Probing the Limits of the Majority-Rules Principle in a Dynamic Supramolecular Polymer

Article abstract of DOI:10.1021/ja9080875

By systematic variation of the chemical structure of benzene-1,3,5- tricarboxamide (BTA) derivatives, the effect of chemical structure on the amplification of chirality was studied and quantified. In combination with temperature-dependent amplification experiments, the limits of the majority-rules principle were also investigated. For all BTA derivatives a high, constant helix reversal penalty was determined, which is related to the intermolecular hydrogen bonds that are present in all studied derivatives. For asymmetrically substituted BTA derivatives an odd-even effect was found in the degree of chiral amplification when changing the position of the stereogenic center with respect to the amide functionality. It was found that the mismatch penalty could be directly related to the number of stereocenters present in the molecules. Increasing this number from one to three resulted in an increase in this energy penalty while leaving the helix reversal penalty unaffected. For the majority-rules principle this implies that a single stereocenter present in the molecule contains sufficient chiral information at the molecular level to result in a chirally amplified state at the supramolecular level. Further evidence that the mismatch penalty is directly related to the number of stereocenters was obtained from mixed majority-rules experiments where two BTA derivatives with different numbers of stereocenters with opposite stereoconfiguration were studied in a majority-rules experiment. Finally, the ultimate limits of chiral amplification for the majority-rules principle were investigated, revealing that, given a certain helix reversal penalty, there is an optimum to which the mismatch penalty can be reduced while also enhancing the degree of chiral amplification. Temperaturedependent majority-rules experiments could indeed confirm these simulations. These findings show the relevance of both energy penalties when trying to enhance the degree of chiral amplification for the majorityrules principle in a one-dimensional helical supramolecular polymer.

Full text of DOI:10.1021/ja9080875

Published on Web 12/16/2009
Probing the Limits of the Majority-Rules Principle in a
Dynamic Supramolecular Polymer
Maarten M. J. Smulders, Patrick J. M. Stals, Tristan Mes, Tim F. E. Paffen,
Albertus P. H. J. Schenning,* Anja R. A. Palmans,* and E. W. Meijer*
Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular
Systems, EindhoVen UniVersity of Technology, P.O. Box 513,
5600 MB EindhoVen, The Netherlands
Received September 30, 2009; E-mail: A.P.H.J.Schenning@tue.nl; A.Palmans@tue.nl; E.W.Meijer@tue.nl
Abstract: By systematic variation of the chemical structure of benzene-1,3,5-tricarboxamide (BTA)
derivatives, the effect of chemical structure on the amplification of chirality was studied and quantified. In
combination with temperature-dependent amplification experiments, the limits of the majority-rules principle
were also investigated. For all BTA derivatives a high, constant helix reversal penalty was determined,
which is related to the intermolecular hydrogen bonds that are present in all studied derivatives. For
asymmetrically substituted BTA derivatives an odd-even effect was found in the degree of chiral
amplification when changing the position of the stereogenic center with respect to the amide functionality.
It was found that the mismatch penalty could be directly related to the number of stereocenters present in
the molecules. Increasing this number from one to three resulted in an increase in this energy penalty
while leaving the helix reversal penalty unaffected. For the majority-rules principle this implies that a single
stereocenter present in the molecule contains sufficient chiral information at the molecular level to result
in a chirally amplified state at the supramolecular level. Further evidence that the mismatch penalty is
directly related to the number of stereocenters was obtained from mixed majority-rules experiments where
two BTA derivatives with different numbers of stereocenters with opposite stereoconfiguration were studied
in a majority-rules experiment. Finally, the ultimate limits of chiral amplification for the majority-rules principle
were investigated, revealing that, given a certain helix reversal penalty, there is an optimum to which the
mismatch penalty can be reduced while also enhancing the degree of chiral amplification. Temperature-
dependent majority-rules experiments could indeed confirm these simulations. These findings show the
relevance of both energy penalties when trying to enhance the degree of chiral amplification for the majority-
rules principle in a one-dimensional helical supramolecular polymer.
Introduction
of the helical polymer. The odd-even effect has also been
reported for poly(isocyanides),7-9 polysilylenes,10 functionalized
Minute changes in the molecular structure can have large
effects on the supramolecular organization of molecules, as has
been observed in liquid crystalline phases and for (supra-
molecular) polymers in solution. For example, for covalent
helical polymers in solution, the effect of small changes in the
side-chain structure has been investigated in great detail by the
group of Masuda for poly(N-propargylamides).1-5 For these
helical poly(N-propargylamides) they reported on the so-called
odd-eVen effect6 upon shifting an (S)-chiral stereocenter from
the carbon atom R with respect to the amide group to the carbon
atom at the ꢀ position.3 The odd-even effect was manifested
in a reversal of the sign of the Cotton effect upon this shift of
the (S)-stereocenter, indicative of a reversal of the handedness
polystyrene derivatives,11 and helical aggregates of oligo- and
polythiophenes,12-14 while it is absent in poly(propiolic ester)s.15
(6) This definition of the odd-even effect is different from the odd-even
effect observed for instance in self-assembled monolayers which
display different properties (including molecular packing, adhesion,
wettability and chemical reactivity), depending an odd or even chain
length. See for more information: Tao, F.; Bernasek, S. L. Chem. ReV.
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620 J. AM. CHEM. SOC. 2010, 132, 620–626
10.1021/ja9080875  2010 American Chemical Society

Majority-Rules Principle in a Supramolecular Polymer
A R T I C L E S
Chart 1. Molecular Structure of the Different Symmetrically and Asymmetrically Substituted Discotics
In addition, also in the liquid crystalline state, odd-even effects
have been observed for chiral nematic phases.16-19
molecule, which for the BTA can vary between 0 and 3, as
well as an effect of the position of the stereocenter with respect
to the amide group, i.e., the odd-even effect. Moreover,
reducing the number of stereocenters in a molecule results in
less chiral information per monomer, which could result in a
system that can no longer reach a fully amplified state.
As each BTA comprises three side groups, also asym-
metrically substituted monomers can be synthesized, which
enabled us to study the effect of the number of stereocenters
on the degree of chiral amplification. The desymmetrization
of monomers has already been described for other self-
assembling systems, including porphyrins and porphyr-
azines,20-24 perylenes,25-27 dehydrobenzo[18]annulenes,28
amphiphilic hexa-peri-hexabenzocoronenes,29,30 triphenyl-
enes,31-36 and bis-urea derivatives.37 Because of their simple
molecular structure, the synthesis of various symmetrically
In the preceding contribution (DOI 10.1021/ja908053d), we
studied the role of temperature on the chiral amplification
behavior in supramolecular polymers comprising C3-symmetrical
alkyl-substituted benzene-1,3,5-tricarboxamides (BTAs, Chart
1). As a result of those investigations we could conclude that
the sergeants-and-soldiers phenomenon for the symmetrical
derivatives (S)-1:2 and the majority-rules phenomenon for the
(S)-1:(R)-1 mixtures are operative and that both phenomena are
characterized by a high helix reversal penalty (HRP). This
energy penalty is paid when in a helical stack of these discotics
the handedness of the stack is reversed, i.e., going from a left-
handed to a right-handed helical segment, or Vice Versa. The
origin of this high HRP was related to the strong intermolecular
hydrogen bonds that, once a handedness is chosen, maintain
this handedness throughout the stack. The selection of either
of the two helicities was governed by the chirality of the
“sergeant” in the case of the sergeants-and-soldiers principle
or by the major enantiomer in the case of the majority-rules
principle.
Given the high and more or less constant HRP, the extent of
chiral amplification was found to be determined by the mismatch
penalty (MMP). This second energy penalty is paid when
incorporating a chiral disc in a stack of its unpreferred helicity.
This MMP was found to be strongly dependent on temperature,
and its origin was ascribed to the steric interactions between
the alkyl side chains, either equipped with or without the
stereogenic centers.
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Considering the molecular origin of both the HRP and the
MMP, we set out to investigate to what extent relatively small
changes in the molecular structure of the BTA derivatives would
affect the chiral amplification behavior. In particular we
anticipated an effect of the number of stereocenters per
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A R T I C L E S
Smulders et al.
or asymmetrically substituted BTA monomers is rather
straightforward.38-41 For example, our group has reported
on the post-assembly photopolymerization of asymmetrically
substituted BTAs in which one of the side chains was
functionalized with a polymerizable sorbyl group.39-41
In a previous study we reported the effect of a subtle change
in the molecular structure of the BTAs on the supramolecular
polymerization behavior in solution and in the liquid crystalline
phase.42 To this end we synthesized asymmetrically substituted
discotics equipped with two achiral n-octyl chains and one chiral
side chain (Chart 1). The stereochemistry and the position of
the stereocenter were both varied. We showed that shifting the
stereogenic center closer to the aromatic core resulted in a more
stable liquid crystalline phase. Also in solution more stable
supramolecular polymers were formed when the stereogenic
center was shifted closer to the amide moiety. Furthermore, in
solution an odd-even effect in the sign of the Cotton effect
was observed. This library of symmetrically and asymmetrically
substituted BTAs (1-6, Chart 1) now allows us to study in detail
the effect of molecular structure on the chiral amplification
phenomena, i.e., the sergeants-and-soldiers and majority-rules
principles. In addition, by quantifying the data with the extended
chiral amplification model, as originally developed by van
Gestel,43-46 we can also predict the limitations of the degree
of chiral amplification in this system, in particular for the
majority-rules principle. These findings can help to understand
the origin of homochirality observed in Nature,47,48 i.e., how a
small enantiomeric excess (ee), in combination with a set of
conditions, can still be amplified to a homochiral state.
Considering the sign of the Cotton effect, also in these sergeants-
and-soldiers experiments an odd-even effect can be discerned,
as for (R)-3 and (R)-5 a positive Cotton effect is observed, while
(R)-4 gives a negative Cotton effect. Normalizing the Cotton
effect at 223 nm yielded the net helicity as a function of fraction
of “sergeant” (Figure 1D).49 For the (R)-3:2 and (R)-5:2 mixtures
very similar results were obtained; i.e., in both of these systems
a net helicity of 1 is obtained at a fraction of “sergeant” of
∼0.15. For the (R)-4:2 mixture more of the “sergeant” solution
needed to be added to obtain a net helicity of 1, i.e., more than
30% “sergeant”.
To fit and quantify the sergeants-and-soldiers data we used
our adapted amplification model,49 originally developed by van
Gestel, which was introduced in the preceding contribution. This
model describes the chiral amplification phenomena in terms
of two free energy penalties, the HRP and the MMP. The former
penalizes a helix reversal in a stack, whereas the latter penalizes
a mismatch when a chiral monomer is introduced into a stack
of its unpreferred helicity.44 Fitting of the data will yield the
dimensionless energy penalties, σ and ω, which are related to
the HRP and the MMP via σ ) exp[-2HRP/RT] and ω )
exp[-MMP/RT], respectively.44
The values of the HRP as well as the MMP, as determined
from fitting the sergeants-and-soldiers data, are given in Table
1. For the (R)-3:2 and (R)-5:2 systems a HRP of 11.2((1.4) kJ
mol-1 was found, which is similar to the value of 12.6((2.0)
kJ mol-1 previously determined for (R)-1:2. Hence, it can be
concluded that moving the stereogenic center closer to the
benzene core has no significant effect on the HRP. This confirms
our hypothesis that the high HRP is the result of the inter-
molecular hydrogen bonds, which can be expected to be equally
strong for the different “sergeant”:“soldiers” mixtures. For the
MMP for the (R)-3:2 and (R)-5:2 systems only a lower limit of
about 0.5 kJ mol-1 could be determined. For a more accurate
determination the MMP fitting of the majority-rules experiments
is required (Vide infra). For the mixtures of (R)-4:2 a consider-
ably weaker sergeants-and-soldiers effect was observed, which
could be explained by assuming either a low HRP of about 6-8
kJ mol-1 or a MMP as low as 0.3 kJ mol-1. Since the
intermolecular hydrogen bonds are expected to be equally strong
for the (R)-4:2 mixtures, we do not assume that the HRP is
reduced in this system. Hence, it was proposed that a low MMP
is responsible for the rather weak sergeants-and-soldiers effect.
This low MMP is also observed for the majority-rules effect
for (R)-4:(S)-4 mixtures (Vide infra).
Upon closer inspection of the CD spectra obtained for the
(R)-3:2 and (R)-5:2 mixtures, two different types of CD spectra
can be discerned. That is, at low fraction of “sergeant”, up to
about 0.25, the CD spectrum has its maximum at 215 nm and
a shoulder at ∼240 nm (which we refer to as a type I spectrum).
At higher fractions of “sergeant”, the CD spectrum resembles
the spectrum of pure “sergeant”, with a maximum CD intensity
at 223 nm (type II spectrum). For the (R)-4:2 mixtures this
distinction could not be made, as in this case the CD spectrum
of pure “sergeant” is similar to the CD spectrum recorded at
low fraction of “sergeant”; i.e., all CD spectra have a maximum
in absorption at 217 nm and a shoulder at ∼240 nm. As was
already discussed in a previous report, the difference in the CD
spectra of the pure “sergeants”, (R)-3, (R)-4, and (R)-5, was
attributed to a slightly different molecular packing in the helical
stacks of (R)-4 as compared to the stacks of (R)-3 or (R)-5.42
Results
Effect of the Position of the Stereogenic Center on the
Chiral Amplification in the Benzene-1,3,5-tricarboxamide
Derivatives. We first varied the position of the stereogenic center
in asymmetrically substituted BTAs (3-5, Chart 1). The
synthesis of these derivatives was reported previously, and in
solution an odd-even effect in the sign of the Cotton effect
was observed.42 At room temperature at a concentration of 3.0
× 10-5 M in methylcyclohexane (MCH), both sergeants-and-
soldiers and majority-rules experiments were performed with
one of the enantiomers and achiral discotic 2 or with the two
enantiomers, respectively. The results of the sergeants-and-
soldiers experiments are shown in Figure 1.
Upon addition of small fractions of “sergeant” for all three
different “sergeants”, (R)-3, (R)-4, and (R)-5, a strong increase
in the Cotton effect was observed, indicative of a strong
sergeants-and-soldiers effect operative in all three mixtures.
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J. Am. Chem. Soc. 2008, 130, 1120–1121.
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Chem. Soc. 2003, 125, 15935–15940.
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A. R. A.; Meijer, E. W. Chem.sEur. J. 2009, 15, 2071–2080.
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2003, 36, 6668–6673.
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(49) See Supporting Information.
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Majority-Rules Principle in a Supramolecular Polymer
A R T I C L E S
Figure 1. CD spectra of mixtures of (R)-3:2 (A), (R)-4:2 (B), and (R)-5:2 (C). Net helicity versus fraction of “sergeant” for mixtures of (R)-3:2, (R)-4:2,
and (R)-5:2 (D) with the corresponding fit. Change in CD effect at 216 nm and at 250 nm as a function of fraction of “sergeant” for mixtures of (R)-3:2 (E)
and (R)-5:2 (F). Concentration, 3.0 × 10-5 M in MCH; temperature, 20 °C.
Table 1. Energy Penalties (in kJ mol-1) Determined from Fitting
is in line with the higher isotropization temperature of (R)-3 in
the Sergeants-and-Soldiers and the Majority-Rules Data
the bulk and a higher temperature of elongation in dilute
sergeants-and-soldiers
majority-rules
solution.42
Along with sergeants-and-soldiers experiments, we also
performed majority-rules experiments. Mixtures of the enanti-
omers of 3, 4, or 5 were mixed in different ratios at room
temperature at 3.0 × 10-5 M in MCH (Figure 2A-C).50 For
all three systems we observed a strong nonlinear increase in
the Cotton effect upon increasing the ee, indicative of a majority-
rules effect. Normalizing these data yielded the net helicity as
a function of ee (Figure 2D).49 Similarly as observed for the
sergeants-and-soldiers experiments, for the enantiomers of 3 and
5 the majority-rules results were virtually identical. Comparing
the majority-rules results for the enantiomers of 4 with those
of 3 and 5, it was found that a stronger amplification of chirality
is observed for the former; i.e., a net helicity of 1 is reached at
lower ee for 4. This is opposite to the sergeants-and-soldiers
experiments where for (R)-4:2 a weaker amplification of chirality
disc
HRP
MMP
HRP
MMP
1
3
4
5
6
12.6 ( 2.0
11.2 ( 1.4
10.5 ( 3.5
11.2 ( 1.4
n.d.
>0.5a
>0.5a
>0.3a
>0.5a
n.d.
15 ( 4
15 ( 4
16 ( 4
15 ( 4
15 ( 4
1.9 ( 0.2
1.0 ( 0.2
0.5 ( 0.2
1.0 ( 0.2
1.6 ( 0.3
a From fitting the sergeants-and-soldiers data it was only possible to
determine a lower limit for the value of the mismatch penalty.
For the (R)-3:2 and (R)-5:2 mixtures the sergeants-and-soldiers
effect was equally strong; i.e., the appearance of the type I CD
spectrum occurs at the same fraction of “sergeant”. However,
the transition from the type I CD spectrum to the type II CD
spectrum, which was probed at 250 nm, occurs at different
fractions of “sergeant” (Figure 1E,F). For the (R)-3:2 system,
this transition occurs at ∼0.45 fraction of “sergeant”, while for
(R)-5:2 this happens at a fraction of ∼0.65. This would indicate
that stacks of (R)-3 are more stable than stacks of (R)-5, which
(50) The ee values of the (S)-4 and (R)-4 disk were only 60%.
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A R T I C L E S
Smulders et al.
Figure 2. CD spectra of mixtures of (R)-3:(S)-3 (A), (R)-4:(S)-451 (B), and (R)-5:(S)-5 (C). Net helicity versus ee52 for mixtures of (R)-3:(S)-3, (R)-4:(S)-4,
and (R)-5:(S)-5 with corresponding fit (D). Concentration, 3.0 × 10-5 M in MCH; temperature, 20 °C.
was observed, as more of the “sergeant” (R)-4 had to be added
to reach a net helicity of 1.
chiral amplification behavior of the asymmetrical BTAs, other
than the odd-even effect described above.
We fitted the majority-rules data for the three systems and found
for 3 and 5 results in agreement with results for the sergeants-
and-soldiers data (Table 1), i.e., a HRP of 15 ((4) kJ mol-1 and
a MMP of 1.0 ((0.2) kJ mol-1. This MMP is smaller than the
value of 1.9 kJ mol-1 found for the (R)-1:2 system at room
temperature. This suggests that the position of the stereogenic center
with respect to the amide moiety does not have an effect on the
MMP, but that the number of stereogenic centers does affect the
degree of chiral amplification. The effect of the number of
stereogenic centers will be discussed below.
Effect of the Number of Stereogenic Centers on the Chiral
Amplification in Benzene-1,3,5-tricarboxamide Derivatives. To
study the influence of the number of stereogenic centers per
molecule, the results obtained for the asymmetrically substituted
monomer 5 equipped with one 3,7-dimethyloctyl side chain can
be compared with those of the symmetrically substituted
derivative 1 with three 3,7-dimethyloctyl side chains. Modeling
the sergeants-and-soldiers and majority-rules data for 1 and 5
resulted in a HRP of about 12 kJ mol-1 for both systems. More
interestingly, for 1 we found a MMP of 1.9 kJ mol-1, whereas
for 5 this energy penalty was only 1.0 kJ mol-1. These results
suggest that the MMP increases with the number of stereogenic
centers present in the molecule, while the HRP remains constant.
To investigate this hypothesis we also synthesized the asym-
metrical derivative 6, comprising two chiral 3,7-dimethyloctyl
side chains and one achiral n-octyl side chain, and studied its
majority-rules behavior (Figure 3A).
When considering the majority-rules results for the three
derivatives, with one (5), two (6), or three (1) stereogenic
centers, we observed a decrease in the degree of chiral
amplification with increasing number of stereocenters. Modeling
of the data for 6 resulted in HRP ) 15((4) kJ mol-1 and MMP
) 1.6((0.3) kJ mol-1. This latter value is nicely between the
values determined for the derivative with one stereogenic center
(1.0 kJ mol-1) and the molecule with three stereogenic centers
(1.9 kJ mol-1). Consequently, it can be concluded that the MMP
can be directly related to the number of stereogenic centers
present in the molecule.
For the enantiomers of 4 HRP ) 16((4) kJ mol-1 and MMP
) 0.5 ((0.2) kJ mol-1 were determined. Again the HRP is high
for all systems, which can be related to the strong intermolecular
hydrogen bonds, as discussed above. The stronger majority-rules
effect for 4, compared to 3 and 5, is reflected in the lower MMP
determined for 4. A lower MMP means it is more favorable to
incorporate the enantiomer in minority in stacks with the helicity
corresponding to the enantiomer in majority. As a result, at lower
ee a fully homochiral system can be obtained.
When considering the effect on chiral amplification of
changing the position of the stereogenic center, the only
difference observed is between the R- and γ-substituted deriva-
tives 3 and 5 on the one hand and the ꢀ-substituted derivative
4 on the other hand. That is, there is an odd-even effect in the
degree of chiral amplification. However, shifting the methyl
closer to the benzene core does not result in a change in the
(51) It should be noted that the majority-rules experiments for 4 were
performed with two enantiomers with an ee of 60%. Recently, (R)-4
was synthesized with high ee (>97%), which was used for the
sergeants-and-soldiers experiments, as well as for the self-assembly
studies.
Inspired by this conclusion, we performed so-called “mixed”
majority-rules experiments in which two monomers with
opposite chirality and different numbers of stereogenic centers
were mixed (Figure 3B-D). Similar experiments have been
(52) A positive ee value corresponds to an excess of the (R)-enantiomer.
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624 J. AM. CHEM. SOC. VOL. 132, NO. 2, 2010

Majority-Rules Principle in a Supramolecular Polymer
A R T I C L E S
Figure 3. Majority-rules results for mixtures of (R)-1:(S)-1, (R)-5:(S)-5, and (R)-6:(S)-6 with corresponding fit (A). Mixed majority-rules results for (R)-
1:(S)-5 (B), (S)-1:(R)-6 (C), and (R)-5:(S)-6 (D). The ee was calculated on a per-molecule basis and a per-stereocenter basis. Concentration, 3.0 × 10-5
in MCH; temperature, 20 °C.
M
reported by Green and co-workers, who investigated the “chiral
conflict” that arises when helical polymers are prepared from
structurally different enantiomeric monomers.53 When perform-
ing the mixed majority-rules experiments, care is needed to
calculate the ee. First of all, the ee can be calculated on the
basis of the number of molecules with a given stereochemistry.
However, as the number of stereocenters per molecule is
different, we can also determine the ee on the basis of the
number of stereocenters with a given stereochemistry.
stereogenic centers. However, there is a limit to the extent to
which the MMP can be lowered and still result in an enhance-
ment of the majority-rules effect. Ultimately, at MMP ) 0, the
enantiomers will become effectively achiral at the supra-
molecular level, as they no longer have a preference to be in a
right- or left-handed helical stack. Indeed, if we simulate, for a
constant HRP, the net helicity versus ee for decreasing values
of the MMP, an optimum in chiral amplification is observed
(Figure 4A).
For each of the three possible mixed majority-rules experiments,
we find that only when we determine the ee on the basis of the
number of stereocenters do we arrive at a proper majority-rules
plot in which no net helicity is found at ee ) 0 and in which the
origin is a point of symmetry. Therefore, these majority-rules results
strongly support the hypothesis that the MMP is determined by
the number of stereogenic centers. Finally, it is good to note that
although the MMP is dependent on the number of stereocenters,
no effect on the HRP was observed.
Limits of the Majority-Rules Principle. The chiral amplifica-
tion behavior observed in the BTA-based supramolecular
polymer can be characterized by a high and more or less constant
HRP and a MMP that can change depending on concentration,
temperature, or chemical structure. Consequently, if we want
to enhance the degree of chiral amplification in this system, we
can only influence the MMP. In case of the majority-rules
principle, this would mean that we have to reduce the MMP to
arrive at a stronger majority-rules effect, as was also observed
experimentally (Vide supra). Lowering the MMP can be
achieved either by increasing the temperature, as was discussed
in the preceding contribution, or by reducing the number of
When the MMP is high, no chiral amplification can occur as
the two enantiomers cannot be incorporated in stacks of their
unpreferred helicity. As a result, the system is reminiscent of a
phase-separated system and the net helicity increases linearly
with the ee. Upon lowering the MMP, chiral amplification
becomes possible. This is evident in Figure 4A from the
nonlinearity of the curves, which show a higher net helicity at
a given ee compared to the linear curve for an infinitely high
MMP. As the MMP is further reduced, however, the curves
decrease to values below the linear curve, and ultimately the
net helicity becomes 0 for every ee. This happens as the MMP
has become 0, meaning that chirality is no longer expressed at
the supramolecular level. To illustrate the effect of lowering
the MMP, the ee required to reach a net helicity of 0.95 can be
plotted as a function of the MMP (Figure 4B). Figure 4B clearly
shows that there is an optimal MMP at which homochirality
becomes 1 at the lowest ee. Also indicated in Figure 4B are the
determined mismatch penalties for the C3-derivatives with one,
two, or three stereocenters, i.e., for 5, 6, and 1, respectively.
As can be seen, the reduction in MMP observed when lowering
the number of stereocenters leads to an enhancement of the
degree of chiral amplification, in agreement with the results in
Figure 3A. This shows that the limit of the majority-rules
(53) Tang, K.; Green, M. M.; Cheon, K. S.; Selinger, J. V.; Garetz, B. A.
J. Am. Chem. Soc. 2003, 125, 7313–7323.
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J. AM. CHEM. SOC. VOL. 132, NO. 2, 2010 625

A R T I C L E S
Smulders et al.
Figure 4. (A) Simulated majority-rules curves for different values of the MMP at a constant helix reversal penalty of 12.6 kJ mol-1. (B) Enantiomeric
excess required to obtain a net helicity of 0.95, assuming a constant HRP of 12.6 kJ mol-1. The determined mismatch penalties for the enantiomers with one
(5), two (6), and three (1) stereocenters are also indicated. (C) Majority-rules experiment for (S)-5:(R)-5 at different temperatures. Concentration, 2.4 × 10-5
M in MCH.
principle is not yet reached by reducing the number of
stereocenters to one.
two (or three)-dimensional structures would be necessary, so
that the chirality can be transferred into more than one
dimension.
To confirm the above simulations, we studied the majority-
rules principle for the (S)-5:(R)-5 system as a function of
temperature. At room temperature already a rather low MMP
of 1.0 kJ mol-1 was determined for this mixture of enantiomers.
Raising the temperature in this system should further decrease
the MMP but not necessarily enhance the majority-rules effect.
Indeed, performing these majority-rules experiments at elevated
temperatures (303 and 313 K) hardly improved the majority-
rules effect (Figure 4C), suggesting that the optimum of the
majority-rules principle was reached. Modeling did reveal that
the MMP decreased from 0.8 kJ mol-1 at 303 K to 0.7 kJ mol-1
at 313 K.
Conclusion
By systematic variation of the chemical structure of benzene-
1,3,5-tricarboxamide derivatives, the effect of chemical structure
on the amplification of chirality was studied and quantified. For
all benzene-1,3,5-tricarboxamide derivatives a high, constant
helix reversal penalty was determined, which is related to the
intermolecular hydrogen bonds that are present in all studied
derivatives. For asymmetrically substituted benzene-1,3,5-
tricarboxamide derivatives an odd-even effect was found in
the degree of chiral amplification when changing the position
of the stereogenic center with respect to the amide functionality.
More interestingly, it was found that the mismatch penalty is
directly related to the number of stereocenters present in the
molecules. Increasing this number from one to three resulted
in an increase in this energy penalty while leaving the HRP
unaffected. Further evidence that the MMP is directly related
to the number of stereocenters was obtained from mixed
majority-rules experiments where two benzene-1,3,5-tricarbox-
amide derivatives with different numbers of stereocenters with
opposite stereoconfiguration were used in a majority-rules
experiment.
These results show that, in order to amplify a small ee (e.g.,
as small as 5% excess) to a homochiral state, simply reducing
the MMP is not sufficient. Such amplification is only possible
if also the HRP is raised. The reason is that the optimal MMP
depends on the HRP: a higher HRP will lead to a lower optimal
MMP and a lower ee, for which a homochiral system can still
be reached. For example, if the HRP is raised to 22 kJ mol-1
,
a net helicity of 1 can be reached already at ∼4% ee, which
49
requires a MMP of 0.10 kJ mol-1
.
Since the HRP is related to the strength of the intermolecular
hydrogen bonds present in the stack, we are currently investigat-
ing how we could vary the strength of these hydrogen bonds,
thereby also changing the HRP. For example, we are currently
investigating chiral amplification phenomena in amide-func-
tionalized porphyrin derivatives, which will form four inter-
molecular hydrogen bonds per supramolecular bond. Another
approach we have investigated is to reverse the amide group
with respect to the benzene core, i.e., synthesis of N-centered
BTAs.54
Finally, the ultimate limits of chiral amplification were
investigated, revealing that, given a certain HRP, there is an
optimum to which the MMP can be reduced while also
enhancing the degree of chiral amplification. Majority-rules
experiments could indeed verify these simulations. These
findings show the relevance of both energy penalties when trying
to enhance the degree of chiral amplification for the majority-
rules principle in a one-dimensional helical supramolecular
polymer.
Acknowledgment. Siamak Shazad is acknowledged for help
during the synthesis. We thank Prof. Jim Feast for scientific
discussions. The authors thank the National Research School
Combination Catalysis (NRSC-Catalysis) and the NWO for funding.
However, a high HRP implies a high amplification length,
which is the distance between two helix reversals, of ∼104
molecules.43 Reaching such lengths in a one-dimensional
supramolecular polymer is not trivial and would require a high
degree of cooperativity in the supramolecular polymerization
mechanism. Alternatively, to attain such amplification lengths,
Supporting Information Available: Experimental conditions,
synthetic procedures, details about the amplification model,
modeling procedures, and supporting figures and tables. This
material is available free of charge via the Internet at http://
pubs.acs.org.
(54) Stals, P. J. M.; Everts, J. C.; de Bruijn, R.; Filot, I. A. W.; Smulders,
M. M. J.; Mart´ın-Rapu´n, R.; Pidko, E. A.; de Greef, T. F. A.; Palmans,
A. R. A.; Meijer, E. W. Chem. Eur. J. 2009, in press.
JA9080875
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