Flexibility of shape-persistent molecular building blocks composed of p-phenylene and ethynylene units

Article abstract of DOI:10.1021/ja102983b

Ethynylene and ρ-phenylene are frequently employed constitutional units in constructing the backbone of nanoscopic molecules with specific shape and mechanical or electronic function. How well these properties are defined depends on the flexibility of the backbone, which can be characterized via the end-to-end distance distribution. This distribution is accessible by pulse electron paramagnetic resonance (EPR) distance measurements between spin labels that are attached at the backbone. Four sets of oligomers with different sequences of ρ-phenylene and ethynylene units and different spin labels were prepared using polar tagging as a tool for simple isolation of the targeted compounds. By variation of backbone length, of the sequence of ρ-phenylene and ethynylene units, and of the spin labels a consistent coarse-grained model for backbone flexibility of oligo(ρ-phenyleneethynylene)s and oligo(ρ-phenylenebutadiynylene)s is obtained. The relation of this harmonic segmented chain model to the worm-like chain model for shape-persistent polymers and to atomistic molecular dynamics simulations is discussed. Oligo(ρ-phenylene butadiynylene)s are found to be more flexible than oligo(ρ-phenyleneethynylene)s, but only slightly so. The end-to-end distance distribution measured in a glassy state of the solvent at a temperature of 50 K is found to depend on the glass transition temperature of the solvent. In the range between 91 and 373 K this dependence is in quantitative agreement with expectations for flexibility due to harmonic bending. For the persistence lengths at 298 K our data predict values of (13.8 ± 1.5) nm for poly(ρ-phenyleneethynylene)s and of (11.8 ± 1.5) nm for poly(ρ-phenylenebutadiynylene)s.

Full text of DOI:10.1021/ja102983b

Published on Web 06/30/2010
Flexibility of Shape-Persistent Molecular Building Blocks
Composed of p-Phenylene and Ethynylene Units
Gunnar Jeschke,*,† Muhammad Sajid,‡ Miriam Schulte,‡ Navid Ramezanian,‡
Aleksei Volkov,§,¶ Herbert Zimmermann,⊥ and Adelheid Godt*,‡
Laboratory for Physical Chemistry, ETH Zu¨rich, 8093 Zu¨rich, Switzerland, Department of
Chemistry, Bielefeld UniVersity, UniVersita¨tsstrasse 25, D-33615 Bielefeld, Germany,
Max Planck Institute for Polymer Research, Postfach 3148, 55021 Mainz, Germany, and
Max Planck Institute for Medical Research, Jahnstrasse 29, 69120 Heidelberg, Germany
Received April 9, 2010; E-mail: godt@uni-bielefeld.de; gunnar.jeschke@phys.chem.ethz.ch
Abstract: Ethynylene and p-phenylene are frequently employed constitutional units in constructing the
backbone of nanoscopic molecules with specific shape and mechanical or electronic function. How well
these properties are defined depends on the flexibility of the backbone, which can be characterized via the
end-to-end distance distribution. This distribution is accessible by pulse electron paramagnetic resonance
(EPR) distance measurements between spin labels that are attached at the backbone. Four sets of oligomers
with different sequences of p-phenylene and ethynylene units and different spin labels were prepared using
polar tagging as a tool for simple isolation of the targeted compounds. By variation of backbone length, of
the sequence of p-phenylene and ethynylene units, and of the spin labels a consistent coarse-grained
model for backbone flexibility of oligo(p-phenyleneethynylene)s and oligo(p-phenylenebutadiynylene)s is
obtained. The relation of this harmonic segmented chain model to the worm-like chain model for shape-
persistent polymers and to atomistic molecular dynamics simulations is discussed. Oligo(p-phenylene
butadiynylene)s are found to be more flexible than oligo(p-phenyleneethynylene)s, but only slightly so.
The end-to-end distance distribution measured in a glassy state of the solvent at a temperature of 50 K is
found to depend on the glass transition temperature of the solvent. In the range between 91 and 373 K
this dependence is in quantitative agreement with expectations for flexibility due to harmonic bending. For
the persistence lengths at 298 K our data predict values of (13.8 ( 1.5) nm for poly(p-phenyleneethynylene)s
and of (11.8 ( 1.5) nm for poly(p-phenylenebutadiynylene)s.
assembly,10 for constructing shape-persistent macrocycles,11-13
and as active or passive spacers between electronically interact-
Introduction
Poly(p-phenyleneethynylene)s (polyPPEs) and related com-
pounds are shape-persistent polymers with applications in
sensing and as organic conductors.1-7 Due to their good
synthetic accessibility oligomeric molecular building blocks of this
type are a popular choice as parts of potential nanomachines,8,9
for shape control of nanostructures in DNA-programmed self-
ing moieties.14-19 In such applications flexibility of the mo-
lecular backbone is an important issue,20-23 but few experi-
mental information appears to be available for this class of
(10) Gothelf, K. V.; Brown, R. S. Chem.sEur. J. 2005, 11, 1062–1069.
(11) Ho¨ger, S. High-Yield Synthesis of Shape-Persistent Phenylene-
Ethynylene Macrocycles. In Functional Organic Materials: Synthesis,
Strategies and Applications; Mu¨ller, T. J. J., Bunz, U. H. F., Eds.;
Wiley-VCH: Weinheim, 2007; pp 225-260.
† ETH Zu¨rich.
‡ Bielefeld University.
§ Max Planck Institute for Polymer Research.
(12) Weber, J.; Leppert, A.; Enkelmann, V.; Ho¨ger, S. Beilstein J. Org.
Chem. 2008, 4, 1–15.
⊥ Max Planck Institute for Medical Research.
¶ Current address: BASF SE, 67063 Ludwigshafen, Germany.
(1) Weder, C., Ed. Poly(arylene ethynylene)s: From Synthesis to Applica-
tion; Advances in Polymer Science, Vol. 177; Springer: Berlin,
Heidelberg, New York, 2005.
(13) Moore, J. S.; Zhang, J. Angew. Chem., Int. Ed. Engl. 1992, 31, 922–
924.
(14) Lu, Q.; Liu, K.; Zhang, H.; Du, Z.; Wang, X.; Wang, F. ACS Nano
2009, 3, 3861–3868.
(2) Bunz, U. H. F. Chem. ReV. 2000, 100, 1605–1644.
(3) Becker, K.; Lagoudakis, P. G.; Gaefke, G.; Ho¨ger, S.; Lupton, J. M.
Angew. Chem., Int. Ed. 2007, 46, 3450–3455.
(15) Albinsson, B.; Mårtensson, J. J. Photochem. Photobiol., C 2008, 9,
138–155.
(16) Rochford, J.; Galoppini, E. Langmuir 2008, 24, 5366–5374.
(17) Azov, V. A.; Schlegel, A.; Diederich, F. Angew. Chem., Int. Ed. 2005,
44, 4635–4638.
(4) Kim, I.-B.; Han, M. H.; Phillips, R. L.; Samanta, B.; Rotello, V. M.;
Zhang, Z. J.; Bunz, U. H. F. Chem.sEur. J. 2009, 15, 449–456.
(5) Thomas III, S. W.; Joly, G. D.; Swager, T. M. Chem. ReV. 2007, 107,
1339–1386.
(18) Guliyev, R.; Coskun, A.; Akkaya, E. U. J. Am. Chem. Soc. 2009, 131,
9007–9013.
(6) Kumaraswamy, S.; Bergstedt, T.; Shi, X.; Rininsland, F.; Kushon, S.;
Xia, W.; Ley, K.; Achyuthan, K.; McBranch, D.; Whitten, D. Proc.
Natl. Acad. Sci. U.S.A. 2004, 101, 7511–7515.
(19) Weiss, E. A.; Ahrens, M. J.; Sinks, L. E.; Gusev, A. V.; Ratner, M. A.;
Wasielewski, M. R. J. Am. Chem. Soc. 2004, 126, 5577–5584.
(20) Ballauff, M. Angew. Chem., Int. Ed. Engl. 1989, 28, 253–267.
(21) Bothner-By, A. A.; Dadok, J.; Johnson, T. E.; Lindsey, J. S. J. Phys.
Chem. 1996, 100, 17551–17557.
(7) James, D. K.; Tour, J. M. Top. Curr. Chem. 2005, 257, 33–62.
(8) Browne, W. R.; Feringa, B. L. Nat. Nanotechnol. 2006, 1, 25–35.
(9) Shirai, Y.; Osgood, A. J.; Zhao, Y.; Kelly, K. F.; Tour, J. M. Nano
Lett. 2005, 5, 2330–2334.
(22) Go¨ller, A.; Klemm, E.; Egbe, D. A. M. Int. J. Quantum Chem. 2001,
84, 86–98.
9
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J. AM. CHEM. SOC. 2010, 132, 10107–10117 10107

A R T I C L E S
Jeschke et al.
Chart 1. Structures of OligoPPE/Bs I, OligoPPEs II, OligoPPEs III,
and OligoPPBs IVa
polymers. To the best of our knowledge no data have been
published on temperature dependence of this flexibility and on
the variation of flexibility with the sequence of ethynylene and
phenylene repeating units. In designing molecular nanome-
chanical devices the type of bending potential and possible
effects of thermal bending have to be considered.
The flexibility of shape-persistent oligomers and polymers
can be elucidated from the end-to-end distance distribution.24
Distances on the relevant length scale of a few nanometers can
be measured between spin labels by pulse electron paramagnetic
resonance (EPR) techniques25-27 and distance distributions can
be extracted from such data.28-30 Recently we have demon-
strated that by varying the length of the oligomer backbone,
the contributions of the backbone and of spin labels attached
to the chain ends can be separated.31 This approach relies on
coarse-grained modeling of the backbone by rigid segments
linked by freely rotating joints with harmonic bending potentials.
By refitting the backbone end-to-end distance distributions by
the worm-like chain (WLC) model,24,32,33 flexibility could be
characterized by a single parameter, the persistence length Lp
of the chain. Alternative EPR-based approaches for character-
izing flexibility of oligoPPEs34 and bis-peptides35 were sug-
gested at about the same time and the latter approach was
recently extended to a coarse-grained model for bis-peptides.36,37
The WLC model approach was recently applied to porphyrin-
based molecular wires and a dependence of the mean end-to-
end distance and width of the distance distribution on glass
transition temperature of the solvent was found.38
Several important questions remained open in our first study.
First, the quality of separation of the backbone and label
contributions with the harmonic segmented chain (HSC) model
was tested only in silico on data from a molecular dynamics
(MD) simulation, but not experimentally. Indeed, when refitting
the data for the individual backbone lengths of oligoPPE/Bs I
(Chart 1) with the WLC model we found a trend in the
persistence length whose origin and extent was not fully
explained. Second, the backbones contained one butadiynylene
a Alk stands for hexyl as well as 6-methoxyhexyl substituents. For the
sake of simplicity no differentiation between these two side chains is made
here. The concrete structural formulae are given in Schemes 1-3.
unit, which may have a flexibility different from the one of
ethynylene units. This structural imperfection may or may not
have contributed to the trend in persistence length. Third, our
measurements are performed at a cryogenic temperature of 50
K. As spontaneous chain bending is a consequence of thermal
excitation, the persistence length needs to be specified together
with a temperature.38 To use our data for predictions of the
behavior of nanomechanical devices on application of mechan-
ical forces, the temperature corresponding to the measured end-
to-end distance distribution and temperature dependence of the
persistence length have to be known. This dependence is related
to the shape of the bending potential.39
In the present work, we address all these questions. In the
Theoretical Calculations section we clarify the relation of the
HSC model to the WLC model. Furthermore, we identify
regimes where flexibility can or cannot be characterized by a
persistence length. By synthesizing two series of oligo(p-
phenyleneethynylene)s, oligoPPEs II and oligoPPEs III (Chart
1), with the same backbone structure but different spin labels,
we are now able to verify experimentally the separation of the
spin label from the backbone contribution. By comparing the
series of oligo(p-phenylenebutadiynylene)s (oligoPPBs) IV to
the series of oligoPPEs II with the same spin label, we can
quantify differences between the flexibility of these two
backbone types. By varying the glass transition temperature of
the solvent over a wide range, we can test the hypothesis that
the end-to-end distance distribution corresponds to the ensemble
of chain structures frozen at the glass transition and the
hypothesis that flexibility conforms to a harmonic bending
potential. The paper concludes with considerations on further
applications and tests of the HSC model.
(23) Allen, B. D.; Benniston, A. C.; Harriman, A.; Mallon, L. J.; Pariani,
C. Phys. Chem. Chem. Phys. 2006, 8, 4112–4118.
(24) Wilhelm, J.; Frey, E. Phys. ReV. Lett. 1996, 77, 2581–2584.
(25) Milov, A. D.; Salikhov, K. M.; Shirov, M. D. Fiz. TVerd. Tela
(Leningrad) 1981, 23, 975–982. SoV. Phys. Solid State 1981, 565-
569.
(26) Saxena, S.; Freed, J. H. Chem. Phys. Lett. 1996, 251, 102–110.
(27) Pannier, M.; Veit, S.; Godt, A.; Jeschke, G.; Spiess, H. W. J. Magn.
Reson. 2000, 142, 331–340.
(28) Jeschke, G.; Koch, A.; Jonas, U.; Godt, A. J. Magn. Reson. 2002,
155, 72–82.
(29) Jeschke, G.; Panek, G.; Godt, A.; Bender, A.; Paulsen, H. Appl. Magn.
Reson. 2004, 26, 223–244.
(30) Chiang, Y. W.; Borbat, P. P.; Freed, J. H. J. Magn. Reson. 2005, 172,
279–295.
(31) Godt, A.; Schulte, M.; Zimmermann, H.; Jeschke, G. Angew. Chem.,
Int. Ed. 2006, 45, 7560–7564.
(32) Kratky, O.; Porod, G. Recl. TraV. Chim. Pays-Bas 1949, 68, 1106–
1122.
(33) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University
Press: Oxford, 2003.
(34) Margraf, D.; Bode, B. E.; Marko, A.; Schiemann, O.; Prisner, T. F.
Mol. Phys. 2007, 105, 2153–2160.
(35) Pornsuwan, S.; Bird, G.; Schafmeister, C. E.; Saxena, S. J. Am. Chem.
Soc. 2006, 128, 3876–3877.
Syntheses of Spin-Labeled OligoPPEs and OligoPPBs
(36) Pornsuwan, S.; Schafmeister, C. E.; Saxena, S. J. Phys. Chem. C 2008,
112, 1377–1384.
Polar tagging is the common theme in the syntheses of the
spin labeled oligomers, oligoPPEs II and III and oligoPPBs
IV. The distinct influence of polar groups on the chromato-
(37) Bird, G. H.; Pornsuwan, S.; Saxena, S.; Schafmeister, C. E. ACS Nano
2008, 2, 1857–1864.
(38) Lovett, J. E.; Hoffmann, M.; Cnossen, A.; Shutter, A. T. J.; Hogben,
H. J.; Warren, J. E.; Pascu, S. I.; Kay, C. W. M.; Timmel, C. R.;
Anderson, H. L. J. Am. Chem. Soc. 2009, 131, 13852–13859.
(39) Wilcoxon, J.; Schurr, J. M. Biopolymers 1983, 22, 2273–2321.
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A R T I C L E S
Scheme 1. Syntheses of Spin-Labeled OligoPPEs 3cn and 5cn, alias OligoPPEs II, and Structural Formulae of Glaser Coupling Products 6n
graphic behavior helped to isolate pure monodisperse oligomers
and to keep the number of synthetic steps low. During the
assembly of oligoPPEs II (Scheme 1) ether linkages in the side
chains were used to make the alkynyl-aryl cross-coupling
product very easily separable from the accompanying Glaser
coupling (oxidative alkyne dimerization) product.40 Ether link-
ages were also the key to obtain pure diiodotolane 2c and were
helpful in the isolation of oligoPPEs III (Scheme 2). The polar
groups tetrahydropyran-2-yloxy (THPO), ether linkage, and
hydroxymethyl were of great advantage for a straightforward
access to the oligoPPBs IV (Scheme 3).
The symmetry of the oligoPPEs II and III with an uneven
number of PPE units suggests to connect alkynes 1n or 7n via
a 1,4-phenylene (Schemes 1 and 2). These alkynes are roughly
half as long as the final oligoPPEs and bring along the required
terminal functional groups, a protected OH group41 or an
isoindolineimide moiety. Deprotection of the hydroxyl group
of the cross-coupling products obtained with alkyne 1n followed
by esterification with 1-oxyl-2,2,5,5-tetramethylpyrroline-3-
carboxylic acid will give oligoPPEs II. Oxidation of the cross-
coupling products from alkyne 7n will yield oligoPPEs III. The
pitfall of this approach is the Glaser coupling which is a regular
companion of the alkynyl-aryl coupling.42 Alkyne dimer will
form from leftover alkyne upon exposure to air during workup.
Traces of alkyne dimer may already be present before workup
due to the use of a Pd(II) salt and the presence of oxygen in the
reaction flask (despite careful degassing through freeze-pump-
thaw cycles). The cross-coupling product and the Glaser
coupling product differ only in one phenylene unit. On the basis
of our finding that the polar end groups dominate the chro-
matographic behavior on silica gel and the number of 2,6-
dihexyl-1,4-phenylene units displays only a marginal influence,43
we expect the separation of the two products on a preparative
scale to be insurmountable if nonpolar diiodobenzene 2b is used
as the connector. Therefore, we opted for polar tagging of the
cross-coupling product with ether moieties in two of the side
chains through the use of polar diiodobenzene 2a as the
connector.40 Purposefully the ether moieties are separated from
the phenylene moiety by a long alkyl spacer in order to avoid
any electronic and/or steric influence on the backbone of the
final oligomers. As expected, the Glaser coupling products 6n
were eluted well ahead of the cross-coupling products 3an from
a silica gel column. This is demonstrated with the following Rf
values (n-pentane/CH2Cl2 1/1): Rf(3a1) ) 0.14, Rf(61) ) 0.83,
Rf(3a2) ) 0.53, Rf(62) ) 0.75. In the case of the bis(isoindo-
lineimide)s 8an the ether moieties turned out to be insufficient
for separating the cross-coupling products 8an from the Glaser
coupling products 10an through standard column chromatog-
raphy. To make the bis(isoindolineimide)s move on silica gel,
ethanol had to be added to EtOAc or CH2Cl2 or CHCl3. Under
these elution conditions two more or less ether moieties seem
to be insignificant if not detrimental, as is suggested by the
finding that the cross-coupling products 8an are eluted shortly
ahead of the Glaser coupling product 10an from a silica gel
HPLC column (CHCl3 with 5-10 vol % of MeOH). Neverthe-
(40) Sahoo, D.; Thiele, S.; Schulte, M.; Ramezanian, N.; Godt, A. Beilstein
J. Org. Chem. 2010, 6; DOI: 10.3762/bjoc.6.57.
(41) The phenolic group does not interfere with the alkynyl-aryl cross-
coupling, i.e. the tetrahydropyran-2-yl group is not necessary as a
protection group. It is used because it eases the isolation of the products
via chromatography.
(42) Carbometalation product is another byproduct which occured oc-
casionally and only in traces. Its chromatographic behavior is similar
to that of the corresponding Glaser coupling product. For further
information see the Supporting Information.
(43) The oligomer that has the same structure as 5a0 [however, with hexyl
instead of methoxyhexyl as the side chains (Rf ) 0.73)] and the dimer
62 [(Rf ) 0.79)] differ in two PPE units. The oligomer that has the
same structure as 5a1 [however, with hexyl instead of methoxyhexyl
as the side chains (Rf ) 0.63)] and the dimer 63 [(Rf ) 0.73)] differ
in three PPE units. Despite these structural differences, the Rf values
(silica gel; n-pentane/CH2Cl2, 1:1) are very similar.
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Scheme 2. Syntheses of Bis(N-oxylisoindolineimide)s 8bn and 9bn, alias OligoPPEs III, and Structural Formulae of Glaser Coupling Products
10n
less, the isolation of bis(isoindolineimide) 8a1 through HPLC
was successful. The isolation of bis(isoindolineimide) 8a0 via
HPLC was not pursued. Instead, the mixture of bis(isoindo-
lineimide)s 8a0 and 10a0 was treated with m-chloroperbenzoic
acid and bis(N-oxylisoindolineimide) 8b0 was isolated by
standard column chromatography.44
graphically easily removable. As had been found for the
bis(isoindolineimide)s, 8an, the isolation of the bis(isoindoline-
imide)s, 9an, through standard column chromatography was
unsuccessful despite polar tagging. Therefore, HPLC was
employed to isolate the compounds before they were trans-
formed into the bis(N-oxylisoindolineimide)s 9bn through
oxidation with m-chloroperbenzoic acid. The alternative pro-
cedure, standard column chromatographical separation of the
species at the stage of the bis(N-oxylisoindolineimide)s 9bn and
10bn, which are much less sticky toward silica gel than the
precursors 9an and 10an, was successfully tested on bis(N-
oxylisoindolineimide)s 9b1 and 10b1 [Rf(9b1) ) 0.59; Rf(10b1)
) 0.78; silica gel, CH2Cl2/Et2O 9/1]. As can be seen from the
given Rf-values, reducing the strong adhesion of the terminal
functionalities through conversion of the amines into N-
oxylamines makes the ether moieties in the side chains act again
as the factor that dominates the rate of elution.
The syntheses of oligoPPBs IV (Scheme 3) resembles that
of the oligoPPEs II: first, construction of the backbone with
two terminal THPO groups, then removal of the THP moiety
and attachment of the spin label through esterification with spin
label 1-oxyl-2,2,5,5-tetramethylpyrroline-3-carboxylic acid.
For the syntheses of the backbones of the spin-labeled
oligoPPBs IV, we decided in favor of the Glaser coupling, even
when aiming for unsymmetrically substituted butadiynes. Glaser
coupling of two different alkynes offers a rapid access to such
butadiynes albeit at the expense of yield because half of the
Polar tagging with the ether moiety in the side chain was
also valuable in the syntheses of oligoPPEs II and III with an
even number of PPE units, i.e. of 5cn and 9bn. The precursors
5an of the oligoPPEs 5cn were assembled in two steps (Scheme
1). First, alkynes 1n were coupled with polar diiodobenzene 2a
which was used in a 3-fold amount to minimize dicoupling.
Second, the products 4n were coupled with alkyne 11 to obtain
the oligoPPEs 5an. The bis(isoindolineimide)s 9an, the precur-
sors of the spin labeled oligomers 9bn, were synthesized in the
same manner as the bis(isoindolineimide)s 8an, however with
exchanging the connector diiodobenzene 2a for diiodotolane
2c (Scheme 2). In the preparation of the latter the ether moieties
played a key role: Reaction of alkyne 11 with an excess of
diiodobenzene 2b gives a mixture mainly consisting of di-
iodotolane 2c and residual diiodobenzene 2b. Minor components
are the Glaser coupling product and oligomers with three and
more PPE units. All of these byproducts have more ether
moieties than the target compound 2c and thus are chromato-
(44) Sajid, M.; Jeschke, G.; Wiebcke, M.; Godt, A. Chem.sEur. J. 2009,
15, 12960–12962.
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A R T I C L E S
Scheme 3. Syntheses of Spin-Labeled OligoPPBs 16c2, 21c, and 16c4, alias OligoPPBs IVa-c
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amount of the alkynes is consumed by the dimerization of
identical alkynes (homodimerization). The Cadiot-Chodkiewicz
coupling45,46 may have been less material wasting. However, it
would have required more synthetic steps because 1-bro-
moalkynes are involved. Furthermore, homodimerization is often
a severe side reaction diminishing the advantage of the
Cadiot-Chodkiewicz coupling over that of a random Glaser
coupling. Whereas by accepting the low yields of a Glaser
coupling with two different alkynes, no compromise was made
in terms of time and effort needed for the isolation of the
targeted compounds. By employing polar tagging, a simple
standard column chromatography was sufficient to separate the
three dimers-two homodimers and one heterodimer. The Glaser
coupling was achieved with a mixture of Pd(PPh3)2Cl2 and CuI
in THF and piperidine in air.47 Under these conditions the Glaser
coupling is fast and, except when alkyne 17 is involved (Scheme
3), no byproducts were detected. Therefore, we decided to stay
with this protocol.
Figure 1. Parameters of segmented chain models. The chain consists of n
segments with lengths lj (j ) 1... n) and intersegment angles θj (j ) 1...
n-1). In freely rotating chain models the torsion angles φj are equally
distributed between 0 and 2π.
The synthesis of spin-labeled oligoPPB 16c2 starts with a
Glaser coupling of the alkynes 121 and 10 (Scheme 3). The three
products 131, 142, and 60 were easily separable because they
differ in the number of the THPO groups and show very
different times for elution from a silica gel column.41 Through
desilylation of heterodimer 131 and subsequent Glaser coupling
the backbone construction was finalized.
θ , 1. The local correlations between segment vectors then
decay on the scale of the persistence length Lp,
Lp ) 2l/θ2
(1)
By letting l f 0 and θ f 0 at constant persistence length,
the WLC model describes an unsegmented chain that can bend
continuously and has a contour length cl ) nl. The mean square
end-to-end distance 〈R2〉 of such a chain is given by
Both spin-labeled oligoPPBs 21c and 16c4 originate from the
nonpolar alkyne 121 and the polar alkyne 17. Glaser coupling
of these two alkynes was troublesome. It proceeded slowly and
gave byproducts of unidentified structure. Nevertheless, het-
erodimer 18 was isolated as a pure compound. Removal of the
polar hydroxymethyl group and Glaser coupling of the resulting
nonpolar alkyne 122 with alkyne 10 gave a mixture of dimers
from which the individual dimers were effortlessly isolated due
to their distinctly different solubility and chromatographic
behavior. The heterodimer 132 was desilylated, and the product,
alkyne 152, was oxidatively coupled with alkyne 20 to complete
the backbone assembly. With alkyne 20 ether moieties were
introduced to simply pick the three individual products 16a4,
21a, and 22a according to their number of polar side chains as
demonstrated by the Rf values (silica gel, CH2Cl2): Rf (16a4) )
0.83, Rf (21a) ) 0.45, Rf (22a) ) 0.05. Alkyne 20 was
synthesized following the protocol developed for the preparation
of alkyne 151 (see Supporting Information).
〈R2〉 ) 2clLp[1 - (Lp/cl)(1 - exp(-cl/Lp))]
(2)
In shape-persistent polymers, such as polyPPEs, the real chain
can only bend at the atom positions, but not within the bonds,
which behave as rigid segments. For such a segmented chain,
deviations from the WLC model are expected, unless both the
number n of segments in the chain and the number of segments
within the persistence length, np ) Lp/l, are large.
For polyPPEs, light-scattering experiments49 and our own
previous EPR results31 indicate a persistence length of the order
of 15 nm, corresponding to np ≈ 100. Thus, significant
deviations from the WLC model are expected only for short
oligomers. However, due to the assumption of a fixed inter-
segment angle θ > 0 the WLC model departs from the physical
reality of a linear polymer, for which bond angles θ are
distributed with maximum probability at θ ) 0. The shape of
the distribution of θ is determined by the bending potential F
and its width by the ratio between F and thermal energy kT.
By abstracting from this distribution, the WLC model loses
information on temperature dependence of the persistence
length. This information has to be reintroduced ad hoc.39
To a good approximation, which is usually made in molecular
force fields, the bending potential between two chemical bonds
is a harmonic potential. This leads to a normal distribution of
bond angles θj with variance
Theoretical Calculations
Both the WLC and the HSC model are modifications of the
freely rotating chain model. In the freely rotating chain model
the polymer chain consists of n rigid segments with lengths l
(lj ) l for all j) linked by joints with fixed intersegment angle
θ (θj ) θ for all j in all chains in an ensemble) and a torsion
angle φ that is uniformly distributed between 0 and 2π
corresponding to free rotation at the joints (Figure 1). The WLC
model, which is a simplification of a more general model for
linear chains by Kratky and Porod,32,48 assumes a fixed angle
〈θ2j 〉 ) kT/2Fj
(3)
(45) Cadiot. P.; Chodkiewicz, W. Chemistry of Acetylenes; Viehe, H. G.,
Ed.; Dekker: New York, 1969; pp 597-647.
The HSC model is based on this approximation. In the basic
form of the HSC model, we assume a uniform segment length
l and a uniform bending potential F at all joints. The end-to-
end-distance distribution P(rEE) for n ) 50 computed with the
(46) Further alternative synthetic strategies to oligoPPBs are opened through
recently published work: Mo¨ssinger, D.; Jester, S.-S.; Sigmund, E.;
Mu¨ller, U.; Ho¨ger, S. Macromolecules 2009, 42, 7974–7978. West,
K.; Wang, C.; Batsanov, A. S.; Bryce, M. R. Org. Biomol. Chem.
2008, 6, 1934–1937.
(47) Kukula, H.; Veit, S.; Godt, A. Eur. J. Org. Chem. 1999, 277–286.
(48) Porod, G. Monatsh. Chem. 1949, 80, 251–255.
(49) Cotts, P. M.; Swager, T. M.; Zhou, Q. Macromolecules 1996, 29,
7323–7328.
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10112 J. AM. CHEM. SOC. VOL. 132, NO. 29, 2010

Flexibility of Shape-Persistent Building Blocks
A R T I C L E S
n-1
〈R2〉HSC ) l2 n +
2(n - k)(1 - kT/4F)k
(5)
∑
[
]
k
By substituting the contour length cl ) nl and the persistence
length given by eq 4, the expression can be written with the
same parameters as eq 2,
n-1
〈R2〉HSC ) (c /n)2 n +
2(n - k)(1 - c /nL )k
(6)
∑
l
l
p
[
]
k
For F/kT ) 25, corresponding to 100 segments within the
persistence length, deviations between the 〈R2〉 predicted by eq
2 and 6 are less than 0.2% for cl < 1.5 Lp. These deviations are
much smaller than the experimental error expected for the
extraction of end-to-end distance distributions from DEER data.
Thus, persistence lengths can be determined from 〈R2〉 by
numerically solving eq 2 for Lp. Compared to our previous
approach31 of fitting the distance distribution by approximate
expressions for the WLC model,14 the new approach avoids the
problem of an apparent dependence of persistence length on
contour length.
Results of DEER Experiments and Simulations
OligoPPE/Bs Ia-d (Chart 1) were available from our previous
study.31 The design of new series of model compounds was
based on the following considerations. OligoPPEs II and III
(Chart 1) consist of strictly alternating benzene and ethyne units
and thus allow to exclude the influence of a butadiyne unit on
flexibility. The use of two different spin labels, the conforma-
tionally flexible 1-oxyl-2,2,5,5-tetramethylpyrroline-3-carbonyl-
oxy in oligoPPEs II and the conformationally unambiguous
1,1,3,3-tetramethyl-2-oxylisoindole-5,6-dicarboximide in oli-
goPPEs III, allows to test for stability of the separation of
backbone and label contributions to the end-to-end distance
distribution and to estimate the error in the backbone bending
potential that arises from uncertainties in this separation. In
particular, the conformationally unambiguous spin label44,51 used
in oligoPPEs III leads to a smaller label contribution to the
width of the distance contribution and thus should allow for a
more precise determination of the backbone bending potential.
Finally, compounds IV are composed of strictly alternating
benzene and butadiyne units. With the backbone bending
potential for oligoPPEs already being known from analysis of
series II and III, these compounds allow for determination of
a separate bending potential for the link between two ethyne
units.
Distance distributions were determined from primary DEER
data of all compounds by background correction and subsequent
Tikhonov regularization. As seen for the example of oligoPPEs
III (Figure 3), these distributions exhibit the asymmetric shape
expected for linear shape-persistent molecules with a contour
length shorter than the persistence length24 (compare Figure 2A).
The width of the distributions increases significantly with
increasing backbone length. This proves that our data contain
information on backbone flexibility.
Preliminary data analysis was performed with the version of
the HSC model used previously.31 This model is moderately
coarse-grained by substituting the benzene group by a single
rigid segment. All other segments refer to bonds between two
Figure 2. Comparison of the HSC and WLC model for shape-persistent
polymers. (A) End-to-end distance distributions P(r) as a function of the
ratio between distance r and segment length l. The solid line is a simulation
with the HSC model with bending potential F/kT ) 10 and 50 segments,
while the dotted line is a WLC model fit to this distribution. (B) Dependence
of the normalized apparent persistence length Lp/l on the number of segments
n in WLC model fits (circles) to end-to-end distance distributions obtained
for HSC models with a bending potential F/kT ) 10. The normalized contour
length cl/l equals n. The dashed line shows the estimate 4lF/kT of the
persistence length for large segment numbers.
HSC model is shown in Figure 2A (solid line) together with its
best fit by the WLC model with variable contour length cl and
Lp (dotted line), using the expressions of Wilhelm and Frey.24
The fit reproduces the known contour length cl ) nl. The shape
of the distribution is also almost perfectly reproduced. Similar
quality of agreement is found for contour lengths up to the
persistence length and slightly beyond that (data for other
segment numbers not shown). However, the persistence length
exhibits a dependence on contour length that is not expected
within the WLC model (circles in Figure 2B). This dependence
can be traced back to deviations of the approximate expressions
for P(rEE) within the WLC model24 from the true distance
distribution (Figure S1A, see Supporting Information).
The persistence length Lp,HSC within the HSC model can be
obtained by substituting 〈θj2〉 from eq 3 for θ2 in eq 1,
Lp,HSC ) 4lF/kT
(4)
This estimate is indicated as a dotted line in Figure 2B. The
number of segments within the persistence length is thus given
by 4F/kT. The mean square end-to-end distance for the HSC
model can be derived by an approach due to Eyring50 using eq
3. We find
(51) Jeschke, G.; Sajid, M.; Schulte, M.; Godt, A. Phys. Chem. Chem. Phys.
2009, 11, 6580–6591.
(50) Eyring, H. Phys. ReV. 1932, 39, 746–748.
9
J. AM. CHEM. SOC. VOL. 132, NO. 29, 2010 10113

A R T I C L E S
Jeschke et al.
Figure 3. Experimental label-to-label distance distributions P(r) obtained
from DEER data by Tikhonov regularization for oligoPPEs IIIa (solid line),
IIIb (dashed line), IIIc (dash-dot line), and IIId (dotted line).
atoms. In our previous work we assumed that the bending
potential at the joint between the benzene group and the adjacent
bond is only half as large as the other bending potentials. Now
we tested how this assumption influenced the backbone end-
to-end distance distributions extracted from the data. We found
no significant dependence on the ratio of the bending potentials.
Therefore, the model was simplified by assuming a uniform
bending potential, except for the two joints in the center of the
butadiyne unit that are encountered only in oligoPPE/Bs I and
oligoPPBs IV. The standard deviation of segment lengths lj was
reexamined with longer 10 ns MD runs at 246 and 298 K,
employing the pcff force field and an Andersen thermostat. The
result suggests mean relative standard deviations σl/l ) 0.0132
for a PPE unit and σl/l ) 0.0126 for a PPB unit at the glass
transition temperature of o-terphenyl, 246 K. We assumed a
constant value of 0.013 and checked that minor variations did
not influence the fits. The mean segment lengths of 0.2795 nm
(benzene), 0.1430 nm (benzene-ethyne bond), 0.1201 nm
(ethyne), and 0.1378 nm (ethyne-ethyne bond), originally taken
from structures optimized with the MMFF94 force field,52 were
independently verified by DFT computations (see Supporting
Information). The small deviations between the two sets of
values are also insignificant.
This version of an HSC model with different segment lengths
as well as an HSC model with uniform segment length l and
the same mean relative standard deviations σl/l ) 0.013 of bond
lengths were tested against backbone end-to-end distance
distributions retrieved from 10 ns long MD trajectories computed
for a temperature of 298 K with the pcff force field (Figure 4).
The WLC model was also included in this test. For the HSC
model with uniform segment length l we assumed the mean
segment length of a given backbone. Distributions for oligoPPE
backbones with n ) 1, 2, 3, .... Six repeating units (see
compound series II and III in Chart 1) were individually fitted
by variation of two parameters. For HSC models these
parameters were a uniform backbone bending potential Fg/kT
and a backbone stretch factor s, while for the WLC model the
free parameters were the persistence length Lp and contour length
cl. Variation of s and cl slightly improved the fits and stabilized
the values found for Fg/kT and Lp, although deviations of s from
unity and cl from the predicted contour length were generally
less than 0.6%. Fit quality of the two HSC models is comparable
and is slightly better than that obtained with the WLC model
(Figures 4A and S2 [Supporting Information]).
Figure 4. Fits of end-to-end distance distributions P(r) extracted from 10
ns MD trajectories (pcff force field, 298 K) for oligoPPE backbones by
HSC models and the WLC model. (A) P(r) extracted from an MD trajectory
for the unlabeled backbone of oligoPPE IIe (solid line), fit by the HSC
model with non-uniform segment lengths (dashed line), and by the WLC
model (dotted line). (B) Dependence of fit parameters on the number n of
PPE units (see Chart 1). Squares and left vertical scale: bending potential
Fg/kT in the HSC model with non-uniform segment lengths. Triangles and
left vertical scale: bending potential Fg/kT in the HSC model with uniform
segment lengths. Open circles and right vertical scale: Persistence length
Lp in the WLC model determined by fitting the distance distributions by
expressions from ref.24 Full circles and right vertical scale: Persistence length
Lp in the WLC model determined from 〈R2〉 by eq 2.
there appears to exist a slight trend in Fg/kT with chain length.
With the more realistic non-uniform segment lengths no such
trend is observed. The scatter of the data is due to statistical
noise in the end-to-end distance distributions extracted from MD
trajectories containing 20000 chain conformations. In contrast
to the constant bending potential Fg/kT in the HSC model with
non-uniform segment lengths, the persistence length Lp in the
WLC model exhibits a clear trend with chain length (circles in
Figure 4B). Note that the two vertical scales are related by eq
4, so that variations of Fg/kT and Lp can be directly compared
in this plot.
In further test fits of individual experimental data series by
the HSC model the stretch factor s assumed values slightly
smaller or larger than unity for all sample series. Fixing this
parameter to 1.0 did not lead to significant deterioration of fits
and fixed values of s between 0.99 and 1.01 resulted in slightly
different fit qualities, but not in significant changes of the other
parameters. We thus eliminated the stretch factor s from the
model to reduce the number of parameters.
The consolidated HSC model thus has five fixed parameters,
the four segment lengths and a uniform relative standard
deviation for them. In a global fit of the 16 experimental data
sets (Figure 5) six further parameters are varied. These variable
parameters are two backbone bending potentials Fg (general)
and Fb (butadiyne unit), two label bending potentials Ff
(conformationally flexible label employed in series I, II, and
IV) and Fcu (conformationally unambiguous label employed in
series III), and two label segment lengths lf (conformationally
flexible) and lcu (conformationally unambiguous). When fitting
The bending potentials Fg/kT obtained with HSC models
(Figure 4B) with non-uniform (squares) and uniform (triangles)
segment lengths differ slightly. With uniform segment length
(52) Halgren, T. A. J. Comput. Chem. 1996, 17, 490–519.
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10114 J. AM. CHEM. SOC. VOL. 132, NO. 29, 2010

Flexibility of Shape-Persistent Building Blocks
A R T I C L E S
uncertainty in separation of the label and backbone contributions.
However, a global fit of all data sets with the same bending
potentials and label parameters does not lead to significant
deterioration of fit quality for the individual series of data sets
(compare last two columns of Table 1). Thus, all our data are
consistent and the difference between bending potentials Fg
obtained with the two different labels can be treated as a
statistical error due to noise and deviations of the HSC model
from experimental distance distributions.
To test the assumption of harmonic bending potentials we
measured oligoPPE IIIc in solvents with different glass transi-
tion temperature Tg. This test is based on the assumption that,
to first approximation, the conformational distribution of
macromolecules is frozen at Tg, where characteristic times of
system dynamics change by several orders of magnitude within
a temperature range of a few Kelvin. Note that the true situation
is somewhat more complex, as small regions may still rearrange
below Tg.53 As the end-to-end distance distribution is dominated
by cooperative rearrangement of large parts of the backbone,
corresponding to the slow modes in a normal-mode analysis,
the smaller adjustments are assumed to be negligible within our
experimental precision. In other words, structural changes that
significantly influence the end-to-end distance distribution rely
on the ability of the backbone to readjust its shape on the length
scale of the end-to-end distance and this appears to be unlikely
below Tg in a glassy matrix with a solvent molecule size that is
much smaller than the end-to-end distance. Part of the remaining
errors due to the assumption of freezing of all conformational
changes at Tg are compensated by the fact that their influence
also roughly scales with Tg and that this scaling is likely to be
approximated by harmonic potentials, too.
Figure 5. Global fit (solid lines) of background-corrected DEER time-
domain data (dots) by the HSC model with non-uniform segment lengths
(see bottom row and last column of Table 1). (A) oligoPPE/Bs I. (B)
oligoPPEs II. (C) oligoPPEs III. (D) oligoPPBs IV.
data of only one series of compounds, only three (oligomers II
and III) or four (oligomers I and IV) parameters are variable.
Fit residuals (Figure S3) indicate that systematic deviations
are most prominent for the compounds with the shortest
backbone, which is expected, as the segment model is a more
serious approximation for the labels than for the backbone. The
smallest systematic deviations are observed for the oligoPPEs
II with flexible labels. This implies that the HSC model performs
slightly worse for oligoPPE/Bs I and oligoPPBs IV with
heterogeneous backbone bending potentials than for PPEs with
homogeneous backbone bending potentials. The slightly larger
residuals for oligoPPEs III (conformationally unambiguous
labels) compared to oligoPPEs II (conformationally flexible
labels) were originally unexpected. They are probably due to
the anisotropy in bending of the conformationally unambiguous
label (in-plane vs out-of-plane with respect to the conjugated
system), which is not accounted for by the segment model. The
systematic deviations even for the longer oligomers demonstrate
that the HSC model does not perfectly describe backbone
flexibility. Similar deviations are seen for the WLC model (data
not shown). However these deviations do not change sign
between different series of compounds and do not increase with
backbone length. Hence, flexibility comparisons between dif-
ferent backbones as well as derivation of persistence lengths
are meaningful.
The additional solvents used were 2-methyltetrahydrofuran
deuterated in the methyl group (2-MTHF-d3, Tg ) 91 K), 1,2-
di-n-butyl phthalate deuterated in the n-butyl groups (1,2-n-
DBP-d18, Tg ) 179 K), and perdeuterated polystyrene (PS, Tg
) 373 K). A factor of more than four between the lowest and
highest glass transition temperature ensures that significant
deviations from the behavior expected for a harmonic bending
potential should be detected. The model compound was selected
from series III, since the best fit quality is obtained with the
conformationally unambiguous label. This makes the test of the
assumption more strict than with conformationally flexible
labels. Within series III the best compromise was sought
between maximizing the influence of backbone flexibility by
increasing backbone length and clearly observing the damping
of the dipolar modulation during the maximum dipolar evolution
time that could be achieved with all solvents.
The experimental data (dots in Figure 6) exhibit a significant
dependence on Tg of the solvent that is most easily recognized
by the shift of the local maximum near 2 µs toward shorter
times for higher Tg. This shift corresponds to a decrease in the
mean distance, as is expected when flexibility increases at higher
temperature. Faster damping of the oscillations is also observed
and corresponds to the expected broadening of the distance
distribution at higher temperature. Both the decrease in mean
end-to-end distance and the faster damping at a higher glass
transition temperature were also observed for porphyrin-based
molecular wires when comparing measurements in a toluene/
pyridine mixture to measurements in perdeuterated o-terphe-
nyl.38
As a first step in analyzing the data we performed fits of the
background corrected time-domain data31 for each individual
series of oligomers with the consolidated HSC model (Figure
S3). As seen in Table 1, highly consistent results for bending
potentials are obtained from data series with the same type of
label (oligomers I, II, IV). A somewhat smaller bending
potential for the butadiyne unit compared to the uniform bending
potential of phenyleneethynylene backbones is found for oli-
goPPE/Bs I and oligoPPBs IV. Together with the shorter
average segment length in oligoPPBs compared to oligoPPEs
this suggests a higher flexibility of oligoPPBs.
The uniform backbone bending potential Fg for oligoPPEs
differs more strongly between series II and III with different
labels and the same backbone than between series I and II with
the same label and different backbones. This indicates some
(53) Debenedetti, P. G.; Stillinger, F. H. Nature 2001, 410, 259–267.
9
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A R T I C L E S
Jeschke et al.
Table 1. Parameters of Least-Squares Fits of the HSC Model to Background Corrected DEER Time Domain Dataa
data sets
Fg/kT
Fb/kT
Ff/kT
lf/nm
Fcu/kT
lcu/kT
rmsdb
rmsdc
Ia-d
25.0
25.2
22.8
24.8
24.2
20.2
-
7.74
7.33
-
7.49
7.33
0.640
0.633
-
0.636
0.638
-
-
17.6
-
17.8
-
-
0.868
-
0.867
0.00874
0.00723
0.00391
0.00815
-
0.00883
0.00732
0.00396
0.00821
0.00638
IIa-e
IIIa-d
IVa-c
Global fit
-
20.5
20.8
a Measured in perdeuterated o-terphenyl with a glass transition temperature of 246 K. Fg general backbone bending potential, Fb butadiyne unit
bending potential, Ff conformationally flexible label bending potential, lf conformationally flexible label length, Fcu conformationally unambiguous label
bending potential, lcu conformationally unambiguous label length, rmsd root-mean-square deviation, Lp apparent persistence length of the backbone.
b Individual fits. c Global fit.
Figure 6. Dependence of backbone flexibility in oligoPPE IIIc on the glass
transition temperature of the solvent. Background-corrected DEER time
domain data (dots) are shown together with simulations by the HSC model
Figure 7. Visualization of the flexibility of the backbone of oligoPPE IIe.
(solid lines). The simulations are based on parameters determined on
A superposition of 25 structures computed with the HSC model with Fg/kT
oligoPPEs III in perdeuterated o-terphenyl with glass transition temperature
) 24.2 is shown. The mean backbone vector is along the [1,1,1] direction.
Tg ) 246 K (see Table 1) and scaling of potential Fg/kT with the assumption
T ) Tg. No parameters were fitted. Dotted vertical lines are guides to the
eyes. (A) Solvent 2-MTHF-d3, Tg ) 91 K. (B) Solvent 1,2-n-DBP-d18, Tg
) 179 K. (C) Solvent perdeuterated o-terphenyl, Tg ) 246 K. (D) Solvent
perdeuterated polystyrene, Tg ) 373 K.
To quantify backbone bending from distance measurements
between spin labels, the contribution of the labels to the distance
distribution has to be separated from the contribution of the
backbone. This requires models for the conformational distribu-
tion of both, the shape-persistent oligomer and the spin label.
The model for the oligomer must provide, at least implicitly,
not only the end-to-end distance distribution P(r), but also the
two-dimensional probability distribution P2(r, ꢀ) that correlates
probabilities for a certain end-to-end distance r and a certain
angle ꢀ between the direction vectors at the chain ends.
Monte Carlo computations of the HSC model provide P2(r,
ꢀ). In this model the chain consists of rigid segments with
normally distributed intersegment angles θj with mean values
〈θj〉 ) 0 and uniformly distributed torsion angles φj. This
corresponds to a harmonic bending potential at the joints
between segments and free rotation. For oligoPPEs and related
compounds the rigid segments are identified with bonds, except
for the benzene ring which is modeled as a single segment. This
coarse graining of the benzene ring is necessary to preserve the
linear topology of the chain.
Compared to the WLC model, which implicitly assumes fixed
nonzero intersegment angles, the HSC model provides a more
realistic description of molecular mechanics of linear, shape-
persistent polymer chains. This is apparent in slightly better fits
of end-to-end distance distributions extracted from atomistic MD
simulations. More significantly, when varying the chain length
in the MD simulations a constant bending potential is found
for the HSC model while an unexpected trend in the persistence
length is observed for the WLC model (Figure 4).
The dependence of the data on Tg is well described by
simulations that assume scaling of the normalized bending
potential Fg/kT with T ) Tg (Figure 6, for residuals see Figure
S6). Note that these simulations are based entirely on model
parameters determined from the measurements of all compounds
of series III in o-terphenyl. No further parameters are varied to
reproduce the data obtained with the other solvents. In particular,
the residual differences between simulation and experimental
data for the other solvents are of similar magnitude and point
to similar systematic deviations as for o-terphenyl, where the
parameters were actually fitted. This implies that a normalized
bending potential Fg/kTg agrees with our data within the error
introduced by the other simplifying assumptions. Except for
2-MTHF-d3 as a solvent, data could also be obtained with a
maximum dipolar evolution time of 9 µs. These data are also
well reproduced by the simulations (Figure S7, Supporting
Information).
Based on these results the ensemble of chain structures of
oligoPPEs and oligoPPBs at ambient temperature can be
computed at ambient temperature. Figure 7 shows a visualization
of such an ensemble for the backbone of oligoPPE IIe.
Discussion
The end-to-end distance of a shape-persistent polymer chain
depends on bending of its backbone. To characterize the
flexibility of polymer backbones assembled from benzene and
ethyne units, distance distributions between spin labels at the
chain ends were measured by DEER spectroscopy for oli-
goPPEs, oligoPPBs, and oligoPPE/Bs. The shapes of these
distributions at any given chain length can be fitted by an
approximate expression for the WLC model, but the dependence
of the shape and width on chain length is not in full agreement
with these expressions (Figures 2, 4).
Unlike the basic WLC model the HSC model can predict
changes in the end-to-end distance distribution with temperature,
eq 2. With the further assumption that the ensemble of chain
conformations observed in frozen glassy solutions at a temper-
ature of 50 K is determined by the glass transition temperature
Tg of the solvent, the dependence of DEER data on Tg can be
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10116 J. AM. CHEM. SOC. VOL. 132, NO. 29, 2010

Flexibility of Shape-Persistent Building Blocks
A R T I C L E S
predicted. Indeed, such a dependence is observed and is well
described by the prediction of the HSC model (Figures 6, S4).
The HSC model is thus in full agreement with experimental
observations for the shape-persistent oligomers studied in this
work.
model in describing our data and data extracted from MD
trajectories proves that the number of parameters can be
significantly reduced if only the conformational distribution of
the polymer backbone is of interest.
Conclusion
Thus, flexibility of polyPPEs and polyPPBs is best described
by harmonic bending potentials within the HSC model. Con-
sidering the variation between experimentally determined bend-
ing potentials for different series of oligomers (Table 1), we
arrive at a uniform bending potential Fg/kT ) 24.2 ( 2.0 for
joints in the HSC model of polyPPEs and a slighly smaller
bending potential Fg/kT ) 20.8 ( 2.0 for joints between two
ethyne units in polyPPBs. These values correspond to the glass
transition temperature of o-terphenyl Tg ) 246 K. Expressed
as molar bending energies per joint, the values are (49.5 ( 4.1)
The flexibility of shape-persistent oligomers can be quanti-
tatively characterized by DEER distance distribution measure-
ments between spin labels attached to their chain ends. Such
experimental data are well described by the newly introduced
HSC model, even for short chain lengths. In the HSC model
for polyPPEs, flexibility is quantified by a uniform harmonic
bending potential. Two separate bending potentials are assumed
for polyPPBs, which are found to have a slightly higher
flexibility. Variation of the spin label structure allows for an
estimate of the error in the separation of spin label and backbone
contributions to the distance distribution. This error causes an
uncertainty of about 10% in the harmonic bending potential.
The HSC model can predict temperature dependence of flex-
ibility. This was tested by varying the glass transition temper-
ature of the solvent between 91 and 373 K and the prediction
was found to be consistent with experimental data. Our data
suggest persistence lengths at 298 K of (13.8 ( 1.5) nm for
polyPPE and of (11.8 ( 1.5) nm for polyPPB.
kJ mol-1 and (42.5 ( 4.1) kJ mol-1
.
Similar to the fits of MD-derived end-to-end distance
distributions by approximate formulas for the WLC model
(Figure 4), fits of the experimental end-to-end distance distribu-
tions extracted by the HSC model by the WLC model result in
an unexpected trend of the apparent persistence length Lp (data
not shown). In contrast, analysis of the mean square end-to-
end distance 〈R2〉 by eq 2 provides values whose variation with
chain length is less than their error estimated from the
uncertainty in the bending potentials (Figure S8). We thus obtain
persistence lengths at 246 K of (16.7 ( 1.5) nm for polyPPE
and of (14.3 ( 1.5) nm for polyPPB. Despite the overlap of
the error bars, the slightly larger flexibility of polyPPB compared
to polyPPE is an established fact, since it is directly seen when
comparing data of oligoPPEs II and oligoPPBs IV. According
to eq 4 these values correspond to persistence lengths at 298 K
of (13.8 ( 1.5) nm for polyPPE and (11.8 ( 1.5) nm for
polyPPB.
Compared to atomistic MD simulations the HSC model
achieves a significant reduction in the number of parameters
and a significant reduction in the computational effort for
computing end-to-end distance distributions P(r) and two-
dimensional probability distributions P2(r, ꢀ). These two-
dimensional distributions correlate the probability to observe a
certain end-to-end distance r with the probability to observe a
certain angle ꢀ between the direction vectors at the chain ends.
Differences in P(r) between MD simulations and the HSC model
are small (Figure 4A), as are differences in P2(r, ꢀ) (Figure S9).
As already found in our previous work31 the flexibility predicted
by molecular force fields deviates strongly from the one found
by fits of experimental distance distributions (compare Fg/kT
in Figure 4 and Table 1). A deviation is expected, as force fields
are parametrized on a limited set of low-molecular weight
compounds and errors in bending potentials become more
serious for extrapolation to polymer chains. As already pointed
out in work on flexibility of bis-peptides,36 improvement of a
molecular force field on the basis of EPR data for end-to-end
distance distributions is not feasible, as the number of variable
force field parameters is too large compared to the information
content of the experimental data. Indeed, the success of the HSC
Experimental Methods
Syntheses of Spin-Labeled Oligomers. The syntheses of spin-
labeled oligoPPE/Bs I31,54 and spin-labeled oligoPPEs IIa54 and
IIIa44 have been described. The syntheses of the other spin-labeled
oligomers and all other experimental methods are given in detail
in the Supporting Information.
Acknowledgment. We thank Rene´ Tschaggelar and Enrica
Bordignon for implementing the second frequency source on the
pulse EPR spectrometer. Financial support by DFG projects JE 246/
4-2 and GO 555/4-3 is gratefully acknowledged.
Supporting Information Available: Computational procedure
for a DFT computation of segment lengths, DFT derived
segment lengths, fit of an MD derived end-to-end distance
distribution by the HSC model with uniform segment length,
fit residuals for the HSC model, HSC model fits of individual
series of data sets, experimental distance distributions for all
compounds, fit residuals for dependence on solvent Tg, depen-
dence on solvent Tg with a dipolar evolution time of 9 µs for
three solvents, comparison of two-dimensional probability
distributions P2(r, ꢀ) derived from an MD run and by the HSC
model, experimental procedures including analytical data of all
1
newly synthesized compounds, and H NMR data of spin-
labeled oligomers and some synthetic intermediates. This
material is available free of charge via the Internet at http://
pubs.acs.org.
JA102983B
(54) Godt, A.; Franzen, C.; Veit, S.; Enkelmann, V.; Pannier, M.; Jeschke,
G. J. Org. Chem. 2000, 65, 7575–7582.
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