# M13 Bacteriophage-Assisted Synergistic Optical Enhancement of Perovskite Quantum Dots
## 3 Results and Discussion
### TRPL Analysis of CsPbI3 PQDs with the M13 Phage in Solution Phase  
To prove the enhancement of PQDs coupled with the M13 phage more theoretically, the TRPL spectra of the solution were measured under the excitation wavelength of a 405 nm picosecond laser diode. As shown in Figure 4, the TRPL spectra indicate that the PQDs coupled with the M13 phage exhibit a significantly higher fluorescence lifetime compared to PQDs alone. This suggests that the M13 phage coating can enhance the radiative recombination efficiency of the QDs. The biexponential TRPL decay curves can be fitted by Equation (1). \[A_{0}+A_{1}\exp\biggl{(}-\frac{t}{\tau_{1}}\biggr{)}+A_{2}\exp\biggl{(}-\frac{ t}{\tau_{2}}\biggr{)} \tag{1}\]  
Figure 3: DFT simulations of pure PQDs and PQDs with the M13 phage. Differential charge density plots for (**a**) pure PQD and (**b–d**) an increasing concentration of M13 phages with PQD. Blue isosurfaces represent a loss in electron density and yellow isosurfaces represent the accumulation. Here, an increase in concentration (green arrow) of M13 phages is mimicked by an increasing number of glutamic acid (E as a unit model) interactions with PQDs. Colors of atoms used are as follows: Cs—purple, I—dark grey, Pb—brown, O—red, C—gray, H—white, and N—blue. Electron localization function results in (**e**) pure PQD and (**f–h**) an increasing concentration of M13 phages with PQD. Here, \(A_{0}\) represents the background signal, \(A_{1}\) and \(A_{2}\) represent the relative amplitude, and \(\tau_{1}\) and \(\tau_{2}\) represent the decay time constants for these components. And, the weighted decay time \(\tau_{w}\) is calculated by considering the relative amplitudes of each time constant, which is defined by \(\tau_{w}=\sum_{i}A_{i}\tau_{i}/\sum_{i}A_{i}\) and presented in Table 1.  
The decay time enhancement for the lowest concentration of M13 was found to be 3.8 ns, and the highest concentration resulted in an enhancement of 12.8 ns. The enhanced decay times at higher concentrations could be due to the increased number of phage particles, which leads to a higher probability of photon emission. This leads to higher photoluminescence efficiency and a brighter emission from the PQDs. The interaction between the M13 phage and PQDs could be attributed to the surface modification of the PQDs, which enhances the radiative recombination rate and reduces the non-radiative processes. In Table 1, we presented the detailed PL decay times information for PQDs versus the M13 phage-coupled PQDs. These curves were fitted using the biexponential TRPL decay curves and the relative amplitudes and decay time constants. For PQDs only: The relative amplitude values are 36.7 and 79.3; decay times are 13.4 ns and 53.8 ns; and the weighted decay time is 41.1 ns. In the case of the M13 phage-coupled PQDs: Relative amplitude values are 15.3 and 71.2; decay times are 16.7 ns and 61.2 ns; and the weighted decay time is 53.3 ns. The results indicate that the presence of the M13 phage in the PQDs sample significantly impacts the decay characteristics. Specifically, the decay time constants are longer, implying a slower decay of fluorescence. This leads to a higher weighted decay time of 53.3 ns, which signifies an extended average lifetime of the excited state when the M13 phage is present. These findings suggest that the interaction between PQDs and the M13 phage modifies the fluorescence properties of the PQDs. Additionally, the elongation in decay time constants could be ascribed to the binding of the M13 phage to the PQDs' surface, potentially obstructing the relaxation of excited states and promoting the radiative decay pathway.