Factorization, transition path sampling

A common alternative configuration is the optically equivalent combination of a spherical with a plane mirror, a semi-confocal cavity. This is more convenient in that the length of the cavity is reduced by a factor of two, but it does mean doubling the number of reflections and therefore the transmission loss for a given transit path of the radiation through the sample. 

Free cw-azobenzene, excited at 480 nm displays a biexponential decay of the excited state Si with time constants of 0.1 ps and 0.9 ps. Here the ultrafast kinetic component dominates the absorption change (it contains 90 % of the whole amplitude). A direct interpretation would relate the fast component to a free isomerizational motion, where the most direct reaction path on the Si and So potential energy surface is used without disturbance. The slower process may be assigned to a less direct motion due to hindrance by the surrounding solvent molecules. This interpretation is supported by the observation of the absorption changes in the APB and AMPB peptides. Here both reaction parts are slowed down by a factor of 2 - 3 and both show similar amplitudes The peptide molecules hinder the motion of the azobenzene switch and slow down considerably the initial kinetics. However, in all samples the transition to the ground state is finished within a few picoseconds. 

The observed intensity of a spectral line is determined by the rate of transition between the initial and final states corresponding to the frequency of that line. The rate of transition is, in turn, governed by the intensity of exciting radiation, the path length of exciting radiation through the sample, the concentration of potential absorbers or emitters in the sample, and the probability that a radiative transition will occur between the initial and final states of the absorber or emitter. In quantitative analysis, it is the concentration of absorbers or emitters in the sample that is of interest. These factors will be discussed further in the experimen-... 

Interpretation of IC-AFM images is complicated by the fact that the tip-sample force is a nonlinear function of tip-sample separation. The tip-surface interactions in IC-AI have been modeled extensively and have been recently reviewed [109, 143]. Two important conclusions have come from the modeling. First, the nonlinear interaction of the dynamic tip with the surface can lead to two stable oscillation states one that follows a net attractive path and the other that follows a net repulsive path [147, 148]. A hint of this is seen in the phase versus frequency plot (see Fig. 3.32) where the cantilever initially oscillates along an adhesive path and then abruptly transitions to the repulsive path. Simulated amplitude and phase (z-sweep) curves can reproduce those determined experimentally. These have been interpreted in terms of force based interaction models that include the effect of capillary forces and adhesive forces when they are known or can be estimated. The transition between the bistable states depends on a number of factors including the cantilever Q, Ao, and r p, and the drive frequency as well as the surface properties [149]. In general high Q cantilevers or small Ao favor the net attractive path. 

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