Gold and Silver Nanoparticles in Sensing and Imaging: Sensitivity of

Sep 6, 2006 - In this work, we investigated the dependence of the sensitivity of the surface plasmon resonance (frequency and bandwidth) response to c...
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19220

J. Phys. Chem. B 2006, 110, 19220-19225

Gold and Silver Nanoparticles in Sensing and Imaging: Sensitivity of Plasmon Response to Size, Shape, and Metal Composition Kyeong-Seok Lee† and Mostafa A. El-Sayed* Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 ReceiVed: April 25, 2006; In Final Form: August 2, 2006

Plasmonic metal nanoparticles have great potential for chemical and biological sensor applications, due to their sensitive spectral response to the local environment of the nanoparticle surface and ease of monitoring the light signal due to their strong scattering or absorption. In this work, we investigated the dependence of the sensitivity of the surface plasmon resonance (frequency and bandwidth) response to changes in their surrounding environment and the relative contribution of optical scattering to the total extinction, on the size and shape of nanorods and the type of metal, that is, Au vs Ag. Theoretical consideration on the surface plasmon resonance condition revealed that the spectral sensitivity, defined as the relative shift in resonance wavelength with respect to the refractive index change of surrounding materials, has two controlling factors: first the bulk plasma wavelength, a property dependent on the metal type, and second on the aspect ratio of the nanorods which is a geometrical parameter. It is found that the sensitivity is linearly proportional to both these factors. To quantitatively examine the dependence of the spectral sensitivity on the nanorod metal composition and the aspect ratio, the discrete dipole approximation method was used for the calculation of optical spectra of Ag-Au alloy metal nanorods as a function of Ag concentration. It is observed that the sensitivity does not depend on the type of the metal but depends largely on the aspect ratio of nanorods. The direct dependence of the sensitivity on the aspect ratio becomes more prominent as the size of nanorods becomes larger. However, the use of larger nanoparticles may induce an excessive broadening of the resonance spectrum due to an increase in the contribution of multipolar excitations. This restricts the sensing resolution. The insensitivity of the plasmon response to the metal composition is attributable to the fact that the bulk plasma frequency of the metal, which determines the spectral dispersion of the real dielectric function of metals and the surface plasmon resonance condition, has a similar value for the noble metals. On the other hand, nanorods with higher Ag concentration show a great enhancement in magnitude and sharpness of the plasmon resonance band, which gives better sensing resolution despite similar plasmon response. Furthermore, Ag nanorods have an additional advantage as better scatterers compared with Au nanorods of the same size.

Introduction Plasmonic Au and Ag metal nanoparticles have attracted great attention due to their potential application in chemical and biochemical sensing,1,2 medical diagnostics and therapeutics,3,4 and biological imaging5,6 due to their unique optical properties originating from the excitation of surface plasmon (SP) resonance. This resonant coupling of incident light to the collective oscillation mode of the conduction electrons in the noble metal nanoparticles is responsible for the commonly observed enhancement in the optical absorption.7 It may also accompany a strong scattering as a secondary process, usually when the particle size is larger than a few tens of nanometers.7-9 The magnitude of the scattering efficiency and the relative contribution to the total extinction have been shown10,11 to vary with the particle size and shape, metal composition, and surrounding medium. The optical scattering is useful in imaging methods to detect attached biosystems and has been used in the diagnostics of cancer cells.3,6 It also has significant potential for single-nanoparticle chemical and biological sensing.12,13 For * To whom correspondence should be addressed. E-mail: [email protected]. † Permanent address: Thin Film Materials Research Center, Korea Institute of Science and Technology, Seoul 136-780, Korea.

a small particle, optical absorption has a dominant effect and the absorbed light energy generally undergoes a thermal dissipation process giving rise to localized heat, which constitutes a basis of biomedical therapeutic applications.3,4,14 In sensor applications, the changes in the plasmonic resonance wavelength of maximum absorption or scattering are monitored as a function of changing the chemical and physical environment of the surface of the nanoparticles. Thus, high sensitivity of the spectral response of the plasmonic resonance absorption (or scattering) band to the changes in the refractive index of the surroundings is desired. Many theoretical and experimental studies13,15-19 have been made on metal nanoparticles with different geometry to find the best nanoparticle configuration to enhance the sensitivity of the plasmon resonance response. From the viewpoint of sensitivity, metal nanorod and nanoshell structures have been at the center of attention. It has been recently reported13,17 that the sensitivity as well as the tunability of the resonance wavelength maximum is closely related to geometrical parameters, namely, the relative ratio of the long axis to short axis for nanorods and the ratio of the shell thickness to the core radius in nanoshells. In general, the longer nanorods and the core-shell particles with thinner metal shell exhibit plasmon resonances in the near-infrared (near-IR) region along

10.1021/jp062536y CCC: $33.50 © 2006 American Chemical Society Published on Web 09/06/2006

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J. Phys. Chem. B, Vol. 110, No. 39, 2006 19221

with high sensitivity. Tunability of the plasmon resonance wavelength in the near-IR region, where human tissue has the highest transmission (i.e., the biological water window) is highly beneficial.20 Most of the researches related to the sensitivity of the plasmon resonance to the environmental change have concentrated on the effect of the geometrical parameters of the nanoparticles, but a systematic study of the dependence of the sensitivity on the metal composition, known to have a significant effect on various aspects of the plasmonic properties, has not yet been reported. In the present work, we present the theoretical results on how the sensitivity of the plasmon response (frequency and bandwidth) and the relative contribution of optical scattering to the total extinction depend on the metal composition of the nanorods. For this purpose, the surface plasmon resonance condition for the metal nanoparticles surrounded by a dielectric medium was carefully examined in correlation with particle geometry and the wavelength-dependent dispersion of the metal dielectric function. The respective effects of real and imaginary dielectric function of metal on the sensitivity and other plasmonic properties are systematically investigated as a function of Ag volume fraction in the Ag-Au alloy nanorod using the discrete dipole approximation (DDA) method. The physical basis for the results is discussed.

d1(ω) | dω ωSP

Theoretical Consideration of Factors Determining the Enhancement of Plasmon Sensitivity and Scattering Contribution

∆ω(1/2) ≈ 22(ωSP)/

In a quasi-static approximation where the electromagnetic phase is assumed to be constant throughout the particle much smaller than the wavelength of light, it is well-known that the surface plasmon resonance (SPR) condition for spheroidal particles is satisfied when the dielectric functions of metal particles, m ) 1 + i2 (which is complex), and surrounding medium, S (which is real), meet the simple relationship of m(ω) + YiS(ω) ) 0. The resonance wavelength can thus be determined from this condition. Here, the parameter Yi is related to the shape or depolarization factor7,21 Li along the axes i of nanoparticles through the equation Yi ) 1/Li - 1. The shape factor L ) 1/3 (2 in Y) represents a sphere, L ) 1 represents a flat disk, and L ) 0 represents an infinite columnar structure along the axis of symmetry of the spheroid. Therefore, the spheroidal particles with prolate geometry have a value of Y greater than 2, increasing as their aspect ratio R, the ratio of long axis to the short axis, increases. For randomly oriented ellipsoidal particles, the absorption cross section in the quasi-static approximation is derived as22

σabs(ω) )

V 3c

3

S3/2

(Yi + 1)2 ∑ i)1

Figure 1. Dispersion relation of the real and imaginary parts of the dielectric function of the binary Ag-Au alloy as a function of wavelength. Two horizontal dashed lines represent the index change in the surroundings from a low value (upper line) to a higher value (lower line) of the medium dielectric constant in terms of an arbitrary value of -YS.

(2)

This equation indicates that the smaller imaginary dielectric function of metal and the steeper gradient of the real part with frequency would give the narrower bandwidth. It should be noticed that the SPR condition cannot be satisfied for all metal elements because the dielectric function of the metal is complex and the imaginary part of the dielectric function of the metals, other than those for several alkali and noble metals, is too large to be neglected and this leads to the suppression of the excitation of the surface plasmon.24 Only noble metals, for example, Ag, Au, and Cu meet the SPR condition in the visible to near-IR region. This is the reason we focus our study on the noble metals. Figure 1 shows the real and imaginary dielectric constants of Ag-Au alloy metals used in our DDA calculation as a function of wavelength. The dielectric constants of Ag and Au nanoparticles are assumed to be the same as that of the bulk metal and obtained by a model fitting of the experimental data from Palik25 using three Lorentz functions with a Drude term.26 The composition-weighted average was used to compute the effective dielectric function of the Ag-Au alloy metal using the following equation27-30

ω2 (1 + YiS)2 + 22

(1)

where V is the particle volume and c is the speed of light in a vacuum. The resonance frequency is determined by the condition of the minimum of the denominator, and this condition can be further simplified to 1(ω) + YiS(ω) ) 0 for noble metals, especially in a frequency window between visible to near-IR where 2 is small and its variation with frequency d2/dω is negligible, as can be confirmed from Figure 1b. The bandwidth (expressed as full width at half-maximum, fwhm) of the SPR can be derived from the analogy with Lorentzian function after the Taylor expansion of σabs near the SPR, as below23

alloy(xAg,ω) ) xAgAg(ω) + (1 - xAg)Au(ω)

(3)

where xAg is the Ag volume fraction. Despite general acceptance, the validity of this simple mixture rule is still in dispute,27,30 mainly due to the probable modification of the electronic band structure of the alloy which gives rise to the change in the interband contribution to the dielectric function. However, this effect, if any, is expected to be significant in the interband transition region and become negligible in the long wavelength region of our concern where the Drude free electrons play a dominant role. The dispersion of the real and imaginary parts of the metal alloy dielectric function is shown as a function of the wavelength in Figure 1. The dielectric constant of the surrounding medium is expressed in terms of an arbitrary value

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Lee and El-Sayed

of -YS and assumed to be real and dispersionless. Two horizontal dashed lines represent the index change in the surroundings, that is, from a low value (upper line) to a higher value (lower line) of the medium dielectric constant. These lines cross the gradually decreasing real part of the alloy dielectric function at certain spectral positions, that is, the SPR condition is satisfied at each of these points. From Figure 1, it is clear that larger values of Y and S move the resonance condition to longer wavelengths. Thus, for a given change in the local dielectric environment, Y determines the extent of the resonance wavelength shift and hence the sensitivity of the nanoparticle plasmon response. This forms the basis of the enhancement in the sensitivity of the metal nanorod with increasing aspect ratio, R. Another factor that determines the sensitivity is the wavelengthdependent dispersion of the real dielectric function of the metal used. If a metal has a gentle spectral dispersion compared with that of Ag-Au alloys shown in Figure 1, greatly enhanced sensitivity to the surrounding medium would be expected. However, noble metals such as Ag, Au, and Cu have a similar dispersion relationship in the real part of the dielectric function. For example, the slope of the real dielectric function with respect to the wavelength is similar for Ag and Au and their alloys as shown in Figure 1. This implies that nanoparticles with the same size and geometry would have the same sensitivity regardless of the metal composition. This fact can be rigorously understood on the basis of a mathematical approach using the Drude free electron model9,31 given by 2

m(ω) ) 1(ω) + i2(ω) ) b b -

ωP

ω2 - iωΓ

)

ωP2

ωP2Γ ωP2 ωP2 + i + i Γ (4) ≈  b ω2 + Γ2 ω(ω2 + Γ2) ω2 ω3

where ω, ωp, and Γ are the optical frequency, the metal plasma frequency, and the damping constant, respectively, and b represents the interband contribution to the dielectric function. In the long wavelength region, where the Drude free electron motion has the dominant effect, the only parameter controlling the spectral dispersion of the real dielectric function of the metal is ωp, which is expressed as follows31

ωp )

x

4πneqe2 m/e

(5)

where ne is a density of free electrons, each with effective mass m/e and charge qe. Thus, the plasma frequency depends only on the free electron density of the metal. Assuming that all valence electrons of each metal atom contribute to the free electron gas, ne can be calculated using the relation

n e ) RA

Zv F A

(6)

where Zv is valence, A atomic weight (g/mol), RA Avogadro’s number (6.02214 × 1023 atoms/mol), and F density (g/cm3). Table 1 summarizes the materials parameters for noble metals Ag, Au, and Cu and the calculated values of free electron density and plasma frequency. Note that the free electron density of Ag and Au has almost the same value, which is in a great agreement with the experimental dispersion of the real dielectric function of the metal shown in Figure 1a. In the case of Cu,

TABLE 1: Summary of the Materials Parameters Such as Atomic Weight and Density and the Calculated Free Electron Density and Plasma Frequency of Ag, Au, and Cu element

A

F (g/cm3)

ne (1022/cm3)

ωp (1016 Hz)

Ag Au Cu

107.868 196.967 63.546

10.5 19.3 8.96

5.86 5.90 8.47

1.366 1.370 1.644

the free electron density has a larger value, indicating that Cu may have a slightly steeper slope in the dispersion curve of real dielectric function than that of Ag and Au. Now, the SPR condition in the spheroidal nanoparticles can be rewritten using the real part of the dielectric function of the Drude metal from eq 4 as below

λSP ωP ) ) (b + YS)1/2 ) (b + YnS2)1/2 λP ωSP

(7)

where λSP and λP represent the SPR and the bulk plasma wavelengths, respectively, and nS is the refractive index of the surrounding medium. By definition,7,32 the parameter Y in the direction of the axis of symmetry can be approximated to be proportional to R2, that is, Y ∝ R2. Therefore, the mathematical sensitivity term can be obtained by the partial differential of the surface plasmon wavelength λSP given in eq 5 with respect to the refractive index of the surrounding medium nS, as below

dλSP ∝ λP xY ∝ λPR dnS

(8)

Equation 6 clearly shows that the sensitivity of the surface plasmon wavelength in response to changes in the refractive index of the local environment depends on the type of metal through the bulk plasma wavelength (λp) and the nanoparticle geometry, that is, the aspect ratio R of nanorods, and is linearly proportional to both. Besides these kinds of physical properties, the chemical interface propertiesse.q. charge transfer between the nanoparticle and its environmentscan affect the SPR sensitivity,33,34 as well, but such a dynamic process is not an aim of our studies. From the viewpoint of materials selection, spectral dispersion of the real part of the metal dielectric function plays a key role on the response of the SPR wavelength to the refractive index change of the surroundings, while the imaginary part of the dielectric function of the metal has a dominant effect on the relative contribution of optical scattering and absorption to the total extinction, as already discussed in our previous work.10 While the dispersion curve in the real part of the metal dielectric function shows a slight shift with the Ag concentration, the imaginary part shows a decreasing trend as the Ag concentration increases (Figure 1). This is expected to promote the relative scattering efficiency to that of the absorption as the Ag concentration is increased. The same argument can be applied to the bandwidth of the SPR peak, in a way that the alloy metal nanoparticles with the higher volume fraction of Ag have the narrower bandwidth, as derived in eq 2. At this point, it should be mentioned that although this theoretical consideration is based on the quasi-static approximation which is regarded valid only for the small metal nanoparticles usually with diameter e20 nm, much smaller than the wavelength of light, there is no doubt that this still gives us a reasonable and qualitative guidance on how the SPR response to the environmental change depends on the materials selection and the geometry of metal nanoparticles unless the retardation

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Figure 2. (a) Calculated spectra of optical extinction efficiencies for Au nanospheres with three different radii (20, 40, and 60 nm) as a function of the relative wavelength shift in response to the refractive index change in surrounding medium from 1.34 to 1.7. (b) Size dependence of the SPR wavelength response to change in the refractive index of the surrounding medium. The sensitivity is estimated from the slope of this linear plot.

effect of the electromagnetic wave becomes so severe as to cause the excitation of multipole mode resonance within the particle. DDA Calculations To verify our theoretical expectations, the DDA calculations were carried out for Ag-Au alloy metal nanorods with different Ag compositions, xAg ) 0, 0.2, 0.5, and 1. The DDA method has been regarded as one of the most powerful and flexible electrodynamic methods for computing the optical scattering of particles with an arbitrary geometry.35,36 For this calculation, we adopted the DDA code developed by Draine and Flatau35 and characterized the case with fixed target orientation where the propagation direction of the incident light is assumed to be perpendicular to the axis of symmetry (long axis) the nanorod. Only one polarization of incident light with a parallel electric field to the long axis is considered in the calculation. The nanorod was considered to have a geometry being a cylinder capped with two hemispheres. The calculations were carried out for varying effective radii of the equal-volume sphere, reff, and varying aspect ratios of the nanorods. The calculated dielectric constants of the Ag-Au alloy shown in Figure 1 were used and the refractive index of the surrounding medium was varied from 1.34 to 1.7 to calculate the sensitivity of the SPR wavelength. Note that the calculated efficiency represents the ratio of the optical cross-section for the nanorods to the geometrical cross-section of equal-volume spheres, πreff2. Details of DDA calculations have been described elsewhere.10 For the application of metal nanoparticles as biochemical sensors, it is important to understand the dependence of the

Figure 3. (a) Calculated spectra of optical extinction efficiencies in longitudinal mode for the Au nanorod with different aspect ratios, as a function of relative wavelength shift in response to the refractive index change in surrounding medium from 1.34 to 1.7. (b) The aspect ratio dependence of the SPR wavelength response to a change in the refractive index of surrounding medium. (c) The dependence of the plasmon response sensitivity on the aspect ratio of Au nanorods with two different effective radii, 20 and 40 nm.

localized surface plasmon resonance wavelength of metal nanoparticles on the refractive index of the surrounding medium, as a function of their size and shape. The sensitivity factor S is defined as the relative changes in resonance wavelength with respect to a change in the refractive index of the surrounding medium, dλRes/dns.16 Calculated values of S were compared for the Ag-Au alloy metal nanorods of different aspect ratios and sizes. As a reference, the sensitivity of Au nanospheres was first investigated for different radii, that is, 20, 40, and 60 nm. Figure

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Figure 4. (a) Calculated spectra of optical extinction efficiencies of the longitudinal plasmon mode for an Ag-Au alloy metal nanorod with a fixed aspect ratio of 3.4 and different Ag concentrations as a function of relative wavelength shift with change in the medium refractive index from 1.34 to 1.7. (b) The quantitative dependence of SPR wavelength responses on the Ag concentration as a function of the refractive index of the surrounding medium. (c) Scattering quantum yield and full width at half-maximum of the SPR peak as a function of Ag concentration in Ag-Au alloy metal nanorods when nS ) 1.34.

2a shows the relative shift in the calculated optical extinction band in response to the refractive index change in surrounding medium from 1.34 to 1.7. The maximum of each spectra obtained at nS ) 1.34 was used as a baseline. For a given index change in the local environment, it is clear that the larger nanoparticles exhibit a higher peak shift. However, increase in the particle size for nanospheres induces undesirable line broadening of the plasmon resonance peak. Such size dependence seems to be general in metal nanoparticles regardless of

Lee and El-Sayed their shape. The quantitative size dependence of the SPR wavelength response is plotted in Figure 2b, and the sensitivity S was estimated from the slope. A value of S of 153.92 nm per refractive index units (RIU) was obtained for r ) 20 nm while an enhanced value of 331.35 nm/RIU was obtained for r ) 60 nm. As shown in this figure, the sensitivity increases with an increase in the particle size. However, excess line broadening restricts a resolution power on whether the spectral change can be distinguished. Figure 3 summarizes the response of optical extinction spectra of Au metal nanorods to a refractive index change in the surrounding medium from 1.34 to 1.7, for different nanorod aspect ratios. The effective radius of Au metal nanorods was assumed to be 20 nm. As shown in Figure 3a, the relative shift in SPR peak position with medium refractive index becomes remarkable as the aspect ratio increases. The sensitivities were obtained from the slope of the linear plot of the SPR wavelength vs the refractive index of the surrounding medium shown in Figure 3b. Figure 3c summarizes the trend in the sensitivity as a function of the aspect ratio. It is observed that the sensitivity, S, increases linearly with the increase in the aspect ratio of Au nanorods, which coincides with our expectation based on eq 6. In the case of R ) 3.4, the nanorod with reff ) 20 nm shows a sensitivity of 491.4 (nm/RIU) which is about 3 times higher than that for sphere (153.92 nm/RIU). It is also observed that the proportional dependence of the sensitivity on the aspect ratio as well as the magnitude of sensitivity is enhanced as the effective radius becomes large. For example, constant of proportionality of sensitivity S with respect to the aspect ratio R, that is, dS/dR ) 141.94 for reff ) 20 nm while dS/dR ) 169.91 for reff ) 40 nm. Figure 4 summarizes the results of DDA calculations of binary Ag-Au alloy nanorods with an aspect ratio of 3.4 as a function of Ag concentration. From Figure 4a, it is observed that the resonance wavelength is sensitive to the refractive index of the surrounding medium, but the sensitivity (as seen from Figure 4b) is independent of the Ag concentration in the alloy. Thus, as expected from the theoretical consideration, the sensitivity seems only to depend on the geometry and the size of the metal nanoparticles and not on the type of noble metal. There exists however a small trend in the sensitivity decreasing as the composition goes from Au to Ag, which is ascribed to the fact that the slope of the real dielectric function of Au as a function of wavelength, employed in this calculation, is slightly gentler than that of Ag. Parts a and c of Figure 4 show that the plasmon bandwidth (fwhm) is sensitive to the fraction of Ag in the alloy. The plasmon band becomes sharper and also increases in intensity as the fraction of Ag increases. A narrower bandwidth allows much easier detection of the change in the surface plasmon band maximum in response to refractive index changes in the surrounding medium. Thus, while Ag and Au nanoparticles would show a similar plasmon wavelength shift in response to analytes, Ag nanoparticles are predicted to be more sensitive in detecting smaller amounts of analyte, by the measurement of the shift in the position of the plasmon bands as well as changes in the band intensity. Quantitative analysis on the relative scattering quantum yield (Figure 4c) exhibits rapidly increasing scattering enhancement with increasing Ag concentration. This is mainly due to a reduced imaginary part of the dielectric function of Ag-Au alloys as shown in Figure 1b. Conclusions We investigated the effect of geometrical parameters and metal composition on the sensitivity of the plasmon response

Au and Ag Nanoparticles in Sensing and Imaging (frequency and bandwidth) of Ag, Au, and their alloy nanorods to changes in the refractive index of the surrounding medium. The trend in the relative contribution of optical scattering to the total extinction was also investigated. These quantities are important in characterizing the use of these nanoparticles for sensing and imaging technology. A theoretical basis for the factors governing the sensitivity was derived by examining the surface plasmon resonance condition incorporated with a dispersion model of the Drude metal. The optical plasmonic properties of metal nanorods were calculated using the discrete dipole approximation method without any approximation on the retardation of the electromagnetic wave within the particle. From the viewpoint of geometrical parameters, solid metal nanospheres have only one degree of freedom, that is, their size for the control of plasmon sensitivity, while the nanorods have two, namely, the size and the aspect ratio. Increase in both parameters is found to enhance the sensitivity. However, large particle size induces an excessive peak broadening of plasmon resonance, which plays a negative role to a sensing resolution. It is found that the spectral dispersion in the real part of the metal dielectric function plays a key role on the response of the SPR wavelength to the refractive index change of the surroundings, while the imaginary part of the dielectric function of the metal has a dominant effect on the relative contribution of optical scattering to the total extinction. Interestingly, our calculations show that the plasmon resonance sensitivity does not change with the metal composition. Ag, Au, and Ag-Au alloy nanorods have similar sensitivity at the same size and shape. This is ascribed to the fact that the noble metals have almost the same bulk plasma frequency, which determines the wavelength dependence dispersion of the real dielectric function of metal. However, it should be mentioned that practical sensing resolution depends on plasmon bandwidth as well as the absolute magnitude of the plasmon intensity. Therefore, it is predicted that the sharper and more intense resonance peaks in the Ag nanorods give them better advantage in their use as sensors. Ag nanorods have an additional advantage as better scatterers compared with nanorods of Au with the same size. Acknowledgment. This research was supported by the Material Research Division of the National Science Foundation (NSF) under Grant No. 0138391 and a grant (Code No. 05K1501-02110) from the “Center for Nanostructured Materials Technology” under “21st Century Frontier R&D Programs” of the Ministry of Science and Technology, Korea. Computations were supported by the Center for Computational Molecular Science and Technology at the Georgia Institute of Technology and partially funded through a Shared University Research (SUR) grant from IBM and the Georgia Institute of Technology. We thank B. T. Draine and P. J. Flatau for use of their DDA code, DDSCAT 6.1. The authors thank Prashant K. Jain for careful proofreading of the manuscript.

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