## 4 Conclusions  
The AgNPs formation and investigation to enhance the photocatalytic efficiency of TiO\({}_{2}\) thin films were investigated in this study. The highest circularity of 0.918 of AgNPs was observed after annealing the Ag/TiO\({}_{2}\) at 400 \({}^{\circ}\)C. This study suggests that an optimal annealing time of 60 min is required to get the highest possible distribution of AgNPs when annealing Ag films of 10 nm. A shorter annealing process results in fractal-like structures. Moreover, the analysis of AgNPs formation dependency on the initial thickness (\(h_{Ag}\)) of Ag thin films suggests that thin films with a thickness lower than 10 nm are discontinuous. The results show that the density of AgNPs is inversely proportional to the thickness of Ag thin films: \(h_{Ag}\) = 5 nm, \(D\) = 398 um\({}^{-2}\); \(h_{Ag}\) = 7.5 nm, \(D\) = 229 um\({}^{-2}\); \(h_{Ag}\) = 10 nm, \(D_{A}\) = 42 um\({}^{-2}\). The photodegradation experiments revealed that the photocatalytic efficiency increases for the AgNP/TiO\({}_{2}\) structure compared to stand-alone TiO\({}_{2}\) (\(k_{TiO2}\) = 0.008 min\({}^{-1}\); \(D_{\textit{{off}}\_TiO2}\) = 36.3%). The highest efficiency of \(D_{\textit{{off}}\_38}\) = 63.5% (\(k_{38}\) = 0.017 min\({}^{-1}\)) was observed for the AgNP/TiO\({}_{2}\), where an average AgNPs diameter was 38 nm, whereas for the AgNPs with \(D_{A}\) = 27 nm\(-D_{\textit{{off}}\_27}\) = 51.2% (\(k_{27}\) = 0.012 min\({}^{-1}\)) and \(D_{A}\) = 82 nm\(-D_{\textit{{off}}\_82}\) = 52.1% (\(k_{82}\) = 0.011 min\({}^{-1}\)). The nonlinear dependence of degradation efficiency on AgNPs size could be expanded by AgNPs density variation.  
Figure 7: The photodegradation of RhB in an aqueous solution using TiO\({}_{2}\) (**a**) and AgNP/TiO\({}_{2}\) (**b**) as a photocatalyst. _CBM_—conduction band minimum; _VBM_—valence band maximum; _E\({}_{g}\)_—energy band gap; _E\({}_{F}\)_—Fermi energy level; _XTiO\({}_{2}\)_—electron affinity; _Inv_—photon energy; _e\({}^{-}\)_—electron; _h\({}^{+}\)_—hole.  
AgNP could block UV light and act as recombination sites when the density of AgNPs is very high, whereas a small number of trapping sites could be created when the density of AgNPs is low.  
V.K.: Formal analysis, Investigation, Writing--original draft, Writing--review and editing, Visualization. P.C.: Formal analysis, Investigation. M.S.: Conceptualization, Methodology, Writing--original draft, Writing--review and editing, Supervision, Data curation. G.L.: Conceptualization, Methodology, Resources, Funding acquisition, Project administration. All authors have read and agreed to the published version of the manuscript.  
This project has received funding from European Social Fund (project No 09.3.3-LMT-K-712-01-0162) under grant agreement with the Research Council of Lithuania (LMTLT).  
Not applicable.  
The authors would like to express their gratitude to the following individuals for their expertise and contribution to the manuscript: [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON].  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.