Thermodynamically Induced Particle Transport: Order-by-Induction and Entropic Trapping at the Nano-Scale

Abstract

A theory for thermodynamic induction (TI) under isothermal conditions is presented. This includes a treatment of the Helmholtz free energy budget available for a gate variable to utilize towards aiding another variable's approach towards thermodynamic equilibrium. This energy budget could be used to help create interesting physical structures and examples of order-by-induction. I also show how to treat TI in the continuum limit which can be obtained from a variational principle. Several important examples of isothermal TI have been discussed, including a type of electromigration that may be detectable in electrolytes, superfluids and semiconductors. As an example of a bottlenecked system exhibiting enhanced TI, manipulation of atoms and molecules by STM has been discussed in detail. My considerations provide strong support for microscopic bond-breaking mechanisms being governed by a general thermodynamic principle. In particular, I show that induced entropy trapping can explain the level of control that sliding-type manipulations demonstrate. The most reasonable choices for the parameters input into the simple formula give a threshold condition for STM manipulations that is strikingly close to what is required to match results reported in the literature. My continuum model predicts the shape of the adsorbate potential well for the STM case and from this I predict a level of force detectable by AFM. A final proposal, and example of order-by-induction, predict a long tether may be constructed between sample and tip that is just one atom thick.