Orientational ordering and dynamics in the columnar phase of a discotic liquid crystal studied by deuteron NMR spectroscopy

Article abstract of DOI:10.1063/1.475833

The quadropolar splittings and the spin-lattice relaxation data measured in the columnar phase of two differently deuterated HAT6 molecules are interpreted. Modeling the splittings using the AP method allows to obtain the orienting potential needed to describe the reorientational dynamics of molecular disks. It is emphasized that the tumbling motion of a disk can be slightly faster than its spinning motion.

Full text of DOI:10.1063/1.475833

Orientational ordering and dynamics in the columnar phase of a discotic liquid crystal
studied by deuteron NMR spectroscopy
X. Shen, Ronald Y. Dong, N. Boden, R. J. Bushby, P. S. Martin, and A. Wood
Citation: The Journal of Chemical Physics 108, 4324 (1998); doi: 10.1063/1.475833
View online: http://dx.doi.org/10.1063/1.475833
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 108, NUMBER 10
8 MARCH 1998
Orientational ordering and dynamics in the columnar phase of a discotic
liquid crystal studied by deuteron NMR spectroscopy
X. Shen
Physics Department, University of Manitoba, Winnipeg Manitoba, R3T 2N2, Canada
Ronald Y. Donga)
Department of Physics and Astronomy, Brandon University, Brandon, Manitoba, R7A 6A9, Canada
N. Boden, R. J. Bushby, P. S. Martin, and A. Wood
Centre for Self-Organising Molecular Systems, The University of Leeds, Leeds, LS2 9JT, United Kingdom
͑Received 22 October 1997; accepted 4 December 1997͒
We report on a deuteron NMR study of quadrupolar splittings and spin-lattice relaxation times T1Q
and T1Z as a function of temperature and at two different Larmor frequencies in the columnar phase
of hexakis(n-hexyloxy͒triphenylene ͑HAT6͒. The additive potential method is used to model the
quadrupolar splittings, from which the potential of mean torque is parameterized, and the order
parameter tensor for an ‘‘average’’ conformer is determined. The small-step rotational diffusion
model is used to find the rotational diffusion constants Dʈ and DЌ for the spinning and tumbling
motions of the molecular core. It is found that DЌ is slightly larger than Dʈ in contrast with the
findings in calamitic liquid crystals. The decoupled model of Dong for correlated internal rotations
in the end chains is used for the first time in a discotic liquid crystal. Both jump constants for one-
and three-bond motions are nearly independent of temperature, while the jump constant for
two-bond motion is thermally activated. The rotational speeds Dʈ and DЌ are some two orders of
magnitude slower than a typical charge hopping frequency between the aromatic cores of adjacent
molecules in the columns. Thus, to a migrating charge, the ‘‘lattice’’ appears static with disorder
being due to the instantaneous displacement of the cores with respect to each other. © 1998
American Institute of Physics. ͓S0021-9606͑98͒51210-X͔
INTRODUCTION
molecular hop. The transport of charges along the column is
dependent on the overlap of ␲-orbitals between adjacent aro-
matic rings, which is very sensitive to the distance of closest
approach and the relative reorientation of the rings and their
time dependence. It is, therefore, important to have a detailed
description of the molecular reorientational motion within
the columns.
The novel charge transport properties of the columnar
phases1 formed by disk-like molecules such as the hexakis-
͑alkyloxy͒triphenylenes ͑HATn) are potentially exploitable
in applications ranging from sensing devices to high-
resolution xerography.2 These disk-like molecules are
stacked, with only short-range positional order, into columns
which are arranged on a two-dimensional lattice, typically
hexagonal ͑Figure 1͒. The fluctuations in columnar orders
are sufficient to suppress inhomogeneously distributed struc-
tural traps and give rise instead to a uniform ‘‘liquid-like’’
dynamic disorder. A consequence of this is that the indi-
vidual molecular columns can transport electronic charge
with well defined Gaussian transits.3–5 Charge carrier mobili-
It is well known8 that deuterium NMR spectroscopy can
provide detailed information on the orientational ordering
and dynamics in mesophases of liquid crystals. In particular,
one can rely on theoretical models to extract relevant mo-
tional parameters from deuteron spin-lattice relaxation times.
The small-step rotational diffusion model9,10 has been suc-
cessfully used in liquid crystals to describe symmetric-top
molecules reorienting in a potential of mean torque set up by
their neighbors. Deuterated HATn molecules have been
studied using proton and deuteron NMR by Luz and
co-workers7,11–13 more than 10 years ago. To explain14 the
spectral densities of aromatic deuterons in HAT6, the Nordio
model9 was used and rotational diffusion constants for the
HAT6 molecule were derived. The quadrupolar splittings of
the chain deuterons were modeled15 using the so-called ad-
ditive potential ͑AP͒ method which was pioneered by
Marcelja16 and extended subsequently by Emsley, Luckhurst,
and Stockley.17 This earlier attempt for the homologous se-
ries HATn unfortunately contained numerical errors and the
good fits were therefore fortuitive. In the present study, the
quadrupolar splittings are used to obtain8 the order param-
ties along the columns ␮ can be as high as 10Ϫ2 cm2 VϪ1
ʈ
sϪ1 and are typically 103 quicker than in the perpendicular
direction.6 In HAT6, ␮ is about 10Ϫ4 cm2 VϪ1 sϪ1 and the
ʈ
intra- and inter-columnar distances are dʈӍ3.5 Å and
dЌӍ19.5 Å, so that using ␮ϭeDt/kBT we calculate the
translational diffusion constants Dtʈϭ5ϫ10Ϫ6 cm2/s and
DЌt ϭ5ϫ10Ϫ9 cm2/s for ionic diffusivity. The latter is two
orders of magnitude smaller than the value of 5ϫ10Ϫ7 cm2/s
measured by NMR7 for the molecular self-diffusion constant
perpendicular to the columnar axis. Thus, the charge carrier,
a positive hole, is carried from column-to-column by the
a͒
Author to whom correspondence should be addressed.
0021-9606/98/108(10)/4324/9/$15.00
4324
© 1998 American Institute of Physics
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J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
4325
dihedral angles (␾ϭ0, Ϯ112°). These ␾ angles correspond
to the trans (t) and two symmetric gauche (gϮ) states. The
gauche states have higher energy in comparison to that of the
trans by an amount Etg . The potential energy U(j,⍀) of a
molecule in a conformation j and a particular orientation ⍀
with respect to the director is given by
U j,⍀͒ϭU j͒ϩU
j,⍀͒,
͑
ext
͑1͒
͑
͑
int
where the potential of mean torque Uext(j,⍀) originates
from the molecular field of its neighbors, and Uint(j), the
internal energy, is assumed to depend on the number (Ng)
and not the location of the gauche linkages in the chain, as
well as NgϮgϯ , the number of gϩgϪ or gϪgϩ linkages in
the chain
FIG. 1. Hexakis͑n-hexyloxy͒triphenylene ͑HAT6͒ shown with coordinate
systems used in the text, and a schematic view of its columnar Dh me-
sophase.
Uint j͒ϭN E ϩNgϮgϯEgϮgϯ
.
͑2͒
͑
g
tg
These gϩgϪ or gϪgϩ linkages have higher internal energy
EgϮgϯ because they bring parts of the chain near to one
another, the so-called ‘‘pentane effect.’’ The potential of
mean torque depends on the polar angles of the director in a
molecular frame that is attached to a particular rigid segment
of the molecule. In the AP method, it is assumed that the
molecule can be divided into a small number of rigid seg-
ments. Each segment is associated with an interaction tensor
that is independent of the conformation. The total interaction
tensor of a particular conformer is calculated by transforming
the tensors from their segmental axis systems into a common
system and then adding them together to give Uext(j,⍀).
The location of this common molecular frame is not critical,
and a convenient choice is a frame set on the aromatic core
of the molecule.
eters
P
and S ϪS
yy
for an ‘‘average’’ conformer.
͘
͗
͘
͗
2
xx
These in turn determine at each temperature the orienting
potential (a20 ,a22)10 needed for solving the rotational diffu-
sion equation. The decoupled model18 is used to deal with
the dynamics of internal bond rotations. In this model, inter-
nal rotations in a flexible chain are assumed to obey a master
equation and are decoupled from the overall reorientation of
the molecule. A realistic geometry is used for HAT6 to gen-
erate all possible conformations in one of the chains using
the Flory model.19 Since the O–C1 bond is taken12 to be on
the plane of the aromatic core, there are 243 conformations
in the chain. The transition rate matrix R, which describes
conformational changes in the chain, is a 243ϫ243 matrix
and contains jump constants18 k1, k2 , and k3 for the one-,
two- and three-bond motions in the chain. We use a global
target approach20 to analyze all the spectral density data at
different temperatures and frequencies in the same fitting
procedure. This has been found to give reliable target model
parameters in calamitic liquid crystals. The paper is orga-
nized as follows. A theory section outlines the required for-
mulae used to analyze the quadrupolar splittings and spectral
density data. This is followed by an experimental section on
the synthesis of deuterated HAT6 samples and on the NMR
method. The last section is on results and discussion.
In a deuterium NMR experiment, one obtains quadrupo-
lar splittings for the methylene deuteron͑s͒ (␩ϭ0) at the ith
site:
3
͑i͒
⌬␯iϭ q P2 cos ⌰͒
p Sn,i
n
bb
͑
͚
CD
2
n
͑3͒
3
͑i͒
͑i͒
CD
ϭ qCDP2 cos ⌰͒S
,
͑
2
(i)
where q ϭ(e2qQ/h)i is the quadrupolar coupling con-
CD
stant, P2(x)ϭ(3x2Ϫ1)/2, ⌰ is the angle between the direc-
(i)
tor and the external magnetic field, and S
is a weighted
CD
n,i
bb
average of the segmental order parameter S for the Ci –2H
THEORY
bond of the molecule with conformation n. Now pn , the
probability of finding the molecule with conformation n in a
mesophase, is given by
The constituent molecules of liquid crystals ͑e.g.,
MBBA, HAT6͒ usually contain an aromatic core and one or
more flexible side chains. NMR studies8 of order parameter
profiles in these molecules have revealed that the ordering of
their rigid segments varies with respect to each other and
with temperature. The AP method of getting a potential of
mean torque for flexible molecules is outlined first.
Marcelja16 was the first to explicitly consider the alkyl chain
in calculating physical properties of liquid crystals. The ro-
tational isomeric state model19 is used to determine all of the
allowed conformations. Each molecular conformer is as-
sumed as a perfectly rigid entity. In this model, the bond
lengths are taken to be fixed. Rotation about each carbon–
carbon ͑C–C͒ bond in the chain may take one of the three
1
p ϭ exp ϪU n͒/k T Q ,
͑4͒
͓
͑
͔
n
int
B
n
Z
where Qn , the orientational partition function of conforma-
tion n, is
Q ϭ exp ϪU n,⍀͒/k T d⍀
͑5͒
and Z, the conformation-orientational partition function, is
Zϭ exp ϪU n͒/k T Q . ͑6͒
͓
͑
͔
͵
n
ext
B
͓
͑
͔
B
͚
int
n
n
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4326
J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
1
4
In writing down Eq. ͑3͒, one sets the principal axis frame
(a,b,c) for the quadrupolar interaction with the b axis in the
direction of the Ci –2H bond. For the aromatic deuterons
(iϭ0), a ␩ value of 0.064 is assumed, and their splitting is
given by
0
0
0
1
4
0
Xcc
,
ͩ ͪ
1
2
0
0
Ϫ
where Xa and Xcc are the core and C–C interaction param-
eters, respectively. In a local ͑1, 2, 3͒ frame where the 3 axis
is along the Cj –Cjϩ1 bond, the 1 axis is in the plane bisect-
ing the HCH angle, and the 2 axis is chosen to complete a
right-handed Cartesian coordinate system, the C–2H vector
is given by
3
␩
͑0͒
⌬␯0ϭ q P2 cos ⌰͒
p
Snb,b0ϩ Snaa,0ϪSn,0͒ .
͑
͑
ͫ
ͬ
͚
n
CD
cc
2
3
n
͑7͒
Now the order parameter for a particular direction k in the
conformer n may be evaluated in the principal (x,y,z) frame
of Uext(n,⍀)
a
b
c
V
CDϭ
,
͑11͒
ͩ ͪ
x,y,z
n,i
n,i
␣k
S
ϭ
Sn␣␣ cos2 ␪
,
͑8͒
͚
kk
␣
where
bϭsin(ЄHCH/2͒,
cϭcos(ЄCCH͒,
and
a2ϭ1Ϫb2Ϫc2. A common molecular frame is picked with
the zM axis perpendicular to the core plane ͑see Figure 1͒,
and the xM axis on the plane bisecting two of the six pendent
chains. Here we construct the total interaction tensor for
HAT6 by explicitly considering two chains as shown. All the
O–C1 bonds are on the xMyM plane. The Car –O bonds are
included in the core when writing down the ⑀(␣a␤) ; also in-
cluded are the remaining four pendent chains. Furthermore,
the conformations of the two chosen chains are assumed to
be identical and non-interacting. These drastic assumptions
are necessary to make the problem tractable. The orientation
where Sn␣␣ , the principal components of the order matrix for
the conformer n, may be written as
1
Snxxϭ
cos2␺ Ϫ d2 ͒,
͘ ͗ ͘
n n
0,0
2
0,2
ͱ6 d
͗
͑
2
1
SnyyϭϪ
cos2␺ ϩ d2 ͒,
͑9͒
2
0,2
ͱ6 d
͗
͑
͘
͗
͘
n
0,0
n
2
Sn ϭ d2
,
͗
͘
n
zz
0,0
of the Cj –2H vector in this frame is given by VCMD
,
n,i
␣k
and ␪ denote angles for the Ci –2H bond between the
VCMDϭRM,1R1,2
¯
jϪ1,jVCD
,
͑12͒
k(ϭa,b,c) axis and a principal axis ␣(ϭx,y,z). The con-
structed interaction tensor Uext(n,⍀) is first diagonalized to
obtain the the interaction tensor components Xn2,0 and X2n,Ϯ2
for the conformer n. In the principal frame,
where RjϪ1,j is a rotation matrix that transforms between the
jth local frame and the (jϪ1)th local frame. The VCMD for
the aromatic deuteron can easily be found for one of the six
deuterons in the core. To obtain the direction cosine in Eq.
͑8͒, it is necessary to get the Cj –2H vector in the principal
frame of the total interaction tensor,
Uext n,⍀͒ϭϪ Xn2,0d20,0 ␪͒ϩ2Xn2,2d20,2 ␪͒cos 2␺
͔
͑10͒
͑
͓
͑
͑
and d2
and d2 cos2␺ can easily be obtained.21
͗ ͘
n
0,2
͗
͘
n
0,0
VCp DϭRp,MVCMD
,
͑13͒
To construct Uext(j,⍀) for the conformer j, one needs
to know the geometry of the chain. The CCC, CCH, and
HCH angles are assumed22 to be 113.5°, 107.5°, and 113.6°,
respectively. For the alkyloxy chain, the O–C bond is taken
to be identical to a C–C bond. However, the COC angle23
and OCC angle are set at 126.4°, and the internal energies
where the rotation matrix Rp,M contains the eigenvectors (ri)
obtained in diagonalizing the total interaction tensor ⑀n␣,␤ for
each conformer. Now ⑀n␣␤ is obtained by
n
͑a͒
n
␣␤
Ϫ1
n
⑀
␣␤ϭ⑀␣␤ϩRM,1
␭
R
M,1ϩRЈ ␭␣␤RЈϪ1
,
M,1
͑14͒
M,1
Ј
EtЈg and Eg
are used due to the presence of the oxygen.
Ϯ
ϯ
g
where
(a)
␣␤
Suppose that the aromatic core has an interaction tensor ⑀
and each C–C segment has an interaction tensor ⑀(␣c␤) . To
write down these interaction tensors, care is needed to dis-
tinguish between calamitic and discotic mesogens. If these
7
n
␣␤
͑c͒ Ϫ1
Ϫ1
1,2
␭
ϭ
R
1,2¯RjϪ1,j
⑀
R
¯R
͑15͒
͚
␣␤ jϪ1,j
jϭ2
local interaction tensors are assumed to have cylindrical
and RM,1 and RЈ are rotation matrices for the two chains
M,1
(a)
which transform between the first local frames to the mo-
lecular frame. We use Eq. ͑4͒ and Eqs. ͑8͒–͑10͒ to evaluate
⌬␯ or S(i) ͓Eqs. ͑3͒ and ͑7͔͒. For flexible molecules whose
symmetry, then the interaction tensor ⑀ for the disk-shaped
␣␤
core can be written as
i
CD
0
0
0
pn and Sn␣␤ are known, it is possible to find a single confor-
mationally averaged ordering matrix in a common molecular
frame and then to find its diagonal elements for the ‘‘aver-
aged’’ conformer17,24 in a mesophase.
1
2
Ϫ
1
2
Xa
0
Ϫ
ͩ ͪ
0
0
1
The Tarroni–Zannoni ͑TZ͒ model10 is briefly surveyed
in order to write down the spectral densities Jm(m␻) due to
the core dynamics of HAT6. To evaluate the orientational
(c)
␣␤
and the interaction tensor ⑀ for the rodlike C–C segment is
now given by
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J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
4327
lar M frame. ٙ and x(j) are the eigenvalues and eigenvec-
correlation functions for the molecular core, one needs to
find the conditional probability by solving the rotational dif-
fusion equation
j
tors from diagonalizing a symmetrized transition rate matrix
R= . The last term in the above equation is due to a cross-term
contribution between internal bond rotations and the molecu-
lar reorientation.
Since HAT6 has ⌬␹Ͻ0, the columnar axes ͑directors͒
are aligned perpendicular to the magnetic field. The mea-
sured T1Z and T1Q give J1(␻,90°) and J2(2␻,90°). These
can be calculated in terms of Jm(m␻,0°)ϵJm(m␻)
(mϭ0,1,2) as follows:8
ˆ
1 ץP ⍀
͉
⍀t͒
͑
0
ˆ
ˆ
ϭ⌫P ⍀
͉
⍀t͒,
͑16͒
͑
0
␳
ץt
ˆ
where the symmetrized diffusion operator ⌫ is given by Eq.
͑14͒ of Ref. 10. The rotational diffusion tensor in the mo-
lecular frame contains principal diffusion elements
ˆ
DxϵDxx , DyϵDyy and DzϵDzz . Now ⌫ is written in
terms of ␳ϭ(DxϩDy)/2, ⑀ϭ(DxϪDy)/(DxϩDy), and
␩ϭDz /␳. For HAT6, the asymmetry parameter for rota-
tional diffusion ⑀ is zero. Therefore, the TZ model reduces to
the Nordio model9 ͑which has DxϭDyϵDЌ , DzϵDʈ , and
a22ϭ0͒. In general, the orientational correlation functions
can be written as a sum of decaying exponentials9,10
1
͑i͒calc
͑i͒
͑i͒
J1
␻,90°͒ϭ
J
␻͒ϩJ ␻͒ ,
͑20͒
͑
͑
͓
͑
͑
͔
1
2
2
3
1
͑i͒
͑i͒calc
͑i͒
J2
2␻,90°͒ϭ J0 2␻͒ϩ J1 2␻͒
͑
͑
8
2
1
8
͑i͒
ϩ
J2 2␻͒.
͑
͑21͒
g2mnn t͒ϭ
␤
͑17͒
2
͑
͑
͓͑
͒ exp ␣2 ͒ t ,
͔
K
͚
K
mnn
mnn
Ј
Ј
Ј
K
Substituting Eqs. ͑18͒ and ͑19͒ into the above equations, the
measured spectral densities in our experiments can be calcu-
lated.
where (␣2mnn )K /␳, the decay constants, are the eigenvalues
Ј
and (␤2mnn )K , the relative weights of the exponentials, are
Ј
ˆ
the corresponding eigenvectors from diagonalizing the ⌫ ma-
trix whose elements are formed using a Wigner basis set.
The solutions of the rotational diffusion equation involve
ranks (L) up to 40 in the basis set, since the order parameter
EXPERIMENTAL METHOD
Synthesis:
P
of HAT6 is rather high. In the above equation, the
͘
͗
2
2,3-„d13…Hexyloxy-6,7,10,11-tetrahexyloxytriphenylene
projection indices (n,n ) in the molecular frame are equal
Ј
due to uniaxial symmetry of the HAT6 molecule.
We first consider spectral densities for the case where
the director is along the magnetic field. The spectral densities
for the ring ͑C0) deuterons of HAT6 arise from molecular
reorientations and are given by
Perdeuterated 1-bromohexane 2
Perdeuterated hexan-1-ol ͑500 mg; 4.3 mmol͒ 1 was
added drop wise to a vigorously stirred solution of hydrobro-
mic acid ͑2.49 g; 48% w/v͒ and concentrated sulphuric acid
͑426 mg͒. The mixture was refluxed for 6 h, cooled and
carefully poured onto water ͑50 ml͒. The aqueous mixture
was extracted with diethylether ͑2ϫ50 ml͒, and washed con-
secutively with sodium hydrogen carbonate solution ͑50 ml͒,
water ͑50 ml͒ and again sodium hydrogen carbonate solution
͑50 ml͒ the organic layer being dried over anhydrous mag-
nesium sulphate. Filtration, and solvent evaporation at RT
yielded deuterated 1-bromo-hexane ͑660 mg; 85%͒ 2 as a
dark brown liquid which was used in its crude state for the
next step.
2
3␲
͑0͒
͑0͒
CD
2
2
Jm m␻͒ϭ
q
͒
d2
␤
͑
n0
͒
͔
M,Q
͑
͑
͓
͚
n
2
2
2
␤
͒
␣
͒
mnn
͑
͑
͑
K
K
mnn
ϫ
,
͑18͒
͚
2
mnn
2
2
K
␣
͒Kϩm2␻
where the ␤M,Q angle between the C–2H bond and the mo-
lecular zM axis is taken to be 90°. In the decoupled model,
the spectral densities J(mi)(m␻) of the Ci methylene deuter-
on͑s͒ are given by8
N
N
2
3␲
Jm m␻͒ϭ
q
͒
͉
d2
␤
͑
n0
͒
M,Q
͑i͒
͑i͒
CD
͑i͒l
2
͑
͑
͚ ͚ ͚
1,2-Dihexyloxy-4-iodobenzene 3
n
jϭ1 lϭ1
2
͑i͒l
͑1͒ ͑ j͒
2
Iodine monochloride ͑60 g͒ was slowly added to a vig-
orously stirred solution of 1,2-dihexyloxy benzene ͑72.5 g;
0.216 mol͒ in chloroform ͑200 ml͒ at 0 °C. After stirring at
room temperature for 1 h the solution was decanted and
washed with aqueous sodium metabisulfite. Evaporation of
the organic layer produced a crude product which was dis-
tilled under reduced pressure to give 1,2-dihexyloxy-4-
iodobenzene 3 ͑69.1 g, 79%͒ as a dark brown oil ͑bp 240–
260 °C at 40 mmHg͒.24 1H NMR ͑CDCl3) ␦: 7.09 ͑s, 1H,
ArH͒, 7.05 ͑d, 1H, Jϭ 8.5 Hz, ArH͒, 6.50 ͑d, 1H, Jϭ8.5 Hz,
ArH͒, 3.97 ͑t, 4H, Jϭ7 Hz, OCH2), 1.81 ͑m, 4H, Jϭ7 Hz,
OCH2CH2), 1.33–1.49 ͑m, 12H, CH2). 0.97 ͑t, 6H, Jϭ7 Hz,
CH3).
ϫexp Ϫin␣
x
͔
xl ͉
l
͓
M,Q
2
mnn
2
␤
͒
␣
͒Kϩ
͉ٙ ͉
͔
j
mnn
͑
͓͑
K
ϫ
ϩ
ϫ
͚
2
2
2ϩm2␻
K
␣
͒Kϩ
͉
ٙ
͉
͓͑
͔
j
mnn
2
3␲
͑i͒
CD
2
q
͒2␦m0
P
͑
͗
͘
2
2
N
N
d2
␤
͒xl xl
͉
/
͉
ٙ
͉
,
͑19͒
͑i͒l
M,Q
͑1͒ ͑ j͒
2
͉
͑
͚ ͚
j
00
jϭ1 lϭ1
where Nϭ243, q(CiD) ϭ165 kHz, ␤
and ␣
are the polar
(i)l
M,Q
(i)l
M,Q
angles of the Ci –2H bond of the conformer l in the molecu-
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4328
J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
3,3Ј,4,4Ј-Tetrahexyloxybiphenyl 4
1,2-Dihexyloxy-4-iodobenzene ͑16 g; 0.04 mol͒ 3 was
intimately mixed with copper powder ͑30 g͒ and heated care-
fully to 270 °C where an exothermic reaction took place
causing the temperature to rise to 310 °C. After cooling the
mixture was extracted with dichloromethane ͑3ϫ50 ml͒, fil-
tered through celite, the solvent was evaporated and the resi-
due crystallized from ethanol ͑50 ml͒ to give
3,3Ј,4,4Ј-tetrahexyloxybiphenyl ͑5.5 g, 50%͒ 4 as a white
crystalline solid ͑mp 68–70 °C͒.25 1H NMR ͑CDCl3) ␦: 7.13
͑m, 4H, ArH͒, 6.90 ͑d, 2H, Jϭ9 Hz, ArH͒, 3.97 ͑t, 8H, Jϭ7
Hz, OCH2), 1.81͑m, 8H, Jϭ7 Hz, OCH2CH2), 1.33–1.49͑m,
24H, CH2), 0.97 ͑t, 12H, Jϭ7 Hz, CH3).
1,2-Di(d13-hexyloxy)benzene 5
Perdeuterated hexylbromide ͑560 mg; 3.39 mmol͒ 2, cat-
echol ͑170 mg; 1.54 mmol͒ 6 and anhydrous potassium car-
bonate ͑500 mg͒ were stirred in refluxing ethanol ͑20 ml͒ for
72 h. On completion, the mixture was decanted onto water
͑20 ml͒, extracted with dichloromethane ͑2ϫ20 ml͒ and the
solvent evaporated to give 1,2-di͑d13-hexyloxy͒benzene 5
͑313 mg; 67%͒ as a clear colorless liquid. 1H NMR ͑CDCl3)
␦: 6.88 ͑s, 4H, ArH͒.
FIG. 2. A typical deuteron NMR spectrum of chain-deuterated HAT6 ͑the
peak assignments are labeled by carbon numbers in the chain͒ and the modi-
fied broadband Jeener-Broekaert pulse sequence.
NMR
We determined the discotic-isotropic transition tempera-
ture Tc of our samples by means of NMR signals. The chain-
deuterated sample exhibited a Tcϭ99.4 °C, while the ring-
deuterated sample a Tcϭ100.4 °C. When comparing the
NMR data of these samples, we scaled the temperatures to
give a common Tc of 99.9 °C. The T1Z and T1Q of the
methylene and ring deuterons were measured as a function of
temperature at two Larmor frequencies. The HAT6 molecule
is schematically shown in Figure 1 and the peak assignments
for the chain-deuterated sample are shown on the represen-
tative spectrum in Figure 2. A home-built superheterodyne
coherent pulse NMR spectrometer was operated for deuter-
ons at 15.1 MHz using a varian 15 in electromagnet and at
46.05 MHz using a 7.1 Tesla Oxford superconducting mag-
net. The sample was placed in a NMR probe whose tempera-
ture was regulated either by an external oil bath circulator or
by air flow with a Bruker BST-1000 controller. The tempera-
ture gradient across the sample was estimated to be better
than 0.3 °C. The ␲/2 pulse width of about 3.8 ␮s was pro-
duced by a ENI power amplifier. Pulse control and signal
collection were performed by a General Electric 1280 com-
puter. Fourier transformation and data processing were com-
pleted by Spectral Calc and Micro Origin softwares on a
IBM-PC computer. Broadband Jeener-Broekaert ͑J-B͒ exci-
tation sequence ͑Figure 2͒ was used to simultaneously mea-
sure T1Z and T1Q . The data manipulation has been detailed
elsewhere.23 The pulse sequence was modified using an ad-
ditional monitoring ␲/4 pulse to minimize any long-term in-
stability of the spectrometer. This pulse was phase-cycled to
have a net effect of subtracting the equilibrium magnetiza-
tion (Mϱ) signal from the J-B sequence. Signal collection
was started 10 ␮s after each monitoring ␲/4 pulse, and av-
eraged over 1024–4096 scans at 46 MHz and 2048–8192
scans at 15.1 MHz depending on the signal strengths of the
2,3-Di(d13-hexyloxy)-6,7,10,11-
tetrahexyloxytriphenylene 7
Anhydrous iron ͑III͒ chloride ͑680 mg͒ was added to a
vigorously stirred solution of 1,2-di͑d13-hexyloxy͒benzene
͑313 mg; 1.03 mmol͒ 5 and 3Ј,3,4Ј,4-tetrahexyloxybiphenyl
͑560 mg; 1.02 mmol͒ 4 in dry dichloromethane ͑25 ml͒.
After 1 h the mixture was poured onto methanol ͑40 ml͒
and the resultant precipitate filtered-off. The crude residue
was purified by column chromatography ͓silica, light petro-
leum:
dichloromethane
͑1:1͔͒
to
give
2,3-di͑d
13-hexyloxy͒-6,7,10,11-tetrahexyloxytriphenylene ͑526 mg;
60%͒ 7 as a white solid. ͑K 69 °C D 99 °C I͒.26 ͑Lit K-D 68
°C, D-I 99 °C͒. 1H NMR ͑CDCl3) ␦: 7.83 ͑s, 6H, ArH͒, 4.23
͑t, 8H, OCH2), 1.94 ͑m, 8H, OCH2CH2), 1.41–1.56 ͑m,
24H, CH2), 0.93 ͑t, 12H, CH3).
Ring deuterated HAT6
2,3,6,7,10,11-Hexahexyloxy-1,4,5,8,9,12-
hexadeuterotriphenylene
2,3,6,7,10,11-Hexahexyloxytriphenylene27 ͑1 g; 1.2
mmol͒ and deuterated trifluoroacetic acid ͑1.1 ml͒ were
stirred in deuterated chloroform ͑10 ml͒ for 72 h. On
completion the mixture was poured carefully onto deuterated
methanol ͑20 ml͒, cooled to 0 °C and the resulting precipi-
tate filtered off to give 2,3,6,7,10,11-hexahexyloxy-
1,4,5,8,9,12-hexadeuterotriphenylene ͑750 mg; 75%͒ as an
off-white solid. ͑K 69.5 °C D 99.7 °C I͒. ͑Lit K-D 68 °C,
D-I 99 °C͒. ͓Mϩ ͑833͔͒. 1H NMR ͑CDCl3) ␦: 7.83 ͑s, 1.5H,
ArH͒, 4.23 ͑t, 12H, Jϭ7 Hz, OCH2), 1.94 ͑m, 12H,
OCH2CH2), 1.41–1.56 ͑m, 36H, CH2), 0.93 ͑t, 18H, Jϭ7
Hz, CH3).
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J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
4329
FIG. 3. Plots of segmental order parameters as a function of temperature in
the columnar phase of HAT6. Square denotes the aromatic sites, open and
closed circles denote C1 and C2, respectively, while open and closed tri-
angles denote C3Ϫ4 and C5, respectively. The solid curves are the theoretical
predictions using the additive potential method.
FIG. 4. Plot of experimental Zeeman spin-lattice relaxation rates versus the
temperature in the columnar phase of HAT6. ͑a͒ and ͑b͒ are for data at 15.1
and 46 MHz, respectively. Circle denotes the aromatic sites, open and
closed triangles denote C1 and C2, respectively, while open and closed
squares denote C3Ϫ4 and C5, respectively. The dashed lines are drawn to aid
the eyes.
various resolvable peaks. For the spectrum with very small
quadrupolar splittings, a larger value of pulse interval
␶(Ӎ10 ␮s͒ was required to maximize the quadrupolar or-
der, comparing to the typical value of ␶(5␮ s͒. Despite using
broadband excitation of quadrupolar order, different sets of
relaxation delays with appropriate repetition times were
used. This was due to a large spread in the magnitude of the
relaxation times for various deuterons. T1Z and T1Q were
derived from a least-squares fit of the sum, S(t), and differ-
ence, D(t), of the component areas of the quadrupolar dou-
blet:
sults were obtained by using Etgϭ3.7 kJ/mol, EtЈgϭ1.9 kJ/
mol, and EgϮgϯϭEЈgϮgϯϭ10 kJ/mol. The Etg value is
closed to the value used in the calamitic liquid crystal
6OCB,23 but it is not clear why the EtЈg should be smaller
than that used in 6OCB. An optimization routine28
͑AMOEBA͒ was used to minimize the sum squared error f
in fitting the splittings
͑i͒
͑i͒,calc
fϭ
͉
SCD
͉
Ϫ
͉
SCD
͉
͒2,
͑22͒
͑
͚
i
S t͒ϰexp Ϫt/T ͒,
͑
͑
where the sum over i includes C1 to C5 and aromatic deu-
terons. The f values are of the order of 10Ϫ3 ͑see Table I͒.
The calculated segmental order parameters are indicated in
Figure 3 as solid lines. Note that ⌬␯ and ⌬␯ were aver-
1Z
D t͒ϰexp Ϫt/T ͒.
͑
͑
1Q
The subtraction of the Mϱ signal in the pulse sequence
meant that the above simple exponential equations could be
used. The experimental uncertainty in these spin-lattice re-
laxation times was estimated to be Ϯ5%. The quadrupolar
splittings of the aromatic site deuterons and chain deuterons
were determined from NMR spectra obtained by Fourier
transforming the free induction decay ͑FID͒ signal after a
␲/2 pulse, and had an experimental error of better than
Ϯ1%. As seen in Figure 2, the doublet splittings from C3
and C4 sites are not resolved. Thus the spin-lattice relaxation
times at these sites cannot be measured separately.
3
4
RESULTS AND DISCUSSION
(i)
CD
Figure 3 shows the experimental S
versus the tem-
perature. The temperature dependencies of the measured re-
Ϫ1
1Z
Ϫ1
1Q
laxation rates T and T are summarized in Figures 4 and
5. The relaxation rates measured at 46 MHz are similar to
those reported in the literature,13 except our values for the
aromatic deuterons are slightly lower and the values for the
C1 deuterons show slightly different temperature behaviors.
In fitting the segmental order profiles, we had inputted vari-
ous values of Etg , EtЈg , EgϮgϯ , and EgЈϮgϯ . We found that
the calculated ⌬␯ and ⌬␯ were different and the best re-
FIG. 5. Plot of experimental quadrupolar spin-lattice relaxation rates versus
the temperature in the columnar phase of HAT6. ͑a͒ and ͑b͒ are for data at
15.1 and 46 MHz, respectively. Circle denotes the aromatic sites, open and
closed triangles denote C1 and C2, respectively, while open and closed
squares denote C3Ϫ4 and C5, respectively. The dashed lines are drawn to aid
the eyes.
3
4
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4330
J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
TABLE I. Model parameters derived from the analysis of quadrupolar splittings at different temperatures in the
columnar phase of HAT6. The interaction parameters Xa and Xcc are in units of kJ/mol. a20 ,a22 are dimen-
sionless second rank coefficients in the orienting potential which is used in the rotational diffusion equation.
T͑K͒
Xa
Xcc
P
S
xxϪSyy
͘
a20
102a22
103 f
͗
͘
͗
2
364.9
362.1
359.2
355.4
351.6
347.8
344.0
340.2
336.4
17.3
17.9
18.5
19.4
20.4
21.2
22.2
23.1
24.1
0.145
0.136
0.124
0.111
0.098
0.085
0.072
0.058
0.050
0.848
0.855
0.862
0.869
0.878
0.884
0.890
0.896
0.902
0.00101
0.00087
0.00073
0.00059
0.00046
0.00037
0.00028
0.00021
0.00016
Ϫ7.0
Ϫ7.3
Ϫ7.6
Ϫ8.1
Ϫ8.6
Ϫ9.0
Ϫ9.5
Ϫ10.0
Ϫ10.6
Ϫ10.5
Ϫ10.0
Ϫ9.3
Ϫ8.4
Ϫ7.5
Ϫ6.6
Ϫ5.7
Ϫ4.7
Ϫ4.1
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
aged for comparison with the experimental values. We sum-
marize in Table I some of the derived parameters
matic site (iϭ0) and decrease monotonically along the chain
to the methyl group. At 336.4 K and 46 MHz, J2(2␻,90°) of
C0 is slightly less than that of C1. We model the spectral
densities by using Eqs. ͑18͒–͑21͒. In particular, we take ad-
vantage of the fact that the target parameters of the model
vary smoothly with temperature by simultaneously analyzing
data at all temperatures. From individual target analyses ͑i.e.,
analyze the data at each temperature͒, we found that the ro-
tational diffusion constants and the jump constant k2 obey
simple Arrhenius-type relations, giving
Xa ,Xcc , P , S ϪS ,a and a22 . As seen in Table I,
͗
yy
͘ ͗
͘
2
xx
yy
20
S ϪS
xx
is vanishingly small indicating that the HAT6
͗
͘
molecule is essentially a uniaxial molecule.
The relations between the relaxation rates ͑measured
with the director at 90° with the field direction͒ and the
spectral densities as given by the general relaxation theory
are
Ϫ1
T
T
ϭ3J1 ␻,90°͒,
͑23͒
͑24͒
͑
1Q
D ϭD0 exp ϪEЌ/RT ,
͑25͒
͑26͒
͑27͒
͓
͔
Ќ
Ќ
a
Ϫ1
1Z
ϭJ1 ␻,90°͒ϩ4J 2␻,90°͒.
͑
͑
2
D ϭD0exp ϪEʈ /RT ,
͓
͔
ʈ
ʈ
a
From the results of Figures 4–5 and the above equations, the
spectral densities of the aromatic and aliphatic deuterons
could be determined. These are summarized in Figures 6 and
7. To show the site dependence of spectral densities, we plot
them in Figure 8 for two different temperatures. The
J1(␻,90°) and J2(2␻,90°) are in general largest at the aro-
k
a
0
2
2
k ϭk exp ϪE /RT .
͓
͔
2
In Eqs. ͑25͒–͑27͒, the global parameters are pre-exponentials
DЌ0 , D0ʈ , k02 , and their corresponding activation energies
EЌa , Eaʈ , Ek2 . For convenience, the diffusion and jump rate
a
FIG. 6. Plots of experimental ͑symbols͒ and calculated ͑lines͒ spectral den-
sities of HAT6. ͑a͒ and ͑b͒ are for data obtained at 15.1 and 46 MHz. The
closed symbols denote J1(␻0,90°), while the open symbols denote
J2(2␻0,90°). The triangles represent data for C5, while the squares and
circles represent data at the aromatic sites and C2, respectively.
FIG. 7. Plots of experimental ͑symbols͒ and calculated ͑lines͒ spectral den-
sities of HAT6. ͑a͒ and ͑b͒ are for data obtained at 15.1 and 46 MHz. The
closed symbols denote J1(␻0,90°), while the open symbols denote
J2(2␻0,90°). The circles represent data for C1, while the squares represent
data at C3Ϫ4
.
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J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
4331
FIG. 9. Plots of ͑a͒ rotational diffusion constants and ͑b͒ jump constants as
a function of the reciprocal temperature. Solid lines denote DЌ in ͑a͒ and k2
in ͑b͒, while dashed lines denote Dʈ in ͑a͒ and k3 in ͑b͒.
Again the calculated spectral densities for C3 and C4 are
quite different. However, we have averaged the calculated
spectral densities at these two sites in our minimization. Be-
cause the ring J1(␻,90°) is larger than all the other spectral
densities, we have adopted the strategy to first minimize the
sum squared error ͑i.e., Q). As the global fit appeared to be
insensitive to the EЌa value, we have chosen to derive nine
global parameters from a total of 432 spectral densities with
several input EЌa values. There was hardly any change in the
Q value when varying EЌa between 10 and 30 kJ/mol. Thus
we have chosen the value EЌa ϭ30 kJ/mol, simply because it
was slightly larger than the derived Eaʈ of 22.0 Ϯ0.6 kJ/mol.
By minimizing Q, a better fit of the ring data was achieved.
We then used the derived motional parameters for the mo-
lecular reorientation, and minimized F using only the meth-
ylene data to get the jump constants. We summarize the ro-
tational diffusion constants in Figure 9a. It is interesting to
note from this figure that the rotational diffusion constant DЌ
is larger than Dʈ in the entire columnar phase of HAT6. This
is quite different from calamitic liquid crystals in which the
spinning motion is much faster than the tumbling motion.
The jump constant k1 is essentially independent of the tem-
FIG. 8. Plots of spectral densities as a function of carbon position at ͑a͒
351.6 K and ͑b͒ 336.4 K. Circle denotes J1(␻0,90°), and square denotes the
corresponding J2(2␻0,90°). Open and closed symbols denote data at 15.1
and 46 MHz, respectively. The dashed and solid lines denote theoretical
predictions at 15.1 and 46 MHz, respectively.
pre-exponentials are not used as global parameters. Rather
Eqs. ͑25͒–͑27͒ are rewritten in terms of the activation ener-
gies and the diffusion and jump constants DЈ , DЈ , kЈ at
ʈ
Ќ
2
T
maxϭ364.9 K. When such a relation does not exist for a
target parameter like k1 or k3, it is still possible to introduce
an interpolating relation linking its values at various tem-
peratures. As k1 and k3 are weakly temperature dependent,
we model them by a linear relation:
k ϭkЈϪkЉ TϪT ͒,
͑28͒
͑
i
max
i
i
where the global parameters kЈi , and kiЉ(iϭ1 or 3͒ are opti-
mized. The diffusion constants DЈ , DЈ and the jump con-
ʈ
Ќ
stants kЈ1 , k2Ј , k3Ј at Tmax were first obtained from an indi-
vidual target analysis. Again AMOEBA was used in our
minimization to fit the spectral density data. The sum
squared percent error F is given by
perature (k1ϭ5ϫ1017 Ϫ1) and describes the fast one-bond
s
͑i͒calc
͑i͒
motion of the last C–C bond in the chain. The k2 and k3 are
given as a function of temperature in Figure 9b. As seen in
the figure, k3 decreases very slightly with decreasing tem-
perature. Although jump constants have been obtained in
several calamitic liquid crystals,8 it is difficult at present to
make comparison among them or with those obtained here.
Jm
m␻,90°͒ϪJ m␻,90°͒
͑
͑
m
Fϭ
͚ ͚ ͚ ͚
ͫ
͑i͒
k
␻
i
m
Jm m␻,90°͒
͑
2
ϫ100
,
͑29͒
ͬ
k
k
2
The activation energy for the two-bond motion is Ea ϭ83.6
kJ/mole. Its error limits range between 39 kJ/mol ͑for 13%
increase in F) to 88.7 kJ/mol. The error limit for a particular
global parameter was estimated by varying the one under
consideration while keeping all other global parameters iden-
tical to those used for the minimum F ͑or Q), to give an
approximate doubling in the Q value ͑e.g., Eaʈ ) or in the F
where the sum over k is for nine temperatures, ␻ for two
frequencies, i for five methylene deuterons ͑and aromatic
deuterons͒ and mϭ1 or 2. The fitting quality factor Q is
given by the percent mean-squared deviation
͑i͒calc
m
͑i͒
2
k
͚ ͚ ͚ ͚ J
͓
m
m␻,90°͒ϪJ m␻,90°͒
͑ ͑ ͔
m
k
␻
i
Qϭ
͑i͒
m
2
k
͚ ͚ ͚ ͚ J
͓
m
m␻,90°͒
͑ ͔
k
k
␻
i
2
value ͑e.g., kЈ1 ,Ea ). When the target parameter becomes in-
sensitive in the calculation, a lower % increase in F was
ϫ100.
͑30͒
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4332
J. Chem. Phys., Vol. 108, No. 10, 8 March 1998
Shen et al.
used. Now the pre-exponentials in Eqs. ͑25͒–͑27͒ are
D0ʈ ϭ7.05ϫ1010 Ϫ1, DЌ0 ϭ3.17ϫ1012 Ϫ1, and k20ϭ1.1
ϫ1025 Ϫ1. The uncertainty in D0ʈ is 5.6–8.5ϫ1010 sϪ1 and
Finlay are gratefully acknowledged. We also acknowledge
the Engineering and Physical Sciences Research Council of
Great Britain for the award of research studentships to A.W.
and P.S.M., and Dr. B. Movaghar for helpful discussion on
the mechanism of charge transport in discotic liquid crystals.
R.Y.D. also acknowledges a travel grant from the Associa-
tion of Universities and Colleges of Canada.
s
s
s
in DЌ0 is between 5ϫ1011 sϪ1 and 1.1ϫ1013 Ϫ1. We note
s
that at the low DЌ0 limit, the Dʈ /DЌ ratio is about 2. The
error limits for k20 are between 1.9ϫ1024 sϪ1 and 1ϫ1028
sϪ1 ͑for 13% increase in F). At Tmax , k1Јϭ5.0ϫ1017 sϪ1
and k3Јϭ9.19ϫ1012
4.25ϫ1012 sϪ1 to 2.4ϫ1014
does not affect the fit, its lower limit is found to be 2ϫ1012
Ϫ1. Finally, the calculated spectral densities for HAT6 (Q
s
Ϫ1. The error bar for kЈ3 ranges between
s
Ϫ1. While any larger kЈ1 value
s
ϭ 0.67%͒ are indicated by curves in Figures 6 and 7. Al-
though the final Q value is quite small, there exist large
systematic deviations between the calculated and experimen-
tal spectral densities at some carbon sites ͑e.g., C5). We at-
tribute these discrepancies to the limitation and assumptions
in the model used in the present study. The predicted site
dependencies of various spectral densities at two tempera-
tures are also shown in Figure 8.
In conclusion, we have given a consistent interpretation
of both the quadrupolar splittings and the spin-lattice relax-
ation data measured in the columnar phase of two differently
deuterated HAT6 molecules. From modeling the splittings
with the AP method, we obtain the orienting potential
needed to describe the reorientational dynamics of molecular
disks. It is clear that the tumbling motion of a disk can be
slightly faster than its spinning motion. Given the rotational
diffusion constants are of the order of 108 sϪ1, the packing
of molecular disks within a column must be viewed as a state
of high dynamic mobility. The decoupled model proposed by
Dong18 for correlated internal rotations has been applied for
the first time to a discotic liquid crystal.
Finally, we comment on the very interesting implications
of the results for electronic transport along the molecular
columns. The rotational speeds Dʈ and DЌ are some two
orders of magnitude slower than a typical charge hopping
frequency ͑1010 sϪ1) between the aromatic cores of adjacent
molecules. The implication is that on the time scale of charge
diffusion the ‘‘lattice’’ appears static with disorder being due
to instantaneous displacement of HAT6 molecules with re-
spect to each other. This dynamically induced disorder has
consequences both in the quantum ͑low temperatures͒ and
the stochastic hopping ͑high temperatures͒ limits. In the
quantum limit, the disorder will cause elastic scattering and
reduce the charge mobility. In the stochastic hopping limit it
produces variations in jump frequencies between adjacent
molecules in the columns. This, in turn, gives rise to a fre-
quency dependent diffusivity.
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ACKNOWLEDGMENTS
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The financial support of the Natural Sciences and Engi-
neering Council of Canada and the technical assistance of N.
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