Cooperative self-assembly of double-strand conjugated porphyrin ladders

Article abstract of DOI:10.1021/ja992821d

A series of conjugated zinc porphyrin oligomers, from the dimer through to the hexamer, form stable ladder complexes with linear bidentate ligands such as 1,4-diazabicyclo[2.2.2]octane (DABCO) and 4,4′-bipyridyl (Bipy). The ¹H NMR spectra of these ladders confirm their structures and show how they fray and dissociate in the presence of excess ligand. The thermodynamics of these equilibria were elucidated by spectrophotometric titration, using multivariate global factor analysis, in two different solvents (chloroform and toluene). Ladder formation and dissociation exhibit many indications of positive cooperativity, including all-or-nothing two-state assembly, sigmoidal isotherms, large Hill coefficients, and narcissistic self-sorting. Ladder formation increases the planarity and conjugation, resulting in a reduction in the gap between the highest occupied and lowest unoccupied molecular orbitals.

Full text of DOI:10.1021/ja992821d

11538
J. Am. Chem. Soc. 1999, 121, 11538-11545
Cooperative Self-Assembly of Double-Strand Conjugated Porphyrin
Ladders
Peter N. Taylor and Harry L. Anderson*
Contribution from the Department of Chemistry, UniVersity of Oxford, Dyson Perrins Laboratory,
South Parks Road, Oxford OX1 3QY, U.K.
ReceiVed August 6, 1999
Abstract: A series of conjugated zinc porphyrin oligomers, from the dimer through to the hexamer, form
stable ladder complexes with linear bidentate ligands such as 1,4-diazabicyclo[2.2.2]octane (DABCO) and
1
4,4′-bipyridyl (Bipy). The H NMR spectra of these ladders confirm their structures and show how they fray
and dissociate in the presence of excess ligand. The thermodynamics of these equilibria were elucidated by
spectrophotometric titration, using multivariate global factor analysis, in two different solvents (chloroform
and toluene). Ladder formation and dissociation exhibit many indications of positive cooperativity, including
all-or-nothing two-state assembly, sigmoidal isotherms, large Hill coefficients, and narcissistic self-sorting.
Ladder formation increases the planarity and conjugation, resulting in a reduction in the gap between the
highest occupied and lowest unoccupied molecular orbitals.
Introduction
measurement. Bisson and Hunter have investigated the length
dependence of the stability of their double-strand “zippers” and
found an intriguing nonlinear free energy length dependence.7
In this paper, we present thermodynamic data on the self-
assembly of a series of double-strand porphyrin ladder structures
and explore how the stability and cooperativity increase with
increasing length, up to the six-rung ladder.
Nature uses multiple-strand formation to increase the con-
formational rigidity of biopolymers. This enables their shape
to be tightly specified by the covalent connectivity of the
components. Self-assembly is the algorithm that translates
covalent connectivity into tertiary structure. There is scope for
transferring this concept from biology to material science,
particularly in the context of electronic materials. For example,
McCullough et al. have shown that formation of multistrand
arrays increases the conjugation in polythiophenes,8 and Charych
et al. have used the interaction of polydiaceylenes with viruses
to change the conjugation in these polymers and thus to achieve
colorimetric virus detection.9 Here, we demonstrate that double-
strand formation increases the conjugation in a series of
porphyrin oligomers.10-13 The potentially useful nonlinear
optical behavior of these materials is likely to be enhanced by
this increased conjugation.14-16
Biological macromolecules tend to self-assemble into non-
covalent multiple-strand arrays.1 Nucleic acid double-, triple-,
and quadruple-helices are the supreme examples.2,3 Peptides
form coiled coils4 (as in leucine zippers and collagen) and
â-sheets (as in silk), and the phenomenon even extends to
polysaccharides.5 Self-assembly processes of this type are
reversible and controlled by thermodynamics. It is difficult to
dissect all of the thermodynamic parameters involved, which
leads to a motivation for studying simpler synthetic double-
strand assemblies. Oligopyridine metal helicates are the most
well-studied artificial multiple-strand arrays,6 and the thermo-
dynamics of their formation has been investigated in detail, but
the change in helicate stability with increasing length has not
been explored, probably because long helicates become too
stable (both thermodynamically and kinetically) for convenient
* Address correspondence to Dr. H. L. Anderson, University of Oxford,
Department of Chemistry, Dyson Perrins Laboratory, South Parks Road,
Oxford, UK OX1 3QY, Telephone: +44 1865 275 704. Fax: +44 1865
275 674. E-mail: harry.anderson@chem.ox.ac.uk.
(1) For reviews of self-assembly, see: Lindsey, J. S. New J. Chem. 1991,
15, 153-190. Whitesides, G. M.; Mathias, J. P.; Seto, C. T. Science 1991,
254, 1312-1319. Williams, D. H.; Westwell, M. S. Chem. Soc. ReV. 1998,
27, 57-63.
(2) (a) Neidle, S. Oxford Handbook of Nucleic Acid Structure; Oxford
University: Oxford, 1998. (b) SantaLucia, J., Jr.; Allawi, H. T.; Seneviratne,
P. A. Biochemistry 1996, 35, 3555-3562.
(3) Hardin, C. C.; Corregan, M. J.; Lieberman, D. V.; Brown, B. A., II.
Biochemistry 1997, 36, 15428-15450.
(4) Su, J. Y.; Hodges, R. S.; Kay, C. M. Biochemistry 1994, 33, 15501-
15510. Lau, S. Y. M.; Taneja, A. K.; Hodges, R. S. J. Biol. Chem. 1984,
259, 13253-13261. Boice, J. A.; Dieckmann, G. R.; DeGrado, W. F.;
Fairman, R. Biochemistry 1996, 35, 14480-14485.
(5) Bezemer, L.; Ubbink, J. B.; de Kooker, J. A.; Kuil, M. E.; Leyte, J.
C. Macromolecules 1993, 26, 6436-6446.
(6) (a) Pfeil, A.; Lehn, J.-M. J. Chem. Soc., Chem. Commun. 1992, 838-
840. (b) Piguet, C.; Bernardinelli, G.; Bocquet, B.; Quattropani, A.;
Williams, A. F. J. Am. Chem. Soc. 1992, 114, 7440-7451. (c) Piguet, C.;
Hopfgartner, G.; Bocquet, B.; Schaad, O.; Williams, A. F. J. Am. Chem.
Soc. 1994, 116, 9092-9102. (d) Kra¨mer, R.; Lehn, J.-M.; Marquis-Rigault,
A. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 5394-5398. (e) Constable, E.
C. In ComprehensiVe Supramolecular Chemistry; Sauvage, J.-P., Hosseini,
M. W., Eds.; Elsevier: Oxford, 1996; Vol. 9, pp 213-252.
Previously, we have demonstrated that a linear zinc porphyrin
(7) Bisson, A. P.; Hunter, C. A. Chem. Commun. 1996, 1723-1724.
(8) McCullough, R. D.; Ewbank, P. C.; Loewe, R. S. J. Am. Chem. Soc.
1997, 119, 633-634. Yue, S.; Berry, G. C.; McCullough, R. D. Macro-
molecules 1996, 29, 933-939.
(9) Okada, S.; Peng, S.; Spevak, W.; Charych, D. Acc. Chem. Res. 1998,
31, 229-239.
(10) Work on conjugated porphyrin oligomers has been reviewed
recently, see: Anderson, H. L. Chem. Commun. 1999, 2323-2331.
(11) Anderson, H. L. Inorg. Chem. 1994, 33, 972-981.
(12) Taylor, P. N.; Huuskonen, J.; Rumbles, G.; Aplin, R. T.; Williams,
E.; Anderson, H. L. Chem. Commun. 1998, 909-910.
(13) Lin, V. S.-Y.; DiMagno, S. G.; Therien, M. J. Science 1994, 264,
1105-1111.
(14) LeCours, S. M.; Guan, H.-W.; DiMagno, S. G.; Wang C. H.;
Therien, M. J. J. Am. Chem. Soc. 1996, 118, 1497-1503.
(15) Anderson, H. L.; Martin, S. J.; Bradley, D. D. C. Angew. Chem.,
Int. Ed. Engl. 1994, 33, 655-657.
10.1021/ja992821d CCC: $18.00 © 1999 American Chemical Society
Published on Web 11/30/1999

Self-Assembly of Porphyrin Ladders
J. Am. Chem. Soc., Vol. 121, No. 49, 1999 11539
Scheme 1
Table 1. Binding Constants for Monomer 1 and DABCO
dimer forms a cyclic 2:2 complex (or two-rung ladder) with
linear bidentate ligands such as 1,4-diazabicyclo[2.2.2]octane
(DABCO) and 4,4′-bipyridyl (Bipy).11 Discrete complexes are
formed because each zinc center coordinates to one ligand,
becoming 5-coordinate, whereas a 6-coordinate metal would lead
to polymeric arrays. Many supramolecular structures have been
assembled using this type of zinc porphyrin-amine coordina-
tion.17 Here, we extend our previous work by investigating the
whole series of complexes 12‚DABCO to 62‚(DABCO)6 formed
solvent
K11/M-1
K21/M-1
R
PhMe
CHCl3
(1.8 ( 0.2) × 106 (2.7 ( 0.3) × 103 0.0060 ( 0.001
(9.9 ( 1.0) × 104 (4.9 ( 0.5) × 103 0.20 ( 0.03
the stability of simple complexes, such as those of the porphyrin
monomer 1 with the bidentate ligand DABCO and those of the
porphyrin oligomers 2-6 with a monodentate analogue of
DABCO, quinuclidine.
When the coordination of DABCO to 1 is probed by UV-
visible titration, only the 1:1 1‚DABCO complex is formed.
Under these dilute conditions (porphyrin concentration ≈ 10-6
M) there is no significant concentration of the 2:1 complex,
12‚DABCO, so the binding isotherm can easily be analyzed to
yield the stoichiometric19 association constant K11 (Scheme 1;
Table 1).20 UV-visible titrations were carried out in two
solvents (toluene and chloroform) to compare the behavior under
these different conditions. The stronger binding in toluene has
been observed previously21 and can be attributed to its lower
dielectric constant and to the ability of chloroform to solvate
the ligand by acting as a hydrogen bond donor.22
Both the 1:1 and 2:1 complexes are observed when this
equilibrium is probed by 1H NMR (porphyrin concentration ≈
10-3 M). When up to 0.5 equiv of DABCO is added to 1 in
CDCl3, unbound 1 and 12‚DABCO are observed in slow
exchange. When more than 0.5 equiv of DABCO is added, a
fast-exchange equilibrium is established between unbound 1,
12‚DABCO, and 1‚DABCO (Scheme 1), which gradually shifts
by the conjugated porphyrin oligomers 1-6.12 We have used
1H NMR and UV-visible titrations to probe the structure and
stability of these double-strand arrays. Some of the binding
curves are quite complicated and could only be analyzed using
multivariate methods which fit a binding model to the whole
series of spectra simultaneously.18 We chose to focus on the
DABCO ligand, because its high basicity was expected to lead
to particularly stable complexes, but most other linear bidentate
ligands would probably behave the same way, and our results
suggest that longer ligands such as Bipy may form even more
stable ladders than those of DABCO. Compounds 1-6 differ
from the porphyrins used in our original ladder complexes11 in
that they have meso-aryl substituents, which greatly reduces their
tendency to aggregate.
(16) Thorne, J. R. G.; Kuebler, S. M.; Denning, R. G.; Blake, I. M.;
Taylor, P. N.; Anderson, H. L. Chem. Phys. 1999, in press. Kuebler, S. M.;
Denning, R. G.; Anderson, H. L. J. Am. Chem. Soc. 2000, 122, in press.
(17) Chi, X.; Guerin, A. J.; Haycock, R. A.; Hunter, C. A.; Sarson, L.
D. J. Chem. Soc., Chem. Commun. 1995, 2563-2565; 2567-2569.
Anderson, S.; Anderson, H. L.; Bashall, A.; McPartlin, M.; Sanders, J. K.
M. Angew. Chem., Int. Ed. Engl. 1995, 34, 1096-1099. Stibrany, R. T.;
Vasudevan, J.; Knapp, S.; Potenza, J. A.; Emge, T.; Schugar, H. J. J. Am.
Chem. Soc. 1996, 118, 3980-3981. Funatsu, K.; Imamura, T.; Ichimura,
A.; Sasaki, Y. Inorg. Chem. 1998, 37, 1798-1804. Reek, J. N. H.;
Schenning, A. P. H. J.; Bosman, A. W.; Meijer, E. W.; Crossley, M. J.
Chem. Commun. 1998, 11-12.
(18) Malinowski, E. R. Factor Analysis in Chemistry, 2nd ed., Wiley-
Interscience: New York, 1991. Maeder, M.; Zuberbu¨hler, A. D. Anal. Chem.
1990, 62, 2220-2224. Gampp, H.; Maeder, M.; Meyer, C. J.; Zuberbu¨hler,
A. D. Talanta 1986, 33, 943-951.
Results and Discussion
Stability of Nonchelated Complexes. The difference be-
tween self-assembly and simple coordination is that self-
assembly processes involve multiple interactions operating in
one or more closed loops; the interaction that closes the loop
becomes intramolecular, resulting in cooperativity through the
chelate effect.1 Nonchelated multicomponent complexes, in
which the interactions do not form a closed loop, do not benefit
by this chelative cooperativity, but they may exhibit other types
of cooperativity, because coordination to one site of a multi-
dentate ligand can affect the affinity of the other sites (through
steric, conformational, or electrostatic communication). Before
exploring the self-assembly of ladder structures, we measured
(19) Stoichiometric association constants (K11 and K12) for multisite
ligands are related to microscopic association constants (Kµ) via statistical
factors, as indicated in Schemes 1 and 2.
(20) For clarity, Schemes 1-3 and the structure of 52‚(DABCO)5 are
drawn with simplified skeletal porphyrins, without aryl substituents.
(21) Walker, F. A.; Benson, M. J. Am. Chem. Soc. 1980, 102, 5530-
5538.
(22) Titrations of 1 and quinuclidine were carried out at a range of
temperatures (288, 293, 298, 303, and 308 K) giving linear van’t Hoff plots
and show that there is dramatic entropy-enthalpy compensation: in toluene,
∆H ) -61 ( 4 kJ mol-1 and ∆S ) -84 ( 13 J K-1 mol-1, whereas in
CHCl3, ∆H ) -31 ( 4 kJ mol-1 and ∆S ) -10 ( 13 J K-1 mol-1. The
much lower entropy of complexation in chloroform shows that desolvation
of the ligand is a significant factor in this solvent.

11540 J. Am. Chem. Soc., Vol. 121, No. 49, 1999
Taylor and Anderson
Scheme 2
Table 2. Binding Constantsa for Monomer 1 and Dimer 2 with
Quinuclidine
K
K11
(dimer 2)
K21
(dimer 2)
R
solv.
(monomer 1)
(dimer 2)
PhMe (1.8 ( 0.2) × 106 (2.9 ( 0.7) × 106 (7.8 ( 2.0) × 105 1.1 ( 0.4
CHCl3 (1.0 ( 0.1) × 105 (2.0 ( 0.5) × 105 (6.4 ( 1.6) × 104 1.3 ( 0.5
a In inverse molarity.
quantified by the interaction parameter, R, defined by eq 7.24
R ) 4K21/K11
(7)
In this case, there is negative cooperativity, R < 1 (Table 1):
coordination to the second nitrogen of DABCO is less favorable
than the first. The greater negative cooperativity in toluene is
obvious from curve a in Figure 1: the solution of 1 with 1.5
equiv of DABCO in d8-toluene contains no significant concen-
tration of 12‚DABCO, whereas in chloroform, this 2:1 complex
survives to higher excesses of DABCO. We have also carried
out this titration in CD2Cl2 and found R ) 0.17 in this solvent.
Previous studies of the interaction of DABCO with metallopor-
phyrins without meso-aryl substituents, in CD2Cl2 and CDCl3,
have concluded that there is rather little cooperativity in these
sandwich complexes (R ) 0.7-1.0);11,25 so, the more negative
cooperativity observed with 1 is probably due to steric interac-
tion between the aryl groups. The greater interaction in toluene
appears to reflect an electrostatic contribution from the lower
dielectric constant of this solvent. This surprisingly large
interaction parameter has a dramatic adverse effect on the
stability of ladder complexes in toluene.
Figure 1. 1H NMR titration of 1 with DABCO in (a) d8-toluene and
(b) CDCl3. ∆δ is the average change in chemical shift of the two
â-protons. The smooth curves are calculated from eqs 1-6; dashed
lines show values of ∆δ(1‚DABCO). In curve b, there are no points in
the range 0 < mole ratio < 0.5 because the system is in slow exchange
in this region.
toward 1‚DABCO with increasing DABCO concentration. The
aromatic and â-pyrrole protons of 1 are strongly shielded in
the 12‚DABCO sandwich complex and return to roughly their
original values in 1‚DABCO. When this titration is carried out
in d8-toluene, rather than CDCl3, similar behavior is observed,
except that the system is in fast exchange throughout the whole
titration. Representative curves, from both solvents, are plotted
in Figure 1. These data fit well to the calculated curves from
eqs 1-6,23 which follow from Scheme 1. δM, δM L, and δML
2
are the chemical shifts of signals from 1, 12‚DABCO, and 1‚
DABCO, respectively; δobs is the observed chemical shift.
We also tested the affinity of compounds 1-6 for quinucli-
dine, a monodentate analogue of DABCO, by spectrophoto-
metric titration. The monomer 1 gives cleanly isosbestic spectra
from which binding constants can easily be obtained (Table 2).22
The titrations of dimer 2 with quinuclidine are nonisosbestic in
both chloroform and toluene. Multivariate global factor analysis
of the whole series of spectra showed that both titrations can
be analyzed in terms of three colored species (free 2 and 1:1
and 1:2 complexes), as shown in Scheme 2, and yielded the
binding constants in Table 2. Similar results were also obtained
by simplex curve fitting at selected wavelengths, but factor
analysis reduces the uncertainty from noise by simultaneously
using data at many wavelengths. Here, the interaction parameter
R is approximately 1.0. There is no significant cooperativity
between quinuclidine binding at the two zinc sites of 2, and
each site has a similar microscopic affinity Kµ to the monomer
1. The higher oligomers 3-6 also gave nonisosbestic titrations
with quinuclidine, but the large number of species present during
these titrations made it impossible to analyze the titration curves.
We assume that these oligomers bind quinuclidine analogously
to the dimer, with each zinc site acting independently with the
same microscopic affinity as the porphyrin monomer.
K11 ) [ML]/[M][L]
(1)
(2)
K21 ) [M2L]/[ML][M]
[M]0 ) [M] + [ML] + 2[M2L]
[L]0 ) [L] + [ML] + [M2L]
(3)
(4)
K11K21[M]3 + {1 + K21(2[L]0 - [M]0)}K11[M]2 +
{1 + K11([L]0 - [M]0)}[M] - [M]0 ) 0 (5)
δobs ) (δM[M] + 2δM L[M2L] + δML[ML])/[M]0 (6)
2
The value of K11 was determined independently by UV-visible
titration; so, the only unknowns during the analysis of this NMR
data were K21 and δML (in CDCl3), and K21, δM L, and δML (in
2
d8-toluene). Binding constants are shown in Table 1.
The most interesting parameter for this type of equilibrium
is the cooperativity between the two binding events, which is
Probing Ladder Assembly by 1H NMR Titration. Addition
of DABCO to solutions of each oligomer 2-5, in CDCl3, results
(23) M and L represent the porphyrin oligomer (or monomer) and
DABCO ligand, respectively; [M]0 and [L]0 are the total concentrations of
M and L.
(24) Connors, K. A. Binding Constants; Wiley: New York, 1987.
(25) Anderson, H. L.; Hunter, C. A.; Meah, M. N.; Sanders, J. K. M. J.
Am. Chem. Soc. 1990, 112, 5780-5789.

Self-Assembly of Porphyrin Ladders
J. Am. Chem. Soc., Vol. 121, No. 49, 1999 11541
remain sharp. Then, the next rung (B) starts to go into fast
exchange, until only the central rung (C) can be observed.
Exchange at the center of the ladder is slowest because it
requires the most disruption of the double-strand structure. This
process is analogous to the fraying of a DNA duplex; the
exchange rates of imine protons in oligodeoxynucleotides26 and
amide protons in R-helical peptides27 have been previously used
to detect fraying. Results presented in the next section show
that ladder dissociation (Scheme 3, equilibrium b) is a two-
state process: frayed structures do not build up to significant
concentrations. The 52‚(DABCO)5 ladder is the predominant
species in solution in all of the spectra (a-e) in Figure 2; even
after 27 equiv of DABCO have been added, the pentamer is
still mostly (>99%) in the form of the ladder complex (as
calculated from the equilibrium constant KB ) 2.7 × 103 M-4
;
see next section). This NMR experiment allows very low levels
of dynamic frayed ladders to be detected.
When DABCO is added to a 1:1 mixture of the dimer 2 and
trimer 3, the only observable complexes are the two homo-
ladders 22‚(DABCO)2 and 32‚(DABCO)3; vernier complexes
such as 23‚32‚(DABCO)6 are not formed. Similarly, when
DABCO is added to a 1:1 mixture of the butadiyne-linked dimer
2 and its 1,4-diethynylbenzene-linked analogue 2b,28 the only
Figure 2. 1H NMR spectra of the pentamer ladder 52‚(DABCO)5 in
the presence of increasing amounts of DABCO showing progressive
exchange-broadening of the bound DABCO resonances (CDCl3, 500
MHz, 298 K).
in the appearance of sharp new signals due to the ladder complex
(this type of titration could not be carried out with 6 because
its solubility is too low). In each case, the equilibrium is in
slow exchange when less than the stoichiometric amount of
DABCO is added. Ladder formation is an all-or-nothing
process: no other complexes are observed apart from the ladder
and the unbound oligomer. For example, addition of 1 equiv of
DABCO to the tetramer 4 gives a 1:2 mixture of the ladder
complex, 42‚(DABCO)4, and unbound 4. Ladder formation
results in an upfield shift of about 0.35 ppm in the aromatic
and â-pyrrole protons, due to the shielding effect of the second
strand. As expected, the ortho-aryl and tert-butyl resonances
are split in the ladders, because the faces of the porphyrins
become nonequivalent. The bound DABCO resonances appear
as sharp singlets around -4 ppm.
When excess DABCO is added to the ladders, the signals
start to broaden, and exchange between free and bound DABCO
soon becomes fast on the NMR time scale. Exchange between
the different DABCO environment in each ladder and free
DABCO is fastest for the outermost rungs of the ladder. For
example, Figure 2 shows part of the spectrum of 52‚(DABCO)5
in the presence of increasing amounts of DABCO. When there
is no excess ligand, this complex gives three DABCO reso-
nances (A-C) with intensities in the ratio 2:2:1 corresponding
to the three different ligand environments. As the concentration
of DABCO is increased, the signal (A) from the ligands at the
ends of the ladder soon broadens out, while the other two signals
complexes formed are 22‚(DABCO)2 and 2b2‚(DABCO)2. This
type of narcissistic self-sorting is characteristic of cooperative
double-strand formation at thermodynamic equilibrium.6d,29
Ladder formation was also observed with Bipy. For example
when Bipy is added to the tetramer 4 in CDCl3, sharp signals
are observed for the 42‚(Bipy)4 ladder, including two pairs of
ligand doublets, as expected. As with DABCO, the equilibrium
shifts into fast exchange in the presence of excess ligand.
Probing Ladder Assembly by UV-Visible Titration.
Addition of DABCO to solutions of oligomers 2-5, in either
chloroform or toluene, results in series of isosbestic spectra,
showing the formation of ladders 22‚(DABCO)2-52‚(DABCO)5.
With compounds 2-4, ladder formation is instantaneous,
whereas with the pentamer 5, it takes a few minutes; with the
hexamer 6, it takes about 1 h to reach equilibrium, which makes
it impractical to carry out this titration with 6. The titration
curves for oligomers 3-5 are essentially straight lines (Figure
3). They reach abrupt end points after addition of 1.5, 2.0, and
2.5 equiv of DABCO, respectively, proving the stoichiometries
of the 32‚(DABCO)3-52‚(DABCO)5 complexes. The overall
stability constants (KF ) [M2LN]/[M]2[L]N; Scheme 3) are too

11542 J. Am. Chem. Soc., Vol. 121, No. 49, 1999
Taylor and Anderson
Scheme 3
Figure 3. Spectrophotometric titration curves for treatment of 3, (open
circles), 4, (filled circled) and 5 (squares) with DABCO in toluene.
strong to measure from these curves. No further changes in the
absorption spectra of these ladders are observed until many more
equivalents of DABCO are added, when dissociation starts to
occur according to equilibrium b in Scheme 3.
The situation with the dimer 2 is more complicated because
here KF is weak enough that, under the dilute conditions of a
UV-visible titration, ladder formation does not reach comple-
tion with 1 equiv of DABCO. Furthermore, these two-rung
ladders soon dissociate in the presence of excess DABCO
(particularly in toluene); so, ladder formation never reaches
completion. Initially, the titration has sharp isosbestic points,
while equilibrium a (Scheme 3) is the main process, but then,
the titration enters a nonisosbestic phase before establishing new
isosbestic points when equilibrium b dominates in the presence
of excess DABCO. We have been unable to adequately analyze
these titrations by simplex curve fitting,30 but global multivariate
factor analysis gave reliable results. For example, Figure 4a
shows the variation in absorbance at two wavelengths (688 and
725 nm), and Figure 4b shows the concentration profiles
obtained by fitting the whole series of spectra to the model
shown in Scheme 3, in toluene. The mole fraction of ladder
22‚(DABCO)2 reaches a maximum of 82% after 1.2 equiv of
DABCO has been added and falls to 50% with 2.9 equiv of
DABCO. The titration curve in chloroform is similar except
dissociation is less favorable: the mole fraction of ladder reaches
Figure 4. Spectrophotometric titration of dimer 2 with DABCO in
toluene: (a) change in absorption at two wavelengths (668 and 725
nm) fitted to the calculated curve for the equilibria in Scheme 3; (b)
mole fractions of 2, 22‚(DABCO)2, and 2‚(DABCO)2 during the course
of the titration, calculated from global factor analysis of binding curves
at all wavelengths in the region 350-850 nm in 1 nm intervals.
a maximum of 93% after 5 equiv and only falls to 50% after
75 equiv has been added. Values of KF and KB are listed in
Table 3.
The longer ladders 32‚(DABCO)3-62‚(DABCO)6 undergo
equilibrium b (Scheme 3) in a separate ligand concentration
regime from equilibrium a; they give titration spectra with sharp
isosbestic points during both phases. For example, Figure 5a
shows spectra recorded during the breaking of the hexamer
ladder. The clean isosbesticity of these spectra demonstrates
that the only colored species present in solution are the ladder
62‚(DABCO)6 and the single-strand complex 6‚(DABCO)6. This
is further evidence for the cooperativity of the self-assembly
process, and it shows it is valid to analyze these titrations in
terms of simple two-state equilibria, which is a valuable
simplification. The titration curves for these ladder-breaking
equilibria were analyzed using eqs 8-12,23 which follow from
equilibrium b of Scheme 3. Ai and Af are the initial and limiting
(26) Nonin, S.; Leroy, J.-L.; Gue´ron, M. Biochemistry 1995, 34, 10652-
10659.
(27) Rohl, C. A.; Baldwin, R. L. Biochemistry 1994, 33, 7760-7767.
(28) Taylor, P. N.; Wylie, A. P.; Huuskonen, J.; Anderson, H. L. Angew.
Chem. Int. Ed. 1998, 37, 986-989.
(29) Rowan, S. J.; Hamilton, D. G.; Brady, P. A.; Sanders, J. K. M. J.
Am. Chem. Soc. 1997, 119, 2578-2579.
(30) The spectrophotometric titration curves for treatment of 2 with up
to 1 equiv of DABCO fit fairly well to the following equation: 2KF[M]4 +
4KF[M]3([L]0 - [M]0) + 2KF[M]2([L]0 - [M]0)2 + [M] - [M]0 ) 0, giving
KF ) (7.0 ( 5.0) × 1019 M-3 in toluene and (2.0 ( 0.8) × 1018 M-3 in
chloroform.23

Self-Assembly of Porphyrin Ladders
J. Am. Chem. Soc., Vol. 121, No. 49, 1999 11543
Table 3. Binding Constants for Porphyrin Oligomers and DABCO
solvent
N
KB/M(1-N)
KF/M-(1+N)
c50/M
PhMe
PhMe
1
2
(6.7 ( 0.6) × 102 (4.9 ( 0.5) × 109 a 7.1 × 10-6
(2.0 ( 0.3) × 105 (9.7 ( 2.8) × 1019 a 8.6 × 10-8
(5.2 ( 1.5) × 1019 b
PhMe
PhMe
PhMe
PhMe
CHCl3
CHCl3
3
4
5
6
1
2
(6.8 ( 2.0) × 107 (5.0 ( 2.0) × 1029 b 1.2 × 10-8
(1.5 ( 0.6) × 1010 (7.3 ( 3.5) × 1039 b 2.7 × 10-9
(1.6 ( 0.8) × 1012 (2.2 ( 1.3) × 1050 b 8.4 × 10-10
(3.4 ( 2.0) × 1014 (3.4 ( 2.3) × 1060 b 4.0 × 10-10
20 ( 2
(4.9 ( 0.5) × 108 a 2.3 × 10-5
(1.8 ( 0.5) × 1018 a 3.3 × 10-7
(8.6 ( 2.5) × 1017 b
107 ( 21
CHCl3
CHCl3
CHCl3
CHCl3
3
4
5
6
(5.7 ( 1.7) × 102 (1.6 ( 0.6) × 1027 b 4.9 × 10-8
(5.0 ( 2.0) × 102 (1.7 ( 0.8) × 1037 b 9.0 × 10-9
(2.7 ( 1.4) × 103 (3.0 ( 1.8) × 1046 b 3.7 × 10-9
(2.6 ( 1.6) × 103 (3.0 ( 2.0) × 1056 b 1.5 × 10-9
a Measured directly. b Calculated from KB by eq 13 using Kµ of
monomer 1.
absorbances; Aobs is the absorbance at any point in the titration.
KB ) [MLN]2/([M2LN][L]N)
[M]0 ) 2[M2LN] + [MLN]
(8)
(9)
[L]0 ) [L] + N[M2LN] + N[MLN]
(10)
KB[M2LN]{[L]0 + N([M2LN] - [M]0)}N -
(2[M2LN] - [M]0)2 ) 0 (11)
Figure 5. Titration of the hexamer ladder 62‚(DABCO)6 with excess
DABCO in toluene ([6]0 ) 2.5 × 10-7 M): (a) selected absorption
spectra during the course of the titration and (b) complexation isotherm,
showing sigmoidal rise in the mole fraction of the 6‚(DABCO)6 single-
strand complex, fitted to the calculated curve for eqs 8-12.
Aobs ) (2Ai[M2LN] + Af[MLN])/[M]0
(12)
We assume that the concentration of unbound porphyrin
oligomer is negligible ([M] ≈ 0) in the concentration regime
of these titrations, as demonstrated by the curves in Figure 3.
Values of KB from these titrations are listed in Table 3.
As the ladders become longer, they become increasingly
reluctant to open up into single-strand complexes. The titration
curve for interaction of excess DABCO with the hexamer ladder
is shown in Figure 5b. In toluene, the amount of DABCO
required to break 50% of the ladders into single strands is 1200
equiv for the hexamer, compared to only 2.9 equiv for the dimer!
The breaking curve for the hexamer is also highly sigmoidal,
as predicted by the theoretical model of eqs 8-11. As the
ladders become longer, their dissociation curves become more
sigmoidal, as reflected by the Hill plots24 in Figure 6. The Hill
coefficients nH increase from 1.3 to 4.0 with increasing ladder
length, reflecting the increasing cooperativity of ladder assembly
and dissociation.31 Hill coefficients of up to 1.75 have been
recorded for the assembly of copper(I) trihelicates.6a
Determination of Ladder Stability. Although the stability
constants of the ladders, KF, are too high to measure directly
(except for the dimer) they can be calculated from the equilib-
rium constants for breaking the ladders with excess DABCO,
KB, using the thermodynamic cycle shown in Scheme 4, which
leads to eq 13.
Figure 6. Hill plots for treatment of the ladders 22‚(DABCO)2-62‚
(DABCO)6 with excess DABCO from spectrophotometric titration data,
fitted to the calculated curves from eqs 8-12. The Hill coefficient nH
is defined as the gradient of the curve at log([MLN]/(2[M2LN])) ) 0.
for all of the oligomers 2-6 Kµ is half the stability constant of
1‚DABCO (Scheme 1; Kµ ) 0.5K11 ) 9.0 × 105 M-1 in toluene
and 4.9 × 104 M-1 in chloroform) and that all of the sites on
an oligomer behave independently when they bind just one end
of DABCO. Two independent lines of evidence validate this
assumption, in both toluene and chloroform: (i) quinuclidine
binds independently to the two sites of 2 with the same
microscopic binding constant as 1 (Scheme 2), and (ii) in the
case of the dimer 2, where KF and KB can be measured directly,
eq 13 is found to be a valid approximation in both solvents.
Values of KF calculated from KB and Kµ using eq 13 are listed
KF ) (2Kµ)2N/KB
(13)
Kµ is the microscopic binding constant for each zinc site on the
porphyrin oligomer for one end of DABCO. We assume that
(31) Hill coefficients are most commonly used to measure cooperativity
in the binding of monovalent ligands L to a multivalent receptors M to
give a MLN complexes, but they have also been applied to multiple-strand
formation equilibria;3,6a they allow cooperativity to be empirically quantified
even when the binding stoichiometry is poorly defined.

11544 J. Am. Chem. Soc., Vol. 121, No. 49, 1999
Taylor and Anderson
Figure 8. Plot of optical gap Eg (from peak Q-band absorption) against
reciprocal chain length N-1, for single-strand DABCO complexes
(circles) and ladders (squares) in toluene.
Figure 7. Gibbs free energy of ladders formation (∆GF ) -RT ln
KF) plotted against the number of porphyrins in the oligomer N, in
toluene (circles) and chloroform (squares).
tronic overlap in the ladder complexes. For example, Figure 5a
shows that the hexamer ladder has a more redshifted Q-band
and a more widely split B-band than those of the single-strand
complex. There is no change in the local coordination environ-
ment of the zinc porphyrin unit during this ladder-breaking
process. Weak interstrand exciton coupling between the face-
to-face porphyrins in the ladder complex must cause a slight
blueshift in the absorption.32 So the redshifted Q-band and the
broader B-band in the ladder complex are clear indications of
a reduction in the interporphyrin dihedral angle. Figure 8 shows
how the transition energy, or optical gap Eg, varies with the
reciprocal of the number of porphyrin units in the oligomer N-1
for ladders and for single-strand complexes.12 The steeper curve
for the ladder complexes shows that they are more conjugated.
It is interesting that no increase in conjugation is evident in the
dimer ladder 22‚(DABCO)2 when compared with that in
2‚(DABCO)2; this indicates that planarization requires at least
three rungs in the ladder.
The increase in interporphyrin conjugation accompanying
ladder formation is probably less than what would be expected
if the unbound oligomers had completely free rotation about
the butadiyne links, suggesting that the distribution of dihedral
angles is weighted toward more planar, more conjugated,
conformers, even without ladder formation, as indicated by work
on related systems.12,13,33
Comparison of the UV-visible absorption spectrum of the
4,4′-bipyridyl ladder 42‚(Bipy)4 with that of 42‚(DABCO)4
confirms that interstrand exciton coupling is not a significant
factor in these spectra. The shapes of the B-bands of the two
complexes are very similar, with that of 42‚(Bipy)4 redshifted
by only 2 nm. However, the spectrum of 42‚(Bipy)4 is noticeably
sharper, particularly in the Q-band, and its Q-band is redshifted
by 16 nm, which indicates that this Bipy ladder is more ordered
and more planar, perhaps because the strands are far enough
apart to avoid steric interactions between the aryl groups.
Scheme 4
in Table 3. It is difficult to compare the stabilities of ladders
with different lengths because the dimensions of KF vary with
N (KF has units [molar]-(N+1)). One way around this problem
is to calculate the concentration, c50, at which each ladder is
50% dissociated into single strands simply by dilution (at the
correct 2:N stoichiometry) using eq 14.
1
c50
)
(14)
4K NN
(N+1)
x
F
The values of c50 calculated from KF (Table 3) show that as the
ladders become longer they become stable to lower concentra-
tions despite the fact that they are higher order assemblies. The
stabilities of the ladders become increasingly concentration
dependent, and this almost compensates for the increasing KF.
Gibbs free energies of ladder formation (∆GF ) -RT ln KF)
are compared in Figure 7. Plots of ∆GF versus N in both
chloroform and toluene give remarkably straight lines. Adding
each new rung to the ladder increases the free energy by the
same amount. The intercepts at N ) 0 correspond to unfavorable
entropies of ladder initiation of 11 J K-1 mol-1 in toluene and
20 J K-1 mol-1 in chloroform. Similar linear free energy
relationships (with positive intercepts at N ) 0) are found for
DNA duplex formation.2b
Change in Conjugation between Single- and Double-
Strand Oligomers. Ladder formation was anticipated to favor
conformations in which neighboring porphyrin macrocycles are
coplanar and thus to increase the interporphyrin electronic
conjugation. The changes in the UV-visible spectra ac-
companying breaking of ladder complexes with excess DABCO
(Scheme 3b) demonstrate that there is indeed increased elec-
Conclusions
Ladder formation-dissociation equilibria exhibit the follow-
ing characteristics of cooperative self-assembly:
(32) Hunter, C. A.; Sanders, J. K. M.; Stone, A. J. Chem. Phys. 1989,
133, 395-404. Hunter, C. A.; Meah, M. N.; Sanders J. K. M. J. Am. Chem.
Soc. 1990, 112, 5773-5780. Mak, C. C.; Bampos, N.; Sanders, J. K. M.
Angew. Chem., Int. Ed. Engl. 1998, 37, 3020-3023. Mak, C. C.; Pomeranc,
D.; Montalti, M.; Prodi, L.; Sanders, J. K. M. Chem. Commun. 1999, 1083-
1084.
(33) Lin, V. S.-Y.; Therien, M. J. Chem. Eur. J. 1995, 1, 645-651.
Stranger, R.; McGrady, J. E.; Arnold, D. P.; Lane, I.; Heath, G. A. Inorg.
Chem. 1996, 35, 7791-7797. Kumble, R.; Palese, S.; Lin, V. S.-Y.; Therien
M. J.; Hochstrasser, R. M. J. Am. Chem. Soc. 1998, 120, 11489-11498.
Wilson, G. S.; Anderson, H. L. Chem. Commun. 1999, 1539-1540.

Self-Assembly of Porphyrin Ladders
J. Am. Chem. Soc., Vol. 121, No. 49, 1999 11545
1
Instrumentation. H NMR titrations were carried out on a Bruker
a. All-or-Nothing Formation and Dissociation. If significant
AM-500 spectrometer (500 MHz). UV-visible spectra were recorded
on a Perkin-Elmer Lambda 20 instrument.
Methods. H NMR and UV-visible titrations were performed by
amounts of partially formed ladders were formed, they would
1
have been observed by H NMR (because ladder assembly is
1
in slow exchange) and the UV-visible spectra would have been
nonisosbestic. There is no such sign of these intermediates.
However, low concentrations of partially formed frayed ladders
can be detected indirectly through the different exchange rates
of the different rungs of the ladders with excess DABCO.
adding solutions of the ligand to a solution of the porphyrin in either
a 5 mm NMR tube or a 1 cm path length quartz cuvette, using microliter
syringes. The porphyrin was present in the ligand at the same
concentration as that in the NMR tube or cuvette, to avoid dilution
effects. All spectra and titrations were performed at 298 K (except those
for van’t Hoff plots22). UV-visible titrations were carried out with
peak absorbances in the range 0.1-1.0, which corresponds to a
porphyrin concentration of ca. 10-6 M. 1H NMR titrations were carried
out at a porphyrin concentration of ca. 10-3 M.
1
b. Narcissistic Self-Sorting. H NMR titrations show that
mixtures of 2, 3, and DABCO give only 22‚(DABCO)2 and 32‚
(DABCO)3, and mixtures of 2, 2b, and DABCO give only 22‚
(DABCO)2 and 2b2‚(DABCO)2.
c. Sigmoidal Binding Curves. The UV-visible titration
isotherms for ladder dissociation become increasingly sigmoidal
as the ladders become longer.34
1
Data Analysis. H NMR titration curves were analyzed by fitting
the experimental data to the theoretically expected curve (see text) using
a simplex nonlinear curve-fitting program, using a combination of
bisection and the Newton-Raphson method to iteratively solve
polynomial equilibrium expressions.35 UV-visible spectrophotometric
titrations were analyzed both by using this simplex method (at several
wavelengths in turn) and by fitting the whole series of spectra at 1 nm
intervals using the software SPECFIT, ver 2.11 (from Spectrum
Software Associates, P.O. Box 4494, Chapel Hill, NC 27515-4494),
which uses a global analysis system with expanded factor analysis and
Marquardt least-squares minimization to obtain globally optimized
parameters.18 The two methods gave very similar results in all cases,
although the second method is certainly more accurate, and in one case
(the full equilibrium of 2, 22‚(DABCO)2, 2‚(DABCO)2, and DABCO),
this was the only applicable method of analysis.
Measurements of simple 1:1 binding constants were found to be
reproducible to within 10%. Errors in higher order binding constants
are correspondingly higher, because they are more sensitive to
inaccuracies in concentration and absorption or chemical shift; values
of KB with units of molarity to the power of (1 - N) have errors of
approximately N × 10%. These estimates of the errors are much higher
that those from statistical analysis of the data from SPECFIT. The
standard deviation σ in quantities such as KF and R, which are derived
from n experimental binding constants (with standard deviation σi),
were calculated using eq 15.36
d. Large Hill Coefficients. The Hill coefficients nH for ladder
dissociation increase gradually from the dimer to the hexamer
and are all greater than unity. In all cases, the Hill coefficients
have the theoretically predicted values for the two-state equi-
librium of Scheme 3b to within two significant figures.
e. Increasing Ladder Stability with Increasing Length. The
Gibbs free energy for ladder formation has a linear length
dependence, as has been observed in DNA oligomers. This is
manifested by the increasingly high concentrations of excess
DABCO required to break the ladders into single-strand
complexes.
f. Self-Assembly Constrains the Conformation. The in-
creased planarity and π-overlap in the ladder structures,
compared to single-strand complexes, is apparent from the
increased splitting in the Q-band and from the reduction in
HOMO-LUMO gap. This is analogous to the way nature uses
self-assembly to control tertiary structure. It remains to be
discovered whether this effect is large enough to be useful in
the optimization of these materials for nonlinear optics, but it
does at least make their electronic spectra highly sensitive to
conformational changes. The dramatic changes in the absorption
spectra that accompany ladder formation and dissociation have
enabled us to probe these equilibria in a level of detail that would
probably not have been possible with nonconjugated analogues.
n
σ )
σi2
(15)
∑
x
i)1
Acknowledgment. This work was generously supported by
the Engineering and Physical Research Council (EPSRC), U.K.
We thank the EPSRC mass spectrometry service (Swansea) for
FAB mass spectra.
Experimental Section
Materials. Compounds 1-6 and 2b were prepared as described
previously;12,28 full experimental details of this synthetic work are
provided in the Supporting Information. Deutero-chloroform was
deacidified by standing over potassium carbonate. Chloroform for UV-
visible titrations contained 0.5% ethanol stabilizer, and this amount of
ethanol was also added to CDCl3 for quantitative NMR titrations, so
that NMR and spectrophotometric results can be directly compared.
Toluene was distilled from calcium hydride. Deutero-toluene, DABCO,
and quinuclidine were used as supplied.
Supporting Information Available: Experimental proce-
dures for the synthesis of compounds 1-6. This material is
available free of charge via the Internet at http://pubs.acs.org.
JA992821D
(35) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T.
Numerical Recipes in Pascal; Cambridge University: Cambridge, U.K.,
1989.
(34) Ladder formation curves would also be sigmoidal if titrations were
carried out at a sufficiently low concentration.
(36) Crumpler, T. B.; Yoe, J. H. Chemical Computation and Errors; J.
Wiley: New York, 1940; pp 180-183.