Journal of the American Chemical Society
Communication
ratio of the local restoring force experienced by a monomer in
its ground state to the stretching force applied at the termini of
its polymer (the chemomechanical coupling coefficient). These
findings are conceptually significant because they demonstrate
the following:
AUTHOR INFORMATION
Corresponding Author
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Notes
The authors declare no competing financial interest.
1. A single physical quantity derived from a continuum
description of matter (the stretching force, obtained from
the bending of an AFM cantilever within Hooke’s law)
uniquely describes intrinsically atomistic dynamics (a
chemical reaction). In other words, force provides a
useful quantitative link between the continuum and
atomistic models needed to describe the chemical
response of soft matter to macroscopic loads.
ACKNOWLEDGMENTS
We gratefully acknowledge support by the NSF (CHE-0748281
CAREER and TG-CHE090066).
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REFERENCES
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(1) For example, see a special issue on mechanoresponsive polymers:
J. Mater. Chem. 2011, 21, 8217.
(2) Black, A. L.; Lenhardt, J. M.; Craig, S. L. J. Mater. Chem. 2011, 21,
2. The micromechanical behavior of a polymer (>108 molecular
degrees of freedom) may not be an emergent property but
rather may be determined uniquely by the properties of an
isolated monomer (<102 degrees of freedom).
1655.
(3) Lenhardt, J. M.; Ong, M. T.; Choe, R.; Evenhuis, C. R.; Martinez,
T. J.; Craig, S. L. Science 2010, 329, 1057.
(4) Ariga, K.; Mori, T.; Hill, J. P. Adv. Mater. 2012, 24, 158.
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A. Mater. Today 2008, 11, 34.
(6) Kucharski, T. J.; Boulatov, R. J. Mater. Chem. 2011, 21, 8237.
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(8) Evans, E. Annu. Rev. Biophys. Biomol. Struct. 2001, 30, 105.
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(11) Directing Matter and Energy: Five Challenges for Science and the
Imagination; Basic Energy Sciences Advisory Committee, U.S.
Department of Energy: Washington, DC, 2007.
(12) Black, A. L.; Orlicki, J. A.; Craig, S. L. J. Mater. Chem. 2011, 21,
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(13) Lenhardt, J. M.; Black, A. L.; Beiermann, B. A.; Steinberg, B. D.;
Rahman, F.; Samborski, T.; Elsakr, J.; Moore, J. S.; Sottos, N. R.; Craig,
S. L. J. Mater. Chem. 2011, 21, 8454.
The ability to estimate the micromechanical behavior of a
polymer from the intrinsic force−reactivity properties of an
individual monomer would facilitate the development of new
stress-responsive polymers,1,11 the molecular interpretation of
single-molecule force and elongational-flow experiments,2,20 and
experimental validation of theoretical and computational chemo-
mechanical models.6 For example, single-molecule force measure-
ments are limited to reactions that result in an elongation of the
polymer contour length by a minimum of several nanometers,
whereas the intrinsic force−reactivity properties of almost any
monomer or reactive site can be measured using a series of
increasingly strained macrocycles.6,10 Likewise, the computational
design of polymers with specific micromechanical properties
remains prohibitively expensive. In contrast, calculations of
intrinsic force−reactivity correlations of individual monomers
are much less resource-intensive and can be carried out at a high
level of theory. Here we found excellent agreement between the
force-dependent barrier lowering calculated for ensembles of
simple cyclopropanes (6a and 7a) and experimental ΔΔG⧧(f)
values. At present we lack sufficient empirical data to be confident
that such an agreement is general, and for many reactions,
optimizations of transition states coupled to a constrained poten-
tial remain challenging. The broad reaction scope and technical
simplicity of measuring intrinsic force−reactivity properties of
individual monomers using macrocyclic series could rapidly
increase the number of reactions with known force−rate cor-
relations. Such data will enable broad benchmarking of com-
putational algorithms and identification of efficient and accurate
strategies for quantum-chemical calculations of intrinsic force−
reactivity properties of diverse monomers. Finally, our results
suggest that intrinsic the force−reactivity property of a mono-
mer and the chemomechanical coupling coefficient of its
polymer are independent determinants of chemically driven
micromechanical behavior and hence could be modified
individually to maximize the diversity of mechanical pro-
perties available in polymers of the same chemical composition.
(14) All converged transition-state structures passed the wave
function stability test. Intrinsic reaction path (IRC) calculations
(Figure S9) confirmed the concerted disrotatory mechanism of
reaction 1 in broad agreement with prior work.15,16
́ ́
(15) Faza, O. N.; Lopez, C. S.; Alvarez, R.; de Lera, A. R. J. Org.
́
Chem. 2004, 69, 9002.
(16) Dopieralski, P.; Ribas-Arino, J.; Marx, D. Angew. Chem., Int. Ed.
2011, 50, 7105.
(17) The force was applied by defining an infinitely soft massless
harmonic potential across the constrained distance. The infinitely long
equilibrium distance q0 of this potential (spring) ensured that it
exerted force kq0 (where k is the harmonic force constant) on any two
points across which it was applied (e.g., terminal C atoms) irrespective
of their equilibrium separation. In other words, the generated force
was identical for all conformers of a constrained molecule regardless of
their structural differences. In addtion, an infinitely soft constraining
potential does not change the harmonic vibrational frequencies of the
molecule, thus allowing the computation of thermodynamic properties
from analytic molecular Hessians.6 Single-molecule force experiments
are often modeled by assuming that the macromolecule is stretched by
an infinitely soft constraint.18
(18) Kreuzer, H. J.; Payne, S. H. Phys. Rev. E 2001, 63, No. 021906.
(19) Hermes, M.; Boulatov, R. J. Am. Chem. Soc. 2011, 133, 20044.
(20) Hyeon, C.; Thirumalai, D. J. Phys.: Condens. Matter 2007, 19,
No. 113101.
ASSOCIATED CONTENT
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S
* Supporting Information
Synthetic procedures; spectroscopic characterization of macro-
cycles 2−5 and the intermediates; details of kinetic measure-
ments and quantum-chemical computations; coordinates and
energies of the optimized structures; and results of IRC
calculations. This material is available free of charge via the
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dx.doi.org/10.1021/ja301928d | J. Am. Chem. Soc. 2012, 134, 7620−7623