Experimental and theoretical study on p-aminophenylthyil radical geminate recombination in ionic liquids; analysis using the Smoluchowski–Collins–Kimball equation

Abstract

Recombination dynamics of geminate p-aminophenylthiyl (PAPT) radicals produced from the photodissociation of bis(p-aminophenyl) disulfide in ionic liquids (ILs) were investigated by transient absorption spectroscopy. ILs with various cationic species were used to examine the effect of viscosity and polarity on recombination dynamics. Experimentally obtained recombination yields and dynamics were found to be virtually independent of the cation species, despite the viscosity range of the solvent ILs being extensive, spanning from a few tens of mPa s to several hundred mPa s. We applied a theoretical analysis model based on the diffusion equation to the time profiles of the experimentally determined recombination yields of geminate PAPT radicals. The square well potential was incorporated into the diffusion equation to consider the concerted dynamics of solvent cage formation and recombination. A long-time asymptotic expression for the survival probability of the photodissociated products was derived and used to simulate the experimentally obtained time profile of the recombination yield. The time profiles in the range of 20–1000 ps and the final yield were successfully simulated by the asymptotic expression of the square well potential model. The optimized parameters used for the fit, including the mutual diffusion coefficient of the radical pairs, cage radius of the potential well, and well depth, were discussed in terms of the diffusion coefficient conventional theory and the potential mean force estimated from the molecular dynamics simulation for the photodissociation reaction in ILs.

Solvent Role of Ionic Liquids in Fundamental Chemical Reaction Dynamics Analyzed by Time‐Resolved Spectroscopy

“…An analytical expression of the SWP model using the Green function method is also given in Ref. [61]. As this expression was only obtained in the Laplace space, the long-time asymptotic form (Eq.…”

“…Among the six coefficients (k a , a, R, E, D, and r 0 ), we fixed three: contact distance a, second-order intrinsic rate constant k a , and cage radius R. The other three parameters, E, D, and r 0 , are assumed to be adjustable. [61] The blue solid curve in Figure 9(b) shows the simulation result with a long-time asymptotic equation. The experimentally determined survival probability in the long-time region was successfully reproduced using the SCK model with SWP.…”

“…Figure 9 shows time profiles of the band integral of the transient absorption of PAPT radical in various ILs obtained by the spectrum decomposition [61] . This initial decay indicates a geminate recombination process that regenerates BPADS.…”

“…where Θ is the Heaviside step function, R is the position of the potential barrier, and E is the depth of the potential well. The following equation is a long‐time asymptotic solution of the SCK equation with the SWP [61] $$$\vcenter{\openup.5em\halign{$\displaystyle{#}$\cr {\rm \Phi }\left(t\right)\sim 1-{{{a}_{{\rm e}{\rm f}{\rm f}}}\over{{r}_{{\rm e}{\rm f}{\rm f}}}}{{{k}_{{\rm e}{\rm f}{\rm f}}}\over{{k}_{{\rm e}{\rm f}{\rm f}}+4\pi D{a}_{{\rm e}{\rm f}{\rm f}}}}\hfill\cr \left[1-\left\{1-\left({r}_{{\rm e}{\rm f}{\rm f}}-{a}_{{\rm e}{\rm f}{\rm f}}\right){\gamma }_{{\rm e}{\rm f}{\rm f}}\right\}{e}^{{\gamma }_{{\rm e}{\rm f}{\rm f}}^{2}Dt}{\rm e}{\rm r}{\rm f}{\rm c}\sqrt{{\gamma }_{{\rm e}{\rm f}{\rm f}}^{2}Dt}\right](t\to \infty )\hfill\cr}}$$$ …”

“…Figure 9 shows time profiles of the band integral of the transient absorption of PAPT radical in various ILs obtained by the spectrum decomposition. [61] This initial decay indicates a geminate recombination process that regenerates BPADS. Owing to the higher viscosity of ILs compared to that of conventional solvents, the geminate recombination dynamics proceeded rapidly and almost completed within 200 ps.…”