This document summarizes the speaker's research on inhomogeneous phenomena in nematic liquid crystals. The speaker studies nematic liquid crystal interfaces, spinodal and nucleation kinetics using techniques like thermodynamics, statistical mechanics, and computational methods. For nematic interfaces, the speaker finds that the de Gennes ansatz is valid without biaxial rigidity, but interfaces become biaxial with rigidity. For spinodal kinetics, the speaker observes diffusive scaling and defects form lines or points. For nucleation kinetics, the speaker finds ellipsoidal droplets without rigidity but defects form within droplets with rigidity. The speaker concludes by thanking their collaborators and plans future work with postdoctoral researchers.

1. Inhomogeneous phenomena in
nematic liquid crystals
Amit Kumar Bhattacharjeee
Matscience, Chennai

2. Intro
Ph.D. @ Matscience
IMScMathematics
Theoretical
Computer
Science
Theoretical Physics
Areas of Research in TP Hard & Soft Condmat, HEP, Quantum
Information, String Theory, Cosmology, Optics.
33 Faculties, 10 PDFs, 40 JRFs
B.Sc. M.Sc.

3. What I work on ...
Nematic liquid crystals (Interfaces, spinodal and nucleation kinetics)
Cell Biophysics (Intra-cellular spatio temporal pattern formation)
Techniques I use
Thermodynamics & Equilibrium
Statistical Mechanics
Stochastic process & Nonequlibrium
Thermodynamics
Classical field theory (elasticity,
Hydrodynamics etc.)
Computational methods : Solving
deterministic coupled-nonlinear PDE's.
Numerics of Stochastic differential
Equation (SDE).
High performance computation
Theory + Computation

4. PlanPlan
Part I
Intro to Soft Condensed Matter (SCM), phase transitions
Conventional methods of study
Intro to liquid crystals (LC), a theoretical framework
Part II
MFT of LC, statics and kinetics
Liquid – nematic interfaces; nonlocal properties
Spinodal kinetics; interplay of topology and energetics
Nucleation kinetics; breakdown of CNT
Part III
Spatio-temporal pattern formation in cell biophysics

5. Part IPart I

6. What is soft matter ?
Complex fuids, soft to touch, easily malleable, can't support shear stress
Examples : milk (colloid), rubber (polymer), LCD (liquid crystal),
shampoo, toothpaste (gels), tissues (bio-polymers) etc ...
F = E – TS; Hard condmat (crystals) = E dominated phases (minimize E);
Soft condmat = S dominated phases (maximize S).
Changes of phases; order of transition (e.g. gas to solid, paramagnet to ferromagnet)
States of matter : solid, liquid, gas.

7. Liquid crystals
Multistage transition process :
mesophases.
Classification of mesophases :Classification of mesophases :
Nematic, Discotic, Cholesteric,
Smectic A – C, Columnar etc
Why study them ?
Technological applications
Interest to physicists :
Statistical field theory, ideas apply from Biophysics to Cosmology !!

8. Methods of study
Mesoscale methods
CFD
LB
TDGL
MC
Atomistic methods
MD
DPD
LD
BD
DFT
CPMD
Ab Initio methods
L

9. Mesoscale methods
How to deal theoretically ?
a) Identify the order parameter, broken symmetry, conservation laws,
type of transition of the phase.
b) Construct a free energy functional; coarse-graining of space.
c) Temporal coarse graining;
d) Measure the equilibrium and non-equilibrium properties.
1st
order transition 2nd
order transition

10. Part IIPart II

11. Nematic mesophases
Consists of anisotropic molecules, e.g. Rods, discs etc. having long
range orientational order devoid of translational order.
Rotational symmetry about the direction of order : uniaxial phase.
Direction of order is described by headless vector (as n -n)
No rotational symmetry : biaxial phase.
Order is quantified through a tensor Q having five degree of freedom :
2 degree of order and 3 angles for specifying principle direction.

12. Statics
Landau – de Gennes free enrgy
a) Bulk contribution (local)
b) Elastic contribution (non-local)
F=∫ d3
xFhFel
Free energy diagram Phase Diagram

13. Kinetics
TDGL model-A kinetics following Lanegevin.
t ℚ   x ,t=−[ AC Tr ℚ
2
ℚ   x ,t B6 E
'
Tr ℚ
3
ℚ
2
 x ,t−L1 
2
ℚ   x ,t−L2   ℚ   x ,t]  x ,t.
Route to equilibrium a) nucleation kinetics above T*
b) spinodal kinetics below T*
How to integrate this equation numerically ?
(I) Determintic equation >
a) MOL with FD discretizeation.
b) Spectral collocation methods.
c) High performance computation to achieve thermodynamic limit.
(II) Stochastic equation >
b) SMOL

14. Equation of motion
Problems
Stochastic
Determinstic
I-N interface
Structure of nematic
droplet
Phase ordering spinodal
kinetics
Structure of nucleating
droplet

15. Questions we ask
Isotropic-nematic interface :
(a) Local and non-local properties of the interface
Spinodal kinetics through quench :
(a) Core structure of point defects in 2D & line defects in 3D
(b) topological glass possible in BN ?
(c) dynamical scaling : exponents, any violation of O(n) theories ?
(d) defect-defect kinetics
Nucleation kinetics :
(a) Shape and structure of droplet
(b) Classical nucleation theory valid for nucleation rate calculation ?
(c) First passage time

16. Answers we get : central results
Isotropic-nematic interface :
(a) de Gennes ansatz valid for .
(b) Biaxial interface for (planar anchoring)
(c) Local degree of uniaxiality & biaxiality, nonlocal tilt angle for oblique anchoring.
L2=0
L20

17. Spinodal kinetics : point defects
Uniaxial nematics in 2D
Biaxial nematics in 2D
Schlieren textureS(x, t), n(x, t) Core structure

18. Nucleation of nematic droplets
L2=0 L20 L20
L20 L20

19. Conclusion
(a) No biaxial rigidity in 3D : interplay to energetics and topology.
(b) Diffusive dynamical scaling at the early stage of kinetics.
(c) Violation of O(n) model is clearly calculated.
(d) Defect-anti defect segment inter-commutation is nicely seen.
(a) Ellipsoidal shape of droplets with uniform director field.
(b) Droplets with nonzero anisotropic elasticity leads to +1 defect
Inside : failure of CNT
(c) Shapes in stochastic nucleation kinetics is not necessarily
ellipsoidal in all cases.
(a) Without anisotropic elasticity, interface is always uniaxial
(b) With anisotropic elasticity, interface becomes biaxial
(c) Local tilt angle is highly non-local while degree of ordering are
Local to the interface.

22. Ronojoy Adhikari
Thanks
Gautam Menon
Somdeb Ghose
P.T. Sumesh (JNC)
S. Sankararaman (UIC)
Mithun Mitra (UMA)
S.M. Kamil (UAM)
Future Post doctoral Collaborators
PD Juergen Horbach Thomas Voigtmann

23. Thanks for your attention