Comment pubs.acs.org/JPCA
Reply to “Comment on ‘Coherence and Uncertainty in Nanostructured Organic Photovoltaics’” Loren G. Kaake,*,† Daniel Moses,† and Alan J. Heeger†,‡,§ †
Center for Polymers and Organic Solids, University of California, Santa Barbara, California 93106-5090, United States Department of Physics, University of California, Santa Barbara, California 93106-9530, United States § Materials Department, University of California, Santa Barbara, California 93106-5050, United States ‡
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J. Phys. Chem. A 2014. DOI: 10.1021/jp411645j
A
recent comment on our paper1 calls into question the basic soundness of our justification for the presence of spatial coherence at short time scales in organic photovoltaic materials. The apparent reasoning behind this criticism is that a sharply localized photon wave function cannot be constructed in most cases2 and is not a meaningful concept in our context. Our paper was not meant to suggest, as the comment seems to indicate, that a photon propagating in free space has a welldefined spatial position. On the contrary, the effective volume of a photon is a nontrivial quantity which, for example, plays an important role in calculations of the refractive index of gases from first principles.3 In a similar manner, an organic bulk heterojunction solar cell should be especially sensitive to the effective interaction volume of the photon because it is a densely packed collection of strong absorbers. We argue that excited state wave functions are not highly localized (single molecule level) at early time scales; localizing the energy of the photon into a particular molecular eigenstate is a time dependent process. Our attempt to estimate a length scale for the effective volume of the photon (and, importantly, the wave function describing the probability amplitude for finding a photoexcitation at a particular point in space) was done using position-momentum uncertainty and assuming the momentum of a single photon as Δp. Although this approach is not rigorous, the problem can be considered classically4 and a very similar estimate of the length scale of the wave function describing the photoexcitation is obtained via the resolution limit of a far-field microscope (λ/2πn).5 It is important to reiterate that these are estimates (not limits), and we encourage further investigations on the connection between molecular excited state wave functions and the fundamental properties of photons, as well as ultrafast energy transfer in general.
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REFERENCES
(1) Kaake, L. G.; Moses, D.; Heeger, A. J. Coherence and Uncertainty in Nanostructured Organic Photovoltaics. J. Phys. Chem. Lett. 2013, 4, 2264−2268. (2) Bialynicki-Birula, I.; Bialynicka-Birula, Z. Why photons cannot be sharply localized. Phys. Rev. A 2009, 79. (3) Andrews, D. L. Physicality of the Photon. J. Phys. Chem. Lett. 2013, 4, 3878−3884. (4) Mukamel, S. Comment on “Coherence and Uncertainty in Nanostructured Organic Photovoltaics. J. Phys. Chem. A 2013, 117, 10563−10564. (5) Novotny, L.; Hecht, B. Principles of nano-optics; Cambridge University Press: Cambridge, U.K., 2006; p 96.
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
Support was provided by the Center for Energy Efficient Materials, an Energy Frontier Research Center funded by the Office of Basic Energy Sciences of the U.S. Department of Energy (DE-DC0001009). © 2014 American Chemical Society
Received: December 9, 2013 Revised: January 21, 2014 Published: January 31, 2014 1539
dx.doi.org/10.1021/jp412052z | J. Phys. Chem. A 2014, 118, 1539−1539
