Self-assembly, dynamics, and phase transformation kinetics of donor-acceptor substituted perylene derivatives

Article abstract of DOI:10.1021/ja102150g

The role of alkyl chain substitution on the phase formation and core dynamics is studied in a series of diphenylamine functionalized perylenemonoimides (PMIs), by X-ray scattering, calorimetry and site-specific solid-state NMR techniques. In addition, the strong dipole associated with the donor-acceptor character of the molecules allow an investigation of the dynamics with dielectric spectroscopy. The self-assembly revealed an ordered phase only in PMIs with branched alkyl chains. This phase comprises a helical stacking of molecules with a molecular twist angle of 60 . Results from solid-state NMR further pointed out the importance of intramolecular hydrogen bonding in stabilizing the intracolumnar packing within the ordered phase. Moreover, the core dynamics are frozen as revealed by the value of the dynamic order parameters and the reduced strength of dipolar relaxation. The kinetics of phase transformation from the isotropic to the ordered phase proceeds via a nucleation and growth mechanism, and the rates are dominated by the nucleation barrier. Within the isotropic phase the core dynamics display strong temperature dependence with rates that depend on the number of methylene units in the alkyl chains.

Full text of DOI:10.1021/ja102150g

Published on Web 05/06/2010
Self-Assembly, Dynamics, and Phase Transformation Kinetics
of Donor-Acceptor Substituted Perylene Derivatives
Nikos Tasios,† Christos Grigoriadis,† Michael Ryan Hansen,‡
Henrike Wonneberger,‡ Chen Li,‡ Hans W. Spiess,‡ Klaus Mu¨llen,‡,* and
George Floudas†,*
Department of Physics, UniVersity of Ioannina, 451 10 Ioannina, Greece and Foundation for
Research and Technology-Hellas (FORTH-BRI), and Max-Planck Institute for Polymer
Research, 55128 Mainz, Germany
Received March 18, 2010; E-mail: gfloudas@cc.uoi.gr; muellen@mpip-mainz.mpg.de
Abstract: The role of alkyl chain substitution on the phase formation and core dynamics is studied in a
series of diphenylamine functionalized perylenemonoimides (PMIs), by X-ray scattering, calorimetry and
site-specific solid-state NMR techniques. In addition, the strong dipole associated with the donor-acceptor
character of the molecules allow an investigation of the dynamics with dielectric spectroscopy. The self-
assembly revealed an ordered phase only in PMIs with branched alkyl chains. This phase comprises a
helical stacking of molecules with a molecular twist angle of 60°. Results from solid-state NMR further
pointed out the importance of intramolecular hydrogen bonding in stabilizing the intracolumnar packing
within the ordered phase. Moreover, the core dynamics are frozen as revealed by the value of the dynamic
order parameters and the reduced strength of dipolar relaxation. The kinetics of phase transformation from
the isotropic to the ordered phase proceeds via a nucleation and growth mechanism, and the rates are
dominated by the nucleation barrier. Within the isotropic phase the core dynamics display strong temperature
dependence with rates that depend on the number of methylene units in the alkyl chains.
Introduction
pigment colors resulted in high grade industrial applications
including automotive coatings. These applications made use of
Discotic liquid crystals (DLCs), 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 the π-π overlap of the disks and the
unfavorable interactions between the cores and the alkyl chains
leading to phase separation and to self-assemblies at the
nanoscale.2,3 Applications of DLCs as electronic devices rely
on the optimal stacking of the aromatic cores that allows for
charge carrier mobility along the columnar axis (i.e., molecular
wires).4 In this respect the self-assembly and electronic proper-
ties of large aromatic cores such as hexa-peri-hexabenzocoro-
nenes (HBC) have been explored extensively.2-5
the high tinctorial strength, light and weather stability, insolubil-
ity, and chemical inertness of PDIs. Other major applications
of PDI derivatives are as organic electronics in all-organic
photovoltaic solar cells8,9 and field-effect transistors.10 These
applications rely on the high charge carrier mobilities that made
PDI the best n-type semiconductors available to date.11 In
addition, the recently synthesized perylenemonoimide (PMI)12-14
and diimide dyes are widely used as chromophores in fluores-
cence experiments15 and for single molecule spectroscopy.16
Central to these applications of HBCs and PDIs is their ability
(8) Schmidt-Mende, L.; Fechtenkotter, A.; Mu¨llen, K.; Moons, E.; Friend,
R. H.; MacKenzie, J. Science 2001, 293, 1119–1122.
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(10) Gsa¨nger, M.; Oh, H.; Ko¨nemann, M.; Ho¨ffken, H. W.; Krause, A.-
M.; Bao, Z.; Wu¨rthner, F. Angew. Chem., Int. Ed. 2010, 49, 740–
743.
Among the different DLCs, perylenediimide (PDI) derivatives
have received considerable attention originally because of their
industrial applications as pigments.6,7 Efforts to optimize
† University of Ioannina and FORTH-BRI.
(11) Dimitrakopoulos, C. D.; Malenfant, P. R. L. AdV. Mater. 2002, 14,
99–117. Avlasevich, Y.; Li, C.; Mu¨llen, K. J. Mater. Chem. 2010,
20, 3814–3826, and references therein.
‡ Max-Planck Institute for Polymer Research.
(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.; Mu¨llen, K. Chem. ReV. 2007, 107, 718–747.
(3) Schmidt-Mende, L.; Fechtenko¨tter, A.; Mu¨llen, 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.; Mu¨llen, K. Nat. Mater. 2009,
8, 421–426.
(12) Li, C.; Schoeneboom, J.; Liu, Z.; Pschirer, N. G.; Erk, P.; Herrmann,
A.; Mu¨llen, K. Chem.sEur. J. 2009, 15, 878–884.
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F.; Sens, R.; Boschloo, G.; Herrmann, A.; Mu¨llen, K.; Hagfeldt, A.
J.Phys. Chem. C 2007, 111, 15137–15140.
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Erk, P.; Herrmann, A.; Mu¨llen, K. J. Mater. Chem. 2009, 19, 5405–
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(5) Pisula, W.; Menon, A.; Stepputat, M.; Lieberwirth, I.; Kolb, U.; Tracz,
A.; Sirringhaus, H.; Pakula, T.; Mu¨llen, K. AdV. Mater. 2005, 17, 684–
689.
(15) Koynov, K.; Mihov, G.; Mondeshki, M.; Moon, C.; Spiess, H. W.;
Mu¨llen, K.; Butt, H.-J.; Floudas, G. Biomacromolecules 2007, 8, 1745–
1750.
(6) Herbst, W.; Hunger, K. Industrial Organic Pigments: Production,
Properties, Applications, 2nd ed.; Wiley-VCH: Weinheim, 1997.
(7) Wu¨rthner, F. Chem. Commun. 2004, 14, 1564–1579.
(16) Wo¨ll, D.; Braeken, E.; Deres, A.; De Schryver, F. C.; Uji-i, H.;
Hofkens, J. Chem. Soc. ReV. 2009, 38, 313–328.
9
7478 J. AM. CHEM. SOC. 2010, 132, 7478–7487
10.1021/ja102150g  2010 American Chemical Society

Kinetics of Substituted Perylene Derivatives
A R T I C L E S
Scheme 1. Schematic of the Five PMI Derivatives Investigated
to organize efficiently in different packing motifs and in
particular their degree of intra- and intermolecular order. The
degree of structural perfection strongly affects their molecular
properties (absorbance, fluorescence, and charge transport) and
results in applications in organic field-effect transistors, light-
emitting diodes, and organic solar cells.
studies also provided the first phase diagrams25 for HBCs and
highlighted the importance of metastable states toward the final
equilibrium structures.26
The present work relies on the strong dipole associated with
the donor-acceptor character of the molecules. It explores the
role of alkyl chain substitution on (i) the phase formation and
(ii) the slow core dynamics in diphenylamine functionalized
PMIs. Five PMIs with alkyl chains substitution were investigated
(Scheme 1), and their self-assembly was found to depend
strongly on the space-filling properties of the branched alkyl
chains rather than the mere number of linear alkyl chains.
Subsequently, we investigated the core dynamics by employing
two measures, the large dipole moment of the core, using
dielectric spectroscopy (DS), and the heteronuclear dipole-dipole
couplings using site-specific solid-state NMR. These probes
provide, for the first time, the rate of disk motion together with
the geometry of motion within the isotropic and ordered phases
of PMIs. The results on the self-assembly and dynamics are
compared with the symmetric cores of HBCs. In the last part,
we explore the kinetic pathways for the formation of the ordered
crystalline phase from the isotropic phase. This study emphasizes
the importance of nucleation barriers that lead to the highly
ordered helical packing found in perylene derivatives.
Several reports exist on the thermotropic liquid crystalline
behavior of symmetrically17,18 and, more recently, asymmetri-
cally19 substituted PDIs, but none exist on the slow molecular
dynamics that include the cooperative disk rearrangements,
which are coupled to the stability of columns.20 The influence
of self-assembly on the charge carrier mobility of PDI deriva-
tives revealed a helical molecular arrangement with a 45° twist
angle between successive molecules.21 However, the optimal
alignment for electron transport was found to be either cofacial
or twisted by 65°.4 When the local molecular order was
investigated by solid-state NMR spectroscopy,22 the twist angle
was in the range of 20-40° and the molecular motion in the
core was practically frozen. By substituting the same PDI core
with tri(ethylene glycol) chains the twist angle increased to
90°.23 Furthermore, the influence of core extension (e.g.,
terrylenediimides and quaterrylenediimides) on the thermotropic
behavior of PDI was studied18 and revealed a helical stacking
of disks with a lateral rotation of 45°. These examples illustrate
the importance of the core and chain substitution in controlling
both the phase behavior and the molecular stacking within the
columns.
Results and Discussion
Self-Assembly. The thermodynamic and structural features of
the perylene derivatives are summarized in Table 1. Figure 1
gives the DSC trace of the PMI-d-C9 compound; the traces of
(17) Cormier, R. A.; Gregg, B. A. Chem. Mater. 1998, 10, 1309–1319.
(18) Nolde, F.; Pisula, W.; Mu¨ller, S.; Kohl, C.; Mu¨llen, K. Chem. Mater.
2006, 18, 3715–3725.
Despite the important knowledge on controlling the self-
assembly of perylenes, little is known on how molecular motion
is related to the phase state and in turn how the dynamics are
coupled to the stability and possibly the self-healing properties
of the columnar assemblies. Prerequisites for the dynamic
investigations are a strong molecular dipole and nearby specific
heteronuclear sites that can be probed independently by dielectric
spectroscopy and site-specific NMR spectroscopies, respectively.
The donor-acceptor character of the substituted perylene core
makes PMIs ideal systems for investigating the molecular
dynamics within the different phases. On the other hand, the
symmetric core of HBCs requires additional dipole function-
alization. Recent work24 on dipole-functionalized HBCs revealed
fast and slower molecular dynamics associated, respectively,
with the disk axial motion and with a collective reorganization
of the columns that completely relaxes the dipole moment. These
(19) Wicklein, A.; Lang, A.; Muth, M.; Thelakkat, M. J. Am. Chem. Soc.
2009, 131, 14442–14453.
(20) Percec, V.; Glodde, M.; Bera, T. K.; Miura, Y.; Shiyanovskaya, I.;
Singer, K. D.; Balagurusamy, V. S. K.; Heiney, P. A.; Schnell, I.;
Rapp, A.; Spiess, H. W.; Hudson, S. D.; Duan, H. Nature 2002, 419,
384–387.
(21) Marcon, V.; Breiby, D. W.; Pisula, W.; Dahl, J.; Kirkpatrick, J.;
Patwardhan, S.; Grozema, F.; Andrienko, D. J. Am. Chem. Soc. 2009,
131, 11426–11432.
(22) Hansen, M. R.; Graf, R.; Sekharan, S.; Sebastiani, D. J. Am. Chem.
Soc. 2009, 131, 5251–5256.
(23) Hansen, M. R.; Schnitzler, T.; Pisula, W.; Graf, R.; Mu¨llen, K.; Spiess,
H. W. Angew. Chem., Int. Ed. 2009, 48, 4621–4624.
(24) Elmahdy, M. M.; Floudas, G.; Mondeshki, M.; Spiess, H. W.; Dou,
X.; Mu¨llen, K. Phys. ReV. Lett. 2008, 100, 107801–107804.
(25) Elmahdy, M. M.; Dou, X.; Mondeshki, M.; Floudas, G.; Butt, H.-J.;
Spiess, H. W.; Mu¨llen, K. J. Am. Chem. Soc. 2008, 130, 5311–5319.
(26) Elmahdy, M. M.; Mondeshki, M.; Dou, X.; Butt, H.-J.; Spiess, H. W.;
Mu¨llen, K.; Floudas, G. J. Chem. Phys. 2009, 131, 114704–114709.
9
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A R T I C L E S
Tasios et al.
Table 1. Thermal Properties, Transition Temperatures, and Structural Details
sample
transition temp (K)
enthalpy (J/g)
phase/phase transition
d10 (nm)d
d01 (nm)d
dintra (nm)d
c
PMI-d-C9
PMI-d-C7
PMI-s-C8
PMI-s-C10
PMI-t-C10
468a (451)b
500a
-
20.6a (19.8)b
23.9a
Cr-I/glass temp
Cr-I
I/glass temp
I/glass temp
I/glass temp
2.054
1.916
1.188
1.114
0.350
0.350
346a (347)b 352c
338a (327)b 344c
281a (274)b 291c
a Heating (differential scanning calorimetry). b Cooling (differential scanning calorimetry). c Cooling (dielectric spectroscopy). Colh: columnar
hexagonal liquid crystalline phase. Cr: crystalline phase. I: isotropic. d At 303 K.
1
d2hk
h2
a2
k2
b2
)
+
(1)
In addition, the image contains two meridional reflections
with spacings of 0.35 and 2 nm that reflect intramolecular
periodicities. The former is the typical distance found in graphite
and corresponds to the intramolecular layer distance in a stacked
columnar arrangement of perylenes. The latter spacing (2 nm)
being 6 times the layer spacing of 0.35 nm, corresponds to a
helical pitch of molecules rotated by 60° (Figure 2). Notice the
absence of tilting of molecules within the Cr phase that contrasts
to the well-known “herringbone” structure found in the Cr phase
of some discotic liquid crystals. Herein the elongated shape of
the core minimizes the π-π overlap and prevents tilting.
Figure 3 gives the temperature dependence of the lattice
parameters a, b, and c of the orthorhombic unit cell and of the
unit cell volume (V ) abc) for both PMI-d-C9 and PMI-d-C7.
The longer alkyl chains in the former result in an expanded
orthorhombic unit cell; however, the intradisk periodicities are
identical. The respective coefficients of thermal expansion (aa
) (∂ ln a/∂T)P), for PMI-d-C9 amount to aa)1.776 × 10-4 K-1,
ab)1.811 × 10-4 K-1, and ac)1.069 × 10-4 K-1, whereas the
volumetric thermal expansion coefficient amounts to ꢀ ) 4.656
× 10-4 K-1. Notice that all values are positive, in contrast to
the Cr phase in HBCs, where a volume contraction (i.e., negative
thermal expansion) was found to result from the increasing
tilting of the HBC cores within the columns of the Cr phase.27
Furthermore, aa ≈ ac, i.e., intra- and intercolumnar thermal
expansions are nearly isotropic, in contrast to the symmetric
cores of triphenylenes and HBCs.27 Again the anisotropic
donor-acceptor character of the core that minimizes the π-π
interactions and promotes the helical stacking of perylene
molecules within the columns is responsible for the more
isotropic thermodynamic properties.
Figure 1. DSC trace of the PMI-d-C9 compound obtained on cooling (blue)
and subsequent heating (red) at 10 K/min. (Top) Two POM images obtained
on cooling at 448 and 464 K depicting spherulites and dendritic textures,
respectively. (Bottom) 2D WAXS structures from oriented fibers obtained
on heating at 303, 453, and 478 K. The images at 303 and 453 K correspond
to the Cr phase, whereas the one at 478 corresponds to the isotropic phase
(I).
the remaining compounds are given in Figure S1in Supporting
Information. With the exception of PMI-d-C9 and PMI-d-C7,
all perylene derivatives undergo an isotropic liquid-to-glass
transformation at different temperatures that depends on the
number of methylene units. On the other hand, PMI-d-C9
undergoes an isotropic (I) to crystalline (Cr) transition at 468/
451 K (heating/cooling) with an associated heat of fusion/
crystallization of 20.6/19.8 J/g. PMI-d-C7 does not undergo any
transformation up to the highest temperature investigated. All
samples were further investigated with polarizing optical
microscopy (POM). As expected, they show an isotropic phase
with the exception of PMI-d-C9 and PMI-d-C7 where massive
structures were observed under very fast (50 K/min) cooling.
Two POM images of the PMI-d-C9 structures obtained on
cooling at 448 and 464 K are depicted in Figure 1. The structures
observed at low temperatures are spherulitic (with the typical
maltese cross) with well-defined boundaries. At higher temper-
atures the structures resemble more a pseudofocal conical fan
shape, with dendritic inner textures showing a 60° branching.
To obtain the required information on the self-assembly at
the unit cell level wide-angle X-ray scattering (WAXS) was
employed. Three WAXS images of PMI-d-C9 are shown in
Figure 1 at 303, 453, and 478 K. The images at 303 and 478 K
correspond to the Cr and I phases, respectively, whereas the
one at 453 K is in the vicinity of the melting process of the Cr
phase. The WAXS image at 303 K, which is typical of the Cr
phase, contains a set of equatorial reflections. These correspond
to the (10) (01) (11) (20) and (21) reflections from an
orthorhombic unit cell that is depicted in Figure 2. The dhk
spacings, where h and k are the Miller indices, are related to
the lattice parameters a ) 1.981 nm, at 333 K and b ) 1.200
nm, at 333 K through
Additional insights into the columnar packing of PMI-d-C9
molecules observed in the WAXS experiments (see above) can
be obtained from solid-state NMR spectroscopy. As we have
1
recently shown, the H NMR chemical shifts of the PDI core
protons represents a sensitive probe with respect to the specific
pitch-angle between successive molecules.22 Moreover, that
study utilized branched alkyl side chains, though symmetrically
attached and slightly shorter (i.e., PDI-C8,7 the molecular
structure is depicted in Supporting Information as Scheme S1),
as in the present case of PMI-d-C9. It was also observed that
for low pitch angles (R < 25°), an intense autocorrelation signal
originating from the branching CH moieties of the side chains
is to be expected in the 2D 1H-1H double-quantum (DQ) single-
quantum (SQ) correlation spectrum.22 This was later explained
with respect to the morphology of the sample using MD
(27) Grigoriadis, C.; Haase, N.; Butt, H.-J.; Mu¨llen, K.; Floudas, G. AdV.
Mater. 2010, 22, 1403–1406.
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A R T I C L E S
Figure 2. Graphical representation of the PMI-d-C9 orthorhombic unit cell (right), extracted from WAXS. The representation on the left depicts a helical
arrangement of 7 units with a successive rotational angle of 60° that is based on the WAXS study.
30°. Taking into account that the pairwise signals observed for
the PDI core protons show a splitting of ∼0.8 ppm (cf. Figure 5
in ref 22), the pitch angle is estimated to be in the range of
50-70°. This is in full agreement with the assignment based
on the WAXS investigation.
To relate the observed 1H chemical shifts in Figure 4a to their
specific carbon sites in PMI-d-C9, a 2D 13C{1H} FSLG-
HETCOR experiment has been performed as depicted in Figure
4c. Here, the experiment is conducted at a significantly lower
spinning frequency (VR ) 15.0 kHz) compared to that of Figure
4a, and in order to achieve the same resolution in the 1H
dimension, a frequency-switched Lee-Goldburg (FSLG) se-
quence has been employed.32,33 In the aromatic region (110-130
ppm) all 13C resonances can be assigned to their directly attached
1H, whereas the assignment in the aliphatic region is less
straightforward. Interestingly, the peak corresponding to the
branching proton of the C9,9 side chain (CH moiety) is split
into two signals, i.e., pairs of signals at 1.7 and 58 ppm and 4.8
and 54 ppm for 1H and 13C, respectively, can be observed. The
Figure 3. Temperature dependence of the orthorhombic unit cell parameters
(a, b, and c) and of the corresponding volume, V, of PMI-d-C9 (filled
symbols) and PMI-d-C7 (open symbols).
existence of two distinct signals for the branching proton
illustrates that two conformations of the C9,9 side chains coexist,
namely, one that is hydrogen bonded (δiso(1H) ≈ 4.8 ppm) and
simulations by Marcon et al.21 In Figure 4a the spatial proximity
thereby coordinated to one of the carbonyls of either side of
the PMI core, and a second conformation, where the proton
(δiso(1H) ≈ 1.7 ppm) is non-hydrogen-bonded. We note that this
kind of splitting was not observed for PDIs with symmetrically
attached C8,7-branching moieties with alkyl and tri(ethylene
glycol) substituents.22,23 In these systems only the hydrogen-
bonded fractions were detected. To investigate the stability of
the hydrogen-bonded species in PMI-d-C9, a series of temper-
ature-dependent 13C{1H} CP/MAS NMR experiments have been
performed as illustrated in Figure 5a. It can readily be seen that
the two different side-chain conformations persist in the
measured temperature range and that the isotropic 13C chemical
shift for both fractions is slightly shifted toward lower fields
with increasing temperature. Moreover, the 13C resonance
corresponding to the non-hydrogen-bonded fraction (∼58.5
ppm) becomes narrower, whereas the resonance for the hydrogen-
of protons in PMI-d-C9 is mapped out using the before-
mentioned NMR technique for a fast spinning frequency of 50.0
kHz. From this spectrum it is evident that the region corre-
sponding to the PMI core protons overlaps with those of the
phenyls in the diphenylamines chains even at this high spinning
frequency. However, taking into account that the PMI core
protonsareshiftedtohighfieldasaresultofπ-πinteractions,28-31
it is possible to perform the assignment as illustrated in Figure
4a. More importantly, the spectrum shown in Figure 4a does
not reveal any autocorrelation signal between the branched C9
side chains of neighboring molecules. This constitutes a clear
evidence that the PMI-d-C9 molecules are packed in columnar
stacks with an angle between successive molecules larger than
(28) Ochsenfeld, C.; Brown, S.; Schnell, I.; Gauss, J.; Spiess, H. W. J. Am.
Chem. Soc. 2001, 123, 2597–2606.
(29) Brown, S. P.; Spiess, H. W. Chem. ReV. 2001, 101, 4125–4155.
(30) Brown, S. P. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 50, 199–
251.
(32) Bielecki, A.; Kolbert, A.; Levitt, M. Chem. Phys. Lett. 1989, 155,
341–346.
(33) van Rossum, B. J.; Fo¨rster, H.; de Groot, H. J. M. J. Magn. Reson.
1997, 124, 516–519.
(31) Brown, S. P. Macromol. Rapid Commun. 2009, 30, 688–716.
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A R T I C L E S
Tasios et al.
1
Figure 4. (a) 2D rotor-synchronized H-1H DQ-SQ correlation spectrum of PMI-d-C9 recorded using a spinning frequency of 50.0 kHz and a BaBa DQ
excitation/reconversion period of 40 µs (2τR). (b) Molecular structure of PMI-d-C9 including the color scheme employed for assignment purposes in this
work. (c) 2D 13C{1H} FSLG-HETCOR spectrum of PMI-d-C9 recorded using a spinning frequency of 15.0 kHz for a short cross-polarization period of 500
µs. The inset in panel c corresponds to an expansion of the region marked by the gray arrow. In panels a and c the dashed lines indicate the internuclear
contacts and directly bonded protons to carbons, respectively.
conformations were found in PDI-C8,7, where the pitch angle
is in the range of 20-45°, is suggestive of a relation between
the helical intracolumnar organization of the cores and the space-
filling requirements of the side chains.21,22 The presence of
hydrogen-bonded conformations (as in PDI-C8,7) drives the
alkyl chains to orient perpendicular to the perylene core,
allowing for a smaller pitch angle. On the other hand, the
presence of a fraction of non-hydrogen-bonded conformations
drives a number of branched side chains away from the
perpendicular orientation, and this may twist the cores to larger
angles to preserve a uniform density within the alkyl domains.
In particular, it has already been pointed out in 198334 that the
columnar mesophase, as realized by rigid aromatic core
molecules and more flexible aliphatic side chains, poses packing
problems because of the incommensurability of the aliphatic
and aromatic moieties. This packing question is particularly
important in cases of elongated cores, where density modulations
as proposed by de Gennes34 were indeed observed.35,36 There-
fore, the question of whether such systems can crystallize is
particularly intriguing.
To draw quantitative conclusions on the rigidity of the PMI-
d-C9 core and on the expected difference in mobility between
hydrogen-bonded and non-bonded branching protons of the C9,9
side chain, we have recorded a series of site-specific hetero-
nuclear rotor-encoded dipolar sideband patterns, using the rotor-
encoded polarization transfer (REPT-HDOR) technique.37 In this
Figure 5. (a) Variable-temperature 13C{1H} CP/MAS NMR spectra
kind of experiment, the local molecular motion is monitored
acquired using a spinning speed of 25.0 kHz and a cross-polarization time
through the effective H-13C dipole-dipole coupling (DCH),
1
of 500 µs. The selected region shows how the ratio between hydrogen-
bonded and non-hydrogen-bonded changes upon heating the samples to
higher temperatures (below melting point). (b) Illustration of how the fraction
of hydrogen-bonded species drops as a function of temperature. The solid
line connecting the data points corresponds to an approximated spline and
is meant as a guide for the eye only.
corresponding to the time-averaged value of the anisotropic
heteronuclear dipolar Hamiltonian, which spatial part is de-
scribed by a second-order Legendre polynomial. The measured
dipole-dipole couplings can be related to an effective order
parameter using the dipole-dipole coupling constant for a static
1H-13C spin pair of 21.0 kHz,37 using the relation
bonded (∼54.5 ppm) remains broad. An integration of the peak
intensities shows that the fraction of hydrogen-bonded protons
decreases with increasing temperature as depicted in Figure 5b.
These observations indicate that the non-hydrogen-bonded
fraction is more mobile than the hydrogen-bonded fraction,
whose mobility appears to be unaffected by temperature.
The fact that two side-chain conformations coexist in PMI-
d-C9 with a pitch angle of 60°, whereas solely hydrogen-bonded
(34) de Gennes, P.G. J. Phys. Lett. 1983, 44, 657–664.
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Kinetics of Substituted Perylene Derivatives
A R T I C L E S
Figure 6. (a) 2D contour plot of the 13C{1H} REPT-HDOR spectrum for PMI-d-C9 recorded at ambient conditions for a spinning speed of 30.0 kHz and
a recoupling period of 134.4 µs (4τR). The site-selective 13C-1H dipolar sideband patterns shown in black in panels b and c have been extracted from the
positions indicated in panel a by dashed lines. The optimized simulations are shown in colors (see Figure 1b) and have been slightly shifted to the right for
a better visual comparison with their experimental contour parts. The upper numbers (black) and lower numbers (red) given in bold correspond to the
dynamic order parameters (eq 2) determined at ambient temperature and 122 °C, respectively.
〈DCH(t)〉t
DCH,static
Perylenes, with a small π-π overlap, do form a crystalline phase
as well, but the molecules do not tilt with respect to the columnar
axis. Because of this, the intercolumnar thermal expansion is
always positive, being similar to the intracolumnar thermal
expansion. This constitutes the primary difference in the self-
assembly motifs of the Cr phase of perylenes as compared to
HBCs. They do share, however, some similarities. As observed
for HBCs, phase formation involves a delicate balance of short-
ranged interactions and packing. From the different perylene
derivatives investigated, only the PMI-d-C7 and PMI-d-C9
derivatives crystallize, whereas the structurally similar PMI-s-
C10 and PMI-t-C10 compounds do not. The fact that the PMI-
t-C10 does not crystallize is, at first sight, surprising given the
presence of three long alkyl chains. The absence of crystalliza-
tion in PMI-s-C10 suggests that chain length alone is not the
rate-determining factor for the formation of the Cr phase. In
view of recent work19,21-23 on other swallow-tail substituted
perylenes and the present results, it is likely that branched chains
substituted away from bay positions are required as space-filling
agents for the formation of the more ordered Cr phase. These
chains are most effective as they lessen the packing problems
discussed earlier.34 The solid-state NMR experiments further
pointed out the importance of hydrogen bonding in stabilizing
the crystalline phase. Within the columnar stacks of the Cr
phase, PMI molecules had a helical arrangement with a pitch
of 2 nm, corresponding to a 60° rotation of successive molecules.
1
2
S ) (3 cos2 θCH(t) - 1) )
(2)
〈
〉
The results from this investigation are shown in Figure 6 at
ambient temperature and at an elevated temperature of 122 °C
but below the melting point. Clearly, at ambient temperature
the measured effective order parameters show that PMI-d-C9
is crystalline and that its core hardly moves within the columns
on the time scale of the NMR experiment. This freezing of
molecular dynamics is expected to have consequences on the
dynamics of the core as probed by dielectric spectroscopy (see
below). Furthermore, the two C9,9 branching points show vastly
different local dynamics with SH-bonded ≈ 0.9 and Snon-H-bonded
≈
0.4, as anticipated from the variable-temperature 13C{1H} CP/
MAS NMR experiments. It seems that mobile non-hydrogen-
bonded branched alkyl chain conformations are required to fill
the space and produce a uniform density. At 122 °C the effective
order parameters are slightly lowered, indicating that the cores
of the PMI-d-C9 stacked molecules are slightly fluctuating. The
effective order parameters for the two different side-chain
conformations are affected in a similar manner.
Summarizing, the structural investigation revealed that the
self-assembly and thermodynamic properties of perylene deriva-
tives are distinctly different from those of the corresponding
HBC compounds. Although both form columnar phases, the self-
assembly within the columnar stacks differs substantially.
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A R T I C L E S
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Figure 8. Temperature dependence of the low-frequency HN shape
parameter for the four perylene compounds: (9) PMI-t-C10, (2) PMI-d-
C9, (b) PMI-s-C8, and (1) PMI-s-C10.
values of the dynamic order parameter found in NMR (S ≈
0.9-0.95). In addition to the dynamics, the dielectric strength
∆ε () εS′ - ε∞′, where εS′ ) limωf0 ε′(ω) and ε∞′ ) limωf∞
ε′(ω)), together with the molecular dipole moment allows an
estimation of the angle between interacting perylene molecules
within the column through38
Figure 7. Dielectric loss spectra of PMI-d-C9 (top) and of PMI-t-C10
(bottom) shown at different temperatures: 398 e T e 473 K and 293 e T
e 393 K, respectively, in 5 K steps. Notice the reduction in the dielectric
loss of PER-d-C9 at 458 K (shown with the thick solid circles) that is absent
in PMI-t-C10.
µ2
3kBT
Ν
V
∆ε ≈
Fg
(3)
Within the Cr phase the molecular dynamics are restricted as
indicated by the NMR local order parameters, and this is
expected to show up in the dynamic studies (see below).
Molecular Dynamics. The molecular dynamics were subse-
quently investigated with dielectric spectroscopy. Figure 7
provides the measured dielectric loss curves for PMI-d-C9 in
comparison to PMI-t-C10. The dielectric response of PMI-d-
C9, which undergoes an I-to-Cr transition, is distinctly different
from that of the remaining compounds. A strong single peak,
albeit broad, is seen in PMI-t-C10 as well as in PMI-s-C8, PMI-
s-C10, and PMI-t-C10, arising from the reorientation within the
I phase. With decreasing temperature the process freezes out at
the liquid-to-glass temperature, defined here as the temperature
where the corresponding relaxation time is at τ ≈ 100 s. The
single dynamic process in PMI-t-C10 clearly violates the
time-temperature superposition principle (not shown here) as
a result of the T-dependent distribution of relaxation times.
Figure 8 provides the temperature-dependence of the low
frequency Havriliak-Negami parameter (m) (eq S1, Supporting
Information) associated with longer range dynamics. At T .
Tg the shape parameter resembles a Debye process. With
decreasing temperature the distribution of relaxation times
broadens and for PMI-t-C10 attains a value of m ≈ 0.5 at T )
Tg. On the other hand, the erratic m(T) for PMI-d-C9 reflects
the loss of dielectric strength on entering the Cr phase (see
below).
In eq 3, µ is the dipole moment for noninteracting dipoles, F
[) (εS(ε∞ + 2)2/3(2εS + ε∞)] is the local field correction, g is
the Kirkwood-Fro¨hlich correlation factor giving the angular
correlations between the dipoles (approximated by g ) 1 +
z〈cos ꢁ〉, where z is the coordination number or number of
closest/interacting neighbors and ꢁ is the angle between the
test dipole and its nearest neighbor), N is the number of dipoles,
and V is the volume. In the calculation we have assumed
intracolumnar dipole-dipole interactions and used the density
of the rectangular unit cell (F ) 1948.8 kg/m3). As for the dipole
moment of isolated dipoles we have used the value of 9.7 D
(using MOPAC2007). The result for the angle between interact-
ing dipoles within a single column is plotted in Figure S2 in
Supporting Information. While the value of the dipole moment
has negligible effect on the angle between successive dipoles,
the number of interacting dipoles has a significant effect. The
estimated angle is higher than the one obtained from WAXS;
however, there are several assumptions that are involved in the
calculation.
The relaxation times of the four perylene derivatives are
summarized in Figure 9. The relaxation times exhibit a strong
non-Arrhenius temperature-dependence that conforms to the
Vogel-Fulcher-Tammann (VFT) equation:
Crystallization has profound consequences on the dipolar
relaxation of PMI-d-C9 and PMI-d-C7. In PMI-d-C7 crystal-
lization is so strong that it suppresses any dielectric activity.
On the other hand, in PMI-d-C9 and at temperatures corre-
sponding to the I phase, the dielectric loss curves are reminiscent
to those of PMI-t-C10 (Figure 7) with typical peak values of
ε′′max ≈ 0.3. The transition to the Cr phase is accompanied by
a discontinuous reduction of the dielectric strength of both the
peak and the ionic conductivity and by peak broadening. The
reduced dielectric strength is suggestive of a restricted dipole
reorientation within the Cr phase, in agreement with the high
B
τ ) τ0exp
(4)
(
)
T - T0
where 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
2). In the case of PMI-d-C9, however, the relaxation times
display a weaker temperature-dependence that can be described
(38) Broadband Dieletcric Spectroscopy; Kremer, F., Scho¨nhals, A., Eds.;
Springer: Berlin, 2002.
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Kinetics of Substituted Perylene Derivatives
A R T I C L E S
Figure 9. Temperature dependence of the relaxation times extracted from
DS for the four perylene compounds: (9) PMI-t-C10, (2) PMI-d-C9, (b)
PMI-s-C8, and (1) PMI-s-C10. Lines are best fits to the VFT equation
except for PMI-d-C9, where a fixed value of the activation parameter
corresponding to the I phase was employed instead.
Table 2. Parameters of the VFT Equation
sample
τ0 (s)
B (K)
T0 (K)
Tg (K)b
Figure 10. Evolution of the effective dielectric strength (T∆ε), low-
frequency Havriliak-Negami shape parameter (m), and relaxation time for
the PMI-d-C9, following a quench from 493 K to different final crystal-
lization temperatures: (9) 458, (b) 459, (2) 460, (1) 461, and ([) 462 K.
PMI-d-C9 (2.5 ( 0.1) × 10-11 2120a
255 ( 1
329 ( 1
PMI-s-C8
(2.7 ( 0.2) × 10-11 2120 ( 20 278.1 ( 0.5 352 ( 1
PMI-s-C10 (5 ( 1) × 10-11
2040 ( 53 272 ( 1
345 ( 1
219 ( 1
PMI-t-C10 (1.9 ( 0.3) × 10-10 1610 ( 36 231 ( 1
a Held fixed. b From DS at τ ) 100 s.
time. The results from the kinetic experiments are plotted in
Figure 10 for the different final crystallization temperatures. The
results for the evolution of T∆ε are more pronounced as
anticipated by the reduced disk mobility found in NMR. They
display a sigmoidal reduction in dielectric strength with a
characteristic time that is a function of the crystallization
temperature. The crystallization process is accompanied by
moderate changes in the shape parameter and the relaxation time
(strictly speaking, the I to Cr transformation is not isochronal).
Aiming at the evolution of the volume fraction of the new
(Cr) phase we employed a parallel element model (Voigt),39
which provides an estimate of the crystalline fraction ꢁc from
by an Arrhenius law. In this case, the green dashed line in Figure
9 is indicative and refers to a VFT-representation of the high
temperature relaxation times, corresponding to the I phase (a
fixed value for the activation parameter B was employed). On
the basis of the τ(T) dependencies and the glass temperatures
extracted from Figure 9 (given in Table 2), it is apparent that
the main effect of alkyl substitution is to increase the rate of
molecular motion (i.e., decrease the glass temperature).
Kinetics of Phase Transformation. The presence of a highly
ordered Cr phase in PMI-d-C9 allows an investigation of the
phase transformation kinetics. In this respect there are several
issues that require attention. First is the identification of the
exact mechanism of crystallization. We mention here that recent
investigations25,26 of the Cr phase formation in HBCs revealed
long-lived metastability and a nucleation and growth mechanism
with kinetics that were dominated by the nucleation barrier.
Furthermore, an intermediate state was found that involved a
change in the unit cell prior to crystallization.26 On the other
hand, the minimal π-π overlap in PMI-d-C9 prevents molecular
tilting along the columns of the Cr phase, and this can influence
the transformation kinetics. The present study addresses in detail
the mechanism of the Cr phase formation in PMIs following
quenches from the high temperature isotropic phase. Emphasis
is given to the possible nucleation sites, the relative importance
of molecular transport as opposed to the nucleation barrier, and
the presence of homogeneous versus heterogeneous nucleation.
To address these questions we have performed “isothermal”
kinetic experiments with DS on samples heated to an initial
temperature of 220 °C, which is well within the I phase, and
then quenched to different final temperatures in the range of
185-189 °C. Subsequently, we monitored the evolution of the
dielectric permittivity and loss peaks. For each spectrum the
Havriliak-Negami equation was employed and the dielectric
strength, ∆ε, the relaxation time, τ, and the low-frequency shape
parameter, m, were extracted as a function of the crystallization
εS ) ꢁcεS,Cr + (1 - ꢁc)εS,I
ε∞ ) ꢁcε∞,Cr + (1 - ꢁc)ε∞,I
(5)
∆ε(t) ) ꢁc(t)∆εCr(t) + (1 - ꢁc(t))∆εI(t)
the subscripts I and Cr, indicate the isotropic and crystalline
phases, respectively. Note that the third equation is obtained
by subtraction of the first two. Another lower bound for ꢁc can
be obtained by assuming additivity of the electric moduli instead,
but the resulting equation is more complicated and requires
additional parameters. Thus, using eq 5c and the known
dielectric strengths of the initial (I) and final (Cr) states we
estimate an upper limit for ꢁc. The resulting evolution of ꢁc(t)
is plotted in Figure 11 in a double logarithmic representation.
The linearity in the latter representation emphasizes that the
volume fraction of the Cr phase increases following the well-
known Avrami equation:40
ꢁc(t) ) 1 - exp(-ktn)
(6)
(39) Coburn, J. C.; Boyd, R. H. Macromolecules 1986, 19, 2238–2245.
(40) Avrami, M. J. J. Chem. Phys. 1939, 7, 1103-1112; 1940, 8, 212-
224; 1941, 9, 177-184.
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A R T I C L E S
Tasios et al.
relaxation times grow exponentially with the domain size, L,
as τ ≈ exp(aL). Within this approach, the longer times of
transformation found at the higher temperatures reflect simply
the larger domain size.
The type of nucleation process can be discussed with respect
o
o
to the undercooling parameter δ ( ) (Tmo - Tc)/Tm , where Tm
is the equilibrium melting temperature and Tc is the crystal-
lization temperature) by plotting the characteristic crystallization
times as a function of the undercooling for both homogeneous
(scales as δ-1) and heterogeneous (δ-2) cases. POM was used
to obtain the Tmo (by following the isothermal crystallization at
selected temperatures and by subsequent slow heating to the
point that the birefringence disappeared). Within the limited
temperature range investigated the nucleation process resembles
more closely the homogeneous case.
In summary, the formation of the ordered phase from the
isotropic phase proceeds via a nucleation and growth mechanism
by overcoming a barrier of 3.2 eV. In addition, the formation
of the crystalline phase, despite being very slow at higher
temperatures, does not involve any intermediate metastable state.
Figure 11. Evolution of the volume fraction ꢁc corresponding to the
crystalline phase in PMI-d-C9, following a quench from 493 K to different
final crystallization temperatures: (9) 458, (b) 459, (2) 460, (1) 461, and
([) 462 K. The lines represent linear fits to the data.
Conclusions
The first systematic investigation of the self-assembly, the
dynamics, and the kinetics of phase formation took advantage
of the strong dipole associated with the donor-acceptor
character of the diphenylamine functionalized perylenemon-
oimides molecules and the presence of heteronuclear dipolar
couplings. The structural investigation revealed that the self-
assembly and thermodynamic properties of perylene derivatives
is significantly different from those of the corresponding HBC
compounds. Perylenes, with a small π-π overlap, do form a
crystalline phase as well, but the residues do not tilt with respect
to the columnar axis. Because of this, the intercolumnar thermal
expansion is always positive, being similar to the intracolumnar
thermal expansion. This constitutes a primary difference in the
self-assembly motifs of the Cr phase of perylenes with the
HBCs. Despite this, phase formation involves a delicate balance
of short-range interactions and packing. The present results
suggest that branched chains substituted away from bay positions
are important as space-filling agents within the alkyl domains
for the formation of the Cr phase. The results from solid-state
NMR experiments further pointed toward the importance of an
intramolecular hydrogen bonding in stabilizing the crystalline
phase as well as the influence of non-hydrogen-bonded moieties
on the twist angle between successive monomers.
With respect to the dynamics, both solid-state NMR and DS
revealed a relatively immobile core, characterized by a dynamic
order parameters S ≈ 0.9-0.95, within the crystalline phase of
PMI-d-C9. The remaining perylene derivatives that do not
crystallize undergo an isotropic liquid-to-glass transformation
at a temperature that was found to depend on the number of
methylene units in the alkyl chains.
The phase transformation kinetics from the high temperature
isotropic phase to the crystalline phase at lower temperatures
revealed a long-lived metastable state as a result of the soft
potential. The crystalline phase is formed via a nucleation and
growth mechanism, and the kinetic times are controlled by the
nucleation barriers. The existence of slow molecular dynamics
and of very slow kinetics of phase transformation suggests that
Figure 12. Half-crystallization times in PMI-d-C9 corrected for the
diffusion term and plotted as a function of inverse temperature. The slope
is proportional to the nucleation barrier (eq 7).
where k and n reflect the rate of transformation and Avrami
exponent reflecting the type of nucleation (homogeneous vs
heterogeneous) and dimensionality of growth. The n values were
in the range of 2-3 for the different temperatures. In a simple
nucleation and growth process, the characteristic time, t1/2, is a
function of the final crystallization temperature, Tc, calculated
through t1/2 ) (ln 2/k)1/n, are related to the nucleation barrier,
∆G*, through
B
∆G*
kBT
t1/2 ) τ0 exp
exp -
(7)
(
)
(
)
T - T0
The first term in the above equation is the usual mobility term,
given by the VFT equation, and the second term is the barrier
to crystallization. The latter (∆G*) is obtained by plotting ln
t1/2 - ln τ0 - B/(T - T0) vs 1/T in Figure 12 and amounts to
3.2 eV. These results show that the kinetics are dominated by
the nucleation term.
Other systems with extremely slow relaxation near the phase
transition are the spin glasses. In this respect, a random Ising
ferromagnetic model with random spin predicts slow relaxation
and nearly degenerate metastable states.41,42 The slow dynamics
reflect the inability of certain magnetization domains, composed
from spins of certain lengths, to spinflip. In particular, the
(41) Takano, H.; Miyashita, S. Phys. ReV. B 1993, 48, 7221.
(42) Kawasaki, T.; Miyashita, S. J. Magn. Magn. Mater. 1992, 104-107,
1595. Kawasaki, T.; Miyashita, S. Prog. Theor. Phys. 1993, 89, 985.
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7486 J. AM. CHEM. SOC. VOL. 132, NO. 21, 2010

Kinetics of Substituted Perylene Derivatives
A R T I C L E S
acknowledges the Carlsberg Foundation for a Post Doctoral
Research Fellowship.
care should be taken in establishing the equilibrium phases of
DLC. Furthermore, these issues could influence the charge
carrier mobilities that are required for applications as photo-
voltaic solar cells and field-effect transistors.
Supporting Information Available: Details on the synthesis,
thermal properties, polarizing optical miscopy, X-ray scattering,
solid-state NMR spectroscopy, and dielectric spectroscopy. This
material is available free of charge via the Internet at http://
pubs.acs.org.
Acknowledgment. The current work was supported by the John
S. Latsis public benefit Foundation with a research grant to G.F.
We thank M. Bach (MPI-P) and G. Tsoumanis (UoI) for
technical support. Financial support of the Deutsche Forschungs-
gemeinschaft, SFB 625 is gratefully acknowledged. M.R.H.
JA102150G
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