n
K3 K2 K1
0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.140.0
0.5
1.0
1.5
2.0
Ki /
n2
n
Ki/S2 as functions of Δn for CB7CB (left) and CB9CB (right).
C1 negative, C2 and C3 about 0
•Transition seems to be driven by increase in S
Problems
• Bend constant increases just before the transition to Nx phase – Bent core molecules also have small bend constant,
but go to Sm phase – perhaps the increase of K3 due to competition with smectic order
• Standard methods based on Frederiks transition give
smaller decrease of the bend constant
Conclusions
• Bend elastic constant in the nematic phase of flexible dimers dramatically decreases with T and is probably the cause of an instability resulting in the modulated phase
• Just above the transition K3 slightly increases – effect of pretransitional fluctuations?
• Below the transition light scattering corresponding to splay fluctuations strongly decreases – analogy with SmA phase?
F
O
F
O
FF
F
N
FN