## 3 Results and Discussion
Figure 3 shows absorbance spectra of the ion-exchanged PTR-M glass samples heat-treated in different conditions. The absorption band peak at 445 nm, related to the growth of SNIF on the ion-exchanged PTR-M glass surface, was observed already after the heat treatment for 15 min at 350 \({}^{\circ}\)C (Figure 3a). The increase in absorption amplitude, red shift of the absorption peak, and emergence of the second band around 355 nm occurred with a longer heat treatment duration. An analogous dependence of the absorbance spectra on the heat treatment time was obtained for the samples heat-treated at 400 and 450 \({}^{\circ}\)C (Figure 3b,c). Similar changes in the absorbance spectra of SNPs dispersed in water solution were observed as a function of increasing size from 46 to 287 nm by [PERSON] and [PERSON] [33]. The authors assigned the observed changes to quadrupolar, octupolar, and hexadecapolar plasmon modes in SNPs with a size of 128-287 nm. As heat treatment temperature governs the kinetics of redox reactions and diffusion process of SNPs growth, it also influences the mean size and size distribution of SNPs. The heat treatment at 500 \({}^{\circ}\)C, i.e., above the glass transition temperature (464 \({}^{\circ}\)C for PTR-M glass), resulted in almost structureless absorbance spectra due to very broad and overlapped bands. To confirm that neither silver molecular clusters (SMCs) nor SNPs were formed in the ion-exchanged PTR-M glass during the heat treatment, the following experiment was conducted: a sample of the Na\({}^{+}\)-Ag\({}^{+}\) ion-exchanged PTR-M glass was repeatedly heat-treated at 500 \({}^{\circ}\)C. The SNIF formed on the PTR glass surface was removed mechanically by polishing the sample for 3-5 s, and absorption spectra were recorded after each cycle. The absorbance spectra obtained during this experiment are shown in Figure 4a. Na\({}^{+}\)-Ag\({}^{+}\) IE in PTR glass is known to induce a long-wavelength shift of the UV absorption edge [34]. The \begin{table}
\begin{tabular}{c c c} \hline \hline
**Glass** & **Sb\({}_{2}\)O\({}_{5}\) mol.\%** & **Br\({}_{t}\) mol.\%** \\ \hline PTR-M & 0 & 0 \\ PTR-Br & 0 & 1.4 \\ PTR-Sb2 & 0.002 & 0 \\ PTR-Sb4 & 0.004 & 0 \\ PTR-Sb10 & 0.01 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Batch concentration of additives in the studied PTR glass samples. Figure 2: Photo of the PTR-M glass sample (**left**) after Na\({}^{+}\)-Ag\({}^{+}\) IE and heat treatment at 500 \({}^{\circ}\)C for 3 h (the resulting surface film was partially removed) and of BK-7 glass ion-exchanged and heat-treated at 600 \({}^{\circ}\)C for 3 h (**right**). reason for the shift is strong absorption of the introduced silver ions that are characterized by the absorption envelope peak at 225 nm [35]. Thus, in contrast to the IE effect on absorbance spectra, a short-wavelength shift of the UV absorption edge was observed in the heat-treated samples. The spectra of the ion-exchanged and heat-treated PTR-M sample after removing SNIF showed no absorbance in the range above 300 nm, where the absorption bands of SMCs and SNPs in PTR glass are located [36]. This result also proved that all the features observed in the spectra presented in Figure 3 are related to SNIF formed on the PTR-M glass surface. Location of the UV absorption edge of the Na\({}^{+}\)-Ag\({}^{+}\) ion-exchanged PTR-M glass is determined by the absorption of Ag\({}^{+}\) ions [37]. Thus, it is possible to roughly estimate the integral silver concentration in the heat-treated samples compared to nontreated ones using the Beer-Lambert law. The differential absorbance spectra obtained by subtracting the spectrum of the as-synthesized sample from the others are shown on Figure 4b. The differential absorbance decreased more than eightfold at 255 nm, from \(\sim\)2.6 to \(\sim\)0.3 after 1 h of heat treatment at 500 \({}^{\circ}\)C. Further treatment led to a slower decrease in differential absorbance, down to \(\sim\)0.1.