J. Phys. Chem. 1987, 91, 5151-5152
5151
Rotational Damping and the Spontaneous Polarization in Ferroelectric Liquid Crystals J. W. Goodby,* J. S. Patel,+ and E. Chin AT& T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: June 29, 1987)
The effect of damping of the motion of the chiral center on the magnitude of the spontaneous polarization in ferroelectric smectic liquid crystals is investigated. It is found that, as the local environment of the chiral center is systematically changed so that its motion becomes increasingly restricted, the magnitude of the spontaneous polarization for the mesophase increases rapidly.
Ferroelectric liquid crystals have been heralded as potentially useful operating media in a wide range of high-technology applications, for example, in light valves,’ displays,* spatial light modulator^,^ and pyroelectric detectors! However, the fulfillment of this promise depends greatly on a better fundamental understanding of the physical nature of the ferroelectric properties of these material^.^ Symmetry arguments show that when a smectic C phase, in which the elongated molecules are tilted in diffusely ordered layers, is composed of chiral material the mesophase exhibits a spontaneous polarization (Ps) that manifests itself along the C, axis of the phase.6 These arguments, however, do not predict the strength of these properties for an individual material. Previously, the magnitude of the spontaneous polarization was suggested to be related to the size- and time-dependent couplings of the molecular Alternatively it was dipoles along the C, axis of the recently suggested that trapment of the dipole at the chiral center, and consequently its time-dependent coupling with the dipoles in its local environment, plays the dominating role in the production of the polarization.8 In this study we describe a systematic investigation into damping of the motion of the chiral center and how it markedly effects the spontaneous polarization. For the purposes of this study a number of ( R ) - or (S)-lmethylalkyl 4-(n-octanoyloxy)biphenyl-4’-carboxylates(Figure 1) were synthesized from 4-methoxy-4’-cyanobiphenyl, by first hydrolyzing the cyanide to the acid, demethylating, and then reesterifying the resultant 4-hydroxybiphenyl-4’-carboxylicacid to the desired products. These materials were selected for study because, when the terminal aliphatic chain is extended on the external side of the chiral center, the environment of the asymmetric carbon atom changes from being in a relatively terminal position to being buried within the overall molecular structure. For molecules that pack in smectic layers the terminal position will have a relatively free mobility associated with it. In comparison, positions along the terminal chain closer to the center of the molecule will have less mobility. Thus, by extending the external part of the aliphatic chain the motion of the chiral center becomes damped. The transition temperatures for the liquid-crystalline phase transitions for the propyl to heptyl homologues are shown in Table I. All of these materials exhibit smectic A phases. The isotropic liquid to smectic A transition temperatures were found to fall rapidly with increasing terminal alkyl chain length. Only the ( R ) and (S)-1methylpropyl 4-(n-octanoyloxy)biphenyl-4’-carboxylates were found to exhibit ferroelectric smectic C* phases. Miscibility studies showed that the other materials have virtual A to C* phase transitions below their recrystallization temperatures. The values are not reported here because extrapolations in order to determine virtual transition temperatures are often inaccurate. However, it should be noted that the value for ( R ) -or (S)-I-methylheptyl 4-(n-octanoyloxy)biphenyl-4’-carboxylateis predicted to be below -30 OC. Thus, the A to C* transition temperatures drop dramatically as the terminal aliphatic chain is increased in length. This result is to be expected if the internal motion of the terminal ‘Present address: Bell Communications Research, 33 1 Newman Springs Road, Redbank, NJ 07701.
TABLE I: Transition Temperatures for C,H,,COOC,H&H,COOC*H(CHq) (CHI),CHq
temp, O
C
n
mp, ‘C
C*-A
A-ISO
1 2 3 4 5
50.2 46.2 29.6 37.0 34.3
(26.4)y
(45.6) (38.4) 32.6 (3 1.9) (26.3)
Parentheses indicate monotropic phase transition. aliphatic chain is damped as the aliphatic chain is lengthened, because this leads to an increase in the steric repulsion between molecules which is detrimental to phase formation. A measure of the extent of the damping can be reached qualitatively by determining the spontaneous polarization of each material. The spontaneous polarizations of these materials, except for the first homologue, could not be measured directly. However, the effective polarization for each member was determined from solution studies when mixed with the achiral host, 4-(n-hexyloxy)phenyl 4-(n-decyloxy)benzoate, which exhibits A and C phases. The spontaneous polarization, as a function of temperature, for each material was determined by extrapolation to 100% from results obtained on binary mixtures with the host. The data obtained for each material was reduced to fit a power law dependency of the formg Ps = PO(7-c - T)* where Ps is the polarization at temperature T (“C) and T , is the A to C* transition temperature. From this equation the values of the exponent ( a ) and the inherent polarization (Po) were determined. The values of the spontaneous polarization were also found for temperatures of 10 and 20 OC below the A to C* phase transition. All of these results were then corrected to take into account the optical purities of the individual esters, as shown in Table 11. The results show that the values for the polarization for ( R ) or (S)-1-methylpropyl 4-(n-octanoyloxy)biphenyl-4’-carboxylate from mixtue studies, and in the pure state, are in good agreement. This provides some confidence in the extrapolations used to determine the values of the polarization. The values obtained for the other materials in the homologous series show a rapid increase in the spontaneous polarization between the 1 -methylpropyl and (1) Clark, N. A.; Lagerwall, S. T. Ferroelectrics 1984, 59, 25; Appl. Phys. Lert. 1980, 36, 899. (2) Patel, J. S . ; Goodby, J. W. Proc. SPIE 1986, 613, 130. (3) Armitage, D.; Thackara, J . 1.; Clark, N . A,; Handschy, M. A. Proc. SPIE 1986, 684, 60. (4) Glass, A. M.; Patel, J. S.;Goodby, J . W.; Olson, D. H.; Geary, J. M . J . Appl. Phys. 1986, 60, 2118. ( 5 ) Goodby, J . W.; Chin, E.; Leslie, T. M.; Geary, J . M.; Patel, J . S. J. A m . Chem. Soc. 1986, 108, 4729. Goodby, J. W.; Chin, E. J . A m . Chem. So?. 1986, 108, 4 7 3 6 . ( 6 ) Meyer, R. B. Mol. Cryst. Liq.Cryst. 1977, 40, 3 3 . (7) Bone, M. F.; Coates, D.; Gray, G. W.; Lacey, D.; Toyne, K. J.; Young, D.J. Mol. Crysf. Liq. Cryst. Lett. 1986, 3, 189. (8) Yoshino, K.; Ozaki, M.; Sakurai, 7.; Sakamoto, K.; Honma, M. Jpn. J . Appl. Phys. 1984, 20, L-75. (9) Goodby, J. W.; Patel, J. S. Proc. SPIE 1986, 684, 5 2 .
0022-3654/87/2091-5151$01.50/00 1987 American Chemical Society
5152
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Letten
TABLE 11: Spontaneous Polarization Values for CBH,,COOC6H4C6H4COOC*H(CH3),CH,
Ps,nC n 1(S) 1(R)
optical purity (e.e.) optical rotation"
0.82 0.88 0.82 0.84 0.87 0.89
2 3 4 5
+9 -10.5 -10.3 +9.5 +7.8 +7.8
PO
ff
8.0 7.7 32 30.7 48.8 42.2
0.389 0.379 0.387 0.374 0.389 0.387
AT = 10'
20 18
75 85 97 1 IO
AT = 20b
A T = 10'
P,d sign
26 24 100
I5
-
+
116
127 143
"he optical purity of each ester was determined from the optical purity of each starting alcohol, the optical rotations for which were determined at [ a I z 3 ~b .A T = TAX-- T . 'P,determined for the pure material. d T h e sign of the polarization was determined by standard methods(5) for the pure materials shown. For the compounds that do not exhibit a smectic C* phase in their pure states no designation is given because extrapolations from mixtures can sometimes lead to false results.
60
0 7
v
50
N
E
-ao
E40
z
E 4
30
3 !A
20
f J
0 v,
m
u
IO
0 2
3
4
5
6
No OF CARBON ATOMS ( n1
Figure 1. The inherent or absolute polarization (Po) (nC cm-* 'C-O) plotted as a function of increasing alkyl chain length for the l-methylalkyl 4-(n-octanoyloxy)biphenyl-4'-carboxylates.
the 1-methylbutyl members. The values then level off with the polarization showing a relatively monotonic increase as the terminal alkyl chain length is increased, see Table 11. This sequence of events is to be expected if damping of the mobility of the chiral center is occurring. For the 1-methylpropyl compound the chiral end group rotates relatively freely, but as
the terminal chain becomes extended the chiral center becomes buried in the overall structure. This restricts its motion and therefore a rapid rise in the polarization is experienced as the full weight of the dipole at the chiral center is perceived via couplings with other dipoles in the system. Thus, there is a sudden jump in the polarization between the 1-methylpropyl and 1-methylbutyl members, and after this point the polarization rises monotonically possibly because each additional methylene unit dampens the motion of the chiral center in an incremental fashion. However, it is expected that the value of the polarization will eventually reach a maximum with respect to alkyl chain length and then level off. If the value of Po, which is expressed here as the inherent or absolute polarization of the material, is plotted as a function of the number of methylene units in the terminal chain, then a strong odd-even effect is observed. This effect may be related to an on-axis-off-axis alternation in the steric positioning of the terminal methyl group in the all trans conformational structure. When it is in an off-axis position, as in the I-methylbutyl and 1methylhexyl derivatives, it will sterically interfere with its nearest neighbors as the molecules rotate rapidly about their long axes. Provided that the trans conformation is the dominant species present this will increase the steric interference, thus increasing the damping, and raising the value of Po. Therefore, the even members lie on the upper curve. Damping of the motion of the chiral center in ferroelectric liquid crystals has the effect of increasing Po, which in turn increases the polarization. However, this concomitantly increases the steric repulsive effects which in turn depress liquid-crystalline phase formation. If this mechanism is involved in the manifestation of the polarization, the viscosity of the phase would also be expected to increase because of steric considerations. The response time for reorientational switching of such phases in an electric field is proportional to the viscosity, and inversely proportional to the polarization.' Thus, an increase in the polarization, leading to an increase in viscosity, will not necessarily reduce the reorientational response times in these phases.
