Effect of cross-linker geometry on equilibrium thermal and mechanical properties
of nematic elastomers
S. M. Clarke,* A. Hotta, A. R. Tajbakhsh, and E. M. Terentjev
†
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, United Kingdom
Received 3 August 2001; published 8 November 2001
We study three monodomain single-crystal nematic elastomer materials, all side-chain siloxane polymers
with the same mesogenic groups but with different types of cross linking: i short flexible siloxane linkage
affine to the network backbone, ii short flexible aliphatic cross links miscible with mesogenic side chain
groups, and iii long segments of main-chain nematic polymer. Equilibrium physical properties of these three
systems are very different, especially the spontaneous thermal expansion and anisotropic stress-strain response
along and perpendicular to the uniform nematic director. In the latter case, we examine the soft elastic plateau
during the director reorientation. We compare the nematic order-parameter Q( T ), provided primarily by the
side mesogenic groups and relatively constant between the samples, and the average backbone chain anisotropy
r ( T ) =l
/ l
, which is strongly affected by the cross-linking geometry. The experimental data are compared
quantitatively with theoretical models of nematic elastomers.
DOI: 10.1103/PhysRevE.64.061702 PACS numbers: 61.30.-v, 61.41.+e, 83.60.Bc
I. INTRODUCTION
In recent years, the behavior of liquid crystalline elas-
tomers has been the subject of significant experimental and
theoretical interest. The behavior of these materials arises
from a coupling between the liquid-crystalline ordering of
mesogenic moieties and the elastic properties of the polymer
network. Many unusual physical effects have been identified
and reported in review articles 1–4. The origin of this equi-
librium behavior has been extensively studied theoretically,
within a molecular model of ideal and nonideal nematic net-
work 5. A more recent development allowed us to combine
the concepts of reptation theory of entangled networks with
the anisotropic nature of nematic polymer strands 6, obtain-
ing the ‘‘tube model’’ corrections to the ideal nematic rubber
elastic free energy.
Two key equilibrium effects stand out in the properties of
liquid-crystalline elastomers, being especially pronounced
when a monodomain single crystal, permanently aligned
7 nematic network is prepared. The first effect is the
anomalous thermal expansion—the spontaneous elongation
of the material along the director axis on cooling from the
isotropic phase 8,9. The reason for this phenomenon is in
the direct coupling between the average polymer chain an-
isotropy and the nematic order parameter see, e.g., 5 for
detail. Depending on this coupling, the magnitude of ther-
mal expansion may differ greatly and even change sign in a
polymer with oblate backbone conformation, reaching a
maximum in a main-chain nematic polymer systems that
could expand, spontaneously and reversibly, by a factor of
three or more 10. The other effect, a macroscopic phenom-
enon termed the ‘‘soft elasticity’’ 11, determines the equi-
librium mechanical and optical responses of monodomain
nematic elastomers, as well as the properties of polydomain-
monodomain transition 12. The physical idea behind soft
elasticity is again in the spontaneous anisotropy of polymer
backbones of rubbery network, coupled to mesogenic moi-
eties that align and form the nematic order. In conventional
elastomers and gels it is the entropic cost of deforming the
average spherical backbone polymer coil that provides the
restoring force and elasticity. When the network strand is
anisotropic ellipsoidal, then instead of deforming the aver-
age polymer conformation, some deformations could be
completely accommodated by simply rotating the average
chain distribution without changing its shape. Accordingly,
no elastic energy cost would be paid for such deformations.
In many cases, the ideal soft response cannot be achieved,
but one still finds a signature of soft elasticity in the decrease
of one of the shear moduli for the same deformation modes
that would lead to a complete softness in an ideal nematic
network.
Here, we examine these two physical effects in some de-
tail. We study three types of nematic elastomer materials,
having essentially the same chemical structure and composi-
tion of side-chain polysiloxane nematic polymer strands but
different in the type of cross linking. We establish the net-
work using exactly the same concentration by reacting
bonds of difunctional cross-linking groups that are i short
flexible dimethylsiloxane chains, ii hydrocarbon divinyl
alkenebenzene units, and iii long chains of main-chain
nematic polymer that create an additional and very high
anisotropy in the composite material. In all cases, we prepare
uniformly aligned monodomain nematic networks—single-
crystal liquid-crystal elastomers in the terminology of Ku
¨
pfer
and Finkelmann 7.
There are several questions to answer from comparing
these three systems. First, in Sec. III, we establish a relation
between the nematic order-parameter Q ( T ) and the effective
backbone anisotropy of chains making the rubbery network,
expressed by a dimensionless ratio of principal step lengths
along and perpendicular to the nematic director, r
=l
/ l
. It is obvious that there has to be a direct relation-
*Present address: The BP Institute, University of Cambridge,
Cambridge CB3 0EZ.
†
Email address: emt1000@cam.ac.uk
PHYSICAL REVIEW E, VOLUME 64, 061702
1063-651X/2001/646/0617028/$20.00 ©2001 The American Physical Society 64 061702-1