**5. Determination of size and shape of SiO2 particles**

A transmission electron microscopy (TEM) image of the SiO2 spheres is shown in **Figure 6A**. It is observed that the spheres are amorphous because of their porosity. In the inset of **Figure 6A** we illustrate the structure of one pore. The formation of the pores takes place when some periodic chains of Si-O were not carried out during the polymerization reaction, in addition, some OH groups may stay on the surface [13].

The optical UV–Vis spectrum is shown in **Figure 6B**. An absorption edge starting at approximately 300 nm and a maximum in 290 nm are observed. The width of absorbance spectrum corresponds to the band gap (Eg) energy of amorphous SiO2. The Eg was estimated by extrapolating the absorption edge to the photon energy axis through a linear fit, then the Eg value in the direct transition of SiO2 turned out to be 3.98 eV. This value is in agreement with the reported Eg of 3.8 eV in the case of SiO2 nanostructures [13, 24]. This value is lower than that reported for crystalline SiO2 (quartz), which is approximately 9 eV [25] and is a consequence of the defects mentioned above.

The zeta potential of the SiO2 colloid is shown in **Figure 7**, a negative surface charge of 44.1 mV is detected. The minus sign is attributed to the oxygens of the OH groups located on the surface or in the pores.

The spherical shape of the SiO2 particles is corroborated by the AFM images in **Figure 8**. A large concentration of SiO2 spheres covering a glass substrate is

**Figure 6.**

superficial charge, a comparison among the optical spectrum of the Ag NPs, the tannic acid and the sodium citrate is presented in **Figure 5**. The last two were used as reducing and stabilizing agents during the synthesis procedure of the NPs. The band of the sodium citrate is out of the measured interval, whereas the optical response of the tannic acid is characterized by one band located at 214 and other at 268 nm. These two bands are well superimposed to the shape line of the Ag NPs spectrum in the interval of ultraviolet light. Therefore, the tannic acid is present in the colloid even after the several washing times. The negative charge of the NPs is explained as follows. Assuming the tannic acid molecules are adsorbed on the surface of the NPs, the negative charge detected is probably because of a partial deprotonation of the OH groups bonded to aromatic ring (see scheme in **Figure 5**). It is worth mentioning the fact that the electronic interband transitions of Ag take place at wavelengths lower than 320 nm, therefore they also contribute to the

*Measured absorbance of the Ag NPs (black line), tannic acid (red line) and sodium citrate (blue line). To the*

*Silver Micro-Nanoparticles - Properties, Synthesis, Characterization, and Applications*

*right a scheme of the adsorption of tannic acid molecules on the NP surface is depicted.*

Absorbance in the UV range [23].

**Figure 4.**

**Figure 5.**

**176**

*Zeta potential of the Ag NPs in solution.*

*(A) a TEM image of SiO2 spheres. (B) UV–vis spectrum of the colloidal solution of SiO2 particles.*

**Figure 7.** *Zeta potential of the SiO2 particles in solution.*

**Figure 8.** *Images obtained by AFM showing the shape and size of the SiO2 particles.*

observed. The main feature is a short-range order with spheres forming hexagonal arrays and multilayers. From a statistical analysis over 120 particles, an average size is estimated in 289 55 nm.

• Laser excitation: wavelength, angle of incidence, power, interval of time.

*A particle with a spherical shape represented by an array of N point dipoles (tiny spheres) in DDA*

*Theoretical and Experimental Study on the Functionalization Effect on the SERS…*

*DOI: http://dx.doi.org/10.5772/intechopen.97028*

• Plasmonic Surface: chemical composition, refractive index, shape, surface

• Analyte: Intrinsic properties such as polarizability tensor or optical cross section, concentration, compatibility to be adsorbed to the metal surface.

*SMEF*<sup>≈</sup> *Eloc*ð Þ *<sup>ω</sup>exc* j j<sup>2</sup>

excitation frequency is similar to the Raman frequency then

this expression is called the j j *<sup>E</sup>* <sup>4</sup> approximation.

matic radiation represented by a plane wave, *E*

**179**

j j *Einc*ð Þ *<sup>ω</sup>* <sup>2</sup>

To quantify the enhancement of the Raman signal factor (EF) the Single-Molecule SERS EF or the Average SERS EF are defined. The first one quantifies the amplification of the Raman signal of one molecule at a particular position, whereas the second one is the average of the intensity when considering random positions along an area of the substrate. Here we are focused on the Single-Molecule SERS EF (SMEF) expressed as

where *Einc*ð Þ *ω* is the incident field, *Eloc*ð Þ *ωexc* and *Eloc*ð Þ *ωRaman* are the local electric field at the excitation frequency and Raman frequency, respectively. When the

To calculate the local field, the DDA and its numerical implementation DDSCAT code have been used [26]. The fundamentals of DDA are widely detailed elsewhere [27]. The basic idea is the representation of the target by a discrete array of N point dipoles. Each dipole is at the site of a cubic lattice with a lattice parameter *d*0, being this smaller than the wavelength of the incident electric field. The chosen N value determines the convergence and numerical error in the calculations, in **Figure 10** a

DDA assumes that the target is illuminated by an external source of monochro-

plane wave with a) y-polarization and b) z-polarization state is depicted. The electric plane wave induces a dipole moment on each dipole (see **Figure 11**). Because of the

!

*inc*ð Þ¼ *ω E* ! 0*e*

*SMEF*<sup>≈</sup> *Eloc*ð Þ *<sup>ω</sup>exc* j j<sup>4</sup>

particle with a spherical shape is represented by N = 462,758 and N = 3,775,

dipole–dipole interaction an induced electric field is originated given by:

j j *Eloc*ð Þ *ωRaman*

2

j j *Einc*ð Þ *<sup>ω</sup>* <sup>2</sup> , (2)

j j *Einc*ð Þ *<sup>ω</sup>* <sup>4</sup> , (3)

*i k*!!�*r* �*ω<sup>t</sup>* 

. In **Figure 11** a

roughness.

**Figure 10.**

*approximation.*
