## 2 Results and Discussion
### Antibacterial Study  
The characterized material was subject to antibacterial tests using _E. coli_ and _S. aureus_ and the colony forming unit assay method for different time contacts. The variation regarding the number of total germs (CFU/mL) and percentage of bacterial reduction (P, %) at different contact times with the two antimicrobial materials are presented in Table S1 in Supplementary Materials. The number of viable cells from each bacteria type was significantly reduced by the studied materials and the inactivation effectiveness was dependent on the treatment time. Both materials, after 18 h of contact with the bacterial suspensions, showed the microbial reduction presented in Table S1. In the case of the action on _E coli_, the percentage reduction in the Bz-DVB-AN substance was 72.2, but the Et-DVBAN substance had a percentage reduction of 84.4. In the case of the _S. aureus_ species, the percentage reduction of the Bz-DVB-AN substance was 75.4, and that of the Et-DVBAN substance was 94.8. The effectiveness of microbial reduction by the studied materials is presented in Figures 9 and 10. The materials exhibit antibacterial activity three times higher than that of the standard sample within the first three hours of contact. Both materials are more effective against _S. aureus_ compared to _E. coli_. The Et-DVB-AN material demonstrates 20% better efficacy than the Bz-DVB-AN material to _E. coli_. The higher effectiveness in Gram-positive bacteria may be explained by the electrostatic interaction between the electronegative charge of the sample Et-DVB-AN and the positive charges on their walls. The reduction of more than 50% of the Gram-positive bacterial load was manifested after 9 h of contact; this point was observed for the Gram-negative ones only after 12 h of contact. In _S. aureus_, the effect of the sample Et-DVB-AN is expressed at a bacteriostatic (94.8%) to bactericidal (99%) efficiency (see Figures 9 and 10). The results regarding the logarithmic survival fraction versus contact time for both pathogens in the case of the two studied materials are presented in Table 3.  
To efficiently optimize treatment settings, a solid mathematical model reflecting the kinetics of microbial cell inactivation must be discussed. In this case, two mathematical models were applied for kinetic inactivation modeling of _E. coli_ and _S. aureus_ onto Bz-DVB-AN and Et-DVB-AN: the first-order kinetic model and Weibull model. The first-order kinetic model is a commonly used predictive tool for microorganism inactivation patterns. It is based on the assumption that the microbial population has a similar level of resistance and that there is a linear relationship between treatment time and the number of surviving cells [25; 26]. Figure 8: Thermogravimetric analysis of the pristine SV4 copolymer (**a**) and Et-DVB-AN (**b**). Figure 10: Percentage of bacterial reduction induced by the Et-DVB-AN sample at different intervals of time. Figure 9: Percentage of bacterial reduction induced by the Bz-DVB-AN sample at different intervals of time. The first-order kinetic model is presented in Equation (1). \[log\frac{N_{t}}{N_{0}}=-\frac{t}{D_{T}} \tag{1}\]  
where the starting and surviving populations of bacteria following treatment time \(t\) (h) are denoted by \(N_{0}\) and \(N_{t}\) (CFU/mL), respectively. The decimal reduction time, or \(D_{T}\) (h), represents the amount of time needed to inactivate 90% of the bacterial population. The linear representations of the first-order kinetic model of _E. coli_ and _S. aureus_ reduction by treatment with Bz-DVB-AN and Et-DVB-AN are presented in Figure 11. The decimal reduction time obtained in each case is presented in Table 4.  
It could be observed that the first-order kinetic model could be accurately applied for the experimental data fitting due to the high obtained values for R\({}^{2}\). Table 4 showed that the D\({}_{\text{T}}\) values for Bz-DVB-AN and Et-DVB-AN were 32.4 and 28.4 for _E. coli_ and 22.6 and 13.4 for _S. aureus_.