## 2 Materials and Methods
### Dye Preparation and Calibration Curve  
The photoelectrochemical reactor and analytical method were developed to address a real-world issue: the degradation of a commercial dye widely used in industry. The chemical composition of such dyes is often protected by industrial property regulations, which adds complexity to their analysis. Consequently, this study aimed to evaluate the composition and proportion of components within a commonly used commercial dye to better understand the system under investigation as a case study for the proposed technology.  
To evaluate the reduction in dye concentration during treatment, a 50% solution of a commercial dye was prepared following the manufacturer's recommendations (1 mL per L or kg of the finished product). Specifically, 0.5 mL of the dye was dissolved in deionized water, and 1% sodium chloride (NaCl) was added as a supporting electrolyte to simulate typical dye conditions and enhance the solution's conductivity.  
A calibration curve was constructed using six different concentrations, prepared through serial dilutions of the initial solution (0.5 mL \(\times\) L\({}^{-1}\)) using the formula \(C_{1}V_{1}=C_{2}V_{2}\). The resulting concentrations were 100%, 75%, 50%, 25%, 5%, and 0%, with 0% serving as the blank, using deionized water. Absorbance measurements were performed using a Thermo Scientific NanoDrop One UV-Vis spectrophotometer (Thermo Scientific, Waltham, MA, USA). Wavelength scans were conducted over the range of 190-700 nm to capture the full absorbance spectrum.  
To identify and quantify the dyes present in the commercial mixture, the UV-Vis spectra were analyzed at characteristic wavelengths commonly associated with industrial dyes, such as Tartrazine (\(\lambda_{\text{max}}\) = 428 nm), Erythrosine (530 nm), and Brilliant Blue (630 nm). While the composition of the commercial dye mixture depends on the manufacturer and may vary, these wavelengths were chosen based on typical dyes widely used in industrial applications. Overlapping peaks in the spectra were deconvoluted using the deconvolution tool in Origin 2024 software. This process allowed precise quantification of individual dye components within the mixture by separating their overlapping spectral contributions.  
The calibration curve was generated by plotting the absorbance values at these characteristic wavelengths against the corresponding dye concentrations. Linear regression analysis, performed using Origin 2024, provided the calibration equation and associated statistical parameters (e.g., coefficient of determination, R\({}^{2}\)). This information was crucial for ensuring the accuracy and reliability of the calibration.  
Changes in dye concentration during the treatment process were monitored by comparing absorbance values at each time interval against the calibration curve. The degradation rates were calculated for each dye based on their specific absorbance maxima. Experimental conditions and parameters during the photoelectrochemical treatment were consistently controlled to ensure reproducibility and validity of the results.  
The results are presented as the degradation of the fraction of each dye, highlighting their individual contribution to the overall composition of the commercial mixture. The properties and characteristics of the dyes identified in the commercial product are included, as they form the basis for the discussion of the results. The chemical composition of the dyes was inferred from the experimental evaluation and the manufacturer's specificationsto provide a comprehensive understanding of the system under study. This detailed characterization enhances the relevance of this research as a case study for the application of photoelectrochemical technology to real-world problems.