## 1 Introduction  
Titanium dioxide (TiO2) is considered to be a widely used and safe material with various applications. It is a semiconductor widely and thoroughly studied by the scientific community regarding its catalytical, self-cleaning, and antibacterial properties [1, 2, 3]. It occurs in three different crystalline phases: rutile (tetragonal), anatase (tetragonal), and brookite (orthorhombic). The first two exhibit a higher catalytic effectiveness and stability, whereas brookite is a more unstable polymorph [4]. The crystalline phase, the size, and the shape of particles are the characteristics leading to TiO2 catalysts with different physical and chemical features [5]. The self-cleaning and antibacterial properties of TiO2 are a result of ultraviolet (UV) irradiation photoactivation, associated with its energy or band gap (E\({}_{\text{g}}\)). To enhance these properties under visible light, a metal or non-metal element doping is applied [6, 7, 8]. The doped TiO2 nanoparticles have various environmental applications and are widely studied by the scientific community, using mainly organic pollutants such as Methylene Blue (MB), Rhodamine B (RhB), Acid Orange (AO7), Brilliant Green (BG), Reactive Red Dye(RRed Dye), etc. [9; 10; 11; 12]. There has been extensive scientific research on how to degrade dyes and organic pollutants, proposing the synthesis of various catalysts [13; 14]. These catalysts can be composite materials with metal nanoparticles and polymers. For example, hybrids with Gold (Au) nanoparticles (NPs) and polymer microgels are used as catalysts for dye reduction [15]; Cobalt (Co) NPs with organic polymers are used for water purification and removal of toxic dyes [16]; Silver (Ag) NPs with Poly(acrylic acid) hydrogel are reported to reduce Methyl Orange (MO) [17]; and S-doped graphite carbon nitride with Nickel (Ni)-doped Zinc Oxide (ZnO) degrades MB under UV and visible light [18]. However, the use of expensive metal NPs is not considered cost effective, especially when upscaling [13]. Moreover, metal NPs exhibit high toxicity and are not biocompatible or environmentally friendly [14]. Therefore, more eco-friendly choices are presented in the recent literature, such as the extraction of NPs from the plant Pulicaria Undulata combined with TiO\({}_{2}\) for the degradation of MB and MO [19]. In some cases, metals are also combined with graphene to form composite materials for catalytic purposes. Graphene with organic or inorganic NPs has been broadly studied, showing a high catalytic activity and adsorption properties [20]. In fact, when doped with Nitrogen (N), it leads to defects in the catalyst and to the formation of more active sites for photocatalysis [21; 22]. An investigation regarding azo dye photocatalysis by using the above-mentioned catalysts is relatively demanding, due to their intricacy and complicated physicochemical characteristics. Therefore, the widely studied, low cost, chemically and biologically inert TiO\({}_{2}\) is chosen for the present study, being doped with Nitrogen [7; 23]. The photocatalysis process is a complex one, with various features affecting the final photodegradation [24]. The nature of the pollutant used for the photocatalytic process, the catalyst's amount used, the distance from the irradiation source, and the time protocol followed are some of these features. The present study focuses on examining those specific features affecting the catalytic behavior of doped TiO\({}_{2}\), as these are commonly researched [25; 26; 27]. The need to investigate the matter more thoroughly arises from the different photocatalytic protocols followed in the literature, which often lead to contradictory results [23]. A useful tool for studying the above is the Taguchi method. The same method is found in the literature applied for optimizing the synthesis of TiO\({}_{2}\) photocatalysts [28; 29]. The Taguchi method is a statistical method developed by [PERSON].