Estimating the shape and size of supramolecular assemblies by variable temperature diffusion ordered spectroscopy

Article abstract of DOI:10.1039/c4ob01373e

Reported is characterization of the self-assembly of π-conjugated oligomers, molecules studied recently in photovoltaic devices, using variable temperature diffusion ordered spectroscopy (VT-DOSY). Iterative fitting of diffusion coefficient versus tempera

Full text of DOI:10.1039/c4ob01373e

Organic &
Biomolecular Chemistry
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Estimating the shape and size of supramolecular
assemblies by variable temperature diffusion
ordered spectroscopy†
Cite this: Org. Biomol. Chem., 2014,
12, 7932
Received 2nd July 2014,
Accepted 28th August 2014
Benjamin M. Schulze, Davita L. Watkins, Jing Zhang, Ion Ghiviriga and
Ronald K. Castellano*
DOI: 10.1039/c4ob01373e
www.rsc.org/obc
Reported is characterization of the self-assembly of π-conjugated
oligomers, molecules studied recently in photovoltaic devices,
using variable temperature diffusion ordered spectroscopy
(VT-DOSY). Iterative fitting of diffusion coefficient versus tempera-
ture data to
a modified Stokes–Einstein equation, molecular
modelling, and comparison to non-assembling model compounds,
has allowed estimation of assembly size, shape, and molecularity.
Diffusion ordered spectroscopy (DOSY) is a diffusion nuclear
magnetic resonance (NMR) technique that is useful for aggre-
gate molecularity, size, and shape determination.1 In
a
number of cases, DOSY NMR has been used to rigorously
characterize synthetic supramolecular
assemblies.1d,f,2
Although not often coupled with variable temperature (VT)
NMR, the combined techniques report on dynamic assembly
processes in solution.2d,f Reported here is an approach using
VT-DOSY to understand the self-assembly of organic π-conju-
gated oligomers, molecules studied recently in thin film
photovoltaic devices, mutually by π-stacking and hydrogen
bonding.3 We believe that this characterization method is
underutilized in a community where drawing relationships
between molecular/supramolecular structure and ultimately
device function is challenging but central to rational materials
design.
We recently demonstrated how the photovoltaic power con-
version efficiency of a branched oligothiophene (BQPH; Fig. 1):
fullerene blend was enhanced (twofold) through hydrogen
bond promoted self-assembly relative to control devices fabri-
cated from chromophores incapable of hydrogen bonding
(e.g., BQPME).3 Elegant previous work of Lehn and Zimmer-
man inspired the molecular design that features the phthal-
hydrazide (PH) heterocycle, a building block shown to form
robust hydrogen-bonded assemblies in solution and on sur-
faces, including cyclic trimers (i.e., (PH)3).4 In the context of
Fig. 1 Chemical and schematic representations of HexBQPH,
HexBQPME, and HexB. Also shown is the self-association of HexBQPH
into trimeric discs via hydrogen bonding followed by the formation of
columnar stacks through π–π interactions.
BQPH, we suspected that its putative H-bonded rosettes (i.e.,
(BQPH)3) might further organize into π-stacked columnar
nanostructures (i.e., [(BQPH)3]n), an appealing chromophore
arrangement (if extendable to thin films) for bulk heterojunc-
tion photovoltaics. Indeed, columnar arrangements of (PH)3-
based assemblies have been characterized before.4a Herein, we
provide supporting evidence of this mechanism of assembly in
solution for HexBQPH by VT-DOSY NMR by employing a modi-
fied Stokes–Einstein equation that allows derivation of mole-
cular size in solution for objects with non-spherical shape.1e
Facilitating the analyses is comparison of the solution behav-
ior of HexBQPH to two molecules incapable of H-bonded
assembly, HexBQPME (a model of the monomer)3 and HexB5
(a covalent analogue of the H-bonded trimer).
Department of Chemistry, University of Florida, P.O. Box 117200, Gainesville,
Florida, USA. E-mail: castellano@chem.ufl.edu
†Electronic supplementary information (ESI) available: Full experimental pro-
cedures and characterization data. See DOI: 10.1039/c4ob01373e
A 1H NMR spectrum of HexBQPH3 (10 mM) in the hydrogen
bond promoting solvent toluene-d8 (see Fig. S1†) shows two
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broadened peaks at δ = 12.78 and 13.75 ppm at 27 °C. The
signals are consistent with the –NH and –OH protons of
HexBQPH, respectively, in its lactim–lactam tautomeric form.
That the peaks are well-separated and shifted far downfield
suggest both H-bonded assembly and slow monomer–aggre-
gate exchange on the NMR time scale.4a Also observed by
1H NMR are significantly broadened and upfield shifted (up to
0.5 ppm) thiophene –CH resonances, indicative of π-stacking.
Fig. 2 Shapes of diffusing entities modelled as a (a) sphere, as in the
Stokes–Einstein equation, or a (b) prolate spheroid, (c) oblate spheroid,
1
and (d) cylinder as accommodated by
a modified Stokes–Einstein
In contrast, HexBQPME displays sharp peaks in the H NMR
equation. Represented within shapes (b)–(d) is RBQPH and its
assemblies.
spectrum under the same conditions (not shown). Upon
warming through 90 °C, the –NH/–OH peaks of HexBQPH
coalesce at ∼ 85 °C (but remain significantly deshielded) and
the aromatic signals sharpen (completely at ∼75 °C) and shift
downfield. The results are consistent with a transition from
π-stacked, H-bonded assemblies to discrete H-bonded assem-
blies in solution.3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ ꢁ
"
#
2
b
1 ꢀ
a
f s
¼
ð4Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
2
2
3
ꢀ ꢁ
b
1ꢀ
2
3
1þ
ꢀ ꢁ
6
6
6
6
4
7
7
7
7
5
Prior to VT-DOSY studies, an analogous 1-D VT 1H NMR
study was performed with comparator HexB (see Fig. S2†). The
design of this compound was suggested by computational
modelling of the anticipated trimeric assembly of HexBQPH,
that gave its approximate molecular dimensions (see Fig. S3–
S5†). Preparation of phenyl cored thiophene dendrimer5 HexB
came via three-fold Suzuki coupling of the boronic ester of
HexBQ3 with 1,3,5-tris(5-bromothiophen-2-yl)benzene (see
Scheme S1†).6 Compared to HexBQPH under identical con-
a
b
a
ln
b
a
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ ꢁ
2ꢀ1
b
a
f s
¼
ð5Þ
2
3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ ꢁ
ꢀ ꢁ
2ꢀ1
b
a
b
1
tanꢀ1
ditions, the H NMR spectrum of HexB shows some broaden-
a
ing and upfield shifting (up to ∼0.15 ppm) of the thiophene
protons (in the 6.9–7.3 ppm region) and benzene core protons where c is a size correlation factor between rh of the diffusing
(at 7.1 ppm) at room temperature; again the aromatic proton species and the van der Waals radius (rvdW) of the solvent1e,8
peaks sharpen and move on average downfield upon raising (eqn (3)), and fs is a system-derived shape friction correction
the temperature. While the result may speak to some aggrega- factor (eqn (4) and (5)).1e,9 The diffusing entities represented
tion through π-stacking, the less pronounced chemical shift by fs are mathematically modelled as prolate (cigar-shaped;
changes suggest weaker π–π association for HexB versus eqn (4) and Fig. 2b) or oblate (pancake-shaped; eqn (5) and
HexBQPH (vide infra).
Fig. 2c) spheroids and are parameterized by the axial (a) and
Obtained from DOSY NMR experiments are translational equatorial (b) axes of the respective spheroids (Fig. 2).1e,9 Alter-
diffusion coefficients (D) which are related to molecular size natively, fs can be modelled as a cylinder (Fig. 2d) parameter-
through the well-known Stokes–Einstein equation:
ized by the length (L) and diameter (d) (see the ESI† for
details).10 An important consequence of using eqn (2) and (3)
is that rh now represents the hydrodynamic radius of a sphere
with equivalent volume to that of the spheroid used to calcu-
late fs.1e
kBT
D ¼
ð1Þ
6πηrh
where kB is the Boltzmann constant, T is the temperature, rh is
the hydrodynamic radius, and η is the viscosity of the sol-
vent.1e,7 Eqn (1) assumes that the diffusing entity is a sphere
(Fig. 2a) and is large relative to the van der Waals volume of
the solvent.1e Given these assumptions, the equation does not
necessarily best describe the diffusion of the molecular enti-
ties considered here, including the self-assembled aggregates
of HexBQPH. Therefore, the equation has been augmented as
discussed by Macchioni and coworkers1e to include shape- and
size correction factors. In modified form (eqn (2)):
Given eqn (2), for a monomeric species a plot of the
diffusion coefficient D versus (T/η) should result in a straight
line with a slope inversely related to c, fs, and rh. One can then
use an iterative fitting procedure to estimate physical para-
meters a and b (or L and d) from the data, given a priori
knowledge and shape/size constraints offered by molecular
modelling (see Fig. S3–S5†). The latter provides critical gui-
dance and can afford, for example, initial values for a and/or b
(L and/or d), an approximation of the molecule’s aspect ratio
(i.e., 2a/2b), and a starting ellipsoid shape model (Fig. 2) for
the fitting. The interdependence of several parameters (e.g.,
c is derived from rh; fs is derived from b/a) means that only a, b,
and rh need to be iteratively varied. Combinations are sought
that arrive at a derived (fitted) slope that matches the experi-
mental one (typically within 0.2%). Then, the values of a and b
kBT
cfsπηrh
6
D ¼
ð2Þ
ð3Þ
c ¼
ꢀ
ꢁ
2:234
rvdW
rh
1 þ 0:695
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7.4 Å, and rh = 9.0 Å, ultimately resulting in fs = 0.69 and c =
5.8 (Table 1). Use of the oblate model for HexBQPME (which
changes the value of fs) does not fit the experimental data
(data not shown).
Two solvent types were selected for variable temperature
DOSY studies of HexBQPH. Results from toluene-d8, an assem-
bly promoting solvent, can be evaluated against the VT-NMR
data discussed above. Studies in assembly suppressive (i.e.,
H-bond competitive) solvents, such as dimethyl sulfoxide-d6
(DMSO-d6), allow direct comparison with the monomeric con-
trols, HexBQPME and HexB. Diffusion coefficients were first
collected for HexBQPH in DMSO-d6. Satisfyingly, fits of the
diffusion coefficient versus temperature data using the prolate
spheroid parameters provides good agreement (Table 1) with
HexBQPME, expected given the similar molecular dimensions
of the two based on modelling (see Fig. S3–S5†). The slightly
larger apparent size of HexBQPH might be explained through
its strong hydrogen bonding with the solvent. Similar evalu-
ation of HexB (in THF-d8 due to solubility) using the oblate
parameters provides values of a and b consistent with its mole-
cular dimensions derived from modelling and an unaggre-
gated species.
●
Fig. 3 Linearized [ ] variable temperature diffusion data for HexBQPME
(24 mM; DMSO-d6). The linear regression fit is shown for data derived
from the prolate [ ] spheroid model and iteratively determined values of
□
a, b, and rh.
can be proportionally varied such that the calculated volume
of the spheroid matches (typically within 1%) a spherical value
derived from rh. Worth noting, since the ratio of a to b directly
determines fs, proportional changes to both do not affect this
parameter. Also clear from the treatment is that the diffusion
behavior fitted via one model cannot be fitted using another
model and that when selected, the prolate model will result in
fs < 1, whereas the oblate model will result in fs > 1. Worth
noting is that compensatory effects involving c and fs can give
rise to a cfs product ∼ 6 and apparent agreement with the clas-
sical Stokes–Einstein equation.1e
The approach is illustrated in Fig. 3 through an evaluation
of HexBQPME in DMSO-d6. Worth noting, temperature gradi-
ents within our samples were minimized by the use of a well
designed heating and cooling system, and a convection correc-
tion was implemented within pulse sequencing to ensure accu-
rate measurements of diffusion coefficients.11 Diffusion
constants were recorded and plotted against (T/η) (Fig. 3, dark
circles); a linear fit provides the slope (i.e., 1.23 × 10−15 m3
kg−1) which is inversely related to c, fs, and rh. An initial esti-
mate of a (13 Å) is entered based on molecular modelling (see
the ESI† for calculations), and an iterative fitting to determine
a reasonable combination of a, b, and rh ensues. In one fit
(open squares), the prolate model yields values of a = 13 Å, b =
Next, variable temperature diffusion data was collected in
toluene-d8 for HexBQPME, HexBQPH, and HexB. Evidence for
the aggregation of HexBQPH is immediately provided through
its small diffusion coefficient (1.03 0.01 × 10−10 m2 s−1) rela-
tive to HexBQPME (5.90
0.06 × 10−10 m2 s−1) at 22 °C.
Linearization of the diffusion versus temperature data and
iterative fitting was first performed on HexBQPME. Using the
prolate spheroid model, values of a = 14 Å, b = 7.8 Å, and rh =
9.5 Å could be derived (Table 2), values which are similar to
HexBQPH and HexBQPME in DMSO-d6 (Table 1). The data is
consistent with the conclusion that HexBQPME is monomeric
in both DMSO-d6 and toluene-d8, and that HexBQPH is mono-
meric in DMSO-d6.
Upon linearization of the diffusion coefficient data for
HexBQPH (Fig. 4), bimodal behaviour is found reflected by the
distinct slope change observed at approximately 60 °C. The
temperature, based on 1-D VT 1H NMR data (vide supra), is
consistent with a transition from π-stacked aggregates to dis-
crete H-bonded aggregates.12 That the dynamic assembly
process likely involves conversion of columnar π-stacks of
trimers (i.e., [(HexBQPH)3]n) to non-π-stacked trimeric assem-
blies (i.e., (HexBQPH)3) comes through iterative fitting of the
two temperature ranges (21.8–52.6 °C and 58.8–92.2 °C) and
Table 1 Size and shape parameters for HexBQPH, HexBQPME, and HexB monomers based on VT-DOSY data
e
e
Molecule
Modelc
a (Å)d [acalcd
]
b (Å)d [bcalcd
]
pf
rh d (Å)
fs
c
HexBQPMEa
HexBQPHa
HexBb
P
P
O
13 [13]
15 [12]
4.7
7.4
8.1
32 [24]
1.8
1.9
6.9
9.0
10
17
0.69
0.71
1.3
5.8
5.8
5.9
a Based on diffusion coefficients measured in DMSO-d6 (HexBQPH = 27 mM; HexBQPME = 24 mM). b Based on diffusion coefficients measured
in THF-d8 (HexB = 30 mM). c O = oblate; P = prolate. d Estimated fitting error: 10% for a, b, and rh. e Calculated parameters are estimated from
molecular modelling (see the ESI for details). f p = (semimajor axis)/(semiminor axis).
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Table 2 Size and shape parameters for HexBQPH, HexBQPME, and HexB in toluene-d8 based on VT-DOSY dataa
Molecule
Modeld
a
e (Å)
b
e (Å)
L
e (Å)
d
e (Å)
rh e (Å)
fs
c
HexBQPME
HexBQPHb
HexBQPHb
HexBQPHc
HexBQPHc
HexB
P
14
26
—
5.0
—
7.8
—
—
38
—
7.0
—
—
—
51
—
51
—
58
9.5
27
27
15
15
16
17
0.69
1.0
1.0
1.2
1.2
1.3
1.2
5.7
6.0
6.0
5.9
5.9
5.9
5.9
O
C
O
C
O
C
28
—
26
—
30
—
4.5
—
HexB
7.8
a Based on diffusion coefficients determined at the following concentrations: HexBQPH = 20 mM; HexBQPME = 20 mM; HexB = 18 mM. b Based
on data acquired at low temperature (21.8–52.6 °C). c Based on data acquired at higher temperature (58.8–92.2 °C). d C = cylinder; O = oblate;
P = prolate. e Estimated fitting error: 10% for a, b, L, d, and rh.
fitting using a cylindrical model (i.e., treatment of the
diffusing entity as a cylinder). Consistent results are obtained
(Table 2), where for HexBQPH only a change in the length (L)
of the cylindrical aggregates is observed as a function of temp-
erature (21.8–52.6 °C: L = 38 Å, 58.8–92.2 °C: L = 7 Å), while the
diameter (d) remains roughly the same. The HexB cylindrical
parameters (L = 7.8 Å; D = 58 Å) are both consistent with those
derived from the HexB oblate fitting and for HexBQPH at
higher temperatures.
The molecularity of the HexBQPH aggregates can be esti-
mated by appropriately scaling the volumes derived from the
rh values.1e Monomeric HexBQPH and HexBQPME have
rh ∼ 9.5 Å (and equivalent sphere volume of ∼ 3600 Å3) and are
assigned a molecularity of 1. Both spheroid fitting routines of
HexBQPH in toluene-d8 (rh = 27 Å) yield an average molecu-
larity of 23 on the basis of equivalent sphere volume for the
low temperature regime, which corresponds to an average
supramolecular assembly of ∼ 6 trimeric discs. The rh value of
15 Å (from both fitting routines) for the high temperature
Fig. 4 Linearized variable temperature diffusion data for HexBQPH
(20 mM; toluene-d8). The slope change at ∼ 60 °C is evident from the
intersection of the solid and dashed linear regression fits.
regime equates to an average molecularity of 3.9. This value,
when coupled with the shape parameters a and b (or L and d)
and molecular modelling results, strongly supports the pres-
comparison to HexB. Using first the oblate model for parame-
ence of a discotic trimeric aggregate.
terization, the low temperature regime returns a = 26 Å and b =
28 Å (rh = 27 Å) while the high temperature regime provides a =
5.0 Å and b = 26 Å (rh = 15 Å). The equatorial radius (b) is very
similar across both ranges and further similar to the calcu-
lated end-to-end length of HexBQPH (25 Å; see ESI† for
Conclusions
details). Shown is that upon increasing the temperature, In conclusion, an iterative method for size and shape approxi-
HexBQPH experiences a significant size change only in one
mation involving variable temperature diffusion measure-
dimension (from a = 26 Å to a = 5.0 Å); this is consistent with ments has been exploited for the characterization of organic
columnar growth. Confirmation that the high temperature π-conjugated chromophore assembly in solution. Diffusion
assembly is highly represented by a discrete trimer comes
coefficients were collected via DOSY NMR, linearized, and
through comparison with HexB. A plot of D versus (T/η) for fitted to a modified Stokes–Einstein equation using prolate
HexB in toluene-d8 gives a linear fit, suggesting that there is spheroid, oblate spheroid, and cylindrical models. HexBQPH
little extended aggregation of this species under these con-
self-assembly showed a bimodal temperature response in
ditions (vide supra). Iterative parameter fitting using the oblate toluene-d8, consistent with a transition from columnar assem-
spheroid model provides a = 4.5 Å, b = 30 Å, and rh = 16 Å. blies to isolated H-bonded trimers based on comparisons
These values indeed match well with both the modelled HexB
structure (see Fig. S5†) and the high temperature values for this approach can serve as a complementary way to explore
with non-assembling model compounds. We are hopeful that
HexBQPH.
To verify our analysis, the diffusion data for HexBQPH and
dynamic supramolecular assembly in solution and facilitate
drawing relationships between structure and function in appli-
HexB in toluene-d8 were alternatively subjected to iterative cation-oriented organic systems.
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A. Ballesteros, J. L. Serrano, T. Sierra and P. Romero, Chem.
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