olecular level models for liquid crystals

1. Tailoring Molecular Organizations in Liquid
Crystals. Simulations and Reality
8th European Conference on Molecular Electronics – ECME8
CNR, Bologna, 29 June - 2 July, 2005
Claudio Zannoni
https://claudiozannoni.it/index.htm
ORCID 0000-0002-7977-1005

2. Liquid crystals provide a variety of self-
assembled molecular organizations

3. Molecular
Orientation Order
Molecular Position
Order
Molecular
Organization
Yes
(3D)
Yes
Crystals
Yes
(2D)
Smectic A
Liquid
Crystals
Yes
Liquids No
No No
No
Yes
No
Yes
(1D)
Yes
Columnar
Discotics
Nematic
Liquid
Crystals
Gases

4. • Molecular Models
• Atomistic Models
Resolution
mesoscale
nanoscale
Liquid Crystal simulations at different resolutions

5. Molecular level models
•Molecular resolution:
•a particle corresponds
to 1 molecule.
•Current typical sample
sizes: N=103-104
particles.
•Applications:
Relating molecular
features to phase
properties.

6. The Gay-Berne intermolecular potential
,
,
,
(
,
,
(
'
4
,
,
(
6
12
0






























c
j
i
c
c
j
i
c
j
i
r
r
U








 

r)
u
u
r)
u
u
r)
u
u
uj
ui
r =rr

7. Orientational order parameters for the (1,3) Gay-Berne
potential (NVT MC simulations with N=1000 at r*=0.3)
Iso
Sm
Nem

8. Gay-Berne potential for discotic mesogens with thickness to
diameter ratio f /e=0.345, f / e=5 and energy parameters =1,=3.

9. <P2>
T*
MC-NVT N=1000, r*=2.5
Order parameter vs. temperature for a GB discotic

10. Going beyond simple ellipsoidal particles

11. Generalized one-body GB models
Biaxial
Tapered
(“pear”)
Uniaxial
ellipsoids
Bowls
CZ, J.Mat.Chem.11,2673(2001)

12. Nematics made of uniaxial molecules are uniaxial

13. T*=2.6 Uniaxial Nematic N=8000

14. A typical nematogen molecule is biaxial
rather than uniaxial

15. Common nematogens are biaxial but ..do not give
biaxial nematics!
R F
F
F
R CN R CN
CF3
R

16. A uniaxial (left) and biaxial (right) Gay-Berne type potential
(x,x)
(y,y)

17. Biaxial Nematics
• Biaxial nematic
phases can be
obtained from system
of molecules with
repulsive and
attractive biaxiality of
opposite sign.
• Optimizing molecular
shape is not enough
to give a biaxial
nematic
R. Berardi, C. Zannoni, J.Chem. Phys. 113, 5971 (2000)

18. Avoid biaxial crystalline stacking!

19. Biaxial Order Parameters
a
b
g

20. Biaxial order parameter

21. T*=2.80 y
x
Biaxial nematic

22. T*=2.80 X T*=2.80 Y
Biaxial nematic. Side views
<AXX >  <AYY >

23. Some recent works on biaxial nematics
• J. L. Figueirinhas, C. Cruz, D. Filip, G. Feio, A. C. Ribeiro, Y. Frere, T.
Meyer and G. H. Mehl, Phys. Rev. Lett. 94, 107802 (2005)
• K. Merkel, A. Kocot, J. K. Vij, R. Korlacki, G. H. Mehl and T. Meyer, Phys.
Rev. Lett. 93, 237801 (2004).
• K. Severing and K. Saalwachter, Phys. Rev. Lett. 92, 125501 (2004)
• G. R. Luckhurst, Nature 430, 413 (2004).
• L. A. Madsen, T. J. Dingemans, M. Nakata and E. T. Samulski, Phys.
Rev. Lett. 92, 145505 (2004).
• B. R. Acharya, A. Primak and S. Kumar, Phys. Rev. Lett. 92, 145506
(2004).
• V. Channabasaveshwar, Y. Prasad, G. G. Nair, I. S. Shashikala, D. Rao,
C. V. Lobo and S. Chandrasekhar, Angew. Chem. Int. Ed. Engl. 43, 3429
(2004).
• D. W. Bruce, Chem. Rec. 4, 10 (2004).

24. J.L.Figueirinhas, C. Cruz, D. Filip, G. Feio, A. C. Ribeiro, Y. Frere, T.
Meyer, G. H. Mehl, Phys. Rev. Lett. 94, 107802 (2005).

25. Biaxial Nematics Switching. A molecular dynamics
simulation study
R. Berardi, L. Muccioli, C. Zannoni (2005)

26. Field switch
x
X
y
Y

27. Biaxial nematic transversal switching time
U =
i=1
N
P2(cos i) x =0.20
transversal
axial

28. Going beyond one component systems

29. Computer Simulation of Liquid Crystal
nanodroplet phase separation
R. Berardi, A. Costantini, L. Muccioli,
S. Orlandi, C. Zannoni (2005)

30. A simple model for the formation of liquid
crystal nanodroplets from an homogeneous
solution
• Method
– Phase separation of GB–LJ mixtures
– MD simulation of nanodroplets formation
• Study
– effect of temperature
– effect of solute–solvent affinity

31. Model
• Mixture of Lennard–Jones (isotropic solvent) and Gay–
Berne (solute) particles that can form I, N, Sm
organizations.

32. Pair potentials

33. Model and thermodynamic conditions are setup to give:
(a) pure solvent in a liquid state
(b) pure solute forming isotropic, nematic, and smectic phases
GB-LJ=3 GB-LJ=(1.0, 2.0, 2.5, 3.0)
(c) Mixture with x=xGB=0.02,0.04,0.08
Methodology

34. N=5000, T*=2.40, x=0.04, t*=0.0

35. N=5000, T*=2.40, x=0.04, t*=20,000

36. N=5000, T*=2.40, x=0.04, t*=40,000

37. N=5000, T*=2.40, x=0.04, t*=60,000

38. N=5000, T*=2.40, x=0.04, t*=80,000

39. N=5000, T*=2.40, x=0.04, t*=120,000

40. N=40000, T*=2.40, x=0.04, t*=0.0

41. N=40000, T*=2.40, x=0.04, t*=20,000

42. N=40000, T*=2.40, x=0.04, t*=20,000

43. N=40000, T*=2.40, x=0.04, t*=60,000

44. N=40000, T*=2.40, x=0.04, t*=80,000

45. N=40000, T*=2.40, x=0.04, t*=100,000

46. N=40000, T*=2.40, x=0.04, t*=120,000

47. N=40000, T*=2.40, x=0.04, t*=140,000

48. N=40000, T*=2.40, x=0.04, t*=160,000

49. N=40000, T*=2.40, x=0.04, t*=180,000

50. N=40000, T*=2.40, x=0.04, t*=200,000

51. N=40000, T*=2.40, x=0.04, t*=220,000

52. N=40000, T*=2.40, x=0.04, t*=230,000

53. N=40000, T*=2.40, x=0.04, t*=480,000~288ns

54. Effect of GB solute concentration

55. Order parameter <P2> at various xGB
LJ solvent freezes

56. “Realistic” Simulations: going to atomistic details

57. Observed odd-even effect on transition temperatures
n
[G.W.Gray et al., 1971]
T/oC
n

58. What is realism? Can we reproduce transition
temperatures with atomistic modelling?
R. Berardi, L. Muccioli, C. Zannoni, ChemPhysChem 5,104(2004)

59. • Molecular dynamics: ORAC multi time step
engine
• Force field: AMBER like potential
• Sample: N=98 molecules of the n=0,1, 2
homologues (4214, 4508 and 4802 atoms),
• Conditions: NPT
• Periodic boundaries
• Electrostatics with Particle Mesh Ewald
Etotal = Ebonds + Eangle + Edihed + ELJ + Echarge
Atomistic simulation approach

60. Ab-initio equilibrium geometries (MP2/3-21G*) and partial
charges. We show the electrostatic potential (a.u./Å at 3Å1)
1CHelpG method. C. M.Breneman; K. B. Wiberg, J. Comput. Chem. 11, 361 (1990).

61. Texp
NI
Results for order and density for n=0

62. Results for order and density for n=1

63. Texp
NI
Results for order and density for n=2

64. n=2 T=485K (iso)

65. n=2 T=445K (nem)
d

66. Orientational order parameter evolution n=2
P2 =
2
3
(d z)2
2
1

67. “Specific” molecular simulations: parametrizing
the atomistic details

68. <P2>
T*
MC-NVT N=1000, r*=2.5
Order parameter vs. temperature for a GB discotic

69. Not all “similar” discs assemble in columnar
phases! Can we understand why?
HTT: LC columnar HAT: not a liquid crystal
e.g. HOTT,K 313 Col 360 I e.g. HOAT,K1 307 K2 366 I
Y.H.Geerts et al. MCLC 396,35(2003) V.Lemaur et al. JACS 126, 3271 (2004)

70. The effect of charge distributions
• A detailed representation is needed, e.g. to
get interdigitation in smectics or proper
ordering of discotics in columns
• Standard way: place a partial charge on
every atom
• Handling a full atomistic distribution of Nq
charges is very time consuming in
simulations. Time grows with O(Nq
3/2)
• Multipoles cannot be reliably used for
anisometric molecules in contact

71. Mimicking electrostatic interactions with a set
of effective charges. A genetic algorithm.
R.Berardi, L.Muccioli, S.Orlandi, M.Ricci, C.Zannoni,
Chem. Phys.Lett., 389,373 (2004)
• Obtain first a QM level description of the
charge distribution and of the corresponding
reference electrostatic potential around the
molecule.
• Assume a certain number nq of effective
charges and determine their optimal positions
and values by fitting their electrostatic potential
surface to the reference one.

72. • We define N trial solutions or genomes gi as sets of nq
charge positions, kept ordered according to their x
component.
• Genomes are combined according to evolution rules
• Determine the charges optimal positions and values by
fitting their electrostatic potential surface to the reference
one.
Genetic algorithm

73. Influence of charge distribution on the
columnar packing
R.Berardi, L.Muccioli, S.Orlandi, M.Ricci,
C.Zannoni, 2005

74. Atomistic (left) and effective (right) charge
distribution for Hexathiotriphenylene (HTT)
QM charge distribution at MP2/6-311G+ level

75. Atomistic (left) and effective (right) charge
distribution for Hexa-thio-azo-triphenylene (HTAT)

76. GB discs parameterization
• GB parameterization by fitting pair energies and
molecular structures in the columnar phase
obtained from a small atomistic simulation.
• MD simulation of N=40 HOTT molecules
preliminarily arranged in a columnar way.
• P = 3 atm, T = 300K, no electrostatic charges
(AMBER FF), time ≈ 5 ns.
• The non-bonded LJ intermolecular energies of the
side-side and face-face configurations have been
fitted using a Gay-Berne potential
• Model disc dimensions σs and σf taken from the
maxima or the radial distribution function

77. Snapshots from small MD simulation
top view side view

79. Molecular level simulation
• (i) NPT Monte Carlo simulation of discotic particles,
without charges, enclosed in a box with periodic
boundary conditions.
• Number of particles N=1000
• Dimensionless pressure P* ≡ Pσo
3/o=3.5 (equivalent
to P = 25MPa.), 0=10Å, 0=1kcal/mol
• Then, simulations with two different sets of Nq fitted
charges:
• (ii) 12 for HOTT and
• (iii) 22 for HOTAT.

80. Charge-less discotics do not give columnar
structures

81. Simulation with added charges: HTT

82. Discotics with HTT charge distribution give
columnar structures

83. Simulation with added charges: HAT

84. Discotics with HAT charge distribution do not give
columnar structures

85. Decorated Gay-Berne particles

86. Ferroelectric response and field induced biaxiality in
the nematic phase of a banana-shaped mesogen
O. Francescangeli, V. Stanic, S.I. Torgova, A. Strigazzi,
N.Scaramuzza, C.Ferrero, I. Dolbnya, R. Berardi, L.Muccioli,
S.Orlandi, C. Zannoni (2005)
Cr Sm N I
115.1 oC 138.3 oC 262.5 oC
118.5 oC 140.0 oC 263.0 oC
Cr Sm N I
Cr Sm N I
115.1 oC 138.3 oC 262.5 oC
118.5 oC 140.0 oC 263.0 oC

87. Ferroelectric like Response in the Nematic Phase
0,0 0,2 0,4 0,6 0,8 1,0
-2
-1
0
1
2
 = 1 Hz
T = 180 °C
t (s)
I (A)
-12
-8
-4
0
4
8
12
V (V)
0,0 0,2 0,4 0,6 0,8 1,0
-6
-4
-2
0
2
4
6
t (s)
I (A)
-12
-8
-4
0
4
8
12
 = 1 Hz
T = 180 °C
V (V)

88. Modelling the banana molecule: single particle
QM calculations
DFT equilibrium geometry with two interatomic distances
measurements and atomic labels
rAF

89. Atomistic (U.A.) molecular dynamics
Snapshot at T=550 K, <P2>=0.62 N=150 molecules/8250 centers

90. Some findings from atomistic simuations
- The two alkyloxy chains (rAB, rEF ) have the same behavior
and their length decreases with temperature.
- The central fragment (oxadiazole and two phenyl rings) (rCD)
is rigid and has constant length.
-The “bent-core” is not completely rigid.
-The effective “wingspan” ( rAF )
depends on the conformational
distribution.
0.10
0.06
0.04
0.08
P(rAF)

91. Modelling banana molecules with 3 biaxial GB
fragments with tailored dipoles
s0=10 Å
f’=120°
f =160o

92. T=300 °C T=225 °C T=160 °C
85
.
0
2 
P
80
.
0
2 
P
10
.
0
2 
P
T=140 °C
88
.
0
2 
P
0°, 180° 90°
0°, 360° 180°
Constant Pressure Monte Carlo simulations
N=1000

93. T=160 °C
s0 = 10 Å
s0 = 10 Å
                
 ij
j
i
j
i
j
i
j
i
j
i
j
i
j
i
j
i
ij y
y
x
x
x
y
y
x
y
y
x
y
y
x
x
x
r
r
r
S ˆ
ˆ
ˆ
ˆ
2
ˆ
ˆ
ˆ
ˆ
2
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
5
1 2
2
2
2
0
,
2
,
2
2
,
2














 
Cybotactic Clusters

94. Glass capillary
Permanent magnet
Temperature regulator
B 2q
x
y
z
q
q = 4psinq/l
k
k0
XRD analysis of axially aligned samples

95. Polar domains formation

96. Biaxiality and polarization evolution in response to
a square wave field, from MC simulations
kcycles

97. Conclusions
 Modelling and simulations at molecular level have reached the
stage where they can help to explain the effect of a specific
molecular feature (shape, attraction range,..) on the phase
organization of systems of increasing complexity (including
some composite systems).
 Atomistic simulations are becoming predictive, but they are still
so extremely demanding in resources that they can be of use
only in very specific cases.
 Molecular level models enriched with specific geometrical and
electrostatic details obtained by auxiliary atomistic simulations
can provide a useful intermediate approach for current
modelling applications.

98. • Alberto Arcioni
• Corrado Bacchiocchi
• Roberto Berardi
• Cesare Chiccoli
• Marco Mazzeo
• Davide Micheletti
• Luca Muccioli
• Silvia Orlandi
• Paolo Pasini
• Adriana Pietropaolo
• Matteo Ricci
• Gregor Skacej
• Giustiniano Tiberio
• Ilaria Vecchi
Group Home page
http://www.fci.unibo.it/~bebo/z/index.html
Thanks to: Bologna University, INSTM, PRIN,FIRB, EU-NAIMO

100. Nanoscale self-organizing
multifunctional organic materials
24 September - 2 October, 2005 – Erice, Sicily, ITALY
International School of Liquid Crystals 12th meeting
Directors: F.Biscarini, Y.Geerts, P.Pasini, C.Zannoni
Lecturers: F. Biscarini, A. Brillante, J. Cornil, D. de Leeuw, R. Friend, A.Furlani,
R.Garcia, Y.Geerts, N.Greenham, P.Heremans, A.Menon, K.Müllen,
M.M.Nielsen, C.Rovira, G.Schmidt, C.Taliani, A.Walker, C.Zannoni
http://www-th.bo.infn.it/islc/erice2005/index.html