Parabolic friction regime

Figure 1. Lateral force (fiiction) measurements as function of tiie applied load on PEP with thickness, t. (a) The parabolic force regime is dominated by the spherical shape of the cantilever tip. (b) In the intermediate load regime the friction coefficient is pi = 2.1. (c) In the high load regime the friction-load ratio is p2 = 0-3. P indicates the location of the transition point.

Kramers approach to rate theory in the underdamped and spatial-diffusion-limited regimes spurred extensions which were applicable to the much more complex STGLE. Grote and Hynes (23) used a parabolic barrier approximation to derive the rate expression for the GLE in the spatial diffusion limit. Carmeli and Nitzan derived expressions for the rate of the GLE (24) and the STGLE (25) in the underdamped limit. The overdamped limit for the rate in the presence of delta correlated friction was solved using the mean first passage time expression (26,27). A turnover theory, valid for space- and time-dependent friction, has only been recently presented by Haynes, Voth, and Poliak... 

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