## 3 Results and Discussion
### Fluorescence Spectra Behaviour of Cimnamaldehyde (CAD) in SDS-Ethanol Media
Therefore, the fluorescence data below the CMC and above the CMC are well fitted in the Stern-Volmer equation as given below:  
\[\frac{\text{F}^{\circ}}{\text{F}}=1+K_{q}\tau^{\circ}\left[Q\right]=1+K_{SV} \left[Q\right], \tag{6}\]  
where, F\({}^{\circ}\) and F are the fluorescence intensities in the absence and presence of quencher, respectively. A linear regression plot is drawn between the F\({}^{\circ}\)/F against the molarity of varying concentration of the quencher [Q] (Figures 6 and 7). \(K_{sv}\) is the Stern-Volmer constant, and its values are listed in Table 2. Below the CMC, the plot is linear, showing lower value of \(K_{sv}\) than in the post-micellar region, i.e., above the CMC, suggesting that the micellization is controlled by the dynamic quenching mechanism rather than the static mechanism. \(K_{q}\) is the quenching rate constant, and the values are evaluated by using Equation (6) [32] in the following form:  
\[K_{q}=\frac{K_{SV}}{\tau^{\circ}} \tag{7}\]  
where, \(\tau^{\circ}\) is the average lifetime of the fluorescent molecule with the value (\(10^{-8}\) s\({}^{-1}\)), and the \(Kq\) values estimated from Equation (7) are presented in Table 2. Hydrophobicity of the SDS molecule in the pre- and post-micelle regions has a significant influence on the binding constant, and the equilibrium between free and bound molecules is given by the Equation (8) [32]. \[\text{Log}_{10}\frac{\text{F}^{\circ}-\text{F}}{\text{F}}=\log_{10}K_{b}+n\ \log_{10}\left[Q\right] \tag{8}\]  
where, \(K_{b}\) is the binding constant and \(n\) is the binding sites, and the value of \(K_{b}\) and \(n\) is obtained from the intercept and slope of the linear regression plot between \(\log_{10}\) (\((\text{F}^{\circ}-\text{F})\)/F) versus \(\log_{10}\) [Q] below and above the CMC. The values are shown in Table 2. The higher value of \(K_{b}\) above the CMC than the binding constant below the CMC is positive evidence of the hydrophobic interaction. The observed comparatively lower fluorescence intensities in pre-micellar concentrations occurred after the repulsive electrostatic forces and dipolar interactions between CAD and SDS molecules in the ethanol medium, in turn resulting in a reduction of the fluorescence intensities. In addition, at pre-micellar concentrations, the partitioning of drug molecules has maximum probabilities as more forces are prevailing to form fewer aggregates in comparison with the micellar region hence, hydrophobic forces are predominating major driving force for micellization in the micellar region. By knowing the binding constant of SDS with the CAD-ethanol system below and above the CMC, thermodynamic parameter free energy change (\(\Delta\)G\({}^{\circ}\)) can also be evaluated easily in the surfactant transition process of monomer to micellar phase by the following equation [32]:  
\[\Delta\)G\({}^{\circ}=-RTln\;K_{b} \tag{9}\]  
The obtained negative values of free energy change (\(\Delta\)G\({}^{\circ}\)) (listed in Table 2) signify the SDS thermodynamic stability and governs the binding process favoring the micellization process. Figure 4: Fluorescence intensities (FI) versus wavelength for pre-micellar concentrations of SDS in CAD + E-OH. Figure 5.0 Fluorescence intensities (FI) versus wavelength for post-micellar concentrations of SDS in CAD + E-OH.