Transformation from kinetically into thermodynamically controlled self-organization of complex helical columns with 3d periodicity assembled from dendronized perylene bisimides

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Transformation from Kinetically into Thermodynamically Controlled

Self-Organization of Complex Helical Columns with 3D Periodicity

Assembled from Dendronized Perylene Bisimides

Virgil Percec,*^,†Hao-Jan Sun,^†,‡Pawaret Leowanawat,^†Mihai Peterca,^†,‡Robert Graf,^§Hans W. Spiess,^§

Xiangbing Zeng,^∥Goran Ungar,^∥,#and Paul A. Heiney^‡

^†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 Science and Engineering, University of Sheﬃeld, Sheﬃeld S1 3JD, United Kingdom

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

S

* Supporting Information

ABSTRACT: The dendronized perylene 3,4:9,10-tetracarbox-

ylic acid bisimide (PBI), (3,4,5)12G1-1-PBI, was reported by

our laboratory to self-assemble into complex helical columns

containing dimers of dendronized PBI with one molecule in

each stratum, with diﬀerent intra- and interdimer rotation

angles but identical intra- and interdimer distance of 3.5 Å,

exhibiting a four-strata 2₁helical repeat. A thermodynamically

controlled 2D columnar hexagonal phase with short-range

intracolumnar order represents the thermodynamic product at

high temperature, while a kinetically controlled monoclinic

columnar array with 3D periodicity is the thermodynamic product at low temperature. With heating and cooling rates higher

than 10 °C/min to 1 °C/min, at low temperature the 2D columnar periodic array is the kinetic product for this dendronized PBI.

Here the synthesis and structural analysis of a library of (3,4,5)nG1-m-PBI with n = 12 to 6 and m = 1 are reported. A

combination of diﬀerential scanning calorimetry, X-ray diﬀraction on powder and orientated ﬁbers, including pattern simulation

and electron density map reconstruction, and solid-state NMR, all as a function of temperature and heating and cooling rate, was

employed for their structural analysis. It was discovered that at low temperature the as-prepared n = 12 to 10 exhibit a 3D layered

array that transforms irreversibly into columnar periodicities during heating and cooling. Also the kinetically controlled 3D

columnar phase of n = 12 becomes thermodynamically controlled for n = 10, 9, 8, 7, and 6. This unprecedented transformation is

expected to facilitate the design of functions from dendronized PBI and other self-assembling building blocks.

by their two- and three-dimensional (2D and 3D) periodic or

quasiperiodic structure.⁹Due to the polymorphic arrangement

of supramolecular structures obtained from PBI building blocks

in their 2D and 3D periodic and quasiperiodic arrays, their

assembly is determined by a delicate combination of kinetically

and thermodynamically controlled pathways and mecha-

nisms.¹⁰Our laboratory is using the generational and

deconstruction library approaches¹¹to discover supramolecular

organizations¹²and predict the primary structure required to

self-organize a certain functional 3D periodic array. This library

approach^11,12is currently applied to PBI dendronized at the

imide positions with the self-assembling dendrons (3,4,5)nG1-

m-PBI,¹³where n is the number of carbons in their n-alkyls and

m is the numbers of methylenic units connecting the dendron

INTRODUCTION

■

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

been elaborated into self-assembling building blocks employed

in the design of complex systems¹and supra-²and macro-

molecular³assemblies that impact ﬁelds such as dyes and

pigments,⁴semiconductors, transistors, light-emitting diodes,

solar cells,^2,3artiﬁcial photosynthesis, life science and biology,⁵

and xerographic receptors.⁶This extraordinary diversity of

functions is facilitated by the excellent thermal and photo-

chemical stability, the ability to functionalize the imide and bay

positions, and the polymorphism^4d−fexhibited by PBIs in their

ordered states.

PBIs dendronized at bay,⁷imide,⁸or both positions with self-

assembling dendrons have emerged as a powerful class of

building blocks used to provide most of the functions and

applications mentioned above. Both in solution and in solid

state, the functions of these complex assemblies are determined

Received: January 19, 2013

Published: February 14, 2013

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to the imide group (Scheme 1). This approach led to the

discovery of a diversity of unprecedented helical columnar

in the second. This allows close and extended π-stacking that is

expected to provide interesting charge carrier mobility and

other properties, unlike the disruptive up−down alternation

from the core of PBI building blocks with m = 0, 2, 3, 4 with n

= 12.^13a,bDue to the presence of the thermodynamically

controlled 2D structure at high temperature and the kinetically

controlled 3D array at low temperature, most of the time the

2D structure represents the kinetic product at low temperature

and the 3D periodicity can be detected only by cooling at rates

of 1 °C/min or less and by suitable annealing.^13aThe kinetically

controlled self-organization of 3D structures is common.¹⁴

However, kinetically controlled 3D structures are diﬃcult to

duplicate and, therefore, provide almost irreproducible path-

ways to discovery, elucidation of the mechanism, and proper

manipulation of structures responsible for functions¹⁴of

interest for technological applications such as organic

electronics. A very fundamental question is illustrated in the

left column of Scheme 1: Can the desirable self-organization of

the 3D periodic four-strata 2₁helical columnar structure be

changed from a kinetically to a thermodynamically controlled

process? And, if so, can it be accomplished via manipulation of

the simplest parameters of the primary structure of the

dendronized PBI (left column in Scheme 1)?

Scheme 1. Schematic of the Self-Assembly of Dendronized

PBIs, (3,4,5)nG1-m-PBI

Here we report the synthesis and structural analysis of a

library of (3,4,5)nG1-1-PBI with n = 12, 11, 10, 9, 8, 7, 6. The

analysis of this library led to the discovery of dendronized PBIs

that transformed the kinetically controlled self-organization of

the 3D crystalline structures containing helical columns of n =

12 and 11 into thermodynamically controlled 3D crystalline

structures for n = 10, 9, 8. It also led to the discovery that the n

= 12 to 10 PBIs as-prepared from solution self-organize in a 3D

layered periodic array that is not obtained during subsequent

heating and cooling scans when only 3D and 2D columnar

periodic arrays form. At high temperature all PBIs with n = 12

to 8 display also a 2D hexagonal columnar lattice with short-

range intracolumnar order. Compounds with n = 7, 6 exhibit

only 3D crystalline structures that are also thermodynamically

controlled. We expect that the discovery of the thermodynami-

cally controlled self-organization of 3D columnar structures

reported here, that we name TCC soft crystals, will impact the

design of functions and the development of technological

application for many ﬁelds, including supramolecular organic

electronics.

arrangements that are brieﬂy outlined in Scheme 1.¹³The

compounds with m = 0, 2, 3, 4 and n = 12 self-assemble during

heating and cooling into helical columns containing tetramers

of PBI as basic repeat units (see right two columns in Scheme

1). These tetramers consist of 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. The

intra- and intertetramer rotation angles and stacking distances

are diﬀerent.^13aThe helical columns generated from m = 0, 2, 3,

4 and n = 12 self-organize at high temperature via a

thermodynamically controlled mechanism in a 2D hexagonal

columnar phase with short-range intracolumnar order, while at

low temperature they assemble in 3D columnar arrays via a

kinetically controlled process. Screening through a library with

m = 3 and n = 14 to 4^13bled to the discovery of a kinetically

controlled self-repairing process that produced a single intra-

and intertetramer distance of 3.5 Å for the helical columns

assembled from m = 3, n = 8, 9 (right column in Scheme 1). In

contrast, for m = 1, n = 12, the helical columns contain dimers

of dendronized PBI with one molecule in each column stratum

having diﬀerent intra- and interdimer rotation angles and a 3.5

Å intra- and interdimer distance generating a four-strata 2₁

helical repeat.^13aAll PBIs face up in the ﬁrst column and down

RESULTS AND DISCUSSION

■

Synthesis of Dendronized PBI (3,4,5)nG1-1-PBI. The

synthesis of twin-dendronized^13,15(3,4,5)nG1-1-PBIs with n =

12, 11, 10, 9, 8, 7, 6 is outlined in Scheme 2. In the ﬁrst step,

methyl 3,4,5-trihydroxybenzoate (1) was etheriﬁed with benzyl

chloride in degassed dimethylformamide (DMF) in the

presence of K₂CO₃at 75 °C to produce methyl 3,4,5-

tris(benzyloxy)benzoate (2) in 92% yield after passing its

CH₂Cl₂solution through a short column of basic Al₂O₃

followed by precipitation into MeOH. Reduction of 2 with

LiAlH₄yielded (3,4,5-tris(benzyloxy)phenyl)methanol (3) in

99% yield. Bromination of 3 with NBS/PPh₃in THF produced

4 (88% yield). The nucleophilic displacement of 4 with

potassium phthalimide in dry DMF produced 5 in 95% yield

which after hydrogenolysis with Pd/C in MeOH/CH₂Cl₂(1/

2) at 24 °C for 12 h yielded 6 (100% yield). Compound 6 was

etheriﬁed with the n-alkyl bromides containing 12, 11, 10, 9, 8,

7, and 6 carbons to produce the corresponding 7a−7g in 65−

91% yields. Treatment of the phthalimide derivatives 7a−7g

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a

Scheme 2. Synthesis of Dendronized PBIs, (3,4,5)nG1-1-PBI, with n = 12, 11, 10, 9, 8, 7, 6

a

Reagents and conditions: (i) BnCl, K₂CO₃, 75 °C; (ii) LiAlH₄, THF; (iii) PPh₃, NBS, THF; (iv) potassium phthalimide, DMF, 70 °C; (v) H₂, Pd/

C, MeOH−CH₂Cl₂; (vi) C_nH_2n+1Br, K₂CO₃, DMF; (vii) H₂NNH_2.H₂O, EtOH, reﬂux; (viii) Zn(OAc)₂, quinoline, 180 °C.

with 64% hydrazine hydrate in absolute EtOH at reﬂux for 12 h

produced compounds 8a−8g in quantitative yield. Imidization

of perylene-3,4:9,10-tetracarboxylic dianhydride with the

amines 8a−8g was performed in quinoline at 180 °C (4−6

h) in the presence of Zn(OAc)₂·H₂O to produce 9a−9g in 34−

92% yield after puriﬁcation by column chromatography (SiO₂,

0 − 2% acetone in CH₂Cl₂), followed by precipitation in

enthalpy changes associated with thermodynamically controlled

phase transitions display also a very small dependence on rate

and on the heating and cooling history of the sample. By

considering these rules, a brief inspection of the DSC traces

from Figures 1 and 2 demonstrates that the temperatures of the

io

transitions from Φ_hto isotropic liquid (i) and from i to Φ_h

for compounds with n = 12, 11, 10, 9, and 8, and their enthalpy

changes are almost identical, regardless of whether they are

determined from heating or cooling scans performed at 10 or 1

°C/min. Regardless of rate, for n = 12 to 8, the temperature

1

methanol from concentrated CH₂Cl₂solution. H and ¹³C

NMR, MALDI-TOF, and HPLC demonstrated a purity higher

than 99% for all (3,4,5)nG1-1-PBI (9a−9g) (Supporting

Information).

io

that corresponds to the i-to-Φ_htransition determined on

io

Analysis of the Supramolecular Assemblies and Their

Periodic Arrays by a Combination of Diﬀerential

Scanning Calorimetry and X-ray Diﬀraction. This analysis

requires a comparative inspection of the diﬀerential scanning

calorimetry (DSC) results obtained at 10 °C/min (Figure 1)

and 1 °C/min (Figure 2). Identiﬁcation of the 2D columnar

cooling is only 1 °C lower than that for the Φ_h-to-i transition

determined on heating. Therefore, at high temperature the

io

supramolecular columns forming the Φ_hperiodic array

represent the thermodynamic product of the self-assembly

process, and their formation is thermodynamically controlled.

In the case of n = 12, 11, and 10, the DSC combined with

XRD data obtained from the ﬁrst heating scans recorded with

10 °C/min (Figure 1) and 1 °C/min (Figure 2) demonstrate

the formation of some layered 3D periodic arrays that are not

reformed during the subsequent heating and cooling scans. The

as-prepared sample used during the ﬁrst heating scan was

obtained by the slow evaporation of a CH₂Cl₂solution, which

generally allows the formation of the phase that is closest to

equilibrium. A closer inspection of the cooling and second

heating scans obtained with 10 and 1 °C/min for n = 12 shows

substantial diﬀerences for the 3D periodic arrays observed at

io

hexagonal phase with short-range intracolumnar order, Φ_h, the

k

3D columnar centered orthorhombic, Φ_c‑o, two diﬀerent

k1

columnar monoclinic lattices, Φ_mand Φ_m^k2, and a columnar

monoclinic superlattice, Φ_m^k‑SL, reported in Figures 1 and 2 was

accomplished by a combination of X-ray diﬀraction (XRD)

experiments performed at small and wide angles on powder and

oriented ﬁbers.^12,13Note that the term “centered orthorhom-

bic” is used here to distinguish this phase from the “simple

orthorhombic” reported previously.¹³

Data from Figures 1 and 2 are summarized in Table 1.

Thermodynamically controlled phase transitions are usually

observed for 2D liquid crystalline periodic arrays.¹⁴The

transition temperatures from 2D to isotropic liquid and from

isotropic liquid to 2D are almost identical, regardless of the

heating and cooling rate of the DSC, and exhibit only a small

degree of supercooling that usually is less than 10 °C. The

io

lower temperature than the Φ_h. After cooling from the

isotropic liquid at 10 °C/min, only the Φ_h^iois obtained, judged

by the absence of any endotherm with a signiﬁcant enthalpy on

second heating (Figure 1). However, after cooling at 1 °C/min,

io

a 3D phase which undergoes a transition to Φ_hat 33 °C and

has a very small enthalpy change is observed (Figure 2).

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Figure 1. DSC traces collected from (3,4,5)nG1-1-PBI with n = 6 to 12 at heating and cooling rates of 10 °C/min. Phases, transition temperatures,

and associated enthalpy changes (in parentheses, in kcal/mol) are indicated. The green circles show the transitions dependent on rate.

Annealing at 24 °C for 1 month increases the transition

enthalpy and temperature (to 39 °C); see inset on second

heating scan for n = 12 in Figure 2. DSC heating scans for n =

12 after annealing at 24 °C for various periods of time are

shown in Figure 3.

engineered to be in the proper range of interest for potential

technological applications.

Inspection of the DSC data for n = 11 by following the same

principles as those used in the case of n = 12 starts to show a

promising change. At both 10 and 1 °C/min, cooling and

k1

second heating scans show the formation of the 3D Φ_m

For n = 12, the 3D phase is the thermodynamic product at

low temperature. However, the formation of the 3D phase is

strongly dependent on rate and, therefore, is kinetically

controlled. Since n = 12 exhibits a 2D thermodynamic product

at high temperature (Φ_h^io) that is thermodynamically

controlled (i.e., independent of rate), with a cooling rate of

10 °C/min we observed at low temperature the Φ_h^iophase that

this time, in this range of temperature, is the kinetic product.

However, for most functions and applications of supra-

molecular periodic array, the 3D thermodynamic product that

is kinetically controlled is the desired structure. Therefore, it is

of great interest to discover the simplest possible changes to the

chemical structure of the dendronized PBI that may allow the

transformation of the 3D thermodynamic product from being

kinetically controlled to thermodynamically controlled. In

addition, it would also be very important if the temperature

of the 3D thermodynamically controlled product could be

monoclinic phase that was not observed for n = 12. However,

the melting of Φ_mat 35 °C with 1 °C/min on heating, and

the formation of Φ_mat 8 °C with the same rate on cooling,

k1

show a diﬀerence of 27 °C. For n = 11, no Φ_h^iois observed as a

kinetic product at low temperature (Figures 1 and 2 compare n

= 12 with n = 11), but the formation of the 3D Φ_m^k1phase near

room temperature for n = 11 remains kinetically controlled.

Compounds with n = 10, 9, and 8 provide an unexpected and

remarkable result. The temperature transition from 2D to 3D

and from 3D to 2D phases and their associated enthalpy

changes are very little dependent on the heating and cooling

rate and on the heating and cooling temperature from which

they are collected (compare Figures 1 and 2). To our

knowledge, these compounds provide the ﬁrst examples of

3D periodic arrays self-organized from complex helical columns

that behave just like the 2D periodic arrays; i.e., they are

thermodynamically controlled. It is also extremely rewarding

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Figure 2. DSC traces collected from (3,4,5)nG1-1-PBI with n = 6 to 12 at heating and cooling rates of 1 °C/min. Phases, transition temperatures,

and associated enthalpy changes (in parentheses, in kcal/mol) are indicated. The green circles show transitions dependent on rate.

that the 3D structures obtained from n = 10 are stable up to

∼139 °C, the one for n = 9 up to ∼183 °C, and the one for n =

8 up to ∼223 °C (Figures 1, 2, and 4b). This range of

temperature stability for the 3D thermodynamically controlled

thermodynamic product is important for technological

applications. Compounds with n = 7 and 6 do not exhibit the

high-temperature 2D Φ_h^iophase. They self-organize only in 3D

arrays that are all the thermodynamically controlled thermody-

namic products. Figure 4a illustrates all 2D and 3D periodic

arrays mentioned above.

solution. This phase cannot be regenerated in the subsequent

heating and cooling treatments. This phase is stable up to 118,

121, and 119 °C for n = 12, 11, and 10, respectively. Only for n

= 12, this layered structure can also be obtained by

precipitation from solution through addition of excess

methanol.

A Brief Description of the 2D and 3D Periodic Arrays

Self-Organized from Dendronized PBIs. Φ_h^iois a 2D lattice

which possesses short-range order along the column axis. The

k

Φ_c‑_i_o_olattice has a column packing related to that observed in

Figure 4b summarizes the dependence of the structures of

2D and 3D periodic arrays self-organized for (3,4,5)nG1-1-PBI

on n and temperature. For n = 12 and 11, the 3D periodic

arrays of interest for electronic applications are stable up to 33

and 92 °C, respectively, and are kinetically controlled. For n =

10, 9, and 8, the 3D periodic arrays are stable up to 139, 183,

and 223 °C, respectively, and are thermodynamically

Φ_hexcept that the angle between neighboring columns is

slightly deviated from 60° (Figure 4a). In addition there is long-

range registry order between the supramolecular columns, and

therefore Φ_c‑o^kis a 3D crystal. The 3D Φ_m^k‑SLphase observed in

n = 7 and 6 at low temperature has its a-axis as the unique axis

with the column tilted with respect to the ab plane, while other

monoclinic phases found in this library have the c-axis as the

io

k‑SL

controlled. These assemblies also display a 2D Φ_hthat is

unique axis. Each unit cell of the Φ_m

phase contains three

useful for the alignment and templated crystallization of their

3D periodic arrays. The compounds with n = 7 and 6 show a

remarkable number of 3D phases that are all thermodynami-

cally controlled. In addition, a layered crystalline structure was

observed in n = 12, 11, and 10 during the ﬁrst heating from the

as-prepared sample obtained by slow evaporation of CH₂Cl₂

subcells along the c-axis, and the length of the c-axis (∼44.1 Å)

is about 3 times longer than that for the Φ_c‑ofound at higher

k

temperature (∼14.7 Å). Notice that this phase does not form in

the as-prepared samples from solution (absent during ﬁrst

heating) and develops only during cooling from high

temperature. Φ_m^k1, with P2₁/b symmerty, is the thermodynamic

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Table 1. Transition Temperatures and Associated Enthalpy Changes of (3,4,5)nG1-1-PBI with n = 6 to 12 Determined by DSC

and XRD

thermal transition (°C) and corresponding enthalpy changes (kcal/mol)

a

n

rate (°C/min)

heating

cooling

k

k‑SL

6

10

Φ_c‑o272 (9.39) i

i 257 (−9.34) Φ_c‑o20 (−1.1) Φ_m

−38 (−1.49) Φ_m

−34 (−1.93) Φ_m

k‑SL

k

Φ_m

−27 (1.93) Φ_m

23 (0.56) Φ_c‑o272 (9.47) i

k

1

10

1

Φ_c‑o272 (9.28) i

i 258 (−9.2) Φ_c‑o21 (−0.80) Φ_m

k‑SL

k

Φ_m

−28 (1.94) Φ_m

23 (0.94) Φ_c‑o272 (9.46) i

k

k‑SL

7

8

Φ_c‑o250 (8.17) i

i 241 (−8.15) Φ_c‑o16 (−1.68) Φ_m

−6 (−3.30) Φ_m

k‑SL

k

Φ_m

9 (4.08) Φ_m

22 (1.26) Φ_c‑o250 (8.18) i

k

k‑SL

Φ_c‑o250 (8.15) i

i 242 (−8.07) Φ_c‑o17 (−1.67) Φ_m

−4 (−3.18) Φ_m

k‑SL

k

Φ_m

9 (3.93) Φ_m

21 (1.41) Φ_c‑o250 (8.12) i

k1

k

io

k

k1

10

1

Φ_m37 (0.85) Φ_c‑o224 (2.49) Φ_h229 (3.07) i

i 228 (−2.85) Φ_h217 (−2.85) Φ_c‑o27 (−7.18) Φ_m

k1

k

io

Φ_m37 (6.04) Φ_c‑o61 (0.12) Φ_c‑o223 (2.71) Φ_h229 (2.98) i

k1

k

io

k

k1

Φ_m35 (0.18) Φ_c‑o223 (2.54) Φ_h229 (2.88) i

i 228 (−2.85) Φ_h219 (−2.71) Φ_c‑o29 (−6.93) Φ_m

k1

k

io

Φ_m35 (6.37) Φ_c‑o59 (0.35) Φ_c‑o223 (2.59) Φ_h229 (2.94) i

k

io

k

9

10

1

Φ_c‑o183 (1.02) Φ_h227 (3.16) i

i 225 (−3.10) Φ_h175 (−1.16) Φ_c‑o15 (−1.05) Φ_m

k1

k2

k

io

Φ_m33 (3.56) Φ_m55 (0.11) Φ_c‑o139 (0.1) Φ_c‑o183 (1.07) Φ_h227 (3.14) i

k

io

k

Φ_c‑o183 (1.10) Φ_h227 (3.06) i

i 226 (−3.04) Φ_h178 (−1.08) Φ_c‑o18 (−0.15) Φ_m

k1

k2

k

io

Φ_m32 (4.65) Φ_m52 (0.08) Φ_c‑o138 (0.1) Φ_c‑o183 (1.11) Φ_h227 (3.05) i

c

io

k

k1

10

11

12

10

1

Lay^k5 (1.32) Lay^k35 (4.12) Lay^k119 (18.01) Φ_h227 (3.65) i

i 225 (−3.63) Φ_h121 (−0.84) Φ_c‑o−5 (−3.05) Φ_m

k1

k2

k

io

Φ_m11 (2.18) Φ_m62 (0.27) Φ_c‑o139 (0.76) Φ_h227 (3.65) i

c

Lay^k3 (1.32) Lay^k35 (4.11) Lay^k114 (19.32) Φ_h227 (3.67) i

i 226 (−3.55) Φ_h129 (−0.78) Φ_c‑o−4 (−3.63) Φ_m

io

k

k1

k2

k

io

Φ_m12 (3.03) Φ_m27 (0.88) Φ_m61 (0.41) Φ_c‑o137 (0.81) Φ_h227 (3.66) i

b

io

k1

10

1

Lay^k121 (24.79) Φ_h227 (3.89) i

i 225 (−3.85) Φ_h

i 226 (−3.90) Φ_h

i 224 (−4.17) Φ_h

i 225 (−4.18) Φ_h



Φ_m

k1

k2

io

Φ_m22 (0.30) Φ_m92 (0.59) Φ_h227 (3.88) i

b

Lay^k116 (26.02) Φ_h227 (3.92) i

Φ_c‑o8 (−5.53) Φ_m

io

k

k1

k2

k

io

Φ_m35 (5.77) Φ_m48 (0.26) Φ_c‑o92 (0.61) Φ_h227 (3.90) i

c

Lay^k−1 (2.16) Lay^k48 (5.42) Lay^k118 (30.87) Φ_h226 (4.47) i

io

10

1

io

Φ_h226 (4.24) i

Lay^k−1 (1.96) Lay^k48 (4.83) Lay^k115 (28.22) Φ_h226 (4.39) i

io

k1

io

Φ_m32 (1.35) Φ_h226 (4.26) i

d

k1

io

Φ_m39 (8.68) Φ_h225 (4.21) i

a

Data from the ﬁrst heating and cooling scans are on the ﬁrst line, and data from the second heating are on the second line with rate indicated in

second column. Phase notation: Φ_c‑o^k, columnar centered orthorhombic crystalline phase, Φ_m^k‑SL, columnar monoclinic crystalline superlattice; Φ_m

,

k1

Φ_m^k2, columnar monoclinic crystalline phase; Φ_h^io, 2D columnar hexagonal phase with intracolumnar order; Lay^k, layered monoclinic crystalline

b

c

d

phase; i, isotropic. This transition is observed by XRD. Lattice parameters changed between the observed Lay^kphase (Table 2). Second heating

data collected after 1 month of annealing at 24 °C. Note: quantitative uncertainties are 1 °C for thermal transition temperatures and ∼2% for the

associated enthalpy changes reported in kcal/mol.

product at low temperature for n = 8, 9, 10, 11, 12. It contains

two columns in one unit cell, and the cell symmetry translates

the columns into alternative left- and right-handed helices along

the b-axis. The Lay^kphase is found only in as-prepared sample

from solution with n = 12, 11, and 10, where molecules pack in

a monoclinic unit cell with the b-axis as the unique axis and cell

symmetry of P2₁. In this structure, the PBI cores are tilted with

respect to the c-axis and phase-separated from the alkyl chains.

As will be discussed in more detail later, this phase possesses

larger π−π stacking distance compared with other columnar 2D

and 3D phases.

the columns in Φ_m^k‑SLare tilted against the ﬁber direction when

an orientated ﬁber is prepared. A similar trend was observed

and reported previously in (3,4,5)9G1-3-PBI,^13bwhere the low-

k

temperature Φ_c‑owas replaced by a more stable Φ_mas the

thermodynamic product after annealing at 110 °C for 600 min

io

in the Φ_h. All these compounds have isotropization temper-

atures above 225 °C, indicating an excellent range of thermal

stability (Figure 4b) of their self-organized structures. The 2D

io

Φ_hformed by compounds with n = 8 to 12 is the

thermodynamic product at high temperature, but that for n =

12 is the kinetic product at low temperature, depending on the

rate of cooling and on annealing. It is interesting to notice that

A ﬁrst-order phase transition separates Φ_m^k1from Φ_h^ioin n =

12 after annealing without going through other intermediary

io

the lower end of the temperature range of the Φ_hphase

k2

k

phases. In compounds with n = 11 to 8, Φ_mand Φ_c‑owere

decreases with increasing n. This drop in the melting point of

the 3D phases is consistent with the increasing transition

entropy due to the increased conformational freedom of the

longer peripheral alkyl chains. The XRD patterns of high-

observed as intermediary phases between high-temperature 2D

Φ_{h k2}and low-temeprature 3D Φ_m^k1. As shown in Figure 4a,

io

Φ_mhas a column arrangement in the unit cell similar to that

of Φ_c‑o^k, but the lattice is distorted in the ab plane. It seems that

Φ_m^k_k²₂is more stable at lower temperature than Φ_c‑o^k; therefore,

Φ_musually develops ﬁrst, before Φ_c‑o^k, during heating from

io

temperature 2D Φ_hphase obtained for n = 8 to 12 and low-

temperature 3D crystalline phases obtained for n = 6 to 12 are

summarized in Figures 5 and 6, respectively. The detailed

structural evolution will be discussed in the following

subsection.

k1

k2

low temperature in the Φ_mphase. Unlike in Φ_mand Φ_m

,

k‑SL

Φ_m

is distorted in the bc plane, where the c-axis is

conventionally assigned as the column axis. This indicates that

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below the isotropic temperature. For all compounds, Φ_m^kis the

thermodynamic product at the temperatures close to room

temperature (24 °C).

The X-ray analysis shows that, at high temperature,

io

compounds with n = 8 to 12 display a 2D Φ_hliquid

crystalline columnar hexagonal phase with intracolumnar order

(Tables 2 and ST1).

As expected, the column diameter of these supramolecular

structures increases with the length of alkyl chains, n, of the

tapered dendron. The supramolecular columns forming the

io

Φ_hphase are constructed by a statistical mixture of the two

arrangements shown in Figure 5g resulting in an all up/all

down, and up−down alternation. The alternative up−down

conformation acts as structural defects that disrupt the helical

packing and generate the weak 7.0 Å diﬀraction in the

meridional plot from Figure 5f. The 3.5 Å π−π stacking

between PBI planes generates the intracolumnar order with a

correlation length that spans in average 34 column strata. The

experimental density values and XRD data (Tables 2, ST1)

were used to ascertain that the supramolecular columns have

only one molecule per 3.5 Å thick stratum. The apparently

meridional 7.0 Å diﬀraction (L = 2, or L = 6 in Φ_m^k‑SLphase) is

thought to be the result of the interdimer spacing, while the 3.5

k‑SL

Å diﬀraction (L = 4 or 12 in Φ_m

phase) comes from the

intermolecular π−π stacking of perylene planes (Figure 6). The

π−π stacking distance is conserved during the transition from

the 2D to the 3D phases. It is apparent from Figure 6 that the

3D phases observed for n = 10, 9, 8, 7, 6 have a higher degree of

order than those for n = 11, 12. This is particularly obvious

from the appearance of sharp oﬀ-meridional diﬀraction arcs at

increasing Bragg angles as n decreases. This indicates

decreasing thermal disorder (Debye−Waller factor), under-

standable as the insulating alkyl sheath separating the columns

is diminished.

Figure 3. DSC heating traces (1 °C/min) for (3,4,5)12G1-1-PBI after

annealing at room temperature for 7 h, 9 h, 12 h, and 1 month and

cooling to the starting temperature at 1 °C/min.

io

The Φ_hphase disappears for compounds with n = 6 and 7

because the primary structure is too rigid to have the required

io

conformational freedom for a 2D Φ_hliquid crystalline phase

Figure 4. Schematic illustration of 2D and 3D periodic arrays self-organized from the supramolecular columns assembled from (3,4,5)nG1-1-PBI

with n = 6 to 12. (a) Column arrangement of supramolecular columns in 2D and 3D lattices; their unit cell axis and angles are indicated. Phase

io

k

notation: Φ_h, 2D columnar hexagonal phase with short-range intracolumnar order; Φ_c‑o, 3D columnar center orthorhombic lattice; Φ_m^k‑SL, 3D

columnar monoclinic crystalline superlattice; Φ_m^k1, Φ_m^k2, 3D columnar crystalline monoclinic phases; Lay^k, layered monoclinic crystalline phase. (b)

Dependence of the nature of 2D and 3D periodic arrays self-organized from (3,4,5)nG1-1-PBI as a function of n and temperature. Data were

obtained from a combination of DSC and ﬁber and powder XRD analyses at the indicated heating rate.

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Figure 5. (a−e) Wide-angle XRD patterns collected from oriented ﬁbers of (3,4,5)nG1-1-PBI with n = 8, 9, 10, 11, 12 in the 2D Φ_h^iophase at the

temperature shown on the diﬀraction patterns. Fiber axis, temperature, phase designation, and π−π stacking features are indicated. (f) The

corresponding meridional plots from diﬀraction patterns shown in a−e. The correlation length (ξ) is calculated as 4π/fwhm, where fwhm

corresponds to full width at half-maximum. (g) The two possible models of the supramolecular column. Color code: 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 atoms, gray.

Simulation of SAXS and WAXS Fiber Patterns. The

ordered 2D and 3D phases reported in Figures 1−3 and Tables

1, 2, and ST1 were determined by the X-ray analysis recorded

at both wide and small angles. XRD patterns for powder

samples and oriented ﬁbers extruded at room and higher

temperatures were recorded as a function of temperature. The

detailed experimental method for ther preparation of oriented

ﬁbers is reported in Supporting Figure SF1. The heating and

cooling rates of these XRD experiments was kept in the range

between 1 and 10 °C/min in order to match the experimental

conditions used in the DSC experiments. The heating and

cooling rates indicate the rate used to reach the required

temperature. After reaching the required temperature with

these rates the XRD pattern was recorded isothermally with an

exposure time of 600 s.

orthorhombic lattice, Φ_c‑o^k, with two columns in the unit cell

possessing opposite helical chirality. The columns are

constructed by stacking of supramolecular dimers along the c-

axis.

For n = 10, the angle between two neighbor columns in the

k

Φ_c‑ophase is 60.4° (indicated in Figure 4a). This value is

slightly deviated from that of a hexagonal lattice where the

angle is 60° and therefore, this phase is a pseudo-hexagonal

phase. The 7.0 Å (L = 2) diﬀraction remains in the

intermediate Φ_c‑o^kphase, which indicates that the π−π stacking

(3.5 Å) and the interdimer stacking distance is preserved and

transferred from the 3D ordered phase to the 2D Φ_h^iophase. It

can be concluded that as n increases, the intermediate

crystalline structure transforms more and more toward

hexagonal packing, and ﬁnally disappears for n = 12, where

only one crystalline structure, Φ_m^k1, can be identiﬁed through a

kinetically controlled process at low temperature.

The SAXS ﬁber patterns for n = 11, 10 and their indexing for

k

the 3D ordered phases Φ_m^k1, Φ_m^k2, and Φ_c‑oare shown in

k1

Figure 7. The supramolecular column of the Φ_mphase is the

Another crystalline phase observed in n = 11, 10, and 9 is

k1

thermodynamic product of the (3,4,5)nG1-1-PBI dendronized

PBIs with n = 8 to 12. The same phase was studied previously

for (3,4,5)12G1-1-PBI, revealing a criss-cross-like packing of

dendronized PBIs within the supramolecular column possessing

2₁helical symmetry.^13aAt low temperature, the formation of

Φ_m^k2, which is an intermediary phase connecting Φ_mand

Φ_c‑o^k. It is obtained during heating from the Φ_m^k1phase (Figure

k2

2). The formation of Φ_mis kinetically controlled in n = 11,

and thermodynamically controlled in n = 10 and 9. The

absence of (100) and (010) diﬀractions implies a monoclinic

unit cell with cell symmetry of Pn that contains two columns in

the unit cell with one column located in the cell center.

Combination with experimental density suggests that the dimer

packing is preserved in the Φ_m^k2phase. This makes the column

k1

Φ_mphase is under kinetic control for n = 12 and 11, and

thermodynamic control for n = 10, 9, 8. It is the stable phase

close to room temperature for compounds with n = 12 to 8.

io

The intermediate crystalline phases between Φ_m^k1and Φ_hfor

k

n = 11 and 10 are Φ_m^k2and Φ_c‑o^kas seen in Figure 7b,c for n =

11, and Figure 7e,f for n = 10. It can be seen from the SAXS

arrangement similar with that of Φ_c‑o, but the unit cell is

distorted in the ab plane (γ > 90°). It can be seen from the

DSC traces that the transition from Φ_m^k1to Φ_m^k2is associated

with a larger enthalpy change (3−6 kcal/mol), and the

k

pattern that the diﬀractions along the equator of Φ_c‑oare

io

similar to those observed in the Φ_hphase (Figure 5),

k2

k

indicating similar column arrangement within unit cell. Detailed

XRD analysis combined with experimental density revealed an

transition from Φ_mto Φ_c‑ois associated with a smaller

enthalpy change (<1 kcal/mol). This suggests that the

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Figure 6. Wide-angle XRD patterns collected from the oriented ﬁbers of (3,4,5)nG1-1-PBI with n = 6 to 12 in the 3D periodic arrays, and the

corresponding meridional plots. For n = 12 the pattern was obtained after 180 min of annealing at 24 °C. For n = 11 the pattern was recorded during

the second heating with a rate of 1 °C/min. Patterns for the other compounds were obtained during the second heating with a rate of 10 °C/min.

Fiber axis, temperature, phase, and layer lines are indicated.

structural diﬀerence between Φ_m^k1and Φ_m^k2is larger than that

By comparison with compounds with longer alkyl chain that

were discussed above, a similar phase behavior was observed in

n = 9. However, the conformational freedom decreases with

decreasing n, and therefore, in n = 9, the 2D Φ_h^iophase exists in

a narrower temperature range (183−227 °C) than for n = 10 or

11 (Figures 1 and 4b). In other words, the stability of the 3D

ordered phase observed in n = 9 has increased to 183 °C, and

the supramolecular columns require more energy to get

released from the coupling interactions with neighboring

columns. At lower temperature, close to room temperature,

the monoclinic phase, Φ_m^k1, was observed as the thermody-

k2

between Φ_mand Φ_c‑o^k. Also, the diﬀraction patterns of all

three crystalline phases possess the same layer line distance,

which implies the same number of strata along the c-axis and

the same π−π stacking distance between the PBI units.

Figure 8 shows the small-angle XRD patterns collected from

the oriented ﬁber of (3,4,5)9G1-1-PBI and (3,4,5)8G1-1-PBI

during second heating at a rate of 10 °C/min. The ﬁgure

reveals the evolution of ordered phases observed in the two

compounds as a function of increasing temperature.

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Table 2. Structural Analysis of (3,4,5)nG1-1-PBI with n = 6 to 12 by XRD and Experimental Density

a

b

c

d

e

f

g

h

n

T (°C)

phase

a, b, c (Å)

α, β, γ (deg)

D_col(Å)

t (Å)

ρ (g/cm³)

M_wt

n

μ

j

k

6

45

15

Φ_c‑o

Φ_m

Φ_c‑o

Φ_m

Φ_h

Φ_c‑o

Φ_m

Φ_h

Φ_c‑o

Φ_m

Φ_c‑o

Φ_h

Φ_c‑o

Φ_m

36.2, 27.4, 14.7

35.1, 29.7, 44.1

36.5, 28.8, 14.7

35.8, 30.4, 44.1

28.2, 28.2, −

37.6, 30.5, 14.5

37.5, 30.9, 14.2

24.5, 47.6, 14.2

29.3, 29.3, −

41.7, 30.8, 14.2

40.5, 30.8, 14.3

32.0, 37.9, 14.3

25.8, 47.3, 14.2

40.7, 30.6, 14.3

29.8, 29.8, −

90.0, 90.0, 90.0

114.6, 90.0, 90.0

90.0, 90.0, 90.0

111.3, 90.0, 90.0

−, −, 120.0

90.0, 90.0, 90.0

90.0, 90.0, 97.2

−, −, 120.0

90.0, 90.0, 90.0

90.0, 90.0, 93.6

90.0, 90.0, 96.8

90.0, 90.0, 90.0

−, −, 120.0

90.0, 90.0, 90.0

90.0, 90.0, 96.2

90.0, 90.0, 97.1

90.0, 90.0, 96.3

90.0, 115.0, 90.0

90.0, 112.2, 90.0

−, −, 120.0

90.0, 90.0, 90.0

90.0, 90.0, 98.5

90.0, 90.0, 94.2

90.0, 116.0, 90.0

−, −, 120.0

90.0, 90.0, 91.8

90.0, 90.0, 94.7

90.0, 115.0, 90.0

90.0, 116.5, 90.0

90.0, 113.5, 90.0

22.7

23.0

23.2

23.5

29.3

24.2

23.9

24.5

29.3

25.9

25.4

24.8

25.8

25.5

30.2

27.9

26.9

26.6

26.2

−

3.5

4.6

4.8

3.5

4.7

3.5

4.8

1.10

1.09

1.08

1171.55

1255.71

1339.86

8

24

8

1

−

1

−

1

−

k‑SL

k

7

8

35

k‑SL

0

24

−

8

io

225

80

j

k

55

8

k1

35

8

io

9

215

178

125

45

1.06

1.04

1424.02

1508.18

−

8

j

k

8

k2

8

k1

25

8

i

k

100

210

125

57

8

io

10

−

8

j

k

46.8, 30.6, 14.5

34.8, 40.9, 14.3

35.1, 40.0, 14.3

26.2, 47.2, 14.0

k2

8

k2

k1

i

25

8

−35

30

8

j

Lay^k

43.9, 24.8, 4.6

2

i

j

110

120

75

41.2, 25.0, 4.8

−

2

io

11

12

Φ_h

Φ_c‑o

Φ_m

30.2, 30.2, −

30.2

29.0

28.2

30.6

−

31.7

32.5

32.1

−

1.03

1.02

1592.34

1676.50

−

8

j

k

46.8, 30.9, 14.3

35.5, 41.2, 14.5

30.6, 47.3, 14.1

k2

k1

i

45

8

25

8

j

100

140

25

Lay^k

45.8, 25.2, 4.7

2

io

Φ_h

Φ_m

31.7, 31.7, −

32.5, 46.9, 14.2

−

8

j

k1

−40

−15

20

32.1, 47.8, 14.0

8

i

j

Lay^k

51.1, 23.2, 4.8

2

i

j

51.7, 24.6, 4.8

−

2

j

60

47.6, 24.8, 4.8

2

a

Phase notation: Φ_h^io, 2D columnar hexagonal phase with intracolumnar order; Φ_c‑o^k, columnar centered orthorhombic crystalline phase; Φ_m

,

k‑SL

b

columnar monoclinic crystalline superlattice; Φ_m^k, columnar monoclinic crystalline phase; Lay^k, layered monoclinic crystalline phase. Lattice

c

parameters determined from ﬁber and powder XRDs. Column diameter calculated using: D_col= a for Φ_h^io, and D_col= a/[2 cos (tan⁻¹b/a)] for

d

e

f

crystalline phases. Stratum thickness calculated from the meriodional pattern. Experimental density measured at 20 °C. Molecular weight of the

g

compound. Average number of molecules per unit cell, calculated using n = N_AρV_c/M_wt, where N_A= 6.022 × 10²³mol⁻¹is the Avogadro’s number,

h

and V_cis the unit cell volume calculated from lattice parameters. Average number of dendrimers forming the supramolecular column stratum,

calculated using μ = N_AρAt/2M_wt, where A is the unit cell area of the ab plane, and t is the average strata thickness calculated from the meriodional

i

j

pattern. Phase observed in as-prepared samples. Fiber direction.

namic product that is generated independent of rate. Upon

heating to 33 °C, a transition from Φ_m^k1to Φ_m^k2was observed

with a transition enthalpy of 3.56 kcal/mol. Similar to the case

of n = 11 and 10, this phase does not form upon cooling from

the isotropic melt. The Φ_c‑o^kphase in n = 9 exists upon heating

regardless of rate at temperature above 55 °C. As in (3,4,5)

nG1-1-PBI with n = 11 and 10, all phases in (3,4,5)9G1-1-PBI

exhibit meridional maxima at 3.5 and 7.0 Å at L = 4 and 2,

respectively. These features along with the experimental density

(1.06 g/cm³) conﬁrm the formation of a supramolecular dimer

structure.

correlations developed without slow cooling or annealing at

high temperature. At low temperature, Φ_m^k1is the stable phase

as in the other compounds with n = 12 to 9. Upon heating to

k1

k

37 °C (Figure 1), the Φ_mtransforms to Φ_c‑odirectly with a

transition enthalpy of 6.04 kcal/mol without the intermediary

k2

k

Φ_mphase. Also, the Φ_c‑ophase with P2₁2₁2₁symmetry in

(3,4,5)8G1-1-PBI is found within a wider temperature range,

60−223 °C. This suggests that Φ_c‑obecomes a more stable

phase with decreasing n within the intermediary temperature

k

range. In fact, for compounds with n = 7 and 6, the same Φ_c‑o

phase dominates the 3D ordered structure in an even wider

temperature range, from close to room temperature up to over

250 °C. Their diﬀraction patterns will be discussed later. In

addition, the temperature range of the 2D Φ_h^iophase from n =

8 is compressed to between 223 °C and the isotropization

transition at 229 °C as a result of further decrease of the

conformational freedom with the decrease of n. In other words,

the stability of the long-range intra- and intercolumnar

correlations is gradually increased by the decreased liquid-like

SAXS ﬁber patterns of 3D and 2D ordered phases observed

in (3,4,5)8G1-1-PBI during second heating with 10 °C/min are

io

shown in Figure 8. The 2D Φ_hphase is generated from

uncorrelated helical columns without intercolumnar order, as

evidenced by the lack of quadrant diﬀractions (Figure 8f), while

the 3D phases observed at low temperature are generated from

coupled helical columns. These patterns demonstrate again that

the transition between ordered phases in n = 8 is

thermodynamically controlled and the column-to-column

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Figure 7. Small-angle XRD patterns collected from an oriented ﬁber of (3,4,5)11G1-1-PBI (a−c) and (3,4,5)10G1-1-PBI (d−f) showing 3D ordered

phase at various temperatures during heating. Fiber axis, lattice symmetry, indexing, and lattice parameters of the Φ_m^k1, Φ_m^k2, and Φ_c‑o^kphases are

indicated. Patterns collected during second heating with a rate of 1 °C/min for n = 11 and 10 °C/min for n = 10.

io

character of the aliphatic jacket. The 2D Φ_hphase disappears

when the length of alkyl chain is smaller than 8 (Figure 1, 2).

Figure 9a−c summarizes the comparison of experimental and

simulated wide-angle ﬁber XRD patterns of (3,4,5)nG1-1-PBI

with n = 9, 10, 11 in the Φ_m^k1phase with P2₁/b symmetry. The

detailed initial supramolecular column and lattice model in top

and side views used for the simulation are shown in Figure 9d−

f.

translation were performed until the simulated pattern ﬁt best

to the experimental XRD pattern. For the clarity of the core

packing of dendronized PBIs, the tapered alkyl chains on both

ends of the molecule are not shown in the unit cell models

presented in all ﬁgures. A detailed ﬂowchart of the phase

determination and simulation process is summarized in

Supporting Figure SF2.

As seen from the model shown in Figure 9, the column

repeat c-axis is formed by stacking four molecules at 3.5 Å

spacing. The dendronized PBIs are shifted inside the

supramolecular column within the ab plane to avoid intra-

columnar steric constrains. This oﬀ-centered molecule arrange-

ment along the column axis shown in Figure 9d generates the

2₁helical symmetry by rotation of molecule pairs by 180° along

the c-axis. Each pair is constructed by two molecules forming a

dimer-like repeating unit with an intradimer rotation around

80°. As shown in the side view of Figure 9f, along the b-axis lie

alternate rows of supramolecular columns with respectively left-

and right-handed helices that results from the P2₁/b symmetry.

The reconstructed relative electron density distributions of the

To conduct the XRD simulation, the energy-minimized

primary molecular structure was ﬁrst constructed by a

combination of software packages including Materials Studio

Modeling software (version 3.1.0) and Discovery Studio

(version 3.5). The preliminary supramolecular columnar

model was then constructed according to the helical parameter

obtained from the XRD data. To build the crystal cell, the

lattice dimension and symmetry group were extracted from the

analysis of the primary XRD data by Datasqueeze (version 2.8),

followed by unit cell construction in Materials Studio. The

initial arrangement of supramolecular columns within the unit

cell was judged by the lattice dimension, unit cell symmetry,

and experimental density. Energy minimization was then

performed to the unit cell to generate the initial model for

XRD simulation. The initial unit cell model was exported to

Accelrys Cerius2 (version 3.8), where the simulation of ﬁber

XRD diﬀraction was performed. To produce the ﬁnal model,

minor model modiﬁcations in Cerius2 including inter- and

intradimer rotation, supramolecular column rotation, and

k1

Φ_mphase in Figure 9g reveal the strong coupling of helical

supramolecular columns in the low-temperature thermody-

namic product. The diﬀerence in the diﬀraction patterns

between compounds results from subtle variation of inter- and

intradimer rotation and also the shift of dendronized PBIs in

the supramolecular column with respect to the column center.

It is apparent that the Φ_m^k1phase observed in n = 11 possesses

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Figure 8. Small-angle XRD pattern collected from the oriented ﬁbers of (3,4,5)9G1-1-PBI (a−c) and (3,4,5)8G1-1-PBI (d−f) during second heating

io

with a rate of 10 °C/min, showing the observed 3D crystalline and 2D Φ_hphases at indicated temperatures. Fiber axis, symmetry, indexing, and

lattice parameters of the corresponding phases are indicated.

a much lower order compared with that in n = 10 and 9, even

though the pattern of n = 11 was collected during very slow

cooling with a rate of 1 °C/min while the other two patterns

were collected with a rate of 10 °C/min. Compared with the

high-temperature 2D hexagonal and 3D orthorhombic arrays,

the 3.5 Å stacking distance is conserved in Φ_m^k1, but the

dendronized PBIs undergo signiﬁcant changes with respect to

their helical arrangement and centering within the column.

These diﬀerences in packing and changes in ordering are

responsible for the slower kinetics and larger enthalpy change

would require a single column in one unit cell with all columns

in the crystal having identical right- or left-handed helical

arrangements. This is unlikely since this library of dendronized

PBIs contains no chiral center that could control the chirality in

the crystal. Therefore, the columns packed into an

orthorhombic unit cell containing two columns with opposite

chirality. The 2₁symmetry operation in the orthorhombic cell

would generate right- and left-handed columns in alternative

rows (Figure 10c) and make the overall crystal achiral. The

resulting column position in the unit cell is similar but deviates

slightly from that in hexagonal arrays.

The undulated nature of the aromatic−aliphatic interface can

also be identiﬁed in the 3D reconstructed electron density

distribution. Figure 10d shows how the coupling of undulated

columns produces the 3D column-to-column correlations. To

construct the supramolecular column along the c-axis, a pair of

molecules forming a dimer-like structure as repeat unit with the

perylene planes stacked parallel but rotated ∼45°. Two dimers

generated the helical symmetry via ∼90° rotation with respect

to each other. The helical rotation along the c-axis is illustrated

in Figure 10b, where a pair of molecules in the dimer are

marked as red and blue, respectively. The sharp 7.0 Å

meridional diﬀraction ((002) in Figure 8) is the result of the

interdimer packing and persists through the whole temperature

range below the isotropic state. The 3.5 Å π−π distance is

conserved in a wide temperature range and displays long-range

order.

k1

observed in the formation of the Φ_mphase.

k

Figure 10 details the lattice model in the Φ_c‑ophase with

P2₁2₁2₁symmetry and a selected example showing the

comparison between experimental and simulated ﬁber WAXS

pattern for (3,4,5)8G1-1-PBI at 55 °C. The strong L = 4

meridional diﬀraction suggests that the column repeat c

contains four molecules spaced at 3.5 Å. The repeat distance

along c is about 14 Å, indicating that the columns in Φ_c‑o^khave

close to 8₁helical symmetry. This is illustrated in Figure 10b. It

can be clearly identiﬁed according to Figure 10c from the top

view that the column packing is similar to that found in

hexagonal arrays. Compared with the 2D hexagonal arrays

obtained at high temperature, where the supramolecular

columns possess no correlation with each other, the 3D

intercolumn correlation developed during the transition from

io

Φ_hto Φ_c‑o^k. In the 2D-to-3D transition, the columns are

diﬃcult to pack into a 3D hexagonal lattice since the symmetry

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Figure 9. Comparison of the simulated and experimental WAXS ﬁber patterns of (3,4,5)nG1-1-PBI with n = 9 (a), 10 (b), 11 (c) in the columnar

monoclinic crystalline phase, Φ_m^k1, at 25 °C, −35 °C, and 25 °C, respectively. The corresponding supramolecular column (d), the lattice model in

top and side views used as the initial model in the simulation (e,f), and the 2D and 3D reconstructed relative electron density distribution of Φ_m^k1are

also shown (g). Color code used in molecular models is the same as in Figure 5.

Figure 10. Comparison of the experimental and simulated wide-angle XRD patterns collected from the oriented ﬁber of (3,4,5)8G1-1-PBI at 55 °C

in the columnar centered orthorhombic crystalline phase, Φ_c‑o^k(a), and detail of the supramolecular column (b) and lattice model (c) used in the

simulation. The 2D and 3D reconstructed relative electron density distributions are also shown (d). Color code used in the molecular model: 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 atoms, gray.

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Figure 11. Comparison of the simulated and experimental ﬁber WAXS patterns of (3,4,5)10G1-1-PBI at 25 °C (a) in the columnar monoclinic

crystalline phase, Φ_m^k2, and the corresponding supramolecular column (b) and lattice model in top and side views (c) used in the simulation. The

2D and 3D reconstructed relative electron density distributions are also shown (d). Color code used in the molecular model: 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 atoms, gray.

Figure 11 shows a selected example from (3,4,5)10G1-1-PBI

that details the comparison between simulated and exper-

imental ﬁber WAXS patterns of the Φ_mphase with Pn

isotropization temperature at 272 °C. During the cooling scan,

k

k‑SL

as shown in Figure 12, a transition from Φ_c‑oto Φ_m

is

k2

identiﬁed at 27 °C (Figures 1, 2). Additional oﬀ-meridional

diﬀractions were observed at L = 1 and 5 (Figure 12b, yellow

arrow), indicating the tilt of the c-axis with respect to the ab

plane. Also the appearance of additional layer lines indicates a

tripling of the c-dimension of the cell compared with that of

Φ_c‑o^k. The phase was indexed as monoclinic Φ_m^k‑SL, with a as

the unique axis. The equatorial indices and spacings remain

unchanged, indicating that the supramolecular column cross-

symmetry collected at 25 °C. The molecular and column

packing models used in the simulation are also illustrated

(Figure 11b,c). This phase is observed during heating from the

k1

low-temperature stable Φ_mphase in n = 11 to 9 before the

columns transform into the Φ_c‑o^k. Judging from the intradimer

(L = 4) and interdimer (L = 2) diﬀractions, the arrangement in

k2

Φ_mis close to an 8₁helix, with the neighbor PBI units

k

separated by 3.5 Å. According to the symmetry operation, the

columns located in the unit cell center possess diﬀerent helical

chirality than those located at corners. Although the stacking

section remains almost constant at the transition from the Φ_c‑o

to the Φ_m^k‑SLlattice. The unit cell of Φ_m^k‑SLcontains three sub-

cells along c, with a tilted c-axis of 14.7 Å. The same transition

was observed at both 10 and 1 °C/min heating rates with

almost identical transition temperature, suggesting that the

transition is thermodynamically controlled, with a fast

crystalline-to-crystalline rate near room temperature. Detailed

XRD 2D patterns and 1D plots for n = 7 and 6 showing the

peak intensities and the agreement between calculated and

experimental d-spacings are in Supporting Figures SF8 and

SF10.

k1

k2

distance is conserved during the transition from Φ_mto Φ_m

,

the molecular rotation along the column axis and the 3D

packing of columns within the unit cell are much diﬀerent. This

diﬀerence results in the slow kinetics observed for the

k2

formation of Φ_min n = 11.

k2

As shown in Figure 11b, the column construction in Φ_m

k

shows helical symmetry similar to that found in Φ_c‑o, but the

ab angle γ changes away from 90°. The small diﬀerences in the

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

In summary, four ordered phases were identiﬁed in the

k

k2

supramolecular columns forming the 3D Φ_c‑oand Φ_mare

responsible for the fast kinetics observed at the transition, and

the associated enthalpy change is relatively small (for example,

ΔH = 0.27 kcal/mol in n = 10, Figure 1). Combined with

experimental density, the simulation reveals that, similar to the

library of (3,4,5)nG1-1-PBI with n = 12 to 6, including one 2D

io

Φ_hphase and three 3D crystalline phases (Φ_m^k1, Φ_m^k2, and

Φ_c‑o^k) that are obtained by cooling from the isotropic melt or

after annealing. Formation of the low-temperature 3D phases is

under kinetic control for n = 12, 11 and thermodynamic control

k2

io

columns generated in other phases, the Φ_mcompound also

for n = 10 to 6, while formation of the 2D Φ_hphase at high

forms columns via helical packing of only one molecule per

stratum, with two columns in one unit cell. The 3D

reconstructed electron density distributions shown in Figure

10d also illustrate the register between neighboring columns in

the 3D Φ_m^k2crystalline phase. Notice that the column diameter

(D_col) is nearly constant for all 3D phases generated by a single

compound but gradually increases with increasing n (Table 2).

Figure 12 shows the SAXS patterns of the (3,4,5)6G1-1-PBI

ﬁber extruded at 20 °C. The diﬀraction arcs with narrow

azimuthal spread indicate that the supramolecular columns are

easily aligned at room temperature. In the ﬁrst heating of the

temperature is under thermodynamic control for n = 12 to 8.

io

The temperature range for the formation of Φ_hphase

decreases as n decreases, and eventually disappears in

compounds with n = 7 and 6. On the other hand, the stable

k

temperature range for Φ_c‑ophase increases with decreasing n.

It is the stable 3D phase for a range of over 200 °C in n = 7 and

6, while it does not form at all in n = 12. At low temperature

near room temperature, it seems that the stable phase is a

monoclinic crystal for all compounds in this library. However,

the larger diﬀerence with respect to intra- and intercolumn

packing makes the phase slower to form and costs more energy.

Interestingly, the as-prepared phase of n = 12, 11, and 10

k

as-prepared ﬁber, Φ_c‑ois the only phase observed below the

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Figure 13. (a) Comparison of the experimental and simulated wide-

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

1-PBI in the as-prepared condition, showing layered crystalline phase

at 20 °C. Fiber axis, diﬀraction peaks, indexing, and lattice parameters

are indicated. (b) Molecular model used in the simulation showing the

construction of lamellar crystal and the layers of alkyl chain and PBI

core.

performing any thermal treatment, from the as-prepared

compounds. The detailed preparation method of oriented

ﬁbers is described in Supporting Figure SF1. Although the

sample with layered structure (as-prepared from solvent

evaporation) is crystalline, the alkyl chains still possess certain

mobility at room temperature that makes the overall sample a

highly viscous material. Therefore, it is possible to prepare

oriented ﬁbers by extrusion at room temperature of the sample

with layered structure. During the extrusion, the alkyl chain

layers can slide between each other and create the c-axis of the

crystallites parallel to the ﬁber axis. The sample of n = 11 and

10 exhibits the same layered as-prepared structure as n = 12

(Supporting Information). Interestingly, this layered crystal is

observed only in the as-prepared samples of n = 12 to 10. For n

= 9 to 6, the layered structure does not form, and the as

obtained samples show only 3D columnar structures. Figure

13a shows a comparison of experimental and simulated wide-

angle XRD patterns of oriented ﬁber prepared from

(3,4,5)12G1-1-PBI at 20 °C before any heat treatment. A 1D

XRD plot showing the layered structure diﬀraction spacings is

Supporting Figure SF6. The diﬀractions on the pattern equator

ﬁt nicely in a rectangular 2D lattice, indicating the γ angle is

90°. Taking the strongest meridional 4.3 Å peak as d₀₀₁and the

4.1 Å peak as d₀₁₁would suggest a monoclinic lattice with b as

the unique axis. The weak diﬀraction on the meridian with

spacing of 4.8 Å implies that β should be larger than 90°.

According to the XRD pattern analysis and simulation

combined with the experimental density, a monoclinic unit

cell with P2₁symmetry and parameters of a = 51.7 Å, b = 24.6

Figure 12. Small-angle XRD pattern collected from the oriented ﬁber

of (3,4,5)6G1-1-PBI at (a) 45 and (b) 15 °C. Fiber axis, diﬀraction

peaks, indexing, and lattice parameters of the columnar centered

orthorhombic crystalline phase, Φ_c‑o^k, and columnar monoclinic

crystalline superlattice, Φ_m^k‑SL, are indicated. Patterns collected during

cooling with a rate of 10 °C/min. The extra diﬀractions that emerged

at the Φ_c‑o^k-to-Φ_m^k‑SLtransition are indicated by yellow arrows in (b).

obtained by slow evaporation of its THF or CH₂Cl₂solution

showed a completely diﬀerent crystal structure that appears to

be a layered crystal instead of a columnar crystal. This layered

crystal structure is brieﬂy discussed in the following session.

As-Prepared Phases of (3,4,5)12G1-1-PBI. The as-

prepared sample refers to the compound puriﬁed repeatedly

by column chromatography, dissolved in CH₂Cl₂, followed by

solvent removal through slow evaporation (cast ﬁlm), and dried

overnight under vacuum. The as-prepared samples of (3,4,5)

nG1-1-PBI with n = 12, 11, and 10 exhibit a layered crystalline

structure in the ﬁrst heating cycle that does not re-form in the

subsequent heating and cooling experiments, and the transition

from the layered crystal to 2D columnar arrays is associated

with a large enthalpy change (Figures 1 and 2). This suggests

that, inside the supramolecular structure, the PBI cores and

alkyl tails are well phase-separated, and the long alkyl chains

possess good packing with neighboring chains in the unit cell.

These phases were investigated by powder and ﬁber XRD

techniques. The oriented ﬁbers were prepared by extrusion at

25 °C, with data shown in Figure 13 for n = 12, without

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Figure 14. ¹H DQ correlation (a−c) and VT ¹H MAS (d−f) spectra of (a,d) (3,4,5)9-G1-1-PBI, (b,e) (3,4,5)10-G1-1-PBI, and (c,f) (3,4,5)12-G1-1-

PBI. The well-deﬁned ¹H sites of the thermodynamically controlled columnar monoclinic structure of (3,4,5)9-G1-1-PBI (a) provides a signiﬁcantly

better deﬁned double-quantum correlation pattern compared to the slightly obscured double-quantum correlation pattern observed in the spectrum

of the kinetically controlled monoclinic structure of (3,4,5)12-G1-1-PBI (c).

Å, c = 4.8 Å, and β = 116.5° is determined where each unit cell

contains two molecules. The molecular model used in the

simulation is shown in Figure 13b. In the model, the layered

feature can be clearly identiﬁed. The PBI long axis and the alkyl

chain direction are parallel to the unit cell a-axis, and the PBI

planes are tilted with respect to the c-axis. In the XRD of

layered crystals, the 3.5 Å π−π stacking diﬀraction that was

found in other columnar phases is absent. According to this

model, the stacking distance has increased to about 4.3 Å. This

suggests that the distance between PBI planes is not optimized

in this structure, and therefore, performance in terms of charge

mobility would not be good compared with the columnar

structures obtained after heating and annealing. We speculate

that the formation of the layered crystal is probably a sacriﬁce

to allow good packing of the long alkyl chains. With the

decreasing of alkyl chain length, the tails would no longer have

the power to keep the perylenes apart, and the stable columnar

phases generated in the as-prepared sample with perylenes

stack at 3.5 Å for n smaller than 10. Recently, functionalized

PBI derivatives equipped with hydrogen-bonding units were

reported to have a similar phase transition between a 2D

supramolecular columnar structure and a layered structure.¹⁶

However, opposite to the dendronized PBIs reported here, the

columnar hexagonal phase was observed in the as-prepared

sample of PBIs obtained by solvent casting. A structural

transition to a highly ordered layered structure was observed

during subsequent heating. Two previous reports published in

2004 and 2005 did not observe the layered structure reported

here for (3,4,5)12G1-1-PBI.^8g,9cThis is most likely because the

as-obtained sample was prepared by precipitation instead of

evaporation, which suppressed the formation of well-ordered

lamellar structure.

Analysis of the Molecular Dynamics of the Supra-

molecular Columns of (3,4,5)nG1-1-PBI with n = 9 and

10 by Variable-Temperature Solid-State ¹H NMR Experi-

ments. In the solid state, NMR chemical shifts and in

1

particular H chemical shifts are very sensitive to the local

molecular packing. Due to the substantial signal broadening

resulting from anisotropic NMR interactions as well as the low

1

spread of H chemical shifts, NMR measurements at high

magnetic ﬁelds and fast magic angle spinning (ω_R> 25 kHz)

are required. Under these conditions, the spectral resolution

obtained for chemically and crystallographically distinguished

¹H sites is limited by the local packing accuracy determining the

electron density distribution at the site. In the case of materials

based on self-organizing supramolecular architectures, minor

variations of the local electron density at a speciﬁc packing site

cause signal broadening, indicating the quality of the molecular

self-organization. When the molecular packing arrangements of

self-organizing systems are thermodynamically controlled with

typically well-deﬁned crystallographic sites, well-resolved,

informative ¹H double-quantum correlation spectra are

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Scheme 3. Schematic of the Self-Assembly of Dendronized PBIs (3,4,5)nG1-m-PBI with m = 0, 1, 2, 3, 4 and n = 14 to 4

observed with common double-quantum recoupling schemes

under fast MAS conditions. In contrast, H NMR spectra of

(3,4,5)12-G1-1-PBI sample shown in Figure 14c, where the

aromatic signals are broadened so much that the identical

underlying correlation pattern of the columnar monoclinic

structure is hardly recognized.

1

samples with kinetically controlled self-organization, which

typically leads to a signiﬁcantly higher molecular disorder in the

material, exhibit substantially broader signals and in most cases

a very poor spectral resolution. This low spectral resolution

cannot be improved by the application of faster MAS, advanced

homonuclear decoupling schemes, or even higher magnetic

ﬁelds, since it is limited by the heterogeneous distribution of ¹H

sites in the locally only partially ordered material.¹⁷

This is illustrated by the double-quantum correlation spectra

given in Figure 14, in which the same correlation pattern of the

columnar monoclinic phase shows a signiﬁcantly lower spectral

resolution for the aromatic signals of the PBI cores in

(3,4,5)10-G1-1-PBI (Figure 14b) compared to those of the

thermodynamically controlled columnar monoclinic phase of

sample (3,4,5)9-G1-1-PBI shown in Figure 14a. Moreover, the

spectral resolution in Figure 14b is signiﬁcantly better

compared to the correlation spectra of the kinetically controlled

In conventional ¹H VT MAS NMR measurements, the

spectra of kinetically controlled (3,4,5)12-G1-1-PBI (see Figure

14f) show a smooth gradual transition from the low-

temperature spectrum of the columnar monoclinic structure,

common to all three samples at 320 K, to the spectrum of the

hexagonal columnar meso-phase, characterized by a single

broad proton signal in the aromatic region at 6.5 ppm. The

1

same transition is observed in the H VT MAS spectra of

sample (3,4,5)10-G1-1-PBI shown in Figure 14e in a much

narrower temperature range between 380 and 410 K. For the

spectra of sample (3,4,5)9-G1-1-PBI shown in Figure 14d, the

transition is not observed. The spectrum at 410 K, the highest

temperature accessible to our 2.5 mm MAS probe, indicates

some changes compared to the spectra at lower temperatures,

which seem to be almost temperature independent. This

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1

spectrum clearly deviates from the H MAS NMR spectra of

arrangement of the m = 1 library is the disruptive up−down

alternation of the tetramer within a column found for m = 0, 2,

3, 4. However, the as-prepared structures resultin from m = 1, n =

12, 11, and 10 are 3D layered rather than 3D columnar and are

not re-formed after heating and cooling (left column in Scheme 3).

Although this structure may represent the equilibrium structure

from solution, it may not be the best structure for potential

applications due to non-optimized PBI core stacking distance and

diﬃculties in alignment. As in the case of m = 0, 2, 3, 4, the 2D

thermodynamic product from high temperature for m = 1 and n

= 12 and 11 is thermodynamically controlled and becomes the

kinetic product at low temperature since the 3D thermody-

namic product from low temperature is kinetically controlled.

For m = 1 and n = 10, 9, 8 the 2D thermodynamic product that

is thermodynamically controlled at high temperature trans-

ferred to the 3D thermodynamic product at low temperature

regardless of cooling rate since the transition from 2D to 3D

phase becomes thermodynamically controlled. For m = 1 and n

= 7 and 6 the transitions between phases are all thermodynami-

cally controlled (independent of rate), similar to those observed

for m = 1 with n = 10 to 8. However, the 3D crystalline phases

dominate the whole temperature range below isotropic

temperature without a transition from 3D crystalline phase to

2D liquid crystalline phase. In addition, a new phase, Φ_m^k‑SL, is

developed below room temperature, generated from tilted

columns of Φ_c‑o^k, which is reminiscent of the self-repairing

process observed from m = 3 and n = 9 and 8.^13bThe helical

supramolecular columns forming 2D and 3D periodic arrays

reported here are chiral, but the unit cell is nonracemic since it

contains a left and a right helical column. However, it is also

important to understand how the chirality of the chemical

structure could aﬀect the self-assembly and the kinetic and

thermodynamic supramolecular products, and if homochirality

could lead to any diﬀerence in the electronic properties of

dendronized PBI. The investigation of chiral compounds will be

discussed in a future publication. Last but not least, we would

like to stress that most of the supramolecular assemblies

reported in the literature are routinely based on structures

involving n-dodecyl alkyl groups.^{1−3,5,7−13,15}The results

reported here demonstrate that shorter than eleven methylene

groups in the self-assembling building block may be more

suitable than n-dodecyl for all reported investigations; there-

fore, we recommend the use of a combination of lengths of

alkyl groups in future investigations.

the two other samples at 410 K, with the single broad peak at

6.5 ppm attributed to the columnar hexagonal phase. From the

DSC and X-ray studies shown before, the transition from the

columnar orthorhombic to the columnar hexagonal phase is

expected at 455 K. It should be noted that phase transitions

being driven by molecular ﬂuctuations or changing the local

molecular mobility of speciﬁc sites in supramolecular

architectures are not necessarily observed at the same

temperature like in DSC traces, because most changes

monitored in NMR spectra resulting from molecular mobility

are sensitive to reorientations with a correlation time in the 100

kHz range which may not match the dynamic process driving

or activated by the phase transition. In conclusion, the solid-

state NMR results are nicely consistent with the experimental

ﬁnding shown before, and thus conﬁrm the transition from

kinetically controlled to thermodynamically controlled colum-

nar structures.

CONCLUSIONS

■

The results reported here, combined with those obtained in the

two previous publications,^13a,bare summarized in Scheme 3.

This scheme, although simpliﬁed, demonstrates the complexity

of the self-assembly of PBI containing self-assembling twin

dendrons at its imide positions. All (3,4,5)nG1-m-PBI with m =

1 and n = 12 to 6 self-assemble into dimers forming 2D and 3D

periodicities shown in the second to fourth columns from the

left of Scheme 3. In the case of m = 0, 2, 3, 4 and n ≤ 12, the

dendronized PBI self-assembles in complex helical columns

based on tetramers of PBI units comprising two columnar

strata, two molecules lying side-by-side in each stratum. The

distances and rotation angle within and between the tetramer

strata are diﬀerent. Exceptions are m = 3, n = 8 and 9, where a

self-repairing process results in the intratetramer and

intertetramer distances being equal. All compounds with m =

0, 2, 3, 4 exhibit at high temperature a 2D thermodynamic

product that is thermodynamically controlled and at low

temperature 3D thermodynamic products that are kinetically

controlled. Therefore, under many conditions, at low temper-

ature the 2D periodicity is observed as a kinetic product. This is

illustrated in the ﬁrst two columns on the right in Scheme 3.

io

Also, at high temperature in the 2D Φ_hphase, the

supramolecular columns constructed by dimers and tetramers

contain a statistical mixture of up and down molecular

arrangements (Figure 5). The random molecular conformation

in columns disrupts the helical packing and generates the weak

diﬀraction at ∼7.0 Å.^13aFor the low-temperature 3D periodic

arrays, the architecture of the repeat unit from 2D phase is

preserved for both dimers and tetramers, but the molecules in

supramolecular columns possess an ordered up-and-down

arrangement within columns and between columns.¹³For the

orthorhombic periodicity observed in m = 0, 2, 3, 4, the

supramolecular columns consist of tetramers with alternate up-

and-down molecular conformations that generate diﬀerent

intra- and intertetramer stacking distances.¹³Compounds with

m = 1 and n = 12, 11 behave in the same way as those with m =

0, 2, 3, 4 except that they form dimers rather than tetramers. All

compounds with m = 1 display equal intra- and interdimer

distances resulting from the all-up or all-down orientation of

the dendron groups within a column. The uniform orientation

and up−down alternation among neighboring columns allows

close and extended π−π stacking that may allow superior

charge carrier mobility and eﬃcient transport. Contrasting the

ASSOCIATED CONTENT

* Supporting Information

■

S

Experimental procedures with 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

■

Notes

The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENTS

■

Financial support by the National Science Foundation (DMR-

1066116, DMR-1120901, DMS-0935165, and OISE-1243313),

the Humboldt Foundation, and the P. Roy Vagelos Chair at

Penn is gratefully acknowledged. This work was also ﬁnancially

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(c) Zhang, X.; Chen, Z.; Wurthner, F. J. Am. Chem. Soc. 2007, 129,

̈

supported by the German Research Foundation (DFG)

through grant SFB 625, by the European FP7 Project

NANOGOLD (grant 228455), and the WCU Program funded

by the Ministry of Education, Science, and Technology of

Korea (R31-10013).

4886−4887. (d) Zhang, X.; Rehm, S.; Safont-Sempere, M. M.;

Wurthner, F. Nat. Chem. 2009, 1, 623−629.

̈

(6) Law, K. Y. Chem. Rev. 1993, 93, 449−486.

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F. C.; Mullen, K. Chem.Eur. J. 2004, 10, 528−537. (b) Cotlet, M.;

̈

Masuo, S.; Lor, M.; Fron, E.; Van der Auweraer, M.; Mullen, K.;

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Transformation from kinetically into thermodynamically controlled self-organization of complex helical columns with 3d periodicity assembled from dendronized perylene bisimides

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