**7. Estimation of the SERS enhancement factor**

As Raman signal of molecules is very weak for detecting them at very low concentrations various proposals for different condition are required. One way to enhance the signal is with the use of metallic surfaces, because of their excitation of the surface plasmon. The magnitude of the Raman signal enhancement is influenced by some factors:

*Theoretical and Experimental Study on the Functionalization Effect on the SERS… DOI: http://dx.doi.org/10.5772/intechopen.97028*

**Figure 10.**

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

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

AFM technique was also used to analyze the structure of the SiO2-Ag composite films, the micrographs are shown in **Figure 9**. In different areas of the film it is observed that the spheres are arranged in a short-range hexagonal packing, a similar spatial distribution than the observed in the SiO2 films. Because of the absence of SiO2 and Ag NPs some voids are created. The single or agglomerates of Ag NPs are located in the interstices among SiO2 spheres. The fact that the Ag NPs do not surround the SiO2 spheres is because of the surface charge, of both Ag NPs and SiO2

**6. Structural composition of the SiO2-Ag composite films**

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

spheres, is negative (52.5 mV and 44.1 mV, respectively).

**7. Estimation of the SERS enhancement factor**

by some factors:

**178**

**Figure 9.**

*NPs are found in the interstices.*

As Raman signal of molecules is very weak for detecting them at very low concentrations various proposals for different condition are required. One way to enhance the signal is with the use of metallic surfaces, because of their excitation of the surface plasmon. The magnitude of the Raman signal enhancement is influenced

*AFM micrographs of the SiO2-Ag composite films at different amplifications. The right panel shows that Ag*

is estimated in 289 55 nm.

**Figure 8.**

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


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

$$\text{LMSE} \approx \frac{|E\_{\text{loc}}(o\_{\text{exc}})|^2}{\left|E\_{\text{inc}}(o)\right|^2} \frac{\left|E\_{\text{loc}}(o\_{\text{Raman}})\right|^2}{\left|E\_{\text{inc}}(o)\right|^2},\tag{2}$$

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 excitation frequency is similar to the Raman frequency then

$$\text{SMEF} \approx \frac{\left| E\_{loc}(o\_{\text{exc}}) \right|^4}{\left| E\_{inc}(o) \right|^4},\tag{3}$$

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

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

DDA assumes that the target is illuminated by an external source of monochromatic radiation represented by a plane wave, *E* ! *inc*ð Þ¼ *ω E* ! 0*e i k*!!�*r* �*ω<sup>t</sup>* . In **Figure 11** a 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 dipole–dipole interaction an induced electric field is originated given by:

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

$$\overrightarrow{E}\_{ind,i} = -\sum\_{j}^{\prime} \mathbb{A}\_{ij} \cdot \overrightarrow{p}\_{j} \mathbf{i} = \mathbf{1}, \ \ldots, \ \mathbf{N}, \tag{4}$$

*<sup>α</sup><sup>i</sup>* <sup>¼</sup> *<sup>α</sup>nr*

where *αnr*

two adjacent dipoles.

in a bulk material.

mean free path.

**181**

*<sup>i</sup>* <sup>¼</sup> *<sup>α</sup>CM*

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

the damping constant is expressed as

<sup>1</sup>þ*αCMk*<sup>2</sup> *<sup>b</sup>*1þ*m*2*b*2þ*m*<sup>2</sup> ½ � *<sup>b</sup>*3*<sup>S</sup> <sup>=</sup><sup>d</sup>*

*i* <sup>1</sup> � <sup>2</sup>*i k*<sup>3</sup>

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

*αnr <sup>i</sup> =*3

wave, *αCM* the well-known Clausius- Mossotti polarizability, *m* the refractive index of the material, *S* contains information of the polarization state and direction of propagation, *b*1, *b*<sup>2</sup> and *b*<sup>3</sup> are constants, and *d* is the separation distance between

The polarizability depends on the dielectric function through the refractive index and the Clausius- Mossotti polarizability. To describe properly the polarizability an analysis of the size-dependent dielectric function was carried out.

Finite size correction (FSC) theory is based in the assumption that the free electrons have instant collisions with the lattice ions and also with the surface of the particle, the last acts as a scatterer of the electrons reflecting them diffusely. Then,

Γ ¼ Γ*bulk* þ

On the other hand, the bulk dielectric function is expressed as

*ϵ ω*ð Þ¼ , *<sup>a</sup> <sup>ϵ</sup>bulk*ð Þ� *<sup>ω</sup> <sup>ϵ</sup>intra* <sup>þ</sup> <sup>1</sup> � *<sup>ω</sup>*<sup>2</sup>

<sup>0</sup>*:*00188, *VF*= 1.39 � <sup>10</sup><sup>6</sup> m/s and *<sup>l</sup>* <sup>¼</sup>52 nm [32].

material is 100 nm matches with that of the bulk Ag.

where Γ*bulk* is the bulk damping constant, *VF* is the Fermi velocity and *l* is the

where the intraband contribution is because of free electron transitions in the conduction band, whereas the interband contribution is because of band-to-band transitions of the core electrons. The interband transitions become important at smaller wavelengths than 320 nm for Ag [23]. Because interband electrons are not notably affected by the surface, *ϵinter*ð Þ *ω* can be assumed size independent. Therefore, considering that intraband electrons behave as Drude electrons with a damping constant as Eq. (9), the dielectric function of a particle with radius *a* is [31].

Γ*bulk* ¼ 1*=τ*, with *τ* the relaxation time and *ω<sup>p</sup>* the plasma frequency. *τ* is also related to the mean free path of the electrons, *l*. For Ag ℏ*ω<sup>p</sup>* ¼ 9*:*6 eV, 1*=ωpτ* ¼

The SPR of a Ag NP in water and with a diameter (D) in the interval between 20 nm and 100 nm is shown in **Figure 13** a). For this interval, as the size increases,

We explore the FSC in the dielectric function in an interval of diameters between 20 nm and 100 nm. In **Figure 12** we present the real and imaginary part of the dielectric function for only the extreme values of the studied interval, the curves of other diameters are in between. The optical response when the size of the

*VF*

*ϵbulk*ð Þ¼ *ω ϵinter*ð Þþ *ω ϵintra*ð Þ *ω* , (10)

*p ω ω*½ � þ *i*Γ*bulk* þ *iVF=a*

, (11)

( )

A size correction in the bulk dielectric function of a material was firstly proposed by Kreigib [30]. He proposed whether the dimensions of the material are smaller than a critical diameter *Dc*, then quantum effects should be considered. As the diameter of the particle becomes of the order or greater than *Dc* then the electronic levels become a finite set of energy levels forming the conduction band, as it occurs

i ¼ 1, 2, *::*N, (8)

*<sup>l</sup>* , (9)

, being *k* the wavenumber of the incident plane

where *ij* represents the dipole–dipole interaction and depends on the relative position between the dipole *i* and *j* ( *r \* ij* ¼ *r* ! *<sup>j</sup>* � *r* ! *<sup>i</sup>*), <sup>P</sup>j' indicates that *<sup>i</sup>* 6¼ *<sup>j</sup>*, *<sup>p</sup>* ! *<sup>j</sup>* is the dipole moment of the *j* dipole. Conventionally *jj* ¼ 0. Considering that *p* ! *<sup>i</sup>* ¼ *αiE* ! *<sup>T</sup>*,*i*, being *α<sup>i</sup>* the polarizability tensor and *E* ! *<sup>T</sup>*,*<sup>i</sup>* the total field at *r* ! *<sup>i</sup>* and that

$$
\overrightarrow{E}\_{T,i} = \overrightarrow{E}\_{inc,i} + \overrightarrow{E}\_{ind,i},\tag{5}
$$

is possible to get a system of 3 N complex equations that in matrix notation is expressed as:

$$
\hat{\mathbb{B}P} = \overline{E}\_{inc},
\tag{6}
$$

with P! ¼ *p* ! <sup>1</sup>, *p* ! 2, … ,*p* ! *N* � �, *<sup>E</sup>* ! *inc* ¼ *E* ! *inc*,1, … , *E* ! *inc*,*N* � �and ^ <sup>a</sup> *<sup>N</sup>* � *<sup>N</sup>* symmetric matrix [27].

Once the Eq. (6) is solved, that is, *p* ! <sup>1</sup>, *p* ! 2, … ,*p* ! *<sup>N</sup>* are known, then the electric field in, on and outside the target can be calculated. To solve Eq. (6) we used the software DDSCAT, which is a numerical implementation of DDA. Because we are interested in the SERS EF, we focused on the electric field on and outside the particle. DDSCAT code allows to calculate the electric field on a point with coordinates ð Þ *x*, *y*, *z* :

$$
\overrightarrow{E}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \overrightarrow{E}\_{\text{inc}}(\mathbf{x}, \mathbf{y}, \mathbf{z}) + \overrightarrow{E}\_{\text{scat}}(\mathbf{x}, \mathbf{y}, \mathbf{z}),
\tag{7}
$$

where an incident field of magnitude 1 is specified, that is, *E* ! *inc* � � � � � � <sup>¼</sup> *Einc* <sup>¼</sup> 1, and

*E* ! *scat* is the scattered field of the N radiating dipoles representing the target [28].

In addition, we used the Lattice Dispersion Relation (an option in the DDSCAT code) to describe the polarizability of each dipole [29].

**Figure 11.**

*Scheme of an incident plane wave on a spherical target with (a) y-polarization and (b) z-polarization. The electric field induces a dipole moment on each dipole (tiny spheres).*

*Theoretical and Experimental Study on the Functionalization Effect on the SERS… DOI: http://dx.doi.org/10.5772/intechopen.97028*

$$\alpha\_{i} = \frac{\alpha\_{i}^{wr}}{1 - 2i \, k^{3} \alpha\_{i}^{wr}/3} \text{ i} = 1, 2, \dots \text{N}, \tag{8}$$

where *αnr <sup>i</sup>* <sup>¼</sup> *<sup>α</sup>CM* <sup>1</sup>þ*αCMk*<sup>2</sup> *<sup>b</sup>*1þ*m*2*b*2þ*m*<sup>2</sup> ½ � *<sup>b</sup>*3*<sup>S</sup> <sup>=</sup><sup>d</sup>* , being *k* the wavenumber of the incident plane wave, *αCM* the well-known Clausius- Mossotti polarizability, *m* the refractive index of the material, *S* contains information of the polarization state and direction of propagation, *b*1, *b*<sup>2</sup> and *b*<sup>3</sup> are constants, and *d* is the separation distance between two adjacent dipoles.

The polarizability depends on the dielectric function through the refractive index and the Clausius- Mossotti polarizability. To describe properly the polarizability an analysis of the size-dependent dielectric function was carried out.

A size correction in the bulk dielectric function of a material was firstly proposed by Kreigib [30]. He proposed whether the dimensions of the material are smaller than a critical diameter *Dc*, then quantum effects should be considered. As the diameter of the particle becomes of the order or greater than *Dc* then the electronic levels become a finite set of energy levels forming the conduction band, as it occurs in a bulk material.

Finite size correction (FSC) theory is based in the assumption that the free electrons have instant collisions with the lattice ions and also with the surface of the particle, the last acts as a scatterer of the electrons reflecting them diffusely. Then, the damping constant is expressed as

$$
\Gamma = \Gamma\_{bulk} + \frac{V\_F}{l},
\tag{9}
$$

where Γ*bulk* is the bulk damping constant, *VF* is the Fermi velocity and *l* is the mean free path.

On the other hand, the bulk dielectric function is expressed as

$$
\epsilon\_{bulk}(a) = \epsilon\_{inter}(a) + \epsilon\_{intra}(a), \tag{10}
$$

where the intraband contribution is because of free electron transitions in the conduction band, whereas the interband contribution is because of band-to-band transitions of the core electrons. The interband transitions become important at smaller wavelengths than 320 nm for Ag [23]. Because interband electrons are not notably affected by the surface, *ϵinter*ð Þ *ω* can be assumed size independent. Therefore, considering that intraband electrons behave as Drude electrons with a damping constant as Eq. (9), the dielectric function of a particle with radius *a* is [31].

$$\varepsilon(o, a) = \varepsilon\_{bulk}(o) - \varepsilon\_{intr} + \left\{ 1 - \frac{o\_p^2}{o[o + i\Gamma\_{bulk} + iV\_F/a]} \right\},\tag{11}$$

Γ*bulk* ¼ 1*=τ*, with *τ* the relaxation time and *ω<sup>p</sup>* the plasma frequency. *τ* is also related to the mean free path of the electrons, *l*. For Ag ℏ*ω<sup>p</sup>* ¼ 9*:*6 eV, 1*=ωpτ* ¼ <sup>0</sup>*:*00188, *VF*= 1.39 � <sup>10</sup><sup>6</sup> m/s and *<sup>l</sup>* <sup>¼</sup>52 nm [32].

We explore the FSC in the dielectric function in an interval of diameters between 20 nm and 100 nm. In **Figure 12** we present the real and imaginary part of the dielectric function for only the extreme values of the studied interval, the curves of other diameters are in between. The optical response when the size of the material is 100 nm matches with that of the bulk Ag.

The SPR of a Ag NP in water and with a diameter (D) in the interval between 20 nm and 100 nm is shown in **Figure 13** a). For this interval, as the size increases,

*E* !

position between the dipole *i* and *j* ( *r*

being *α<sup>i</sup>* the polarizability tensor and *E*

� �

Once the Eq. (6) is solved, that is, *p*

*E* !

expressed as:

with P!

matrix [27].

*E* !

**Figure 11.**

**180**

coordinates ð Þ *x*, *y*, *z* :

¼ *p* ! <sup>1</sup>, *p* ! 2, … ,*p* ! *N*

*ind*,*<sup>i</sup>* ¼ �X<sup>0</sup>

*j*

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

*\* ij* ¼ *r* ! *<sup>j</sup>* � *r* !

dipole moment of the *j* dipole. Conventionally *jj* ¼ 0. Considering that *p*

*E* ! *<sup>T</sup>*,*<sup>i</sup>* ¼ *E* !

, *E* !

ð Þ¼ *x*, *y*, *z E*

code) to describe the polarizability of each dipole [29].

*The electric field induces a dipole moment on each dipole (tiny spheres).*

!

where an incident field of magnitude 1 is specified, that is, *E*

!

^P ! ¼ *E* !

> ! <sup>1</sup>, *p* ! 2, … ,*p* !

in, on and outside the target can be calculated. To solve Eq. (6) we used the software DDSCAT, which is a numerical implementation of DDA. Because we are interested in the SERS EF, we focused on the electric field on and outside the particle. DDSCAT code allows to calculate the electric field on a point with

*inc* ¼ *E* !

*ij* � *p* ! *j*

where *ij* represents the dipole–dipole interaction and depends on the relative

*inc*,*<sup>i</sup>* þ *E* !

*inc*,1, … , *E* ! *inc*,*N*

*inc*ð Þþ *x*, *y*, *z E*

*scat* is the scattered field of the N radiating dipoles representing the target [28]. In addition, we used the Lattice Dispersion Relation (an option in the DDSCAT

*Scheme of an incident plane wave on a spherical target with (a) y-polarization and (b) z-polarization.*

!

� �

is possible to get a system of 3 N complex equations that in matrix notation is

*<sup>T</sup>*,*<sup>i</sup>* the total field at *r*

i ¼ 1*;* … *;* N*;* (4)

*<sup>i</sup>*), <sup>P</sup>j' indicates that *<sup>i</sup>* 6¼ *<sup>j</sup>*, *<sup>p</sup>*

*<sup>i</sup>* and that

*ind*,*i*, (5)

*inc*, (6)

and ^ <sup>a</sup> *<sup>N</sup>* � *<sup>N</sup>* symmetric

*<sup>N</sup>* are known, then the electric field

*scat*ð Þ *x*, *y*, *z* , (7)

� �

� <sup>¼</sup> *Einc* <sup>¼</sup> 1, and

! *inc* � � �

!

! *<sup>j</sup>* is the

! *<sup>i</sup>* ¼ *αiE* ! *<sup>T</sup>*,*i*,

*E* ! 

acid.

**Figure 14.**

**183**

NP with a D = 100 nm.

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

 (not the intensity or irradiance) *vs* D is shown in panel d). For the sizes studied here the magnitude of the electric field varies from 4 to 6, therefore the SERS EF of

Because a common laser to study SERS signal is that with a 632 nm wavelength, and based on the results shown in **Figure 13**, the Ag NP with a SPR wavelength close to the laser has a diameter of 100 nm. Therefore, in the following sections we have

From the experimental techniques we observed that the Ag NPs have a preferred location at the interstices of the SiO2 spheres when in substrate, particularly creating clusters or agglomerates. Moreover, the Ag NPs are covered by a layer of tannic

To estimate the SERS EF of the composite material the layer of the tannic acid

D = 290 nm (see panel a)), of a single Ag NP with a D = 100 nm (see panel b)), same NP as in b) with a shell of 1 nm of tannic acid (see panel c)), a SiO2 sphere and a Ag NP touching (see panel d)), and same array as in d) with the tannic acid shell of the NP (see panel e)). For all the cases mentioned, the plane wave with the same characteristics as in **Figure 13** were considered. The refractive index is 1.46 for SiO2 [33], 1.704 for tannic acid [34], and 1.0003 for the surrounding medium (the composites are in air). Clearly, the electric field on and away from the surface of the dielectric SiO2 sphere is less intense than that of the Ag NP. The presence of the dielectric tannic acid layer affects the plasmonic response of the NP and the result is a less intense electric field with a spatially symmetric distribution. There is a "screening" effect because of the presence of the dielectric shell, this is observed in the presence and absence of the SiO2 sphere. When a Ag NP with/without a tannic

was taken into account and a study of the agglomerated NPs was carried out. **Figure 14** shows the electric field magnitude of a single SiO2 sphere with a

acid shell is touching a SiO2 sphere a SERS EF can be as high as 1 � <sup>10</sup><sup>3</sup>

where this value can be reached are smaller when the dielectric layer is present.

*Local electric field of (a) a single SiO2 sphere, (b) a single nude Ag NP, (c) a single Ag NP with a tannic acid shell of 1 nm thick, (d) nude Ag NP touching a SiO2 sphere, and (e) Ag NP-tannic acid shell touching a SiO2 sphere.*

considered a Ag NP with that size and an excitation wavelength of 632 nm.

! 4

<sup>¼</sup> <sup>1</sup>*:*3*x*10<sup>3</sup> for a Ag

, the zones

a molecule located at the zenith of the sphere is SERS EF = *E*

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

**7.1 Electric field magnitude of the composite thin film**

**Figure 12.**

*Real and imaginary part of the dielectric function of silver in bulk (blue line) and taking into account FSC with a diameter of 20 nm (yellow line) and 100 nm (dashed blue line).*

#### **Figure 13.**

*The SPR* vs *diameter (D) of a spherical Ag NP is shown in panel (a). The magnitude of the electric field of a Ag NP with a D = 20 nm and D = 100 nm is shown in panel (b) and (c), respectively, the incident plane wave has a wavelength of 632 nm. In panel (d) E*j j *at a point in the zenith of the NP* vs *D is presented. The NP is in water (refractive index of 1.33).*

the SRP is red shifted. In addition, the magnitude of the complex electric field vector on a plane crossing the center of the NP is shown in panel b) and c) for a D = 20 nm and D = 100 nm, respectively. The plane wave has a wave vector *k* ! in x-direction, a linear polarization state in y-direction and a wavelength of 632 nm. Along the xy plane the small NP has the characteristic field intensity distribution of a dipole plasmon. Whereas, for the large NP the intensity distribution is slightly distorted from that of a dipole surface plasmon. To visualize the relation *E* ! *vs* D a specific hot spot in the zenith of the sphere was chosen, its electric field magnitude

*Theoretical and Experimental Study on the Functionalization Effect on the SERS… DOI: http://dx.doi.org/10.5772/intechopen.97028*

*E* ! (not the intensity or irradiance) *vs* D is shown in panel d). For the sizes studied here the magnitude of the electric field varies from 4 to 6, therefore the SERS EF of a molecule located at the zenith of the sphere is SERS EF = *E* ! 4 <sup>¼</sup> <sup>1</sup>*:*3*x*10<sup>3</sup> for a Ag NP with a D = 100 nm.

Because a common laser to study SERS signal is that with a 632 nm wavelength, and based on the results shown in **Figure 13**, the Ag NP with a SPR wavelength close to the laser has a diameter of 100 nm. Therefore, in the following sections we have considered a Ag NP with that size and an excitation wavelength of 632 nm.

#### **7.1 Electric field magnitude of the composite thin film**

From the experimental techniques we observed that the Ag NPs have a preferred location at the interstices of the SiO2 spheres when in substrate, particularly creating clusters or agglomerates. Moreover, the Ag NPs are covered by a layer of tannic acid.

To estimate the SERS EF of the composite material the layer of the tannic acid was taken into account and a study of the agglomerated NPs was carried out. **Figure 14** shows the electric field magnitude of a single SiO2 sphere with a D = 290 nm (see panel a)), of a single Ag NP with a D = 100 nm (see panel b)), same NP as in b) with a shell of 1 nm of tannic acid (see panel c)), a SiO2 sphere and a Ag NP touching (see panel d)), and same array as in d) with the tannic acid shell of the NP (see panel e)). For all the cases mentioned, the plane wave with the same characteristics as in **Figure 13** were considered. The refractive index is 1.46 for SiO2 [33], 1.704 for tannic acid [34], and 1.0003 for the surrounding medium (the composites are in air). Clearly, the electric field on and away from the surface of the dielectric SiO2 sphere is less intense than that of the Ag NP. The presence of the dielectric tannic acid layer affects the plasmonic response of the NP and the result is a less intense electric field with a spatially symmetric distribution. There is a "screening" effect because of the presence of the dielectric shell, this is observed in the presence and absence of the SiO2 sphere. When a Ag NP with/without a tannic acid shell is touching a SiO2 sphere a SERS EF can be as high as 1 � <sup>10</sup><sup>3</sup> , the zones where this value can be reached are smaller when the dielectric layer is present.

#### **Figure 14.**

*Local electric field of (a) a single SiO2 sphere, (b) a single nude Ag NP, (c) a single Ag NP with a tannic acid shell of 1 nm thick, (d) nude Ag NP touching a SiO2 sphere, and (e) Ag NP-tannic acid shell touching a SiO2 sphere.*

the SRP is red shifted. In addition, the magnitude of the complex electric field vector on a plane crossing the center of the NP is shown in panel b) and c) for a D = 20 nm and D = 100 nm, respectively. The plane wave has a wave vector *k*

*The SPR* vs *diameter (D) of a spherical Ag NP is shown in panel (a). The magnitude of the electric field of a Ag NP with a D = 20 nm and D = 100 nm is shown in panel (b) and (c), respectively, the incident plane wave has a wavelength of 632 nm. In panel (d) E*j j *at a point in the zenith of the NP* vs *D is presented. The NP is in water*

*Real and imaginary part of the dielectric function of silver in bulk (blue line) and taking into account FSC with*

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

*a diameter of 20 nm (yellow line) and 100 nm (dashed blue line).*

**Figure 12.**

**Figure 13.**

**182**

*(refractive index of 1.33).*

x-direction, a linear polarization state in y-direction and a wavelength of 632 nm. Along the xy plane the small NP has the characteristic field intensity distribution of a dipole plasmon. Whereas, for the large NP the intensity distribution is slightly distorted from that of a dipole surface plasmon. To visualize the relation *E*

specific hot spot in the zenith of the sphere was chosen, its electric field magnitude

! in

! *vs* D a

the tannic acid shell, respectively. For both cases, the magnitude of the electric field

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

To inquire about the electric field intensities in the composite material, we explore the case with one and three Ag NPs at the interstice of three SiO2 spheres. Again, the size of the SiO2 sphere is D = 290 nm and of the Ag NP D = 100 nm. The refractive index of the medium is air and the incident electromagnetic field travels in the positive x-direction with a y-polarization, its wavelength is 632 nm. It is worth mentioning that in these cases the tannic acid layer was not considered. To illustrate the systems under study, their respective array of dipoles is shown in **Figure 16**. Because of the complexity of the 3D arrays we chose only the yz-plane to exemplify the field magnitude. As expected, the electric field of the Ag NP in presence of three SiO2 spheres is weak because of the screening effect promoted by the dielectric material, whereas, in the array of three Ag NPs, relative hot spots are present in the space among them. The hot spots may provide a SERS EF of the order

In this chapter we present the synthesis, structural composition and optical response of composite films with two main components, Ag nanoparticles and SiO2 spheres. The independent production of Ag NP and SiO2 sphere colloids were the basis to fabricate the composite films by evaporation solvent method. According to the analysis made to Atomic Force microscopy images, measurements of Absorbance and Dynamic light scattering, and numerical calculations supported on Mie theory, we conclude that single NPs and also agglomerates of Ag NPs were produced with a NP mean diameter of 96 � 9 nm. In addition, the presence of a tannic acid layer covering the surface of the NP is deduced. With the synthesis method followed to produce the SiO2 particles it was possible to obtain porous spherical

The composite films are characterized by a short-range order with local hexago-

When the separation distance between the surface of a NP and that of a SiO2 sphere is varied from 0 to 3.5 nm the intensity of the field is practically the same. The last was observed with a nude NP and with a NP covered by the tannic acid shell. Furthermore, the dielectric tannic acid layer generates a screening effect on the field intensity, besides, a different intensity distribution is observed when compared to that of a nude NP. With both a nude or covered Ag NP when in presence of the SiO2 sphere, a maximum SERS EF estimated is of the order of

. The difference is that this EF can be reached in smaller regions when the

NP is covered compared to that when the NP is nude. Finally, the SERS EF of an agglomerate of three Ag NPs surrounded by three SiO2 spheres was estimated. Even with the presence of the dielectric SiO2 spheres that screens the electric field intensity, relative hot spots are observed in the regions where the nude NPs are very close one each other, giving place to a maximum SERS EF of the order of 2.4 � <sup>10</sup><sup>3</sup>


.

nal arrays of SiO2 spheres with Ag NPs, single or agglomerated, located at the interstices. Some voids are also observed, that is spaces without the presence of NPs and/or spheres. We attribute the preferred location of the NPs to the negative surface charge of both, Ag NPs and SiO2 spheres. Another aspect deduced from the same sign of the surface charge is that the NP and sphere are not touching, that is, there is no surface-to-surface contact. To have an insight about how this affects the

!

particles with a mean diameter about 289 � 55 nm.

magnitude of the electric field |*E*

were carried out.

<sup>1</sup> � <sup>10</sup><sup>3</sup>

**185**

presents inappreciable changes.

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

of 2.4 � <sup>10</sup><sup>3</sup>

**8. Conclusions**

.

**Figure 15.**

*Magnitude of the electric field along a center-to-center path, see red line in the inset of panel (B). When the sphere and NP are touching d = 0 and a point on the surface of SiO2 sphere is at a position of 145 nm (D = 290 nm of a SiO2 sphere). Panel (A) shows |E| values as d increases and the Ag NP is nude, whereas in panel (B) the tannic acid shell has been considered.*

Because SiO2 spheres and Ag NPs have a negative superficial charge, �44.1 mV and � 52.5 mV, respectively, we deduce there is not surface-to-surface contact. We explore surface-to-surface separation distances (*d*Þbetween 0.5 nm and 3.5 nm and how this modifies the electric field.

In **Figure 15** is shown the magnitude of the electric field along a straight path starting at the center of the SiO2 sphere and ending at the center of the Ag NP, this is illustrated as the red line shown in the inset of panel B). The size of the SiO2 sphere is D = 290 nm and of the Ag NP D = 100 nm, therefore when *d* ¼ 0, that is, the sphere and Ag NP are in contact, the contact point is at a position of 145 nm. Panel (A) and (B) shows |E| values as d increases when the Ag NP is nude and with

#### **Figure 16.**

*Dipoles array and |E| values along the yz-plane of an array of 3 SiO2 spheres with (a) one Ag NP, and (b) 3 Ag NPs with no coplanar centers, at the interstice. For both cases, the incident field has a wave vector along x, y-polarization and a wavelength of 632 nm.*

*Theoretical and Experimental Study on the Functionalization Effect on the SERS… DOI: http://dx.doi.org/10.5772/intechopen.97028*

the tannic acid shell, respectively. For both cases, the magnitude of the electric field presents inappreciable changes.

To inquire about the electric field intensities in the composite material, we explore the case with one and three Ag NPs at the interstice of three SiO2 spheres. Again, the size of the SiO2 sphere is D = 290 nm and of the Ag NP D = 100 nm. The refractive index of the medium is air and the incident electromagnetic field travels in the positive x-direction with a y-polarization, its wavelength is 632 nm. It is worth mentioning that in these cases the tannic acid layer was not considered. To illustrate the systems under study, their respective array of dipoles is shown in **Figure 16**. Because of the complexity of the 3D arrays we chose only the yz-plane to exemplify the field magnitude. As expected, the electric field of the Ag NP in presence of three SiO2 spheres is weak because of the screening effect promoted by the dielectric material, whereas, in the array of three Ag NPs, relative hot spots are present in the space among them. The hot spots may provide a SERS EF of the order of 2.4 � <sup>10</sup><sup>3</sup> .

#### **8. Conclusions**

Because SiO2 spheres and Ag NPs have a negative superficial charge, �44.1 mV and � 52.5 mV, respectively, we deduce there is not surface-to-surface contact. We explore surface-to-surface separation distances (*d*Þbetween 0.5 nm and 3.5 nm and

*Magnitude of the electric field along a center-to-center path, see red line in the inset of panel (B). When the sphere and NP are touching d = 0 and a point on the surface of SiO2 sphere is at a position of 145 nm (D = 290 nm of a SiO2 sphere). Panel (A) shows |E| values as d increases and the Ag NP is nude, whereas in*

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

In **Figure 15** is shown the magnitude of the electric field along a straight path starting at the center of the SiO2 sphere and ending at the center of the Ag NP, this is illustrated as the red line shown in the inset of panel B). The size of the SiO2 sphere is D = 290 nm and of the Ag NP D = 100 nm, therefore when *d* ¼ 0, that is, the sphere and Ag NP are in contact, the contact point is at a position of 145 nm. Panel (A) and (B) shows |E| values as d increases when the Ag NP is nude and with

*Dipoles array and |E| values along the yz-plane of an array of 3 SiO2 spheres with (a) one Ag NP, and (b) 3 Ag NPs with no coplanar centers, at the interstice. For both cases, the incident field has a wave vector along x,*

how this modifies the electric field.

*panel (B) the tannic acid shell has been considered.*

**Figure 15.**

**Figure 16.**

**184**

*y-polarization and a wavelength of 632 nm.*

In this chapter we present the synthesis, structural composition and optical response of composite films with two main components, Ag nanoparticles and SiO2 spheres. The independent production of Ag NP and SiO2 sphere colloids were the basis to fabricate the composite films by evaporation solvent method. According to the analysis made to Atomic Force microscopy images, measurements of Absorbance and Dynamic light scattering, and numerical calculations supported on Mie theory, we conclude that single NPs and also agglomerates of Ag NPs were produced with a NP mean diameter of 96 � 9 nm. In addition, the presence of a tannic acid layer covering the surface of the NP is deduced. With the synthesis method followed to produce the SiO2 particles it was possible to obtain porous spherical particles with a mean diameter about 289 � 55 nm.

The composite films are characterized by a short-range order with local hexagonal arrays of SiO2 spheres with Ag NPs, single or agglomerated, located at the interstices. Some voids are also observed, that is spaces without the presence of NPs and/or spheres. We attribute the preferred location of the NPs to the negative surface charge of both, Ag NPs and SiO2 spheres. Another aspect deduced from the same sign of the surface charge is that the NP and sphere are not touching, that is, there is no surface-to-surface contact. To have an insight about how this affects the !

magnitude of the electric field |*E* |, and therefore, the SERS EF, DDA calculations were carried out.

When the separation distance between the surface of a NP and that of a SiO2 sphere is varied from 0 to 3.5 nm the intensity of the field is practically the same. The last was observed with a nude NP and with a NP covered by the tannic acid shell. Furthermore, the dielectric tannic acid layer generates a screening effect on the field intensity, besides, a different intensity distribution is observed when compared to that of a nude NP. With both a nude or covered Ag NP when in presence of the SiO2 sphere, a maximum SERS EF estimated is of the order of <sup>1</sup> � <sup>10</sup><sup>3</sup> . The difference is that this EF can be reached in smaller regions when the NP is covered compared to that when the NP is nude. Finally, the SERS EF of an agglomerate of three Ag NPs surrounded by three SiO2 spheres was estimated. Even with the presence of the dielectric SiO2 spheres that screens the electric field intensity, relative hot spots are observed in the regions where the nude NPs are very close one each other, giving place to a maximum SERS EF of the order of 2.4 � <sup>10</sup><sup>3</sup> .

Despite this order of magnitude is not as large to the usually reported with plasmonic NPs, this composite films have the advantage of being prepared by inexpensive methods, moreover, the NPs are located at specific positions, a fact that can be taken advantage of for SERS applications, as proposed here, or many others.

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