## 3 Results and Discussion  
### Nanoparticle Synthesis and Characterization  
#### 3.1.1 Silver Nanoparticles Synthesis  
* Microwave-assisted synthesis  
Building on our previous work synthesizing gold nanoparticles using a microwave oven and CDs as reducing and capping agents [30], we adapted this method to synthesize silver colloids, focusing on \(\beta\)-cyclodextrintrin (\(\beta\)-CD) due to its optimal cavity size and effectiveness in forming inclusion complexes in medical applications, discriminating between propranolol enantiomers [15]. Sodium hydroxide (NaOH) was used to create an alkaline environment for the activation of CD groups, facilitating the reduction of silver ions (Ag\({}^{+}\)) to metallic silver (Ag\({}^{0}\)). We examined the impact of varying the Ag:\(\beta\)-CD ratio (1:2, 1:1, 1.5:1) while keeping NaOH constant at 5 mM. Spectrophotometric measurements confirmed colloid formation, with absorption maxima around 404 nm and full width at half maximum (FWHM) below 70 nm, indicating a uniform nanoparticle size distribution (Figure 1a). Higher silver nitrate concentrations increased absorbance values, demonstrating \(\beta\)-CD's reduction capability even at ratios exceeding unity. TEM images (Figure S2) revealed a uniform size distribution (<10 nm) with low polydispersity for colloids at a 1:2 Ag:\(\beta\)-CD ratio. Since the plasmonic resonance peak for all colloids was observed at approximately the same wavelength, we varied precursor proportions to examine their effects on the plasmonic peak position (related to nanoparticle size), FWHM (indicating size distribution), and nanoparticle stability. Ag colloids were synthesized under identical microwave conditions (2100 W for 60 s) with Ag:\(\beta\)-CD ratios from 0.5:1 to 3:1 and increasing NaOH concentrations. The UV-Vis spectra (Figure 1b) show the plasmonic peak shifting from 404 to 424 nm, with the lowest wavelength at a 1:2 ratio and the highest at 2:1. Higher Ag and NaOH concentrations led to an increased FWHM, indicating larger colloids with broader size distribution and greater polydispersity. Increasing AgNP size by raising the pH (using NaOH) also increased polydispersity and affected stability over time, as seen bythe reduction in plasmonic maximum and absorption broadening (Figure 1c). The most stable Ag colloids were obtained with an Ag:\(\beta\)-CD ratio of 0.5-1 and a pH of 9-10. No silver colloids formed at pH \(<\) 9, indicating \(\beta\)-CD cannot reduce Ag+ ions to metallic Ag under these conditions. Achieving monodisperse colloids with long-term stability is essential for applications involving plasmonic NPs. However, for surface-enhanced Raman spectroscopy (SERS), larger NPs are preferred as they generate strong electric fields or form 'hot spots' between aggregated NPs, greatly enhancing the Raman signal of nearby analytes. Our findings indicate that increasing the pH of the synthesis medium enlarges colloids but reduces their stability. To counter this, we adjusted the heating rate by lowering microwave power during synthesis. Using a \(\beta\)-CD to Ag molar ratio of 1:2 at a pH of 9-10, we found that reducing microwave power to 50% or 20% with longer exposure times yielded stable Ag colloids with plasmonic maxima at 402 nm and 404 nm. At 50% power, the maximum absorption was higher, suggesting incomplete silver ion reduction at lower power. The FWHM at 50% power was 64 nm, indicating reduced dispersity. Lowering the power further degraded the AgNPs' quality, resulting in lower absorbance and higher FWHM, and led to aggregation over time.