How flexible are poly(paraphenyleneethynylene)s?

Article abstract of DOI:10.1002/anie.200602807

Magnetic ends: By measuring the distribution of distances between two spin labels it is possible to quantify the flexibility of shape-persistent molecules (see picture). It is found that even the flexibility of short oligomers is described well by the wor

Full text of DOI:10.1002/anie.200602807

Communications
Molecular Dynamics
DOI: 10.1002/anie.200602807
How Flexible Are Poly(para-
phenyleneethynylene)s?**
Adelheid Godt, Miriam Schulte, Herbert Zimmermann,
and Gunnar Jeschke*
Molecules are often seen as geometrically well-defined
building blocks for nanosized objects. Prominent examples
are oligo(para-phenyleneethynylene)s (oligoPPEs),which
are viewed as molecular rods despite their distinct flexibility.[1]
Quantitative knowledge about intrinsic flexibility is required
for designing functional nanostructures as well as for under-
standing the mechanical and dynamic properties of molecules.
This knowledge can,in principle,be gained from the end-to-
end-distance distribution.[2] Information about distance dis-
[*] Prof. Dr. G. Jeschke[+]
Max-Planck-Institut für Polymerforschung
Postfach 3148, 55131 Mainz (Germany)
Fax: ( +49)6131-379-100
E-mail: gunnar.jeschke@uni-konstanz.de
Prof. Dr. A. Godt, M. Schulte
Universität Bielefeld, Fakultät für Chemie
Universitätsstrasse 25, 33615 Bielefeld (Germany)
Dr. H. Zimmermann
Max-Planck-Institut für medizinische Forschung
Jahnstrasse 29, 69120 Heidelberg (Germany)
[+] Current address:
Universität Konstanz, Fachbereich Chemie
Universitätsstrasse 10, 78457 Konstanz (Germany)
[**] This work was supported by the Deutsche Forschungsgemeinschaft.
The authors thank M. K. Bowman for an insightful discussion on
orientation selection and C. Bauer for technical assistance.
Supporting information for this article is available on the WWW
under http://www.angewandte.org or from the author.
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tributions in the nanometer range has recently become
accessible by techniques that measure the dipole–dipole
interaction between two spin labels.[3] Such measurements can
be performed with high precision by pulsed electron–electron
double resonance (ELDOR) methods.[4] Recently,this tech-
nique was used to characterize the flexibility of bispeptide
nanostructures on the basis of the standard deviation of the
label-to-label distance distribution.[5] Quantification in terms
of a reliable persistence length does,however,require
elimination of the contribution of the labels to the distance
distribution. Herein we show that such an elimination is
Pulsed electron paramagnetic resonance (EPR) techni-
ques[9] are well suited for characterizing structures of 2–8 nm
in length.[4,10] At these distances backbone flexibility strongly
influences the shape of P(rEE) for persistence lengths of the
order of 15 nm. Such a persistence length is expected for
polyPPEs on the basis of an earlier extensive light-scattering
study.[7] The principal limitation of EPR techniques is their
requirement for spin labeling,so that the label-to-label-
distance distribution P(rLL) rather than P(rEE) is measured
(Scheme 1). The contribution of the labels to P(rLL) can be
eliminated and thus P(rEE) obtained by synthesizing[11] and
measuring a series of compounds with the same labeling
pattern and backbone structure but different backbone
length.
possible and that the end-to-end distance distribution P(rEE
)
of oligoPPE backbones can be obtained from pulsed ELDOR
data to provide an estimate of the persistence length of
polyPPEs.
Elimination of the label contribution requires a model for
the distribution of conformations of both the label and the
We concentrate on oligomers because their comparatively
small size allows their step-by-step synthesis and therefore a
better control of the molecular structure than is possible for
polymers. Side products that result from oxidative alkyne
dimerization and carbometalation during the Sonogashira–
Hagihara coupling,the key reaction for the synthesis of these
oligomers and polymers,can be separated from the product. [6]
Additionally,the limited purity of the monomers speaks in
favor of oligomers: If one assumes that the monomers 1,4-
diiodobenzene and 1,4-diethynylbenzene are contaminated
with only 0.1% of the constitutional 1,3-isomers, nearly all
chains of a polymer batch with a polymerization degree of
1000 contain one meta linkage. This polymerization degree is
typical for samples used in light-scattering experiments,[7]
which is the standard technique for determining the persis-
tence length. Meta linkages will reduce the radius of gyration
and hence the apparent persistence length.[8] In contrast,only
one out of 100 molecules has this defect in the case of a
decamer.
backbone. It is necessary to model the backbone,as P(rEE
)
can only be obtained from P(rLL) when the distribution of the
relative orientations of the backbone ends is also known. We
model the backbone as a sequence of jointed stiff segments.
As segments we define the phenylene ring,the bond between
a phenylene and an ethynylene unit,the triple bond,and the
bond between two ethynylene units. The relative segment
lengths rj are taken from the MMFF force field.[12] The angle
qj at the joint between two segments (Figure 1) is determined
by a harmonic bending potential. The bending potential for
joints at a phenylene segment is half as large as that for all
other joints within the backbone. All torsion angles fj are
equally likely; that is,the chain rotates freely at its joints,
which agrees well with our molecular dynamics (MD)
simulations of oligoPPEs. A general stretch factor s for the
segment length and the bending potential FB for the non-
phenylene joints are the two fit parameters of the backbone
model. The labels are modeled as additional stiff segments of
Scheme 1. Structures of the biradicals used and definition of the label-to-label distance rLL and backbone end-to-end distance rEE.
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in dipolar spectra and caused a systematic deviation of the
experimental time-domain data from fits during the first
dipolar oscillation. Such a systematic deviation might com-
promise the fitting of the conformational model,in particular
for the longer oligomers 4 and 5,for which only few
oscillations can be observed. We therefore introduce orienta-
tion averaging by varying the magnetic field so that the
observer position is swept between the low-field maximum of
the nitroxide spectrum and the global maximum in 23 steps of
0.1 mT. The difference between pump and observer frequency
is kept constant at 65 MHz. This procedure virtually elimi-
nates orientation selection and systematic deviations of the fit
(Figure 3).
Figure 1. Coarse-grained model for the conformation of the PPE back-
bone consisting of consecutive segments j and j+1 with lengths rj and
j+1. The segment j+1 rotates freely about the dotted axis. For angle
qj, a normal distribution with a mean value of zero is assumed. The
same model is used for the end labels.
r
length l jointed to the first and last phenylene unit of the
backbone with an effective bending potential B. The distri-
bution of label conformations is thus accounted for by two
additional fit parameters l and B.
To test whether this model properly separates the label
and backbone contribution to P(rLL),we applied it to results
of MD simulations for 2–4 that were obtained with the PCFF
force field. The P(rLL) and the true P(rEE) were extracted
from the MD trajectories. The model was fitted to the P(rLL
of the three compounds simultaneously. Fit parameters are
given in Table 1,and the apparent P(rEE) for the ensemble of
)
Figure 3. Improved orientation averaging in dipolar spectra obtained
by the four-pulse DEER experiment on 2 (a,b) and 5 (c,d). Black dots
correspond to experimental data and gray solid lines to simulations
for which an ideal powder average is assumed. a,c) Fixed observer and
pump positions. Arrows mark deviations due to the suppression of
orientations along the spin–spin vector. b,d) Orientation averaging.
Table 1: Best-fit values of the stretch factor s, backbone bending
potential FB, label length l, and effective label bending potential B in
the conformational model for oligoPPEs.
Fitted data
s
FB [kBT]
l [nm]
B [kBT]
To obtain the end-to-end distance distributions P(rEE
from the orientation-averaged DEER data,we simulta-
)
MD
DEER
0.993
0.991
38.4
20.0
0.650
0.646
2.023
2.019
neously fitted the conformational model to the experimental
form factors F(t) of all five compounds. The F(t) values were
obtained from the primary experimental data by correcting
for the intermolecular background. In our approach the label-
to-label distance distributions P(rLL) computed with the
conformational model are converted into simulated form
factors by straightforward matrix multiplication. The other
possible approach of converting the experimental F(t) values
into distance distributions P(rLL) would require the solution
of an ill-posed inverse problem and thus compromise the
reliability of the fit.[3]
modeled conformations is compared to the true P(rEE) in
Figure 2 for each compound. The good agreement justifies
the use of the same model for extracting P(rEE) from pulsed
ELDOR data.
In earlier four-pulse double electron–electron resonance
(DEER) measurements on compounds 1 and 3[3a,4d] we
noticed that effects of orientation selection[13] were apparent
Our conformational model with four variable parameters
fits the experimental form factors of all five compounds quite
closely (Figure 4). Furthermore,the label length l and
Figure 2. End-to-end distance distributions P(rEE) from MD simulations
of compounds 2–4. Black dots correspond to the true P(rEE) extracted
directly from the MD trajectories and gray solid lines to the apparent
P(rEE) obtained by model-based elimination of the label contribution
from the label-to-label distance distribution P(rLL).
Figure 4. Global fit of the conformational model for oligoPPEs to
experimental form factors F(t). Black dots represent experimental data,
gray solid lines simulations corresponding to the parameters in
Table 1.
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effective label bending potential B agree nicely with the
results for the MD data (Table 1),which suggests that an MD
simulation in vacuo describes the conformational distribution
of the nitroxide end labels quite well. Likewise,good agree-
ment between the MD and DEER data was found for the
stretch factor s for the contour length of the backbone. The
stretch factor s is close to the ideal value of unity.
In contrast,the bending potential FB of the backbone
joints is smaller for the DEER than for the MD data by
almost a factor of two (Table 1). This deviation by far exceeds
experimental error. We therefore conclude that the backbone
of oligoPPEs is significantly more flexible than suggested by
our MD simulations (Figure 2). This greater flexibility is in
line with calculation-based predictions for related semiflex-
ible polymers.[14]
lengths of between 13.5 and 16 nm.[7] The difference between
the two sets of results may be partially due to the different
[15]
side groups.
It may also hint at the presence of constitu-
tional defects,such as meta linkages. For validation,samples
of polyPPEs of different origin formed by different synthetic
routes[16] need to be investigated.
In summary,we have introduced a new approach for the
experimental characterization of the flexibility of shape-
persistent molecules. This approach is based on the synthesis
of a series of oligomers,spin labeling,the measurement of
spin-to-spin distance distributions,and the extraction of the
end-to-end distance distribution of the backbone by modeling
the conformational ensemble. As information on the residual
flexibility of shape-persistent molecules is a key requirement
for the rational design of well-defined nanostructures,this
approach should find applications well beyond the determi-
nation of the persistence length of semiflexible polymers.
The experimental P(rEE) results for all compounds are
shown in Figure 5 together with a global fit by the Kratky–
Porod wormlike-chain (WLC) model; an analytical expres-
sion[2] for P(rEE) has been used. Within the limits of
experimental precision our data agree with this model. The Experimental Section
Synthesis: Compounds 1–3 were synthesized as described previ-
best-fit persistence length is 17.5 nm.
ously.[11] Compounds 4 and 5 were synthesized analogously. Synthetic
procedures and analytical data are given in the Supporting Informa-
tion.
DEER measurements: Glassy frozen solutions of biradical (1, 2:
1.5 mmolLÀ1; 3, 4, 5: 0.4 mmolLÀ1) in perdeuterated o-terphenyl
were analyzed by a variable-time four-pulse DEER experiment on a
Bruker E580 spectrometer at a temperature of 50 K.[4b,c,d] Details are
given in the Supporting Information.
Modeling: Molecular-dynamics simulations were run for a total
time of 2 ns with the program package Cerius2 (v.3.8,Molecular
Simulations,Inc.) by using the PCFF force field and a NosØ–Hoover
thermostat to generate a canonical ensemble. Distance distributions
P(rLL) and P(rEE) within our conformational model were computed by
Monte Carlo simulations by using a home-written Matlab (The
MathWorks,Inc.,Natick,MA,USA) program. Details are given in
the Supporting Information.
Figure 5. End-to-end distance distributions P(rEE) for oligoPPE back-
bones. Black dots correspond to P(rEE) extracted from DEER data, and
gray solid lines show a global fit by the WLC model.
Received: July 14,2006
Published online: October 18,2006
Keywords: chain model · EPR spectroscopy · polymers ·
.
shape persistence · spin labeling
If we fit the WLC model to the individual P(rEE) of the
five compounds,we find persistence lengths of 14.3,16.9,18.2,
19.2,and 19.1 nm for 1, 2, 3, 4,and 5,respectively. This trend is
probably due to the fact that our conformational model,
unlike the WLC model,allows for some variation in the
contour length by bond-stretching vibrations. The longer the
oligomer,the more backbone flexibility dominates the
broadening of the distance distribution,so that the data for
4 and 5 are more reliable. Apparently,the persistence length
approaches an asymptotic limit of about 19 nm for theses two
oligomers. From the contour lengths obtained by the WLC fits
we find that one para-phenyleneethynylene repeat unit
increases the contour length by 0.688 nm.
Although the investigation is restricted to oligomers with
a length of up to 8 nm,it provides the persistence length of
polyPPE,because the persistence length is a property that
depends only on the structure of the repeating units and not
on the length of the molecule. Light-scattering experiments
on polydisperse polyPPEs gave distinctly shorter persistence
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