Buckled nano rod - a two state system and its dynamics using system plus reservoir model

摘要

We consider a suspended elastic rod under longitudinal compression. Thecompression can be used to adjust potential energy for transverse displacementsfrom harmonic to double well regime. As compressional strain is increased tothe buckling instability, the frequency of fundamental vibrational mode dropscontinuously to zero (first buckling instability). As one tunes the separationbetween ends of a rod, the system remains stable beyond the instability anddevelops a double well potential for transverse motion. The two minima inpotential energy curve describe two possible buckled states at a particularstrain. From one buckled state it can go over to the other by thermalfluctuations or quantum tunnelling. Using a continuum approach and transitionstate theory (TST) one can calculate the rate of conversion from one state toother. Saddle point for the change from one state to other is the straight rodconfiguration. The rate, however, diverges at the second buckling instability.At this point, the straight rod configuration, which was a saddle till then,becomes hill top and two new saddles are generated. The new saddles have bentconfigurations and as rod goes through further instabilities, they remainstable and the rate calculated according to harmonic approximation aroundsaddle point remains finite. In our earlier paper classical rate calculationincluding friction has been carried out [J. Comput. Theor. Nanosci. {\bf 4}(2007) {\it 1}], by assuming that each segment of the rod is coupled to its owncollection of harmonic oscillators - our rate expression is well behavedthrough the second buckling instability. In this paper we have extended ourmethod to calculate quantum rate using the same system plus reservoir model. Wefind that friction lowers the rate of conversion.