Article pubs.acs.org/JPCC
Effects of LSPR of Gold Nanospheres by Surface Vacancies and Protruding Tips Tae Kyung Lee and Sang Kyu Kwak* School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 689-798 Korea S Supporting Information *
ABSTRACT: Effects on the optical properties of gold nanospheres are investigated by using discrete dipole approximation (DDA) with respect to variations of surface morphology resulting from introducing protruding tips and vacancy defects. Varied numbers and sizes of tips are attached perpendicular to faces of regular hexahedron and tetrahedron. Surface vacancy defects follow two types; the one with a rotationally carved system and the other with random exclusions of unit systems of DDA. The size of the nanosphere is varied from 10 to 50 nm in radius, and direct comparisons of its effects with modified surfaces have been done. The alteration of optical spectra is investigated with the following properties; extinction, absorption, or scattering cross sections with respect to wavelengths of the incident light in water environment and induced electric field. This work shows that, even with small degree of surface modification, whether it is vacancy or tip, their effects should be taken into consideration, especially for the application to single particle spectroscopy for the aim of extreme sensitivity.
I. INTRODUCTION Research on noble metals was extensively conducted soon after the discovery of their surface plasmon resonance (SPR) phenomena induced by an incident light. With recent advances in nanotechnology, those materials are synthesized on the nano scale; thus, the phenomena become localized (i.e., LSPR) such that the sensitivity and resolution highly increase. Therefore, it has been well adopted for sensing applications of, to name a few, biomolecular and gas detection,1,2 catalytic monitoring of reactant adsorption,3−5 sensing of electron charge-transfer events,6 etc. It also allows researchers to explore deeper into science and engineering fields such as bioimaging,7−9 drug delivery systems,10,11 solar energy harvesting,12 photothermal cancer therapy, and thin-film photovoltaics.3,13−15 LSPR is now becoming a monumental work. Among various shapes of LSPR nanoparticles, nanosphere with the dipolar resonance due to its perfect symmetry has been quickly used for a sensor application.16 This particular shape was actively pursued due to the generality of shape and easy synthesis, yet the sensitivity of nanosphere is found to be somewhat inferior to other shapes in terms of sensing low concentrations of molecules.16,17 One can consider two approaches for improving and covering up its © 2014 American Chemical Society
deficit sensing ability; one is well-known, and the other has been initiated recently. The first is grafting acute tips, which can play roles as antenna to condensate plasmonic resonances passing throughout their host material. The nanostar, which has protruding tips surrounding a spherical core, is the resulting product. It has been synthesized to induce greater plasmonhybridization18−20 leading to multiple optical peaks.16,20,21 Its application has been successful, although the study is not done with the isolation of single particle, to detect zeptomole (i.e., ∼10−21) of 1,5-naphtalenedithiol (15NAT) in a dielectric environment.17 The second is the effect on the sensing when a surface defect exists. Note that the term defect is used to represent vacant sites and we will call it vacancy hereafter. It has not been a serious concern because the notion of negligible variations of optical spectra due to its existence is naturally accepted. As shown in Kwak and Yong’s work,22 however, a few missing unit-blocks (i.e., 3 dipoles out of 1024 on the surface) on the flat surface cause an ∼3.5% increase of the absorption Received: January 11, 2014 Revised: February 16, 2014 Published: February 24, 2014 5881
dx.doi.org/10.1021/jp500325c | J. Phys. Chem. C 2014, 118, 5881−5888
The Journal of Physical Chemistry C
Article
efficiency at the wavelength around ∼760 nm. Depending on the size of the nanoparticle, the effect of surface vacancy might be more problematic especially in applications of the single particle spectroscopy. Collective LSPR from array or film of nanoparticles does not show whether surfaces of nanoparticles are smooth or defective since their optical intensities are too large to distinguish small variances originated from surface vacancies. On the contrary, optical intensity of single nanoparticle is much lesser so that small variation in the property due to surface vacancy is no longer indistinguishable; this phenomenon can be intensified as the size ratio of vacancy to particle becomes larger. Since that variation includes the shift of optical wavelength and/or unpredictable change of its intensity, sensing molecules in countable number might be difficult or incorrectly done. Current trend of nanotechnology in the LSPR research is to synthesize more size-and-shapecontrolled nanoparticle and to push the sensing limit to detect trace amount (e.g., yoctomole level,∼10−24). Thus, it is of great importance to study how and to what extent the existence of surface vacancies alters optical properties of LSPR. For more fundamental understandings for better applications of LSPR materials, we bring up several important issues, which embrace two topics above-introduced but have been rarely considered in the LSPR study, and resolve them with details of optical spectra and electric field analyses by a computational method. Our focus in this study is on the single particle spectroscopy. Those issues are (1) the effect of surface vacancies on optical properties, (2) the effect of collective feature of surface vacancies, and (3) the identities of small LSPR peaks due to the existence of tips in terms of number, size, and orientation. There are several theoretical methods available, which are well-known to compute optical properties of noble metal nanoparticle; discrete-dipole approximation (DDA),23,24 finite-difference time-domain (FDTD),25 Mie theory,26,27 T-Matrix null-field (T-Matrix),28 and the finiteelement method (FEM).29 In this study, the DDA method is chosen by considering convenient modeling of arbitrary shapes, capability of treatment of missing dipoles, and reasonable computation time. By using DDA, we investigate and define subtle effects from rare modifications of nanospheres with size variations. To this end, four types of model gold nanoparticles have been constructed: (S1) perfect nanospheres for the reference purpose, (S2) defective nanospheres with varying number of surface vacancies and with a rotationally squarecarved vacancy, and (S3) nanostars with varying number and orientation of protruding tips, of which height, base length, and grafted positions are also changed. All systems are subject to change their sizes. For the reason of choosing the rotationally square-carved vacancy, we consider two factors linked to each other: first, introducing edges, which are more reactive than smooth surface, in the expectation of producing more LSPR peaks, and second, observing collective features of vacancies at the same time. Interestingly, we will show later that this particular model produces multiple peaks only in the visible region unlike nanostar covering both visible and near-infrared (NIR) peaks.
introduced by DeVoe, who obtained optical properties of molecular aggregates.30,31 Later, Purcell and Pennypacker adopted his idea to study interstellar dust grains by applying the notion of discretized dipoles.32 Their approximation takes the retardation effect, which occurs roughly when the distance between dipoles is greater than 10% of the wavelength,33 into account. The core idea of DDA is briefly explained in the following derivation.23,24 When an object undergoes the dipole discretization to make N polarizable points, the dipole moment Pi is calculated as
Pi = αi·E loc(ri)
(1)
where αi is a polarizability tensor and Eloc(ri) is the external electric field where i = 1, 2, 3, ..., N. The electric field is the sum of the incident field and the dipole field, which are shown as the first term and the second term, respectively, on the right-hand side of the following equation: N
∑ AijPj)
Pi = αi(E inc, i −
j=1
(2.1)
i≠j
Aij =
⎤ exp(ikrij) ⎡ 2 ikr − 1 ⎢k (riĵ riĵ − I ) + ij ⎥ (3 r r I ) − ̂ ̂ ij ij ⎢⎣ rij rij2 ⎦⎥i ≠ j (2.2)
where Einc,i is the electric field at ri (i.e., spatial position i) due to the external incident plane wave, k is the angular frequency over the speed of light (i.e., inverse wavelength, 2π/λ), rij ≡ |ri − rj|, r̂ij = ((ri − rj)/rij), and I is a 3 × 3 identity matrix. αi can be defined as the inverse of diagonal of the matrix Ajj24 then eq 2.1 becomes N
∑ AijPj = Einc,i (3)
j=1
One way is to apply direct inversion of Aij, but it is only efficient if N is small in consideration of computation storage and time. On the other hand, iterative computations can be implemented; for instance, in eq 2.1 Pi is expanded in powers of αi and inserted to Pj until two quantities are converged or the conjugate gradient algorithm for the better convergence is used. In any cases, the iteration scheme for calculating Pj has been generally adopted.23 Once the dipole moments P j ’s are obtained and, subsequently, the forward-scattering amplitude using the optical theorem is applied to compute cross sections of extinction, absorption, and scattering (i.e., Cext, Cabs, and Csca), which are shown below Cext =
Cabs =
II. COMPUTATIONAL METHODS AND NANOPARTICLE MODELS A. DDA. To measure optical properties of gold nanoparticles, we use the DDA method, which divides an arbitrary shape into a finite array of points, which respond to the local electric field and form dipole moments. The original idea was
Csca =
N
4πk |Einc|2
* jPj) ∑ Im(Einc,
4πk |E inc|2
∑ j=1
{
k4 |E inc|2
∫
dΩ |∑ [Pj − n(̂ n·̂ Pj)] exp( −iknr̂ j)|2
(4)
j=1 N
Im[Pj(αj−1)*P*j ] −
⎫ 2 3 *⎪ k PP j j⎬ ⎪ 3 ⎭
(5)
N j=1
(6) 5882
dx.doi.org/10.1021/jp500325c | J. Phys. Chem. C 2014, 118, 5881−5888
The Journal of Physical Chemistry C
Article
where the superscript * represents conjugates of corresponding properties, n̂ is a unit vector of the direction of scattering, and dΩ is the element of the solid angle, which are subject to integration.23 Note that the three quantities satisfy a relation of Cext = Cabs + Csca. This method derived above has been implemented to a computer program called DDSCAT, which is developed by Draine and Flatau.23,24 Arbitrary shape of LSPR materials is possible to study in this program. To use it, the validity of DDA must be checked with a necessary condition of |m|kd < 0.5, where m is the complex refractive index, k is the inverse of the incident wavelength, and d is the distance between dipoles. By following the criterion, a small d compared to the wavelength of the plane wave in the target material is acquired. B. Simulation Details. Gold has been chosen for the target model, and its dielectric constants depending on the wavelength follow Johnson and Christy’s work.34 It resides in the medium of water, of which the refractive index is taken to be 1.335. The range of the wavelength applied is from 0.4−1 μm. Figure 1 shows representing gold nanoparticles of this study
with propagation directions of the incident light (k) and the electric field (E). To investigate size effects of nanoparticles, the radius (R) of all models shown in Figure 1 are varied from 10 to 50 nm with an interval of 10 nm. Note that R represents the radius of the central core of nanostar. Figure 1a shows a perfect gold nanosphere. In Figure 1b, surface vacancies are introduced from 10 to 50% as in the number density by removing unit cells and the outmost surface-layer was only subject to be vacant. We limited the depth of vacancy to 1 nm since the vacancy depth makes low degrees of vacancies for our interest in this study. Figure 1c shows a rotationally square-carved one with varying width as 10 to 30% of the radius of the nanosphere. For the channel, the deeper is the wider. We aligned it with respect to an incident light in three ways to obtain different optical properties. The protruding tip from Figure 1d is also aligned to show four distinct directions depending on directions of E and k. To obtain the effect of the size of the tip, the height (H) has been changed with respect to the aspect ratio (AR) of R to H and the base radius (R′) of the conical tip was varied from 5 to 20 nm. Also, from Figure 1d,e, we systematically added the number of tips aligned in the facial directions of the regular hexadron while fixing the height of the tip as 45 nm (i.e., AR = 1:1.5). In this way, an intrinsic effect by the number of oriented tips may be captured. The nanoparticle model in Figure 1f, which has the tetrahedral shape of tips, was specially constructed to compare with the four-tip nanostar following the shape of hexahedron. For all models, we chose d as 1 nm and every other parameter was set to satisfy the criterion of DDA introduced in the preceding section. Additional criterion about the smallness of d (or largeness of N) was checked by changing d to 0.5 nm, and all results of nanospheres obtained in this work were not altered. However, one must consider intrinsic surface roughness of nanoparticles shown in Figure 1
III. RESULTS A. Perfect and Surface-Vacant Nanospheres. The radiation spectra for perfect gold nanospheres are calculated as a basis for the reference data, and Figure 2 shows the results. As R increases, Cext, Cabs, and Csca shift to the visible red (i.e.,
