J. Phys. Chem. B 2006, 110, 15075-15079
15075
ARTICLES Comparative Study of Planar Motion in Monomeric and Dimeric Discotics J. Zhang† and Ronald Y. Dong*,†,‡ Department of Physics and Astronomy, UniVersity of Manitoba, Winnipeg, MB, Canada R3T 2N2, and Department of Physics and Astronomy, Brandon UniVersity, Brandon, MB, Canada R7A 6A9 ReceiVed: May 2, 2006; In Final Form: June 13, 2006
Deuterium NMR spectra are reported in powder samples of discotic monomer and dimer as a function of temperature in their column Colho phases. To simulate the observed powder patterns, a threefold jump model is used in the monomer, while in the related dimer the libration motion of the monomeric core is described using the infinitesimal jump method under a restricting potential due to the spacer. By comparing the diffusive rates for the two samples, it is concluded that the planar motion in the dimer is at least 30 times smaller than that of the monomer. This could lead to an enhancement of charge and energy transport in discotic dimer systems.
1. Introduction Self-organizing disc-shaped liquid crystalline molecules,1 which form columnar phases, show special anisotropic physical properties such as one-dimensional photoconductivity2,3 and electron conductivity.4 Among them, those of triphenylene derivatives have been the most studied, not only because the molecular engineering for these materials is relatively simple, but also because they show good thermal stability.5 In the discotic columnar phase, molecular disks (separated by ca. 0.35 nm) are stacked into columns, which in turn aggregate to give a two-dimensional lattice (e.g., hexagonal, or rectangular). The π shells of adjacent disklike molecules in the stack tend to overlap. Indeed, the π overlap between the electronically active transport units provides a one-dimensional pathway for charge and energy migration. However, the charge transport properties of discotic liquid crystals (DLC) are highly influenced by the structural disorder such as changing orientations and/or positions of the disklike molecules within the stacks.6 For example, it was found experimentally that hole mobility increases with decreasing chain length in a homologue series of hexaalkoxytriphenylenes (HATn).3 This is attributed to an increase in order within the columnar phase. Another way to increase hole mobility is by dimerization. The triphenylene dimers are formed by linking two monomeric units via a spacer of roughly twice the length of the free side chain. The dimeric triphenylene derivatives exhibit a liquid crystalline phase over a much wider temperature interval than monomers from just below their isotropic transition points at close to 400 K down to at least 130 K.7 Experiments have indicated that they show values exceeding those for commonly used photoconductive polymers by 2 or 3 orders of magnitude.2 The novel charge transport properties are potentially exploitable in applications ranging from sensing devices to high resolution xerography. * Corresponding author. † University of Manitoba. ‡ Brandon University.
Deviations from an ideal stacking in the columns will lead to incoherent energy transport along the one-dimensional pathway, and the transport proceeds by successive transitions from one localized site to another. In fact, the temperaturedependent disorder is related to the temperature-dependent broadening of the density of states in the “hopping” model.8 For this reason, understanding the charge transport in relation to the dynamical behaviors in DLC is an important issue. To this end, nuclear magnetic resonance (NMR) has been shown as a powerful method9 to investigate molecular motions and order in LC. Many NMR investigations of discotic compounds have been reported10-13 in the literature. Both order and dynamics in LC promote dynamical transport processes. In monomeric DLC, there is in general no lateral correlation between the molecules in neighboring columns. The columns may freely slide relative to each other, and the molecules randomly rotate about the columnar axes and diffuse between columns. It is well-known that when in a sufficiently strong magnetic field monomeric DLC can be aligned by cooling from the isotropic liquid to the mesophase. In dimeric discotics, the columns may not freely slide over each other, mainly due to restrictions imposed by the spacers. If the two subunits of a dimer reside in the same column, they may undergo, as a pair, limited diffusive reorientation, while if they occupy neighboring columns their monomeric units perform only large amplitude librations as a result of intercolumnar interactions.7 In the past, several papers have been published on dimeric DLC.6,7,14 It is known that the length of the spacer and of the side groups will affect the clearing temperature. The charge transport has been shown to be highly anisotropic with a conductivity up to 3 orders of magnitude higher in the direction of columnar stacks.15 However, few NMR studies of dimeric DLC have appeared7,16 in the literature, partly due to the difficulty of aligning their discotic phases in the NMR magnetic field. Here, we have chosen to study a core deuterated triphenylene dimer DHAT5C14 whose structure is given in Figure 1. Since DHAT5-C14 cannot be aligned in our NMR field of 9.4 T even by cooling
10.1021/jp0626925 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/18/2006
15076 J. Phys. Chem. B, Vol. 110, No. 31, 2006
Zhang and Dong 9.4 T. The sample temperature was controlled by an air flow, and the temperature gradient across the sample was estimated to be better than 0.5 °C. A two-pulse quadrupole echo sequence (90°-τ-90°)21 was used to generate 2H 1D spectra. The time interval between the two 90° pulses was 30 µs unless stated otherwise, and the recycle time between scans was 0.3 s. The 90° pulse width was 2.6 µs. To get a good free induction decay (FID), signal averaging required 2000 scans in DHAT5-C14. 3. Theory The spin Hamiltonian for a deuterium spin in a magnetic field is22
H ) HZ + HQ ) -γpH·I + 1 e2qQ 3IZ2 - I(I + 1) + η(I+2 + I-2) (1) 2 4I(2I - 1)
[
]
where HZ and HQ denote the Zeeman and quadrupolar interaction, respectively. The principal (X, Y, Z) axes of the electric field gradient tensor Vij give |VZZ| g |VYY| g |VXX| with η ) ((VXX - VYY)/VZZ). In liquid crystalline phases, molecules undergo rapid rotational and translational diffusion motions and the quadrupolar Hamiltonian becomes time averaged to H h Q. In the high field limit, H h Q can be treated as a first-order perturbation on the HZ Hamiltonian. An absorption spectrum (for a powder sample) consists of subspectra, each has two lines whose spectral frequencies are given by7
3 1 ν(φ) ) ( νQ [3 sin2 β cos2(R - φ) - 1 4 2 η(cos2 β - sin2 β sin2(R - φ))] (2) Figure 1. Molecular structure of HAT5a (a), DHAT5-C14 (b), and a schematic sketch of dimer potential (c).
from the isotropic melt, the deuterium study is carried out in a powder sample. A “corresponding” core deuterated monomer 2,7,10,11-tetrapentyloxy 3,6-diacetoxy triphenylene (HAT5a), shown in the same figure, is also studied in its powder form for direct comparison. In HAT5a, two of the six pendant chains are much shorter in length.17 A better core deuterated monomer to compare with DHAT5-C14 would be one that has only one short (-OCOCH3) chain. However, this was not available. The aligned HAT5a sample has recently been studied by us to give the planar reorientation rate in its columnar Colho phase.18 It was found that the deuterium line shapes can be simulated equally well by either the three-site jump model19 or a planar diffusive process.20 The paper is organized as follows. Section 2 contains the experimental method. Section 3 gives the relevant theory for describing the dynamic motion and simulation of experimental spectral features. Section 4 gives the results and discussion. A brief conclusion is given in the last section. 2. Experimental Method A core deuterated HAT5a sample was that used previously.18 The reported clearing temperatures between the Colho and isotropic phase for the protonated HAT5a and DHAT5-C14 samples are 442 and 420 K, respectively.17 The clearing temperature of our deuterated HAT5a sample was estimated18 at 438 ( 2 K. This slightly lower transition temperature is likely due to impurities introduced in the deuteration. The deuterium powder spectra were collected at 61.4 MHz on a Bruker Avance 400 solid state system in conjunction with a magnetic field of
where νQ ) (eQVzz)/h is the quadrupolar coupling constant. The polar angles R and β specify the long molecular axis in the laboratory frame defined by the external magnetic field. The φ angle specifies the azimuthal angle of a C-D bond in the molecular frame. In the case of a core deuterated triphenylene, the molecules have different orientations in a powder sample and produce a powder NMR spectrum. To treat the planar reorientation of HAT5a, the threefold jump mechanism19 is adopted for simplicity. Here, the magnetizations G(φ, t), G(φ + 2π/3, t), and G(φ - 2π/3, t) are coupled by the jump process with jump matrix R
(
R) i2πν(φ) + 2KJ + -KJ -KJ
1 T2
-KJ
-KJ
2 1 i2πν φ + π + 2KJ + 3 T2
-KJ
-KJ
2 1 i2πν φ - π + 2KJ + 3 T2
(
)
(
)
)
(3)
where KJ is the jump rate and 1/T2 is a jump-independent relaxation term to account for the line broadening. To obtain the time-domain free induction decay (FID) signal, one needs to solve the Bloch-McConnell equation of motion:23,19
d G(φ, t) ) -R G(φ, t) dt
(4)
where G(φ, t) is a column vector of magnetizations from the molecules with different φ orientations. In a quadrupolar echo
Planar Motion in Discotics
J. Phys. Chem. B, Vol. 110, No. 31, 2006 15077
experiment, the FID for a particular crystallite24 is given by
f(R,β, t) ) Re{1·G} ) 1·Re[e-R(t+τ)(e-Rτ)*·P0]
(5)
where 1 is a unity row vector and P0 is a column vecor of the initial fractional populations at different sites. The exponentials in the above equation can become tractable by means of matrix diagonalization.25 The final FID intensity is obtained by summing over all R and β to give
F(t) )
∫0π∫02πf(R,β, t) dR sin β dβ
(6)
The simulated spectrum is obtained by Fourier transform of F(t), i.e.
S(w) )
∫0∞F(t)·e-iwt dt
(7)
To simulate the powder spectra of dimer DHAT5-C14, we have adopted the potential model proposed some time ago by Zamir et al.7 to mimic the effect of the spacer on the core’s reorientations. The potential energy (see Figure 1c) is assumed to be
V(φ) ) Voφ2
(8)
where Vo is a positive parameter with dimensions J rad-2, while φ is the angular deviation of the spacer from its equilibrium (minimum energy) direction. The probability to find each C-D bond at φi obeys a normalized equilibrium distribution:
Pi )
x
V0 -Voφi2/kT e kTπ
(9)
Adopting the infinitesimal jump method under the above potential to describe the librational motion of the monomeric core, one needs to solve a set of Bloch-McConnell equations:7
d dt
[
Gi(t) ) - i2πν(φ) +
1
kji + ∑ T j*i
]
Gi(t) +
2
ki,i+1Gi+1(t) + ki,i-1Gi-1(t) (10)
where the jump is taken to occur among neighboring segments and kij specifies the jump rate between the ith and jth segments corresponding to different φ values. The width of each segment is δφ, and the range of φ, outside of which Pi is negligible (
