Yes, it is possible to calculate the bandgap of a colloidal photonic crystal thin film from its transmittance spectra measured via UV-Vis spectroscopy. The bandgap of a photonic crystal is related to its structural properties, such as the lattice constant, the refractive index contrast, and the filling fraction. The transmittance spectrum of a photonic crystal film shows a sharp decrease in transmission at the bandgap energy due to the photonic bandgap effect. The position of the bandgap can be determined by locating the maximum of the first derivative of the transmittance spectrum.
To calculate the bandgap energy, you can use the Bragg equation, which relates the bandgap energy to the lattice constant and the refractive index contrast. The filling fraction of the photonic crystal can also be determined from the transmittance spectra by comparing the position of the bandgap to the expected bandgap position for a perfect crystal with the same lattice constant and refractive index contrast.
However, it is important to note that the bandgap energy of a colloidal photonic crystal thin film may be affected by various factors, such as defects, disorder, and surface roughness, which can cause deviations from the ideal crystal structure. Therefore, it is recommended to carefully analyze the transmittance spectra and compare them to simulations or theoretical models to ensure the accuracy of the calculated bandgap energy.