2.1.

Experimental

Colloidal gold particles with diameter of $100\mathrm{nm}$ were purchased from British Biocell (GC100). A diluted solution of gold colloid was directly deposited on a glass substrate with well-separated interparticle distances to measure the spectra from individual single particles. The deposited particles were physically bound to the glass substrate stable enough for water rinsing and a drying process by nitrogen blow. The measured particles had interparticle distances of $>2\mu \mathrm{m}$ from the neighboring particles, which is enough to avoid interparticle optical coupling.

A dark-field microscope (Axiovert 200, Carl Zeiss, Gottingen, Germany) equipped with a spectrophotometer (SpectraPro 2150, PIXIS 400, Princeton Instruments, Trenton, NJ, USA) was used to measure the scattering spectra. Numerical aperture (NA) of the illumination was 0.8–0.95, and NA of the objective 0.4. These correspond to the illumination angle of $53–72\mathrm{deg}$ and the detection angle within $24\mathrm{deg}$ in ambient condition. The measurement was performed in aqueous condition in a flow cell. A halogen lamp $\left(100\mathrm{W}\right)$ was used for illumination. Kinetic measurements were recorded and evaluated by a custom-made program that can eliminate the effect of focus-dependent peak shifts.

The molecular adsorption measurements were conducted using a $160\text{-}\mathrm{mM}$ buffer solution consisting of $10\mathrm{mM}$ 4-(2-hydroxyethyl)piperazine-1-ethanesulfonicacid with $150\mathrm{mM}$ NaCl, adjusted to pH 7.4 (HEPES). The concentration of the Immunoglobulin G (IgG) for the protein adsorption measurements was $100\mu \mathrm{g}∕\mathrm{mL}$ .

In this particular measurement set, we measured seven particles simultaneously and selected the largest, a midsized, and the smallest spherical particles, and a tetrahedral one, as representatives in this paper. Including separate measurement sets, we observed over 17 particles and basically saw the same effect, which will be described in the following sections.

A scanning transmission microscope [(SEM), Supra 50VP, Carl Zeiss, Germany] was used to observe the shape of the particles. The samples were coated with amorphous carbon for conductivity required for SEM imaging. All the images were taken at the acceleration voltage of $5\mathrm{kV}$ by an in-lens secondary electron detector. The same particles as the optical dark-field imaging were identified by comparing the orientation of the particles at low magnification with the previously taken optical dark-field images.

2.2.

Simulation

When the size of a plasmonic particle is $<150\mathrm{nm}$ and the illuminated wavelength is around visible, dipolar oscillation mode is dominant and, therefore, s-scattering is dominant.⁸ To calculate the scattering intensity, we measured $90\mathrm{deg}$ s-scattering at $2\mu \mathrm{m}$ away from the scattering object, where the evanescent component is negligible. We approximated all the particles as solids of rotation, and the illuminating plane wave was along the symmetry axis in order to take advantage of symmetry decomposition: only the first Fourier component [cos(1) type] around the symmetry axis should be considered for the (ring-)multipole expansions on the symmetry axis. The matching point slices are set at $45\mathrm{deg}$ from the electric- and magnetic-field vector of the excitation plane wave to include both components. Such treatment of symmetry decomposition reduces the virtual dimension of the 3-D problem to 2-D.¹⁵ The maximum relative error at the matching point was always $<0.5\%$ .

For the dielectric constant of gold, measured data by Johnson and Christy were used.²² The dielectric constants of solution and the protein adsorption layer were considered to be real and constant as the value of 1.777 $(n=1.333)$ and 2.1 $(n=1.45)$ , respectively.

3.1.

Spectra and Adsorption Kinetics

Figure 1 shows experimentally acquired scattering spectra of four individual gold nanoparticles in the buffer solution. LSPR peaks are observed around the wavelength of $600\mathrm{nm}$ . Particles A (blue) and B (pink) exhibited similar resonance intensities while the peak position of particle A is more redshifted than B. The spectral shape of particles C and D is similar to that of B with smaller intensities and more blueshifted resonance position.

Fig. 1

Experimental scattering spectra of four individual gold particles.

These four particles were used for a sensitivity test. The resonance peak shifts were plotted as functions of time in Fig. 2 to see the kinetics of the protein adsorption. The protein injections were conducted at 5, 300, 600, 2500, 2800 and 3200 s and rinsing with buffer solution at 950 and 2000 s. All four particles showed redshift of the resonance when protein molecules were injected, which saturated after a few minutes of adsorption. The redshift remained same after rinsing by buffer, confirming the sensing of the expected irreversible adsorption of proteins. Interestingly, particle A exhibited larger peak shift than the other three particles.

Fig. 2

Adsorption kinetics of IgG $(100\mu \mathrm{g}∕\mathrm{mL})$ on four individual particles of Fig. 1. Peak shift of each particle is plotted as a function of time. The thin lines represent the raw data. Smoothed data (thick lines) are superimposed to guide the eye. Rinsing was conducted at 5, 300, 600, 2500, 2800 and 3200 s by buffer solution, and at 950 and 2000 s by IgG solution.

3.2.

SEM Observation

We observed the four particles used for sensing by SEM. Figure 3 shows SEM images and corresponding optical dark-field images (insets), which confirm that same particles were observed in the optical measurements and in SEM. The measured particles are indicated by circles. Even after sample washing by water, drying, and subsequent carbon coating, the particles remained at the same position. The magnified SEM images of these particles are shown in Fig. 4 . The particles were imaged at different observation angles to clarify the 3-D shape of each particle. The image in the center corresponds to the observation angle normal to the substrate plane. The surrounded four images were taken at the zenithal angle of $30\mathrm{deg}$ with different azimuthal angles with $90\mathrm{deg}$ steps. A schematic of the observation condition is shown in Fig. 4e.

Fig. 3

SEM images and corresponding optical darkfield images (inset) of four measured particles to verify the same observation position. The measured particles are indicated by circles. The color of the indication circle and the numbering correspond to Figs. 1 and 2.

Fig. 4

Magnified SEM images of the four particles with different observation angles. The observation angles are schematized in (e).

The SEM images at different observation angles revealed that particle A was actually not spherical but tetrahedral because it looks triangular, square, and hexagonal, depending on the observation angles. On the other hand, the other three particles have rather spherical shapes. The sizes of the spherical particles B, C, and D are roughly estimated as 100, 90, and $80\mathrm{nm}$ , respectively. It should be noted that the particles were coated by carbon, which makes the particles appear larger with complicated contrast effects at the edges.

3.3.

Simulated Spectra and Sensitivity

On the basis of the SEM images, we have modeled the particles with different sizes and shapes: namely, sphere, rotated triangle, and rotated rhomboid with rounded edges. (See schematics in Figs. 5 and 6 .) We expected that the cone-shape particle (rotated triangle) emulates the tetrahedral particle A in the experiment. The sizes of the spherical particles were set to be 100, 90, and $80\mathrm{nm}$ , which are equal to the estimated sizes of particles B, C, and D in the experiment. For comparison, a rotated rhomboidal particle was also simulated. The volume and surface area of the simulated particles are summarized in Table 1 . The simulated scattering spectra of these particles are shown in Fig. 5. The shapes of nonspherical particles are also shown in Fig. 5b and 5c. Triangular particle gives higher and redshifted resonance peak compared to other particles.

Fig. 5

(a) Simulated spectra of gold particles with different sizes and shapes. The illustration (b,c) describes the simulated (b) rotated-triangle-shaped particle and (c) rotated-rhomboid-shaped particle.

Fig. 6

Simulated peak-shift plot as a function of layer thickness. Layer models at the thickness of $10\mathrm{nm}$ are shown for triangle, $100\mathrm{nm}$ sphere, and rhomboid particles.

Table 1

Volume, surface area, and electric-field enhancement factor of the simulated particles. The electric-field enhancement factors are extracted from the field pattern at the resonance as in Fig. 6.

The electric-field patterns of these particles at their resonance wavelength are shown in Fig. 7 . Only the cross sections along the excitation electric-field vector are shown. Clearly, the pointing edges of the triangular particle and the rhomboid particle accumulate the energy and create stronger field than spherical particles. The field enhancement factors (strongest field/illumination field) are also listed in Table 1.

Fig. 7

Simulated electric-field patterns of the cross section along the excitation electric-field vector of the five simulated particles at their resonance wavelengths: (a) triangular at $\lambda =615\mathrm{nm}$ , (b) $100\mathrm{nm}$ sphere at $\lambda =559\mathrm{nm}$ , (c) $90\mathrm{nm}$ sphere at $\lambda =567\mathrm{nm}$ , (d) $100\mathrm{nm}$ sphere at $\lambda =576\mathrm{nm}$ , and (e) rhomboid $\lambda =580\mathrm{nm}$ . The intensity of the electric field is scaled logarithmically in the color scheme.

To estimate the sensitivity as a biosensor, we covered the particle with a solid layer with higher refractive index. The layer thickness was varied, and the peak shift was monitored same as in the experiment of Fig. 2. Figure 6 shows the peak-shift plots as functions of the layer thickness. As the layer thickness increases, the peak shift also increases in the positive direction. In terms of peak shift, the triangular particle is more sensitive than the other particles. The largest spherical particle showed least sensitivity among the simulated particles.

4.1.

Spectra and Field Enhancement

It is quite well known that rod-shaped or facetted particles show more redshifted LSPR peaks.^{1, 9, 23} The redshift of reso-nance can be explained by easier polarization of pointy structures. The redshifted resonance of particle A compared to spherical particles in Fig. 1 is due to the pointy structure of tetrahedral shape as seen in Fig. 4. We expected that the triangle particle in the simulation emulates particle A. Indeed, the simulated spectrum of the triangle particle well reproduced that of particle A of the experiment (Figs. 1 and 5). The scattering spectra of all the four measured particles were nicely represented by simulated triangular and spherical particles. Actually, the substrate, which is not included in the simulation, can affect the peak position when the edge of the particle is pointing toward the substrate because the enhanced field would sense the substrate stronger than spherical particles (see field patterns of Fig. 7).

The triangular particle in the simulation exhibits higher scattering intensity at the resonance than the spherical $100\text{-}\mathrm{nm}$ particle despite its smaller volume. This is probably due to the stronger polarization of the particle. The field enhancement factor of the triangle particle is indeed stronger, which is clearly shown also in the field pattern in Fig. 7. The simulated rhomboid particle has equivalent volume and surface area to the $90\text{-}\mathrm{nm}$ spherical particle (Table 1), which implies a small difference in shape. Nevertheless, it gives stronger scattering intensity (Fig. 5) and stronger field enhancement (Fig. 6 and Table 1) by the pointing structure. The field enhancement factor of spherical particles is higher for smaller particles. Similar to the pointing structure, the curvature plays a role to accumulate the field for spherical particles.

4.2.

Sensitivity

The tetrahedral shaped particle A performed a bigger peak shift upon protein adsorption than the other spherical particles, as seen in Fig. 2. The simulated sensitivity of the equivalent triangular particle shows coherent results in Fig. 7. The signal multiplication from the spherical particle is roughly factor of 2. There are only minor differences in the sensitivity among the spherical particles both in the measurement and simulation. The simulated rhomboidal particle showed slightly better sensitivity than spherical particles. These suggest a direct correlation between the sensitivity and the field enhancement factor.

Looking more into the details of the results with the spherical particles, the sensitivity of the $100\text{-}\mathrm{nm}$ particle in the experiment and simulation gives an opposite relation regarding the particle size. This is probably due to the imperfect spherical shape of the real particles. A larger particle tends to have more facets by crystalline growth with pointing edges, which would compensate its intrinsically lower sensitivity of the larger particle by a more enhanced field at the pointing edges.²⁴

The protein layer of IgG molecule is expected to have $5–15\mathrm{nm}$ thickness considering the molecular size.^{7, 25} However, the magnitude of the peak shift by IgG adsorption in the experiment is considerably less than the expected peak shift of $5–15\mathrm{nm}$ layer in the simulation. This difference probably originates from the unrealistically sharp well-defined boundary of the protein layer in the simulation. Non-negligible scattering happens at the protein-water boundary. In reality, the boundary of the protein layer is most likely diffuse, giving suppressed scattering at the protein-water boundary. The substrate would also reduce the sensitivity especially for the triangular (tetrahedral) particle as discussed above.