Correction to Combined Extinction and Absorption UV–Visible Spectroscopy as a Method for Revealing Shape Imperfections of Metallic Nanoparticles

Metallic nanoparticle solutions are routinely characterized by measuring their extinction spectrum (with UV−vis spectroscopy). Theoretical predictions such as Mie theory for spheres can then be used to infer important properties, such as particle size and concentration. Here we highlight the benefits of measuring not only the extinction (the sum of absorption and scattering) but also the absorption spectrum (which excludes scattering) for routine characterization of metallic nanoparticles. We use an integrating spherebased method to measure the combined extinction−absorption spectra of silver nanospheres and nanocubes. Using a suite of electromagnetic modeling tools (Mie theory, T-matrix, surface integral equation methods), we show that the absorption spectrum, in contrast to extinction, is particularly sensitive to shape imperfections such as roughness, faceting, or edge rounding. We study in detail the canonical case of silver nanospheres, where small discrepancies between experimental and calculated extinction spectra are still common and often overlooked. We show that this mismatch between theory and experiment becomes much more important when considering the absorption spectrum and can no longer be dismissed as experimental imperfections. We focus in particular on the quadrupolar localized plasmon resonance of silver nanospheres, which is predicted to be very prominent in the absorption spectrum but is not observed in our experiments. We consider and discuss a number of possible explanations to account for this discrepancy, including changes in the dielectric function of Ag, size polydispersity, and shape imperfections such as elongation, faceting, and roughness. We are able to pinpoint faceting and roughness as the likely causes for the observed discrepancy. A similar analysis is carried out on silver nanocubes to demonstrate the generality of this conclusion. We conclude that the absorption spectrum is in general much more sensitive to the fine details of a nanoparticle geometry, compared to the extinction spectrum. The ratio of extinction to absorption also provides a sensitive indicator of size for many types of nanoparticles, much more reliably than any observed plasmon resonance shifts. Overall, this work demonstrates that combined absorption−extinction measurements provide a much richer characterization tool for metallic nanoparticles. T study of the optical properties of metallic nanoparticles (NPs) began as an attempt to understand fundamental interactions between light and nanomaterials. It has now become a fruitful source of practical applications for physicists, biologists, chemists, and engineers, in fields as diverse as drug delivery, nanocatalysis, single-molecule detection, and solar cells. Following chemical or physical synthesis, NPs are usually thoroughly characterized to verify whether they will serve their intended purpose. UV−vis extinction spectroscopy is the most commonly used tool to measure their optical properties, not only because UV−vis spectrometers are readily available in most laboratories, but also because it potentially provides indirect information such as size, size distribution, state of aggregation, and NP concentration. For this, the spectra must be compared to theoretical predictions. The optical properties of spheres and spherical nanoshells can be modeled accurately using Mie theory, which solves analytically the electromagnetic scattering problem. For more general nanoparticle shapes, numerical methods such as the finite-difference time domain (FDTD) method, finite-element method (FEM), or discrete dipole approximation (DDA) can be used. Accuracy may be difficult to establish with these methods as the finesse of the mesh and/or the size of the bounding box may result in errors. More advanced approaches such as the Tmatrix or the surface integral equation (SIE) methods provide more accurate and efficient predictions but are more complicated to implement. It is also worth noting that accurate and simpler approximations exist for NPs that are small enough (typically under 100 nm) in the case of nanospheres and nanoshells, nanospheroids, and even more complex Received: August 20, 2019 Accepted: October 17, 2019 Published: October 17, 2019 Article pubs.acs.org/ac Cite This: Anal. Chem. 2019, 91, 14639−14648 © 2019 American Chemical Society 14639 DOI: 10.1021/acs.analchem.9b03798 Anal. Chem. 2019, 91, 14639−14648 D ow nl oa de d vi a V IC T O R IA U N IV O F W E L L IN G T O N o n D ec em be r 10 , 2 01 9 at 1 9: 57 :4 4 (U T C ). Se e ht tp s: //p ub s. ac s. or g/ sh ar in gg ui de lin es f or o pt io ns o n ho w to le gi tim at el y sh ar e pu bl is he d ar tic le s. shapes. To date, the vast majority of experimental UV−vis spectra have been explained or reproduced using theoretical or numerical predictions, even for relatively complex shapes. Any discrepancy is usually attributed to size distribution (for ensemble measurements), minor changes in the geometric parameters (which are not always known accurately), or uncertainties in the metal dielectric function. With such practical limitations in characterizing precisely the samples, the overall fair agreement between theory and experiment suggests that the extinction spectrum does not in fact strongly constrain the nanoparticle properties. We will demonstrate below that absorption spectroscopy can provide much tighter constraints on the precise shape of metal nanoparticles. Standard UV−vis spectroscopy measures transmission over a fixed path length (typically 1 cm), from which the extinction spectrum can be inferred (Beer’s law). Although sometimes called an absorption spectrum, it is in fact extinction that is measuredthe sum of absorption and scattering of light by the NPs. These two processes are fundamentally different and thus provide different insights into the NPs’ interaction with light. Depending on the application, one may want to exploit one property over the other, for example, absorption for photothermal therapy, and extinction for plasmonic sensors. Absorption dominates for small NPs, and scattering for large NPs, but for intermediate sizes (in the range of 40− 100 nm), absorption and scattering can be of a similar order of magnitude. Some relevant information on the NPs may then be missed by measuring only the extinction spectrum. However, because of the relative difficulty in measuring absorption spectra, little effort has been dedicated to exploiting both extinction and absorption spectra for nanoparticle characterization. Over 30 years ago, Kreibig et al. used photothermal spectroscopy to show that the two spectra were indeed different. More recently, such measurements have been further improved to measure the absorption spectrum of a single nanoparticle. This approach is, however, not practical for nanoparticle routine characterization. A simpler method based on measuring scattering at 90° has also been proposed, but inferring the absorption from it remains very approximate. A more appealing alternative, similar to standard UV−vis in many respects, is to place the sample solution inside an integrating sphere and deduce its absorption from a measurement of the sphere throughput. This method has been primarily used in the context of seawater measurements, with only sporadic reports of its application to NPs. With careful calibration, the absolute scatteringindependent absorption spectrum can be retrieved, and the scattering spectrum can then be obtained by subtraction from the extinction spectrum. This was measured in ref 45 for silver nanospheres over a wide range of sizes between 30 and 140 nm, but only an approximate calibration was applied to obtain absolute absorption spectra and no comparison was attempted with theory. Here we show that an integrating sphere-based measurement of both absorption and extinction UV−vis spectra provides much more insight into the NP properties than the standard extinction-only measurement. We focus in particular on a well-tested system that is used in many applications: 60 nm citrate-coated silver nanospheres dispersed in water. Similar NPs have been used in a number of contexts including surface-enhanced Raman spectroscopy, single-molecule detection, surface-enhanced fluorescence, and molecule−plasmon resonance coupling. We show that, while the experimental extinction matches to some extent the theoretical predictions, the absorption spectrum does not, neither in absolute intensity nor in spectral shape. To further investigate these large discrepancies, we use a suite of accurate electromagnetic calculation tools, including the Mie theory, the T-matrix method, and the surface integral equation method. By comparing these predictions to our experiments, we discuss possible explanations including the choice of Ag dielectric function, the elongation of the NP, faceting, and surface roughness. We conclude that these factors typically have a much more pronounced effect on the absorption spectrum than on extinction, emphasizing the importance of the former for routine NP characterization. We also show that the ratio of extinction to absorption provides a strong constraint on the nanoparticle size. Finally, examples of combined absorption/extinction measurements for nonspherical particles, namely, silver nanocubes, are also given to further assert the generality of these conclusions. The extension of this approach to gold nanoparticles is also discussed. ■ EXPERIMENTAL RESULTS Comparisons between experimental and predicted absorption, extinction, and scattering spectra are shown in Figure 1 in the case of 60 nm radius Ag nanospheres dispersed in water. In the case of extinction, the agreement between theory and experiment is reasonable but far from perfect. The position of the main dipolar localized surface plasmon (LSP) resonance is predicted at 423 nm and observed at 433 nm. Theory predicts a small peak associated with the quadrupolar LSP at 377 nm, which is not visi