Semi-soft Response in Nematic Elastmers Tom C. Lubensky, University of Pennsylvania, DMR 0404670

1
Semi-soft Response in Nematic Elastmers Tom C.
Lubensky, University of Pennsylvania, DMR 0404670
Elastomers (rubbers) are materials that can be
reversibly stretched to more than twice their
length without breaking. Nematic liquid crystals
are materials that flow like a liquid yet have an
anisotropy axis like a crystal. Nematic
Elastomers (NEs) combine the mechanical
properties of rubber with the orienational
properties of a nematic liquid crystal. NEs
prepared with a preferred anisotropy direction n
exhibit semi-soft elasticity characterized by an
unusual plateau in the stress-strain curve on
which very small stress increments produce large
strain. We have determined the global conditions
under which semi-soft behavior can occur as a
function of temperature r, imposed anisotropy h,
and external stress, sxx. Ye, Fangfu
Mukhopadhyay, Ranjan Stenull, Olaf and
Lubensky, T. C., Semi-soft Nematic Elastomers
and Nematics in Crossed Electric and Magnetic
Fields, Phys. Rev. Lett. 98, 147801/1-4 (2007)
Above Schematic of a NE stressed in the
horizontal direction. Right Experimental
stress-strain curve Finkelmann, et al., J. Phys.
II 7, 1059 (1997) Warner, J. Mech. Phys. Solids
47, 1355 (1999)
Global phase diagram showing the surface of
continuous biaxial coexistence, SY, responsible
for semi-soft behavior
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Soft Elasticity and Dynamics in SmC Elsatomers
Tom C. Lubensky, University of Pennsylvania, DMR
0404670
Fig. 1 Schematic representation of (a) SmA and
(b) SmC elastomers, showing layers and rigid
mesogens and shear in the SmC phase
Fig. 2 Different realizations of the SmC phase
with the same energy.
Smectic elastomers are crosslinked layered
structures. In SmA elastomers, rod-like mesogens
attached to the polymer network align
perpendicular to the layers. When SmC elastomers
transform to SmC elastomers, the mesogens develop
a component parallel to the layers, and the
sample shears as shown in Fig. 1, thereby
breaking the rotational symmetry in the layer
planes of the SmA phase. All of the sheared
states in Fig. 2 have the same energy, and they
can be transformed one into the other with the
application of vanishingly small forces. The
broken symmetry of the SmC phase gives rise to
three types of sound waves with sound velocities
that vanish along symmetry directions as shown in
Fig. 3. Stenull, O. and Lubensky, T.C., Soft
Elasticity in biaxial smectic and smectic-C
elastomers, Phys. Rev. E 74, 051709/1-24 (2006)
Dynamics, dynamic soft elasticity, and rheology
of smectic-C elastomers, Phys. Rev. E 73,
03071/1-18 (2006) 
Fig. 3 (a) Sound velocity of the (i) mode in
3-dimensions (b) and (c) sound velocities of all
three modes in the y-z and x-z planes