A Kinetic Model of LiC₆₀⁺ Formation Pressure Dependence

        In contrast to Li_nC₆₀⁺ (n>0), LiC₆₀⁺ formation depends strongly on helium background pressure. This suggests competition between vibrational relaxation and unimolecular dissociation. Analysis of this pressure dependence yields an estimate of the Li--C₆₀⁺ binding energy, E₀, and the vibrational relaxation rate k_vib.

Vibrational Relaxation Rate vs He Pressure

A kinetic model to determine E₀ and k_vib is made as follows:

This model expresses a rate equation determining the fraction of LiC₆₀⁺ formed during the interval t_c to t_c+delta.t and integrating the solution over all time 0 to t to find the LiC₆₀⁺ number. This is required to correctly account for the loss and relaxation processes which only act during the interval tau = (t-t_c). The parameters k_vib and E₀, are determined by fitting the solution for the number of LiC₆₀⁺ measured in the pressure dependent mass spectra. The LiC₆₀⁺ cluster formation data is fit by minimizing chi-squared for 12 pressures over the range 4x10^-6 to 2.5x10^-4 Torr as shown above. The best fit parameters k_vib and E₀ obtained for E_int(0) = (7.6-5.39) eV + E₀ yields a value of E₀=1.4 +/- 0.1 eV and 1 sec^-1 <= k_vib <= 3 sec^-1. The rate k_vib could only be estimated to within this range since these parameters cannot be determined independently and small changes in E₀ can easily compensate for a larger variation in k_vib. However, by fixing E₀ at the estimated binding energy, a value of k_vib was obtained at each pressure resulting in an estimate of the vibrational rate constant as shown in the plot.

        Although this analysis yields only a rough estimate of the vibrational relaxation rate, it provides a description of the relaxation process for low energy He-Li_nC₆₀⁺ collisions. These collisions will involve energy exchange only with the lowest Li_nC₆₀⁺ vibrational modes comparable to the low frequency collective modes of C₆₀ having hv=200-500cm^-1. Since these collisions will involve a large portion of the cluster mass M, on average only a fraction of the mode energy (m/M)hv ~= 2 cm^-1 will be transferred per collisions. This is comparable to the energy transferred per collision estimated by the pressure analysis, delta E_vib ~= tau_ck_vibE_int(0) ~= 1.5 cm^-1 where 1/tau_c is the collision rate