Analysis of pyrene fluorescence emission by fast Fourier transformation

The transfer function, H(omega), for fluorescence emission of pyrene in ethanol has been calculated from the excitation ray and fluorescence time profiles by the fast Fourier transformation (FFT) process. The H(omega) describes a clear semicircle on the Nyquist plane at low pyrene concentration. On the other hand, at high pyrene concentration the real part of H(omega) takes a negative value and the locus deviates from a semicircle at high frequency region. The theoretical expressions of the H(omega) have been derived on the basis of the fluorescence emission model containing the formation of excimer: H(omega)=2.3 alpha epsilon lCPp{k(f1)(j omega+K-2)+k(f2)k(e)CP}/{(j omega+K-1)(j omega+K-2)-K-3} K-1=k(q1)+k(f1)+k(e)CP, K-2=k(b)+k(f2)+k(q2,) K-3=k(b)k(e)CP where alpha is correction factor, epsilon is the molar extinction coefficient, l is the cell length and CP is the concentration of pyrene. k(e) and k(b) are the formation rate constant and its reverse rate constant, respectively. k(fl) and k(q1) represent rate constants of fluorescence emission and quenching of excited pyrene, respectively. k(f2) and k(q2) represent rate constants of fluorescence emission and quenching of excimer, respectively. The results simulated by this equation were in good agreement with experimental results. In the course of simulation, kinetic parameters for the pyrene fluorescence were obtained.