ARTICLE pubs.acs.org/Langmuir
Morphology-Dependent Voltage Sensitivity of a Gold Nanostructure Yu Huang,* Mark C. Pitter, and Michael G. Somekh IBIOS, Department of Electrical and Electronic Engineering, University of Nottingham, Nottingham NG7 2RD, U.K. ABSTRACT:
Gold nanostructures of various morphologies, including nanospheres, nanorods, nanoprisms, and thin films, were immobilized on ITO-coated coverslips in order to investigate the response of their scattering to potential. Shifts in the plasmon band obtained by potential-modulated spectroscopic imaging indicated that the voltage sensitivity of the gold nanostructure is dependent on its morphology, with nanospheres exhibiting the lowest sensitivity and ultrathin gold films exhibiting the highest. The effects of potential on gold nanoparticles are in qualitative agreement with Mie and Gans’ theories in which the shift of the gold plasma frequency is due to the chargingdischarging of the nanoparticles.
’ INTRODUCTION Recent experimental work has demonstrated that it is possible to detect action potentials (APs) in live cells both ex vivo1 and in vitro2 by exploiting plasmon resonance. In ref 1, surface plasmon resonance was used to image nerve cells, and in ref 2, a structured gold nanoparticle array was employed. These results are significant and of great interest to the neuroscience and cardiac imaging communities because traditional methods of visualizing the physiological potential all suffer from serious limitations. Currently, extracellular and intracellular neural recording are the prime techniques used to access the neural network in order to try to monitor and understand neural activity. Traditionally, direct electrical access to nerve tissue in vitro and in vivo is achieved by the patch-clamp method, where sensors ranging from metal wires to micropipets are inserted directly into the neuron.2,3 However, the simultaneous recording of the activities of even a small number of cells over extended periods of time requires strategic innovation to replace the invasive microelectrode method. To this end, voltage-sensitive fluorescent dyes have been developed as a relatively noninvasive method to record the neural signal optically. Fluorescence probes the change in membrane potential and transduces it as a change in its emission intensity or spectrum. But fluorescent dyes’ inherent drawbacks, such as photobleaching and phototoxicity, severely restrict their applications.4 The plasmon frequency of a noble metal nanostructure is determined by its electron density. An increase in the electron density results in an increase in the plasmon frequency and leads to a blue shift of the plasmon band, as demonstrated by either adding chemical reductant5,6 or with the aid of an electrode to transfer electrons to particles.711 The existence of r 2011 American Chemical Society
an electron-density-dependent LSPR response brings about a possible new application for metal particles in monitoring neural activities. References 1 and 2 present convincing experimental results that nonlabeled wide-field optical methods can be used to perform the task of voltage sensing. The size and shape are known as important factors in determining the particle’s optical and electronic properties. The high voltage sensitivity will determine the success of recording extremely small, fast cellular signals. In this article, we report the experimental and simulation results of a systematic study on a range of possible voltage-sensitive gold nanostructures consisting of nanospheres, nanorods, nanoprisms, and films. The observed change in scattering was mainly due to the chargingdischarging process of the nanostructures. The relationship between the morphologies of the gold nanostructures and their ability to sense voltage has been investigated in detail. Nanospheres exhibited the smallest voltage sensitivity, and the inexpensive ultrathin gold film provided the greatest voltage sensitivity.
’ EXPERIMENTAL SECTION Substrate Preparation. Indium tin oxide (ITO)-coated coverslips (surface resistivity of 1530 Ω/sq, Structure Probe, Inc.) were cleaned by immersion in acetone and isopropanol for 5 min each in an ultrasonic bath and then rinsing copiously with water purified on a Milli-Q 18 MΩ cm system. This procedure was repeated at least three times, and then the coverslips were dried at room temperature. Received: July 31, 2011 Revised: September 24, 2011 Published: September 27, 2011 13950
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light from the nanostructure, and the reference camera monitored the light-intensity stability at each wavelength and therefore minimized the effect of any fluctuations in the light source. The potential of the working electrode was controlled with a VersaSTAT 3 potentiostat (Princeton Applied Research). An Ag/AgCl (saturated NaCl) wire and a coiled Au wire were immersed in the 0.1 M NaCl electrolyte and functioned as reference and counter electrodes, respectively. The potentials cited are with respect to the reference electrode.
Figure 1. Schematic of the dark-field imaging spectrometer configuration. L, achromatic lens; BS, pellicle beamsplitter; ND, neutral density filter; MS, motorized stage; OD, opaque disk; and FS, field stop.
Nanostructure Preparation. Gold nanospheres of 100 ( 5 nm diameter and two types of cetyltrimethylammonium bromide (CTAB)stabilized gold nanorods with d = 25 ( 4 nm, L = 60 ( 4 nm and d = 25 ( 4 nm, L = 73 ( 6 nm (d is diameter, L is length) were purchased from BB International and Nanopartz Inc., respectively. A drop of the diluted colloidal solution was casted in the center of a cleaned ITO-coated coverslip in order to immobilize the nanoparticles as the solvent evaporated from the substrate. Sufficient spatial separation between each nanoparticle was maintained to permit single-particle measurements. The Au nanoprisms studied in this work were fabricated by nanosphere lithography (NSL).1214 A suspension of diluted polystyrene polymer that was 2 μm in diameter (Invitrogen Detection Technologies) was dropcoated onto the ITO substrate. The microspheres dispersed freely across the substrate, allowing self-assembly into a close-packed, hexagonal 2D colloidal crystal on the substrate. Au films with nominal thicknesses of 16 and 50 nm were thermally evaporated over the microsphere masks. Evaporation was performed under high vacuum at a base pressure of (12) 106 Torr. An Edwards FTM-5 film thickness monitor was used to monitor the evaporation rate and the mass thickness of the Au film during the deposition. The thickness of the Au film was measured after deposition by a Rank Taylor Hobson Talystep surface profilometer. Following gold deposition, the microsphere mask was removed to leave gold triangles by ultrasonicating the sample in ethanol. In addition, two sets of plain Au films with nominal thicknesses of 16 and 50 nm were also prepared in the thermal evaporation system as described above. Standard glass coverslips were used for the plain gold films because the gold itself was used as an electrode. Spectroelectrochemical Measurements. An in-house-constructed spectroelectrochemical cell permitted the backscattered light of the Au nanostructure prepared on the substrate (which served as the working electrode) to be recorded by a custom-built reflected-light darkfield imaging inverted microscope, which employed a linear variable interference filter (VIS-NIR 200, Edmund Optics) to select the wavelength of unpolarized white light provided by a halogen lamp and two CCD cameras (SXVF-M7, Starlight Xpress) performing as imaging and reference sensors, respectively. A schematic of this dark-field imaging spectrometer is shown in Figure 1. The angle of incident light was designed to be 44°. The imaging camera was used to detect the scattered
’ POTENTIAL-DEPENDENT OPTICAL PROPERTIES OF GOLD NANOPARTICLES The plasmon resonance of nanoparticles of noble metals such as Au and Ag is dependent on their conduction band electron density. The chargingdischarging of the nanoparticle initially takes place at the particleelectrolyte interface.7,8,15,16 The counterions attracted by the electrified nanoparticle move toward the nanoparticle surface and establish an electrical double layer.17,18 Because of electron screening, the charge stored by the double-layer capacitor accumulates at the nanoparticle surface but affects only the electron density of the nanoparticle within the ThomasFermi screening length.19,20 The modulation of the electron density leads to a change in the gold plasma frequency within the ThomasFermi screening length and a consequent change in the plasmon resonance of the entire particle. An increase in the electron density within the nanoparticle results in an increase in its plasma frequency and leads to a blue shift in its plasmon resonance band. A coreshell nanoparticle consisting of confocal ellipsoids was used to model the response of gold nanoparticles to the potential, where the core ellipsoid with semiaxes a1, b1, and c1 is coated with a confocal shell representing the ThomasFermi screening layer with semiaxes a2, b2, and c2. The dielectric function of the core (ε1) was assumed to be unperturbed by the potential; however, the dielectric function of the shell (ε2) was dependent on the applied potential. The gold nanoparticle is illuminated by light in the visible and near-infrared regions, so its dielectric function is described by a DrudeLorentz mode21 with a consideration of surface scattering to correct for nanoparticle size.22,23 The potential-modulated optical scattering of a gold nanosphere was calculated by using a custom program based upon functions of Mie scattering for concentric sphere geometry written by M€atzler.22,24,25 In the case of nanospheres, the diameter d (a2 = b2 = c2 = d) of the particle and the complex refractive indices of the core and shell are the required parameters for the calculation. The Mie model can account only for the spherical particles, so the optical response of gold nanorods to the potential was modeled using Gans’ theory, an extension of Mie theory to particles with a spheroidal shape.26,27 The expression for the particle polarizability is22 αi ¼
4πa2 b2 c2 3
ðε2 εm Þ½ε2 þ ðε1 ε2 ÞðL1i fL2i Þ þ f ε2 ðε1 ε2 Þ ½ε2 þ ðε1 ε2 ÞðL1i fL2i Þ½εm þ ðε2 εm ÞL2i þ fL2i ε2 ðε1 ε2 Þ
ð1Þ where subscript i denotes the three semiaxes a, b, and c, εm is the relative permittivity of the surrounding medium, f = a1b1c1/a2b2c2 is the fraction of the total particle occupied by the inner ellipsoid, and L1i and L2i are the depolarization factors characterized by the 13951
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ratio of three principal semiaxes of inner and outer ellipsoids, respectively. For the case of a prolate spheroid, a > b = c, 1 e2 1 1 þ e ln 1 ð2aÞ La ¼ 1e e2 2e Lb ¼ Lc ¼
1 La 2
ð2bÞ
where e is dependent on the length of three semiaxes, e = (1 (b1/a1)2)1/2 for the calculation of L1a , and e = (1 (b2/a2)2)1/2 for the calculation of L2a .
Figure 2. Dark-field images of nanorods (d = 25 ( 4 nm, L = 60 ( 4 nm) at a wavelength of 680 nm (a) exposed to air and (b) immersed in solvent.
The scattering cross section of the particle, averaged over all orientations, is given by Csca ¼
k4 ½jαa j2 þ jαb j2 þ jαc j2 18π
ð3Þ
where k = 2π(εm)1/2/λ is the wave vector in the surrounding medium.
’ SCATTERING OF GOLD NANOPARTICLES MODULATED BY THE POTENTIAL Individual gold nanoparticles were immobilized on a substrate. The dark-field images of gold nanorods (d = 25 ( 4 nm, L = 60 ( 4 nm) at an illumination wavelength of 680 nm are shown in Figure 2 as an example. The nanorods were well distributed and isolated to reduce the probability of plasmonic interactions. The scattering spectra of the gold nanoparticles were acquired by using the dark-field imaging spectrometer. The shift in scattering spectra of three kinds of eight nanoparticles with known sizes and shapes from air to NaCl aqueous solution and the representative SEM images of these nanoparticles used to obtain these optical measurements are illustrated in Figure 3. The red shift of their scattering spectra and the decrease in scattering magnitude when the nanoparticles were immersed in solvent are very noticeable.
Figure 3. Scattering spectra of gold nanoparticles and corresponding SEM images. Solid and dashed lines in a, c, and e represent nanoparticles exposed to air and immersed in solvent, respectively. (a, b) Nanospheres with a diameter of 100 ( 5 nm. (c, d) Nanorods with d = 25 ( 4 nm and L = 60 ( 4 nm. (e, f) Nanorods with d = 25 ( 4 nm and L = 73 ( 6 nm. 13952
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Figure 4. Scattering of nanorods (d = 25 ( 4 nm and L = 60 ( 4 nm) at wavelengths of (a, b) 662, (c, d) 684, and (e, f) 729 nm. (a, c, and e) Scattering response to (200 mV from an individual nanoparticle. (b, d, and f) Ensemble response of eight individual particles at their corresponding wavelengths.
Nanoparticles grown by the seed-mediated method undergo small variations in their morphologies, causing each individual nanoparticle to have its own unique spectrum. It is anticipated that the spectra of nanorods have two plasmon resonance peaks instead of the single peak observed from spherical particles, a longitudinal and a transverse resonance. However, the scattering spectra of the nanorods exhibited a pronounced longitudinal resonance peak but a barely visible transverse resonance at around 510520 nm even for the larger nanorods. This is different from their absorption spectra, where the two resonance peaks can be observed. It is reasonable to take the absorption into account because it dominates the spectral response. The weak scattered light exhibited by electron oscillation along the transverse direction compared to the strong enhancement of longitudinal resonance enlarges the ratio of these two peaks. In addition, the gold interband absorption threshold of 2.5 eV overlapping the transverse resonance further damps the transverse resonance amplitude.2830 To discern the response of each nanoparticle to a potential, the scattering strength modulated by a square wave of (200 mV (mode A) was recorded at several single wavelengths. The imaging and reference cameras recorded three images during the application of
each half period for the purposes of imaging and calibration, respectively. A sequence of 120 images was acquired with 60 corresponding to 200 mV and 60 corresponding to 200 mV. It is clear that the sign of the response to a potential changes on either side of a scattering peak for the nanorods (d = 25 ( 4 nm, L = 60 ( 4 nm, peak scattering in aqueous solution λmax = 680690 nm), as shown in Figure 4. A positive potential reduced the scattering at 662 nm to the left side of the spectral peak, and enhanced the scattering at 729 nm to the right side of the peak. As expected, very little response was observed at wavelengths close to the resonance peak. To characterize the optical response of nanoparticles to a potential, a measure of the contrast, which is defined as the ratio of the difference to the sum of the scattering at each potential, is used i ¼ 60
i ¼ 60
i ¼ 60
i ¼ 60
ð Cscattering ¼ ð 13953
∑ Ihigher_i i∑¼ 1 Ilower_i Þ i¼1 ∑
i¼1
Ihigher_i þ
∑
i¼1
ð4Þ
Ilower_i Þ
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Figure 5. Scattering contrast of (a, b) 100 ( 5 nm nanospheres, (c, d) d = 25 ( 4 nm and L = 60 ( 4 nm nanorods, and (e, f) d = 25 ( 4 nm and L = 73 ( 6 nm nanorods. (a, c, and e) Scattering contrast of eight individual particles and (b, d, and f) their corresponding ensemble scattering contrasts calculated as the average contrast of eight individual particles.
where Ihigher_i and Ilower_i are the ith scattering intensities recorded at higher and lower potentials, respectively. The wavelengthdependent scattering contrast of the nanoparticles is shown in Figure 5, including eight individual nanoparticles and their ensembleaveraged contrast. The contrast from nanorods is clearly greater than for 100-nm-diameter nanospheres. The different signs on either side of the nanorods’ spectral peak coincide with the modulated scattering observed in Figure 4. A positive potential produces the opposite effect on the particle’s scattering on the left and right of the spectral peak, which is strong evidence to support the fact that a positive potential red shifts the spectrum and a negative potential induces it to blue shift. Taking the scattering spectra collected in Figure 3 into account, the largest contrast is detectable at the shoulder of the spectrum whereas the spectral peak is the least sensitive. The aspect ratios of the nanospheres (100 ( 5 nm) and nanorods (d = 25 ( 4 nm, L = 60 ( 4 nm and d = 25 ( 4 nm, L = 73 ( 6 nm) increase as 1, 2.4, and 2.92, which corresponds to the same order as their scattering contrast. It implies that their voltage sensitivities are correlated to their morphologies.
The optical characteristics of nanoparticles undergo a dramatic change as their shape changes from spherical to elongated rods.26,3134 To explore the influence of the particle’s morphology on its voltage sensitivity, Figure 6 shows the two calculated measures of the scattering contrast and the signal-to-noise ratio (SSNR) for a range of sizes and shapes of gold spheres and spheroids in the presence of (200 mV. (The calculation procedure is outlined in the Appendix.) The scattering contrast and SSNR of gold nanospheres whose diameter increases from 1 to 100 nm are shown in Figure 6a,b, respectively. Two features are apparent in this figure. First, smaller particles have a larger scattering contrast. Second, as the diameter increases, the effect of a potential on larger particles is more easily detectable because of the higher SSNR. The scattering contrast and SSNR of spheroidal particles with volume equivalent to that of a 20-nm-diameter sphere are presented in Figure 6c,d, respectively. The increase in the aspect ratio of this spheroid caused an increase in the surface area to volume ratio from 1.346 109 to 1.521 109 m1 and correspondingly resulted in a large scattering contrast and SSNR. Figure 6e,f shows the calculated results of the spheroid with a constant width of 25 nm and an elongated length. Although the 13954
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Figure 6. Calculated scattering contrast and SSNR for (a, b) a gold nanosphere with diameter increasing from 1 to 100 nm, (c, d) a gold spheroid with the same equivalent volume to a sphere diameter of 20 nm, with the major axis increasing from 20 to 80 nm and the minor axis decreasing from 20 to 10 nm, and (e, f) a gold spheroid with a constant width of 25 nm and an elongating length from 25 to 100 nm.
surface area to volume ratio decreased from 7.757 108 to 3.273 108 m1 when the size of the spheroid increased with its length in this case, the enlarging aspect ratio sustains the high scattering contrast and SSNR. These trends are in good agreement with the experimental data. In contrast, larger particles result in overwhelmingly greater SSNR values whatever the scattering contrast, especially for spheres that have only a weak scattering contrast. This is due to larger particles scattering much more strongly so that there are more photons available for detection even if the larger particle only has a small spectral shift.
’ POTENTIAL-MODULATED SCATTERING OF A GOLD FILM AND GOLD NANOPRISMS The morphology of nanoparticles has been shown in the previous section to be a key factor in determining a particle’s voltage sensitivity. A powerful attribute of the surface plasmon resonance frequency is that it can be tuned across the whole visible and nearinfrared spectrum by tailoring the particles’ geometry. An obvious method of improving the voltage sensitivity is to exploit the nanostructure with different morphologies. Two kinds of Au films and Au nanoprisms with 16 and 50-nmhighs, respectively, were prepared. Their dark-field images, spectra, and SEM images are shown in Figures 7 and 8. The scattering
Figure 7. Dark-field images of (a) a 16-nm-thick Au film, (b) a 50-nmthick Au film, (c) a Au nanoprism with an in-plane length of ∼466 nm and an out-of-plane height of ∼16 nm, and (d) a Au nanoprism with an in-plane length of ∼466 nm and an out-of-plane height of ∼50 nm. The Au nanostructures were immersed in solvent. Images a, b and c, d were taken at wavelengths of 707 and 653 nm, respectively. 13955
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Figure 8. Scattering spectra of a gold film, a gold nanoprism, and representative SEM images. (a, b) A 16-nm-thick gold film. (c, d) A 50-nm-thick gold film. (e, f) A gold nanoprism with an in-plane length of ∼466 nm and an out-of-plane height of ∼16 nm. (g, h) A gold nanoprism with an in-plane length of ∼466 nm and an out-of-plane height of ∼50 nm. Solid and dashed lines in a, c, e, and g represent the spectra of the Au nanostructure measured in air and solvent, respectively.
strength of eight regions on the gold film (Figure 8a,c), each corresponding to a sample area of approximately 0.5 μm2, continued to increase with wavelength across the whole instrument range, indicating that the resonance peak was in the infrared part of the spectrum. The 16 nm Au film scattered more strongly than did the 50 nm film because of its rougher surface, which can be seen in SEM images in Figure 8b,d. The scattering spectra of two kinds of eight single Au nanoprisms fabricated by NSL using a
2 μm sphere, whose in-plane length was ∼466 nm and out-ofplane heights were ∼16 and ∼50 nm, are shown in Figure 8e,g. The approximately 14 nm red shift caused by changing the nanoprisms’ surrounding environment from air (λmax = 808 nm) to 0.1 M NaCl (λmax = 822 nm) was observed from the average spectra of 50-nm-high nanoprisms (Figure 8g). By decreasing the height of the nanoprism from 50 to 16 nm, the aspect ratio of the thin nanoprism was increased 3-fold compared to that of the 13956
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Figure 9. Wavelength-dependent scattering contrast of (a, b) a 16 nm Au film, (c, d) a 50 nm Au film, (e, f) 16-nm-high Au nanoprisms, and (g, h) 50-nm-high Au nanoprisms under potential applied as mode A. (a, c, e, and g) Scattering contrast of eight individual objects. (b, d, f, and h) Their corresponding ensemble scattering contrast.
50-nm-high nanoprism.14 Its peak wavelength in solvent was shifted further into the infrared region from it spectrum in air (λmax = 832 nm), outside of the wavelength range of analysis (Figure 8e). Because there is a significant change in the morphology of the gold film and gold nanoprism compared to that of the gold nanoparticle, their responses to the voltage are obviously different, as shown by their wavelength-dependent scattering contrast under the voltage application of mode A in Figure 9. The maximum
ensemble scattering contrast of the 16 nm Au film is 1 102 at about 600 nm. The trend in the individual scattering contrast against wavelength was similar in each region, although there were distinct differences between values. Compared to the potentialdependent scattering contrast of the 16 nm Au film, the 50 nm Au film's response to voltage was much reduced. It should be noted that the current experimental setup, the unspecific polarization of the incident beam, and the incident angle lower than the total 13957
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Figure 10. Potential-induced scattering of (a) a 16 nm Au film and (b) 16-nm-high Au nanoprisms, which was averaged from eight corresponding objects. The sequence of the potential was (200 > (150 > (100 > (50 > (25 > (10 > 0 mV. The red upward and blue downward triangles represent positive and negative potentials, respectively. The cyan line is drawn as a guide to the eye. Experimental scattering contrast as a function of potential for (c) a 16 nm Au film and (d) a 16-nm-high Au nanoprism (red squares) and their corresponding fits (blue circles) using eq 5.
internal reflection angle are different from those in the 50 nm Au film employed in the electrochemical surface plasmon resonance with the KretchmannRaether configuration. This indicates that the experimental conditions can determine the measurement result. Differing from the 50 nm Au film, the effect of voltage on the 50nm-high nanoprism was recognizable and comparable to the response of the nanorods. Because of the high aspect ratio possessed by the 16-nm-high nanoprisms, they exhibit a contrast of almost 0.7%. Because the range of illumination wavelengths employed were to the left side of the Au film and Au nanoprisms’ spectral peak, the positive potential decreased the scattering (by causing a red shift) but the negative potential enhanced it (corresponding to a blue shift), resulting in the negative scattering contrast. Because the 16 nm Au film and 16-nm-high Au nanoprism provide a high scattering contrast, it was possible to investigate their sensitivity to smaller voltages. The scattering modulated from seven potential-modulated modes applied consecutively, whose potential decreased as (200 > (150 > (100 > (50 > (25 > (10 > 0 mV, and the corresponding scattering contrast are shown in Figure 10. The illumination wavelengths for the 16 nm Au film and 16-nm-high Au nanoprisms were 618 and 640 nm, respectively, because they were the location of the highest scattering contrast induced by mode A as shown in Figure 9. The higher and lower scattering induced by the two polarized potentials clearly indicated that the positive and negative potentials had opposite effects on the properties of the Au film and Au nanoprism. The relationship between the scattering contrast and the potential was fitted to CðV Þ ¼ AV c
power to determine the nonlinearity. The best fits of (A, c) to the Au film and Au nanoprism were (0.1227, 1.319) and (0.0298, 0.901), respectively. Comparing the value of c determined from the Au film and Au nanoprism, the voltage sensitivity of the Au nanoprism improves slightly at lower potential and is much more linear than that of the 16 nm Au film.
’ DISCUSSION There are two reasons that can be proposed for the change in the spectrum and intensity of the Au nanostructure in response to an applied potential. The first is a change in the dielectric environment surrounding the metal as a result of the arrangement of ions, and the second is the chargingdischarging of the Au nanostructure. In the current experiment, a series of positive and negative potentials have been applied to a 16 nm Au film and 16-nm-high Au nanoprisms, which produced an approximately symmetric trend in scattering with respect to its value at 0 V as shown in Figure 10a,b. This indicates that the scattering of the Au nanostructure was predominately affected by the electron transport to and from the Au nanostructure because the associated change in the index of the solvent would lead to an asymmetrical response. The potential-induced shift of the plasmon scattering band is attributed to the chargingdischarging of Au nanostructure. If we ignore the electron interband transition and the size effect, the dielectric behavior of gold is well described by the Drude model εðωÞ ¼ ε∞
ð5Þ
where A is the parameter used to scale the fitting value, V is the absolute potential in units of volts used in each mode, and c is the
ωD 2 ωðω þ iγD Þ
ð6Þ
where ω is the angular frequency of light, ε∞ is the dimensionless high-frequency limit contributed by the interband transition 13958
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of electrons, and γD is the damping coefficient due to the dispersion of the electrons. The plasmon frequency ωD is given by sffiffiffiffiffiffiffiffiffiffi Ne2 ωD ¼ ð7Þ m ε 0 where N is the free electron density, e is the charge of an electron, ε0 is the permittivity of vacuum, and m* is the effective mass of an electron. Applying a potential to the particle alters its free-electron density because of the properties of particle double-layer charging discharging. Consequently, the plasmon frequency can be written as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðN þ ΔNÞe2 ωDf ¼ m ε 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8Þ ffi ΔN ¼ 1 þ ωD N In the dipole approximation, the polarizability of an ellipsoidal particle is22 α¼
4πabc ε1 εm 3 εm þ ðε1 εm ÞL
ð9Þ
At wavelengths where the imaginary part of the dielectric function of gold has a weak dispersion, the condition for the presence of longitudinal wavelength peak λp is that the denominator of polarizability α corresponding to the major axis vanishes L1 εm ð10Þ L Using eqs 6 and 10, the longitudinal wavelength peak is then expressed as Reðε1 Þ ¼
2πc 2πc ffi ≈ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λp ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u u ωD ωD 2 u γD 2 u t t 1L 1L εm εm ε∞ þ ε∞ þ L L
ð11Þ
where c is the speed of light in vacuum and γD , ωD. The change in the longitudinal wavelength peak as a result of the applied potential is Δλp
¼ λp f λp i 2πc 2πc vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u u ωDf ωD 2 u u t t 1L 1L εm εm ε∞ þ ε∞ þ L L 0 1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C 2πcB 1 1L B C r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi B1 C ε∞ þ εm ¼ A ωD @ L ΔN 1 þ N ð12Þ
The shift of the longitudinal wavelength peak is assumed to represent the shift of the whole spectrum. Therefore, eq 12
indicates the relationship between the shift of the spectrum and the alteration of the electron density and particle aspect ratio AR. Because Δλp is proportional to ΔN and AR (AR is inversely proportional to L and is proportional to (1 L)/L), a larger value of ΔN and a higher AR are expected to achieve a greater spectral shift. For particles with the same aspect ratio, the change in electron density determines the spectral shift. The perturbed scattering in the presence of an applied potential is attributed to the electrical double layer that provides the charging and discharging process of electrons to particles. The change in electron density is confined to the domain of the ThomasFermi screening layer. The surface charging of the particle is dependent on the sizeindependent double-layer capacitance per unit surface area.15 The capability of accumulating electrons is elevated by a larger surface area, and the electron density is inversely proportional to the volume. A particle with a larger surface area but a smaller volume experiences an enormous alteration of its electron density as a function of the applied potential. Considering a particle much smaller than the wavelength of light, the electric field is quasiconstant throughout the particle and the incident light induces all of the electrons in the particle, including the electrons in the ThomasFermi layer, to have a collective oscillation and give rise to the surface plasmons at the particle surface. Hence, the surface area to volume ratio has a positive correlation to the scattering contrast. The influence of the surface area to volume ratio is weaker compared to that of the particle’s aspect ratio. As predicated by eq 12, for a fixed surface area to volume ratio that results in a constant ΔN or even smaller ΔN shown in Figure 6e, the wavelength shift is higher for particles with a larger aspect ratio. In the dipole approximation, the depolarization factor L represents the ease with which an electron cloud can be polarized to the particle surface against the Coulombic restoring force of a positive atomic lattice by light.35,36 From eq 9, a smaller value of L produced by a higher aspect ratio results in a larger polarizability of the particle, and the electron cloud will be displaced more easily. The larger aspect ratio leads to a greater ease of polarization of the particle, which compensates for the same or a smaller electron density modification. Thereby, a particle with a higher aspect ratio can exhibit a greater scattering contrast, even if its geometry constrains its change in electron density. Both the 16 nm and the 50-nm-high nanoprisms have sharp tips and corners,37 leading to a high charge density in the surface region and a large enhancement of the electric field intensity.38,39 The high curvature of 50-nm-high nanoprisms led to a large scattering cross section and resulted in a scattering contrast that was comparable to that of nanorods and much better than that of the 50 nm Au film. The higher aspect ratio of the 16-nm-high nanoprisms led to a scattering contrast that was nearly 3 times larger than its counterpart. When two noble metal nanoparticles approach each other closely, the plasmon resonance oscillations on the individual nanoparticle overlap and couple with each other, strongly affecting the plasmonic resonance energies.35,37 The Au nanoprism array is a periodic tip-to-tip structure with a 1.1 μm interparticle spacing (approximate separation between the centers of the two particles), and two neighboring particles could produce weak electromagnetic coupling.14,40 This is different from the continuous 16 nm Au film, where conductively overlapped nanoislands41 produce a higher surface area to volume ratio and stronger plasmonic coupling. Stronger coupling leads to a higher value of particle polarizability and a greater ease of electron cloud displacement,35 which has a similar effect to the higher 13959
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aspect ratio and improves the particle’s response to the potential. Because of the nonlinear capacitance of the electrical double layer formed at the surface of the 16 nm Au film,17 a nonlinear quantity of charges as a function of voltage accumulated at this surface is reflected by the accelerated decline in its scattering contrast with reduced voltage shown in Figure 10c. Possibly as a result of the weakly coupled particle system, the scattering contrast of the 16nm-high Au nanoprisms is somewhat lower than that of the 16 nm Au film, but its scattering contrast is far more linear with voltage.
’ CONCLUSIONS The sensitivity of a range of plasmonic gold nanostructures to the modulated potential has been studied experimentally and theoretically. The difference in the scattered light performance among the Au nanoparticles, Au film, and Au nanoprisms under potential control confirms the size and shape effects on the surface plasmons and the important role that morphology plays in the determination of the voltage detection capability. The improvement in voltage sensitivity is proportionally correlated with a large surface area to volume ratio, a high aspect ratio, and strong plasmonic coupling. A larger surface area to volume ratio makes the particle undergo a drastic change in its electron density. The increase in the aspect ratio and plasmonic coupling strength leads the particle to have a larger polarizability. Sharp surface curvature is an additional factor that improves the sensitivity due to the electric field enhancement. The relationship between the morphology of the Au nanostructure and its voltage sensitivity provides an extremely useful guideline for exploring, designing, and developing ultrasensitive plasmonic nanoparticle voltage sensors. ’ APPENDIX We first consider the calculation of two measures, the scattering contrast and the signal-to-shot noise ratio (SSNR). The measure of the scattering contrast of the particle is defined as Ccontrast ¼
Csca_higher Csca_lower Csca_higher þ Csca_lower
ðA1Þ
where Csca_higher and Csca_lower represent the scattering cross section at the higher and the lower potentials, respectively. The measure of the signal-to-shot noise ratio (SSNR) was used to characterize the detected signal with regard to the number of detected photons. In the detection system, the overall detection efficiency η is written as ( 4 sin1 η¼
NA ncoupling π2
! )2
Idet_sca ¼ Isca ηTintegration
ðA4Þ
The numerous advantages of CCD sensors allow them to be applied widely, but CCD sensors are of course subject to noise, with the three primary components being photon noise, dark noise, and readout noise. In general, the effect of dark noise and readout noise can be reduced by the design of the CCD sensor. The shot noise generated by the arrival of photons within the sensor determines the fundamental limit of detection sensitivity. The scattered energy detected by the CCD sensor expressed in terms of the photon number is Ndet_sca ¼
Idet_sca Ephoton
ðA5Þ
where Ephoton is the energy of one photon, equivalent to hc/λ, h is Planck’s constant, λ is the wavelength of the beam, and c is the speed of light. The magnitude of the shot noise is governed by Poisson statistics and is equivalent to the square root of the signal in an integrating detector, so the signal-to-shot noise ratio (SSNR) is pffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ndet_sca SSNR det_sca ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ Ndet_sca Ndet_sca
ðA6Þ
The procedure for the utilization of SSNR to investigate the influence of the potential on a gold nanoparticle is described as follows. Spectra for the scattered light in terms of the detected number of photons induced by a higher potential and a lower potential were obtained. The difference in the detected number of photons due to the two potentials is the signal and the numerator of this ratio. The square root of the total number of photons is the noise and the denominator of this ratio. The division of the numerator by the denominator is the SSNR related to the potential, which is defined as Nhigher Nlower SSNR ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nhigher þ Nlower
ðA7Þ
where Nhigher and Nlower are the numbers of photons detected as scattered light at the higher and lower potentials, respectively. Ttran Q Eλ
ðA2Þ
’ AUTHOR INFORMATION Corresponding Author
where both the numerical aperture of the objective NA and the refractive index of the medium ncoupling separating the objective and the specimen determine the detection angle of the objective. In addition, the optical transmission Ttran and the quantum efficiency QEλ of the detection sensor contribute to the overall detection efficiency η as well. The total power of scattered light from the particle in all directions Isca is equal to the incident power falling on its scattering cross section Isca ¼ Iinc Csca
where Iinc is the irradiation of the incident beam and Csca is the particle’s scattering cross section. The energy of scattered light Idet_sca detected on the CCD sensor is the product of the scattering, the overall detection efficiency η, and the integration time Tintegration of the detection sensor
ðA3Þ
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC), U.K. ’ REFERENCES (1) Kim, S. A.; Byun, K. M.; Lee, J.; Kim, J. H.; Kim, D. G. A.; Baac, H.; Shuler, M. L.; Kim, S. J. Opt. Lett. 2008, 33, 914. (2) Zhang, J. Y.; Atay, T.; Nurmikko, A. V. Nano Lett. 2009, 9, 519. 13960
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