# Plasmonic Nanomaterials for Micro- and Nanoplastics Detection
## 4 SERS-Based MNPs Detection
### The SERS Effect, Enhancement Factors, and Qualitative Information  
The SERS effect is the result of the interplay between the physical and chemical surface processes occurring in the molecule-nanostructure system [114; 115; 116]. However, the predominance of one or more of these mechanisms is hardly linked to the type of nanostructures used as SERS substrates. As highlighted by the overview of recent SERS works on plastics detection reported in Table 3, the most widely used substrates are composed of nanostructured metals. Thus, the description on the mechanisms at the bases of the SERS effect will only be present for metallic systems, since it was beyond the aim of this review to also report a detailed illustration of all the SERS theories explaining the effect on dielectric and/or hybrid systems. However, it is worth mentioning this type of substrate since they are increasingly occupying a prominent place in the SERS landscape [117]. Let us consider the simplest and illustrative case of a single molecule excited by monochromatic incident light. The inelastic component of the radiated scattered light by the molecule itself corresponds to the Raman scattering. The source of this phenomenon is the generation of an induced oscillating dipole in the molecule due to the displacement of the electron cloud with respect to the positive charges, in response to an applied external electric field, that from a classical point of view is given by: \(\overline{p}=\overline{\alpha}\cdot\overline{\mathrm{E}}_{0}\), where \(\overline{\alpha}\) is the polarizability, a second-rank tensor, and \(\overline{\mathrm{E}}_{0}\) is the incident electric field vector. If we now consider a metallic nanosphere in the proximity of our molecule, the equation for the induced electric dipole still holds, and it can be re-written as: \(\overline{p}^{*}=\overline{\alpha}^{*}\cdot\overline{\mathrm{E}}_{\mathrm{ loc}}\). This simple equation encloses the two main mechanisms at the basis of the enhancement. Indeed, \(\overline{\mathrm{E}}_{\mathrm{loc}}\) encloses the so-called electromagnetic enhancement (EE), occurring when the incident frequency matches the LSPRs. The term, \(\overline{\alpha}^{*}\), is the modified polarizability due to the interaction of the molecule with the metal nanosphere. According to [118], all modifications to the polarizability tensor due to the adsorption of the molecule on the metal surface correspond to the chemical enhancement (CE). A key parameter that allows us, in some way, to quantify the enhancement of the Raman signal, is the so-called enhancement factor (EF). EF is theoretically defined as the ratio between SERS and the Raman (RS) intensity of the same investigated analyte. Neglecting the frequency shifts between incident and Raman light (this holds in particular for modes at low Raman shifts), the theoretical expression for EF is given by the well-known approximation to the fourth power of the local field:  
\[\mathrm{EF}=\frac{\mathrm{I}_{\mathrm{SERS}}}{\mathrm{I}_{\mathrm{RS}}}\approx \left|\frac{\alpha_{\mathrm{SERS}}}{\alpha_{\mathrm{RS}}}\right|\left|\frac{ \mathrm{E}_{\mathrm{loc}}}{\mathrm{E}_{0}}\right|^{4} \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Polymer**} & **Wavenumber** & \multirow{2}{*}{**Assignment**} \\  & **(cm\({}^{-1}\))** & \\ \hline  & 361 & C-Cl in-plane bending (in trans HClC=CHCl) \\  & **625** & **Crystalline C-Cl (in Cl2C=CHCl) stretching** \\  & **686** & **C-Cl symmetric stretching (in H2C=CHCl)** \\  & 961 & C–Cl asymmetric stretching (in H2C=CHCl) \\  & 1100 & C–O stretching \\  & 1179 & CH2 twisting \\  & 1255 & C–H rocking \\ PVC [74; 110; 111; 112; 113] & 1325 & CH2 deformation and –C–H bending \\  & **1420** & **CH2 symmetric deformation** \\  & 1724 & Ester CO stretching \\  & 2819 & \(\sim\)–H stretching vibration \\  & 2851 & CH2 symmetric stretching \\  & 2914 & CH2 asymmetric stretching \\  & 2940 & CH2 asymmetric stretching \\  & 2975 & \(\sim\)–H stretching \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cont.