Kneipp replies: Pablo Etchegoin and coauthors raise two concerns in response to my article: the order of magnitude of surface-enhanced Raman scattering enhancement (1014) and the Poisson distribution in the single-molecule SERS regime.
Achievable total SERS enhancement factors on the order of 1014 are supported by experimental and theoretical studies. Electromagnetic enhancement factors on the order of 1013 have been established. 1 Chemical enhancement can result in factors of 102 or greater. 2 Still, the relative contribution of electromagnetic and chemical effects to the total SERS enhancement remains under discussion. As an experimental example, effective SERS cross sections on the order of 10−16 cm2 for the UV-absorbing molecule adenine have been inferred from vibrational pumping using 830-nm excitation. Such cross sections imply that a SERS enhancement factor of around 1014 is required to bring a typical nonresonant Raman cross section on the order of 10−30 cm2 to this level. 3 Further, it is common knowledge that for larger intrinsic Raman cross sections of the analyte under resonant conditions, the requirements for the size of surface enhancement in single-molecule SERS can be greatly reduced. 4 Moreover, the level of enhancement required for single-molecule SERS depends on the experimental parameters and improvements in the Raman technique, and reducing the background level in SERS samples may make it easier to see single molecules.
SERS signals measured from a sample with an average of approximately one analyte molecule in the probed volume follow a Poisson distribution that indicates the probability of probing 0, 1, 2, and 3 molecules during the actual measurement. With an order-of-magnitude increase in the average number of molecules, the Poisson distribution becomes a Gaussian distribution. 3,5 One of the most important requirements to measure Poisson statistics is that all molecules experience a relatively uniform enhancement level. That can be achieved when the concentration of target molecules is one to two orders of magnitude below the concentration of silver nanoaggregates. In contrast to that requirement, Etchegoin and coauthors discuss experiments that measure the “long-tail distribution of SERS enhancement factors.” Those experiments, as set up by Etchegoin and coauthors, must fail in measuring a Poisson distribution and cannot be used as “proof” that, in general, a Poisson distribution in single-molecule SERS is an artifact. Also in single-molecule tip-enhanced Raman scattering, variations that occur in enhancement factors due to scanning the tip might preclude the observation of a Poisson distribution. Recently, Richard Van Duyne and coworkers demonstrated single-molecule SERS by tracking the statistics of appearances of the distinguishable spectral signatures of two similar molecules. 6 I am pleased to have this opportunity to point out this complementary approach to proving single-molecule SERS, published after the Physics Today article.
