Linear and Nonlinear Photoexcitation Dynamics in $\pi$-Conjugated Polymers

Linear and nonlinear recombination kinetics with various lifetime distributions were identified for long-lived photoexcitations in a series of $\pi$-conjugated polymer films using modulation frequency and excitation intensity dependencies of the photoinduced absorption. This includes monomolecular, bimolecular, and defect-limited recombination processes that lead to saturation. Using generalized kinetics parameters, we found characteristic plots for all recombination processes. Specifically, the bimolecular recombination process shows superlinear intensity dependence away from the steady state; on the contrary, dispersive bimolecular recombination leads to sublinear dependence.

Figure 1

(a) MR and BR kinetics plotted as $\mu$ vs $\chi$ (see text). The in-phase (quadrature) component shows ${\chi }^{3/2}$ (${\chi }^1$) and ${\chi }^{1/2}$ (${\chi }^{\approx 0}$) dependencies at low and high values of $\chi$, respectively. (b) PIA dynamics for the HE band in $p$-PBV plotted as ($-\Delta T/T\omega$) vs $I/I_0{\omega }^2$, where $I_0$ is a normalizing parameter. Inset: Chemical structure of $p$-PBV.

Figure 2

(a) $N_I$ vs $g$ calculated for BR and DBR kinetics. $N_I\propto g^{3/2}$ away from the steady state. Near steady state $N_I\propto g^{\gamma }$ where $\gamma =1/2$ for BR and $\gamma <1/2$ for DBR. (b) Experimental in-phase component of the PIA vs $I$ for the HE band in $p$-PBV. The straight lines, marked $I^{1/2}$ and $I^{3/2}$, signify the two dynamic regions indicating BR. Inset: PIA spectra of $p$-PBV for acid saturated and free base forms [6].

Figure 3

(a) As in Fig. 1 but for dispersive BR process. (b) PIA measurements of the LE band in $p$-PBV plotted using the generalized coordinates. The solid line corresponds to dispersive BR with $\alpha =0.5$.

Figure 4

(a) As in Fig. 2 but for dispersive BR process with $\alpha =0.6$. Note the sublinear $g$ dependence. (b) The PIA bands of TE and $P^{\pm }$ in PFO vs $I$. The approximate $I^{0.9}$ ($I^{0.5}$) dependence at low (high) $I$ corresponds to dispersive BR with $\alpha \approx 0.8$. Inset: Chemical structure of PFO.