# Investigation of Gentamicin Release from
## 3 Results and Discussion
### Kinetic Study of Gentamicin Release  
The implementation of mathematical models is critically important to evaluate the mechanism and kinetics of drug release from drug delivery systems. The drug release from the polymer matrix could be divided into three categories, viz. ; diffusion-controlled; erosion-controlled and swelling-controlled, which are applied on non-degradable polymer and degradable and swellable polymer matrices, respectively. Table S1 (Supplementary Materials) shows various mathematical models and their mechanisms investigated so far, relating to the various drug delivery systems [31; 32; 33; 34]. In this study, the kinetic release of gentamicin from PDA NPs was determined by employing two mathematical models, the Ritger-Peppas and Higuchi models. These models were found to be best fitted to the drug release data, supported by high correlation coefficient (R\({}^{2}\)) values. These models suggested the diffusion-controlled release of gentamicin in response to change in pH of the environment. The Ritger-Peppas model is represented by the following equation:  
\[\mathrm{M_{t}}/\mathrm{M_{\infty}}\mathrm{=kt^{n}} \tag{1}\]  
where, \(\mathrm{M_{t}}\) and \(\mathrm{M_{\infty}}\) are cumulative drug release at time t and at equilibrium, respectively. \(\mathrm{M_{t}}/\mathrm{M_{\infty}}\) represents the fraction of drug release at time t. k is the kinetic release rate constant of the Ritger-Peppas model (h) and n is the diffusional exponent characteristic of the  
Figure 3: Comparison between % drug release from G-PDA 0.6:1 and G-PDA 1:1 at various pH conditions. release mechanism. According to the Ritger-Peppas model, the value of n demonstrates the drug release mechanism which can be divided into various categories, as described in the literature [35; 36]. If 0.45 \(\leq\) n, it corresponds to the Fickian diffusion mechanism by following [PERSON]'s law, and 0.45 \(<\) n \(<\) 0.89 shows non-Fickian transport (anomalous diffusion). Moreover, if the value of n = 0.89 and n \(>\) 0.89, it corresponds to case II transport and super case II transport respectively. Therefore, the experimental data were plotted, and non-linear fitting was performed for the G-PDA NPs 1:1 at pH 7.4, 5 and 3 into the Ritger-Peppas model to determine the exact mechanism involved. Figures 4A, 5A and 6A show the fitting of drug release data at pH 7.4, 5 and 3, respectively, in the Ritger-Peppas model. Figure 4: Fitting of cumulative % drug release data to (**A**) Ritger–Peppas and (**B**) Higuchi model for pH 7.4. Figure 5: Fitting of cumulative % drug release data to (**A**) Ritger–Peppas and (**B**) Higuchi model for pH 5. Please note that the Fickian diffusion is the classical diffusion process that is controlled by the concentration gradient with the constant diffusion coefficients (\(0.45\leq\) n) and relatively simple kinetic profiles of penetrant redistribution in the polymer matrix. On the other hand, in non-Fickian or anomalous diffusion, the diffusion coefficient is not constant (such as time- or concentration-dependent. Therefore, the relationship between the time and concentration changes could be because of factors such as chemical interactions between the medium and diffusant, chemical reactions, swelling and mechanical stress. Table 2 shows various drug release parameters obtained after non-linear fitting in the Ritger-Peppas and Higuchi models. All of the particles showed the n value between 0.45 and 1, hence indicating a non-Fickian diffusion of the gentamicin from the PDA NPs. The drug release data show that the release mechanism of the gentamicin from the PDA NPs is strongly dependent on the pH of the environment which acts as a driving force for the gentamicin to diffuse from the PDA NPs to the PBS solution. Moreover, the release mechanism of the G-PDA NPs is also influenced by the structural behavior of the PDA at different pH conditions. It was previously discussed that the zwitterionic nature of PDA makes it negatively charged at alkaline pH and positively charged at acidic pH.