Synclinic-anticlinic phase transition in tilted organosiloxane liquid crystals

Article abstract of DOI:10.1039/b104960g

In this paper, we considered the case of low molecular weight bimesogenic liquid crystals containing a siloxane moiety as the central part of their molecular architecture. For some of these compounds, both ferro- and antiferroelectric mesophases are prese

Full text of DOI:10.1039/b104960g

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Synclinic–anticlinic phase transition in tilted organosiloxane liquid
crystals{
Daniel Guillon,*a Michael A. Osipov,a,b{ Ste´phane Me´ry,a Michel Siffert,a
Jean-Franc¸ois Nicoud,a Cyril Bourgognea and P. Sebastia˜oa,c
aInstitut de Physique et Chimie des Mate´riaux de Strasbourg, Groupe des Mate´riaux
Organiques, 23 rue du Loess, Strasbourg Cedex, France 67037. Tel: 33 388 10 71 59;
Fax: 33 388 10 72 46; E-mail: daniel.guillon@ipcms.u-strasbg.fr
bSchool of Physics, University of Exeter, Stocker Road, Exeter, UK EX4 4QL
cCentro de F´ısica da Mate´ria Condensada, Av. Prof. Gama Pinto 2, Lisboa, Portugal 1649-003
Received 5th June 2001, Accepted 18th July 2001
First published as an Advance Article on the web 5th October 2001
In this paper, we considered the case of low molecular weight bimesogenic liquid crystals containing a siloxane
moiety as the central part of their molecular architecture. For some of these compounds, both ferro- and
antiferroelectric mesophases are present. Two distinct smectic structures can develop as a function of
temperature, the first one at high temperature corresponding to a synclinic molecular arrangement with
elongated molecules, and the second one at lower temperature corresponding to an anticlinic organisation with
V-shaped molecules. Numerical calculations of the energy of different conformations of these bimesogenic
molecules presented here indicate that there is no difference in energy between V-shaped and linear
conformations regardless of the number of silicon atoms in the siloxane moiety. Thus a microscopic model of
the synclinic–anticlinic phase transition is developed where the driving force is indeed a free energy difference
between the two phases, and not a difference of energy between the V-shaped and linear conformations. The
model explains why the anticlinic SmCA phase is more stable than the synclinic SmC one, why the synclinic
SmC phase is generally the higher temperature one, and why in some organosiloxane materials the anticlinic
SmCA phase is not present.
completely disappear in siloxane materials. The majority of the
Introduction
existing organosiloxane liquid crystals are chiral and thus
they possess ferroelectric or antiferroelectric properties in the
Smectic C* (SmC*) or Smectic CA* (SmCA*) phase, respec-
tively. At the same time these materials maintain the
mechanical stability typical of their polymer analogues. The
combination of these two properties opens up interesting
possibilities for display application.5
Low molecular weight organosiloxane liquid crystals form an
interesting class of liquid crystal materials in which one or two
mesogenic moieties are attached to a short siloxane chain.
In a liquid crystal phase, siloxane groups have a tendency
to microseparate and to aggregate in layers thus strongly
promoting smectic phases and depressing the nematic phase.1–3
In a certain sense the smectic layer formed by organosiloxane
liquid crystals with one mesogenic group is analogous to a
Langmuir–Blodgett film. In Langmuir–Blodgett films strongly
anisotropic amphiphilic molecules are attached to the water
surface via a polar head. The phase state of such a film strongly
depends on the surface density, i.e. on the average area per
polar head.4 In particular, the film may undergo a transition
into the tilted phase as the surface area increases. This tilting
transition is determined by an attraction between alkyl chains
and by packing effects. In a similar way, the mesogenic groups
in the organosiloxane smectic liquid crystals are attached to a
‘plane’ formed by siloxane groups. In this plane the average
area occupied by one siloxane group is significantly larger then
the cross-section of a classical mesogenic moiety. As a result the
mesogenic groups have a strong tendency to tilt and the system
undergoes a transition into the smectic C (or smectic CA) phase
directly from the isotropic phase. One notes that the
corresponding mesogenic groups without siloxane chains
may form smectic A and/or nematic phases. These phases
The main problem which we are going to address in this
paper is the microscopic origin of the anticlinic ordering (i.e.
herringbone structure) in bimesogenic organosiloxane com-
pounds and the nature of the SmC*–SmCA* transition in these
systems. Recently one of the present authors together with
Fukuda6 has developed a model of the anticlinic SmCA phase
in conventional monomesogen liquid crystals. In that model
the anticlinic ordering is stabilised by the orientational
correlations between permanent transverse molecular dipoles
in neighbouring smectic layers. Such correlations are particu-
larly effective if the dipoles are located in bent chiral chains. It
should be noted however that this mechanism cannot be
applied to organosiloxane liquid crystals. It has already been
stressed by Carboni and Coles7 that the anticlinic structure
observed in materials with bimesogen organosiloxane mole-
cules should not be determined by any anticlinic coupling
between molecules in adjacent layers but should rather be due
to the V-shaped conformation of the dimer molecules. The
packing of such V-shaped molecules would result in the
anticlinic arrangement of mesogenic groups which, in turn,
would give rise to the antiferroelectric ordering of molecular
dipoles. This idea is confirmed by the fact that the
corresponding monomesogen compounds (with or without
the siloxane group) do not form the anticlinic phase.8
{Basis of a presentation given at Materials Discussion No. 4, 11–14
September 2001, Grasmere, UK.
{Present address: Department of Mathematics, University of Strath-
clyde, 26 Richmond Street, Glasgow, UK G1 1XH.
2700
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This journal is # The Royal Society of Chemistry 2001
DOI: 10.1039/b104960g

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It should also be noted that the anticlinic SmCA phase is
formed only if the bimesogen molecule possesses a short
siloxane chain with an odd number of silicon atoms. Experi-
mentally the anticlinic phase has not been observed for
monodisperse compounds which contain more than five silicon
atoms in the chain. One may assume that for longer siloxane
chains the corresponding V-shaped conformation is not ‘rigid’
as the siloxane link between two mesogenic groups behaves
more like a flexible polymer chain. In this case the specific
packing effects of V-shaped molecules are not strong enough
and the anticlinic ordering disappears. These experimental
results support the conclusion that the anticlinic ordering in
bimesogen organosiloxane compounds is not determined by an
interaction between mesogenic groups but is related to a
difference between V-shaped and linear conformations.
chirality. On the other hand, in the synclinic SmC phase a polar
ordering in the tilt plane is absent due to symmetry reasons.
Thus the additional polar ordering of V-shaped molecules
reduces the free energy of the anticlinic SmCA phase which may
become more stable than the synclinic SmC phase.
The mechanism described above makes it possible to
understand why the anticlinic phase, composed of V-shaped
bimesogen molecules may be more stable than the synclinic
phase composed of linear molecules. However, it remains
unclear why several bimesogen compounds exhibit the synclinic
SmC phase in preference to the anticlinic one, or even do not
form the anticlinic phase at all. The model presented in this
paper enables one to answer this question. It will be shown that
the stability of the synclinic SmC phase at low temperature is
determined by two main factors.
Firstly, it is important to note that the anticlinic phase
formed by V-shaped molecules is usually characterised by a
nearly temperature independent tilt angle which is apparently
and mainly determined by the molecular conformation. In a
sense the relatively ‘rigid’ V-shaped conformation works as a
mechanical constraint. At a given temperature the correspond-
ing fixed tilt angle may differ from the ‘equilibrium’ tilt which
corresponds to the minimum of the free energy determined by
interactions between mesogenic units. One notes that the
equilibrium tilt is expected to be temperature dependent and
should be nearly the same for synclinic and anticlinic
configurations, i.e. it weakly depends on the direction of the
tilt. This is related to a small free energy difference between
the synclinic and anticlinic phases compared to the energy
associated with the tilt. Indeed, the antiferroelectric anticlinic
SmCA* phase can easily be switched to the synclinic ferro-
electric SmC* phase by a moderate electric field.8 At the same
time a small tilt in the Smectic A phase can only be induced in
the vicinity of the second order SmA*–SmC* phase transition
due to the electroclinic effect.12 Thus, at higher temperatures
directly below the transition into the tilted smectic phase the
equilibrium tilt angle may be significantly smaller than the tilt
determined by the V-shaped molecular conformation. In this
case the free energy of the anticlinic phase with approximately
fixed tilt may be too high and the synclinic configuration with
the equilibrium tilt appears to be more stable. The actual
transition temperature from the synclinic SmC* to the
anticlinic SmCA* phase is then determined by a balance
between the negative free energy associated with the polar
ordering of V-shaped molecules in the anticlinic phase and the
positive free energy cost related to the deviation of the actual
tilt from its equilibrium value.
Another factor which acts in the same direction is related to
the intermolecular interactions which stabilise the synclinic
configuration in the smectic phase composed of monomesogen
molecules. These interactions make a positive contribution to
the free energy of the anticlinic phase, and this contribution
should also be counterbalanced by the decrease of the total free
energy associated with more favourable V-shaped conforma-
tions. One notes that in the present model the liquid crystal
phase is considered as a mixture of molecules adopting
V-shaped or linear conformations. However, the concentration
of V-shaped conformers in the synclinic phase is very low
because such conformations are strongly suppressed. The same
is valid for linear conformations in the anticlinic phase. As a
result, the SmC*–SmCA* transition should be accompanied
by a steep change of relative concentrations of the two
conformers.
It has been assumed in ref. 7 that the V-shaped conformation
possesses a lower energy in comparison with the linear
conformation. In this case the anticlinic SmCA phase should
be preferable to the synclinic SmC phase, and the driving force
of the synclinic–anticlinic transition should be determined by a
difference in energy between the V-shaped and linear
conformations of bimesogen molecules. In the present paper
we have made an attempt to check that assumption by
performing some extensive numerical calculations of the
energy of different conformations of bimesogen organosilox-
ane molecules. However, the results of these calculations,
presented in the next section (Structure and properties of
the SmC and SmCA phases), are quite surprising as they
indicate that there is practically no difference in energy
between V-shaped and linear conformations of such bimesogen
molecules regardless of the number of silicon atoms in the
siloxane chain. This result does not confirm the phenomen-
ological model of the SmCA–SmC transition in organosiloxane
liquid crystals proposed in ref. 7.
In this paper we propose a different microscopic model of the
synclinic–anticlinic phase transition in a liquid crystal com-
posed of bimesogen molecules. In this model the SmC–SmCA
transition is driven by a free energy difference between the two
phases which is determined by a strong polar ordering (or polar
packing) of V-shaped molecules in the anticlinic phase. Indeed,
a V-shaped molecule apparently possesses a strong polar
asymmetry of the molecular shape. This polar asymmetry may
qualitatively be represented by the so-called ‘steric dipole’9,10
which is introduced using an analogy with the electric dipole.
The steric dipole points to the direction of maximum shape
anisotropy. The steric dipole of a V-shaped molecule is parallel
to the molecular C2 symmetry axis. In each layer of the
anticlinic SmCA phase the steric dipoles are ordered due to the
optimum packing of V-shaped molecules (see Fig. 1), as for
the banana-shaped molecules.11 The corresponding electric
dipoles, which are rigidly bound to the molecular skeleton, are
simultaneously ordered as well. One notes that this polar
ordering of V-shaped molecules is parallel to the tilt plane
and thus it is qualitatively different from the spontaneous
polarisation of a chiral tilted smectic layer which is perpendi-
cular to the tilt plane and which is determined by molecular
The paper is arranged as follows. In the following section,
the molecular organization of the SmC* and SmCA* phases
will be described, along with molecular simulation of these
organosiloxane compounds. In the next two sections a
theoretical approach of the transition between these two
phases is developed in agreement with most of the experimental
Fig. 1 Optimum packing of V-shaped molecules in a smectic layer.
J. Mater. Chem., 2001, 11, 2700–2708
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data available and the nature of the synclinic–anticlinic phase
transition in organosiloxane materials is discussed.
Structure and properties of the SmC and SmCA phases
The organosiloxane compounds considered in the present work
are described in Scheme 1.
The synthesis and thermal behaviour of Br–Sin–Br com-
pounds has already been reported in the literature.13 S–Si3–S is
a new compound, and its synthesis and chemical characteriza-
tion are reported in detail in the Experimental section.
Let us concentrate first on the dimesogen S–Si3–S (contain-
ing the sulfinate moieties), for which an extensive structural
study has been performed, and which represents the very
interesting case of a pure compound exhibiting a transition
from a synclinic SmC* (ferroelectric) to an anticlinic SmCA*
(antiferroelectric) phase. The layer spacing, d, as a function of
temperature is represented in Fig. 2. On cooling from the
isotropic phase, one observes the usual decrease of d in the
SmC* phase in connection with an increase of the tilt angle;
then after a small discontinuity at the transition it levels off
Fig. 2 Layer spacing as a function of temperature in the synclinic
SmC* and anticlinic SmCA* phases of S–Si3–S.
aromatic cores. The molecular area of a dimethylsiloxane
polymer chain (ssil)15 is approximately 43 A . The ratio of S to
2
˚
ssil is such that the orthogonal siloxane cross-section is
considerably smaller than the molecular area. This indicates
that the siloxane part does not lie fully extended, but instead
should slightly bend back on itself, running in part parallel to
the smectic layer, thus increasing the transverse area occupied.
Such a behaviour is in agreement on one hand with the diffuse
band observed in the X-ray pattern corresponding to an
˚
to a constant value of about 33.6 A at low temperature in
the SmCA* phase. Even if the jump in the layer spacing
between the two phases is only of 1%, it is however the
signature of a weakly first order nature for the corresponding
transition.
˚
average distance of 11 A between siloxane moieties, and on the
other with molecular simulations presented further in the
paper. The structural model of molecular organisation is
represented in Fig. 4 for both the SmC* and SmCA* phases. It
consists essentially of tilted mesogenic moieties separated by
Dilatometry experiments have been performed as a function
of temperature in the whole stability range of the mesophases.
The molecular volume thus determined varies linearly from
3
3
˚
˚
2190 A at 50 uC to 2260 A at 95 uC with no significant jump at
the SmC*–SmCA* transition. Combining these results with
those of the layer spacing, it is straightforward to deduce the
variation of the molecular area, S, i.e. the area occupied by one
dimer molecule in the plane of the smectic layers, as a function
of temperature. Such a behaviour is represented in Fig. 3. The
important point to notice is the high value of S which ranges
2
between 63.5 and 65.5 A . The calculated S is more than twice
˚
the molecular area of the aromatic cores14 (sar#22–24 A ).
2
˚
These results suggest a monolayered arrangement of tilted
aromatic groups with a tilt angle of cos21 (sar/S)#40–45u,
which is consistent with previous values of similar organo-
siloxane mesogens and with the optically measured tilt angles.
Regarding the aliphatic chains, the molecular area (spar) may
2
vary between 20 and 40 A depending on the chain conforma-
tion, again consistent with the monolayered arrangement of the
˚
Fig. 3 Molecular area as a function of temperature in the synclinic
SmC* and anticlinic SmCA* phases of S–Si3–S.
Scheme 1
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Fig. 6 Molecular simulation of the central siloxane moiety of
bimesogenic molecules, showing the quasi-helical conformation of
the siloxane backbone. The conformer represented here is
dodecamethylpentasiloxane.
a
and 5 silicon atoms and substituted by a methyl group at both
extremities. Only one conformer with a minimum energy has
been chosen which is the best candidate to obtain elongated
and V-shaped molecules when the mesogenic group is attached
to the siloxane part. It can be seen in Fig. 6 that this conformer
is rather compact and close to a helical shape.
Fig. 4 Schematics of molecular organisation of dimesogenic organo-
siloxane liquid crystal molecules within the synclinic SmC* and
anticlinic SmCA* phases. The yellow rectangles stand for the rigid
aromatic mesogenic moieties, the blue ellipses for the siloxane moieties
and the wavy lines for the aliphatic chains.
The next step was to substitute the terminal methyl groups of
the siloxane chain as a function of the orientation wanted for
the substituent to obtain elongated or V-shaped molecules. As
a matter of fact, the direction of the substituent was found to be
mainly determined by the rotation around the two terminal
O–Si bonds of the siloxane part. Then the aliphatic spacers
have been attached and the resulting molecules minimized
again, thus leading to one elongated and two V-shaped
conformers. It should be noted that the potential barrier
between the two conformations appears to be very small. This
has been evaluated from a molecular mechanics calculation on
the siloxane moiety containing 5 silicon atoms, using the
Discover3 software (Molecular Simulations Inc.) with the cvff
forcefield.18 The energy of the molecule has been minimized
with a fixed value of the torsion angle around one specific Si–O
bond. This angle is then increased stepwise from 0 to 360u. In
that way, we can calculate the energy of the molecule as a
function of the rotation angle around one single bond in the
siloxane part. It turns out that in this case the potential barrier
is only 4 kcal mol21, representing a fraction of kT. Even if one
assumes that several bonds are involved in the process of
conformational change of the siloxane part at the SmC*–
SmCA* transition, the potential barrier between the two
conformations still remains only a small fraction of kT, which
is indeed negligible.
The previously optimized mesogenic groups are bonded to
the spacers on each conformer of the central moiety and the
energy of the whole molecule is then calculated. The results
appear to be quite surprising. The energy for each individual
molecule is the same (within a fraction of kcal) for the three
conformers (elongated, V-shaped conformers with 90 and
150u), i.e. 570 kcal for S–Si3–S, 848 kcal for Br–Si5–Br and 605
kcal for Br–Si3–Br respectively. As an example, three
conformations of Br–Si5–Br (elongated, V-shaped with large
and smaller angle) are represented in Fig. 7 and all of them
have the same internal energy. In other words, this indicates
clearly that the transition from the synclinic SmC* phase to
the anticlinic SmCA* one is not driven by an energy differ-
ence between the conformations adopted by the molecule.
Moreover, the particular chemical structure of the chiral
part and of the mesogenic group itself appears to have no
effect at all.
siloxane groups, the total layer being formed by the super-
position of three distinct sublayers, one made of the aromatic
cores, the other one with the aliphatic chains and the third one
with the siloxane moieties. These three sublayers microseparate
in order to respect the amphiphatic character of such
mesogenic molecules. This structure is similar to that already
reported by us for the Br–Sin–Br compounds.16
The variation of the tilt angle of the aromatic parts can
directly be deduced from the values of S reported above
(Fig. 5). It is important to notice a small but sharp increase of
the tilt angle at the transition when cooling down in
temperature. From a molecular point of view, the transition
can be seen as illustrated in Fig. 4. The molecule changes its
conformation from an elongated one to a V-shaped one
through essentially a conformational change of the siloxane
part itself. It is important to note that the angle between the
two arms of the V is about 90u, since the tilt angle of the
mesogenic groups with respect to the layer normal is 44–45u in
the whole range of the antiferroelectric phase. Such an angle is
rather small and is in favour of a contribution of a polar
ordering due to steric constraints.
As discussed in the Introduction, it is interesting to know
whether there is a significant difference in energy between linear
and V-shaped conformations of the same molecule because it
may be responsible for the transition under consideration.
Molecular simulations have been performed using the semi-
empirical AM1 method from the MOPAC 6 program.17 First
we have considered the dimethylsiloxane moieties containing 3
Finally, let us remark that the organosiloxane compounds
present in general rather high values of spontaneous polarisa-
tion,19 of the order of some hundreds of nC cm22. An example
of such a behaviour is given in Fig. 8 for S–Si3–S.
Fig. 5 Tilt angle of the rigid aromatic moieties (yc) and average tilt
angle of the disorganised aliphatic chains (ych) in the synclinic SmC*
and anticlinic SmCA* phases of S–Si3–S.
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molecules located in the same smectic layer and in adjacent
layers, respectively.
In the first approximation one may also neglect an
interaction between mesogenic groups located in adjacent
layers. This interaction is expected to be much weaker than the
one between the groups which belong to the same layer. It
should be noted, however, that this does not mean that we
neglect the total interaction between dimer molecules located in
adjacent layers. In fact, for any two molecules with siloxane
groups located in neighbouring ‘siloxane’ layers, there are two
neighbouring mesogenic groups which interact strongly within
the same mesogenic layer (see Fig. 4). In eqn. (2) the constants
UVV and ULL are determined by an interaction between parallel
mesogenic groups plus an interaction between siloxane chains.
At the same time the constant UVL is determined by an
interaction between a V-shaped and a linear molecule. In this
case all interacting mesogenic groups cannot be parallel. We
assume that a V-shaped molecule in the synclinic phase adopts
an orientation when one of its mesogenic groups is parallel to
the director while another group makes an angle 2H0 with the
director. In a similar way, one of the mesogenic groups of a
linear molecule in the anticlinic phase is assumed to be parallel
to the local director while the other group makes an angle
of 3H0 with the director in the adjacent layer. Here 2H0 is the
angle between two mesogenic groups in the V-shaped
conformation.
Fig. 7 Molecular simulation of three optimised conformations (one
elongated (a) and two V-shaped (b, c) of Br–Si5–Br. The angles between
the mesogenic moieties in the V-shaped conformations are 150u (b) and
90u (c) respectively.
Now the energies UaHb and UaIb can be expressed as eqn. (3).
UL\L~UV\V~2V0(H)zVss
ULEL~UVEV~V0(H)
(3)
UL\V~V0(H)zV(H,H0)zVss
1
ULEV
~
(V0(H)zV(H,H0)
2
Here V0(H) is an average energy of interaction between two
parallel mesogenic groups within one layer. This energy
depends on the tilt angle H. By contrast, V(H, H0) is an
average energy of interaction between two nonparallel neigh-
bouring mesogenic groups, one belonging to a linear molecule
and another to a V-shaped one. That energy depends on the tilt
angle H and on the angle H0 between two mesogenic groups in
the V-shaped dimer. Finally, Vss is an interaction energy
between two adjacent siloxane chains. It does not depend on H
in a first approximation.
Fig. 8 Spontaneous polarisation as a function of temperature in the
synclinic SmC* and anticlinic SmCA* phases of S–Si3–S.
Theoretical model
The siloxane bimesogen liquid crystal materials under con-
sideration undergo a strong first order transition from the
isotropic to the SmC* phase. In our model of the synclinic–
anticlinic transition we assume for simplicity that both nematic
and smectic order are perfect. In this case the free energy of the
system can be written as eqn. (1):
From eqns. (3) and (2) one obtains eqns. (4) and (5), the
expressions for the interaction constants in eqn. (1).
U
LL~UVV~c(1zs)V0(H)zcsVss
(4)
(5)
1
UVL
~
c(1zs)½V0(H)zV(H,H0)ꢀzcsVss
2
F
~xV log xVzxL log xL{xVW0
rkT
The energies V0(H) and V(H, H0) can further be expressed as
the corresponding averages of the pair interaction potential
between the mesogenic groups [eqns. (6) and (7)]:
(1)
1
2
1
z
x2VUVVzxVxLUVLz xL2 ULL
2
ð
where r is the total number density of molecules, xV and xL are
the molar fractions of V-shaped and linear conformations
V0(H)~ V(n0,r12,n0)d(u12:e)r212dr12du12
(6)
(7)
respectively, xVzxL~1, and the dimensionless constants Uab
,
ð
V0(H,H0)~ V(n0,r12,n1)d(u12:e)r212dr12du12
(a, b~V, L) are the average interaction energies between the
conformers a and b multiplied by the number of nearest
neighbours and divided by temperature.
The interaction constants can further be expressed as
eqn. (2):
where r12 is the vector pointing from the center of the
mesogenic group ‘1’ of one molecule to the center of the
mesogenic group ‘2’ of the neighbouring molecule, the unit
vector u12~r12/r12 is in the direction of r12 and the unit vector e
is the smectic layer normal. Here V(1,2)~V(n1, r12, n2) is the
simplified interaction potential for mesogenic groups parallel to
local directors n1 and n2, respectively.
U
ab~csUa\bzc(1{s)UaEb
(2)
where c is the total number of nearest neighbours and s is a
fraction of nearest neighbours located in the same smectic layer
and where UHab and UaIb are the energies of interaction between
Now the free energy [eqn. (1)] can be written in the form of
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eqn. (8):
synclinic one in the system of organosiloxane bimesogen
molecules.
F
One notes that, apparently, there exists an additional
qualitative factor which favours the anticlinic phase, and
which has not been taken taken into account so far. We suggest
that this factor is related to the additional polar ordering of
V-shaped molecules in the anticlinic SmCA phase. Indeed,
although the smectic C phase is biaxial, one may assume in the
first approximation that short molecular axes are distributed
randomly in the planes perpendicular to the long molecular
axes. This is related to a relatively low biaxiality of the linear
molecular conformation. At the same time the V-shaped
conformation possesses a strongly biaxial polar shape. As a
result there exists a strong polar ordering of such molecules in
the anticlinic phase, determined by polar packing effects. One
notes that the existence of the spontaneous polarisation parallel
to the tilt plane in the anticlinic SmCA phase follows from
symmetry arguments.6 As shown experimentally by Miyachi
et al.20 and Link et al.,21 this polarisation oscillates from layer
to layer together with the direction of the tilt. This polarisation
is not related to molecular chirality. One notes that such
polarisation also exists in conventional anticlinic smectic
phases although it is not related to polar packing effects.
This polarisation, however, is generally rather small and it does
not influence the stability of the anticlinic phase.
In the anticlinic SmCA phase the packing of V-shaped
molecules results in a strong polar molecular ordering (see
Fig. 1). This ordering can be interpreted as an ordering of
transverse molecular steric dipoles. In the case of a symmetric
V-shaped molecule the steric dipole, which characterises the
polar asymmetry of the molecular shape, is parallel to the
molecular C2 axis. The ordering of steric dipoles is determined
by excluded volume effects and is not related to any
electrostatic interaction. At the same time, if molecules also
possess transverse steric dipoles, they will be automatically
ordered as well, and the macroscopic spontaneous polarisation
(within one smectic layer) will appear. In any case, the
additional polar ordering of V-shaped molecules leads to a
decrease of the total free energy of the synclinic SmCA phase in
comparison with that of the synclinic phase.
~xV log xVzxL log xL{xVW0
rkT
1
(8)
z
xVxLc(1zs)(V(H,H0)
2
{V0(H))zc(1zs)V0(H)zcsVss
where we have taken into account that xVzxL~1.
The equilibrium concentration of dimer molecules in the
V-shaped conformation can be determined by minimisation of
the free energy [eqn. (8)] taking into account the constraint
xLzxV~1. One obtains eqn. (9) for the normalised molar
fraction xV.
xV
~ exp½{(1{2xV)(V(H,H0){V0(H))zW0ꢀ
(9)
1{xV
In eqn. (9) V(H, H0) is the average energy of interaction
between two neighbouring mesogenic groups which make an
angle of H0. This energy is expected to be significantly higher
than V0(H) which is the averaged energy of interaction between
two parallel mesogenic groups. Thus the difference DV~
V(H, H0)2V0(H) in the rhs of eqn. (9) is expected to be positive
and sufficiently large. One notes that qualitatively the main
contribution to DV comes from the Maier–Saupe orientational
potential V2P2(cos H). The contribution from this potential to
the difference DV is equal to 2(3/2)V2sin2 H0. This contribution
is positive because V2v0 and is expected to be larger than kT
because in the context of the Maier–Saupe model V2#5 kT.
We also assume that the conformational energy W0 is smaller
than DV. In this case eqn. (9) has two stable solutions. One
solution corresponds to a very small concentration of V-shaped
conformers [eqn. (10)].
xV& exp½{(V(H,H0){V0(H))zW0ꢀ%1 (10)
By contrast, the second solution [eqn. (11)] corresponds to a
very low molar fraction of linear conformations xL~12xV%1.
xL~1{xV& exp½{(V(H,H0){V0(H)){W0ꢀ
(11)
These ideas can be made more quantitave by considering a
simple Landau–de Gennes expansion of the free energy of the
anticlinic phase. Assuming that the nematic and smectic
ordering is perfect, the free energy density of the SmCA
phase can be written as eqn. (12):6
Nature of the SmC–SmCA transition in organosiloxane materials
The solutions xL%1 and xV%1, given by eqns. (10) and (11),
actually correspond to the anticlinic SmCA and synclinic SmC
phases, respectively, because V-shaped molecules are expected
to form the anticlinic phase while the linear ones will form the
synclinic phase. One notes that in the present system the
SmC–SmCA transition is driven by an abrupt change of
concentration of V-shaped conformations. Thus, from the
formal point of view the concentration xV can serve as an order
paramater for this transition. At the same time the correspond-
ing SmC–SmCA transition temperature is determined, as usual,
by the condition that the free energies of the coexisting phases
are equal.
The theory presented above is based on the same main
assumptions as the semiphenomenological model of Carboni
and Coles.7 In that model the transition from the synclinic to
the anticlinic phase is driven by a difference in energy between
the V-shaped and linear conformations of a bimesogen
molecule, specified by the parameter W0. However, our
numerical calculations of the energies of the two conformations
(see earlier section: Structure and properties of the SmC and
SmCA phases) suggest that the parameter W0 is negligibly
small. Then one can readily see from eqn. (8) that in this case
the free energies of the synclinic and anticlinic smectic phases
are exactly the same, at least in the framework of this simple
model. This means that the model described above does not
explain why the anticlinic phase is often more stable than the
1
F
CA~FC0A(w,T)zk(p:½+|wꢀ)z P2z:::
(12)
2x
where p is the polar order parameter within one layer, x is the
generalised susceptibility and w is the vector order parameter of
the smectic C phase. The order parameter w is expressed in
terms of the director n and the smectic layer normal ko,
w~(nko)[n6ko]cos kz, where k is the wave vector of the density
wave in the smectic phase. The absolute value of w is
determined by the tilt angle H, i.e. w~sin 2H/2#H if H2%1.
The second term in eqn. (12) describes the coupling between
the gradient of the tilt order parameter w and the polarisation
in the tilt plane. In the anticlinic SmCA phase the polarisation
parallel to the tilt plane is determined by an oscillation of the
tilt direction from layer to layer. In the ideal anticlinic SmC
structure the vector w possesses opposite signs in adjacent
layers and the polarisation p is located at the boundary between
them.
Minimisation of the free energy [eqn. (12)] with respect to the
polar order parameter p yields eqn. (13):
p~{xk½+|wꢀ~xkk½ko|wꢀ sin kz
Substituting eqn. (13) back into eqn. (12) and averaging over
two adjacent smectic layers (i.e. from z~0 to z~2d) one
(13)
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obtains the simplified expression given in eqn. (14) for the free
energy of one smectic layer:
five silicon atoms, an antiferroelectric phase may occur also.
For some of them, both ferro- and antiferroelectric meso-
phases are present. The ferroelectric phase appears when the
molecules have an elongated conformation, whereas the
antiferroelectric phase does appear when the molecules have
a V-shaped conformation. Thus these compounds may develop
two distinct smectic structures as a function of temperature, the
first one corresponding to a synclinic one at high temperature,
and the second one to an anticlinic one at lower temperature.
Temperature variations of the tilt angle and layer spacing in the
vicinity of the synclinic–anticlinic phase transition presented in
this paper indicate that the transition between synclinic
ferroelectric phase and anticlinic antiferroelectric phase is of
the first kind, as it should be according to the symmetries of the
two phases.
Up to now it has been assumed7 that the V-shaped
conformation possesses a lower energy in comparison with
the linear conformation. In such a case, the anticlinic SmCA
phase is preferable to the synclinic SmC phase, the driving force
for the synclinic–anticlinic SmC–SmCA transition being
determined by a difference of energy between the V-shaped
and linear conformations. However, numerical calculations of
the energy of different conformations of these bimesogenic
molecules presented in the present paper indicate that there is
no difference in energy between V-shaped and linear con-
formations regardless of the number of silicon atoms in the
siloxane moiety.
This led us to develop a different microscopic model of the
synclinic–anticlinic phase transition, which is driven indeed by
a free energy difference between the two phases. Such a
difference is determined by a strong polar ordering (or polar
packing) of V-shaped molecules in the anticlinic phase. Thus
the model explains why the anticlinic SmCA phase is more
stable than the synclinic SmC one, even if the energy of the
V-shaped conformation is the same as that of the linear
conformation. Moreover, it explains why the synclinic SmC
phase is generally the higher temperature one, and why in some
organosiloxane materials the anticlinic SmCA phase is not
present. It follows from the model that the tilt angle in the
anticlinic phase should be weakly temperature dependent
because it is mainly determined by the geometry of the
V-shaped conformation. By contrast, the tilt angle in the
synclinic phase is determined by relevant intermolecular
interactions and thus it is expected to have a much stronger
temperature dependence similar to that observed in conven-
tional smectics C. The actual transition from the synclinic to
the anticlinic phase occurs when the tilt angle of the synclinic
phase is sufficiently close to its value in the anticlinic phase
determined by molecular geometry. The tilt in the synclinic
phase remains to be lower than that in the anticlinic one, and
there is a discontinuity of the tilt angle at the transition point
related to the first order nature of the synclinic–anticlinic phase
transition. These qualitative features of the transition are
confirmed by our measurements presented in this paper.
Further experimental work is required to validate the model in
full.
k2xd2
F
CA~2dFC0A(H,T){
~
(14)
4p
where d is the half period of the smectic structure. One notes
that the last term in eqn. (14) is negative. This term describes a
contribution from the polar ordering of V-shaped molecules to
the total free energy of the anticlinic phase. Thus the free
energy is indeed decreased as a result of such ordering.
The first term in eqn. (14) describes the free energy associated
with the tilt of the director in the synclinic or anticlinic smectic
C phase which has been discussed in detail in the first part of
this section. It should be noted that in the synclinic phase the
tilt angle H(T) increases continuously with the decreasing
temperature. By contrast, in the anticlinic phase composed of
bimesogen molecules the tilt is nearly temperature independent
because it is mainly determined by the geometry of the
organosiloxane V-shaped molecule. Thus the free energy of the
anticlinic phase is given by eqn. (14) where F0CA (H,T)~FC0 A
(H0,T) depends on the constant tilt angle H0#const. One notes
that the angle H0 is directly related to the angle between the two
mesogenic groups in the V-shaped conformation a~p22H0.
However, the constant tilt angle H0 generally does not
correspond to the minimum of the free energy of the anticlinic
phase at a given temperature T. Therefore, at the same
temperature T the free energy F0CA (H0,T), associated with the
constant tilt in the anticlinic SmCA phase, should be higher
than the corresponding free energy F0C (H(T),T) of the synclinic
SmC phase which depends on the tilt angle H(T) which does
correspond to the minimum of the total free energy of the
phase. This effect favours the synclinic SmC phase.
At sufficiently low temperatures (within the SmC range) the
equilibrium tilt angle H differs significantly from H0 and thus
the difference F0CA (H0,T)2FC0 A (H,T) is expected to be rather
large. For some materials this difference may be larger than the
absolute value of the second term in eqn. (14) which is
determined by additional polar ordering in the anticlinic phase.
In this case the synclinic phase is more stable than the anticlinic
one at low temperatures. With the decreasing temperature,
however, the equilibrium tilt angle H(T) approaches H0 and the
F0CA (H0,T)2FC0 A (H,T) decreases. Finally the transition from
the synclinic to the anticlinic SmCA phase occurs when:
FC0A(H0,T){FC0 (H,T)~p2k2x=d2
One notes, however, that the actual transition temperature may
be lower because there exist several other factors which favour
the synclinic phase. For example, the synclinic structure
corresponds to a minimum of the isotropic intermolecular
dispersion interaction modulated by anisotropic molecular
shape.6 Other relevant intermolecular interactions are dis-
cussed in detail in ref. 6. Thus the model presented in this
section enables one to explain why the anticlinic SmCA phase
may be more stable than the synclinic one even if the energy of
the V-shaped conformation is the same as that of the linear
conformation. The model also explains why the synclinic SmC
phase is always the higher temperature one (if it exists at all),
and why in some organosiloxane materials the anticlinic phase
does not appear.
Experimental
X-Ray patterns were recorded on samples filled in Lindemann
glass capillaries with a setup based on a focalised linear CuKa1
beam produced with sealed tube and bent quartz monochro-
mator. Patterns were systematically recorded as a function of
temperature by using a home made oven controlled by an
INSTEC unit (residual temperature fluctuations of ¡0.02 uC)
and an INEL CPS120 counter.
The dilatometry technique used to measure the molar
volume as a function of temperature was developed by
Kovacs22 for the study of polymers, and afterwards applied
Conclusion
In this paper, we considered the case of low molecular weight
bimesogenic liquid crystals containing a siloxane moiety as the
central part of their molecular architecture. These materials are
now well known to develop ferroelectric phases with high
values of the spontaneous polarisation and reasonably short
response times, thus opening interesting possibilities for display
application. When the siloxane moiety contains no more than
2706
J. Mater. Chem., 2001, 11, 2700–2708

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1
to liquid crystals.23 The measurements were performed with a
high precision home-built apparatus, automatically computer
controlled, including data acquisition and temperature control
¡0.03 uC.
(yield: 70%). Mp~45 uC. H NMR (200 MHz, CDCl3, TMS),
d(ppm) 1.55 (m, 2H, CH2LCH-CH2-CH2), 1.7 (m, 2H, CH2-
CH2O), 2.1 (dd, 2H, CH2LCH-CH2), 4.02 (dd, 2H, CH2-OAr),
5.0 (m, 2H, CH2LCH), 5.34, (s, 2H, CH2Ar), 5.8 (m, 1H,
CH2LCH), 6.9 (d, 2H, ArH), 7.45 (m, 5H, ArH), 8.03 (d, 2H,
ArH).
Synthesis
The synthetic route of the preparation of the dimer S–Si3–S is
outlined in Scheme 2. The full detailed procedure for the
preparation of the chiral precursor n-decyl (R)-(z)-4-[(4-
hydroxyphenyl)ethynyl]benzenesulfinate can be found in pre-
vious publications.24
Siloxane dimer with benzyl benzoate moieties (2). To a
degassed solution of 7.13 g (23 mmol) of compound 1 in 50 ml
of anhydrous toluene, were added 2.6 ml (10 mmol) of
1,1,3,3,5,5-hexamethyltrisiloxane. The solution was stirred
under argon atmosphere and 1.6 mL of
a solution of
dicyclopentadienylplatinum(II) chloride in anhydrous dichloro-
methane (2 mg ml21, e.g. 400 ppm per silane function) were
introduced. The reaction mixture was heated up to 70 uC for
24 hours. Then, toluene was evaporated and the residue was
subjected to column chromatography on silica gel (dichloro-
methane–hexane) to give 7.6 g of colorless oil (yield: 92%).
Anal. Calcd (found) for Si3C46H64O8: C 66.63 (66.69); H 7.78
(7.85). 1H NMR (200 MHz, CDCl3), d(ppm) 0.05 (18H, Si-
CH3), 0.52 (t, 4H, Si-CH2), 1.27–1.43 (m, 12H, Si-CH2-(CH2)3-),
1.7 (m, 4H, CH2-CH2-O), 4.02 (t, 4H, CH2-OAr), 5.34 (s, 4H,
CH2Ar), 7.45 (m, 10H, ArH), 6.9 (d, 4H, ArH), 8.02 (d, 4H,
ArH).
Benzyl 4-(hex-5-enyloxy)benzoate (1). To 10.95 g (48 mmol)
of benzyl 4-hydroxybenzoate, 4.8 g (48 mmol) of hex-5-en-1-ol,
and 13.4 g (51 mmol) of triphenylphosphine were introduced
150 ml of anhydrous tetrahydrofuran. To this mixture was
added dropwise a solution of 8.0 ml (51 mmol) of diethyl
azodicarboxylate in 20 ml of anhydrous tetrahydrofuran. The
reaction mixture was kept under argon atmosphere and stirred
overnight at room temperature. After evaporation of the
solvent, the oily residue was purified by column chromato-
graphy on silica gel (dichloromethane–hexane). Further
recrystallisation from isopropanol gave 10.4 g of white crystals
Scheme 2
J. Mater. Chem., 2001, 11, 2700–2708
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Siloxane dimer with benzoic acid moieties (3). A suspension
of 450 mg of 5% palladium on activated carbon in 20 ml of
anhydrous tetrahydrofuran was charged with a solution of
3.05 g (3.68 mmol) of benzyl benzoate-based siloxane dimer 2
in 15 ml of anhydrous tetrahydrofuran. Hydrogen gas was
allowed to slightly bubble into the reaction mixture at room
temperature. The reaction was run to completion as followed
by thin layer chromatography. The mixture was filtered
through Celite, then through a 0.45 mm pore size filter. The
filtrate was finally concentrated and dried out without further
purification to give 2.29 g of white crystals (yield: 96%).
Mp~133 uC. Anal. Calcd (found) for Si3C32H52O8: C 59.22
References
1
2
3
4
5
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1
(59.52); H 8.08 (8.18). H NMR (200 MHz, CDCl3), d(ppm)
0.05 (18H, Si-CH3), 0.52 (t, 4H, Si-CH2), 1.25–1.45 (m, 12H, Si-
CH2-(CH2)3-), 1.7 (m, 4H, CH2-CH2-O), 4.0 (t, 4H, CH2-OAr),
6.9 (d, 4H, Ar-H), 8.0 (d, 4H, Ar-H).
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Siloxane dimer with mesogenic moieties (S–Si3–S). To a flask
equipped with a CaCl2 drying tube were introduced 1.24 g
(1.91 mmol) of the acid-based siloxane dimer 3, 1.68 g
(4.21 mmol) of the phenolic chiral moiety, 170 mg (0.6 mmol)
of catalyst 4-(dimethylamino)pyridinium toluene-p-sulfonate
(DPTS) and 20 mL of anhydrous dichloromethane. The
suspension was stirred for a few minutes then 870 mg
(4.21 mmol) of dicyclohexylcarbodiimide (DCC) were added.
The mixture was stirred for 2 days at room temperature. The
precipitate of dicyclohexylurea was filtered off and the filtrate
was washed with brine and water. After drying the solution
over Na2SO4, the solvent was removed, and the residue
chromatographed on silica gel (dichloromethane–hexane) to
give 2.47 g of white wax-like product (yield: 92%). Enantio-
meric excess, ee~90% (R configuration), was determined by
1H-NMR (200 MHz in CDCl3) by using tris[3-(hepta-
fluoropropylhydroxymethylene)-(z)-camphorato]europium(III)
[Eu(hfc)3, Aldrich, 98%] as chiral shift reagent. Anal. Calcd
(found) for Si3C80H108O12S2: Si 5.98 (5.89); C 68.14 (68.36); H
7.72 (7.75); S 4.55 (4.42). 1H NMR (200 MHz, CDCl3), d(ppm)
0.07 (18H, Si-CH3), 0.53 (t, 4H, Si-CH2), 0.9 (t, 6H, CH3),
1.30–1.60 (m, 40H, CH2), 1.65 (m, 4H, SOO-CH2-CH2), 1.83 (m,
4H, CH2-CH2-OAr), 3.62 (m, 2H, SOO-CH2), 4.05 [m, (4H,
CH2O) and (2H, SOO-CH2)], 6.98 (d, 4H, ArH), 7.24 (d, 4H,
ArH), 7.61 (d, 4H, ArH), 7.70 (d, 4H, ArH), 8.15 (d, 4H, ArH).
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2708
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