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Helical Metal Nanoparticle Assemblies with Defects: Plasmonic Chirality and Circular Dichroism Zhiyuan Fan and Alexander O. Govorov* Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, United States ABSTRACT: Metal nanoparticle structures with a helical arrangement are able to create strong optical chirality and associated circular dichroism (CD). The CD effect in these chiral structures comes from the electromagnetic dipoledipole interaction between nonchiral nanoparticles. In general, the calculated CD spectra are sensitive to the parameters. The shape of the CD spectrum depends on the helix pitch and radius and, sometimes, on the number of particles in a helix. Simulating several geometries, we were able to identify the sets of parameters for which the CD spectrum is very stable against defects or disorder. These results are important for designing novel nanocomposite materials with strong optical chirality in the visible wavelength region.
’ INTRODUCTION Presently, chiral nanostructures are a very active field of research. Chiral nanoscale structures can be assembled from semiconductor quantum dots, metal nanocrystals, and molecules.116 For a recent review on the chiral nanoscale structures and associated CD mechanisms, one can see ref 17. New CD lines in chiral assemblies may come from various mechanisms of interaction between building blocks constituting a nanoscale structure. Building blocks themselves (molecules and nanocrystals) can be either chiral or nonchiral. In the case of nonchiral building blocks, chirality of a nanostructure should come from a chiral (nonsymmetric) arrangement of nanocrystals.6,18 In the structures with chiral molecular elements, CD spectra can acquire new lines19,20 as a result of dynamic Coulomb interaction between chiral molecules and nonchiral metal nanocrystals. In this case, new CD lines appear at the plasmon frequencies of nonchiral nanocrystals. Considering only nonchiral nanocrystals as building blocks, optical chirality and associated CD signals appear if nanocrystals are arranged in a chiral geometry.6,18 Then, the optical chirality comes from the dynamic Coulomb interaction between nanocrystals.18 Such internanocrystal interaction is especially strong for metal nanoparticles since plasmonic dipoles are very strong and able to create a strong coupling between individual plasmonic blocks.2124 Then, a collective plasmonic resonance of assembly becomes chiral, i.e., exhibits nonzero CD response.18 This type of optical chirality in a plasmonic system is predicted to be especially strong in helices composed of metal nanocrystals18 which resemble helical biomolecules such as proteins or DNA. Indeed, very recent experiments8,11,15,25 reported strong CD signals in the helical-like nanocrystal assemblies. This plasmonplasmon interaction mechanism of CD in metal nanoparticle structures resembles a well-known CD r 2011 American Chemical Society
mechanism in molecular helices (proteins and DNAs) in which nonchiral molecular blocks (chromophores) couple via the dipoledipole Coulomb interaction.26,27 Here, we focus on the plasmonic CD effect in helical structures composed of spherical nanoparticles (NPs). This geometry looks especially promising for experimental realization of plasmonic chirality in comparison, for example, with chiral pyramids.18 In our previous study on this effect,18 we found that, in general, the CD lines of plasmonic assemblies can be very sensitive to their geometry. Therefore, since many groups are presently working on plasmonic helical assemblies, it is important to identify geometries which give stable CD signals in these structures in the presence of disorder. The helical structures described in our previous paper18 exhibited strong CD signals, but they did not have an optimized geometry. In addition, our previous paper18 did not include some important properties of CD spectra of plasmonic helices (such as a CD signal as a function of helix pitch, for example) that can be very important for experimental realizations and for understanding of experiments. In particular, the previous helical structure18 showed large changes of CD (with flipping of sign) as a function of the number of NPs (NNP) in helices with small NNP. Here we vary the parameters of helix (helical pitch, helix radius R0, and NP radius aNP) and find the geometries that produce very stable CD spectra without flipping of sign. These CD spectra do not change much with the number of particles in a helix, and in addition, they are very stable against defects (missed NPs, variations of pitch, and positional and size disorder). Received: May 7, 2011 Revised: June 1, 2011 Published: June 03, 2011 13254
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The Journal of Physical Chemistry C Recently, it was shown both experimentally and theoretically25 that nanorods attached to a twisted fiber exhibit a plasmonic CD signal, which is consistent with a model of interacting dipoles of metal ellipsoids. The theoretical part of the paper25 has a statement that the spherical-NP helix system is expected to show only negligible CD in the presence of a finite amount of disorder. We do not agree with the above statement and show here that the spherical-NP helix can have strong CD in the presence of disorder. In particular, we probe the CD strength of NP helices for several types of disorder: Fluctuations of helix length and pitch, defects (missed NPs), and randomized positions and sizes of NPs. Then, our calculations show that CD signals from the spherical-NP helices are amazingly stable when we average the CD signal over a length of helix or when we create defects. Regarding the above calculations on the stability of NP CD, we obtain these results for several sets of parameters, including the parameter sets used for NP-helices in refs 18 and 25. Testing several possibilities, we identify the optimal parameters which maximize the CD signal in a helix. Our conclusions about the stability of CD are consistent with the recentexperiments on helical assemblies of spherical NPs8,11 which demonstrated strong plasmonic CD signals. The
Figure 1. Nanoparticle helix: (a) 3D model and (b) geometry.
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helical geometry with nanorods introduced in ref 25 may produce strong CD signals because of an enhanced Coulomb coupling between oriented nanorods. At the same time, we expect that, in general, CD of spherical NP helices can be more robust in the presence of disorder compared to CD signals from the nanorod helices. The calculations of ref 25 were done for an ideal system without orientational disorder; the nanorods in ref 25 are oriented exactly along the helical line. In many experimental cases, control of orientation of the nanocrystal is an additional challenge. If an orientational control of nanorods is challenging, a spherical NP helix can be more advantageous and convenient compared to a nanorod helix because spherical NPs have no orientational disorder. This comment is applied, for example, in the cases when an assembly is made with the help of DNA nanotechnology.2831
1. MODEL The calculations will be done, in general, within the electromagnetic dipolar approach used in our previous paper.18 However, in contrast to ref 18, we include here the electromagnetic scattering effect and consider long and very long helices for which the scattering plays an important role. The formalism develops in a way similar to the dipolar approach to calculate a linear chain of NPs.32 We note that this dipolar approach is valid if NPs are not so close to each other23,32 so that rij > 3aNP, where rij is the centerto-center distance between neighboring NPs; aNP is the NP radius; and NPs have the same size. In other words, a gap between two NPs should be equal to and larger than their radius. In addition and importantly, our dipolar formalism is valid for relatively small NPs: aNP , λ0, where λ0 is the wavelength of light in vacuum. The plasmonic system (Figure 1) experiences an external electro1/2 Bext,ω 3 eiωt], where B Eext,ω = Be 0E0eikB(ε0) Br magnetic field: B Eext = Re[E
Figure 2. (a) Calculated normalized extinction CD, εextin,CD/NNP, for Au-NP helices with a variable number of particles, NNP = 420. (b) Averaged CD spectra over the intervals of parameter NNP. This is a simple example of disorder when helical complexes of different length are present in a macroscopic ensemble. Inset: As an example, we show to scale the geometry of helix NNP = 8. Parameters used: the NP radius aNP = 5 nm; the distance from a NP to the helical axis R0 = 12 nm; the helix pitch = 15 nm; the background dielectric constant is taken for water (ε0 = 1.8). 13255
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Figure 3. Calculated normalized scattering CD, εextin,CD/NNP, for helices with various numbers of spherical particles (NNP = 420). The helix parameters are similar to those in Figure 2.
and B e 0 is the polarization vector, k = 2π/λ0. The energy flux of the incident wave is given by I0 = ((E20)/(8π))c0(ε0)1/2, where ε0 is the dielectric constant of the matrix. In the following, we will take water as a matrix material (ε0 = 1.8). In the dipole approximation, the electric dipole of a single NP is given by
Figure 4. Calculated normalized extinction CD, εextin,CD/NNP, for the optimized Au-NP helices with pitch = 25 nm. The other parameters: aNP = 5 nm and R0 = 12 nm.
Correspondingly, the extinction and scattering cross sections will then be σextin, ( ¼ ε0
8π pffiffiffiffiω Im½ð 2 3 E20 3 c0 ε0 3
dBω, i ¼ Ri 3 E Binduced, ω, i Þ Bω, i ¼ Ri 3 ð E Bext, ω, i þ E
σ scat, ( ¼ σextin, ( σ abs, (
where B E ω,i = B E ext,ω,i þ B E induced,ω,i is the field acting on the i-NP; E ext,ω(rBi), and B E induced,ω,i is the field induced by all B E ext,ω,i = B other NPs with j 6¼ i. Considering a point-like dipole, we obtain33 2 3ð dBj 3 n pffiffiffiffi Bji Þ 3 nBji dBj Binduced, ω, i ¼ 4 E ð1 ik ε0 rij Þ 3 r ij j6¼ i
The CD cross sections are given by
∑
# ε0 ω2 dBj ð dBj 3 nBji Þ 3 n Bji ikpffiffiffi þ 2 e ε0 rij c0 rij
ð1Þ
where Ri (ω) = a3NP,i(εNP,i ε0)/(εNP,i þ 2ε0) is the i-NP polarizability, and εNP,i = εNP,i(ω) is the Au dielectric function that will be taken from the experimental tables.34 Then, we calculate the absorption cross section for incident circularly polarized waves (() Z 1 r Þ3 E Btot, ω, ( ð B r ÞdV Qabs, ( ¼ Re Bj ω, ( ð B 2 V whereBj ω,( * and B E tot,ω,( are the complex amplitudes of induced electric current and total electric field, respectively; the actual iωt current and field are then given byBj (r) = Re[j Bω,((r) 3 e ] and iωt Btot,ω,((rB) 3 e ], respectively. Then, assuming B E tot(rB) = Re[E that aNP , λ0, we obtain σ abs, ( ¼
Qabs, ( I0
¼ ε0
2
8π 6 pffiffiffiffi ω Im4 2 3 E20 3 c0 ε0 3
∑i
3
dBi, ( 3 dBi, ( 7 5 Ri ðωÞ
ð2Þ
∑i Eext, ω, i, ( 3 dBi, ( Þ,
σ extin, CD ¼ Æσextin, þ σ extin, æΩ , σ scat, CD ¼ Æσscat, þ σscat, æΩ
ð3Þ
ð4Þ
where the averaging over the solid angle, Æ...æΩ, is needed since complexes are in a solution and have random orientations. Then, the molar extinction CD in the convenient units (cm1 M1) is written as NA ð5Þ εextin, CD ¼ 104 σ extin, CD 0:23 Since the electric dipoles dBi interact, we have to solve the selfconsistent problem. With the help of eq 1, the system of E ω,i can be written as equations dBi = Ri 3 B 0 2 3ð dBj 3 nBji Þ 3 nBji dBj dBi ¼ Ri @ E Bext, ω, i þ 4 rij3 j6¼ i # ! dBj ð dBj 3 nBji Þ 3 nBji ikpffiffiffi pffiffiffiffi 2 ε0 rij ð1 ik ε0 rij Þ þ ε0 k e ð6Þ rij
∑
This system will be solved numerically below for several geometries.
2. IDEAL HELICAL STRUCTURES We start with a right-handed Au-NP helix that has similar parameters to the structures in refs 18 and 25. However, we now calculate the extinction CD for longer helices when the scattering CD becomes involved. The smallest chiral helix is one with NNP = 4 since three (or less) spheres do not form a chiral object. 13256
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Figure 5. (a) Calculated normalized extinction CD, εextin,CD/NNP, for the helix with pitch = 15 nm and 4 NPs per turn. Other parameters are taken as before: aNP = 5 nm and R0 = 12 nm. (b) Calculated normalized extinction CD at two selected wavelengths λ = 530 and λ = 560 nm. These selected wavelengths approximately correspond to the extreme points of the CD spectra. Inset shows a helix NNP = 8 to scale.
Figure 6. (a) Calculated normalized extinction CD, εextin,CD/NNP, for the helices with pitch = 25 nm and 4 NPs per turn. Other parameters are taken as before: aNP = 5 nm and R0 = 12 nm. (b) Calculated normalized extinction CD at two selected wavelengths λ = 525 and λ = 555 nm. These selected wavelengths approximately correspond to the extreme points of the CD spectra. Inset shows a helix NNP = 9 to scale.
Figure 2a shows the results for normalized CD, εextin,CD/NNP, for NNP = 420. The parameters of the helix are: R0 = 12 nm, aNP = 5 nm, and pitch = 15 nm. The calculated CD spectra have a very typical, bisignated shape which appears in a system of interacting dipoles arranged in a chiral chemistry.18,27 The helix geometry in Figure 2 is relatively compressed, and therefore, the CD spectrum develops in a nontrivial way as NNP increases. The helix NNP = 4 shows the dip-peak CD line (blue curve in Figure 2a). The chirality here comes from the interaction of neighboring NPs located along a helical line. However, the helix NNP = 5 in this geometry has two closely located NPs along the zaxis. These NPs are a vertical pair, NP#1 and NP#5. Since an additional strong interaction contribution becomes involved, we may expect that a CD signal will change. Indeed, the CD line for NNP = 5 flips compared to the helix NNP = 4. Then, for the helix NNP = 6, the CD line appears to be similar to the case NNP = 5.
However, for NNP = 7, we again see a CD spectrum similar to the case of NNP = 4. For helices NNP = 820, we observe a very stable pattern—all CD spectra are similar and have a peak-dip shape. Our interpretation for this behavior is that the CD signals in helices NNP = 820 are governed by the Coulomb interaction in the vertical pairs (NP#1 and NP#5, NP#2 and NP#6, etc). In Figure 2b, we now show a normalized CD signal averaged over some interval of NNP ε extin, CD ¼
εextin, CD ∑ NNP ∑ eN eN
Nmin e NNP e Nmax Nmin
NP
ð7Þ
max
This averaging represents a simple type of disorder in a macroscopic ensemble containing helices with different lengths. We see that the CD is very consistent and does not change sign when we 13257
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Figure 7. (a) Calculated normalized extinction CD (εextin,CD/NNP) for 6-NP-per-turn helices with a variable pitch and a constant helical radius R0 = 8.5 nm; NNP = 13; and aNP = 2.5 nm. Inset: A model of the helix to scale. (b) Normalized CD extinction as a function of the pitch at the wavelength of the CD maximum λ = 552 nm.
Figure 8. (a) Calculated normalized extinction CD (εextin,CD/NNP) for 6-NP-per-turn helices with various defects. (a) A model of a perfect helix. (b) CD of the helix with one missed NP. (c) and (d): CD signals from the helices with two missed NPs (c) and three missed NPs (d). The parameters are: pitch = 19.2 nm, NNP = 10, aNP = 2.5 nm, and R0 = 8.5 nm. Insets show the structures to scale.
change the interval of averaging. This tells us that the CD signal is stable against this type of disorder. It is interesting to look at the scattering CD to understand the role of scattering in the CD effect (Figure 3). We see that, with increasing the length of the helix, the scattering contribution
grows, as expected, and becomes essential in the formation of the net extinction CD response. Overall, the behavior of scattering CD in Figure 3 is nontrivial because of electromagnetic interference effects of scattering NPs in a complex geometry. 13258
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Figure 9. Calculated normalized extinction CD for a 4-NP-per-turn helix with randomized positions of NPs (a) and randomized sizes of NPs (b). The ideal helix has the parameters: pitch = 25nm, aNP = 5 nm, and R0 = 12 nm. The graphs involve computer-generated random numbers for ∼45 trials. The amplitude of random variation of position of every NP was 1 nm in one direction. The amplitude of variation of NP size was taken as 1 nm.
We now look at a more stretched helical geometry: aNP = 5 nm, R0 = 12 nm, and pitch = 25 nm (Figure 4). We see that the signal becomes much stronger, and the CD shape does not change with increasing the length of the helix. The CD pattern is a dip-peak structure, like the CD spectrum of a compressed helix NNP = 4 in Figure 2a. This is consistent with our interpretation that the CD signals in the stretched helix (pitch = 25 nm) come from the Coulomb interaction between the neighboring NPs on the helical line. Since the CD spectrum does not change much with NNP, this geometry is more suitable for experimental realizations. If we increase the pitch further, the CD signal will decrease since the NPNP interaction will weaken. So, there is an optimal pitch (Poptimal) to achieve the maximum CD signal, and for aNP = 5 nm and R0 = 12 nm, this optimal pitch depends on a helix length; if NNP = 4, Poptimal ∼ 27.9 nm; for NNP = 10, Poptimal ∼ 36.5 nm. For another case (a helix with six NPs for a pitch and NNP = 13), we can see similar properties in Figure 7. In particular, one can see in Figure 7b that the system has an optimal pitch for the CD signal. Comparing the results for compressed and stretched helices, we can see that, for short helices (NNP ∼ 10), one can expect that the CD spectrum can flip with increasing pitch. For pitch = 15 nm, the most typical spectra have a peak-dip shape, while for pitch = 25 nm all CD spectra have a dip-peak pattern. In helical NP structures assembled with soft biomolecules, the geometry can be controlled chemically, and therefore, the pitch can be varied. Such variation of pitch may result in flipping of the plasmonic CD signal.15 Often a NP bioassembly does not contain a large number of NPs.28,29 In this case, our results for NNP = 420 are applicable. Nevertheless, it is also interesting to look at the CD signals of long helices (Figures 5 and 6). The stretched helix with pitch = 25 nm has a strong, positive CD at λ = 555 nm, and the normalized CD (εextin,CD/NNP) first increases and then becomes saturated, as expected (Figure 6b). For the relatively compressed helix (pitch = 15 nm), we see a different and more complex picture. First, the CD signal at λ = 560 nm becomes two times positive for NNP = 4 and NNP = 7, and then it stays negative until NNP ∼ 20. However, for very long helices, the CD signal at λ =
560 nm becomes always positive. We attribute these complex behaviors to the interplay between near-field Coulomb (short helices) and long-range electromagnetic (long helices) interactions in the NP assembly. Interestingly, by looking at the geometry of the helices shown to scale in the insets of Figures 5 and 6, it seems that the geometry is not so much changed when the pitch goes from 15nm to 25nm, but the CD signals can be significantly different. This tells us that, in experiments, we should expect that the CD signal depends on how much a NP helix is stretched or compressed. In other words, a sign of CD signal at a fixed wavelength is expected to be dependent on a linear NP density in a helix. Finally, we also look at the helix with six NPs for one pitch (6-NP-per-turn helix). We now take smaller NPs: the NP radius aNP = 2.5 nm. The other parameters are: R0 = 8.5 nm and NNP = 13. Then, it is interesting to observe how the CD signal varies with the pitch of the helix (Figure 7). For a small pitch, CD is weak because the helix has not well expressed chirality; the twisting pattern is not developed yet. For large pitches, the NPNP interaction is weak, and CD should rapidly decrease (∼1/R8).18 Therefore, there is an optimal pitch of the helix, and it is ∼20 nm for the helix with the chosen parameters (Figure 7b).
3. HELICAL STRUCTURES WITH DEFECTS We now look at a few types of disorder possible in experimental systems. 3.1. Missed NPs. Assume that one or a few NPs in a helix are missed. We take the helix with the following parameters: aNP = 2.5 nm, R0 = 8.5 nm, NNP = 10, and pitch = 19.2 nm. In Figure 8, one can see CD spectra of this helix in the presence of various defects. The CD spectral shape (bisignated structure) is amazingly stable against the considered defects. When we introduce one, two, or three missed NPs, the CD signal does not change its shape. Of course, the CD signal weakens with increasing number of defects since the NPNP interaction becomes reduced. 3.2. Variation of Helix Length. This case was briefly considered above in Section 2. Assuming that a solution includes helices of various lengths, we can model this type of disorder by 13259
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The Journal of Physical Chemistry C averaging the CD signals over different helices (eq 7). For the case of pitch = 15 nm and NNP = 420, we show the results in Figure 2b. One can see that the averaged CD signal has the same shape for all averaging methods used in Figure 2b. For the case of pitch = 25 nm and NNP = 420, we obtain a similar result. 3.3. Variation of Helix Pitch. The influence of this type of disorder can be understood from Figure 7. If a helix structure has on average a pitch ∼20 nm, a moderate variation of the pitch in an ensemble (by a few nanometers) can not change substantially the shape of the CD signal. Therefore, the averaged CD signal should remain strong in the presence of variations of pitch. 3.4. Helix with Randomized Positions and Sizes of NPs. Finally, we consider the case when NP positions in a helix are somewhat randomized (Figure 9a). Our helical complex now has NPs at the positions defined in the following way: ri = ri0 þ δri, where ri0 is the i-NP position in an ideal helix and δri is a random vector. The random vector is generated by a computer using a random-number generator. The amplitude of a position variation is 1 nm in one direction, i.e., 1 < δrR,i < þ1 nm, where R = x, y, z. The distribution of random numbers, δrR,i, within the variation interval is uniform. The results for helix NNP = 10 are shown in Figure 9a. We can see that the positional disorder does not disturb much the CD spectrum, and the CD response remains strong and pronounced. Fluctuations of CD amplitudes due to the disorder are relatively small. The CD signal averaged over the trials does not change essentially. For example, we look now at the CD maximum at λ = 560 nm, and we see that CDdisordered helix, 1 averaged ∼ CDideal helix ∼ 14 000 (M cm) . In Figure 9b, we show a similar plot for a helix with randomized NP sizes: 4.5 nm < aNP,i < 5.5 nm. Again, we see that the CD spectra in the presence of disorder show consistently the dip-peak structure as a function of the wavelength.
’ CONCLUSIONS We have shown that the plasmonic CD spectrum in a spherical NP helix is stable against an introduction of disorder. This tells us that the helical geometry and spherical NPs are very suitable for designing optical chiral meta-fluids composed of plasmonic nanoscale complexes. The calculated anisotropy factors in our dipolar theory are moderate (εextin,CD/εextin ∼ 2 104) since the theory is dipolar and the interparticle distance cannot be made very small. It is likely that much larger anisotropy factors are possible to achieve by considering structures with smaller interparticle distances within the multipolar theory. Another possibility to increase the anisotropy factor is to involve continuous helical nanostructures.35,36 The property of robustness of CD signals in disordered NP helices, observed in our calculations, somewhat resembles the well-known case of helical biomolecules such as proteins.26,27 It is known that proteins exhibit strong CD signals in the UV wavelength range even in the random coil conformational state.27 From this point of view, it may look natural that disordered AuNP helices have stable, defect-tolerant CD signals. Yet, it is important to identify optimal parameters for the plasmonic NP helices. In fact, any macroscopic system of nanoscale plasmonic complexes with some amount of chiral correlations in its geometry is expected to show some nonzero CD signal, but again the problem is to identify the best conditions when the CD signal is strong and defect-tolerant. This paper predicts that the helical NP complexes with optimized parameters should produce strong CD in the presence of defects. Many molecules are chiral and
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exhibit strong CD but mostly in the UV range. In contrast, the plasmonic NP structures are able to create CD signals in the visible range that may be very useful for the design of new optical materials and devices.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by Volkswagen Foundation and NSF (project number CBET-0933415). ’ REFERENCES (1) Moloney, M. P.; Gun’ko, Y. K.; Kelly, J. M. Chem. Commun. 2007, 3900. (2) Gautier, C.; B€urgi, T. ChemPhysChem 2009, 10, 483. (3) Molotsky, T.; Tamarin, T.; Moshe, A. B.; Markovich, G.; Kotlyar, A. B. J. Phys. Chem. C 2010, 114, 15951. (4) Cathcart, N.; Mistry, P.; Makra, C.; Pietrobon, B.; Coombs, N.; Jelokhani-Niaraki, M.; Kitaev, V. Langmuir 2009, 25, 5840. (5) Ha, J.-M.; Solovyov, A.; Katz, A. Langmuir 2009, 25, 10548. George, J.; Thomas, K. G. J. Am. Chem. Soc. 2010, 132, 2502. (6) Chen, W.; Bian, A.; Agarwal, A.; Liu, L.; Shen, H.; Wang, L.; Xu, C.; Kotov, N. A. Nano Lett. 2009, 9, 2153. (7) Goldsmith, M.-R.; George, C. B.; Zuber, G.; Naaman, R.; Waldeck, D. H.; Wipf, P.; Beratan, D. N. Phys. Chem. Chem. Phys. 2006, 8, 63. (8) Oh, H. S.; Liu, S.; Jee, H. S.; Baev, A.; Swihart, M. T.; Prasad, P. N. J. Am. Chem. Soc. 2010, 132, 17346. (9) Rezanka, P.; Zaruba, K.; Kral, V. Colloids Surf., A 2011, 374, 77. (10) Graf, P.; Mantion, A.; Haase, A.; Th€unemann, A. F.; Masic, A.; Meier, W.; Luch, A.; Taubert, A. ACS Nano 2011, 5, 820. (11) Qi, H.; Shopsowitz, K. E.; Hamad, W. Y.; MacLachlan, M. J. J. Am. Chem. Soc. 2011, 133, 3728. (12) Zhou, Y.; Yang, M.; Sun, K.; Tang, Z.; Kotov, N. A. J. Am. Chem. Soc. 2010, 132, 6006. (13) Carmeli, I.; Lieberman, L.; Kraversky, L.; Fan, Z.; Govorov, A. O.; Markovich, G.; Richter, S. Nano Lett. 2010, 10, 2069. (14) Slocik, J. M.; Govorov, A. O.; Naik, R. R. Nano Lett. 2011, 11, 701. (15) Wang, R.-Y.; Wang, H.; Wu, X.; Ji, Y.; Wang, P.; Qu, Y.; Chung, T.-S. Soft Matter 201110.1039/C1SM05590A. (16) Hendler, N.; Fadeev, L.; Mentovich, E. D.; Belgorodsky, B.; Gozin M.; Richter, S. Chem. Commun. 2011, online. (17) Xia, Y.; Zhou, Y.; Tang, Z. Nanoscale 2011, 3, 1374. (18) Fan, Z.; Govorov, A. O. Nano Lett. 2010, 10, 2580. (19) Govorov, A. O.; Fan, Z.; Hernandez, P.; Slocik, J. M.; Naik, R. R. Nano Lett. 2010, 10, 1374. (20) Govorov, A. O. J. Phys. Chem. C. 2011, 115, 7914. (21) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. Science 2003, 302, 419. (22) Halas, N. J. Nano Lett 2010, 10, 3816. (23) Maier, S. A.; Kik, P. G.; Atwater, H. A. Phys. Rev. B 2003, 67, 205402. (24) Cao, L.; Fan, P.; Brongersma, M. L. Nano Lett. 2011, 11, 1463. (25) Guerrero-Martinez, A.; Auguie, B.; Alonso-Gomez, J. L.; Gomez-Grana, S.; Dzolic, Z.; Zinic, M.; Cid, M. M.; Liz-Marzan, L. M. Angew. Chem., Int. Ed. 201110.1002/anie.201007536. (26) Circular dichroism and the conformational analysis of biomolecules; Fasman, G. D., Ed.; Plenum: New York, 1996. (27) Woody, W. W. Circular dichroism and the conformational analysis of biomolecules; Fasman, G. D., Ed.; Plenum: New York, 1996; pp 2567. 13260
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