Helical Twisting Power of Ru(III) 1,3-Diketonates
A R T I C L E S
3
3
3
3
Qxx ) -
r0 , Qyy ) 0, Qzz ) +
r0
(4)
x8
x8
It is safely concluded that Qxx < 0 and Qzz (∼ -Qxx) > 0 for
∆-1, and this yields Q < 0 (hence â < 0) from eq 2 in a uniaxial
ordering potential (Szz is positive and the largest element).12
The signs of Qxx and Qzz flip upon transforming the axis
system from (x, y, z) to (z, -y, x) for ∆-[Ru(acac)2Lpara], and
therefore a positive Q should result (hence â > 0). This is
exactly as reported above for ∆-2. In fact, this complex carries
bis-chelate group at its terminus, and this must be a disadvantage
in achieving a large Szz. Just one 1,4-phenylene group in Lpara
ligand may not be sufficient either, and this very group may
also be in hindered rotational state, possibly making a nonneg-
ligible contribution to Qyy. At any rate, not only the sign but
also the magnitude of HTP can thus be interpreted consistently.12
Table 1 shows that the shortening of two tails in 1 (from n
) 12 to 6) has only a small enhancing effect on the HTP, which
seems to justify the approach based on the rigid part of a dopant.
A more quantitative analysis of the magnitude of HTP requires
knowledge of the proportionality constant relating Q to â, which
include such temperature-dependent properties as “orienting
strength”9d ê, twist elastic constant K22, and molar volume for
the nematic medium Vm, within the above theoretical framework.
Although we evaluated the âM values over only a small range
of reduced temperatures (T/TN*I ) 0.95-0.96, except for the
ZLI formulation), the nature in the interactions between the
dopant and liquid crystal molecules can vary from one host to
another. In fact, it came to our surprise that N-(4-ethoxyben-
zylidene)-4-n-butylaniline (EBBA), which is a higher homologue
of MBBA by only one methylene unit, experiences the HTP of
1-12 nearly half that of MBBA. It is suggested by a literature
report13a that the solvent elastic constant K22 for EBBA amounts
to roughly twice that for MBBA at temperatures of the
experiments, and this could account for the large gap observed,
since â is inversely proportional to K22. Effects of other
parameters cannot be excluded, however, and weakening in the
solute-solvent interactions (lowering ê/Vm) and the solute
orientational disordering (lowering Szz) in EBBA at a higher
temperature may also contribute to the decrease in â. The ZLI
formulation has also reported on generally lower HTP for the
dopants studied here, but this we previously observed for a
similar complex of Ru(II).7b Higher temperature ranges of some
Figure 2. ICD spectra for MBBA* materials doped with ∆- and
Λ-enantiomers of 1-12 (0.1 mol %, left) and 2 (0.3 mol %, right). Each
spectrum was recorded at 30 °C in a glass cell of 25-µm gap at normal
incidence.
are traceless,10 and the principal axis system of the latter is
usually chosen for eq 2. Most plausible axis systems are included
in Chart 1 for our complexes ∆-1-n and ∆-2. Of primary
importance is that the direction along which the ligand Lper in
1 or Lpara in 2 has been elongated by design should be designated
as the z axis, as it should have the highest propensity of
alignment.
2
Q ) -
(QxxSxx + QyySyy + QzzSzz)
(2)
x3
In short, the HTP depends not only on how chiral the dopant’s
surface is seen along each axis x, y, or z, but also on how well
these axes are aligned to the local nematic director. The surface
elements are defined by eq 3:9d
3
Qij )
[s (sˆ × br) + (sˆ × br) s ]dbr
(3)
∫
i
j
i j
S
x8
where br is a vector giving the position of a point on the
molecular surface, sˆ is the surface normal outward at the same
point, and the integral covers the whole molecular surface.
While the theory has been applied with much success to the
structure-performance relations for organic chiral dopants,9,11
it involves extensive calculation of each of the tensor elements.
In contrast, the rigid and orthogonal coordination geometry of
metal chelates allows one to estimate principal elements Qij’s
with little computational efforts and with reasonable accuracy.
Our reasoning is explained for the ∆-enantiomers first. As a
crude but useful approximation, the acac ligand can be regarded
as a rectangular blade of side length r0 and the backbone ligand
Lper constrained in the xz plane. The elements can then be
analytically estimated as follows for ∆-[Ru(acac)2Lper].
(12) Input in eq 2 of a test parameter set, Qxx ) -Qzz ) -77 Å3 (r0 ) 5 Å),
for the ∆-(acac)2 moiety of 1 together with plausible order parameters for
uniaxial rodlike behavior, Sxx ) -0.3 and Szz ) 0.6, leads to â ) -1.2 ×
102 µm-1, reproducing the HTP of ∆-1-12 (the proportionality constant
between â and Q, which is appropriate for MBBA at 300 K, has been
taken from ref 9c). If Qxx ) -Qzz ) 77 Å3 is assumed instead for ∆-2,
with the constant unchanged, an order parameter set such as Sxx ) -0.1
and Szz ) 0.2 yields â ) 39 µm-1. This means a far less ordered state,
while rodlike behavior is still assumed. Further disordering towards Sxx
0 (while Szz ) 0.2) would yield â diminishing toward 26 µm-1
)
.
(13) (a) Tolmachev, A.; Ferdoryako, A.; Lisetski, L. Mol. Cryst. Liq. Cryst.
1990, 191, 395-399. From the plots reported therein of temperature
dependences of the elastic constants for a homologous series of N-(4-
alkoxybenzylidene)-4-n-butylanilines, the “K22” readings for EBBA and
MBBA at TNI - T ) 13 °C compare at about 2:1 ratio, although the axis
labeling for these plots is not clear. (b) Karat, P. P.; Madhusudana, N. V.
Mol. Cryst. Liq. Cryst. 1977, 40, 239-245. The odd-even effect is also
seen in the K22 values of 4′-n-alkyl-4-cyanobiphenyls (nCB). The values
interpolated at TNI - T ) 15 °C compare roughly at 8:5 (in pN) for 6CB
to 7CB, for instance. (c) Bualek, S.; Patumtevapibal, S.; Siripitayananon,
J. Chem. Phys. Lett. 1981, 79, 389-391. The odd-even alternation in the
HTP values of certain chiral dopants has been observed in the presence (at
20 mol %) of 4,4′-dialkoxyazoxyzenzenes in a nematic host, although the
effect upon elongation from methoxy to ethoxy terminal groups is much
weaker (2-5% diminution) in this case.
(10) The definition of Q being traceless, and consequently eqs 2 and 3, involves
an approximation in which the isotropic contribution of a dopant is left
out of consideration. In reality, effects of chirality are not necessarily
canceled by the isotropic distribution, and Q is better regarded as anisotropic
content of the surface chirality. For a full tensorial approach, see: Kuball,
H.-G.; Ho¨fer, T. In Chirality in Liquid Crystals; Kitzerow, H.-S., Bahr,
C., Eds.; Springer-Verlag: New York, 2001; Chapter 3, pp 67-100.
(11) (a) Ferrarini, A.; Gottarelli, G.; Nordio, P. L.; Spada, G. P. J. Chem. Soc.,
Perkin Trans. 2 1999, 411-417. (b) Pieraccini, S.; Donnoli, M. I.; Ferrarini,
A.; Gottarelli, G.; Licini, G.; Rosini, C.; Superchi, S.; Spada, G. P. J. Org.
Chem. 2003, 68, 519-526.
9
J. AM. CHEM. SOC. VOL. 127, NO. 23, 2005 8455