Subscriber access provided by Mount Allison University | Libraries and Archives
Article
Benchmarking Common Approximations for Determining the Particle-Size Dependence of Adsorbate-Induced Localized Surface Plasmon Resonance Shifts Luca Bergamini, and Stefano Corni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp4016905 • Publication Date (Web): 28 May 2013 Downloaded from http://pubs.acs.org on June 3, 2013
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Benchmarking Common Approximations for Determining the Particle-Size Dependence of Adsorbate-Induced Localized Surface Plasmon Resonance Shifts Luca Bergamini†,‡ and Stefano Corni∗,‡ Department of Physics, University of Modena & Reggio Emilia, I-41125 Modena, Italy, and Center S3, CNR Institute of Nanoscience, I-41125 Modena, Italy E-mail:
[email protected] Phone: +39 059 2055205. Fax: +39 059 2055651 KEYWORDS: Gold nanoparticle, Silver nanoparticle, Mie theory, dielectric shell, adsorbatecoated nanoparticle
∗ To
whom correspondence should be addressed Modena & Reggio Emilia ‡ CNR Inst Nanosci † Univ
1 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Abstract Anomalies are investigated that exist between many long-standing theoretical models of the optical behavior of sensors based on changes in the localized surface plasmon resonance upon analyte adsorption. In particular, we focus on single metal nanoparticles which represent the core building-block of many recent sensing devices. Theoretical approaches include the Retarded Mie theory, the Non-Retarded quasi-static-dipole-approximation and two radiative corrections to the Non-Retarded case (radiative damping and radiative damping+depolarization). We find that the most accurate Non-Retarded approximation to the Retarded Mie theory varies strongly on a case by case basis; anyway, for particle radii beyond a few tens of nanometers, none of the considered approximations represents properly the adsorbate induced plasmon shift. We also find that the size-dependent peak shift has a complex dependence on the metal dielectric function. Accordingly, the peak shift trend as a function of the particle radius reveals an unexpected non-monotonic behavior. We eventually identify an interesting range of particle radii over which the adsorbate-induced plasmon shift is unaffected by the particle size. Moreover, we give examples where nanoparticle batches with large size dispersion provide higher sensor reproducibility than monodisperse samples. On the other hand, in light of our findings, single particle measurements are pivotal to disclose the exact structure of the peak shift trend as a function of the particle radius.
Introduction Localized Surface Plasmon is a well-known phenomenon which takes place in metal nanoparticles (NPs) due to collective oscillation of free electron in nanosized structures when subjected to an electromagnetic field. In the last few years, the development of new techniques which allow to synthesize nanoparticles with different sizes and shapes in a very controllable way and without aggregation, 1,2 has enabled to built up many devices relying on single or well patterned ensemble of metal nanoparticles. The working mechanism of these devices is mainly based on the optical properties of metal nanoparticles, which have wide application in nanoelectronics, diagnostics,
2 ACS Paragon Plus Environment
Page 2 of 29
Page 3 of 29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
therapeutics, optical sensing, and in general as building blocks in nanotechnology. 3–8 One of the most employed techniques, especially for sensors and analytical applications, is based on the Localized Surface Plasmon Resonance (LSPR), which permits to reveal a change in the surrounding environment or a deposition of material on the surface of metal nanoparticles by monitoring the shift in frequency of the plasmon peak. The LSPR spectrum dependence on the nanoparticle shape, 9–14 size, 12,14–17 interparticle distance, 18 nonlinear optical response, 19,20 dielectric properties of the nanoparticle material 16,21,22 and, most importantly, on the dielectric properties of the surrounding environment 8,13,14,23–28 has been already widely explored. These studies demonstrate not only that the plasmon is very sensitive to the presence of substances attached on the nanoparticle surface, but also that the displacement in LSPR maximum is precisely related to the amount of adsorbed material. In order to predict and interpret the optical behavior of these systems different theoretical approaches 29 can be applied. The most used is the Non-Retarded approach, which, even though it provides an approximated solution, is simple and allows a straightforward interpretation of the outcomes. The neglect of the magnetic field effects reduces the electromagnetic Maxwell equation problem to the resolution of the Poisson equation. 30–32 Under these conditions the physical properties of the system can be inferred by the knowledge of its polarizability. The full Retarded electromagnetic approach is less frequently explored. Since both the electric and the magnetic fields are involved in the calculation, an analytical solution is not always achievable. Even when such solutions are achievable, as for spherical particles by Mie theory, they involve evaluating non-trivial mathematical functions and summing (truncated) series, that makes the simpler NonRetarded approaches attractive at least to grasp, hopefully, the qualitative trends. In other cases, namely for particle shapes more complex than spheres or ellipsoids, one can obtain a solution only exploiting numerical approaches, e.g. Boundary Element Method (BEM). 33,34 Although devices based not only on single nanoparticles, 3,4,35–37 but also on pattern of nanoparticles, 3,8,38,39 in which the mutual interaction between the particle cannot be neglected, are realized, a complete understanding of the isolated nanoparticle optical behavior is a fundamental step.
3 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
In this work we focus on the simplest LSPR systems, namely single spherical metal nanoparticle in solution enlightened by an electromagnetic field. The study is carried out from the theoretical point of view and shows the difference between employing the Non-Retarded approximation in place of the general Retarded theory. Since the former is often stated to be valid when the condition d
