Extraordinary Acceleration of Cogwheel Helical Self-Organization of Dendronized Perylene Bisimides by the Dendron Sequence Encoding Their Tertiary Structure

Article abstract of DOI:10.1021/jacs.0c03353

The cogwheel model of hierarchical self-organization provides a route to highly ordered crystalline helical columnar hexagonal arrays of perylene bisimides (PBIs) conjugated to (3,4,5)-dimethyloctyl (racemic dm8*, r) minidendrons. Cogwheel PBIs assemble with identical structural order irrespective of molecular chirality to generate helical columns jacketed with an alkyl coat with length equal to half the helical pitch, exhibiting helical deracemization in the crystal state. These assemblies were accessible only via annealing or cooling and reheating at 1 °C/min. Recently it was discovered that hybrid rr8 sequence-defined dendrons with r and linear n-octyl (8) chains enabled the formation of the cogwheel phase at 10 °C/min upon heating but not cooling. Here we report four libraries of hybrid PBIs with sequence-defined dendrons containing r and n-alkyl (CnH2n+1) chains with n = 6, 7, 9, and 10. Structural analysis of these libraries by fiber X-ray diffraction and differential scanning calorimetry reveals that the 9r9 sequence enables an extraordinary acceleration of cogwheel assembly at rates of up to 50 °C/min on heating and cooling, providing, to the best of our knowledge, the fastest crystallizing supramolecular or covalent macromolecule known. Solid-state NMR studies help to elucidate this unexpected and unprecedented extraordinary acceleration of hierarchical self-organization, which arises from a combination of crystal packing of the ideal tertiary structure and alkyl chain dynamics. This general model raises questions about the use of achiral motifs to achieve high structural order in chiral systems and the need for disorder to create order in complex biological and bioinspired synthetic systems.

Full text of DOI:10.1021/jacs.0c03353

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Article
Extraordinary Acceleration of Cogwheel Helical Self-
Organization of Dendronized Perylene Bisimides by the
Dendron Sequence Encoding their Tertiary Structure
Li Wang, Benjamin E. Partridge, Ning Huang, James T Olsen, Dipankar Sahoo,
Xiangbing Zeng, Goran Ungar, Robert Graf, Hans W. Spiess, and Virgil Percec
J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 28 Apr 2020
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Extraordinary Acceleration of Cogwheel Helical Self-Organization of Dendronized
Perylene Bisimides by the Dendron Sequence Encoding their Tertiary Structure
Li Wang,†,○ Benjamin E. Partridge,†,□ Ning Huang,† James T. Olsen,† Dipankar Sahoo,† Xiangbing Zeng,§
Goran Ungar,§,# Robert Graf,◊ Hans W. Spiess◊ and Virgil Percec†,*
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† Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia,
Pennsylvania 19104-6323, United States
○
College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing
100029, China
§
Department of Materials Science and Engineering, University of Sheffield, Sheffield, S1 3JD, United
Kingdom
# State Key Laboratory for Mechanical Behavior of Materials, Xi’an University, Xi’an 710049, China
◊ Max-Planck Institute for Polymer Research, 55128 Mainz, Germany
*E-mail: percec@sas.upenn.edu
ABSTRACT: The cogwheel model of hierarchical self-organization provides a route to highly ordered
crystalline helical columnar hexagonal arrays of perylene bisimides (PBIs) conjugated to (3,4,5)-
dimethyloctyl (racemic dm8*, r) minidendrons. Cogwheel PBIs assemble with identical structural order
irrespective of molecular chirality to generate helical columns jacketed with an alkyl coat with length
equal to half the helical pitch, exhibiting helical deracemization in crystal state. These assemblies were
accessible only via annealing or cooling and reheating at 1 °C/min. Recently it was discovered that hybrid
rr8 sequence-defined dendrons with r and linear n-octyl (8) chains enabled the formation of the cogwheel
phase at 10 °C/min upon heating but not cooling. Here we report four libraries of hybrid PBIs with
sequence-defined dendrons containing r and n-alkyl (CnH2n+1) chains with n = 6, 7, 9, and 10. Structural
analysis of these libraries by fiber X-ray diffraction and differential scanning calorimetry reveals that 9r9
sequence enables an extraordinary acceleration of cogwheel assembly at rates of up to 50 °C/min on
heating and cooling, providing, to the best of our knowledge, the fastest crystallizing supramolecular or
covalent macromolecule known. Solid state NMR studies help to elucidate this unexpected and
unprecedented extraordinary acceleration of hierarchical self-organization, which arises from a
combination of crystal packing of the ideal tertiary structure and alkyl chain dynamics. This general model
raises questions about the use of achiral motifs to achieve high structural order in chiral systems and the
need for disorder to create order in complex biological and bioinspired synthetic systems.
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INTRODUCTION
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Function in natural systems arises from the hierarchical transfer of structural information encoded in a
primary structure, such as DNA or an amino acid sequence, and expressed by a tertiary structure, such as
the folded state of a protein.1 These structures are often helical2 and are invariably homochiral, the origin
of which remains one of the greatest unsolved fundamental questions within the natural sciences.3 The
emergence of homochiral life necessitates a means to resolve chirality within racemic mixtures, by
enriching a statistical chiral imbalance4 or by separating racemates into enantiopure domains.5 This
separation – known as deracemization – was demonstrated for the first time in the solution state by Pasteur
in the 1840s.6
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Supramolecular polymers7 provide a tunable platform for exploring helical assembly,8 responsive
materials,9 and the role of chirality in generating order.10 Deracemization in the crystal state of
supramolecular systems was first observed recently for racemic mixtures of hat-shaped dendronized
molecules,11 and was driven by the demand of the hexagonal unit cell of the columnar crystal that all
columns be identical, exhibiting the same helical sense, within each crystal domain. The mechanism of
deracemization, which depended on weak interactions between individual molecules, could only be
understood using solid state NMR.12 Supramolecular deracemization does not occur in systems with
strong intermolecular interactions, such as chiral dendritic dipeptides,13 which instead give lower order
assemblies when not enantiopure.14 Indeed, incomplete deracemization of mixtures of hat-shaped
molecules containing inseparable, diastereomeric combinations of stereocenters gave reduced order in the
crystal state. This observation is analogous to the amorphous nature of atactic poly(propylene) compared
to the crystallinity of its isotactic counterpart.15
Subsequently a perylene bisimide (PBI)16 with two chiral minidendrons17 that assembles into 3D helical
columnar hexagonal (Φh) arrays with identical single crystal-like order irrespective of molecular chirality
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was discovered (Figure 1a).18 The Φh array exhibited helical deracemization, whereby even statistical
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mixtures of all possible diastereomers generated crystalline domains with a single helical sense.
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Figure 1. The cogwheel model of self-organization. (a) Molecular structure of rrr-PBI where r stands
for racemic dm8*. Chiral methyl group is indicated in pink. (b) The two crystalline columnar hexagonal
k
(Φh ) phases are generated via hierarchical self-organization of PBI dimers rotated around the column
axis being offset from the column axis in Φhk1 and centered on the column axis in Φhk2. Due to its
columnar shape and the absence of alkyl groups perpendicular or tilted to the long axes of the column,
k2
intercolumnar interdigitation of alkyl chains is absent and therefore, we denote Φh as the “cogwheel”
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assembly. (c) Formation of a Φh array with only one helical column in the unit cell drives helical
deracemization between columns. (d) Key aspects of the cogwheel model. (e) The supramolecular
columns assembled from r8r-, rr8-, 8r8-, and 88r-PBI19, where 8 represents the n-octyl group, and insets
illustrating the incomplete space filling by the alkyl ends from the 3- and 5- positions of the dendron.
Dashed circles in insets indicate empty space on the column periphery. Panels (a)–(d) are adapted from
ref. 19.
This chirality-invariant structural order was rationalized using a model in which alkyl chains on the
periphery of the supramolecular column act like the “teeth” of a cogwheel, covering the exterior of a
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column assembled from molecular dimers (Figure 1b). X-ray diffraction (XRD) and variable rate
differential scanning calorimetry (DSC) experiments confirmed that the cogwheel phase (denoted Φhk2),
which was discovered by chance during XRD annealing studies, is formed only by annealing at 100 °C or
upon slow cooling and reheating at 1 °C/min.
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This cogwheel model had not been observed in assemblies of PBIs with exclusively linear n-alkyl chains
that interdigitate,20 likely because the key attributes of the cogwheel model (Figure 1d) not only demand
peripheral alkyl chains which lie parallel to the column axis and are of approximately equal length to the
half-pitch of the helical column, but also depend on the chiral methyl group of the dimethyloctyl (dm8*)
chain to efficiently fill space within the center of the column and adopt an appropriate secondary structure
that may disfavor intercolumnar interdigitation21 of chains (Figure 1a). Therefore, PBIs with sequence-
defined hybrid dendrons containing mixtures of linear n-octyl and dm8* chains were investigated, leading
both to the discovery that linear alkyls can be tolerated together with dimethyloctyl by the cogwheel
assembly and, in addition, to a hybrid sequence of dm8*/linear chains that forms the cogwheel Φhk2 phase
under relatively fast heating and cooling at 10 °C/min with the phase transition being observed only on
heating (Figure 1e).19 However, the role of the linear alkyl chain in accelerating the formation of the
k2
cogwheel Φh phase remained unclear and raised the question: how do linear n-alkyl chains affect
assembly via the cogwheel model?
To answer this question, this study reports the investigation of four libraries of hybrid PBIs with sequence-
defined mixtures of racemic dm8*, r, chains and linear n-alkyl (CnH2n+1) chains with n = 6, 7, 9, and 10
carbons in the alkyl group. Structural and retrostructural analysis of these libraries by XRD and DSC
reveals a dendron sequence that enables an extraordinary acceleration of the formation of the cogwheel
Φhk2 phase at rates of up to 50 °C/min. This is the highest rate that any current instrumentation including
DSC and XRD can be used for quantitative, temperature dependent structural analysis in conventional
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research laboratories. Together with solid state NMR and previous work with r/n-octyl dendrons,19 this
extraordinary acceleration of the rate of Φhk2 formation relies on a complex interplay of crystal packing
and chain dynamics. These findings raise questions about the role of non-chiral building blocks in
achieving a high degree of structural order in chiral systems, support the power of constitutional isomerism
to dictate self-assembly.19,22 and provide insights into the design of highly ordered assemblies with
extraordinary acceleration of their formation and bulk helical deracemization.
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Synthesis of Libraries of PBIs Containing Sequence-Defined Hybrid Dendrons. Defining the
sequence23 of biological and bioinspired molecules is a powerful means to control supramolecular
assembly24 and elucidate fundamental biological concepts such as protein-carbohydrate binding.25 Here,
sixteen sequence-defined hybrid dendronized PBIs were synthesized using an iterative methodology
elaborated in a previous communication (Scheme 1).19
The nomenclature for these PBIs is dictated by the alkylation pattern on the (3,4,5)-minidendron, using r
to denote the r chain and n to denote a linear n-alkyl, CnH2n+1, where n = 6, 7, 9, or 10. This
functionalization pattern, or sequence of alkyl chains on the dendron periphery, is uniquely defined during
synthesis. Sequence-defined dendrons 5 were prepared either from symmetrically-protected methyl gallate
derivative 2 (for rnr- and nrn-PBI) or its asymmetrically-protected analog 6 (for rrn- and nnr-PBI).
These four sequences should not be interconverted just like in the case of proteins and are independent of
each other irrespective of dendron rotation. Alkylation with an initial alkyl chain, followed by deprotection
and a second alkylation, provided dendrons 5. Functional group manipulation of the benzyl esters 5 to
benzyl amines 12, and subsequent imidation of perylene tetracarboxylic dianhydride (PTCDA) per
procedures elaborated in our laboratory,20a gave PBIs with sequence-defined dendrons (Figures S1–S48).
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Scheme 1. Synthesis of PBIs with Sequence-Defined Linear-Racemic Hybrid Minidendronsa
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Symmetric Racemic-Linear Hybrid Minidendrons
HO
BnO
HO
R1O
BnO
R1O
3-6: R1 = C6H13
3-7: R1 = C7H15
3-9: R1 = C9H19
3-10: R1 = C10H21
3-r: R1 = (rac)-dm8*
R1O
HO
R1O
R2O
R1O
HO
HO
HO
O
O
O
O
O
i
ii
iii
ii
71%
90-95%
92-99%
91-99%
OMe
OMe
OMe
OMe
OMe
R1O
9
4-6: R1 = C6H13
4-7: R1 = C7H15
4-9: R1 = C9H19
5-6r6: R1 = C6H13, R2 = (rac)-dm8*
5-7r7: R1 = C7H15, R2 = (rac)-dm8*
5-9r9: R1 = C9H19, R2 = (rac)-dm8*
5-10r10: R1 = C10H21, R2 = (rac)-dm8*
5-r6r: R1 = (rac)-dm8*, R2 = C6H13
5-r7r: R1 = (rac)-dm8*, R2 = C7H15
5-r9r: R1 = (rac)-dm8*, R2 = C9H19
5-r10r: R1 = (rac)-dm8*, R2 = C10H21
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4-10: R1 = C10H21
4-r: R1 = (rac)-dm8*
Asymmetric Racemic-Linear Hybrid Minidendrons
R2O
HO
HO
HO
HO
O
O
O
O
O
O
O
OMe
iv
v
vi
v
O
O
R2O
HO
87%
98-99%
99-100%
OMe
OMe
OMe
OMe
91-93%
R1O
R1O
R1O
HO
7-6: R1 = C6H13
7-7: R1 = C7H15
7-9: R1 = C9H19
7-10: R1 = C10H21
7-r: R1 = (rac)-dm8*
8-6: R1 = C6H13
8-7: R1 = C7H15
8-9: R1 = C9H19
8-10: R1 = C10H21
8-r: R1 = (rac)-dm8*
5-rr6: R1 = C6H13, R2 = (rac)-dm8*
5-rr7: R1 = C7H15, R2 = (rac)-dm8*
5-rr9: R1 = C9H19, R2 = (rac)-dm8*
5-rr10: R1 = C10H21, R2 = (rac)-dm8*
5-66r: R1 = (rac)-dm8*, R2 = C6H13
5-77r: R1 = (rac)-dm8*, R2 = C7H15
5-99r: R1 = (rac)-dm8*, R2 = C9H19
5-1010r: R1 = (rac)-dm8*, R2 = C10H21
1
6
Racemic-Linear Hybrid Dendronized Perylene Bisimides
R1O
R2O
R1O
R1O
R1O
vii
88-100%
vii
viii
ix
91-100%
R2O
R2O
R2O
5
90-100%
100%
NH2
OH
Cl
N3
R3O
R3O
R3O
R3O
9
10
11
12
R2O
R1O
OR3
O
6r6-PBI: R1 = R3 = C6H13, R2 = (rac)-dm8*
7r7-PBI: R1 = R3 = C7H15, R2 = (rac)-dm8*
9r9-PBI: R1 = R3 = C9H19, R2 = (rac)-dm8*
10r10-PBI: R1 = R3 = C10H21, R2 = (rac)-dm8*
r6r-PBI: R1 = R3 = (rac)-dm8*, R2 = C6H13
r7r-PBI: R1 = R3 = (rac)-dm8*, R2 = C7H15
r9r-PBI: R1 = R3 = (rac)-dm8*, R2 = C9H19
r10r-PBI: R1 = R3 = (rac)-dm8*, R2 = C10H21
rr6-PBI: R1 = R2 = (rac)-dm8*, R3 = C6H13
rr7-PBI: R1 = R2 = (rac)-dm8*, R3 = C7H15
rr9-PBI: R1 = R2 = (rac)-dm8*, R3 = C9H19
rr10-PBI: R1 = R2 = (rac)-dm8*, R3 = C10H21
66r-PBI: R1 = R2 = C6H13, R3 = (rac)-dm8*
77r-PBI: R1 = R2 = C7H15, R3 = (rac)-dm8*
99r-PBI: R1 = R2 = C9H19, R3 = (rac)-dm8*
1010r-PBI: R1 = R2 = C10H21, R3 = (rac)-dm8*
O
O
O
O
O
O
N
O
x
12 +
N
47-84%
OR1
OR2
O
O
PTCDA
R3O
aReagents and conditions: (i) BnCl, KHCO3, DMF, 60 °C, 24 h; (ii) RBr, K2CO3, DMF, 120 °C, 3.5–12 h; (iii) H2,
Pd/C, CH2Cl2/MeOH, 23 °C, 24 h; (iv) triethyl orthoformate, Amberlyst-15(H), toluene, reflux, 6 h; (v) RBr, K2CO3,
DMF, 65–70 °C, 4 h; (vi) HCl, methanol, 60 °C, 7 h; (vii) LiAlH4, THF, 23 °C, 1 h; (viii) SOCl2, cat. DMF, 23 °C,
CH2Cl2, 0.5 h; (ix) NaN3, DMF, 23 °C, 9 h; (x) PTCDA, Zn(OAc)2•2H2O, imidazole, 180 °C, 6 h.
The Discovery of the Extraordinary Acceleration of the Cogwheel Self-Organization. The thermal
analysis of the sixteen PBIs with hybrid dendrons (n = 6, 7, 9, 10), as well as fully racemic rrr-PBI, fully
linear nnn-PBI (n = 6–10),20c and hybrid rac-dm8*/n-octyl dendrons,19 was determined by DSC (Figures
2, 3, and S49–S57 and Supporting Table ST1).
Phases were assigned by XRD and will be discussed later. Whereas the cogwheel Φhk2 phase was observed
for all four hybrid PBIs with n-octyl chains upon both heating and cooling (Figures S51 and S56),
changing the length of the alkyl chain to n = 6, 7, or 10 eliminates the Φhk2 phase from all hybrid dendron
k2
sequences except rrn-PBI, for which Φh is observed only upon heating (Figures S49, S50, and S53).
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Changing the alkyl chain to n-nonyl also generates the Φhk2 cogwheel phase in rr9-PBI and in 9r9-PBI
(Figures 2 and S52). This observation suggests that (1) there is something inherent in the rrn-sequence
that tolerates different alkyl chain lengths, and (2) alkyl chains that are 8 or 9 carbons in linear length (i.e.
dimethyloctyl, n-octyl, and n-nonyl) are best tolerated by the cogwheel model in other dendron sequences.
The DSC traces of rrn-PBI (n = 6-9; Figures S49-S52) all exhibit an endothermic peak at about 140 °C
upon heating, assigned to the first order transition from the cogwheel Φhk2 phase to a lower order columnar
hexagonal phase, Φhk1 (Figure 1b, left). A corresponding exothermic crystallization peak upon cooling is
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k2
not observed, suggesting that crystallization into the Φh phase is a continuous, very slow process
occurring under kinetic control. By contrast, the DSC trace of 9r9-PBI upon cooling (Figures 2 and S52)
shows a distinct crystallization exotherm at 107 °C, suggesting that the transition from low order Φhk1 to
high order cogwheel Φhk2 is well-defined, even upon fast cooling (10 °C/min).
Figure 2. DSC traces of PBIs with sequence-defined hybrid r/n-nonyl dendrons recorded upon second
heating and first cooling at 10 °C/min. Phases determined by fiber XRD, transition temperatures (in °C),
k1
and associated enthalpy changes (in parentheses, in kcal/mol) are indicated. Phase notation: Φh
-
columnar hexagonal crystal with offset dimers; Φhk2-columnar hexagonal crystal with cogwheel assembly;
Φc–ok-columnar centered orthorhombic crystal; Φmk - columnar monoclinic crystal, i-isotropic liquid.
To probe the kinetics of the Φhk1–Φhk2 transition in 9r9-PBI based assemblies, DSC traces were measured
at rates from 10 to 50 °C/min (Figure 3). Unexpectedly, a discrete exothermic crystallization peak is
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observed at the transition between Φhk1 and Φhk2 upon cooling at all rates. The enthalpy of the transition
(1.04 kcal/mol) does not vary for cooling rates from 20 to 50 °C/min, although the transition temperature
decreases from 103 °C at 20 °C/min to 96 °C/min at 50 °C/min. It should be noted that 11 °C of extra
k2
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supercooling necessary to form the Φh phase at 50 vs 10 °C/min (compare Tonset of 96 and 107 °C)
represents only a 15-second delay in the onset of the phase transition at 50 °C/min. These data suggest
that the Φhk1-Φhk2 transition for 9r9-PBI assemblies was extraordinarily accelerated and is much faster
than has been observed for any other cogwheel assembly including homochiral.
Figure 3. DSC traces of 9r9-PBI assemblies measured upon heating and cooling at 10 to 50 °C/min during
(a) 1st heating, (b) 1st cooling, and (c) 2nd heating. Phases determined by fiber XRD, transition temperatures
k1
(in °C), and associated enthalpy changes (in parentheses, in kcal/mol) are indicated. Phase notation: Φh
k2
– columnar hexagonal crystal with offset dimers; Φh – columnar hexagonal crystal with cogwheel
assembly; Φc–o – columnar centered orthorhombic crystal; Φm – columnar monoclinic crystal, i –
k
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isotropic liquid.
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Structural and Retrostructural Analysis by XRD Confirms High-Order Helical Cogwheel Assembly
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Irrespective of Rate. The phases annotated on all DSC traces were determined by XRD of oriented
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fibers.2526 Fiber XRD diffractograms for PBIs with hybrid r/n-nonyl dendrons are shown in Figure 4. In
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each case, a higher order phase is observed at low temperature (columnar centered orthorhombic, Φc–o
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for r9r- and 99r-PBI; cogwheel Φhk2 for rr9- and 9r9-PBI) and the lower order Φhk1 phase is observed
at higher temperature (Supporting Tables ST2–ST4). The XRD data for rr9- and 9r9-PBI are both
consistent with the cogwheel Φhk2 and lower order Φhk1 phases observed previously.18,19
Reconstruction of the XRD by the molecular models depicted in Figure 5 support the description of the
higher order phases as cogwheel phases (Figure 4, grayscale images on right). The Φc–ok phase observed
for r9r- and 99r-PBI is a pseudohexagonal phase that represents a distortion of a hexagonal array along
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the a- or b-direction of the unit cell. The ratio of b/a for a Φc–ok unit cell that is equivalent to a perfect Φh
cell would be 1.73 (= √3). For r9r- and 99r-PBI this ratio is 1.60 and 1.61, respectively, suggesting a
consistent deviation from a hexagonal array as dictated by the cogwheel model. However, the high number
of sharp, bright off-axis features supports a high degree of order in these Φc–ok arrays rivalling that of the
cogwheel phase.
To correlate the DSC traces from Figure 3 with the structure of 9r9-PBI, diffractograms of the cogwheel
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Φh phase were measured at 100 °C upon first heating and cooling at rates of 10 to 40 °C/min (Figure
S58). The XRD data shown in Figure 4 were recorded at 100 °C, heated at 10 °C/min and with 2 × 2.5 min
recording time. The time it takes to record XRD patterns with reasonable signal/noise ratio means that we
k2
were not able to monitor the formation of the Φh phase in real-time by XRD at high heating/cooling
rates. However, pleasingly, near-identical XRD patterns are observed at 100 °C, irrespective of heating
and cooling rate (Figure S58). This demonstrates the extraordinary acceleration of the formation of the
cogwheel Φhk2 of 9r9-PBI.
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Figure 4. Fiber XRD of 9r9-PBI assemblies measured upon heating and cooling at 10 °C/min (red scale,
left) and XRD simulated from the models in Figure 5 (gray scale, right). Phases, lattice parameters, and
temperatures (in °C) are indicated. The time employed to record each XRD is 5 min. The 5 min scan
consists of two 2.5 min XRD scans. In a single 2.5 min scan, gaps between eight individual panels in the
detector (Pilatus 1M, Dectris) are recorded as black stripes with no data. The detector is moved for a
subsequent 2.5 min scan, which collects data in the previously unrecorded areas. The combination of the
two 2.5 min scans provides a 5 min scan in which the black stripes are mostly eliminated.
To illustrate the practical implication of this rate acceleration, we consider how long it would take to
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Starting with a freshly extruded macroscopic fiber at 25 °C, rrr- and rr8-PBI require heating to 100 °C
(i.e. 7.5 min at 10 °C/min), followed by annealing for 3 hours and 30 min, respectively. After cooling to
25 °C at 10 °C/min (7.5 min), fibers of Φhk2 would have been prepared in ~3 hours and 15 min for rrr-
PBI and ~45 min for rr8-PBI. In contrast, Figure 4 shows that 9r9-PBI transforms into Φhk2 within 150
s at 100 °C. Therefore, including heating and cooling at 50 °C/min (90 s between 25 °C and 100 °C) the
total time is only 330 seconds, i.e. 5.5 min. Reducing the processing time from over 3 hours for rrr-PBI18
to ~5 min for 9r9-PBI represents a substantial time saving that demonstrates how molecular design can
affect both fundamentally- as well as industrially-relevant time-saving material parameters.
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Structural Basis for Accelerated Cogwheel Formation in Assemblies of 9r9-PBI. To gain insight
about the structural basis for the rapid formation of the cogwheel Φhk2 by 9r9-PBI, molecular models of
supramolecular assemblies were generated using an iterative methodology described previously.26,27
Diffraction features and lattice parameters were determined from fiber XRD data using Datasqueeze28 and
analyzed using helical diffraction theory.2a,26,29 An initial molecular model consistent both with XRD data
and with the experimental density of the macroscopic fiber was constructed using Accelrys Materials
Studio software (version 5.0).17c,26 Geometry optimization was performed using the VAMP module. The
fiber XRD pattern expected from this model was simulated using Accelrys Cerius2 run on a Silicon
Graphics (SGI) Tezro workstation.11,17c The simulated and experimental XRD patterns were compared,11
the molecular model refined, and the XRD pattern simulated again. This iterative process continued until
either the level of agreement between simulated and experimental XRD patterns was agreeable and no
substantial improvement was observed upon further iteration.
Models of Φhk2 phases observed in rrn-PBI (n = 6–10) and 9r9-PBI reveal subtle differences in the alkyl
chain periphery of their supramolecular columns (Figure 5). The column diameters of rrn-PBI generally
increase with increasing linear alkyl chain length, from 25.4 Å (rr6-PBI) to 28.5 Å (rr10-PBI). The
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diameter of ultrafast 9r9-PBI (26.7 Å) lies between that of rr8- (26.4 Å) and rr9-PBI (27.0 Å), suggesting
that this diameter falls within a particularly preferable range accessible only to hybrids of r with n-octyl
and n-nonyl chains. In all cases, the intracolumnar π–π distance is 3.7 Å.
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Figure 5. Models of the cogwheel columns of Φhk2 self-organized from rr6-, rr7-, rr8-, rr9-, 9r9-, and
rr10-PBI. Intramolecular spacing and column diameter are indicated. Insets illustrate the space filling by
the alkyl ends from the 3- and 5- positions of the dendron as a function of their length and sequence.
Dashed circles in insets indicate empty space on the column periphery.
One of the key requirements of the cogwheel model (Figure 1d) is the alkyl chain coat length being almost
equal to the helical half-pitch of 14.8 Å ( = 4 × 3.7 Å). Both previous studies of the cogwheel model have
utilized homochiral dm8*18 or dm8* (r)-n-octyl hybrids,19 with a linear length of 8 carbons. This length
forms a coat that almost covers the entire column periphery, leaving small gaps between the end of the
alkyl chains of the ith molecule without steric hindrance from the (i + 4)th molecule in the column (see
inset for rr8-PBI in Figure 5). Shorter alkyl chains do not adequately cover the column exterior (see inset
for rr6-PBI and dashed circular marks denoting empty space in Figure 5) whereas longer alkyl chains
lead to steric hindrance and an unfavorable tilting of the alkyl chain away from the column axis (such as
for rr10-PBI). The small degree of unoccupied space in r/n-octyl hybrids is sufficient to accommodate a
9th carbon in the alkyl chain without significant steric penalties; hence rr9- and especially 9r9-PBI most
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efficiently fill the column periphery with aliphatic chains. A close inspection of the structures of the
cogwheel columns of rr9- and 9r9-PBI (Figure 5) demonstrates a perfect tertiary structure for 9r9-PBI
assembly and a small imperfection in the column derived from rr9-PBI (see dashed circle in the 3-position)
due to the shorter r group at the 3-position of the dendron. Therefore, the ideal place for the r group is in
4-position of the dendron while the ideal places for the 9 groups are in the 3- and 5-positions. This
conclusion is also supported by solid state NMR experiments to be discussed in a later subsection. The
Φhk1-Φhk2 transitions are observed on heating and cooling for 9r9-PBI and are present irrespective of the
heating and cooling rate (Figure 3b). However, rr9-PBI assembly does not show the first order transition
on cooling at 107 °C that 9r9-PBI assembly shows (Figure 2) upon cooling at 10 oC/min. It is tempting
to attribute such observations to the perfect 9r9-PBI sequence that provides the ideal tertiary structure.
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However, DSC studies of rr9-PBI and 9r9-PBI (Figure 2) provide near-identical Φhk1-Φh transition
temperatures (136 and 137 °C, respectively) and enthalpies (1.40 and 1.42 kcal/mol) upon heating,
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suggesting that the thermodynamic driving force for Φh formation is very close for rr9-PBI and 9r9-
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PBI. Since the rate of formation of the Φh phase transition is almost independent of the heating and
cooling rate (Figure 3 and Figure 4) we can conclude that the formation of cogwheel assembly in 9r9-PBI
is extraordinarily accelerated vs that of rr9-PBI, and all other sequence-defined assemblies, although both
assemblies have almost identical thermodynamic driving forces (vide infra, Figure 2). Hence the observed
difference in the rate of Φhk2 formation must be due to kinetic effects.
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We propose that the Φhk1–Φh transition is so fast in 9r9-PBI because there are many more local
fluctuations of the favorable cogwheel Φhk2 structure within the Φhk1 phasebelow, and perhaps even above,
the transition temperature, compared to rr9-PBI. Due to the increased degree of branching in rr9-PBI,
such fluctuations are expected to have higher free energy and thus are less favorable. This is linked to the
higher entropy that involves disorder, and hence mobility, of the linear chains compared to branched
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ones.30 More Φh fluctuations increase the probability that a fluctuation reaches critical nucleus size,
thereby dramatically accelerating the nucleation of the Φhk2 and leading to an extraordinarily accelerated
rate of self-organization and crystallization. The lack of cogwheel phases in PBIs dendronized with all n-
alkyl chains20c suggests that the methyl branch of the r chain is required for cogwheel packing, and the
ideal length and position of the n-nonyl chains in 9r9-PBI unpredictably lead to the formation of the
cogwheel phase being kinetically accessible even at very fast heating and cooling rates.
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Solid State NMR Probes Distribution of Local Chain Conformations and Molecular Fluctuations.
The formation of columnar arrays with long-range order is not only affected by the π–π stacking of the
PBI cores, but also by the local conformations of the aliphatic side chains, in particular if the volume
locally available for molecular fluctuations changes in amount or shape. Solid state 13C NMR chemical
shifts are very sensitive to local intracolumnar packing arrangements, acting as probes for local
conformational distributions12 and thus nicely augmenting the information available from XRD and DSC.
13C cross-polarization magic angle spinning (CP-MAS) experiments on hybrid PBIs with r/n-nonyl
dendrons show that the conformational distribution is largely determined by the attachment site at the
phenyl ring (Figure 6).
Dimethyloctyl (r) chains in the 3- and 5-positions (Figure 6a) show a broad chemical shift distribution
resulting from a broad conformational distribution of the CH2 groups next to the chiral center (green) and
the chiral methyl group (yellow), whereas r chains in the 4-position (9r9-PBI spectrum in Figure 6b)
exhibit sharp peaks for those sites. The narrower conformational distribution of 4- vs 3- or 5-r chains is
hardly affected by neighboring chains (Figure 6b), general for all hybrid r/n-alkyl dendrons with n = 6–
10 (Figure S60), and invariant to temperature (Figure S61). In addition, the sum spectrum of 9r9- and
99r-PBI (broken red line, Figure 6b) is significantly narrower in the region of the chiral methyl group
(green) than rr9-PBI (solid black line). This suggests a higher local mobility of the chiral methyl groups
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in 9r9- and 99r-PBI, more efficiently averaging different packing arrangements of the methyl group
within the supramolecular column. This higher local mobility may be aided by the presence of two, more
dynamic, linear n-nonyl chains in 9r9- and 99r-PBI compared to the single n-nonyl chain in rr9-PBI.
General Design Principles for Cogwheel Assembly Beyond the Current System. The discovery of
ultrafast cogwheel assembly for 9r9-PBI enhances our understanding of the role of alkyl chain design in
the cogwheel mechanism of self-assembly. This mechanism provides a route to highly ordered arrays of
homochiral helical supramolecular columns irrespective of molecular chirality, a structure of potential
interest for numerous applications and fundamental studies on complex systems. To date this model has
been demonstrated only with dendronized PBIs, but cogwheel assembly is applicable to a broader range
of molecular cores.
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Figure 6. 13C CP-MAS NMR spectra of hybrid PBIs with dm8*/n-nonyl dendrons. (a) The NMR spectra
of 99r- and r9r-PBI differ only at the 14.7 ppm signal assigned to the chain end of the linear n-nonyl
chains, as seen in the red difference spectrum. (b) Superimposing the NMR spectra of dm8* chains in
meta- (99r-PBI) and para-position (9r9-PBI) provides the NMR spectrum for rr9-PBI for the main chain
sites (yellow and blue). Green region denotes chiral methyl group.
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To facilitate this process, we propose three criteria that must be satisfied for cogwheel assembly (Figure
7). The acceleration of cogwheel formation for 9r9-PBI demonstrates that complete space-filling is
needed to achieve the kinetically most favorable crystallization. First, the length of the alkyl chain coat
jacketing the supramolecular column must match the helical half-pitch and, most preferably, completely
fill all available space on the column exterior. Molecules of 9r9-PBI are stacked with a π–π distance of
3.6 Å, giving a helical half-pitch of 14.4 Å (= 4 × 3.6 Å, Figure 7a). The shortest distance for close-contact
planar aromatic cores is 3.3 Å31 (i.e., helical-half pitch of 13.2 Å), corresponding to an ideal alkyl chain
length of between 7 and 8 carbons (Figure 7a). In contrast, increasing the spacing between aromatic cores,
such as with non-planar 1,6,7,12-tetrachloroperylene bisimide (Cl4-PBI),32 would require a longer alkyl
chain to cover the column exterior.
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Figure 7. Design principles for the translation of the cogwheel model to other systems. (a) The length of
the alkyl chain must match the helical half-pitch, which is dictated by intermolecular π–π stacking distance.
(b) There must be a “pocket” of available space in which the branch group (i.e. a chiral methyl group in
dm8*) can be accommodated. (c) The alkyl chain jacket on the column periphery must be continuous.
(left) Cores smaller than PBI, e.g. naphthalene bisimide, need fewer alkyl chains for complete jacketing,
whereas (right) cores larger than PBI, e.g. coronene bisimide, need more alkyl chains.
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The second criterion, established previously,19 is that the minidendron must contain at least one branched
alkyl chain to prevent column interdigitation with alkyl tails being perpendicular rather than parallel to
the long axis of the column. The methyl branch in 9r9-PBI is accommodated jn a pocket defined by
adjacent PBIs in the supramolecular column (Figure 7b). Most likely, the cogwheel model will tolerate
alternative branching point positions, if space is available to accommodate the chiral group without
disrupting the column periphery. Geometric considerations suggest that the methyl group should be closer
to the dendron phenyl ring rather than the free end of the alkyl chain.
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Finally, the number of alkyl chains must be modified to fill the entire periphery of the column for different
core sizes, to account for differences in column diameter and intermolecular rotation. This intermolecular
rotation, and thus helical pitch, will vary depending on size and shape of the aromatic core; for the current
PBIs, 45° is favorable (Figure 1b). A compound with a different aromatic core may have a different
minimum energy rotation angle that would favor a helix with a different pitch. It is then necessary to
match both the length and the number of the pendant chains to the half-pitch of that helix. For example
(Figure 7c), smaller cores (e.g. naphthalene bisimide,33 NBI) may require fewer, longer alkyl chains than
9r9-PBI, whereas larger cores (e.g. coronenes34) may require more, potentially shorter chains. Dendrons
provide a particularly powerful tool to precisely modulate alkyl chain number and length, ranging from
AB2 to AB5 in a single dendron generation.35 Higher numbers of alkyl chains may require multi-generation
dendron designs22a–d or new methodologies to program first degeneration ABn self-assembling dendrons
with n larger than 3.
CONCLUSIONS
Taken together, the combination of DSC, XRD, and solid state NMR presented here suggest that the
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both favorable crystal packing and local chain dynamics. The results show that even just one branched
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chain out of three on a dendron is sufficient to disfavor intercolumnar interdigitation and instead favor
axial chain alignment. The second condition for cogwheel assembly is matching the chain length to the
half-pitch length of the helix. DSC and XRD (Figures 2–4 and S49–S57) suggest that the optimal chain
length satisfying this condition is 8 and especially 9 carbons. More specifically, molecular modeling and
reconstruction of fiber XRD by molecular models (Figures 4 and 5) indicate that the periphery of the
supramolecular column is incompletely filled by linear and branched octyl chains, but that incorporation
of n-nonyl chains can be tolerated and leads to better occupation of the aliphatic column periphery. Hence
a mixture of r and 9 best in 9r9 sequence is most favorable for filling space within the crystalline
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assemblies of the cogwheel Φh phase. Solid state NMR (Figure 6) has further demonstrated a higher
mobility of linear compared to the branched chains, supporting the increased Φhk1-Φhk2 transition rate of
9r9- and 99r-PBI compared to that of rr9- and r9r-PBI. NMR results also show that the presence of a r
chain in the 4-position of the (3,4,5)-minidendron experiences a narrower distribution of conformations
within the columnar array, likely indicating that the tertiary structure necessary for the cogwheel model is
preferentially accessible to dendrons with 4-r substitution. Therefore, the 9r9-sequence represents the
ideal dendron to cover the column periphery, enabling rapid formation of the highly ordered Φhk2 crystal.
To the best of our knowledge the formation of the Φhk2 crystal represents the fastest self-organizing and
crystallizing supramolecular or covalent natural or synthetic macromolecule known to date. This
substantial acceleration in self-organization could not be predicted, neither from our previous knowledge
of the cogwheel model nor from our preliminary experiments reported in the previous communication.19
These insights provide design guidelines for highly ordered, self-healing, and rapidly forming columnar
structures, properties that are highly desirable in stable, fast-switching, fast-forming and thermoresponsive
defect-free functional materials. The methodology described here, relying on not just XRD but also DSC
and solid state NMR, may bring new insights for other complex soft matter.36 Indeed, the presently
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employed n-semiconducting PBI core16 is only one option (Figure 7), replaceable with other core moieties
forming similar Φhk2-type structures. The precise design of aliphatic chains may have relevance not just
for the directed supramolecular assembly of columnar assemblies, but also for even more complex
assemblies self-organized from spheres such as the Frank-Kasper phases assembled from supramolecular
dendrimers and from self-organizable dendronized polymers,37 and as synthetic cells generated from
amphiphilic including sequence-defined Janus-dendrimers and Janus-glycodendrimers.24,38
AUTHOR INFORMATION
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Corresponding Author
percec@sas.upenn.edu
Present Addresses
□B.E.P.: Department of Chemistry and International Institute of Nanotechnology, Northwestern
University, Evanston, Illinois 60208, United States.
Notes
The authors declare no competing financial interests.
Supporting Information
Experimental methods, synthetic procedures with complete characterization data, structural and thermal
analysis parameters, additional DSC, XRD and solid state NMR data and associated discussion
ACKNOWLEDGMENTS
Financial support by the National Science Foundation (DMR-1066116 and DMR-1807127 (V.P.), DMR-
1120901 (V.P. and P.A.H.)), the Humboldt Foundation (V.P.) and the P. Roy Vagelos Chair at Penn (V.P.)
is gratefully acknowledged. B.E.P. thanks the Howard Hughes Medical Institute for an International
Student Research Fellowship. We also thank Professor Paul A. Heiney from the Department of Physics
and Astronomy, University of Pennsylvania for helpful discussions concerning the X-ray experiments.
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(a) Nanda, V.; Andrianarijaona, A.; Narayanan, C. The Role of Protein Homochirality in Shaping
the Energy Landscape of Folding. Protein Sci. 2007, 16, 1667–1675. (b) Chen, Z.; Lichtor, P. A.;
Berliner, A. P.; Chen, J. C.; Liu, D. R. Evolution of Sequence-Defined Highly Functionalized
Nucleic Acid Polymers. Nat. Chem. 2018, 10, 420–427. (c) Cecconello, A.; Simmel, F. C.
Controlling Chirality across Length Scales Using DNA. Small 2019, 15, 1805419.
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