Self-assembly of dendronized perylene bisimides into complex helical columns

ARTICLE

pubs.acs.org/JACS

Self-Assembly of Dendronized Perylene Bisimides into Complex

Helical Columns

Virgil Percec,*^,†Mihai Peterca,^†,‡Timur Tadjiev,^||Xiangbing Zeng,^||Goran Ungar,^||,#Pawaret Leowanawat,^†

Emad Aqad,^†Mohammad R. Imam,^†Brad M. Rosen,^†Umit Akbey,^§Robert Graf,^§Sivakumar Sekharan,^§

Daniel Sebastiani,^§Hans W. Spiess,^§Paul A. Heiney,^‡and Steven D. Hudson^{^}

^†Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323,

United States

^‡Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, United States

^§Max-Planck Institute for Polymer Research, 55128 Mainz, Germany

Department of Materials Engineering and Science, University of Sheﬃeld, Sheﬃeld S1 3JD, United Kingdom

^{^}National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8544, United States

^#WCU C2E2, School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea

S Supporting Information

b

ABSTRACT: The synthesis of perylene 3,4:9,10-tetracar-

boxylic acid bisimides (PBIs) dendronized with ﬁrst-generation

dendrons containing 0 to 4 methylenic units (m) between the

imide group and the dendron, (3,4,5)12G1-m-PBI, is reported.

Structural analysis of their self-organized arrays by DSC, X-ray

1

diﬀraction, molecular modeling, and solid-state H NMR was

carried out on oriented samples with heating and cooling rates

of 20 to 0.2 ꢀC/min. At high temperature, (3,4,5)12G1-m-PBI

self-assemble into 2D-hexagonal columnar phases with intraco-

lumnar order. At low temperature, they form orthorhombic

(m = 0, 2, 3, 4) and monoclinic (m = 1) columnar arrays with 3D periodicity. The orthorhombic phase has symmetry close to

hexagonal. For m = 0, 2, 3, 4 ,they consist of tetramers as basic units. The tetramers contain a pair of two molecules arranged side by

side and another pair in the next stratum of the column, turned upside-down and rotated around the column axis at diﬀerent angles

for diﬀerent m. In contrast, for m = 1, there is only one molecule in each stratum, with a four-strata 2₁helical repeat. All molecules

face up in one column, and down in the second column, of the monoclinic cell. This allows close and extended π-stacking, unlike in

the disruptive upꢀdown alteration from the case of m = 0, 2, 3, 4. Most of the 3D structures were observed only by cooling at rates of

1 ꢀC/min or less. This complex helical self-assembly is representative for other classes of dendronized PBIs investigated for organic

electronics and solar cells.

’ INTRODUCTION

bay-^7a,band imide-^7cꢀgpositions. An isodesmic mechanism of self-

assembly was reported for J- and H-aggregates of PBIs dendro-

nized at their imide position.⁸Some dendronized PBIs self-

organize in bulk in 3D and 2D columnar periodic arrays^1a,2e,7k,8,9

exhibiting high charge carrier mobility^{1a,2e,7k,8,9cꢀ9g,10}of interest

for photovoltaic and other electronic applications.^1a,2e,10When

PBIs were dendronized at the bay position, J-aggregates that self-

assemble via a cooperative nucleationꢀelongation mechanism

were observed.¹¹Dendronized PBIs have also been used to mimic

photosynthetic charge separation and storage.¹²Amphiphilic-

Janus dendronized PBIs self-assemble in water into vesicles,¹³

while dendronized strapped PBIs have been shown to exhibit

chiral self-recognition and self-discrimination.¹⁴The solid-state

Perylene 3,4:9,10-tetracarboxylic acid bisimides (PBIs) have

received considerable interest as building blocks for the design of

functional supramolecular assemblies,^1aꢀcpolymers^2aꢀgand complex

molecular systems.³PBIs exhibit excellent photochemical and

thermal stability and display high ﬂuorescence quantum yields.^1a,bAs

aconsequence, PBIshavebeenextensivelyusedinthedevelopment

of industrial dyes and pigments,⁴xerographic photoreceptors,⁵

organic n-type semiconductors,^1a,2a,2b,2ftransistors,^{1a,2a,2c,2e,2f}light

emitting diodes,^1a,2fsolar cells,^{1a,2a,2c,2eꢀ2g}ﬂuorescent labels and

sensors in life science and biology,⁶and as artiﬁcial photosyn-

thetic systems.³

Recently, PBIs dendronized at the bay and/or imide positions

have started to impact almost all these areas. Site-isolation and

ﬂuorescence quantum yields up to 100% in organic solvents and

in water were accomplished when PBIs were dendronized at

Received: May 12, 2011

Published: June 24, 2011

r

2011 American Chemical Society

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Scheme 1. Synthesis of the First-Generation Self-Assembling Dendrons and of the Corresponding Dendronized PBI

(3,4,5)12G1-m-PBI with m = 0, 1, 2, 3, 4

functions of supramolecular assemblies generated from dendro-

nized PBIs have been reported to be dependent on the thermal

treatment of the assembly,^1a,8,9c,9gand on their chirality.^7kPBI is

a very rigid aromatic unit which exhibits strong πꢀπ interactions

while the self-assembling dendron attached to it is ﬂexible.^1a,8ꢀ10

Therefore, self-assembling dendronized PBIs are expected to

provide a complex self-assembly process that should be strongly

aﬀected by the nature of the interconnecting group between the

dendron and the bay or imide position of the PBI. This inter-

connecting group can couple the dendron to PBI and therefore

increase the rigidity of PBI or decouple the dynamics of PBI from

that of the dendron.

In order to elucidate the structure of the supramolecular

assemblies generated from dendronized PBIs, the dynamics, the

mechanism of self-assembly, and the role of the interconnecting

group, ﬁve dendronized PBIs containing 0 to 4 methylenic units

between the imide group of PBI and the 3,4,5-tris(dodecyl-1-

oxy)phenyl group, (3,4,5)12G1-m-PBI with m = 0, 1, 2, 3, and 4,

were synthesized and their self-assembly in solid state was

analyzed. The ﬁrst-generation (3,4,5)12G1 self-assembling dendron

was selected because it is the most widely used in the ﬁeld of

dendronized PBIs.^1a,7,9,10A combination of diﬀerential scanning

calorimetry (DSC), small- (SAXS) and wide-angle (WAXS) X-ray

diﬀraction (XRD) experiments performed with powder and

oriented ﬁbers using laboratory and synchrotron X-ray sources,

together with solid-state ¹H NMR analysis coupled with molec-

ular modeling have been used to demonstrate that all twin-^10a,15

dendronized PBIs self-assemble into helical columns exhibiting a

complex intracolumnar structure. The supramolecular helical columns

self-organize at high temperature via a fast self-assembly process

into 2D columnar lattices. At low temperatures, the columns maintain

most of their supramolecular helical structure from high tempera-

ture and self-organize in 3D lattices via a very slow self-assembly

process. The supramolecular structures of these complex helical

columns and the dynamics of self-assembly are determined by

the number of methylenic units interconnecting the dendron and

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Figure 1. DSC traces collected from (3,4,5)12G1-3-PBI with heating and cooling rates varying from 20 ꢀC/min to 0.2 ꢀC/min. The dotted green circles

mark the phase transitions which are strongly dependent on rate and cooling and heating cycle. Transition temperatures, associated enthalpy changes

k

(in brackets in kcal/mol), and corresponding lattices assigned by XRD are indicated. Phase notations: Φ_x^k, unidentiﬁed crystalline columnar; Φ_s-o

,

crystalline columnar simple orthorhombic; Φ_h^io, columnar hexagonal phase with intracolumnar order; Φ_h, crystalline columnar hexagonal phase and

k

i-isotropic.

the PBI. Only for (3,4,5)12G1-4-PBI can the transition from

the 2D to the 3D lattices be detected by DSC scans performed

with 10 ꢀC/min. Because of the very slow dynamics of (3,4,5)-

12G1-m-PBI with m = 3, 2, and 1, the transition from 2D to 3D

lattices can be detected only by DSC experiments performed with

1 ꢀC/min. For the dendronized PBI with m = 0, the transition

from 2D to 3D periodic arrays is not observed even by DSC

experiments with 1 ꢀC/min. However, the 2D to 3D transition for

self-assembly and in technological developments based on dendro-

nized PBIs.^{1,2,7,9,10,12}

’ RESULTS AND DISCUSSION

Synthesis of Twin-Dendronized Perylene Bisimides (PBI).

A series of perylenebisimides (PBIs) dendronized with first-generation

self-assembling identical dendrons (twin-dendronized^10a,15

)

1

(3,4,5)12G1-0-PBI can be detected by X-ray and solid-state H

containing 0, 1, 2, 3, or 4 methylenic units between their branched

periphery and the PBI imide groups, (Scheme 1, structures

(3,4,5)12G1-m-PBI, where m = 0 to 4), was synthesized. All

dendronized PBIs were prepared in 60 to 99% yield through

Zn(OAc)₂-mediated imidization of perylenetetracarboxylic dia-

nhydride in quinoline at 180 ꢀC with 2 equiv of the correspond-

ing dendritic amine containing 0 to 4 methylenic units between

the branched aromatic moiety and the amino group.

NMR experiments. Because the structure of the supramolecular

columns is not signiﬁcantly changed at the transition from 2D to

3D lattices, aligned crystalline domains can be obtained by the

proper cooling of oriented ﬁber specimens from the 2D into the

3D phase. This combination of dynamics and the complex helical

2D/3D supramolecular structures is expected to have an im-

portant impact both in the elucidation of fundamental aspects of

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Figure 2. DSC traces collected from (3,4,5)12G1-m-PBI with m = 0 (top) and m = 1 (bottom) with heating and cooling rates varying from 30 ꢀC/min

to 1 ꢀC/min. Transition temperatures, associated enthalpy changes (in brackets in kcal/mol), and corresponding lattices assigned by XRD are indicated.

Phase notations: Φ_x^k, unidentiﬁed crystalline columnar; Φ_s-o^k, crystalline columnar simple orthorhombic; Φ_h^io, columnar hexagonal phase with

intracolumnar order; Φ_m^k, crystalline columnar monoclinic phase and i- isotropic.

For m = 0, imidization was performed with 3,4,5-tris(dodecyl-

1-oxy)aniline [(3,4,5)12G1-NH_2,2] to provide (3,4,5)12G1-0-

PBI in 60% yield. Dendritic aniline 2 was prepared by the

graphite catalyzed reduction of (3,4,5)12G1-NO₂(1) with

hydrazine hydrate, as described previously.^15b,16For m = 1,

perylenetetracarboxylic dianhydride was condensed with 3,4,5-

tris(dodecyl-1-oxy)benzylamine [(3,4,5)12G1-CH₂NH₂, 7] to

generate (3,4,5)12G1-1-PBI in 90% yield. Dendritic benzyl-

amine 7 was prepared through the sequential LiAlH₄reduction

and SOCl₂-mediated chlorination of (3,4,5)12G1-CO₂CH₂(3)

according to established procedures.^17,18Substitution of the corre-

sponding dendritic chloride (5) with sodium azide in DMF

provided 3,4,5-tris(dodecyl-1-oxy)benzyl azide (6) in 96% yield.

Azide 6 obtained via substitution of 5 with sodium azide in DMF

was reduced with LiAlH₄in THF at 0 ꢀC to form (3,4,5)12G1-

CH₂NH₂(7) in 89% yield.

For m = 2, 2-[3,4,5-tris(dodecyl-1-oxy)phenyl]ethylamine

[(3,4,5)12G1-CH₂CH₂NH₂, 10] was imidized with perylene-

tracarboxylic dianhydride to provide (3,4,5)12G1-2-PBI in 99%

yield. Previously synthesized¹⁸(3,4,5)12G1-CH₂OH (4) was

oxidized with pyridinium chlorochromate (PCC) to the corre-

sponding benzaldehyde (8)¹⁹(90% yield). 1,2-Addition of nitro-

methane through a nitroaldol reaction provided the dendronized

vinyl nitro 9 (85% yield), which was subsequently reduced with

LiAlH₄to generate (3,4,5)12G1-CH₂CH₂NH₂(10) in 84%

yield. For m = 3 and 4, (3,4,5)12G1-3-PBI and (3,4,5)12G1-4-

PBI were prepared through imidization with 3-[3,4,5-tris(dodecyl-

1-oxy)phenyl]propylamine [(3,4,5Pr)12G1-CH₂NH₂, 16] and

4-[3,4,5-tris(dodecyl-1-oxy)phenyl]butylamine [(3,4,5)12G1-

(CH₂)₄NH₂, 18] in 83% and 96% yield, respectively. Both the

dendritic propyl 16 and butyl 18 amines were synthesized by

similar routes. Methyl 3-(3,4,5-trihydroxyphenyl)propionate (11)

prepared as reported previously¹⁹was tris-alkylated with n-dodecyl

bromide to provide (3,4,5Pr)12G1-CO₂CH₃(12). Subsequent

reduction with LiAlH₄and bromination with CBr₄/PPh₃gener-

ated (3,4,5Pr)12G1-CH₂Br (14).¹⁹Displacement of dendritic

bromide (14) with sodium azide provided the corresponding

dendritic azide (15) in 90% yield. 15 was reduced with LiAlH₄to

produce (3,4,5Pr)12G1-CH₂NH₂(16) in 92% yield. Alterna-

tively the dendritic bromide (14)¹⁹was displaced with potassium

cyanide in DMSO to provide (3,4,5)12G1-CH₂CH₂CH₂CN

(17) in 90% yield, which after reduction with LiAlH₄furnished

(3,4,5)12G1-(CH₂)₄NH₂(18) in 80% yield.

Identification of Supramolecular Assemblies via DSC and

XRD Performed with Different Heating and Cooling Rates.

(3,4,5)12G1-m-PBI (19) with m = 0,^8a,9cand m = 1^8b,9cas well as

related dendronized perylene bisimides with chiral^7k,8bor hydro-

gen-bonding promoting linker groups^7j,8h,8ihave been investi-

gated. Previous studies on derivatives of (3,4,5)12G1-0-PBI and

(3,4,5)12G1-1-PBI were focused largely on the effect of bay-

substitution on photophysical properties.^8a,d,gNevertheless, pre-

liminary evaluation of their self-organized structures revealed what

was deemed a disordered Φ_hliquid crystalline phase for (3,4,5)12G1-

0-PBI and (3,4,5)12G1-1-PBI with a diffuse halo indicating

melted alkyl chains.^8a,b,9cIt was proposed that the columnar

assembly of (3,4,5)12G1-0-PBI might display rotational offset

between layers, while analogues with bulky bay-substituents would

exhibit translationaloffsetandmoreorderedcolumnarassemblies.^8a

The steady-state limited current (SCLC) technique was used

to measure the charge carrier mobility of (3,4,5)12G1-0-PBI

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Table 1. Thermal Transitions and Associated Enthalpy Changes of (3,4,5)12G1-m-PBI (m = 0, 1, 2, 3, 4) Determined by DSC and

XRD

thermal transitions (ꢀC) and corresponding enthalpy changes (kcal/mol)

m

rate (ꢀC/min)

heating^a

cooling

io

0

30

Φ_h^io373 (5.84) i

Φ_h^io371 (5.29) i

Φ_h^io372 (5.40) i

Φ_h^io370 (4.94) i

i 365 (5.36) Φ_h

20

10

5

i 366 (5.40) Φ_h

io

kb

io

k b

Φ_hꢀΦ_s-oꢀΦ_hꢀ372 (5.28) i

i 364 (5.22) Φ_hꢀΦ_s-o

kc

io

Φ_s-oꢀΦ_hꢀ367 (4.67) i

io

kb

io

k b

Φ_hꢀΦ_s-oꢀΦ_hꢀ372 (4.87) i

i 358 (4.85) Φ_hꢀΦ_s-o

kb

io

Φ_s-oꢀΦ_hꢀ361 (4.56) i

io

1

10

1

Φ_x^k10 (1.47) Φ_x^k249 (4.38) Φ_x^k3116 (29.05) Φ_h^io224 (3.93) i

Φ_h^io225 (4.03) i

i 224 (4.06) Φ_h

io

Φ_x^k1ꢀ2 (0.90) Φ_x^k248 (3.46) Φ_x^k3115 (29.62) Φ_h^io225 (4.00) i

i 224 (4.16) Φ_h

Φ_m^k33 (1.86) Φ_h^io225 (4.04) i

Φ_m^k113 (1.07) Φ_m^k36 (6.26) Φ_h^io225 (4.04) i^d

k₁39 (0.47) k₂65 (16.87) Φ_h^io134 (0.29) i

io

k

2

3

4

10

1

i 130 (0.28) Φ_hꢀ27 (2.66) Φ_h

Φ_hꢀ20 (4.38) Φ_h^io134 (0.3) i

k

k₁36 (0.48) k₂62 (19.93) Φ_h^io84 (ꢀ0.53) Φ_s-o^k98 (0.54) Φ_h^io134 (0.27) i

i 131 (0.30) Φ_hꢀ25 (3.56) Φ_h

io

k

Φ_hꢀ22 (3.80) Φ_h^io91 (ꢀ0.18) Φ_s-o^k101 (0.20) Φ_h^io134 (0.28) i

io

10

1

Φ_x^k80 (28.91) Φ_h^io125 (0.55) i

i 121 (0.62) Φ_hꢀ23 (3.96) Φ_h

k

Φ_hꢀ17 (4.44) Φ_h^io73 (ꢀ0.25) Φ_s-o^k84 (0.46) Φ_h^io125 (0.59) i

Φ_x^k78 (26.75) Φ_s-o^k84 (0.37) Φ_h^io125 (0.54) i

i 123 (0.55) Φ_h^io67 (0.2) Φ_s-oꢀ22 (0.76)^cΦ_s-o

k

Φ_s-oꢀ20 (4.63) ^cΦ_s-o^k85 (0.97) Φ_h^io125 (0.55) i

k

10

1

Φ_s-o^k151 (2.27) Φ_s-o^k269 (4.62) Φ_h^io113 (0.65) i

i 109 (0.68) Φ_h^io83 (0.1) Φ_s-oꢀ21 (4.98)^cΦ_s-o

Φ_s-oꢀ15 (6.43) ^cΦ_s-o^k87 (0.14) Φ_h^io113 (0.66) i

k

Φ_s-o^k146 (2.45) Φ_s-o^k268 (5.39) Φ_s-o^k86 (0.08) Φ_h^io113 (0.66) i

i 111 (0.66) Φ_h^io84 (0.1) Φ_s-oꢀ17 (5.85)^cΦ_s-o

k

Φ_s-oꢀ14 (5.48) ^cΦ_s-o^k86 (0.12) Φ_h^io113 (0.68) i

k

^aFirst heating data on the ﬁrst line and second heating data on the second line. ^bThe crystalline Φ_s-ophase of m = 0 was observed only in XRD

experiments. ^cThis ﬁrst-order transition between Φ_s-o^kphases is associated with the crystallization of the alkyl chains; XRD data indicate no change in

lattice symmetry (Supporting Information section 4.2). ^dSecond heating data collected after 3 h annealing at 24 ꢀC. Note: i- isotropic; quantitative

uncertainties are (1 ꢀC for thermal transition temperatures and ∼2% for the associated enthalpy changes reported in kcal/mol.

(m = 0) and (3,4,5)12G1-1-PBI (m = 1).^9cSCLC revealed that

the disordered Φ_hLC-phase for m = 0 exhibited a maximum

benzyl imide linkers, to more signiﬁcant conformational freedom

for m = 2, 3, 4, which is facilitated by the more ﬂexible ethyl,

propyl, and butyl imide linkers. The importance of conducting

DSC studies with slow heating rate is exempliﬁed by the analysis of

(3,4,5)12G1-3-PBI (Figure 1). As expected, the propyl imide

linkage between the polyaromatic PBI core and the dendritic

periphery provides substantial conformational freedom. Both

during ﬁrst and second heating and ﬁrst cooling scans, the

transition from the high-temperature thermodynamically stable

charge carrier mobility of 0.2 cm²V^ꢀ1^ꢀ1, whereas for m = 1

s

mobilities even higher than amorphous silicon, 1.3 cm²V^ꢀ1s^ꢀ1

was observed.^9cThe structural origin for the enhancement of the

mobility of m = 1 is not known because the DSC and XRD

analysis reported previously for (3,4,5)12G1-m-PBI with m = 0

and 1 showed only one phase for each compound.^8a,b,9cThese

results demonstrate the promise of dendronized PBIs in molec-

ular electronics. However, to fully empower the use of dendro-

nized and similar substituted PBIs in tailored optoelectronic

materials, the understanding of the interplay between the den-

dritic periphery unit, thermal history, and the detailed structure

of the supramolecular assembly must be elucidated.

io

columnar hexagonal 2D phase with intracolumnar order²²(Φ_h)

to the isotropic melt (i) and its corresponding enthalpy change

exhibits very little dependence on rate (Figure 1). This demon-

io

strates that, at high temperature, the Φ_his the thermodynami-

Self-organized systems often exhibit polymorphism^20,21that

requires combined analysis by DSC and XRD with various

heating and cooling rates. When subunits are connected through

conformationally rigid tethers, slower heating and cooling rates

may be required to resolve otherwise kinetically inaccessible

supramolecular structures. In considering the library of dendro-

nized PBIs described herein, (3,4,5)12G1-m-PBI (m = 0 to 4),

we expect a transition from reduced conformational mobility for

m = 0, 1, which could be due to restricted phenyl imide and

cally controlled product of self-assembly. However, the transition

k

from the crystalline columnar simple orthorhombic phase, Φ_s-o

,

to Φ_h^ioand the reverse transition show a much stronger depen-

dence on rate. Cooling rates with 20 ꢀC/min and 10 ꢀC/min do

not detect this transition (see green circles in Figure 1). In addition,

the enthalpy change associated with this transition is strongly rate

dependent, increasing with the decrease in rate. At low tempera-

ture, the thermodynamic product is the 3D assembly while the

kinetic one is the 2D structure.

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Figure 3. DSC traces collected from (3,4,5)12G1-m-PBI with m = 2, 3, and 4 with 10 ꢀC/min (blue colored traces) and 1 ꢀC/min (red colored traces).

Transition temperatures, associated enthalpy changes (in brackets in kcal/mol), and corresponding lattices assigned by XRD are indicated. Phase

notations: k₁and k₂, unidentiﬁed crystalline phases; Φ_x^k, unidentiﬁed crystalline columnar phase; Φ_s-o^k, crystalline columnar simple orthorhombic;

k

Φ_h^io, columnar hexagonal phase with intracolumnar order; Φ_h, crystalline columnar hexagonal phase and i- isotropic.

(3,4,5)12G1-0-PBI and (3,4,5)12G1-1-PBI possess restricted

phenyl imide and benzyl imide linkages. Therefore, the dynamics

of (3,4,5)12G1-0-PBI is so slow that DSC experiments with rates

between 10 ꢀC/min and 1 ꢀC/min are not able to detect a

transition is not detected in the second heating DSC experiments

performed with 10 ꢀC/min (bottom of Figure 2).

For (3,4,5)12G1-1-PBI, XRD experiments revealed that the

formation of the crystalline Φ_m^kphase is slow, requiring anneal-

ing of 3 h at 24 ꢀC. Subsequent second heating DSC experiments,

carried out after 3 h annealing at 24 ꢀC, revealed an additional

crystalline phase that was observed only by XRD experiments

io

(top of Figure 2). The enthalpy change associated with the Φ_h

-

k1

isotropic transition, indicated on the top of Figure 2 for m = 0,

exhibits a small rate dependence. The slight decrease of this trans-

ition temperature and of its associated enthalpy change (Table 1

and Figure 2) was observed in subsequent heating and cooling

cycles and upon reducing the rate (Table 1). These data suggest

that a very small extent of thermal decomposition may occur at

very high temperatures only for m = 0. For (3,4,5)12G1-1-PBI,

the ﬁrst heating and cooling DSC scans carried with 10 ꢀC/min

and 1 ꢀC/min are similar (bottom of Figure 2). However, during

the second heating and cooling scans, the DSC experiments

carried out with 1 ꢀC/min revealed a crystalline columnar

monoclinic phase, Φ_m^k, formed at low temperatures. At 33 ꢀC,

on the second heating scan with 1 ꢀC/min, a transition from the

transition Φ_mꢀΦ_m^kat 13 ꢀC and a signiﬁcant increase of the

k

enthalpy change associated with the Φ_mꢀΦ_h^iophase transition

from 1.86 kcal/mol before annealing to 6.26 kcal/mol after

annealing (Table 1 and Figure 2).

Pronounced changes are observed between the DSC traces

obtained with these two rates for (3,4,5)12G1-m-PBI with m = 2

and 3 (Figure 3). (3,4,5)12G1-2-PBI behaves similarly with

(3,4,5)12G1-1-PBI. Only a Φ_h^iophase is observed on ﬁrst heating

and cooling, on heating scans carried out with 10 ꢀC/min, and on

the ﬁrst cooling scan with 1 ꢀC/min. However, ﬁrst and second

heating DSC scans with 1 ꢀC/min demonstrate the very slow

formation of a Φ_s-o^kphase on heating (exotherm at 91 ꢀC) and

its melting into a Φ_h^iophase at 101 ꢀC. Therefore, the formation

of the Φ_s-o^kphase is kinetically controlled. The Φ_h^ioarray is the

k

Φ_m^kphase to a Φ_h^iophase is observed. The Φ_mꢀΦ_h^iophase

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Table 2. Structural Analysis of (3,4,5)12G1-m-PBI (m = 0, 1, 2, 3, and 4) by XRD

d₁₀, d₁₁, d₂₀(Å)^f

d₂₀₀, d₁₁₀, d₀₂₀, d₄₀₀, d₁₃₀, d₆₀₀, d₂₀₁, d₁₁₁, d₂₁₁, d₀₀₁, d₀₀₂, d₀₀₃(Å) ^g

d₁₀, d₂₀, d₃₀, d₁₁, d₄₀, d₅₀, d₄₁, d₅₁, d₆₁, d₇₀(Å)^h

d₁₀₀, d₀₂₀, d₁₂₀, d_1-20, d₂₀₀, d₀₁₁, d_2ꢀ20, d₁₀₁, d₁₁₁, d₀₂₁, d₀₄₀, d₂₄₀, d₀₀₂, d₀₂₂(Å)ⁱ

d₂₀₀, d₂₀₁, d₂₁₁, d₀₀₂, d₃₁₀, d₀₁₂, d₂₀₂, d₄₀₀, d₄₀₁, d₃₁₂, d₄₀₂(Å)^j

d₁₁, d₂₁, d₀₃, d₃₂, d₄₂, d₅₁(Å)^k

d₀₀₁, d₁₁₀, d₀₁₁, d₁₁₁, d₀₀₂, d₂₁₀, d₂₁₁, d₁₁₂, d₀₂₀(Å)^l

d₁₂₀, d₂₁₂, d₂₂₀, d₀₁₃, d₁₁₃, d₀₂₂, d₄₁₀, d₂₁₃, d₄₀₂, d₁₃₀, d₃₃₀, d₀₄₀, d₂₄₀(Å)^m

d₁₀₀, d₀₁₀, d₁₁₁, d₂₀₀, d₂₁₁, d₀₀₈, d_{00 14}, d_{00 15}, d_{00 16}(Å)ⁿ

compound

T (ꢀC) phase^a

a, b, c (Å)^b

33.5

D_col(Å)^ct (Å)^d/μ^e

io

(3,4,5)12G1-0-PBI

25

Φ_h

33.5

35.1

33.5

4.8/2

28.9, 16.7^f

30.4, 17.5^f

io

280

25

35.1

k

Φ_s-o

56.9, 33.5, 19.3

46.7, 12.4

46.3, 12.3

45.7, 12.8

31.7

28.5, 28.9, 16.8, 14.2, 10.8, 9.5, 16.0, 16.1, 14.4, 19.3, 9.7, 6.4 ^g

46.8, 23.4, 15.5, ꢀ, 11.7, 9.3, 8.5, 7.5, ꢀ, 6.7^h

46.5, 23.2, 15.4, 11.9, 11.6, 9.3, 8.4, 7.4, ꢀ, 6.6^h

45.9, 23.0, 15.3, 12.3, ꢀ, ꢀ, 7.4, 6.5^h

27.5, 15.9, 13.7^f

32.5, 23.4, 19.3, ꢀ, 16.2, 13.6, 13.2, 13.0, 12.6, 12.1, 11.7, 9.6, 7.1, 6.8ⁱ

31.9, 23.8, 19.9, 18.3, 15.9, 13.4, ꢀ, 12.8, 12.5, 12.1, 11.9, 9.9, 7.0, 6.7ⁱ

42.7

(3,4,5)12G1-1-PBI

(3,4,5)12G1-2-PBI

ꢀ15

20

Φ_x^{k o}

60

io

140

25

Φ_h

31.7

32.5

3.5/1

k

Φ_m

32.5, 46.9, 14.2

32.1, 47.8, 14.0

k1 p

ꢀ40

20

Φ_m

o

k₁

n

50

k₂

41.9

k

97

Φ_s-o

70.2, 41.1, 45.5

39.1

40.5

39.1

41.7

35.3, 27.9, 23.1, 22.8, 20.5, 20.0, 19.2, 17.7, 16.5, 15.2, 13.9^j

33.8, 19.5, 16.9^f

36.1, 20.8, 18.0^f

52.6, 33.9, 23.9, 20.9, 20.5, 17.0, 15.0^k

60.5, 37.2, 35.1, 31.7, 30.3, 28.3, 25.6, 23.5, 21.6^l

20.7, 20.6, 18.5, 18.3, 17.7, 17.5, 17.0, 16.4, 15.9^m

34.7, 20.0, 17.3^f

io

130

30

Φ_h

41.7

3.7/2

(3,4,5)12G1-3-PBI

(3,4,5)12G1-4-PBI

20

Φ_x^{k o}

76.9, 71.8

74.4, 43.2, 60.6

k

80

Φ_s-o

42.9

40.0

io

110

20

Φ_h

40.0

k o

Φ_s-o

40.8, 34.0, 57.1

74.9, 34.3, 63.1

74.5, 43.0, 40.2

40.8, 34.0, 23.8ⁿ

ko

60

ꢀ, 34.3, ꢀ, 37.5, 23.5, 7.9, 4.5, 4.2, 3.9ⁿ

ꢀ, 36.9, 29.3, ꢀ, ꢀ, ꢀ, 23.1, ꢀ, 21.5^l

ꢀ, ꢀ, 18.6, ꢀ, ꢀ, ꢀ, ꢀ, ꢀ, ꢀ, 14.1, 12.4, 10.7, 10.3^m

k

80

43.0

42.9

3.8/2

io

90

Φ_h

42.9

37.2^f

k

^aΦ_h^io: columnar hexagonal phase with intracolumnar order; Φ_s-o^k: crystalline columnar simple orthorhombic phase; Φ_h: crystalline columnar

hexagonal phase; Φ_x^k: unidentiﬁed crystalline columnar phase; Φ_m^k: crystalline columnar monoclinic phase; k₁and k₂: unidentiﬁed crystalline phases.

^bLattice parameters (with uncertainty of ∼1%) calculated using: d_hk= 1/(4(h²+ k²+ hk)/(3a)²)^1/2for hexagonal, d_hk= 1/((h/a)²+ (k/b)²)^1/2for the

indexing of the equatorial peaks of Φ_x^k, d_hkl= 1/((h/a)²+ (k/b)²+ (1/c)²)^1/2for orthorhombic lattices, and d_hkl= 1/((h/a sin γ)²+ (k/b sin γ)²+

(1/c)²ꢀ (2kh cos γ/ab sin²γ))^1/2for monoclinic phases with γ = 91.8ꢀ and 95.1ꢀ for Φ_m^kand Φ_m^k1, respectively. ^cColumn diameter calculated using:

D

_col= a for Φ_h^io, and D_col= a/3^1/2for Φ_s-o^k. ^dAverage column stratum thickness calculated from the meridional axis features of the WAXS ﬁber patterns.

^eAverage number of dendrimers forming the supramolecular column stratum with thickness t, calculated using: μ = N_AD_col²(3^ꢀ1/2)tF/(2M_wt).

N_A= 6.022 ꢁ 10²³mol ^ꢀ1= Avogadro’s number. F and M_wtare the density and molecular weight. The values for m = 0, 1, 2, 3, and 4 are, respectively,

F = 1.06, 1.02, 1.02, 1.03, and 1.02 g/cm³, and M_wt= 1648, 1676, 1704, 1732, and 1760. ^fExperimental diﬀraction peak d-spacing for the Φ_h^iophase.

^gExperimental diﬀraction peak d-spacing for the Φ_h^kphase. ^h,kExperimental diﬀraction peak d-spacing for the Φ_x^kphase. ⁱExperimental diﬀraction peak

k

d-spacing for the Φ_mphase. ^j,l,m,nExperimental diﬀraction peak d-spacing for the Φ_s-ophase. ^oPhases observed only in the ﬁrst heating of the

as-prepared compound. ^pΦ_m^k1phase observed in the second heating after 3 h annealing at 24 ꢀC.

thermodynamic product at high temperature and the kinetic one

at low temperature.

The transition from (3,4,5)12G1-3-PBI to (3,4,5)12G1-4-PBI

eliminates almost completely the diﬀerence between the DSC

traces recorded with 10 ꢀC/min and 1 ꢀC/min. The faster dynamics

A faster dynamics is seen in the DSC scans of (3,4,5)12G1-3-

PBI. No crystallization is observed during the cooling scan with

10 ꢀC/min for this compound, while a transition from Φ_h^ioto

k

of (3,4,5)12G1-4-PBI allows the formation of the Φ_s-ophase

both on heating and cooling with 10 ꢀC/min and with 1 ꢀC/min

(Figure 3). Therefore, while in the case of (3,4,5)12G1-m-PBI

with m = 0, 1, 2, and 3 the crystalline 3D assembly is the

thermodynamic product that is formed by a slow self-assembly

process from the 2D kinetic product, in the case of m = 4 the

assembly of the 3D structure is very fast. The high-temperature

Φ_h^iois the thermodynamic product in all dendronized PBI and

forms very fast. The low-temperature crystalline phases observed

only in the ﬁrst heating scans but not in subsequent heating and

k

Φ_s-ois already observed on cooling with 1 ꢀC/min. On the

second heating scan performed with 10 ꢀC/min, a crystallization

io

exotherm is observed at 73 ꢀC, followed by melting into a Φ_h

phase at 84 ꢀC. The second heating scan with 1 ꢀC/min does not

exhibit the crystallization exotherm but only the melting at 85 ꢀC.

This melting is accompanied by an enthalpy change of 0.97 kcal/

mol that is more than twice larger than the enthalpy change of the

melting calculated with 10 ꢀC/min (0.46 kcal/mol).

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Figure 4. Wide-angle XRD patterns collected from the oriented ﬁber of (3,4,5)12G1-0-PBI prepared by extrusion at 25 ꢀC from the as-prepared sample

indicating the gradual development of crystalline order only upon heating and annealing at various temperatures (a), and the corresponding meridional

plots at the indicated temperatures (b, c). In c, the dotted vertical line indicates the expected position of the πꢀπ stacking features, and ξ = correlation

length along the column axis was calculated from the full width at the half-maximum (fwhm) of the indicated diﬀraction feature. The yellow arrows from

a and b indicate the oﬀ-meridional features observed on L = 4 only in the Φ_s-o^kphase.

cooling scans are detailed in section 4.1 of the Supporting

Information.

Table 1 summarizesallphasetransitionsobtainedwith10ꢀC/min

and 1 ꢀC/min together with their enthalpy changes. The detailed

phase assignment and structural analysis of all the structures are

reported in Table 2. The next subchapters present and discuss

this analysis in increasing order of m.

Analysis and Simulation of SAXS and WAXS Patterns

Recorded from Oriented Fibers of (3,4,5)12G1-0-PBI. The

XRD patterns collected from the oriented fiber of (3,4,5)12G1-

0-PBI, prepared by extrusion at 20 ꢀC, are shown in Figure 4. In

the first heating of the as-prepared fiber, a Φ_h^iophase is observed

from 20 to 135 ꢀC. Upon heating from 135 to 200 ꢀC, additional

sharp off-meridional features are observed (Figure 4a, b). The

(L = 4), respectively (Figures 4 and 5). These values indicate that

t = 4.8 Å stacking distance between the PBI units along the

column axis is signiﬁcantly larger than the expected value of

about 3.5 Å indicated in Figure 4c.^8a,d,g

Note from Table 2 that the diameter of the supramolecular

column (D_col) remains almost unchanged at the transition from

the 2D to the 3D lattice. Calculations based on the experimental

density (Table 2) of (3,4,5)12G1-0-PBI indicate that within a 4.8

Å column stratum (t) there are on average two dendronized PBIs

(μ = 2). The features observed in the XRD ﬁber pattern suggest

that the (3,4,5)12G1-0-PBI forms a supramolecular tetramer

repeat unit with a thickness of 9.7 Å. This tetramer is generated

from two pairs of side by side dendronized PBI stacked on top

of each other and rotated with a constant angle δ (Figure 6).

Therefore, along the c-axis of 19.3 Å of the unit cell there are two

supramolecular tetramers with a helical parameter j = 90ꢀ. The

helical parameter j characterizes the rotation of adjacent tetra-

mers within the supramolecular column (Figure 6). This para-

meter was calculated by taking into account the 2-fold symmetry

of the dendronized PBI that translates into a 2-fold symmetry for

the supramolecular tetramer. The 2-fold symmetry of the tetra-

mer demonstrates that after two consecutive rotations of j = 90ꢀ,

the structure repeats itself. Therefore, it appears that two stacked

tetramers form the unit cell along the c-axis. The average corre-

lation length along the axis of the supramolecular columns, ξ,

spans in average through about 28 column strata, or equivalently

28/4 = 7 unit cells. The average correlation length was calculated

from the width of the 9.7 Å tetramer stacking feature using the

k

WAXS fiber pattern obtained at 20 ꢀC was indexed to a Φ_s-o

io

k

phase (Figure 5b, Table 2). Interestingly, a Φ_hꢀΦ_s-otransi-

tion was not detected in DSC experiments performed with rates

between 30 ꢀC/min and 1 ꢀC/min (Figure 2). XRD experiments

io

showed that at around 250 ꢀC, the Φ_s-o^ktransforms into a Φ_h

phase (Figure 4). Upon cooling from 250 to 20 ꢀC with rates

k

lower than 20 ꢀC/min, the Φ_s-ophase, identified in the first

heating in the temperature range from 135 to 200 ꢀC, is observed

again at 20 ꢀC. These results indicate a very low rate of crystal-

lization from the Φ_h^iophase.

The π-stacking correlations of the PBI core are expected to be

around values of 3.5 Å.^8a,d,gIn the case of (3,4,5)12G1-0-PBI

(m = 0), two stacking features are observed on the meridional

axis of the oriented ﬁber XRD pattern at 9.7 Å (L = 2), and 4.8 Å

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Figure 5. Wide-angle XRD patterns collected from the oriented ﬁber of (3,4,5)12G1-0-PBI (a, b), simulation of the WAXS ﬁber pattern and molecular

model of the supramolecular column (c). For clarity, the pattern from b is shown with higher contrast. In a and c, the vertical arrows indicate the layer line

principal maxima identiﬁed in the high-temperature Φ_h^iophase. Color code used in the molecular model from c: O atoms, red; H atoms, white; N atoms,

blue; C atoms of the PBI, green; C atoms of the dendron phenyl, orange and light blue (Figure 6); all other C atoms, gray.

io

k

similarity of the WAXS ﬁber patterns of the Φ_hand Φ_s-o

phases compared in Figure 5a suggests that the majority of the

diﬀraction features of the Φ_s-o^kphase are generated by intraco-

lumnar correlations. Nevertheless, the additional meridional diﬀrac-

tion features observed on the ﬁrst and third layer lines and oﬀ-

k

meridional features on the fourth layer line observed in the Φ_s-o

phase (indicated by the yellow arrows in Figure 4a,b), as well as

the signiﬁcant sharpening of the features observed on the fourth

layer line (Figures 4a and 5a) indicate an increase of the degree of

io

intra- and intercolumnar order at the Φ_hꢀΦ_s-o^ktransition.

Analysis and Simulation of SAXS and WAXS Patterns

Recorded from Oriented Fibers of (3,4,5)12G1-1-PBI. A com-

bination of XRD analysis and molecular modeling demonstrated

that the change from m = 0 to m = 1 induces a tilted conformation

of the dendron in (3,4,5)12G1-1-PBI (Figure 7e). This is in

agreement with the change from a phenyl ring axis coplanar with

the perylene to one highly inclined to the perylene plane. The

presence of strong and sharp meridional features at 3.5 Å in the

XRD fiber patterns (4th layer line in Figures 7f and 8a) indicates

that the stacking distance of the PBI core is reduced from t = 4.8 Å

for (3,4,5)12G1-0-PBI (Figures 4 and 5) to t= 3.5 Å for (3,4,5)12G1-

1-PBI. Calculations based on the experimental density (Table 2)

demonstrated that within every t = 3.5 Å column stratum there is

one (3,4,5)12G1-1-PBI unit (μ = 1).

Figure 6. Schematic of the supramolecular dimers and tetramers

assembled from dendronized PBI and of their self-assembly into supra-

molecular helical columns. For clarity, the alkyl chains of the dendron are

not shown. The aromatic part of the dendrons is schematically illustrated

by the light blue and orange rectangles, and the aromatic PBI core is

illustrated by the green rectangles.

The WAXS ﬁber pattern collected from (3,4,5)12G1-1-PBI in

the Φ_h^iophase exhibits a weak meridional maximum on the L = 4

(7.0 Å, Figure 7d,f) at double value of the 3.5 Å πꢀπ stacking

distance of the PBI core. Additional oﬀ-meridional weak and

broad features were observed on the second and third layer lines.

The two simulations of the WAXS ﬁber pattern collected in the

Φ_h^iophase presented in Figure 7d were based on the two mol-

ecular models shown in Figure 7e. The simulation based on these

two alternative models for the supramolecular columns of the

m = 1 ﬁt the intensity proﬁles of the L = 2, 3, and 8 layer lines.

However, only the simulation based on the molecular model 1

shown in Figure 7e ﬁts the weak meridional maxima observed on

L = 4. Therefore, the supramolecular helical columns forming the

azimuthal integration of the XRD ﬁber pattern (ξ ∼ fwhm^ꢀ1

indicated in Figure 4c). This method was preferred to the

horizontal or vertical line proﬁle due to the fact that this diﬀrac-

tion feature is broad.

Figure 5c shows the simulation of the WAXS ﬁber pattern

collected from (3,4,5)12G1-0-PBI. The simulation was calcu-

lated from the molecular model presented in Figure 5c. The

agreement between the experimental and simulated position of

the layer line principal maxima is indicated by the vertical arrows

in Figure 5a,c. This simulation suggests that the rotation around

the column axis of adjacent tetramers is j = 90ꢀ and that the

io

Φ_hphase are generated by a statistical mixture of the con-

formations proposed in Figure 7e for the dimers formed by m = 1

compound. These simulations suggest that the dimer rotation j

is 45ꢀ and that the intradimer rotation δ is 60ꢀ (Figure 7e). The

average correlation length ξ of the diﬀuse oﬀ-meridional features

observed on the L = 2 and 3 is ∼10 strata. This indicates that the

average correlation length of the helical order is about one third

io

k

intratetramer rotation is δ = 65ꢀ. At the transition Φ_hꢀΦ_s-o

,

the features observed in WAXS ﬁber pattern collected in the

high-temperature Φ_hphase are preserved, indicating that the

io

supramolecular columns have similar helical organizations. The

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Figure 7. Wide- (a, d) and small-angle (b) X-ray diﬀraction patterns collected from the oriented sample of (3,4,5)12G1-1-PBI at the indicated

temperatures, corresponding plot, and diﬀraction peaks of the Φ_m^kphase (c), molecular models used in the ﬁber pattern simulations shown in d (e), and

the meridional plots of the patterns collected in the Φ_m^kand Φ_h^iophases (f). Color code used in the model from e: O atoms, red; H atoms, white;

N atoms, blue; C atoms of the PBI, green; C atoms of the dendron phenyl, orange and light blue; all other C atoms, gray.

Figure 8. Comparison of the experimental and simulated XRD patterns collected from the oriented ﬁber of (3,4,5)12G1-1-PBI at 20 ꢀC in the columnar

monoclinic crystalline phase, Φ_m^k(a), and detail of the molecular model used in the simulation (b, c).

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Figure 9. Small-angle XRD ﬁber patterns collected at the indicated thermal cycle for the (3,4,5)12G1-2-PBI (a) and (3,4,5)12G1-3-PBI (b).

The patterns were collected on second heating with 10 ꢀC/min that followed a ﬁrst cooling with 10 ꢀC/min from the high-temperature Φ_h^iophases.

of the ξ ∼34 strata corresponding to the 3.5 Å πꢀπ stacking

features (Figure 7f). Therefore, it is most probably that the

conformation proposed in model 1 from Figure 7e disrupts the

helical packing of model 2 by acting as a structural “defect” that

generates the weak feature observed on the fourth layer line.

Figure 8 details the simulation of the WAXS ﬁber pattern

from (3,4,5)12G1-2-PBI and (3,4,5)12G1-3-PBI (Figure 9) de-

monstrate that the formation of the 3D column-to-column

correlations requires annealing at high temperature. Combined

DSC and variable temperature XRD experiments demonstrated a

significant dependence between the kinetics of crystallization

and the value of m (Figure 3 and section 4.2 of the Supporting

Information). In the case of m = 2, a Φ_s-o^kphase with P2₁2₁2₁

symmetry forms only upon slow heating above the 91 ꢀC exother-

mic transition (ΔH = ꢀ0.18 kcal/mol, Figure 3). In addition,

independent of the cooling rate, this phase does not form upon

cooling from the isotropic melt (Supporting Information Figure

SF7). In the case of m = 3, a Φ_s-o^kphase with P2₁2₁2 symmetry

forms upon heating with fast rates above the exothermic transi-

tion from 73 ꢀC (ΔH = ꢀ0.25 kcal/mol, second heating DSC

trace with 10ꢀ/min shown in Figure 3). In contrast to m = 2, the

Φ_s-o^kphase formed by m = 3 is observed also upon slow cooling

from the isotropic melt (Supporting Figures SF8 and SF9). The

k

collected in the low-temperature Φ_mphase with P2₁/b sym-

metry. Four (3,4,5)12G1-1-PBI molecules stack at 3.5 Å spacing

along the column axis to form a column repeat c. The criss-cross-

like packing of the dendronized PBIs within the supramolecular

column with 2₁helical symmetry, provided by the simulation of

the XRD data, is shown in Figure 8b. In order to minimize the

intracolumnar steric constrains, each (3,4,5)12G1-1-PBI from

k

the supramolecular column is shifted in the aꢀb plane of the Φ_m

unit cell with respect to the center of the column, as shown in the

top view of the unit cell from Figure 8c. Along the c-axis, the

helical symmetry is generated via rotation by j = 180ꢀ of pairs of

stacked (3,4,5)12G1-1-PBI (each pair forming a dimer-like struc-

ture with δ ∼ 80ꢀ, Figure 6) as detailed in Figure 8b. Further-

io

WAXS fiber patterns collected from m = 2 in the Φ_s-o^kand Φ_h

k

phases are shown in Figure 10a and 10c, respectively.

more, along the b axis of the Φ_mphase, the P2₁/b symmetry

The indexing of the Φ_s-o^kphase of (3,4,5)12G1-2-PBI with a

lattice symmetry consistent with the P2₁2₁2₁chiral space group

is shown in Figure 11. Interestingly, t = 3.6 Å πꢀπ stacking

correlation features of the PBI core are seen in the high-

temperature Φ_h^iophase (Figure 10d), but not in the low-tempera-

translates into alternate rows of respectively left- and right-handed

supramolecular helical columns, as indicated in the side view

io

k

along the b-axis from Figure 8c. Therefore, upon the Φ_hꢀΦ_m

transition the dendronized PBIs conserve their 3.5 Å πꢀπ

stacking distance (Figure 7f) but undergo signiﬁcant changes

in respect to their helical packing and centering within the

column, as well as in respect to the 3D organization of the helical

k

ture Φ_s-ophase (Figure 10c). As in (3,4,5)12G1-m-PBI with

m = 0 and 1, (3,4,5)12G1-2-PBI also exhibits a meridional maxi-

k

io

mum at 7.6 Å on the L = 6 in the P2₁2₁2₁low-temperature Φ_s-o

supramolecular columns (“triangular”-like packing in Φ_hand

io

“rectangular”-like packing in Φ_m^k). These diﬀerences in the

arrangement within the column and of the 3D packing of the

supramolecular columns forming the 2D columnar hexagonal

array with intracolumnar order (Φ_h^io, Figure 7d) and of the 3D

columnar monoclinic phase (Φ_m^k, Figure 8) are responsible for

phase, and at 7.2 Å in the Φ_hphase at high temperature

(Figure 10). These features, combined with the experimental

density demonstrate that (3,4,5)12G1ꢀ2-PBI self-assemble in a

supramolecular tetramer (Table 2). Remarkably, the presence of

the tetramer stacking features observed at 7.2 Å in the Φ_h^iohigh-

temperature phase suggests that the tetramer packing is preserved

io

the extremely slow kinetic observed at the Φ_hꢀΦ_m^ktransition

io

both below and above the ﬁrst-order transition Φ_s-o^kto Φ_h. The

(Figure 2).

short-range order within the inner aromatic region, jacketed by a

liquid-like aliphatic sheath, is preserved due to the strong aromatic

πꢀπ interactions between the PBI units.

Analysis and Simulation of SAXS and WAXS Patterns

Recorded from Oriented Fibers of (3,4,5)12G1-2-PBI. SAXS

fiber patterns collected during second heating with 10 ꢀC/min

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Figure 10. Wide-angle X-ray diﬀraction patterns collected from an oriented ﬁber of (3,4,5)12G1-2-PBI at the indicated temperatures (a, c) and the

corresponding meridional plots (b, d).

Simulation of the oriented ﬁber XRD pattern collected in the

low-temperature Φ_s-ophase with P2₁2₁2₁symmetry based on

between model and experiment in Figure 12 is that the intensity

on higher layer lines in the experimental pattern are weaker than

those in the simulated one. The reason is that we have not included

the DebyeꢀWaller factor (thermal disorder) in the simulation.

The eﬀect of this factor is a reduced diﬀraction intensity at increas-

ing angles. Further reﬁnement of this model will be reported in a

more specialized publication.

k

the molecular model of (3,4,5)12G1-2-PBI is presented in

Figure 12. The ﬁber pattern from Figure 12, collected on a syn-

chrotron, also demonstrates the formation of large well-aligned

domains by cooling the oriented ﬁber obtained in the Φ_h^iophase,

from 95 ꢀC, which is above the temperature of the monotropic

io

transition Φ_hꢀΦ_s-o^kat 91 ꢀC (indicated in Figure 3), to 25 ꢀC.

It is important to notice that the absence of 3.5 Å πꢀπ

The molecular model of the supramolecular columns produced

by (3,4,5)12G1-2-PBI consists of undulated distorted 6₁helical

columns generated by supramolecular tetramers with their

centers positioned at a radius of 2.7 Å from the center of the

supramolecular columns. The molecular model as well as the

electron density distribution that provided the helix radius of

2.7 Å will be detailed in a later section. Figure 12 illustrates the

good agreement between the experimental XRD ﬁber pattern

collected in the Φ_s-o^kphase with P2₁2₁2₁symmetry and the ﬁber

pattern calculated from this model. There are several diﬀerences

between the intensity of the experimental and simulated diﬀrac-

tion features. For example, the (211) diﬀraction peak was

observed experimentally but is weak or absent in the simulated

ﬁber pattern presented in Figure 12. The other main discrepancy

stacking and the presence of the 7.5 Å tetramer features in the

k

ﬁber pattern of the Φ_s-ophase indicate that the PBI cores are

stacked at 4.0 Å within tetramer and at 3.5 Å between tetramers.

On the other hand, the presence of 7.2 Å tetramer and 3.6 Å πꢀπ

stacking features in the ﬁber pattern of the Φ_h^iophase indicate

that the PBI cores within and between tetramers are equally

spaced at 3.6 Å along the column axis, suggesting a self-repairing

process.²³The broad intensity proﬁle of the 7.2 Å features

(Figure 10d) also suggest that this strict 3.5 Å and 4.0 Å stacking

alteration, demonstrated for the Φ_s-o^kphase, is relaxed above the

k

io

Φ_s-oꢀΦ_htransition. This indicates that most probably a

signiﬁcant stacking alteration is still preserved in the Φ_h^iophase

and that the self-repairing process is only partial.

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Figure 11. SAXS pattern collected from an oriented ﬁber of (3,4,5)12G1-2-PBI with the diﬀraction peaks indexed (left) and the corresponding

diﬀraction plot, indicating the agreement between the position of the calculated and experimental diﬀraction peaks (right). Fiber axis, temperature,

lattice symmetry, and parameters are indicated.

established in other classes of self-assembling dendron^24,25and

dendrimers.²⁶Similar to the structures generated from (3,4,5)12G1-

m-PBI with m = 0 and 2, (3,4,5)12G1-3-PBI also forms a

supramolecular tetramer (Table 2). Furthermore, the wide angle

meridional feature observed at 7.6 Å in the high-temperature

io

Φ_hphase indicates that the packing of the supramolecular

k

tetramer is preserved upon the Φ_s-oꢀΦ_h^iotransition (Figure 13

and Supporting Information Figure SF9). It is important to

notice that while (3,4,5)12G1-2-PBI exhibits the 3.6 Å πꢀπ

stacking features in the high-temperature Φ_h^iophase (Figure 10c,d),

(3,4,5)12G1-3-PBI does not exhibit significant πꢀπ stacking

features (Figure 13c,d). This difference suggests that the increase

of the number of methylenic units m from 2 to 3 provided add-

itional steric constrains which inhibit the self-repairing process

observed for m = 2.

Figure 15 details the comparison of the experimental and

simulated ﬁber patterns of m = 3 collected in small- and wide-

angle in the Φ_s-o^kphase. The detailed molecular model used in

the simulation will be presented and discussed in a later section.

The simulation shown in Figure 15 reveals that similarly with the

columns formed by m = 2, the columns of m = 3 are generated via

helical packing of supramolecular tetramers. The thickness of

the tetramers slightly increases from 7.5 Å for m = 2 to 7.6 Å for

m = 3. However, the helical parameter j is signiﬁcantly reduced

Figure 12. Comparison of the simulated and experimental ﬁber pat-

terns of (3,4,5)12G1-2-PBI collected at 80 ꢀC in the Φ_s-o^kphase.

from 60ꢀ for m = 2 to 22.5ꢀ for m = 3. This signiﬁcant diﬀerence

Analysis and Simulation of SAXS and WAXS Patterns

k

Recorded from Oriented Fibers of (3,4,5)12G1-3-PBI.

(3,4,5)12G1-3-PBI self-assemble in a supramolecular column

similar to that generated by (3,4,5)12G1-2-PBI. At low tempera-

ture, (3,4,5)12G1-3-PBI exhibits a columnar crystal phase with

intra- and intercolumnar correlations (Figure 13a) and at high

can be attributed to the change in the symmetry of the Φ_s-o

phases from P2₁2₁2₁for m = 2 to P2₁2₁2 proposed for m = 3. It is

most probable that the 2.7 Å shift in the aꢀb plane of the center

of the tetramers formed by m = 2 in respect with the column

center, which is a direct consequence of the P2₁2₁2₁symmetry, is

smeared out by the increased conformational freedom of the

dendron-PBI linker for m = 3. This partial “decoupling” of the

transfer of structural information from the PBI core to the dendritic

part of m = 3 can explain this signiﬁcant reduction of the helical

parameter j.

io

temperature the Φ_hphase (Figure 13c). Indexing of the low-

temperature phase (Figure 14) is consistent with a Φ_s-o^kphase

with P2₁2₁2 symmetry. It seems that the helicity from the

aromatic core of (3,4,5)12G1-3-PBI generated by the intrinsic

2-fold symmetry is transferred to the aliphatic periphery. Com-

bination of this transfer of helical information with the subse-

quent strong coupling of undulated helical columns induces the

Analysis and Simulation of SAXS and WAXS Patterns Re-

corded from Oriented Fibers of (3,4,5)12G1-4-PBI. The WAXS

fiber patterns collected from the oriented fiber of (3,4,5)12G1-4-PBI

k

formation of the Φ_s-ophase. This mechanism was previously

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Figure 13. Wide-angle X-ray diﬀraction patterns collected from the oriented sample of (3,4,5)12G1-3-PBI at the indicated temperatures (a, c) and the

corresponding meridional plots (b, d).

in the Φ_s-o^k(Figure 16b) and Φ_h^io(Figure 16c) phases exhibit a

strong meridional maximum on the L = 5 at ∼7.9 Å. This feature

combined with the experimental density and lattice dimensions

indicates that (3,4,5)12G1-4-PBI also forms a supramolecular

tetramer repeat unit (Table 2). Indexing of the SAXS fiber pattern

(Figure 16a,c), allowed for the assignment of the phase as Φ_s-o^kand

suggested a P2₁2₁2 symmetry. The reduction of the c-axis of the Φ_s-

the m = 3 and will be detailed in a later section. The simulation

suggests that as in the m = 2 and 3 compounds, the columns of

m = 4 are generated via helical packing of supramolecular

tetramers. The helical parameter j slightly increases from 22.5ꢀ

for m = 3 to 36ꢀ for m = 4. Furthermore, the m = 4 continues the

trend of a gradual increase of the intra- and intertetramer stacking

distance. The tetramer thickness increases from 7.5 Å for m = 2

to ∼7.6 Å for m = 3, and to ∼7.9 Å for m = 4. However, the

simulated ﬁber pattern of m = 4, presented in Figure 17, exhibits a

number of diﬀraction peaks larger than that of the experimental

pattern. This diﬀerence can be explained by a signiﬁcantly larger

conformational freedom of the supramolecular columns than

those that can be accounted for by the Cerius2 simulation.

Both the experimental and simulated ﬁber patterns presented

in Figure 17 exhibit a similar number of sharp hk0 reﬂections.

However, in the case of hkl reﬂections with l ¼ 0 there are more

diﬀraction peaks in the simulated pattern than in the experi-

mental ﬁber pattern. This suggests that although the columns

generated by m = 4 are helical, their 3D column-to-column

correlations are subject to a larger degree of conformational

freedom. This is generated in part by the increased liquid-like

^kphases formed by the dendronized PBIs with m = 3 and 4 from

o

60.6 Å for m = 3 to 40.2 Å for m = 4 suggests a change of their helical

k

packing. Interestingly, the Φ_s-ophase formed by (3,4,5)12G1-4-

PBI is the only crystalline high-temperature phase from the entire

series with m = 0, 1, 2, 3, and 4, that forms regardless of the heating

and cooling rate (Figure 3 and Supporting Information Figure

SF10). The absence of ∼3.5 Å πꢀπ stacking and the presence of

the ∼7.9 Å tetramer stacking features in both Φ_s-o^kand Φ_h^iophases

indicate that the columns generated by m = 4 are formed via stacking

of tetramers with the PBI cores spaced at ∼4.4 Å within the tetramer

and ∼3.6 Å between tetramers.

Figure 17 details the simulation of the SAXS and WAXS ﬁber

k

patterns collected from m = 4 in the low-temperature Φ_s-o

phase. The molecular model used in the simulation is similar with

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Figure 14. SAXS pattern collected from the oriented sample of (3,4,5)12G1-3-PBI with the diﬀraction peaks indexed (left) and the corresponding

diﬀraction plot indicating the agreement between the calculated and experimental diﬀraction peaks position (right). Fiber axis, temperature, lattice

symmetry, and parameters are indicated.

io

at lower temperature. The high-temperature Φ_hphase is

generated from uncorrelated helical columns, while the low-

temperature 3D phases are generated from coupled helical

columns.^24,26The helical supramolecular columns forming the

Φ_h^iophases and various crystalline 3D phases are self-assembled

from supramolecular dimers for m = 1 and tetramers for m = 0, 2,

3, and 4 (Figure 6). The diameter and intracolumnar structure

are almost identical in the high-temperature 2D and low-

temperature 3D periodic arrays generated by m = 0, 2, 3, 4.

However, the supramolecular column changes at the transition

from the 2D to the 3D phase when m = 1. The rate of formation

of the crystalline phases decreases with the decrease of m from 4

to 0. Therefore, the rate of formation of long-range intra- and

intercolumnar correlations is gradually facilitated by the increase of

temperature and conformational freedom of (3,4,5)12G1-m-PBI.

This conformational freedom increases from m = 0 to m = 4.

Electron Density Distribution of the Low-Temperature 3D

and High-Temperature 2D Periodic Arrays of (3,4,5)12G1-m-

PBI. Figure 18a,b provides a side-by-side comparison of the

reconstructed relative electron density distribution of the low-

temperature 3D arrays of the five (3,4,5)12G1-m-PBI, m = 0 to 4,

Figure 15. Comparison of the simulated and experimental ﬁber pat-

terns of (3,4,5)12G1-3-PBI collected at 80 ꢀC in the Φ_s-o^kphase.

investigated. Figure 18c details their corresponding relative electron

io

density maps reconstructed for the high-temperature Φ_h2D

phases. The electron density distributions from Figure 18a indicate

character of the aliphatic jacket, which is characteristic also for m = 3,

that the aromaticꢀaliphatic interface of the supramolecular

and by the signiﬁcantly diminished transfer of structural information

via the more ﬂexible dendronꢀPBI core linkage of the m=4structure.

This combination explains the signiﬁcant reduction of the number hkl

reﬂections with l ¼ 0 observed experimentally in the Φ_s-o^kphase of

m= 4 in comparison with m= 3. For example, the hkl diﬀraction features

observed experimentally with l = 3, 4, or 5 are much broader than the

features provided by the simulation shown in Figure 17 demonstrating

the increased liquid-like character of the periphery of the columns.

In summary, all (3,4,5)12G1-m-PBI investigated exhibit a

high-temperature 2D Φ_h^iophase as well as a 3D columnar phase

columns is undulated. This suggests that the 3D column-to-column

correlations are due to coupling of undulated columns.^24,26

Figure 18b shows the electron density distribution of the cross-

section ofthesupramolecularcolumns.Thecross-sectionspresented

in Figure 18b indicate the pseudohexagonal close-packing of

the columns for (3,4,5)12G1-m-PBI with m = 0, 2, 3, and 4. The

small deviation of the packing of the Φ_s-o^kphases relative to the

hexagonal packing of the high-temperature Φ_hphases are

indicated by the angles marked in yellow in Figure 18b. Inter-

estingly, the reconstructed electron density distribution of the

io

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Figure 16. Small- (a) and wide- (b, c) angle X-ray diﬀraction patterns collected from the oriented ﬁber of (3,4,5)12G1-4-PBI at the indicated

temperatures and the corresponding diﬀraction plots demonstrating the agreement between the position of the calculated and experimental diﬀraction

peaks (d, e).

(3,4,5)12G1-2-PBI (Figure 18a) also demonstrates that the

supramolecular columns are helical. The electron density distribu-

tion provided that the helix has a radius of 2.7 Å.

optimization (section 2, Supporting Information). Figure 19b

details the structure of the supramolecular tetramers formed by

(3,4,5)12G1-m-PBI with m = 0, 2, 3, and 4, and of the supra-

molecular dimer formed by (3,4,5)12G1-1-PBI.

As indicated in Table 2, the diameter of the supramolecular

columns exhibits a very small change at the transition from 3D to

2D lattices. The to-scale comparison of the electron density maps

presented in Figure 18b for the 3D lattices and Figure 18c for the

2D lattices indicates that the centers of the columns, that corre-

spond to the centers of the high electron density regions, are

almost unchanged with the exception of m = 1. This suggests that

within the resolution of the experiment, the inner parts of the

columns are identical in the 3D and 2D periodic arrays. The only

signiﬁcant change occurring at the transition from 3D to 2D

lattices is the smearing out of the variations of the electron density

shown in Figure 18a, which were generated by the strong

coupling of helical supramolecular columns in the low-temperature

crystalline phases.

Molecular Structure of Helical Supramolecular Columns

Self-Organized from Supramolecular Dimers and Tetramers

of (3,4,5)12G1-m-PBI. The molecular models of the supramo-

lecular columns assembled from (3,4,5)12G1-m-PBI with m = 0,

1, 2, 3, and 4 are presented in Figures 19 and 20. They were

constructed using the analysis and simulation of the XRD data

discussed in the previous sections. Figure 19a illustrates the

molecular model of the aromatic core region after geometry

The supramolecular structures and the dynamics of self-

organization of (3,4,5)12G1-m-PBI are profoundly inﬂuenced

by the value of m. The diversity of the pathways of self-assembly

followed by the ﬁve (3,4,5)12-m-PBI with m = 0, 1, 2, 3, and 4 are

exempliﬁed by the conformations of (3,4,5)12G1-m-PBI obtained

from the retrostructural analysis of their supramolecular columns.

The formation of a tetramer by (3,4,5)12G1-0-PBI can be attri-

buted to the tendency of the supramolecular assemblies to

maximize their strong πꢀπ PBI interactions. The conformations

presented in Figure 19a demonstrate that the phenyl groups of

the dendron (colored in orange and light blue in Figures 19 and

20) generate steric constraints that increase the PBI core stacking

distance from the typical value of 3.5 Å, to approximately t = 4.8 Å

for (3,4,5)12G1-0-PBI. At the transition from m = 0 to 1, the size

of the aromatic core region is reduced (Figure 19). This shorter

distance between the aromatic side groups of the dendrimer restricts

the formation of supramolecular tetramers for (3,4,5)12G1-1-PBI.

Therefore, (3,4,5)12G1-1-PBI forms a supramolecular dimer

structure characterized by strong t = 3.5 Å πꢀπ stacking corre-

lations. From the structures summarized in Figure 19, the 3.5 Å

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close-packing of the PBI cores in the case of the m = 1 structure is

most probably more suitable for applications based on organic

electronic materials. Upon subsequent increase of m from 1 to 2,

3, and 4, the distance between the aromatic side groups of the

dendrons is suﬃciently large to accommodate the formation of

the supramolecular tetramers presented in Figure 19. At the same

time, the average πꢀπ stacking distance of the PBI core is

slightly increased from the 3.5 Å close-packed distance of the

m = 1, to an intratetramer stacking distance of 4.0ꢀ4.4 Å for

m = 2, 3, and 4 (Figure 19c). Simultaneously, the column

diameter decreases with 9% upon the change from the supra-

molecular tetramers of (3,4,5)12G1-0-PBI to the supramolecular

dimers of (3,4,5)12G1-1-PBI (Figures 18c, 19). The change

from supramolecular dimers for (3,4,5)12G1-1-PBI to supramo-

lecular tetramers for (3,4,5)12G1-2-PBI, increases the column

diameter by 24% from that of (3,4,5)12G1-1-PBI. The increase

of m from 2 to 3 and 4, respectively, does not dramatically aﬀect

the column diameter (ΔD_cole 7%, Figure 18c). Such a small

change is in fact expected considering that (3,4,5)12G1-2-PBI,

(3,4,5)12G1-3-PBI, and (3,4,5)12G1-4-PBI followed the same

pathway of self-assembly into supramolecular tetramers.

The helical parameter j, that corresponds to the rotation of

adjacent supramolecular dimers (for m = 1) and tetramers (for

m = 0, 2, 3, and 4) within the helical column, is determined by the

orientation of the dendron phenyl group (Figures 19 and 20) due

to the diﬀerence in m.

Figure 21 summarizes the structure of the helical supramole-

cular columns self-assembled from (3,4,5)12G1-m-PBI forming

the 3D and 2D columnar phases.

Analysis of the Molecular Dynamics of the Supramolecu-

lar Dimers and Tetramers by Variable Temperature Solid-

1

State H NMR Experiments. Solid-state H magic angle-spin-

ning (MAS) NMR experiments²⁷performed at low temperature

(Figure 22a) yield a broad distribution of aromatic H signals

1

observed in the 6.5ꢀ9.0 ppm region. For (3,4,5)12G1-m-PBI

with m = 0, 2, 3, and 4, that form supramolecular tetramers, a

separate nomenclature is required to describe the protons in the

Figure 17. Comparison of the simulated and experimental ﬁber pat-

terns of (3,4,5)12G1-4-PBI collected at 80 ꢀC in the Φ_s-o^kphase.

Figure 18. Reconstructed relative electron density distributions of the low-temperature crystalline phases shown in 3D view (a) and 2D maps (b).

io

(c) 2D electron density maps of the high-temperature Φ_hphases. The structure of (3,4,5)12G1-m-PBI, crystalline phase symmetry, and lattice

parameters are indicated in a, b. In b, c, the unit cells are indicated by the white lines. The angles marked in yellow in b for the Φ_s-o^kphases indicate a very

small deviation of their packing relative to the high-temperature Φ_h^iophase.

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Figure 19. The inﬂuence of m on the architecture of the supramolecular columns self-assembled from (3,4,5)12G1-m-PBI. Molecular models of the

aromatic core region (a), top (b) and side (c, d) views of the supramolecular structures determined from the analysis and simulation of the WAXS ﬁber

patterns (e). In e, the stacking features are indicated for the corresponding dimer for (3,4,5)12G1-1-PBI and tetramer for (3,4,5)12G1-m-PBI with m = 0,

2, 3, and 4. Color code used in aꢀd: O atoms, red; H atoms, white; N atoms, blue; C atoms of the PBI, green; C atoms of the dendron phenyl, orange and

light blue; all other C atoms, gray.

solid-state NMR assignment (Figure 22a). All four inner protons

are chemically equivalent when considering a single molecule but

become spectroscopically inequivalent when the (3,4,5)12G1-m-

PBI form the supramolecular tetramers (Figure 19). Clear diffe-

rences could be observed in the NMR spectra as a function of m,

most notably in the aromatic region (Figure 22). The proton

resonances of the outer phenyl ring, observed at ∼6.5 ppm, and

of the PBI ring proton resonances are spectrally resolved and can

easily be distinguished.

The liquid-state NMR resonances of the PBI protons have

very similar chemical shifts. The peaks are separated from each

other by ∼0.1 ppm and are located at ∼8.6 ppm, slightly

changing for diﬀerent samples (Supporting Information, Figures

SF16ꢀSF20). In the solid state, either a very broad line for m = 2,

3, and 4, or a set of signals, which are distinct but poorly resolved,

for m = 0 and 1 are observed in the region around 6.5ꢀ9 ppm.

The existence of diﬀerent NMR resonances is a sign of packing

eﬀects and indicates that the chemically equivalent protons have

diﬀerent chemical environments which make them spectrosco-

pically inequivalent.²⁸In the case of the m = 1 dendronized PBI

that forms a supramolecular dimer (Figure 19), the proton of the

dendronꢀPBI spacer appears at 5.5 ppm, whereas in all other

compounds with m values generating supramolecular tetramers,

these resonances are appearing at ∼3ꢀ4 ppm.

Variable temperature ¹H MAS experiments were performed in

order to understand the nature of dynamic processes within the

PBI stacks (Figure 22bꢀd). For (3,4,5)12G1-0-PBI and (3,4,5)12G1-

1-PBI, the aromatic region of the spectra showed no changes

upon heating up to 132 ꢀC. For m = 2, 3, and 4, however, a

signiﬁcant line narrowing was observed, in particular for the

aromatic NMR resonances (red lines in Figure 22c,d, regions

7ꢀ9 ppm). This line narrowing suggests that hydrogen atoms

which previously were spectroscopically inequivalent, because of

diﬀerent local environments due to the pairwise packing, have

become equivalent. This can be explained by an exchange process

between the diﬀerent chemical environments, which in turn means

that the PBI molecules must be able to leave the column’s stack

temporarily, ﬂip around the molecular axis, and reinsert them-

selves into the column. Alternatively, a change in the morphology

of the samples could be occurring, which could lead to a genuine

spectroscopic equivalence between the core and periphery sides.

While this process cannot be ruled out completely, it is unlikely,

considering that the m = 2, 3, and 4 compounds preserve their

packing into supramolecular tetramers upon the transition from

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k

Figure 20. Molecular models of the supramolecular columns self-assembled from (3,4,5)12G1-m-PBI forming the Φ_s-o(m = 0, 2, 3, 4) and

Φ_m^k(m = 1) columnar phases. In all structures, the lattice parameter c and the helical parameter j are indicated. For clarity, only the aromatic core region

of the supramolecular column is shown. Color code used: O atoms, red; H atoms, white; N atoms, blue; C atoms of the PBI, green; C atoms of the

dendron phenyl, orange and light blue; all other C atoms, gray.

Figure 21. Schematic of the supramolecular columns self-assembled from (3,4,5)12G1-m-PBI (m = 0, 1, 2, 3, 4). In c, the supramolecular columns of the

high-temperature Φ_h^iophase are generated by a statistical mixture of the indicated conformations.

io

3D phase, formed by strong coupled helical columns, to the Φ_h

high-temperature phase, formed by uncoupled or weakly corre-

lated columns (Figures 4, 10, 13, and 16).

liquid-state chemical shift value. This π-shift is unchanged with

respect to the tetramer-packed column, which shows that there

is still the same or a very similar packing eﬀect. Furthermore,

a simple rotation of the PBI pairs around the central column axis

(i.e., liquid crystalline behavior) would not yield the observed

narrowing. Instead, it would simply make the individual lines

sharper.

Additionally, the narrowed NMR line appears precisely at the

average position between the values observed for the core and

periphery hydrogen atoms. The averaged chemical shifts (e.g., at

7.2 ppm for m = 2) is still shifted by ∼1.4 ppm compared to the

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Figure 22. ¹H MAS NMR spectra collected at 47 ꢀC (a) and corresponding variable temperature spectra of the indicated (3,4,5)12G1-m-PBI (bꢀd).

In a, the aromatic structure of m = 2 is indicated together with the proton nomenclature. Spectra collected at 30 kHz MAS frequency and 850 MHz

(a), 700.12 MHz (bꢀd) ¹H Larmor frequency.

Table 3. Ab Initio Calculations of the Solid-State NMR

Chemical Shifts for (3,4,5)12G1-2-PBI

assigned proton

average δ (ppm)

standard deviation (ppm)

outer periphery

inner periphery

outer core

6.18

6.20

4.42

4.48

5.30

5.34

0.42

0.33

0.30

0.31

0.26

0.31

inner core

outer averaged

inner averaged

Figure 23. Structure of the two model systems. Tetramer packing motif

for the supramolecular column (left) and defective stack (right), created

by removal of one of the (3,4,5)12G1-m-PBI.

process wherein a (3,4,5)12G1-2-PBI (1) leaves the column, (2)

ﬂips, and (3) returns into the column is plausible and can explain the

narrow NMR lines in the high-temperature 2D Φ_h^iophase.

Ab Initio Molecular Dynamics Study of the Stability of a

Defect. It is possible that the suggested exchange process (Figure 24)

could lead to instability of the columnar structure. To gauge whether

instability might be generated, CPMD simulations were performed

on a periodic perylene stack in which one of the perylenes of the pair

has been removed. The MD simulations showed no sign of instability.

The now-isolated perylene moves somewhat toward the center of the

stack, so that a return of the flipped perylene to its old position

remains possible. No signs of collapse are observed in the time frame

of the simulation. This implies that the helical columns not only allow

for a remarkable dynamics of the PBI moieties but also offer a route to

‘self-repair’ defects.

Ab Initio NMR Chemical Shift Calculations. For quantitative

analysis, the spectroscopic results have to be quantified with the

aid of ab initio calculations for the specific packing.²⁹We have

constructed a simplified model of the supramolecular tetramers

(Figure 23). A reasonable degree of disorder was added by means

of CarꢀParrinello Molecular Dynamics (CPMD) simulations.

The columns are modeled via an infinite stack under periodic

boundary conditions, with four molecules per unit cell forming

the supramolecular tetramer. A few configurations were extracted,

and NMR chemical shifts were computed for all protons (Table 3.

The packing eﬀects (π-shifts) with respect to the liquid-state

NMR are well reproduced by the ab initio calculations and reﬂect

the packing eﬀects in the columns. The chemical shifts of inner

and outer hydrogen atoms are almost equal. It only matters

whether they are at core or periphery positions. The diﬀerent

chemical shifts explain the broad NMR line. The core and periphery

averaged NMR values almost coincide. Therefore, an exchange

’ CONCLUSIONS

Dendronized PBIs, (3,4,5)12G1-m-PBI, with m = 0, 2, 3, 4,

self-assemble into complex helical columns generated from

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Journal of the American Chemical Society

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in solution. Dimerization was also predicted by computation studies.³⁰

However, this report demonstrates for the ﬁrst time the self-

assembly of complex helical columns generated from dimers and

tetramers of dendronized PBIs that are persistent in 2D and 3D

lattices formed in solid state. In the 2D columnar hexagonal

phase with intracolumnar order, the dendronized PBI displays a

remarkable dynamics able to leave the columns without disrup-

tion thereby oﬀering a mechanism to self-repair architectural

defects. These complex helical columnar 2D and 3D periodic

arrays are unprecedented for self-assembling dendritic structures.¹⁰

However, these supramolecular structures are encountered in

many other self-assembling dendronized PBIs. The general self-

assembly processes reported here are expected to be important in

the elucidation of the mechanism of charge carriers transport and

in the design of eﬃcient supramolecular electronic materials based

on PBI and other electron-deﬁcient structures that are funda-

mental building blocks for solar cells and other optoelectronic

applications. The complex helical columns reported here are

racemic. However, it is important to understand the role of

nonracemic chirality on the self-assembly³¹and electronic prop-

erties of dendronized PBI, considering the strong inﬂuence of the

molecular structure on their kinetic vs thermodynamic supra-

molecular products.³²These investigations are in progress.

Figure 24. Calculated chemical shift distribution for (3,4,5)12G1-2-

PBI along an ab initio molecular dynamics trajectory (left). The indivi-

dual NMR chemical shifts were convoluted with Gaussians to yield a

continuous spectrum. Prior to the convolution, all inner and all outer

hydrogen atoms were averaged, which corresponds to the eﬀects of a

ﬂip-exchange process (right).

tetramers of PBI. When m = 1, the dendronized PBI self-assemble

in helical columns produced from dimers of PBI. At high temp-

erature, all helical columns self-organize in thermodynamically

stable 2D columnar hexagonal lattices with intracolumnar order

via a fast self-assembly process. At low temperatures, dendronized

PBI self-organize in the thermodynamically stable 3D columnar

simple orthorhombic (for m = 0, 2, 3, 4) and in 3D columnar

monoclinic (for m = 1) lattices via a very slow self-assembly

process that takes place from the closely related kinetic 2D

product. Only for (3,4,5)12G1-4-PBI is the self-assembly of the

3D structure from the 2D structure fast enough that both the 3D

and 2D structures can be detected by DSC and XRD with heating

and cooling rates of 10 ꢀC/min. The 3D lattices of dendronized

PBIs with m = 1, 2, 3 can be observed by DSC and XRD only if

cooled from the 2D columnar arrays at rates of 1 ꢀC/min or

lower. In the case of (3,4,5)12G1-0-PBI a ﬁrst-order transition

from the high-temperature 2D to the low-temperature 3D phase

could not be detected by DSC even with a rate of 1 ꢀC/min.

However, this 3D phase could be observed by XRD experiments

performed with 1 ꢀC/min. The structures of the helical columns

self-assembled from dendronized PBIs with m = 0, 2, 3, 4 retain

many common features at the transition from the 2D to the 3D

arrays. However, the dendronized PBI with m = 1 undergoes a

substantial change in the architecture of its supramolecular column

at the 2D to 3D periodic array transition. As a consequence,

cooling oriented samples of (3,4,5)12G1-m-PBI (with m = 0, 1, 2,

3, 4) only with a rate of 1 ꢀC/min provides a mechanism to gen-

erate highly oriented 3D samples that are required for structural

analysis and electronic application experiments. Analysis of the

phases in as-prepared dendronized PBI compounds with m = 1,

2, 3, 4 showed them to be crystalline, but although they are

formed from supramolecular columns, their internal architecture

diﬀers signiﬁcantly from the 3D structures formed in subsequent

heating and cooling experiments. These as-prepared 3D struc-

tures do not exhibit any strong πꢀπ stacking correlations in the

range of 3.5ꢀ3.9 Å. The lower degree of intracolumnar order in

these as-prepared samples is expected because they are produced

by precipitation with methanol. Therefore, it is very important to

investigate and elucidate the supramolecular structures generated

from ﬁlms produced from solvophobic and from good solvents.

These experiments are in progress. Dimerization^7k,8dand

even pentamerization^12bof related dendronized PBIs were observed

’ ASSOCIATED CONTENT

S

Supporting Information. Experimental procedures with

b

complete spectral and structural analysis. This material is available

free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION

Corresponding Author

percec@sas.upenn.edu

’ ACKNOWLEDGMENT

Financial support by the National Science Foundation (DMR-

0548559, DMR-0520020, DMR-1066116, and DMS-0935165)

and the P. Roy Vagelos Chair at Penn are gratefully acknowledged.

B.M.R. gratefully acknowledges funding from an NSF Graduate

Research Fellowship and an ACS Division of Organic Chemistry

Graduate Fellowship (Roche). This work was also ﬁnancially

supported by the German Research Foundation (DFG) through

grants SFB 625 and Se 1008/5 5 and by the WCU program through

the National Research Foundation of Korea funded by the Ministry

of Education, Science and Technology (R31-10013). We thank Drs.

Nick Terrill and Jen Hiller of Diamond Light Source for help with

the synchrotron experiments.

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Self-assembly of dendronized perylene bisimides into complex helical columns

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