Role of dimensionality in thermolubricity Sample Clauses

Role of dimensionality in thermolubricity. The theoretical model we have discussed so far has an obvious inadequacy in that it has framed the problem in a single dimension. In reality, the tip moves over a two- dimensional surface and has the freedom to approach neighboring potential wells not just via a single trajectory but, instead, a variety of two-dimensional walks over the surface. This increases the complexity of the problem tremendously, because the tip may for example choose to move between two potential energy minima via a lower-energy, but non-trivial (e.g. non-straight) trajectory or it may for instance take advantage of the existence of a large number of slightly-higher-energy trajectories. We naturally end up with the picture of driven, two-dimensional Brownian type motion of the tip in the 2D potential energy landscape. In a two-dimensional Tomlinson picture, the tip perceives local potential minima around it that may be more easily accessed (lower energy barrier) than the next potential minimum strictly along the direction of the support motion. We have performed computer simulations of tip trajectories in two dimensions, which show that at low velocities, instead of overcoming the potential barrier in front of it, the tip may indeed prefer to jump sideways to a temporarily more favorable, local minimum, before jumping to the next minimum along the direction of the support motion. Figure 4.13 shows a two-dimensional total potential profile for tip motion on the HOPG lattice, sensed by a cantilever of spring constant 0.5 N/m in the case of U0= 0.5eV. Two trajectories with different energy barriers are indicated in the grey-scale representation of this potential.