Angewandte
Chemie
After determination of the binding constants Ktrans and
Kcis, the previously reported multiple-equilibrium model was
modified to assess the switchability of the cooperative self-
assembly upon photoirradiation of the ligand (Figure 3a).[5]
The model considers the cooperative assembly of the
porphyrins, which is described by a moderate dimerization
constant K2 and a more-preferable elongation constant K.
Free monomers (S-Zn) are removed from the stacking
process by complexation described by Ktrans and Kcis, and the
resulting Me-S-Zn:trans/cis-1 (1:1) complexes dimerize; this
dimerization is described by Kd.[10] Model simulations dem-
onstrate that the binding constant ratio g = Ktrans/Kcis assisted
by high conversion ratios is an important factor to enhance
the photoswitchability of the entire system. On the other
hand, the magnitude of binding constants and porphyrin
concentration have less influence on self-assembly since they
merely affect the critical amount of ligand necessary to fully
depolymerize the stacks.[8]
The simulation of the pyridine-induced stack-dimer
transition provides insights into the switchability of the
fraction of aggregated porphyrins (f; Figure 3b). At a por-
phyrin concentration of 4.0 ꢁ 10ꢀ5 m, a critical ligand excess of
40 equivalents of trans-1 will lead to the full depolymerization
of the porphyrin stacks (f= 0). At g = 4.4, the simulation
shows a considerable change in the fraction of aggregated
monomers; f= 0.02 at PSStrans (97%), whereas this value
increases to f= 0.90 at PSScis (95%). Obviously, this change is
accompanied by a difference in aggregate size. At 40 equiv-
alents of 1, only 2% of short stacks are predicted at PSStrans
,
whereas an average stack length of 3100 monomers is
calculated at PSScis (Figure 3c). In contrast, when analyzed
with the isodesmic model (K2 = K), photoinduced isomer-
ization only leads to a stack size of 22, thereby showing the
marked effect that cooperative self-assembly has on aggre-
gate size.[8] Furthermore, the characteristically sharp transi-
tion for the latter mechanism fulfils a prominent role in
switching. Strengthened by high conversion ratios, the rela-
tively weak stimulus characterized by g provides, neverthe-
less, high-contrast switching properties.
The simulated behaviour exhibited by the system was
experimentally verified by a titration experiment of trans-1 to
S-Zn at 4.0 ꢁ 10ꢀ5 m and subsequent irradiation experiments of
a sample with the critical amount of ligand excess. In the UV/
Vis spectra acquired at room temperature (Figure 4a, upper
panel), titration of trans-1 led to an isosbestic point in the
transition of the Soret band from stacks (lmax = 390 nm) to
dimer complexes (lmax = 428 nm). Depolymerization was also
evidenced by the disappearance of the Cotton effect at lmax
=
392 nm, while a weak CD effect (Demax = 30 Lmolꢀ1 cmꢀ1)
appears in the dimer absorbance region (Figure 4a, lower
panel). As observed in the titration curve (Figure 4b) the
dimer spectrum has fully developed after the addition of
ꢁ 50 equivalents trans-1, while a critical amount of ligand
excess of only 40 equivalents was estimated by the simulation
(see above). Considering the high stimuli responsiveness of
the system owing to its cooperativity, this difference could be
related to minor experimental deviations, slow supramolec-
ular dynamics, and temperature fluctuations. For the latter,
we remarkably observe that a lower critical amount of ligand
is required when the temperature is slightly raised from room
temperature to 308C (Figure 4b).[11] Since the CD intensity of
S-Zn stacks is hardly affected at this concentration, we expect
a stronger response in CD activity when photoirradiation is
performed at 308C. Considering the inability to reach high
conversion ratios in the presence of porphyrins (see above),
we investigated a sample containing 54 equivalents of 1.
After irradiation of the sample with 360 nm light, the
generation of cis-1 was evidenced by a decreased absorbance
at 330 nm (Figure 4c). After a delay of ꢁ 30 minutes after
reaching PSScis (estimated at ꢁ 90%), the absorbance at
428 nm decreases, while the aggregate Soret band at 390 nm
increases. Concomitantly with the latter, the CD signal at
Figure 3. a) Multiple-equilibrium model of the thermodynamic system
comprising the cooperative aggregation of S-Zn stacks, free mono-
mers, S-Zn:trans/cis-1 (1:1) complexes, and their hydrogen-bonded
homo/hetero dimers. b) Fraction of porphyrin stacks (f) at 4.0ꢀ10ꢀ5
m
against the molar excess of ligand at different conversion ratios
(stack–dimer transition). c) Size distribution of the porphyrin stacks at
4.0ꢀ10ꢀ5 m with a fixed excess of 40 equivalents of 1 at different
conversion ratios. Thermodynamic parameters applied in the simula-
tions: K2 =685mꢀ1, K=1.37ꢀ107 mꢀ1, Kd =1.1ꢀ106 mꢀ1
K
,
trans =3.6ꢀ104 mꢀ1 and Kcis =8.1ꢀ103 mꢀ1 (g=4.4).
Angew. Chem. Int. Ed. 2012, 51, 1 – 6 ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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