Effect of Dipole Functionalization on the Thermodynamics and

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Effect of Dipole Functionalization on the Thermodynamics and Dynamics of Discotic Liquid Crystals Nino Haase,‡ Christos Grigoriadis,† Hans-Jurgen Butt,‡ Klaus M€ullen,*,‡ and George Floudas*,† †

Department of Physics, University of Ioannina, 451 10 Ioannina, Greece and Foundation for Research and Technology-Hellas, Biomedical Research Institute (FORTH-BRI), Ioannina, Greece ‡ Max-Planck Institute for Polymer Research, 55128 Mainz, Germany

bS Supporting Information ABSTRACT: The effect of dipole substitution on the self-assembly, thermodynamics, and dynamics has been studied in a series of hexa-peri-hexabenzocoronenes (HBCs). The HBCs bear the same number and type of aliphatic chains, but different dipoles directly attached to the cores ranging from ∼0 to ∼3.4 D. Dipole substitution alters the energetics and reduces the transition temperature favoring the columnar hexagonal liquid crystalline phase at the expense of the crystalline phase. The equation of state was obtained by independent pressure
volume
temperature measurements in both phases that resulted in the equilibrium phase diagram. According to the latter, increasing pressure imparts stability to the crystalline phase. The molecular and supramolecular dynamics investigated, respectively, by dielectric spectroscopy and rheology, identified a hierarchy of motions comprising a fast axial motion, a slower process that completely relaxes the dipole moment, and an even slower soliton-like relaxation of structural defects.

’ INTRODUCTION Discotic liquid crystals (DLC), consisting of rigid disk-shaped aromatic cores and disordered alkyl substituents, tend to organize into columnar supramolecular structures.1 Their self-assembly is driven by noncovalent intermolecular interactions favoring the π-stacking of aromatic cores and the unfavorable interactions between the cores and the alkyl chains leading to nanophase separation.2,3 Applications of DLC as electronic devices rely on the optimal stacking of the aromatic cores that allow for charge carrier mobility along the columnar axis (i.e., molecular wires).4,5 Recently, the controlled synthesis of DLC bearing large aromatic cores, such as hexa-peri-hexabenzocoronenes (HBCs), allowed extensive investigations of the self-assembly and electronic properties.2,6,7 Earlier investigations6
8 with X-ray scattering revealed two main columnar structures in HBCs: a hexagonal liquid crystalline phase (Colh) and a crystalline phase (Cr) at higher and lower temperatures, respectively. More recently, with the aid of pressure, the complete phase diagrams of two HBCs9,10 were constructed that in addition to the two equilibrium phases contain also a kinetically arrested (i.e., glassy) phase. Other studies emphasized the anisotropy in the thermal expansion of DLCs.11,12,9 The latter reflects the anisotropy in the molecular interactions: intra- versus intercolumnar, originating from π
π stacking and van der Waals interactions, respectively. Recently, HBCs were shown to have large thermal expansion within the Colh phase but thermal contraction within the Cr phase.13 The latter originates from the increasing disk tilt with respect to the columnar axis and reflects the tendency toward increasing the packing density within the Cr phase.13 r 2011 American Chemical Society

With respect to the molecular dynamics, earlier investigations14,15 identified the main R-process as reflecting the axial motion of disks around the columnar axis as well as regions of high and low packing density along the columns, first described by de Gennes as pincements.16 Recently, concerted efforts9 by site-specific NMR and dielectric spectroscopy (DS) in addition to the “fast” axial process associated with in- and out-of-plane motions identified slower dynamics reflecting a collective reorganization of disks within the columns that result in the complete relaxation of the dipole moment. In addition, a recent investigation17 reported on the kinetic pathways of the Colh to Cr phase transformation. This study revealed extremely slow kinetics and the presence of an intermediate state prior to crystallization.17 Despite these important earlier investigations only a few studies have attempted to correlate the phase behavior to the effect of dipole substitution, and these were performed mainly on DLCs bearing smaller cores.18
24 In HBCs in particular, the effect of dipole substitution on the self-assembly, thermodynamics, and dynamics of HBCs has not been investigated in detail because the studied molecules had different number and/or type of side alkyl chains attached to the HBC core.6 A systematic investigation addressing the effect of dipole functionalization on the HBC core requires (i) the synthesis of a series of molecules bearing dipoles directly attached to the cores keeping all other molecular parameters unchanged, i.e., the same number and type (linear or branched) Received: February 16, 2011 Revised: April 7, 2011 Published: April 25, 2011 5807

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liquid crystalline phase (Colh) at higher temperatures. As we will discuss below, the Cr to Colh transition temperature varies substantially in going from HBC-H to HBC-Cl. Within the Colh phase, the WAXS images reveal a set of strong meridional reflections associated with the typical intracolumnar periodicity of graphite (of 0.35 nm) and a set of equatorial reflections with ratios 1:31/2:41/2 relative to the primary peak. The latter correspond to the (10), (11), and (20) reflections of a hexagonal lattice. The dhk spacings, where h and k are the Miller indices, are related to the lattice parameter a through 1 ¼ dhk

Figure 1. Schematic of the five HBC-X derivatives investigated.

of aliphatic chains, and (ii) the implementation of techniques that can probe the molecular and supramolecular structure, the thermodynamics of Cr to Colh phase transformation, and the associated dynamics over a broad range of time and length scales. For this purpose a series of pentaalkyl-substituted HBCs was synthesized with monofluoro, monochloro, monobromo, and monoiodo substituents that together with the hydrogeneous and trifluoromethyl derivatives form a series of functional groups with dipole moments ranging from ∼0 to 3.4 D. In this study we (i) show that dipole substitution alters the energetics and produces a large reduction in the transition temperature favoring the Colh phase, (ii) obtain the corresponding equation of state for the Colh and Cr phases that result in the construction of the pertinent phase diagram, and (iii) explore the effect of dipole substitution on the molecular and supramolecular dynamics by dielectric spectroscopy and rheology.

’ RESULTS AND DISCUSSION Synthesis. A series of pentaalkyl-substituted hexa-peri-hexabenzocoronenes (HBCs) was synthesized with monofluoro, monochloro, monobromo, and monoiodo derivatives (Figure 1) aiming at investigating the effect of dipole substitution on the self-assembly, thermodynamics, and dynamics. These monohalogenated HBCs (denoted as HBC-X) make up a series of structurally similar derivatives differing only in their strength of dipole substitution. In addition, a trifluoromethyl-substituted HBC was synthesized that comprises a stronger dipole moment. The latter together with the X = H case form the two extreme cases of dipole moments investigated. Figure 1 gives a schematic of the synthesized structures, and Table 1 summarizes their structural and thermodynamic results. All synthetic details are provided in the Supporting Information. Thermodynamics. The self-assembly and underlying thermodynamics were investigated in the different HBC-X species. The self-assembly was first investigated with wide-angle X-ray scattering (WAXS) from extruded fibers as a function of temperature. Figure 2 provides some representative 2D WAXS images at selected temperatures. All HBC-X exhibit two phases: a crystalline (Cr) phase at lower temperatures and a columnar hexagonal

rffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 h2 þ hk þ k2 3 a

ð1Þ

The observed spacings reveal the formation of a columnar hexagonal liquid crystalline structure with lattice parameter a [obtained as a = (4/3)1/2d10], compared in Table 1. Four additional reflections are evident in the 2D WAXS images of HBC-I, HBC-Br, and HBC-Cl with equivalent Bragg spacings of d ∼ 0.5 nm that reflect dipole
dipole correlations. The Cr phase is characterized by a set of strong equatorial reflections that correspond to the (10), (01), (20), (11), and (21) reflections of a monoclinic unit cell with representative lattice parameters a = 2.52 nm, b = 1.78 nm, and γ = 85
for HBC-I, and a = 2.34 nm, b = 1.87 nm, and γ = 82
for HBC-H (both obtained at 303 K by cooling from the high temperature phase). These reflections are more prominent in HBC-I that possess the highest orientational order. The dhk spacings are now related to the lattice parameters through 1 ¼ dhk

rffiffiffiffiffiffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2   1 h k 2hk cos γ þ 2
sin2 γ ab a2 b

ð2Þ

The off-meridional reflections (more evident in HBC-I and to a lesser extent in HBC-Cl, HBC-Br, and HBC-H) originate from a tilt of the discotic cores with respect to the columnar axis, which is the characteristic of the “herringbone” structure identified earlier by NMR and WAXS. The thermodynamics of the Cr to Colh transformation were subsequently investigated with differential scanning calorimetry (DSC) and, for the first time, pressure
volume
temperature (PVT) measurements. Figure 3 gives the associated change in enthalpy (DSC) as a function of the Cr
Colh transition temperature. These results reveal an 86 K reduction in the transition temperature and a 2-fold reduction in the corresponding change in enthalpy in going from the nearly nonpolar HBC-H to the more polar HBC-Cl. In the same figure we include data from a monoethynyl HBC bearing the same number and type of aliphatic chains.9 The change in enthalpy can be parametrized as ΔH =
77 þ 0.323Tm. Dipolar interactions certainly lower the transition temperature and stabilize the high temperature Colh phase at the expense of the Cr phase. However, dipole
dipole interactions alone cannot fully account for the observed changes. For example, HBC-Cl with the strongest dipole among the monohalogenated compounds has indeed the lower transition temperature and heat of fusion; however, HBC-Br with a comparable dipole moment has a much higher transition temperature/heat of fusion. Thus, other interactions apart from the purely enthalpic dipolar interactions contribute to the enhanced stability of the Colh phase. 5808

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Table 1. Thermal Properties, Transition Temperatures, and Structural Details sample

dipole moment

transition

enthalpy

enthalpy

d10

lattice parameter

dintra

(Debye)a

temperature (K)

(J g
1)

(kJ mol
1)

phase transitiond

(nm)e

a (nm)e

(nm)e

Cr
Colh

2.33

2.70

0.365

HBC-I

1.63

344 (305)

38 (39)

56.6b

Cr
Colh

2.43

2.80

0.356

HBC-F

1.63

332b(303)c

28b(31)c

38.7b

Cr
Colh

2.42

2.79

0.358

HBC
CH

1.66

305b(280)c

24b(18)c

33.0b

Cr
Colh

2.25

2.60

0.354

HBC-Br

1.78

340b(301)c

36b(39)c

51.9b

Cr
Colh

2.44

2.82

0.355

HBC-Cl

1.80

312b(287)c

22b(26)c

30.7b

Cr
Colh

2.48

2.87

0.356

HBC-CF3

3.38

331b(296)c

26a(27)c

37.2b

Cr
Colh

2.46

2.84

0.357

HBC-H

∼0

398b b

51b c

b

69.5b c

a

Calculated as phenyl-X with PM6. b Heating (differential scanning calorimetry, heating rate: 10 K/min). c Cooling (differential scanning calorimetry, cooling rate: 10 K/min). d Colh, columnar hexagonal liquid crystalline; Cr, crystalline phase. e At T = 403 K

Figure 2. 2D-WAXS images from all HBC-X derivatives corresponding to the columnar hexagonal liquid crystalline phase (Colh) (top) and to the crystalline phase (Cr) (bottom) at the indicated temperatures. The patterns were recorded with a near vertical orientation of the filament axis with the X-ray beam being perpendicular to the filament. Arrows indicate the fiber direction.

where the subscript LC refers to the Colh phase. From eq 3 we obtain the total energy change at the transition as ΔU ¼ TΔS
PΔV

Figure 3. Enthalpy of melting as a function of the melting temperature for the HBC-X derivatives: (black square) HBC-H, (red square) HBC-I, (green square) HBC-Br, (blue square) HBC-F, (magenta square) HBCCF3, (cyan square) HBC-Cl, and (yellow square) HBC-CH (monoethynyl). The dashed line is the result of a linear fit (ΔH =
77 þ 0.323Tm). The solid line represents a line with a constant change of entropy at the Cr to Colh transition of ΔS = 0.134 J/g K. The inset gives the calculated change of entropy at the Cr to Colh transition (the line is guide to the eye).

To account for this we start from the continuity of the Gibbs free energy (G = H
TS = U þ PV
TS) at the transition GLC ¼ GCr ULC þ PVLC
TSLC ¼ UCr þ PVCr
TSCr

ð3Þ

ð4Þ

The two terms in eq 4 can be obtained independently as follows. The entropic term can be readily calculated from the transition temperature and heat of fusion (Table 1) (as ΔS = ΔH/T) and is plotted in the inset to Figure 3. It can be seen that the change in entropy at the transition is highest for HBC-H but reduces substantially for HBC-CF3. The second term in eq 4 requires knowledge of the equation of state. For this reason independent PVT measurements were made for HBC-Br for pressures in the range 10
200 MPa. The resulting change in specific volume is shown in Figure 4. As expected, the Cr to Colh transition is accompanied by a significant change of volume (ΔV) with a magnitude that depends on the applied pressure. To obtain the equation of state, the PVT results were fitted to the empirical Tait equation according to   V ðθ, PÞ ¼ ðV0 þ V1 θ þ V2 θ2 Þ 1
c ln 1 þ

p B0 expð
B1 θÞ



ð5Þ where θ is the temperature in
C and c = 0.0894. These parameters together with the material density (obtained from the unit cell) were used in obtaining the values of the specific volume at 0.1 MPa that are also shown in Figure 4. The equation of state parameters corresponding to the Cr and Colh phases are 5809

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Figure 4. Pressure
volume
temperature “isobaric” data of HBC-Br obtained on heating showing the change in the material specific volume: (filled squares) extrapolated data at P = 0.1 MPa, (circles) 10 MPa, (up triangles) 20 MPa, (down triangles) 40 MPa, (rhombi) 60 MPa, (left triangles) 90 MPa, (right triangles) 120 MPa, (hexagon) 160 MPa, and (pentagon) 200 MPa. The solid lines are fits to the Tait equation (see text). The arrow indicates the pressure dependence of the Cr to Colh transition.

Table 2. Parameters of the Equation of State (Tait) Corresponding to the Cr and Colh Phases of HBC-Br parameter 3


1

Cr

Colh

V0 (cm g )

0.83046

0.86413

V1 (cm3 g
1
C
1)

2.32358  10
4

3.50147  10
4

V2 (cm3 g
1
C
2)

1.03267  10
6

6.38782  10
7

c

0.0894

0.0894

B0 (MPa) B1 (
C
1)

288.4 0.00426

153.8 0.00295

summarized in Table 2. We need to mention here that the large sample quantity needed for the PVT measurements (ideally ∼1 g) precluded a similar investigation for the remaining compounds; in this case the ΔV from HBC-Br was employed for the remaining compounds but as we will see below this does not influence our conclusions. From the thus obtained PΔV value at 0.1 MPa and eq 4 the change in energy at the transition was calculated for the different compounds, and the result is plotted in Figure 5. It can be seen that ΔU at the transition is dominated by the first term of eq 4 (the second term contributes to ∼0.01% of the total energy change and is thus insignificant). The change of the energetics at the transition as obtained above contains all possible interactions. At this point it would be interesting to obtain an estimate of the contribution of pure dipolar interactions to ΔU. We calculate the corresponding energetics ΔUd-d in the Cr and Colh phases by using the interaction energy between two dipoles as U12 ¼

! ! ! μ1 3 ! μ2
3ð n B 3 μ1 Þð nB 3 μ2 Þ jx1
x2 j3

ð6Þ

where n is a unit vector in the (x1
x2) direction. In the calculation we have employed 12 neighbors, the van der Waals radii of X,25 and the dipole moments and unit cell parameters of Table 1 corresponding to the Colh and Cr phases. We have assumed the same tilt angle of the disks within the Cr phase as the

Figure 5. Calculated change in energy at the Cr to Colh transition as a function of the transition temperature for the different HBC-X. The line is a guide for the eye.

one obtained for HBC-I possessing the highest orientational order, and further assumed the same dipole orientation in both phases. Under this premise the calculated ΔUd-d amounts to only 8% and 3% from the measured ΔU at the transition for the CF3 and Cl cases bearing the strongest dipoles. Hence dipole
dipole interactions are only a part of the energetics, and all types of interactions (van der Waals interactions of all atoms including the alkyl chains) as well as entropic contributions control the transition temperature and increased stability of the Colh phase. This is not surprising given the dominance of van der Waals interactions even in small molecules possessing strong dipoles.26 An earlier investigation in DLCs bearing smaller cores18 reported a relationship between the functional groups and the stability of the Colh phase as well as a quantitative correlation of the clearing temperatures with the electron-withdrawing ability of the substituents. However, the latter relation cannot be tested here because of the inaccessible clearing temperature in HBCs. With respect to the former, we find that despite the electron donating ability of H, a stable Colh phase is formed in HBC-H. Molecular and Supramolecular Dynamics. The molecular dynamics within the Cr and Colh phases were investigated by rheology and dielectric spectroscopy (DS) probing, respectively, the viscoelastic and dipolar response to an external mechanical and electric field. In both cases the low strain amplitude and electric field strength ensured probing the linear properties of the unaligned state. Figure 6 gives the storage and loss moduli of HBC-Br obtained on heating and subsequent cooling under isochronal conditions (ω = 10 rad/s) with a rate of 2 K/min. At this frequency, the storage modulus exceeds the loss modulus indicating a solidlike response. On heating, HBC-Br undergoes the Cr to Colh phase transition that is manifested by an abrupt decrease of the moduli by about two decades at ∼339 K, which is in good agreement with the DSC results (Figure S1, Supporting Information, and Table 1). On subsequent cooling, the Colh phase is undercooled down to ∼311 K before entering the Cr phase. The reduced undercooling relative to the DSC result (Table 1) reflects the lower cooling rate used in rheology. Nevertheless, the presence of undercooling is characteristic of the first order transition and implies nucleation and growth kinetics. To explore the viscoelastic properties of the two phases in more detail isothermal frequency sweeps at temperatures 5810

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Figure 6. Temperature dependence of the storage (triangles) and loss (squares) moduli of HBC-Br obtained at 10 rad/s on heating (red) and subsequent cooling (blue) with 2 K/min. The vertical dashed and dashed
dotted lines indicate the Cr to Colh transition on heating and cooling, respectively.

Figure 7. Frequency dependence of the storage (triangles) and loss (squares) moduli of HBC-Br at two temperatures (a) T = 308 K and (b) T = 353 K, corresponding to the Cr to Colh, respectively. The arrow gives the characteristic frequency corresponding to the crossing of the storage and loss moduli at 353 K.

corresponding to the Cr (T = 308 K) and Colh (T = 353 K) phases were performed with respective strain amplitudes of 0.05% and 0.1% (Figure 7). This representation is more informative than the mere isochronal data of Figure 6 as the two phases possess distinctly different viscoelastic signatures. Within the Cr phase, the storage modulus is significantly higher than the loss modulus both being frequency independent (G0 ∼ ω0, G00 ∼ ω0) revealing an elastic response. It is only at lower frequencies that the storage and loss moduli indicate the beginning of some dispersion suggesting the presence of some molecular relaxation at lower frequencies that are experimentally unattainable. We mention here that this result is consistent with a recent heteronuclear NMR investigation on a dimethoxy substituted HBC (a compound that is structurally similar to the present HBCs, however bearing two dipoles and four alkyl chains) that provided

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Figure 8. Comparison of the dielectric loss spectra for the different HBC-X at 353 K. A representative fit is shown for the HBC-Br spectrum that includes the conductivity contribution (dotted line), the slow process (dashed line), and the fast axial motion (dashed
dotted line). The solid line is the result of the fit against the experimental data.

site-specific information of the molecular motion through the effective 1H
13C dipolar coupling.10 There the value of the obtained dynamic order parameter (S ∼ 0.9) suggested a relatively rigid aromatic core within the Cr phase allowing only for smallangle disk fluctuations. Despite the nearly frozen core, the aliphatic chains retained significant mobility (S ∼ 0.4) even within the Cr phase, but this does not affect the viscoelastic response. On the other hand, the response within the Colh phase turns viscoelastic. The crossing of the moduli identifies a characteristic frequency, ωc, associated with the solid-to-liquid transformation within the Colh phase. From the modulus, a characteristic length scale can be obtained as G0 ∼ kBT/d3(ωτ)2.27 At the characteristic frequency, ωcτ ≈ 1, the value of the storage modulus G0 = 3.5  105 MPa results in a characteristic length scale of 2.4 nm that exceeds any molecular dimension. The expectation is that this length scale relates to the defect texture of the unaligned HBC.28 Indeed, a length of 2.4 nm corresponds to a columnar stack composed of ∼8 disks (with a separation of 0.35 nm). This estimate is in agreement with the correlation length of the columnar stacks obtained from the width of the strong meridional reflection (Figure 2). Thus, the values of the moduli at ωc reflect either a soliton-like motion of defects along the columns or even an exchange of stacks in adjacent columns. These supramolecular dynamics are facilitated by the mobile alkyl chains as seen in NMR. Additional information on the molecular and supramolecular dynamics can be obtained through DS below. Dielectric spectroscopy (DS) is capable of providing the time-scales of motions by probing the dipoles directly attached to the HBC core.12,15,29
35 Recent combined investigations9,10,36 on core-substituted HBCs with DS and NMR that took advantage of the strong molecular dipole and the nearby specific heteronuclear sites identified two main relaxation mechanisms. A “fast” mechanism reflecting the collective disk axial motion, i.e., the in- and out-of-plane motion of the dipoles about the columnar axis that leaves an uncompensated dipole moment that relaxes through the “slower” process. Figure 8 depicts representative dielectric loss spectra of the six HBC-X at 353 K, corresponding to the Colh phase and obtained on cooling. The spectra reveal a peak corresponding to the “fast” disk axial motion with dielectric strength, 5811

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Table 3. Parameters of the VFT Equation within the Colh Phase sample

Figure 9. Temperature dependence of the disk axial motion (top) and the slower DS mode (bottom) in HBC-X. The circle in the bottom corresponds to the crossing of the storage and loss moduli of HBC-Br as obtained from rheology.

Δε, which is a function of the dipole moment, as

37

Δε 

μ2 N Fg 3kB T V

ð7Þ

In eq 7, μ is the dipole moment for noninteracting dipoles, F [=(εS(ε¥ þ 2)2/3(2εS þ ε¥)] is the local field correction, g is the Kirkwood
Fr€ohlich correlation factor giving the angular correlations between the dipoles, N is the number of dipoles, and V is the volume. From the dielectric strength of the compounds the calculated effective dipole moment (μeff = μg1/2) amounts to 1.18, 1.15, 1.44, 1.46, and 2.28 D for I, F, Br, Cl, and CF3, respectively. These values, being lower than the dipole moments of single disks, reflect the destructive interference of dipoles within the columns. The relaxation times of the fast disk axial motion for the different HBC-X species within the Colh phase are compared in Figure 9. Notice that the disk dynamics within the Colh phase are different by only 0.3 of a decade. This demonstrates that the thermodynamic state (i.e., Colh vs Cr) is controlling the rate of the disk axial motion. The relaxation times exhibit a non-Arrhenius T-dependence that conforms to the Vogel
Fulcher
Tammann (VFT) equation: 

B τ ¼ τ0 exp T
T0

 ð8Þ

log(τ0/s)

B (K)

T0 (K)

HBC-H


10 ( 0.2

2050 ( 60

148 ( 6

HBC-I HBC-F


9.30 ( 0.08
9.9 ( 0.2

1750 ( 70 2200 ( 200

141 ( 5 127 ( 9

HBC-Br


9.3 ( 0.1

1700 ( 80

146 ( 5

HBC-Cl


9.2 ( 0.04

1700 ( 30

157 ( 2

HBC-CF3


8.90 ( 0.03

1470 ( 20

158 ( 2

Figure 10. Pressure-driven Colh to Cr transformation under isothermal conditions (T = 343 K) in HBC-Br. The dielectric loss curves correspond to the following: (open squares) P = 20 MPa, (open circles) 60 MPa, (up triangles) 100 MPa, (down semifull triangles) 160 MPa, (filled squares) 190 MPa, and (filled circles) 220 MPa.

Here, τ0 is the characteristic time in the limit at very high temperatures, B is the activation parameter, and T0 is the “ideal” glass temperature (the VFT parameters are summarized in Table 3). Both the τ(T) dependence and the broadening of the relaxation function (with low-frequency shape parameters in the range from 0.77 to 0.96, for details see Figure S3, Supporting Information) are characteristic of a collective process. At lower temperatures, the systems enters the Cr phase with direct consequences on the shape (broadened) and intensity (reduced) of the spectra. A slower process is also evident in the DS data of Figure 8. The corresponding relaxation times within the Colh phase are also depicted in Figure 9. This process is some ∼5 and 6 decades slower than the fast axial process in HBC-Br and HBC-Cl, respectively, and reflects the collective reorganization of disks that completely relax the dipole moment. Notice that the characteristic viscoelastic time of HBC-Br is even longer than the DS slow process. This again suggests that rheology is probing the slowest possible dynamics within the Colh phase (defect diffusion). Investigation of the dynamics as a function of temperature and pressure is advantageous as it can result in the phase diagram for the different compounds. This in turn provides information on the stability of the Colh and Cr phases for the different processing conditions that could be encountered, for example, in the fabrication of electronic or other devices. Figure 10 shows the effect of increasing pressure on the dynamics of HBC-Br under isothermal conditions (T = 343 K). The main process, reflecting the fast axial motion, is slowed due to densification. Above a certain critical pressure, the system enters the Cr phase, and as a consequence, the 5812

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Figure 11. Relaxation times of HBC-Br corresponding to the disk axial motion plotted as a function of pressure at different temperatures: (squares) T = 373 K, (circles) 363 K, (up triangles) 353 K, (down triangles) 343 K, (left triangles) 333 K, and (right triangles) 323 K. Solid lines are linear fits within the Colh phase. The dashed line gives the times and corresponding pressures of the Colh to Cr transition.

Figure 12. Phase diagram for HBC-Br obtained through the following: (red rhombi) PVT on heating, (blue rhombi) PVT on cooling, (squares) DS in cooling, and (circles) DS glass temperature (defined at 100 s). The lines separate two equilibrium phases (Colh and Cr) and one kinetically arrested phase (glass).

dielectric strength of the process diminishes. The relaxation times within the Colh phase are plotted in Figure 11 as a function of pressure for the different isotherms. The data depict the slowingdown of all relaxation times that is more effective at the lower temperatures. The dashed line in the figure provides the relaxation times at the onset of the Colh to Cr transformation. Notice that the phase transformation is not “isochronal”. The results from the dynamic investigation together with the DSC and PVT results can be combined in creating the T
P phase diagram for HBC-Br (Figure 12). The diagram consists of the PVT data (Figure 4) on the pressure-dependent Cr to Colh phase transition on heating and subsequent cooling together with the results from the pressure-induced Colh to Cr transition as obtained from DS (Figure 11). The two sets of data, both obtained on cooling, are in excellent agreement. The resulting T(P) dependence can be described by the well-known Clausius
Clapeyron equation dP/dT = ΔH/TΔV, where ΔH and ΔV are the change in enthalpy and specific volume at the Cr to

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Colh transformation and T is the transition temperature at ambient pressure. From the T(P) dependence of the PVT data obtained on heating we extract dP/dT = 3.9 MPa/K that predicts a change of volume at the transition of ΔV = 0.027 cm3/g. This change of volume in HBC-Br is smaller than the actual one obtained from the Tait equation of state and the PVT data of Figure 4 (ΔV = 0.037 cm3/g). The reason for this discrepancy is the curvature in the T(P) dependence. Indeed, using only data from lower pressures (P < 60 MPa) results in a change of volume (ΔV = 0.031 cm3/g) that is closer to the actual one. Nevertheless, the obtained phase diagram suggests that increasing pressure results in an increased region of the Cr phase as a result of the positive change of volume at the transition (Figure 4). In addition, the figure contains data for the kinetically arrested disk axial motion (obtained by extrapolation to a relaxation time of τ∼100 s). This dependence can be described by the empirical equation   k 1=k Tg ðPÞ ¼ Tg ð0Þ 1 þ P λ

ð9Þ

where Tg(0) (=159 K) is the glass temperature at atmospheric pressure and κ (=3.87), λ(=238 MPa) are fitting parameters resulting in (dT g /dP)Pf0 = 0.67 K/MPa. Equation 8 was originally proposed38 to describe the melting of solid gases under pressure and subsequently employed by others to describe the Tg(P) of glass-forming systems.39,40 It basically shows that densification facilitates the freezing of molecular dynamics. Overall these results suggest three parameters that control the phase state. One is purely molecular and reflects the change in the energetics associated with the dipole functionalization. As it was shown, the latter synthetic approach can lower the transition temperature by 86 K (in going from H to Cl). The other parameters are the intensive variables of temperature and pressure. With respect to the latter, it was shown that pressurization at 200 MPa results in the increase of the transition temperature by 60 K. These parameters should be taken into account in the design of DLCs for particular applications.

’ CONCLUSIONS The synthesis of a series of dipole functionalized HBCs bearing the same number and type of alkyl chains allowed a systematic investigation of the effect of dipole substitution on the self-assembly, the thermodynamic stability, and the molecular and supramolecular dynamics. With respect to the self-assembly, the equation of state has been determined within the Colh and Cr phases that resulted in the associated phase diagram of a dipole functionalized HBC. The phase diagram revealed a large change of volume (ΔV = 0.037 cm3/g) at the Cr to Colh transition. Dipole substitution results in the stabilization of the high temperature Colh phase at the expense of the Cr phase. However, dipole
dipole interactions are only part of the energetics as one needs to consider all possible interactions. Pressure, on the other hand, has the opposite effect as it increases the stability of the Cr phase. With respect to the dynamics, we found a hierarchy of dynamic processes. Starting from the fast side, dielectric spectroscopy identified a fast axial motion with a rate that is nearly independent from the type of dipole substitution. Thus, the phase state dictates to a large extent the molecular dynamics. A slower dielectrically active process completely relaxes the dipole moment. In addition 5813

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The Journal of Physical Chemistry B to these processes, rheology identified a soliton-like relaxation of structural defects as the slowest possible process in HBCs.

’ ASSOCIATED CONTENT

bS

Supporting Information. Materials and Methods section containing details on the synthesis (including the NMR data), the thermal properties (differential scanning calorimetry), the self-assembly (X-ray scattering, the thermodynamics (pressure
volume
temperature measurements), and the dynamics as obtained from dielectric spectroscopy (DS) and rheology. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: gfl[email protected] (G.F.), [email protected] (K.M.). Phone: þ30-2651-008564. Fax: þ30-2651-009693.

’ ACKNOWLEDGMENT The current work was supported by the John S. Latsis Public Benefit Foundation with a research grant. We thank A. Best for the PVT measurements, and M. Bach (MPI-P) and G. Tsoumanis (UoI) for technical support. Financial support of the Deutsche Forschungsgemeinschaft, SFB 625, is gratefully acknowledged. ’ REFERENCES (1) Handbook of Liquid Crystals; Demus, D., Goodby, J., Gray, G. W., Spiess, H.-W., Vill, V., Eds.; Wiley-VCH: Weinheim, 1998. (2) Wu, J.; Pisula, W.; M€ullen, K. Chem. Rev. 2007, 107, 718–747. (3) Schmidt-Mende, L.; Fechtenk€otter, A.; M€ullen, K.; Moons, E.; Friend, R. H.; MacKenzie, J. D. Science 2001, 293, 1119–1122. (4) Feng, X.; Marcon, V.; Pisula, W.; Hansen, M. R.; Kirkpatrick, J.; Grozema, F.; Andrienko, D.; Kremer, K.; M€ullen, K. Nat. Mater. 2009, 8, 421–426. (5) van de Craats, A. M.; Warman, J. M.; Fechtenk€otter, A.; Brand, J. D.; Harbison, M. A.; M€ullen, K. Adv. Mater. 1999, 11, 1469. (6) Ito, S.; Wehmeier, M.; Brand, J. D.; K€ubel, C.; Epsch, R.; Rabe, J. P.; M€ullen, K. Chem.—Eur. J. 2006, 6, 4327–4342. (7) Fischbach, I.; Pakula, T.; Minkin, P.; Fechtenk€otter, A.; M€ullen, K.; Spiess, H. W. J. Phys. Chem. B 2002, 106, 6408–6418. (8) Ochsenfeld, C.; Brown, S.; Schnell, I.; Gauss, J.; Spiess, H. W. J. Am. Chem. Soc. 2001, 123, 2597–2606. (9) Elmahdy, M. M.; Floudas, G.; Mondeshki, M.; Spiess, H. W.; Dou, X.; M€ullen, K. Phys. Rev. Lett. 2008, 100, 107801–4. (10) Elmahdy, M. M.; Dou, X.; Mondeshki, M.; Floudas, G.; Butt, H.-J.; Spiess, H. W.; M€ullen, K. J. Am. Chem. Soc. 2008, 130, 5311–5319. (11) Gl€usen, B.; Kettner, A.; Kopitzke, J.; Wendorff, J. H. J. NonCryst. Solids 1998, 241, 113. (12) M€oller, M.; Wendorff, J. H.; Werth, M.; Spiess, H. W. J. NonCryst. Solids 1994, 170, 295–299. (13) Grigoriadis, C.; Haase, N.; Butt, H.-J.; M€ullen, K.; Floudas, G. Adv. Mater. 2010, 22, 1403–1406. (14) Leisen, J.; Werth, M.; Boeffel, C.; Spiess, H. W. J. Chem. Phys. 1992, 97, 3749. (15) Vallerien, S. U.; Werth, M.; Kremer, F.; Spiess, H. W. Liq. Cryst. 1990, 8, 889. (16) de Gennes, P. G. J. Phys., Lett. 1983, 44, 657–664. (17) Elmahdy, M. M.; Mondeshki, M.; Dou, X.; Butt, H.-J.; Spiess, H. W.; M€ullen, K.; Floudas, G. J. Chem. Phys. 2009, 131, 114704–9. (18) Foster, E. J.; Jones, R. B.; Lavigueur, C.; Williams, V. E. J. Am. Chem. Soc. 2006, 128, 8569.

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