# Plasmonic Nanomaterials for Micro- and Nanoplastics Detection
## 4 SERS-Based MNPs Detection
### The SERS Effect, Enhancement Factors, and Qualitative Information
However, a currently still open issue is the lack of a universal operative formula for the practical estimation of the EF. The variety of different approaches to the EF calculation is also highlighted by the literature reported herein. In the following, we illustrate the most commonly used EF formulations in the papers cited in this review (Equations (2)-(5)), although an exhaustive treatment on the different common operative formula can be found in [119]. \[\text{EF}=\frac{\text{I}_{\text{SERS}}/\text{N}_{\text{SERS}}}{\text{I}_{\text{ NRS}}/\text{N}_{\text{NRS}}} \tag{2}\]  
\[\text{EF}=\frac{\text{I}_{\text{SERS}}/\text{C}_{\text{SERS}}}{\text{I}_{\text{ NRS}}/\text{C}_{\text{NRS}}} \tag{3}\]  
\[\text{EF}\approx\int_{\text{v}}\frac{\left|\text{E}_{\text{loc}}(\omega_{0}, \text{r})\right|^{4}}{\left|\text{E}_{0}(\omega_{0},\text{r})\right|^{4}}\text {d}\text{v}\ast \tag{4}\]  
\[\text{EF}=\frac{\text{I}_{\text{SERS}}}{\text{I}_{\text{NRS}}} \tag{5}\]  
where \(\text{J}_{\text{SERS}}\) is the intensity of the selected SERS peak; \(\text{I}_{\text{NRS}}\) is the intensity of the selected normal Raman peak; \(\text{N}_{\text{SERS}}\) is the number of particles contributing to the intensity of SERS signal; \(\text{N}_{\text{NRS}}\) is the number of particles contributing to the intensity of the normal Raman signal; \(\text{C}_{\text{SERS}}\) is the sample concentration in SERS measurements; \(\text{C}_{\text{NRS}}\) is the sample concentration in Raman measurements; \(\text{E}_{\text{loc}}\) is the E-field at the scatterer (e.g., E-field in the presence of metal nanoparticles); \(\text{E}_{0}\) is the incident field at the position of molecules of interest (E-field in the absence of metal nanoparticles). * It must be stressed that this equation is only applied in theoretical studies. In our research works [120; 121], we proposed another declination of the general definition of Equation (1), with \(\text{N}_{\text{SERS}}\) and \(\text{N}_{\text{RS}}\) defined as the product between the scattering volume and molecular concentrations in the two cases (\(\text{c}_{\text{SERS}}\) and \(\text{c}_{\text{RS}}\)), respectively. In particular, since we used the same experimental configuration for both the Raman and SERS experiments, namely, a wet drop between two blank glass slides or, for SERS, one blank glass slide and the SERS substrate, the investigated area was the same and the only operative parameter that changed was the height of the scattering volume. Thus, our operative formula can be written as  
\[\text{EF}=\frac{\text{I}_{\text{SERS}}}{\text{I}_{\text{RS}}}\frac{\text{c}_ {\text{RS}}\text{H}_{\text{RS}}}{\text{c}_{\text{SERS}}\text{H}_{\text{SERS}}} \tag{6}\]  
where \(\text{H}_{\text{SERS}}\) is about 10 nm, since for a greater distance, the SERS enhancement drops [120; 122], while \(\text{H}_{\text{RS}}\) is equal to the interspace between the two blank glass slide, namely, the height of the spread drop, since in the Raman effect, all of the molecules contribute to the recorded signal.