# Bacterial Cellulose-Polyvinyl Alcohol Based Complex Composites for Controlled Drug Release
## 2 Materials and Methods
### Drug Release Studies  
Aiming to observe the influence of structural configuration and layers composition, the investigation of drug release was conducted in a simple system: 100 mL water was used as a desorption solution, at a constant temperature (25 \({}^{\circ}\)C), under continuous stirring to accelerate diffusion and maintain a homogenous diffusion environment. The experiments were performed in an apparatus similar to the one reported by [PERSON] et al., 2010 [33]. Samples of the solution (0.1 mL) were removed at predefined time intervals and the concentration of TC-HCL was measured by a UV/VIS spectrophotometer (CINTRA 6-GBS Scientific-Australia) at 365 nm. The samples' volume was considered very low to influence diffusion.  
Antibiotic release was modeled using the classical unsteady state Fick's diffusion equation. Films were considered as plane thin sheets with an initially homogenous TC-HCl concentration distribution and constant diffusivities (in a simplistic approach):  
\[\frac{\partial C}{\partial\tau}=D(\tau)\cdot\frac{\partial^{2}C}{\partial x^{ 2}} \tag{4}\]  
where: \(C\) is the drug concentration (kg m\({}^{-3}\)), \(D\) is the diffusion coefficient (m\({}^{2}\) s\({}^{-1}\)), \(x\) is the space coordinate in the diffusion direction (m), and \(\tau\) is the immersion time (s).  
When the stirring rate of the release medium provides the perfect mixing conditions, the amount of drug released after a period of time can be calculated with Equation (5) [34]:  
\[M_{Fickian}(\tau)=M_{\infty}\cdot\left(1-\frac{8}{\pi^{2}}\sum_{n=0}^{\infty} \frac{1}{\left(2n+1\right)^{2}}\cdot\exp\left(-\frac{\left(2n+1\right)^{2}\pi ^{2}}{4\delta^{2}}\cdot D\cdot\tau\right)\right) \tag{5}\]  
where: \(M_{\infty}\) is the amount of TC-HCl released at equilibrium (kg) and \(\delta\) is the film thickness (m).  
Overall diffusion coefficients were calculated using Equation (6), valid for the early stages of diffusion:  
\[\text{D}=\left(\frac{\text{k}\,^{\prime}\cdot\delta}{4}\right)^{2}\pi \tag{6}\]  
where: \(k^{\prime}\) is the slope of the linear regression of M\({}_{\tau}\)/M\({}_{\infty}\), versus \(\tau^{1/2}\).  
Additionally, the two-stages washing/diffusion mathematical model of [PERSON] (1986) was used to describe TC-HCl release from multi-layered membranes. The following exponential equation was adapted for this study [35]:  
\[c^{*}=c_{w}^{*}\cdot\left(1-e^{-k_{w}\cdot t}\right)+c_{d}^{*}\cdot\left(1-e^{ -k_{d}\cdot t}\right) \tag{7}\]  
where: \(c^{*}=c/c_{\infty}\) is the solute concentration in the solution (solvent) at any time of the diffusion/release process, mg L\({}^{-1}\); \(c_{\infty}\) is the hypothetical TC-HCl concentration in the solution at equilibrium (at time equal to infinity), mg L\({}^{-1}\); \(c_{w}^{*}=c_{w}/c_{\infty}\), where \(c_{w}\) is the final hypothetical concentration in the solution due to the washing stage alone, after the release process has been completed, mg L\({}^{-1}\); \(c_{d}^{*}=c_{d}/c_{\infty}\), where \(c_{d}\) is the final hypothetical concentration in the solution due to the diffusion stage alone, after the release process has been completed, mg L\({}^{-1}\); \(k_{w}\) is the kinetics coefficient for the washing stage, min\({}^{-1}\); and \(k_{d}\) is the kinetics coefficient for the diffusion stage, min\({}^{-1}\).