Influence of the sensor element size on the response of the LSPR sensor

For further studying the LSPR sensitivity of spherical gold nanoparticles with molecular shell, extinction simulations were performed for nanoparticles of different sizes and molecular layers of different thicknesses. First, the above-described theoretical model was applied to the system mentioned in Ref. [69], specifically, a spherical gold nanoparticle with a radius of 5, 10, 15, and 20 nm coated with a homogeneous layer of polymethylmethacrylate (РИМА) with thickness of 0-30 nm located in air. Results of LSPR response simulation are presented in Fig. 2.16. In the thickness range of 0-15 nm, results similar to those presented in Ref. [69] were obtained. However, the behavior of the LSPR response at shell thicknesses larger than 15 nm differs from the expected: it is obvious that the shift in the LSPR peak in the extinction spectrum does not indicate a plateau. In addition, for a nanoparticle with a radius of 5 nm, the response begins to decrease when the thickness of the shell exceeds 20 nm.

To clarify this special behavior of the dependence of the LSPR peak shift on the thickness of the molecular layer, the LSPR response of a spherical gold nanoparticle with a wide range of radii, namely 1, 5, 20, and 50 nm, was simulated. The molecular coating on the surface of the nanoparticle was considered as a densely packed monolayer of globular molecules, as described in Subsection 2.3.1.

The size of the molecules, and the shell thickness, respectively, varied in the range from 0 to 20 nm, which includes the typical sizes of most globular molecules studied by LSPR. Such a molecular layer was treated as a homogeneous shell with an index of refraction n₂, obtained according to the effective medium theory provided by Eqs. (2.37), (2.38), and (2.40). First it should be noted that the properties of LSPR of small gold nanoparticles (for example, with a radius of 1 nm) are not described in the literature as widely as the properties of nanoparticles of larger size. This may be due to experimental difficulties, as well as the complexity of the theoretical description of such system due to the significant influence of quantum and other size effects. Simulated shifts in the extinction peak are shown in Fig. 2.17. There are several typical features that should be noticed.

Figure 2.16 Response of LSPR sensor based on a gold nanoparticle with a radius of 5,10,15, and 20 nm depending on the thickness of the homogeneous PMMA shell (n = 1.496). Reprinted with permission from Ref. [63], Copyright 2011, IEEE.

First, the growth rate of the LSPR shift for the small shell thickness depends on the size of the nanoparticle: the smaller nanoparticle provides faster growth of the LSPR response, which is consistent with the results in Ref. [69]. However, the response for a nanoparticle with a radius of 50 nm grows faster than a response for a nanoparticle with a radius of 20 nm, which does not coincide with the general trend. Second, nanoparticles with a radius of 5, 20, and 50 nm show an ordinary response, which tends to saturation for d> R, where d = 2r is the thickness of the molecular layer. As for the LSPR response of a gold nanoparticle with a radius of 1 nm, two significant features are observed: very fast growth at a thickness of 0 to 2 nm compared with nanoparticles of other sizes and a significant decrease in the large thicknesses of the coating, even to the negative shifts in the wavelength position of the LSPR peak.

Figure 2.17 Response of the LSPR sensor on the basis of a gold nanoparticle with a radius of 1, S, 20, and 50 nm depending on the thickness of the molecular layer. Reprinted with permission from Ref. [63], Copyright 2011, IEEE.

Features of the response of LSPR sensor based on small-size gold nanoparticles

Due to the importance of detecting small-size molecules such as toxins or pesticides, the dependence of the LSPR shift on the size of a molecule for a nanoparticle with a 1 nm radius is most interesting; therefore, the features shown in Fig. 2.17 were studied more precisely. For the complete study of the first feature, the LSPR response of small gold nanoparticles with a radius of 0.5-1 nm and a thickness of the molecular layer of 0-5 nm (Fig. 2.18a) was calculated.

Figure 2.18a shows that when the size of the nanoparticle is reduced, the initial LSPR response at d < 1 nm increases significantly, reaching a maximum value of about 5 nm for a nanoparticle with a radius of 0.5 nm, which is almost twice larger than for a nanoparticle with a radius of 1 nm. The reason for such increase in response was found after the same simulation with values of optical constants of gold nanoparticles same as of bulk gold. This approach results in the dependence of the LSPR peak shift shown in Fig. 2.18b. Obviously, the aforementioned growth in response in this figure is absent; so the growth of the LSPR response for small gold nanoparticles with a thin molecular coating is a consequence of the modification of the gold optical constants by taking into account the size-dependent electron relaxation time. The effect of this significant shift in the LSPR wavelength can be used for the better detection of small molecules with the size of about 1 nm using LSPR sensor based on nanoparticles with a radius of up to 1 nm.

Figure 2.18 Response of the LSPR sensor on the basis of a gold nanoparticle with a radius of O.S-1 nm depending on the thickness of the molecular layer: The simulation is carried out (a) with and (b) without correction of the electron relaxation time (using the optical constants of bulk gold). Reprinted with permission from Ref. [63], Copyright 2011, IEEE.

As for the decrease of LSPR response for a nanoparticle with a radius of 1 nm with molecular layer thickness increasing (see Fig. 2.17), it was discovered that the reason for this phenomenon is the ratio between the components that contribute to extinction. It is known that the total extinction of light is the sum of the scattering and absorption of light by a nanoparticle [59,70]. For the simulation of the scattering and absorption cross-sectional spectra of a gold nanoparticle with a radius of 1 nm (Fig. 2.19a), Eqs. (2.42) and (2.43) of the Mie theory were used. Peak shifts in absorption and extinction cross-sectional spectra were also plotted depending on the thickness of the molecular layer (Fig. 2.19b).

Figure 2.19 Spectra of light extinction, scattering, and absorption cross sections by a gold nanoparticle with a radius of 1 nm with a molecular coating thickness of 0, 5, 10, IS, 20 nm; (b) wavelength shifts of extinction and absorption peaks for a gold nanoparticle with a radius of 1 nm depending on the thickness of the molecular layer. Reprinted with permission from Ref. [63], Copyright 2011, IEEE.

Figure 2.19a shows that the contribution of scattering to the total extinction increases with the molecular shell thickness. This also can be observed in Fig. 2.19b where the change in the absorption peak shift matches with the change in the shift of the extinction peak only for thin molecular layers. With increasing thickness of molecular layers, the contribution of scattering for short wavelengths is greater than for long ones (Fig. 2.19a). Since the absorption contribution in this case is almost independent of the shell thickness, this results in an extinction peak shift toward shorter wavelengths. With the molecule size larger than 17 nm, the extinction peak is located at a wavelength even shorter than the initial position of the extinction peak of the uncoated nanoparticle.

Dependence of LSPR sensor response on the ratio of extinction components (scattering and absorption)

The distribution of contributions from scattering and absorption to extinction for larger gold nanoparticles with a radius of 5, 20, and 50 nm (Fig. 2.20a-f) was also investigated. For these nanoparticles, the scattering cross-sectional spectrum reveals a peak whose position also depends on the thickness of the molecular coating on the nanoparticle. Figure 2.20 shows the dependences between the cross-sectional spectra (and corresponding peak shifts) and the thickness of the molecular layer. Obviously, the contribution of

Figure 2.20 Spectra of light extinction, scattering, and absorption cross sections by a gold nanoparticle with a radius of (a) 5, (c) 20, and (e) SO nm with a molecular coating thickness of 0, 5, 10, 15, 20 nm, and corresponding extinction, scattering, and absorption peak shifts for a gold nanoparticle with a radius of (b) 5, (d) 20, and (f) SO nm depending on the thickness of the molecular layer. Reprinted with permission from Ref. [63], Copyright 2011, IEEE.

scattering to total extinction depends on the size of the nanoparticle: the larger the nanoparticle, the stronger the influence of scattering. The contribution of scattering to extinction for a gold nanoparticle with a radius of 5 nm is not significant (Fig. 2.20a). However, the scattering spectrum has a peak with position that is much more sensitive to the change in the thickness of the molecular layer than the absorption and extinction peaks: the peak of scattering shifts by almost 8 nm in comparison with saturated displacements of absorption peaks and extinction with a value near 2.5 nm (Fig. 2.20b). For a nanoparticle with a radius of 20 nm, the contribution of scattering to full extinction does not exceed 7-8% (based on a comparison of peak height) (Fig. 2.20c). It has a small effect on the position of the peak of extinction; the extinction peak shift slightly prevails over the absorption peak shift. The scattering peak shift for this nanoparticle exceeds the extinction peak shift by a value of 28% (for a thickness of the molecular layer at 20 nm) (Fig. 2.20d).

For a nanoparticle with a radius of 50 nm, scattering becomes the main component (Fig. 2.2Oe). This leads to the fact that the shifts of extinction and scattering peak position show similar behavior and differ from each other by no more than 11% in the investigated thickness range (Fig. 2.20f). It is clearly seen from the graphs presented that the scattering peak shifts faster with the growth of the thickness of the molecular layer than the absorption and extinction peaks for the core-shell configurations investigated. This fact indicates that high-sensitivity sensors based on the scattering of light by nanostructures can be created, although they may require more complex experimental equipment than sensors based on extinction measurements of light due to the weak light intensities scattered by small nano particles.

LSPR sensor response description using the number of molecules and surface concentration parameters

Using the effective medium theory allows the introduction of such parameters of the molecular layer as the number of molecules in the layer, which can be calculated according to Eq. (2.39). The dependences of the LSPR extinction peak shift on the thickness of the molecular shell and the number of molecules for gold nanoparticles of different radii are shown in Fig. 2.21.

It is also possible to determine the surface concentration of molecules on the surface of a nanoparticle, which for a saturated monolayer is equal to

Figure 2.21 LSPR extinction peak shift dependence on the thickness of the molecular shell and the number of molecules for a gold nanoparticle with a radius of 5, 20, and 50 nm. Reprinted with permission from Ref. [63], Copyright 2011, IEEE.

These parameters can be used to describe submonolayer molecular coatings.