Structure-property correlations in model compounds of oligomer liquid crystals

Article abstract of DOI:10.1021/jp040135h

Structure-property correlations of the following model compounds for oligomer liquid crystals (LCs) have been investigated: monomers, C ₆H₅O(CH₂)_xCH₃ (x = 4 and 5); dimers, C₆H₅O

Full text of DOI:10.1021/jp040135h

J. Phys. Chem. B 2004, 108, 13163-13176
13163
Structure-Property Correlations in Model Compounds of Oligomer Liquid Crystals
Yuji Sasanuma,*,† Tetsushi Ono,† Yoshihiko Kuroda,† Emi Miyazaki,† Ken Hikino,† Jun Arou,†
Kohji Nakata,† Hideaki Inaba,‡ Ken-ichi Tozaki,‡ Hideko Hayashi,‡ and Kentaro Yamaguchi§
Department of Materials Technology, Faculty of Engineering, Faculty of Education, and
The Chemical Analysis Center, Chiba UniVersity, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
ReceiVed: February 16, 2004; In Final Form: May 25, 2004
Structure-property correlations of the following model compounds for oligomer liquid crystals (LCs) have
been investigated: monomers, C6H5O(CH2)xCH3 (x ) 4 and 5); dimers, C6H5O(CH2)xOC6H5 (x ) 3, 4, 5,
and 6); and tetramers, C6H5O(CH2)xOC6H4O(CH2)xOC6H4O(CH2)xOC6H5 (x ) 5 and 6). Deuterium NMR
quadrupolar splittings observed from the deuterated model compounds dissolved in a nematic solvent, 4′-
methoxybenzylidene-4-n-butylaniline (MBBA) or p-azoxyanisole (PAA), were analyzed by the rotational
isomeric state scheme with the maximum entropy method to yield the orientational order parameters, bond
conformations, and molecular dimensions. For the dimers in particular, the solute shapes were estimated
from phase diagrams of the dimer/MBBA systems, the crystal structures were determined by X-ray diffraction,
and the melting points and enthalpies of fusion were evaluated from DSC measurements. From the dimers,
the so-called odd-even effect was clearly observed in not only the orientational order and molecular shape
in the nematic solution but also the crystal structure and thermal properties; that is, the dimers of x ) 4 and
6 have larger order parameters, more anisotropic shapes, better-arranged crystal structures, higher melting
points, and larger enthalpies of fusion than those of x ) 3 and 5. In the nematic solution, the model compounds
preserve the inherent conformational preferences of the ether chain and enhance the shape anisotropy by
increasing the trans fractions. As the orientational correlation is expected to persist only within a short range,
conformations of the tetramers may represent those of polymer LCs with the same ethereal spacers. The
chainlike molecules adjust their spatial configuration to the LC environment, and consequently, physical
properties of the LC system are affected.
1. Introduction
If the concept of liquid crystallinity is defined as a capability
of compounds to form liquid crystalline phases by themselves
(liquid crystallinity in a narrow sense), such properties are often
found for compounds with a rigid (mesogen) component or an
alternation of rigid and flexible (tail or spacer) components:1,2
for example, 4′-methoxybenzylidene-4-n-butylaniline (MBBA,
Figure 1a), p-azoxyanisole (PAA, Figure 1b), 4′-n-alkoxyl-4-
cyanobiphenyl, R,ω-bis[(4,4′-cyanobiphenyl)oxy]alkanes (CBA-
x, x is the number of spacer carbons). These compounds have
been referred to as liquid crystals (LCs).
If a nematic LC is mixed with a nonrigid solute, the nematic-
to-isotropic (NI) transitional temperature (TNI) of the pure LC
is lowered, and a two-phase region is formed between TN and
TI: On heating, the isotropic phase appears at TN, and the
nematic phase completely disappears at TI. The ability of the
solute to destabilize the nematic phase is represented by the
slopes (âN and âI) of the (T/ , x2) and (T/, x2) boundaries in the
Figure 1. Nematic solvents used in this study: (a) 4′-methoxyben-
zylidene- 4-n-butylaniline (MBBA) and (b) p-azoxyanisole (PAA). For
MBBA, the XR, YR, and ZR axes are defined as shown.
of the solutes. The â∞N values of the branched molecules
increase with V/2, whereas those of the n-alkanes appear to be
invariant. The globular solutes are shown to disturb the nematic
order more effectively than the n-alkanes; therefore, chain
molecules are suggested to be closer to LCs than spherical ones.
If we extend the concept of liquid crystallinity to a capability
of molecules to adapt themselves to liquid crystalline phases
(liquid crystallinity in a broad sense), we can consider that all
compounds possess this property to a greater or lesser extent.
Figure 2 shows that the n-alkanes are superior in liquid
crystallinity to the branched molecules.
N
I
T* ()T/TNI) versus x2 (molar fraction of solute) plot.3-7 In
Figure 2, the â∞N values of various compounds dissolved in a
nematic solvent, MBBA, obtained by extrapolation of the âN’s
to the infinity dilution, are plotted against core volumes (V/2’s)
* To whom correspondence should be addressed. E-mail: sasanuma@
faculty.chiba-u.jp. Fax: +81 43 290 3394.
† Department of Materials Technology, Faculty of Engineering.
‡ Faculty of Education.
§ The Chemical Analysis Center.
10.1021/jp040135h CCC: $27.50 © 2004 American Chemical Society
Published on Web 08/06/2004

13164 J. Phys. Chem. B, Vol. 108, No. 35, 2004
Sasanuma et al.
ties about the geometries and dipole-dipole and electrostatic
interactions may impede modeling for conformational analysis.
Although the model compounds here are not LCs in the narrow
sense, they are free from the above problems. Crystal-to-nematic
(CN) and NI transition temperatures, enthalpies, and entropies
of LCs largely depend on the spacer length (i.e., the number of
atoms in the spacer chain). This phenomenon has been found
for oligomer to polymer LCs and designated as the odd-even
effect or odd-even oscillation.1,25-29 To elucidate its origin and
nature, we have adopted the oligomeric models with ether chains
of different lengths.
In this study, ab initio molecular orbital (MO) calculations
were carried out for the monomers and dimers to obtain the
conformational energies for the isolated (free) states. Thermal
properties of the dimers and tetramers were investigated from
DSC measurements. Crystal structures of the dimeric models
were determined by single-crystal X-ray diffraction. Phase
behaviors of the dimer/MBBA systems were investigated at low
solute concentrations to estimate the molecular shapes in the
nematic solutions. The deuterated model compounds were
prepared, dissolved in a nematic LC (either MBBA or PAA),
Figure 2. Correlation between â∞N’s and core volumes (V2/’s) of
various compounds dissolved in MBBA: open circle (O), n-alkanes
(in order of V/2, hexane, octane, nonane, decane, undecane, dodecane,
tridecane, tetradecane, hexadecane, icosane, tetracosane; refs 3 and 7);
open square (0), branched molecules (cyclopentane, 2,2-dimethyl-
butane, tetramethyltin, cyclooctane, 2,2,4-trimethylpentane, cis-decalin,
hexamethyldisiloxane, 2,2,4,6,6-pentamethylheptane, 2,2,4,4,6,8,8-hepta-
methylnonane, tetrabutyllead, tetrabutyltin, decamethyltetrasiloxane; ref
3); filled circle (b), dimers-3, -4, -5, and -6 (this study).
2
and measured by H NMR spectroscopy. The NMR data were
analyzed by our improved method to evaluate the orientational
order parameters, bond conformations, and molecular dimen-
sions; the applicability of the method to the complicated LC-
like molecules has been examined. From the theoretical and
experimental investigations, the liquid crystallinity of oligomer
to polymer LCs as well as the model compounds is discussed
here.
At an early stage of our studies on LCs, the rotational isomeric
state (RIS) scheme,8.9 which has been applied mainly to
polymers, was extended to conformational analysis of chain
molecules dissolved in nematic solvents. To facilitate the
analysis, the cylindrical-symmetry and single-ordering-matrix
approximations were adopted. In the former, biaxiality SXX
-
SYY is neglected, and the latter means that the orientational order
parameter SZZ is identical for all conformers. By this method,
2. Materials and Methods
2
we analyzed H NMR data for n-alkanes10,11 and ethers11-13
2.1. Ab Initio MO Calculations. Ab initio MO calculations
were carried out for representative conformers of the monomeric
and dimeric model compounds with the Gaussian98 program30
installed on an HPC-P4L/IAX computer. The geometrical
parameters were fully optimized, and the thermal corrections
were calculated at the Hartree-Fock (HF) level using the 6-31G-
(d) basis set (abbreviated as HF/6-31G(d)). Then, a scale factor
of 0.9135 was used to adjust the thermodynamic quantities.31,32
With the geometrical parameters determined, the single-point
calculation was performed by including up to the second-order
Møller-Plesset (MP2) perturbation with the 6-311+G(3df,2p)
basis set (MP2/6-311+G(3df,2p)). The Gibbs free energies
(∆Gk’s, k ) conformer) were evaluated from the SCF energy
and the thermal correction. In addition, geometries of some
conformers were optimized at the B3LYP/6-31G(d) level to be
dissolved in nematic solvents. However, the simplification tends
to overestimate fractions of the extended conformers, and hence,
the solutes appear to be considerably rigid.
Recently, we have improved the simulation scheme. From
the shape anisotropy of solute, the SZZ and SXX - SYY terms are
evaluated for each conformer. The maximum entropy (MaxEnt)
method14 is employed in the fitting procedure to derive the most
probable solution from a limited amount of experimental data.
Using the modified method, we have investigated orientational
and conformational characteristics of n-alkanes,15,16 1,6-
dimethoxyhexane,16 and alcohols17,18 dissolved in nematic LCs
and successfully obtained results consistent with those obtained
by other methods.19-23 The simulation scheme has been further
extended to lyotropic LCs of sodium octanoate/1-decanol/
water24,17 and sodium octanoate/1-butanol/water.18
2
used in simulations for H NMR data.
In this study, we have treated model compounds of oligomer
LCs (i.e., oligomeric models for polymer LCs with different
spacer lengths; see Figure 3): monomeric models, 1-phenoxy-
pentane (monomer-5) and 1-phenoxyhexane (monomer-6);
dimeric models, 1,3-diphenoxypropane (dimer-3), 1,4-diphenoxy-
butane (dimer-4), 1,5-diphenoxypentane (dimer-5), and 1,6-
diphenoxyhexane (dimer-6); tetrameric models, 1,5-bis{p-[5-
(phenoxy)pentyloxy]phenoxy}pentane (tetramer-5) and 1,6-
bis{p-[5-(phenoxy)hexyloxy]phenoxy}hexane (tetramer-6). In
this paper, these compounds are referred to by the abbreviations
in the parentheses. The benzene ring and ether chain are
considered to be the mesogenic core and spacer (or tail),
respectively. The abbreviations represent the number of benzene
rings and carbon atoms in the ether chain: For example,
tetramer-5 has four benzene rings and three ethereal spacers
with five methylene units. The reasons we have adopted these
model compounds are as follows: Mesogens of LCs mostly
have rotatable bond(s) and polarized substituent(s). The obscuri-
2.2. Sample Preparation. Here, only deuterations of the
model compounds and MBBA are described;33 however, the
nondeuterated compounds were similarly prepared and used in
measurements other than 2H NMR. Symbols o and φ represent
the ortho and ortho + meta positions of the benzene rings,
respectively. Nondeuterated MBBA and PAA were, respectively,
purchased from Tokyo Kasei Kogyo and Sigma-Aldrich and
used without further purification.
2.2.1. Monomer-5-d11.34 Pentanoic acid (30.6 g) was dissolved
in methanol (100 mL), and sodium hydroxide was added so
that the pH would be 8.0. The solution was condensed, the
residue was dried under reduced pressure, and sodium pen-
tanoate (24.7 g) was obtained. The sodium pentanoate (24.7
g), sodium hydroxide (5.4 g), platinum on activated carbon (Pt/
C, Pt 5%, 7.6 g), and deuterium oxide (99 atom % D, 100 mL)
were sealed in a 300-mL autoclave and heated at 220 °C for
110 h. After being cooled to room temperature, the reaction

Models for Oligomer Liquid Crystals
J. Phys. Chem. B, Vol. 108, No. 35, 2004 13165
Figure 3. Examples of the model compounds: (a) monomer-6, (b) dimer-6, and (c) tetramer-6. The methylene and methyl groups in the ether
chain are referred to by Greek letters (R, â, γ, δ, ꢀ), and the bonds and the aromatic carbons are numbered as indicated. For the tetramers, the
atomic groups and bonds are designated in the same manner as for the dimers. In tetramer-6-d12, only the central spacer is deuterated. The XR, YR,
and ZR axes are defined for the phenyl groups of the monomers and dimers. The ortho and ortho + meta positions of the aromatic ring are represented
by o and φ, respectively.
mixture was filtered, acidified to pH ) 4 with hydrochloric acid
(5.0 mol L-1), and extracted with diethyl ether. After being dried
over sodium sulfate, the organic extract was filtered and
condensed to yield perdeuterated pentanoic acid. The above
procedures were repeated to obtain an adequate amount for the
next step. The total yield was 15.7 g.
The deuterated pentanoic acid (15.7 g) was dissolved in dry
THF and added dropwise to a solution of LiAlD4 (10.1 g) in
THF (300 mL), and the mixture was refluxed for 2 h. The
residual LiAlD4 was quenched with water, and Wakogel C-200
(13.0 g) was added to absorb inorganic deposits. After being
stirred for 1 h, the mixture was diluted with THF (300 mL)
and allowed to stand. The top clear layer was filtered with
suction and condensed, and 12.3 g of 1-pentanol-d11 was
obtained.
Phosphorus tribromide (12.8 g) was added dropwise to the
1-pentanol-d11 (12.3 g). The mixture was refluxed for 2 h,
washed with water (100 mL), and filtered with suction. The
filtrate separated into three layers: 1-pentanol-d11, water, and
1-bromopentane-d11. Only the bottom layer (1-bromopentane-
d11) was collected, then Wakogel C-200 (5.0 g) was added, and
the mixture was stirred and filtered. After being dried over
sodium sulfate overnight, the solution was filtered, and 10.0 g
of 1-bromopentane-d11 was obtained.
The 1-bromopentane-d11 (10.0 g), 1-bromopentane (9.4 g),
potassium hydroxide (7.1 g), and phenol (11.7 g) were dissolved
in ethanol (85 mL), and the solution was refluxed for 8 h. The
reaction mixture was filtered, distilled to remove ethanol, and
extracted with diethyl ether (100 mL) and water (100 mL). The
organic extract was washed successively with potassium hy-
droxide (10%), water, dilute sulfuric acid, and water again. After
being dried over sodium sulfate, the solution was filtered and
distilled under pressure to yield monomer-5-d11 (1-phenoxy-
pentane-1,1,2,2,3,3,4,4,5,5,5-d11, 7.3 g).
2.2.4. Phenol-o-d2. Phenol (25.0 g) was dissolved in ethanol-
d6 (50 g), deuterium chloride (20 wt % solution in deuterium
oxide, 100 g) was added, and the solution was refluxed for 50
h. The reaction mixture was condensed to remove deuterium
oxide, dried over sodium sulfate, and filtered. After the filtrate
was cooled, precipitated phenol-2,6-d2 (phenol-o-d2, 16.5 g)
was collected by suction filtration and dried under reduced
pressure.
2.2.5. Dimer-3-d6, Dimer-4-d8, Dimer-5-d10, and Dimer-6-
d12. These deuterides were prepared by procedures similar to
those in section 2.2.1. Malonic, succinic, glutaric, and adipic
acids were deuterated with NaOH, Pt/C, and D2O, and reduced
with LiAlD4 to yield 1,3-propanediol-d6, 1,4-butanediol-d8, 1,5-
pentanediol-d10, and 1,6-hexanediol-d12, respectively. These
diols were converted to the corresponding R,ω-dibromoalkanes
with phosphorus tribromide. Dimer-3-d6 (1,3-diphenoxypropane-
1,1,2,2,3,3-d6), dimer-4-d8, dimer-5-d10, and dimer-6-d12 were
prepared from the R,ω-dibromoalkanes and phenol. The end
products were purified by recrystallization in methanol.
2.2.6. Dimer-3-o-d4, Dimer-4-o-d4, Dimer-5-o-d4, and Dimer-
6-o-d4. As described in section 2.2.5, these compounds were
prepared with the phenol-o-d2 obtained in section 2.2.4.
2.2.7. Tetramer-5-d10.35 Phenol (2.5 g) and potassium hy-
droxide, dissolved in ethanol (90 mL), were added dropwise to
a solution of 1,5-dibromopentane (44.0 g) in ethanol (100 mL).
To avoid formation of 1,5-diphenoxypentane, 1,5-dibromopen-
tane was used in large excess. The mixture was refluxed for 8
h, filtered, condensed, and extracted with water and diethyl ether.
The organic extract was washed successively with sodium
hydroxide (10%), water, dilute sulfuric acid, and water again.
The solution was dried over sodium sulfate, filtered, and distilled
under reduced pressure to yield 1-bromo-5-phenoxypentane (3.2
g).
Chlorobenzene (20 mL), hydroquinone (6.12 g), sodium
hydroxide (1.67 g), and water (20 mL) were mixed, stirred into
a uniform solution, and heated to 100 °C. To the mixture, 1,5-
dibromopentane-d10 (3.2 g), prepared as in section 2.2.5, was
added dropwise. After reflux for 10 h, the solution was acidified
with hydrochloric acid. The precipitate was collected by suction
filtration and dried under pressure, and 1.8 g of 1,5-bis(p-
hydroxyphenoxy)pentane-d10 was obtained.
2.2.2. Monomer-6-d13. This compound was prepared in the
same way as in section 2.2.1, except that hexanoic acid and
phosphorus trichloride were used in place of pentanoic acid and
phosphorus tribromide, respectively.
2.2.3. Monomer-5-R-d2 and Monomer-6-R-d2. These partial
deuterides were prepared from nondeuterated pentanoic and
hexanoic acids, as described in sections 2.2.1 and 2.2.2.

13166 J. Phys. Chem. B, Vol. 108, No. 35, 2004
Sasanuma et al.
The 1,5-bis(p-hydroxyphenoxy)pentane-d10 (1.3 g), 1-bromo-
5-phenoxypentane (3.2 g), and potassium hydroxide (0.5 g) were
dissolved in ethanol (100 mL) and refluxed for 10 h. Precipitated
tetramer-5-d10 was collected by suction filtration. The solubility
of the product was examined to find proper solvents for
recrystallization. It is slightly soluble in chloroform but insoluble
in methanol, water, dimethyl sulfoxide, n-hexane, THF, and
diethyl ether. The crude product was recrystallized with
chloroform, and 2.1 g of the end product, tetramer-5-d10 (1,5-
bis{p-[5-(phenoxy)pentyloxy]phenoxy}pentane-1,1,2,2,3,3,4,4,5,5-
d10), was obtained.
were performed using the teXsan crystallographic software
package.38
Crystal data on dimer-3: C15H16O2, monoclinic crystal
system, space group C2/c, a ) 21.697(7) Å, b ) 5.134(2) Å, c
) 11.2054 Å, â ) 99.721(4)°, V ) 1230.3(6) Å3, Z ) 4, Fcalc
) 1.232 g cm-3, data collection at -100 °C, residual R ) 0.088.
Crystal data on dimer-4: C16H18O2, monoclinic crystal system,
space group P21/c, a ) 14.883(3) Å, b ) 5.541(1) Å, c )
7.966(2) Å, â ) 99.759(3)°, V ) 647.3(2) Å3, Z ) 2, Fcalc
)
1.243 g cm-3, data collection at -110 °C, residual R ) 0.062.
Crystal data on dimer-5: C17H20O2, monoclinic crystal system,
space group C2/c, a ) 26.042(8) Å, b ) 5.110(2) Å, c )
11.162(3) Å, â ) 107.019(4)°, V ) 1420.3(7) Å3, Z ) 4, Fcalc
) 1.199 g cm-3, data collection at -100 °C, residual R ) 0.075.
Crystal data on dimer-6: C18H22O2, monoclinic crystal system,
space group P21/c, a ) 15.835(5) Å, b ) 7.133(2) Å, c )
2.2.8. Tetramer-6-d12. This compound was prepared as in
section 2.2.7, except that 1,6-dibromohexane was used instead
of 1,5-dibromopentane.
2.2.9. Tetramer-5-φ-d8 and Tetramer-6-φ-d8. Hydroquinone
(27.2 g) was dissolved in deuterium oxide (100 mL). Sulfuric
acid-d2 (3.4 g) was added dropwise, and the solution was
refluxed for 5 days. After the reaction mixture was cooled in a
refrigerator, the precipitate was collected by suction filtration,
and 19.7 g of perdeuterated hydroquinone was obtained.
Tetramer-5-φ-d8 and tetramer-6-φ-d8 were prepared with the
hydroquinone-d6, as in section 2.2.7.
6.534(2) Å, â ) 92.143(4)°, V ) 737.6(4) Å3, Z ) 2, Fcalc
)
1.217 g cm-3, data collection at -153 °C, residual R ) 0.073.
2.6. Phase Behavior Observations. The procedure for the
sample preparation and measurement has been described previ-
ously.11,18
3. Results and Discussion
2.2.10. MBBA-2,6-d2. This compound was prepared from
p-anisaldehyde and p-butylaniline-2,6-d2 as described previ-
ously.11,36
2.3. 2H NMR Measurements. The required amounts of the
model compound (solute) and nematic solvent (MBBA or PAA)
were weighed in a standard NMR tube of 5 mm o.d. The sample
tube was degassed, filled with dry nitrogen, and sealed to avoid
thermal degradation of the solvent by oxygen.
3.1. Ab Initio MO Calculations and Conformational Free
Energies. According to the RIS scheme,8,9 statistical weight
matrices for bonds 2 and n (n g 3) (see Figure 3) of the ether
chains of the monomers, dimers, and tetramers may be written
as
σ2 σ2
1
U2 ) 0 0
0
0
(1)
[
]
Deuterium NMR spectra were recorded at 76.65 MHz on a
JEOL JNM LA-500 spectrometer equipped with a variable-
temperature controller. During the measurement, the probe
temperature was maintained at a given temperature within (0.1
°C fluctuations. The free induction decays (FIDs) were ac-
cumulated 256-2048 times by using the single pulse excitation
scheme. The π/2 pulse width was so determined as to maximize
the signal-to-noise ratio as 15 µs for the monomers and dimers
or 20 µs for the tetramers, and the recycle delay was 1.0 s. The
FID underwent Fourier transformation by the gNMR program.37
In the apodization, an exponential function was used; the
broadening factor was set to 5-20 Hz.
2.4. Thermal Analysis. Thermal analyses were carried out
for the dimers and tetramers with a Rigaku DSC8230 differential
scanning calorimeter at a heating rate of 5 °C min-1 under a
flow of dry nitrogen. The melting points and enthalpies of fusion
were calibrated from those of indium, tin, and lead of high
purity.
0 0
and
σn
σn
σnωn σn
σn
σnωn
1
Un ) 1
(2)
[
]
1
where σn is the statistical weight for the first-order interaction
(between atoms and groups separated by three bonds) of bond
n, and ωn is the second-order interaction (by four bonds)
occurring in g(g- conformations for bonds n - 1 and n. The
statistical weight is the Boltzmann factor of the corresponding
conformation energy (e.g., σn ) exp(-Eσn/RT), where R is the
gas constant and T is the absolute temperature). Both MO
calculations and X-ray diffraction indicate that the phenyl C1-C2
and ethereal O-CR bonds are fixed in an eclipsed form;
therefore, the internal rotation of bond 1 has not been considered
(see Figure 3).
2.5. X-ray Diffraction. Single crystals of dimers-3, -4, -5,
and -6 were prepared by recrystallization at room temperature
from the 1-butanol, n-hexane, 1-butanol, and methanol solutions,
respectively. It took several days to a few weeks for the crystals
to grow large and thick enough (ca. 0.4 × 0.4 × 0.2 mm3) for
X-ray measurements. Dimers-3 and -5 yielded colorless needle
crystals, and dimers-4 and -6 gave colorless plate crystals. The
latter crystallized faster than the former.
In the RIS scheme, the ∆Gk value relative to the all-trans
state is approximated as a function of Eσ’s and Eω’s. For
example, the g+tt..., tg+t..., and ttg+... conformations have
weights of σ2, σ3, and σ4, respectively; therefore, the individual
∆Gk values may correspond to Eσ , Eσ , and Eσ , respectively.
2
3
4
Here, for example, the g+tt... conformation represents that bonds
2, 3, 4... adopt gauche+, trans, trans... states, respectively. The
tg+g-t... conformation has a weight of σ3σ4ω4. Thus, the Eω
4
+g-
The X-ray diffraction was measured with a Bruker SMART-
1000 CCD system, and monochromatic Mo KR radiation was
generated at 45 kV and 35 mA. The single crystal was mounted
on a glass fiber and cooled to a low temperature. Reflection
intensities were collected to a maximum 2θ value of ca. 57°
with 0.60° oscillations and 20 s exposures. The crystal-to-
detector distance was 50 mm. All crystallographic computations
value may be obtained from ∆Gtg t... - Eσ - Eσ . Similarly,
3
4
all Eσ and Eω values of the monomers and dimers were evaluated
from ∆Gk’s at the MP2/6-311+G(3df,2p)//HF/6-31G(d) level,
as shown in Table 1.
The Eσ value corresponds to the gauche energy. In the C-O
n
bond, the trans conformation is stable (Eσ ≈ 1 kcal mol-1),
2
whereas its adjoining C-C bond shows a gauche preference

Models for Oligomer Liquid Crystals
J. Phys. Chem. B, Vol. 108, No. 35, 2004 13167
TABLE 2: Melting Points (TM’s) and Enthalpies (∆HM’s)
and Entropies (∆SM’s) of Fusion of Dimeric and Tetrameric
Model Compounds
∆HM
∆SM
TM (°C)
(kJ mol-1
)
(J mol-1 K-1
)
dimer-3
dimer-4
dimer-5
dimer-6
59.1
98.0
44.1
80.5
38.3
54.6
41.8
56.0
115
147
132
158
tetramer-5a
77.3
99.3
143.7
39.0
83.4
166.2
111
224
399
tetramer-6
a On heating, two endothermic peaks were observed.
smaller than that (2-3 kcal mol-1) of n-alkanes.8,41 These energy
parameters represent the inherent conformational features of the
model compounds in the isolated (free) state. One should be
allowed to assume that the central spacers of tetramers-5 and
-6 have essentially the same conformational energies as those
of dimers-5 and -6, respectively.
3.2. Thermal Analysis. In Table 2, DSC data for the dimers
and tetramers are listed. Melting points (TM’s) and enthalpies
(∆HM’s) and entropies (∆SM’s) of fusion of the dimers show
clear odd-even oscillations: Dimers-4 and -6 exhibit larger
values than dimers-3 and -5. As mentioned in the Introduction,
similar phenomena have been found for oligomer to polymer
LCs. For example, CBA-x’s exhibit CN and NI transitions.25
The sums of both transition enthalpies for x ) 3, 4, 5, and 6,
equivalent to the enthalpy of fusion, were evaluated as 47.5,
50.2, 32.7, and 55.8 kJ mol-1, close to those obtained here for
the dimers.
Figure 4. Examples of second-order ωn interactions occurring in the
g(g- conformations for the n - 1 and n bond pairs: (a) ω4 of dimer-
3, (b) ω4 of dimer-4, and (c) ω5 of dimer-5.
TABLE 1: Conformational Energies of Monomeric and
Dimeric Model Compounds, Evaluated from ab Initio MO
Calculations at MP2/6-311+G(3df, 2p)//HF/6-31G(d) Levela
monomer-5 monomer-6 dimer-3 dimer-4 dimer-5 dimer-6
First-Order Interaction
Eσ
Eσ
Eσ
Eσ
Eσ
0.91
-0.31
0.65
0.90
-0.33
0.61
0.94
1.13
0.86
0.89
2
3
4
5
6
-1.18 -0.30 -0.61 -0.39
0.69
0.49
0.65
0.52
0.59
0.59
0.63
Tetramer-5 undergoes two transitions to the melting point:
the first occurring at 77.3 °C is probably a crystal-to-crystal
transition, and the second at 99.3 °C is the actual melting point.
Second-Order Interaction
Eω
Eω
Eω
0.45
1.55
0.43
1.40
1.71
2.62 -0.66
0.52
1.35
0.13
1.34
4
5
6
The sum of the two transition enthalpies is 122.4 kJ mol-1
.
Tetramer-6 melts at 143.7 °C, and the enthalpy of fusion is 166.2
kJ mol-1. Because the tetramers have three spacers, enthalpies
per spacer of tetramers-5 and 6 are, respectively, 40.8 and 55.4
kJ mol-1, almost the same as those of dimers-5 and -6.
a In kcal mol-1
.
(Eσ ) -0.3 to -1.2 kcal mol-1), which is known as the
3
attractive gauche effect in X-C-C-Y bond sequences (X, Y
) electronegative atoms).39,40 The Eσ values (0.5-0.7 kcal
mol-1) for other C-C bonds are essentially equivalent to that
3.3. Crystal Structures of Dimers. Figure 5 shows crystal
structures of the four dimers, and the individual molecules are
depicted in Figure 6. The molecules of dimers-3 and -5 are bent
at right angles; angles (θ’s) between para axes of the two phenyl
rings (see Figure 7) are 86.6° (dimer-3) and 85.8° (dimer-5).
The two C-C bonds adjacent to the C-O bond adopt the g-
conformation. Accordingly, dimers-3 and -5 crystallize to be
in one of the most stable states predicted by the MO calculations.
Dimer-4 forms an effective intermolecular stacking arrange-
ment of the phenyl rings. Its spacer adopts a stable tg+tg-t
conformation, which yields a parallel arrangement of the two
phenyl groups (θ ) 0.0°). These facts suggest that dimer-4 forms
a thermally stable crystal. The molecules of dimer-6 are arranged
parallel to each other but are forced to be in the all-trans state
(∼0.5 kcal mol-1) of n-alkanes.8,41 The Eω value represents
n
the additional energy occurring in the g(g- conformations for
bonds n - 1 and n. In bonds 2 and 3, the ω3 conformation
does not exist because of a steric conflict between the benzene
ring and γ methylene group; therefore, the Eω value has been
3
assumed to be ∞, being absent from Table 1. For the dimers,
the magnitude of Eω depends on the number of methylene units
4
in the spacer. Dimer-3 exhibits a large positive value of 2.62
kcal mol-1 due to the O‚‚‚O repulsion (Figure 4a). On the other
hand, dimer-4 gives a negative value of -0.66 kcal mol-1. This
is due to the (C-H)‚‚‚O attraction between the oxygen and the
R methylene group (Figure 4b). This phenomenon has also been
found in poly(ethylene oxide),42-45 poly(propylene oxide),45-48
poly(tetramethylene oxide),47,49 and their model compounds.
(θ ) 0.0°), despite the gauche preference of bond 3 (Eσ
)
3
-0.39 kcal mol-1).
The odd-even effect in the crystal structure corresponds to
the effect in the thermal properties. Dimers-4 and -6 can attain
the parallel molecular arrangement and effective benzene
stacking and, hence, give larger ∆HM values than dimers-3 and
-5. Crystal densities of dimers-3, -4, -5, and -6 are 1.232, 1.243,
1.199, and 1.217 g cm-3, respectively. The ∆SM values of
tetramers-5 and -6 are 335 () 111 + 224) and 399 J mol-1
K-1, respectively. From these data, their entropies per spacer
can be estimated as 112 (tetramer-5) and 133 (tetramer-6) J
mol-1 K-1, comparable to those of dimers-5 and -6, respectively.
Dimers-5 and -6 have small positive Eω values of 0.52 and
4
0.13 kcal mol-1, respectively. A similar variation in Eω with
the number of methylene units has been found for R,ω-
dimethoxyalkanes CH3O(CH2)xOCH3 (x ) 4-8); the Eω values
for x ) 4, 5, and 6 were evaluated from ab initio MO
calculations at the MP2/6-31+G*//HF/6-31G* level to be -0.43,
0.66, and 0.24 kcal mol-1, respectively.49 The ω5 and ω6
interactions correspond to the so-called pentane effect (Figure
4c); however, the Eω and Eω values (1.3-1.7 kcal mol-1) are
5
6

13168 J. Phys. Chem. B, Vol. 108, No. 35, 2004
Sasanuma et al.
Figure 7. Molecular axis system for, for example, dimer-3. The origin
is located at the center of gravity, G. The principal axes of inertia are
assumed to be the molecular axes, X, Y, and Z. The dimension along
the Z axis, AZ,k, calculated from the van der Waals radii of the
constituent atoms, is considered to be the conformer length. The angle
between two para-axis vectors (shown by the arrows) of the phenoxy
groups is designated as θ.
Figure 5. Crystal structures of (a) dimer-3, (b) dimer-4, (c) dimer-5,
and (d) dimer-6. For the details, see section 2.5.
Figure 8. Phase diagram of the dimer-3/MBBA system. Slopes of the
upper (âI) and lower (âN) boundaries were determined as 0.993 and
1.269, respectively, on the scale of T/TNI versus mole fraction. Here,
TNI stands for the NI transition temperature of pure MBBA.
â∞N values are plotted against the core volume V/2 of the
solute.50
If two solutes have the same V/2 value, the one with a larger
â∞N is expected to be more globular than the other. The âN∞
values for the dimer/MBBA systems are plotted with filled
circles in Figure 2. The four points, showing a large odd-even
oscillation, are located in the region of spherical solutes. In
the nematic LC, the dimers are spherical rather than linear,
and dimers-3 and -5 are more isotropic in shape than dimers-4
and -6.
2
Figure 6. Molecules in the crystal: (a) dimer-3, (b) dimer-4, (c) dimer-
5, and (d) dimer-6. The conformations of the C-C bonds adjacent to
the ether linkage are shown.
3.5. H NMR Spectra. 3.5.1. Monomers. Panels a and b of
Figure 9 show 2H NMR spectra observed from monomer-5-d11
and monomer-5-d11 + monomer-5-R-d2 dissolved in MBBA at
25 °C and 2.0 mol % (of solute), respectively. By a comparison
of the two spectra, we could assign the second peaks from the
outside to the R methylene group. The interpeak distance
corresponds to the quadrupolar splitting (|∆νR|). The other
quadrupolar splittings were so assigned as to decrease in the
order of the Greek alphabet. Figure 9c shows a 2H NMR
spectrum of monomer-6-d13 in MBBA at 25 °C and 2.0
mol %. Similarly, the quadrupolar splittings were assigned as
shown in Figure 9.52 The |∆ν| values are given in the caption
of Figure 9.
In the crystal, therefore, tetramers-5 and -6 may be similar in
spacer conformation to dimers-5 and -6, respectively.
3.4. Phase Behaviors of Dimers. In Figure 8, as an example,
the phase diagram of the dimer-3/MBBA system is shown. The
filled circles and squares represent the experimental data. Linear
least-squares fitting to the lower and upper boundaries yielded
the slopes of 1.269 (âN) and 0.993 (âI), respectively. The slopes
at the infinite dilution, â∞N and â∞I , can be evaluated from the
âN and âI values, as in previous papers:3-7,11,18 dimer-3/MBBA,
â∞N ) 1.194 and âI∞ ) 1.059; dimer-4/MBBA, â∞N ) 0.912 and
â∞I ) 0.831; dimer-5/MBBA, âN∞ ) 1.207 and â∞I ) 1.069;
dimer-6/MBBA, â∞N ) 0.930 and â∞I ) 0.846. In Figure 2, the
2
3.5.2. Dimers. Panels a and b of Figure 10 show H NMR
spectra of dimer-3-d6 + dimer-3-o-d2 and dimer-4-d8 + dimer-
4-o-d2 dissolved in MBBA at 25 °C and 2.0 mol %, respectively.

Models for Oligomer Liquid Crystals
J. Phys. Chem. B, Vol. 108, No. 35, 2004 13169
Figure 11. Deuterium NMR spectra observed from (a) dimer-5-d10
+
dimer-5-o-d2 and (b) dimer-5-d10 + dimer-5-R-d2 dissolved in MBBA
at 25 °C and 2.0 mol %. As indicated, the peaks were assigned to the
individual atomic groups. The |∆ν| values of the R, â, and γ methylene
groups and the ortho C-D bond are, respectively, 27.74, 36.31, 30.64,
and 0.62 kHz. The |DHD| value is 310 Hz.
Figure 9. Deuterium NMR spectra observed from (a) monomer-5-
d11, (b) monomer-5-d11 + monomer-5-R-d2, and (c) monomer-6-d13
dissolved in MBBA at 25 °C and 2.0 mol % (of solute), respectively.
As indicated, the peaks were assigned to the individual atomic groups
(see Figure 3). The |∆ν| values of the R, â, γ, and δ methylene and
methyl groups of monomer-5-d11 are, respectively, 27.30, 30.55, 25.27,
25.27, and 3.55 kHz, and those of the R, â, γ, δ, and ꢀ methylene and
methyl groups of monomer-6-d13 are respectively 31.35, 35.44, 31.35,
31.35, 25.52, and 11.63 kHz.
Figure 12. Deuterium NMR spectra observed from (a) dimer-6-d12
+
dimer-6-o-d2 and (b) dimer-6-d12 + dimer-6-R-d2 dissolved in MBBA
at 25 °C and 2.0 mol %. As indicated, the peaks were assigned to the
individual atomic groups. The |∆ν| values of the R, â, and γ methylene
groups and the ortho C-D bond are, respectively, 35.67, 40.74, 39.83,
and 4.68 kHz. The |DHD| value is 390 Hz.
Shown in Figure 11 are 2H NMR spectra of deuterated
dimer-5 species dissolved in MBBA at 25 °C and 2.0 mol %:
(a) dimer-5-d10 + dimer-5-o-d2 without (upper) and with (lower)
1H broad-band decoupling and (b) dimer-5-d10 + dimer-5-R-
d2. Comparison of these spectra enabled us to assign the third
peaks from the outside to the R methylene group. Dimer-5 has
two R, two â, and one γ methylene units; therefore, the
outermost and the smallest peaks stem from the â and γ
methylene groups, respectively. The quadrupolar splitting due
to the ortho C-D bond is so small that two H-D dipolar
doublets overlap and appear to be a triplet.
Figure 10. Deuterium NMR spectra observed from (a) dimer-3-d6 +
dimer-3-o-d2 and (b) dimer-4-d8 + dimer-4-o-d2 dissolved in MBBA
at 25 °C and 2.0 mol %. As indicated, the peaks were assigned to the
individual atomic groups. The |∆ν| values of the R and â methylene
groups and the ortho C-D bond are, respectively, 19.56, 27.31, and
3.11 kHz (dimer-3); and 35.64, 35.64, and 4.31 kHz (dimer-4). The
|DHD| values of dimers-3 and -4 are 230 and 410 Hz, respectively.
The upper and lower spectra were measured without and with
1H broad-band decoupling, respectively. Dimer-3 has two R and
one â methylene units; the former peaks must be more intense
than the latter peaks. Therefore, the outermost and second pairs
of peaks were assigned to the â and R methylene groups,
respectively. The two innermost doublets come from the ortho
C-D bonds of the phenyl ring. The doublet is due to dipolar
coupling (DHD) between the ortho D and meta H, and the spacing
corresponds to 2|DHD|. For dimer-4, signals from the R and â
methylene groups overlap and form a single pair of intense
peaks.
2
Figure 12 shows H NMR spectra of deuterated dimer-6
species in MBBA at 25 °C and 2.0 mol %: (a) dimer-6-d12
+
1
dimer-6-o-d2 without (upper) and with (lower) H broad-band
decoupling and (b) dimer-6-d12 + dimer-6-R-d2. By a compari-
son of the spectra, we could assign the second peaks to the R
methylene group. The outer peaks are larger and, hence, include
signals from the â and γ methylene groups. The |∆ν| and |DHD
|
values for the four dimers are given in the individual figure
captions.

13170 J. Phys. Chem. B, Vol. 108, No. 35, 2004
Sasanuma et al.
where e2qQ/h is the quadrupolar coupling constant (equal to
163 kHz for aliphatic C-D bond54 or 186 kHz for aromatic
C-D bond55); the X, Y, and Z axes are the principal axes of the
order matrix; SZZ and SXX - SYY are the order parameters of
k
k
k
the conformer; and, for example, θX,i,k is the angle between the
X axis and the Ci-D bond. The X, Y, and Z axes are assumed
to be coincident with the principal axes of inertia (see Figure
7),56,57 whose directions are calculated with the atomic weights
located at the nuclei. The order parameter SZZ of conformer k
k
is assumed to be given by58
aZ
k
1
2
SZZ ) C(T,c)
-
(5)
k
(
)
aX + aY
k
k
where C(T,c) is a measure of the solute-solvent interaction as
a function of temperature T and solute concentration c. The
biaxiality is calculated from
Figure 13. Deuterium NMR spectra observed from (a) tetramer-5-d10
+ tetramer-5-φ-d8 and (b) tetramer-6-d12 + tetramer-6-φ- d8 dissolved
in PAA at 120 °C and 2.0 mol %. As indicated, the peaks were assigned
to the individual atomic groups. The |∆ν| values of the R, â, γ
methylene groups and the phenylene C-D bond are, respectively, 27.96,
33.59, 23.26, and 6.43 kHz (tetramer-5); and 36.34, 40.25, 40.25, and
12.49 kHz (tetramer-6).
aX - aY
k
SXX - SYY
)
kSZZ
k
(6)
k
k
aZ
k
2
Here, aR is a semiaxis obtained from the principal moments of
3.5.3. Tetramers. Figure 13 shows H NMR spectra of (a)
k
inertia, IRR , Iââ , and Iγγ (R, â, and γ ) X, Y, and Z, respectively;
tetramer-5-d10 + tetramer-5-φ-d4 and (b) tetramer-6-d12
+
k
k
k
aZ g aX g aY ):
tetramer-6-φ-d4 dissolved in PAA at 120 °C and 2.0 mol %.
The tetramers are insoluble in MBBA but slightly soluble in
PAA. Thus, PAA has been used as the nematic solvent.
Intensity ratios of the outer to inner peaks of tetramer-5 are
approximately 1.5:2.0:1.0:1.9. Tetramer-5 has two R, two â,
and one γ methylene groups. Thus, the smallest (third) peaks
from the outside may come from the γ methylene group. The
deuteration grade must be highest in the R methylene group,
which was generated by reduction with LiAlD4 (98 atom %
D). The â and γ methylene units underwent a replacement
reaction with D2O under Pt/C. The outermost peaks may be
assigned to the â methylene unit, because all of the monomers
and dimers exhibit the largest quadrupolar splitting in the â
methylene group. On these grounds, all of the peaks were
assigned as shown in Figure 13. The eight deuteriums in the
two phenylene rings (see Figure 3c), yielding only a single
splitting, are essentially equivalent. Two notable differences can
be found between the spectra of tetramer-5 and dimer-5: The
R and γ signals appear in reverse order, and tetramer-5 gives a
much larger |∆νφ| than dimer-5. Because tetramer-6 gave a
spectrum analogous to that of dimer-6, the assignment was
carried out in a similar manner for dimer-6.
k
k
k
1/2
I
+ I - I
RRk
ââk
γγk
5
2
aR
)
(7)
(
)
k
M
where M is the molecular weight.
The dipolar coupling between proton and deuteron, DHD, can
be calculated by substituting DHD,k given below for ∆νi,k in
eq 3:53,59
γHγDp
2πr3HD
3 cos2 θZ,HD,k - 1
DHD,k ) -
S
+
[
ZZk
2
cos2 θX,HD,k - cos2 θY,HD,k
(SXX - SYY
)
(8)
]
k
k
2
where γH and γD are gyromagnetic ratios of proton and deuteron,
respectively, rHD is the proton-deuteron distance, and θR,HD,k
is the angle between the R axis and rHD vector.
The maximum entropy (MaxEnt) method has been used to
derive the most reliable results from a restricted amount of
experimental data.60 The conformer fractions must reproduce
the experimental observations. Agreement between theory and
experiment may be monitored by
3.6. Simulation for Quadrupolar Splittings. 3.6.1. Proce-
dure for Analysis. Deuterium quadrupolar splitting ∆νi from
the C-D bond at atomic group i (i ) R, â, γ, δ, ꢀ, CD3, o, or
φ) is given by
2
(∆νi,calcd - ∆νi,obsd
)
ø2 )
(9)
∑
K
ꢀi2
i
∆ν ) ∆νi,k fk
(3)
∑
i
k
where ∆νi,calcd and ∆νi,obsd are the calculated and observed
quadrupolar splittings, respectively, and ꢀi is the experimental
error.
where K is the number of conformers and fk is the fraction of
conformer k. The quadrupolar splitting from the conformer,
∆νi,k, is expressed as53
The entropy of conformer fractions is defined as14
K
fk
3 cos2 θZ,i,k - 1
3 e2qQ
S(f ) )
f - m - f ln
(10)
∑
k)1
k
k
k
k
(
)
∆νi,k
)
S
+
mk
[
ZZk
2
h
2
cos2 θX,i,k - cos2 θY,i,k
where mk is the initial model of fk. The MaxEnt method
hypothesizes that the most probable solution of fk’s maximizes
(SXX - SYY
)
(4)
]
k
k
2

Models for Oligomer Liquid Crystals
J. Phys. Chem. B, Vol. 108, No. 35, 2004 13171
TABLE 3: Bond Lengths and Bond Angles of Model
Compoundsa
bond length
Å
bond angle
deg
Aromatic Ringb
1.397
1.086
1.367
C-C
C-H
C1-O
CCC
CCH
C2C1O
120.0
120.0
124.6
Ether Chainc
O-C
C-C
C-H
1.425
1.530
1.099
OCRH
CCH
C1OCR
OCRCâ
CCC
110.0
109.1
118.8
107.7
112.8
Figure 14. Quadrupolar splittings of monomer-5-d11 (b and ‚‚‚) and
monomer-6-d13 (9 and - - -) dissolved in MBBA at 25 °C and 2.0 mol
%: symbol, observation; line, calculation.
a Determined from ab initio MO calculations at the B3LYP/6-31G(d)
level. For the atom numbers and labels, see Figure 3. b The benzene
ring is assumed to be a regular hexagon. The aromatic carbons and
hydrogens and the ethereal O and CR atoms are located on the same
plane. c C3 symmetry is assumed for the methyl terminal group of
monomer-5 and monomer-6.
TABLE 4: Dihedral Angles for Gauche+ States of
Monomeric and Dimeric Model Compoundsa
bondb monomer-5 monomer-6 dimer-3 dimer-4 dimer-5 dimer-6
2
3
4
5
6
98.5
116.0
114.1
114.5
98.5
116.0
114.1
113.4
114.5
98.2
118.3
99.6
116.4
111.4
97.4
116.8
115.0
99.4
116.4
113.2
114.8
Figure 15. Bond conformations (trans fractions, pt’s) of the alkoxy
tails of (a) monomer-5 (b and ‚‚‚) and (b) monomer-6 (9 and - - -):
symbol, in MBBA at 25 °C and 2.0 mol %; line, in the free (isolated)
state.
a In degrees. Determined from ab initio MO calculations at B3LYP/
6-31G(d) level. Dihedral angles for the trans states were set equal to
0°, and those for the gauche- states were set to the corresponding
negative values. b For the bond numbers, see Figure 3. For tetramers-5
and -6, the geometries of dimers-5 and -6 were used, respectively.
The ensemble average L of quantities Lk’s can be obtained
from
the S(fk) value. In the simulation, the conformer fractions are
calculated from the statistical weight parameters and optimized
by the MaxEnt method,61,62 with the weight parameters, σn’s
and ωn’s, and the interaction parameter, C(T,c), adjusted by the
K
L ) L f
(11)
∑
k
k
k
Simplex method.63 The Eω value is so large even in the free
1
The orientational order parameter of the molecular Z axis, SZZ
,
state that ω1 was set equal to zero. For further details of the
methodology, see refs 15-18.
of the solutes at 25 °C and 2.0 mol % was evaluated, and results
are as follows: monomer-5, 0.282; monomer-6, 0.324. The
longer monomer-6 molecule has a larger SZZ value than
monomer-5. Figure 16 illustrates the distribution of molecular
lengths (AZ,k’s) along the Z axis of the conformers (see Figure
7). The AZ,k value was calculated from the van der Waals radii
of Bondi.51 The average dimension AZ was evaluated from eq
11 with the following results: monomer-5, 13.4 (13.0) Å;
monomer-6, 14.3 (13.7) Å. Here, the values in the parentheses
represent those for the free state.
3.6.4. Dimers. Figure 17 shows results of the simulations for
dimers-3, -4, -5, and -6 dissolved in MBBA at 25 °C and 2.0
mol %. For the four dimers, the calculations are in agreement
with the observations. The dipolar couplings between the ortho
deuteron and meta proton of the phenyl group were concomi-
tantly calculated (values in parentheses are the experimental
data): dimer-3, 190 (230) Hz; dimer-4, 330 (410) Hz; dimer-5,
250 (310) Hz; dimer-6, 320 (390) Hz. The calculated values
seem to be underestimated. The DHD value is proportional to
r-HD3 , and thus is sensitive to the H‚‚‚D distance. The geo-
metrical parameters adopted here give an rDH value of 2.483
Å, whereas the X-ray analysis for the dimers yielded a wide
range (2.156-2.383 Å) of rHD. Adoption of the latter average
of 2.273 Å improves the DDH values to 250 Hz (dimer-3), 430
Hz (dimer-4), 320 Hz (dimer-5), and 420 Hz (dimer-6).
Bond conformations of the ethereal spacers, obtained from
the simulations, are plotted in Figure 18. In the nematic solution,
3.6.2. Geometrical Parameters. X-ray diffraction measure-
ments for the four dimers gave their crystal structures. The
geometrical parameters were dependent on the molecular
packing and somewhat distorted. Therefore, the bond lengths
and bond angles, which were evaluated for the monomers and
dimers from ab initio MO calculations at the B3LYP/6-31G(d)
level, were averaged prior to use in the above-mentioned
simulations (see Table 3), because the B3LYP calculations
yielded the geometries accordant with the X-ray data. On the
other hand, the dihedral angles were determined at the B3LYP/
6-31G(d) level for the individual bonds and compounds (see
Table 4). For tetramers-5 and -6, dihedral angles of dimers-5
and -6 were substituted, respectively. The benzene ring has been
assumed to be a regular hexagon. All of the aromatic carbons
and hydrogens and the ethereal O and CR atoms are located on
the same plane.
3.6.3. Monomers. In Figure 14, the |∆ν| values of mono-
mers-5 and -6, obtained from the RIS + MaxEnt simulations,
are compared with the experiments. In general, the calculations
reproduced the experiments well. The calculated bond confor-
mations in the alkoxy tails are plotted in Figure 15, where the
dotted and dashed lines were obtained from the energy
parameters listed in Table 1. The monomers keep their inherent
conformational preferences even in the nematic phase.

13172 J. Phys. Chem. B, Vol. 108, No. 35, 2004
Sasanuma et al.
Figure 16. Distribution of the conformer length, AZ,k, of (a) monomer-5
and (b) monomer-6: solid line (s), in MBBA at 25 °C and 2.0 mol
%; dotted line (‚‚‚), in the free state.
Figure 18. Bond conformations (trans fractions, pt’s) of the ethereal
spacers of (a) dimer-3, (b) dimer-4, (c) dimer-5 (b) and tetramer-5
(9), and (d) dimer-6 (b) and tetramer-6 (9): circle (b) in MBBA at
25 °C and 2.0 mol %; square (9) in PAA at 120 °C and 2.0 mol %;
dotted line (‚‚‚), in the free state.
Figure 17. Quadrupolar splittings of (a) dimer-3-d6 (b and ‚‚‚) and
dimer-4-d8 (9 and - - -) and (b) dimer-5-d10 (b and ‚‚‚) and dimer-6-
are, respectively, 15.3 and 14.7 Å (dimer-3), 16.8 and 13.6 Å
(dimer-4), 16.9 and 15.5 Å (dimer-5), and 17.8 and 17.1 Å
(dimer-6).
d
12 (9 and - - -) dissolved in MBBA at 25 °C and 2.0 mol %: symbol,
observation; line, calculation.
As a measure of the parallelism of two aromatic rings, the θ
angle was defined (see Figure 7).67 The distributions for the
four dimers, shown in Figure 20, exhibit a distinct odd-even
effect. For dimers-3 and -5, the peaks are concentrated around
θ ) 30-90°, indicating that the molecules are sharply bent in
the nematic solvent. On the contrary, the peaks of dimers-4 and
-6 may be divided into two regions: 0-30° and 80-135°. For
dimer-4, marked differences between the solid and dotted lines
are seen in the latter region (80-135°), where the ω4 conformers
the gauche preference of the C-C bond adjacent to the ether
linkage is weakened but preserved. Distributions of the molec-
ular dimensions in the Z direction are illustrated in Figure 19.
Compared with the dotted lines (free state), the solid lines
(nematic state) are generally shifted rightward; the dimers are
elongated in the nematic field. Such molecular elongations have
been found for polymer LCs.64-66 For dimer-4 in particular,
outstanding changes can be found around 10-11 and 13 Å;
the large peaks, mainly due to the conformers with the attractive
ω4 interactions (Figure 4b), are considerably reduced. This
indicates that the crooked ω4 conformers rarely occur in the
nematic solution. The AZ values for the nematic and free states
exist. The
θ values for the nematic and free states are,
respectively, as follows: dimer-3, 63° and 68°; dimer-4, 41°
and 83°; dimer-5, 67° and 76°; dimer-6, 63° and 64°. For the
reason stated above, dimer-4 shows the largest θ difference
between the two states.

Models for Oligomer Liquid Crystals
J. Phys. Chem. B, Vol. 108, No. 35, 2004 13173
Figure 20. Distributions of the θ angle of (a) dimer-3, (b) dimer-4,
(c) dimer-5, and (d) dimer-6: solid line (s), in MBBA at 25 °C and
2.0 mol %; dotted line (‚‚‚), in the free state.
Figure 19. Distributions of the conformer length, AZ,k, of (a) dimer-3,
(b) dimer-4, (c) dimer-5, and (d) dimer-6: solid line (s), in MBBA at
25 °C and 2.0 mol %; dotted line (‚‚‚), in the free state.
2
3.6.5. Tetramers. From the similarity in H NMR between
dimer and polymer LCs, the intermolecular orientational cor-
relation has been assumed to persist only up to dimeric units.67
On this assumption, we have partly adapted the above simulation
scheme and applied it to the tetramers. The principal-axis system
has been determined only from the central dimeric portion (i.e.,
the central spacer and two phenylene rings). The principal
moments of inertia and the orientational order parameters were
evaluated from eqs 5-7, and the simulation was carried out as
above.
In Figure 21, the |∆ν| values thus calculated for tetramers-5
and -6 are compared with the experimental data. In Figure 18,
bond conformations of the central spacers are plotted, together
with those of dimers-5 and -6. Figure 22 shows the θ
distributions. For the tetramers, PAA was used as the solvent.
However, the results here may be compared with those for the
dimers.
Figure 21. Quadrupolar splittings of tetramer-5-d10 (b and ‚‚‚) and
tetramer-6-d12 (9 and - - -) dissolved in PAA at 120 °C and 2.0 mol
%: symbol, observation; line, calculation.
The bond conformations appear as if those for the free state
(the dotted lines in Figure 18) are somewhat shifted upward.

13174 J. Phys. Chem. B, Vol. 108, No. 35, 2004
Sasanuma et al.
TABLE 5: Orientational Order Parameters of Solutes and
Nematic Solvents
order parameter
of solutea
order parameter
of solventb
R
R
c
c
d
d
solute
SZZ
SZZ
SXX - SYY
SZZ
monomer-5
monomer-6
0.282
0.324
0.049
0.051
0.529
0.537
dimer-3
dimer-4
dimer-5
dimer-6
0.193
0.339
0.255
0.318
0.245
0.346
0.351
0.457
0.038
0.051
0.053
0.065
0.479
0.489
0.487
0.500
tetramer-5
tetramer-6
0.403
0.522
0.071
0.072
a At 2.0 mol %. b MBBA at 25 °C for the monomers and dimers;
PAA at 120 °C for the tetramers. c The order parameter of the para
axis of the aromatic ring. d The order parameter of the molecular axes.
The SRZZ values of the dimers exhibit a distinct odd-even
oscillation. This parameter represents the orientation of the para
axis with respect to the nematic director. The SZZ value seems
not to be simply proportional to SRZZ of the solute, because the
former parameter tends to increase with the chain length. The
SRZZ value of MBBA only depends on the solute a little,
because both temperature (25 °C) and solute concentration (2.0
mol %) are so low that the orientational order of MBBA is only
slightly disturbed. The â∞N values of the dimer/MBBA systems,
discussed in section 3.4, are inversely correlated to the SRZZ and
SZZ values of the solutes. The tetramers also exhibit an odd-
Figure 22. Distributions of the θ angle of (a) tetramer-5 and (b)
tetramer-6 dissolved in PAA at 120 °C and 2.0 mol %.
even oscillation in SZZ
.
3.8. Transition Entropies. For CBA-x’s, the ratios between
the NI and CN transition entropies, ∆SNI/∆SCN, were evaluated
from DSC measurements (e.g., 0.05 (x ) 3), 0.19 (x ) 4), 0.08
(x ) 5), and 0.16 (x ) 6)).25 For polymer LCs, [-CO-C6H4-
O(CH2)xO-C6H4-COO-C6H4- O(CH2)yO-C6H4-O-]n, the
∆SNI/∆SCN ratios for x ) 3, 4, 5, and 6 were, respectively,
determined as 0.05, 0.11, 0.08, and 0.17 (y ) 6) and 0.08, 0.11,
0.09, and 0.14 (y ) 8).26 In general, the ∆SNI values of LCs are
much smaller than ∆SCN’s. For CBA-9 and CBA-10, pressure-
volume-temperature measurements were carried out, and the
isopiestic transitional entropies were divided into the isochoric
((∆S)v) and volume-change (∆SV) terms.69,70 The former
Figure 23. Deuterium NMR spectrum observed without 1H decoupling
from MBBA-2,6-d2 (Figure 1a) mixed in the monomer-5 (2.0 mol %)/
MBBA system at 25 °C.
Compared with the dimers, the nematic tetramers seem close
to being in the free state. The θ distributions of the tetramers
are similar to those of the corresponding dimers. However, the
small peaks observed around 135-180° for dimer-5 (Figure 20c)
completely disappear from the θ distribution of tetramer-5. In
the nematic field, tetramer-5 may be so long that it does not
take the antiparallel arrangement of the phenylene groups,
because the arrangement leads to a fold of the molecule. The
θ angles for the nematic tetramers-5 and -6 were calculated
to be 68° and 61°, respectively.
contribution, mostly due to the conformational change (∆Sconf
)
in the spacer, accounts for 40-60%. The above facts indicate
that the spacer changes its conformation less in the NI transition
than in the CN one. For CBA-9 and CBA-10, the (∆SNI)v/
(∆SCN)v ratio (∼∆Sconf/∆Sconf) was estimated as 15/85.69,70 If
NI
CN
the conformation in the isotropic phase is similar to that in the
free state,71 the above discussion is consistent with the results
here.
4. Conclusions
3.7. Orientational Orders of Solutes and Solvents. Figure
23 shows a 2H NMR spectrum observed without 1H decoupling
from MBBA-2,6-d2 (2.0 mol %) mixed in the monomer-5 (2.0
mol %)/MBBA system at 25 °C. A pair of doublets due to the
quadrupolar splitting (∆νo) and dipolar coupling (DHD) between
the ortho deuteron and meta proton (see Figure 1a) is observed.
From the DHD and ∆νo values, orientational order parameters
of the phenylene ring were derived as SRZZ,MBBA ) 0.529 and
The model compounds treated here are not LCs in the narrow
sense. Nevertheless, they exhibit distinct odd-even oscillations
in â∞, SZZ’s, and so on, and behave in the nematic solution as
N
if they were LCs. Once a molecule is placed in a nematic field,
it reveals its potential liquid crystallinity in the broad sense.
The odd-even effect is not peculiar to LCs but common to all
chainlike molecules. However, the combination of mesogen and
anisotropic field amplifies the effect. In the nematic field, the
model compounds keep their inherent conformational prefer-
ences, somewhat rigidify and stretch themselves, and turn the
aromatic ring toward the nematic director. These compounds
act as models for LCs of the corresponding degree of polym-
erization. The central part of the tetramers may represent the
(SRXX - SR )MBBA ) 0.042.68 For the coexistent monomer-5, the
YY
above simulation yielded the orientational order parameters of
the molecular axes: SZZ ) 0.282 and SXX - SYY ) 0.049.
The order parameters for the monomer-6/MBBA and dimer/
MBBA systems at 25 °C and 2.0 mol % are also listed in
Table 5.

Models for Oligomer Liquid Crystals
J. Phys. Chem. B, Vol. 108, No. 35, 2004 13175
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2
Acknowledgment. We thank Prof. Kishikawa, Dr. Taka-
hashi, Prof. Akutsu, and Dr. Seki of Chiba University for helpful
advice on sample preparation and NMR measurements. This
work was supported partly by the Izumi Science and Technology
Foundation and a Grant-in-Aid for Scientific Research (C)
(14550842) from the Japan Society for the Promotion of
Science.
Supporting Information Available: The |∆ν| values ob-
served at different temperatures from monomers-5 and -6 and
dimers-3, -4, -5, and -6 dissolved in MBBA at 2.0 mol %. This
material is available free of charge via the Internet at http://
pubs.acs.org.
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