Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies
The inter- and intracolumnar arrangements of the perylene tetracarboxylic diimide (PDI) was investigated experimentally and theoretically by using X-ray diffraction with combined DFT computation and molecular dynamics simulation. The structure was found to be hexagonal with a packing parameter of ne...
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Інститут проблем матеріалознавства ім. І.М. Францевича НАН України
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| Zitieren: | Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies / A. Pokropivny // Наноструктурное материаловедение. — 2010. — № 1. — С. 53-58. — Бібліогр.: 20 назв. — англ. |
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irk-123456789-627022014-05-25T03:01:53Z Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies Pokropivny, A. Методы исследования наноструктур и наноматериалов The inter- and intracolumnar arrangements of the perylene tetracarboxylic diimide (PDI) was investigated experimentally and theoretically by using X-ray diffraction with combined DFT computation and molecular dynamics simulation. The structure was found to be hexagonal with a packing parameter of nearest column a = 2.025 nm characterized by a ~ 45° twist of molecules within the columns. Меж- и внутриколоночные упорядочения перилена были исследованы экспериментально и теоретически при использовании рентгеновской дифракции с комбинированными вычислениями методами функционала плотности и молекулярной динамики. Структура кристалла определена как гексагональная с упаковочным параметром самой близкой колонки a = 2,025 нм с характерным твистом ~ 45° молекул в пределах колонок. Між- і внутрішньоколончасті впорядкування перилену було досліджено експериментально й теоретично при використанні рентгенівської дифракції з комбінованими обчисленнями методами функціоналу густини та молекулярної динаміки. Структуру кристала визначено як гексагональну з пакувальним параметром найближчої колонки a = 2,025 нм із характерним твістом ~ 45° молекул у межах колонок. 2010 Article Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies / A. Pokropivny // Наноструктурное материаловедение. — 2010. — № 1. — С. 53-58. — Бібліогр.: 20 назв. — англ. 1996-9988 http://dspace.nbuv.gov.ua/handle/123456789/62702 541.183.24:576.8 en Наноструктурное материаловедение Інститут проблем матеріалознавства ім. І.М. Францевича НАН України |
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Методы исследования наноструктур и наноматериалов Методы исследования наноструктур и наноматериалов |
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Методы исследования наноструктур и наноматериалов Методы исследования наноструктур и наноматериалов Pokropivny, A. Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies Наноструктурное материаловедение |
| description |
The inter- and intracolumnar arrangements of the perylene tetracarboxylic diimide (PDI) was investigated experimentally and theoretically by using X-ray diffraction with combined DFT computation and molecular dynamics simulation. The structure was found to be hexagonal with a packing parameter of nearest column a = 2.025 nm characterized by a ~ 45° twist of molecules within the columns. |
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Article |
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Pokropivny, A. |
| author_facet |
Pokropivny, A. |
| author_sort |
Pokropivny, A. |
| title |
Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies |
| title_short |
Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies |
| title_full |
Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies |
| title_fullStr |
Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies |
| title_full_unstemmed |
Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies |
| title_sort |
supramolecular organization and electronic structure of perylene tetracarboxylic diimide: x-ray diffraction and theoretical studies |
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Інститут проблем матеріалознавства ім. І.М. Францевича НАН України |
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2010 |
| topic_facet |
Методы исследования наноструктур и наноматериалов |
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http://dspace.nbuv.gov.ua/handle/123456789/62702 |
| citation_txt |
Supramolecular organization and electronic structure of perylene tetracarboxylic diimide: X-ray diffraction and theoretical studies / A. Pokropivny // Наноструктурное материаловедение. — 2010. — № 1. — С. 53-58. — Бібліогр.: 20 назв. — англ. |
| series |
Наноструктурное материаловедение |
| work_keys_str_mv |
AT pokropivnya supramolecularorganizationandelectronicstructureofperylenetetracarboxylicdiimidexraydiffractionandtheoreticalstudies |
| first_indexed |
2025-07-05T13:34:35Z |
| last_indexed |
2025-07-05T13:34:35Z |
| _version_ |
1836814147646390272 |
| fulltext |
Íàíîñòðóêòóðíîå ìàòåðèàëîâåäåíèå, 2010, ¹ 1
ÓÄÊ 541.183.24:576.8 A. Pokropivny
Frantsevich Institute for Problems of Materials Science, National Academy of Sciences of Ukraine
03142, Ukraine, Kiev, Krzhuzhanovsky str., 3
SUPRAMOLECULAR ORGANIZATION
AND ELECTRONIC STRUCTURE
OF PERYLENE TETRACARBOXYLIC DIIMIDE:
X-RAY DIFFRACTION AND THEORETICAL STUDIES
The inter- and intracolumnar arrangements of the perylene tetracarboxylic diimide (PDI)
was investigated experimentally and theoretically by using X-ray diffraction with combined
DFT computation and molecular dynamics simulation. The structure was found to be
hexagonal with a packing parameter of nearest column a = 2.025 nm characterized by a
~ 45° twist of molecules within the columns.
In the last years the self-assembly of organic molecules presented
the perspectives of developing novel materials for electronics. A special
attention was made on the mesophases, characterized by p-conjugated
molecules and formation of columnar superstructures in both the solid
and liquid crystalline states. The arrangement of the molecules allows a
charge carrier transport along the one-dimensional structures by increasing
of coupling of p-electrons, which make them unique materials for device
applications, such as field-effect transistors and solar cells. The
perspectives of such materials became clear taking into account the
anisotropy of electronic properties, low-cost and facile device fabrication,
self-healing of defects within the columns, and relatively high local one-
dimensional charge carrier mobility [1].
Most of the alkyl substituted low molecular weight species which
organize into columnar superstructures are p-type semiconductors. Rylene
diimide molecules, such as perylene tetracarboxylic diimide (PDI),
terrylene tetracarboxylic diimide (TDI) and quaterrylene tetracarboxylic
diimide (QDI) form a unique class of n-type organic semiconductors [2].
Both n-and p-types molecules can be used separately in field-effect
transistors, while only their mixture are required in bulk-heterojunction
photovoltaics, like hexabenzocoronene (HBC)-PDI and polycarbazolA. POKROPIVNY, 2010©
ÌÅÒÎÄÛ ÈÑÑËÅÄÎÂÀÍÈß
ÍÀÍÎÑÒÐÓÊÒÓÐ È ÍÀÍÎÌÀÒÅÐÈÀËÎÂ
Key words: liquid crystals, X-ray
diffraction, non-covalent interac-
tions, electronic properties, molecu-
lar dynamics, quantum-chemistry
calculation
54
Íàíîñòðóêòóðíîå ìàòåðèàëîâåäåíèå, 2010, ¹ 1
(CPz)-PDI, revealed the highest efficiencies for
columnar phases [3]. PDI derivatives are used to
control the molecular deposition [4], as an injector
of charge carriers for different polymers employing
the time-of-flight technique [5], and as fluorescence
switch [6]. Furthermore, perylene has been utilized
as convenient precusor for a consequent synthesis
of more complex molecules, such as terrylene
derivatives [7], perylenebisimide and bisbenzi-
midazole [8], fullerene-perylene and perylenebi-
simide-triphenyldiamine dyads [9]. These sub-
stances are widely used for optoelectronic appli-
cations [5–10] owing to their dyes cover the visible
light [11] and due to their high thermal and
photostability [12]. Nevertheless, the supramolecular
structure into which PDI self-assemblies is not yet
fully understand. An intracolumnar arrangement was
proposed with a twist of the adjacent molecules [11,
13], or without any twist [14]. A detailed knowledge
about the supramolecular organisations is necessary
for the calculation of the electronic properties, since
the electron and hole transfers strongly depend on
the molecular arrangement [15].
The aim of this communication is to determine
the supramolecular structure of heptyloctyl sub-
stituted PDI (1), namely inter- and intracolumnar
arrangements by using both X-ray diffraction
analysis and simulations.
Molecular dynamics simulation (total 30 ns run)
had been done at a pressure P = 0.1 MPa and a
temperature T = 300 K by using usual OPLS force
field. GROMACS [20] software was used. The
equations of motion were integrated using Varlet’s
algorithm with a time step of 2 fs. After constructing
topology of single PDI molecule, a periodic box
of 4x4x12 molecules with hexagonal arrangement
of columns with a 45° twist within columns were
created. DFT calculations (BH&H/6–31G(d) level
of theory) were done for dimers constructed from
optimized monomers at the fixed distance of 0.35 nm
between molecular cores. Gaussian 03 and
GAMESS software were used. The total energy
and electronic spectra were calculated with for
different rotational angles.
2D-WAXS experimental setup [1, 11] consisted
of a rotating anode (Rigaku 18 kW) X-ray beam
with a pinhole collimation and a 2D Siemens
detector, that use a double graphite monochromator
for the Cu-Ka radiation (λ = 0.154 nm).
The two-dimensional wide-angle X-ray scat-
tering (2D-WAXS) pattern of a mechanically
aligned PDI (1) is presented in Fig. 1. On the basis
of two distinct equatorial reflections an orthorhombic
intercolumnar arrangement was previously proposed
with a unit cell of a = 1.67 nm and b = 2.08 nm.
Later It is possible to consider the unit cell as a
hexagonal lattice with a = 4.05 nm [11] leading to
the assignment of the two equatorial reflections
as (110) and (200).
The intracolumnar packing is more complex and
can be characterized by the meridional reflections.
The major distinct (004) wide-angle meridional
reflection is related to the π-stacking period of 0.345 nm,
as shown in Fig. 1. The molecular cores arrange
orthogonally with respect to the columnar axis. The
appearance of additional (001) meridional reflections
suggests a further intracolumnar correlation. Taking
into account the π-stacking distance in relation with
the high order distance of 1.39 nm, it is derived that
Fig. 1. The 2D-WAXS pattern of PDI (1) at a temperature
T = 300 K. Two meridional (004) and (001) reflections
correspond to 0.345 nm and 1.39 nm periodicities in a
direction of the columnar axis. Inset highlights the two
major (110) and (200) equatorial reflections of hexagonal
intercolumnar arrangement of a = 4.05 nm
(004)
(001)
(200)
(110)
ÌÅÒÎÄÛ ÈÑÑËÅÄÎÂÀÍÈß ÍÀÍÎÑÒÐÓÊÒÓÐ È ÍÀÍÎÌÀÒÅÐÈÀËÎÂ
55
М
АТ
ЕР
ИА
ЛО
ВЕ
Д
ЕН
ИЕ
Íàíîñòðóêòóðíîå ìàòåðèàëîâåäåíèå, 2010, ¹ 1
every fourth molecule within the column is in the
same position and laterally rotated by 45° to each
other, providing the excellent agreement with
π-stacking distance of 1.39/4 = 0.3475 nm with a
divergence average of less than 1%.
The large hexagonal packing parameter of a =
= 4.05 nm contradicts the theoretical size of the PDI (1)
molecules, while orthorhombic one with a > b
parameters disagrees with the possible 45° twist of
molecules. In comparison, the more extended rylene
molecules, i.e. TDI and QDI revealed even a smaller
hexagonal lattice with a = 2.94 nm and a = 3.09 nm,
respectively. It is reasonably to assume that the
parameter of a = 4.05 nm involves every second
column leading to a simple intercolumnar distance
of 2.025 nm in the hexagonal unit cell. Indeed, such
a non-usual distribution of reflections with absence
Table 1. Experimental (WAXS) and simulation data for
a PDI columnar phase at 300 K
of the (100) reflection has been reported for discotic
liquid crystals [16] and fullerene-like crystals [17].
In such a case PDI belongs to columnar liquid
crystals with p6 mm symmetry, like other rylenes.
In order to confirm the experimentally observed
hexagonal packing of columns, molecular dynamics
(MD) simulation was performed (see for details [18]).
As a test, a single column of 12 molecules was
simulated. During the simulation the column was
tilted in the simulated box, already indicating rather
a hexagonal than rectangular or orthorhombic
Fig. 2. Calculated positional correlation functions: perpendicular (squares) and parallel (circles). Inset highlights the
hexagonal columnar arrangement of a simulation box after 30 ns run
9
6
3
0 1 2 3
Distance (nm)
(100) (110)
(200)
g
0
56
Íàíîñòðóêòóðíîå ìàòåðèàëîâåäåíèå, 2010, ¹ 1
columnar arrangement. MD simulations revealed a
unit cell parameter of 1.98 nm and a π-stacking
distance of 0.35 nm (Fig. 2 and Fig. 3a) which were
in a good agreement with the experimental values,
from above discussed X-ray diffraction analysis.
The hexagonal structure was slightly disordered so
that the (100) reflection entirely could not be visible.
The packing of PDI molecules in the columns
revealed strong dependence on the molecular
rotational angle, see Fig. 3b. At the 0° angle, i.e.
only translations without twist, appropriate branches
of dimer tails were closely connected with each
other. Thus, a rotation of tails and a tilting of
molecules were expected in order to minimize a
total energy within the columns as shown in Fig. 3c.
The total energetic profiles for different dimers with
D6h and D3h symmetries revealed that the global
energy minimum was rather unpredictable [15].
Fig. 4 shows the dependence of the total energies
for PDI (1) and hydrogen substituted PDI (2) dimers
calculated with BH&H/6–31g(d) method without
optimisation at the fixed intermolecular distance of
0.35 nm. This method was successfully tested for
calculation of vdW interactions on benzenes and
pyridines [19]. The results indicated that the global
energy minima for PDI (2) dimer were disposed in
the ~30° and ~150° rotational angle position. At the
90° there was also a local minimum (see Fig. 4) for
both types of dimers.
For PDI (1) dimer the evolution of the total
energy was more complicated with non-symmetric
dependence on the rotational angle. The absolute
minimum of function equals to ~24°. The local
minimum equaled to ~139° (see Fig. 4), corres-
ponding to ~41° twist, in full agreement with
experimental value. It was expected the helical
arrangement of molecules on the values of both
minima, i.e., the absolute minimum at ~24° also
might be achieved during slow crystallization
process. The helical stack of the single column is
reproduced in Fig. 3a and Fig. 3b. Comparisons of
the WAXS experimental data with the simulations
are shown in the table 1. The comparison shows
Fig. 3. The single column of simulated box after MD
simulation (a). Molecular architecture of PDI (1)
molecules in the stack (every molecule is rotated to its
neighbour by 45° around the columnar axis as shown by
arrows) (b). Geometry of dimer of PDI molecules (at 30°)
during quantum-chemistry calculations (c)
a b
c
+ C
+ H
+ H
+ O
Fig. 4. Evolution of a difference of the total energies of a
dimer made of D2 symmetry PDI–C8,7 (1) (circles) and D2h
symmetry PDI–H (2) (squares) when rotating one core
along the stacking axis, as calculated at DFT (BH&H)
level of theory
50
40
30
20
10
0
0 30 60 90 120 150 180
Rotation (degrees)
Energy (kcal/mol)
1
2
ÌÅÒÎÄÛ ÈÑÑËÅÄÎÂÀÍÈß ÍÀÍÎÑÒÐÓÊÒÓÐ È ÍÀÍÎÌÀÒÅÐÈÀËÎÂ
57
М
АТ
ЕР
ИА
ЛО
ВЕ
Д
ЕН
ИЕ
Íàíîñòðóêòóðíîå ìàòåðèàëîâåäåíèå, 2010, ¹ 1
that simulations fully agreed with experimental data
and the structure of PDI is determined.
Fig. 5 shows the results of the HOMO and
LUMO splittings calculations, which are the double
from the intermolecular transfer integral (t). As
clearly seen, the electronic structures of PDI
derivatives strongly depends on the substitutions:
the alkyl chain causes a change of geometry that
leads to distortion of the electronic structure. In
particular, the dependence of HOMO splitting of
PDI (1) and LUMO splitting of PDI (2) are
practically identical. The dependence of splittings
on the angle is non-symmetric, according to slight
twisting of molecular skeletons in order to balance
the massive branches of opposite alkyl chains. The
rate of electron hopping (k) depends on LUMO
splitting as k~t2 [15]. Thus, PDI electron mobility
equals to zero for the PDI (2) at the 45° expe-
rimental twist angle, while the perylene derivative
carrying the branched side chains reveals the
relatively high t values of ~0.01 eV (Fig. 5). Thereby,
substitution of branched tails has a strong influence
on the charge carrier mobility as major factor,
besides angle of twist, temperature and defects.
The calculated value of t at ~25° angle
is ~0.1 eV. Reorganisation energies for PDI equals
to 0.18 eV and 0.20 eV for positive and negative
polarons, respectively, which are very close to the
HATNA energies of 0.1 1–0.2 eV. According to
the Marcus formalism [15] the charge transfer rate
and charge mobility for PDI at the absolute minimum
position are expected to be comparable with that of
HATNA derivatives, promising electron trans-
porters.
In summary, the molecular and supramolecular
arrangement has been determined for columnar
phase of a perylene derivative bearing branched alkyl
substituents. Analysis of 2D-WAXS patterns clearly
indicated a hexagonal arrangement of columns and
a helical packing of the molecules within the columns,
like other rylene mesophases. Molecular dynamics
simulation confirmed the stability of the hexagonal
intercolumnar structure with a packing parameter
of ~2 nm and π-stacking distance of ~0.35 nm. The
helical intracolumnar arrangement of molecules was
also verified by the DFT calculations. The calculated
optimal rotational angles were proved to be 24° and
41° with the last value been very close to the
experimental value of 45°. The electronic spectra
revealed an essential dependence from the nature
of the tails: the substitutes (tails, rings etc.) must be
taken into account during transfer integral and charge
mobility calculations.
Ìåæ- è âíóòðèêîëîíî÷íûå óïîðÿäî÷åíèÿ ïåðèëåíà áûëè
èññëåäîâàíû ýêñïåðèìåíòàëüíî è òåîðåòè÷åñêè ïðè èñïîëü-
çîâàíèè ðåíòãåíîâñêîé äèôðàêöèè ñ êîìáèíèðîâàííûìè
âû÷èñëåíèÿìè ìåòîäàìè ôóíêöèîíàëà ïëîòíîñòè è ìîëå-
êóëÿðíîé äèíàìèêè. Ñòðóêòóðà êðèñòàëëà îïðåäåëåíà êàê
ãåêñàãîíàëüíàÿ ñ óïàêîâî÷íûì ïàðàìåòðîì ñàìîé áëèçêîé
êîëîíêè a = 2,025 íì ñ õàðàêòåðíûì òâèñòîì ~ 45° ìîëåêóë
â ïðåäåëàõ êîëîíîê.
Êëþ÷åâûå ñëîâà: æèäêèå êðèñòàëëû, ðåíòãåíîâñêàÿ äè-
ôðàêöèÿ, íåêîâàëåíòíûå âçàèìîäåéñòâèÿ, ýëåêòðîííûå
ñâîéñòâà, ìîëåêóëÿðíàÿ äèíàìèêà, êâàíòîâî-õèìè÷åñêèå
âû÷èñëåíèÿ
̳æ- ³ âíóòð³øíüîêîëîí÷àñò³ âïîðÿäêóâàííÿ ïåðèëåíó áóëî
äîñë³äæåíî åêñïåðèìåíòàëüíî é òåîðåòè÷íî ïðè âèêîðèñ-
òàíí³ ðåíòãåí³âñüêî¿ äèôðàêö³¿ ç êîìá³íîâàíèìè îá÷èñëåí-
íÿìè ìåòîäàìè ôóíêö³îíàëó ãóñòèíè òà ìîëåêóëÿðíî¿ äèíà-
ì³êè. Ñòðóêòóðó êðèñòàëà âèçíà÷åíî ÿê ãåêñàãîíàëüíó ç
ïàêóâàëüíèì ïàðàìåòðîì íàéáëèæ÷î¿ êîëîíêè a = 2,025 íì
³ç õàðàêòåðíèì òâ³ñòîì ~ 45° ìîëåêóë ó ìåæàõ êîëîíîê.
Êëþ÷îâ³ ñëîâà: ð³äê³ êðèñòàëè, ðåíòãåí³âñüêà äèôðàêö³ÿ,
íåêîâàëåíòíi âçàºìî䳿, åëåêòðîíí³ âëàñòèâîñò³, ìîëåêó-
ëÿðíà äèíàì³êà, êâàíòîâî-õ³ì³÷í³ îá÷èñëåííÿ
Fig. 5. Evolution of the HOMO (squares) and LUMO
(circles) splittings of PDI (1) (filled types) and PDI (2)
(open types) dimers when rotating around the stacking
axis
0,8
0,6
0,4
0,2
0
0 30 60 90 120 150 180
Rotation (degrees)
Splitting (ev)
58
Íàíîñòðóêòóðíîå ìàòåðèàëîâåäåíèå, 2010, ¹ 1
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