Selinger Group:
Shape evolution of nematic elastomers
and lipid membranes:
chirality, curvature, and topological defects
Robin Selinger
Jonathan Selinger
Vianney Gimenez Pinto
Andrew Konya
Thanh Son Nguyen
Jun Geng
Controllable Apertures: Andrew Konya
Nematic elastomer: controllable aperture
Angular Deficits in Flat Space: Remotely Controllable
in a “blueprinted” elastomer
Apertures in Nematic Solid Sheets C.D. Modes, M. Warner,
C. Sanchez-Somolinos, L.T. de Haan, D. Broer
Proc. R. Soc. A, 2012
cold
hot
Our FEM simulation of design in Modes et al
Video here:
http://www.youtube.com/watch?v=5DOitztPL1U
Our new design:
Blueprinted chiral iris
FEM simulation: Grooves accommodate
azimuthal strain; color shows strain energy
Chiral iris:
http://www.youtube.com/watch?v=f1G-nXIeOm4
Achiral iris:
http://www.youtube.com/watch?v=rLNTEiDKxi0
Auto-origami: Andrew Konya
Temperature-driven folding in a
nematic elastomer sheet:
FEM simulation
Top Alignment
Bottom Alignment
Film formed between patterned substrates with
strong anchoring
Center has imposed director gradient
through thickness
=
=
=
=
homeotropic
planar
cold
hot
Bas Relief: Andrew Konya
Temperature-driven emergence of
bas relief pattern: FEM simulation
Top Alignment
Sheet formed between patterned substrates with
strong anchoring
Boundary given by:
FEM simulation…. Video here:
http://www.youtube.com/watch?v=1x7afwQO4rE
Bottom Alignment
Modeling Actuation of Nematic Elastomers: Finite Element Elastodynamics
tetrahedral
element -t
H
node-p
1
1
t
t
t
t
t
2
t
t
m
v

V
C




V

(
Q

Q
)
init



p p
ijkl ij kl
ij
ij
ij
2 p
2 t
t
kinetic
energy
elastic
deformation
energy
Coupling between strain
and nematic order
Green Lagrange strain tensor:
 ij 
1
iu j   jui  iuk  juk 
2
Q-tensor:
Qij 
S
3ni n j   ij 
2
• FEM elastodynamics code developed in-house
• Can be run on one processor, in parallel via MPI, or on GPU (fast!)
• Typical mesh=80,000 elements, up to 106 time steps
Twist Nematic Elastomer ribbons change shape with Temperature-Vianney Gimenez-Pinto
S drops with increasing Temperature
Nematic director twists 90°
from bottom to top

n
… Contraction along
… Expansion in other directions
Experiments by Kenji Urayama: Non-uniform strain  complex shape evolution
Y. Sawa, F. Ye, K. Urayama, T.
Takigawa, V. Gimenez-Pinto, R. L.
B. Selinger, J. V. Selinger
PNAS 2011
Spiral
Helicoid
Our goal:
Model shape evolution as function of: T, aspect ratio, twist geometry
Chirality reversal with temperature-Vianney Gimenez-Pinto
FEM simulation, aspect ratio 50-5-1
High T : Left-handed
Theoretical predicted phase diagram
Spiral
ribbon
Helicoid
ribbon
Spiral
ribbon
Y. Sawa, F. Ye, K. Urayama, T. Takigawa,
V. Gimenez-Pinto, R. L. B. Selinger,
J. V. Selinger PNAS 2011
Low T : Right-handed
Helicoid or Spiral? Shape depends on twist geometry. aspect ratio-V. Gimenez-Pinto
Aspect ratio
50-5-1
Equilibrium shape
Helicoid ribbon
Movie:
http://youtu.be/Wpume8jqthc
Helicoid ribbon
50-15-1
Helicoid ribbon
50-20-1
Helicoid ribbon
Pitch grows
50-10-1
Shape transition!
50-25-1
Spiral ribbon
Movie: http://youtu.be/seESh8YPtVE
L geometry
S geometry
Nematic elastomer sheet with point defect -Vianney Gimenez-Pinto
T < Tflat : Cone
T > Tflat : Saddle-like Anti-cone
Movie: http://youtu.be/AmEygZQMZmw
Movie: http://youtu.be/Gw_MeeueWwc
Radial +1
“blueprinted” director
field:
Radial
(cooling, ΔS>0)
Cone height
Azimuthal
(heating, ΔS<0)
When ΔS < 0.3, no distortion
Due to finite bending energy
Aspect ratio: 500-500-10
ΔS
Modeling lipid vesicles: Thanh Son Nguyen
Modeling lipid vesicles: Thanh Son Nguyen
Vesicle modeled via Finite Element Method as a triangulated surface of zero thickness
(Actual mesh much finer)
Transient shape
evolution , coupled
to defect dynamics
Equilibrium shape
and defect
positions depend
sensitively on Frank
elastic constant
Modeling lipid vesicles: Jun Geng and Thanh Son Nguyen
Nematic vesicle shape
Coarse-grained particle simulation
Coarse-grained particle
simulation
Frank
elasticity
weak
Model also used to
study shape
evolution in tilted
gel phase vesicles
"Morphology transition in lipid vesicles due to inplane order and topological defects"
L.S. Hirst, A. Ossowski, M. Fraser, J. Geng, J.V.
Selinger and R.L.B. Selinger, PROC. NATL. ACAD.
SCI. 110 (9) 3242-3247 (2013)
Video here:
https://ksutube.kent.edu/playback.php?playthis=v3104edv2
strong
Continuum
FEM