## 3 Results and Discussion
### Role of the Cationic Modifier in the Dyeing Process of Cotton  
The general reaction mechanism of reactive dyes with unmodified cellulose surfaces consists of two major steps. First, the physical contact of the molecules through the sorption of dyes from the dye bath on the cotton fiber, and second, the chemical reaction with the cellulose. The reaction proceeds only in the presence of an alkaline bath which is used to activate the cellulose reactive site (fixation phase) [49; 50]. Vinyl sulfone is the reactive group of both dyes used in the present study. In fact, during the dyeing process, the masking sulfate group is removed by a 1,2-trans elimination reaction, to form the free vinyl sulfone group, able to react with fiber nucleophiles by the Michael addition reaction [33]. Vinyl sulfone dyes are applicable at the range of 40-60 \({}^{\circ}\)C [51]. Novacron Ruby S-3B is bifunctional since it contains also one chloro-triazine reactive site, able to react with cellulose through the classical SN\({}_{2}\) bimolecular substitution from a nucleophilic attack of the electron-rich oxygen in the cellulose anion on electron-deficient carbon atoms in the triazine heterocycle (chlorine leaving group). The most important disadvantage of this dye category is the increased requirement of alkaline concentration (sodium carbonate) and temperature (80 \({}^{\circ}\)C) in the dye bath [49; 50; 51]. When investigating the role of cationic modification of cotton, it is necessary to understand the effect on increasing the retention of dye. To demonstrate the capabilities of cotton modification with the present cationic modifiers, we applied the same dyeing protocols on modified and unmodified fabrics. The protocol involved high and low temperatures with and without salt (Section S2). Cationization resulted in fibers characterized by a thin modified layer. The thickness of the modified layer is so small that spectroscopic techniques, such as FTIR and Raman scattering with a penetration depth of very few microns, offer marginal information, and extremely sensitive surface techniques, such as XPS, could identify and provide insight into the physical chemistry associated with the modification process. This argument is also supported by scanning electron microscopy images (Figure S1), where the morphology of untreated, dyed untreated, and dyed treated fibers remains similar in the scale of hundred nm. This observation indicates that both modifier and dye are covering just a few nm of the fibers' surface, which is similar to the order of XPS electron escape depth. The quantity of dye retained on the cellulose fibers' surface can be qualitatively extracted by XPS and more clearly in the carbon 1s spectral region. XPS spectra obtained from the samples after the dyeing process (using Novacron Ruby S-3B) in this particular spectral region can be seen in Figure 11. The most characteristic peak of cotton is the one at 286.6 eV; we use this peak as an internal standard in order to semi-quantify the degree of modification as well as of dyeing, taking into account that both modifier and dyes exhibit a characteristic band at \(\sim\)285 eV. We thus observe a small intensity increase of the latter band after dyeing unmodified cotton at ambient temperatures. This small intensity increase agrees well with the macroscopic poor fabric color intensity (Figure 12), while similar color intensity is observed in the modified fabrics with the copolymer. Modified fabrics exhibit strong contributions in the \(\sim\)285 eV band indicating grafting of the cationic polymer to the cellulose fibers, while subsequent dyeing of the modified fabric resulted in a further increase of the same band intensity. The ability of the XPS to semi-quantify the quantity of dye on fabrics may be furthermore demonstrated in the inset of Figure 11 where small differentiation of the 285 eV intensity is resolved for fabrics dyed with and without salt at ambient temperatures, the first of which was characterized by slightly better retention of dye.