On the conformational structure of a stiff homopolymer

In this paper we complete the study of the phase diagram and conformational states of a stiff homopolymer. It is known that folding of a sufficiently stiff chain results in formation of a torus. We find that the phase diagram obtained from the Gaussian variational treatment actually contains not one, but several distinct toroidal states distinguished by the winding number. Such states are separated by first order transition curves terminating in critical points at low values of the stiffness. These findings are further supported by off-lattice Monte Carlo simulation. Moreover, the simulation shows that the kinetics of folding of a stiff chain passes through various metastable states corresponding to hairpin conformations with abrupt U-turns.Comment: 9 pages, 16 PS figures. Journal of Chemical Physics, in pres

Computation of periodic solution bifurcations in ODEs using bordered systems

We consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous ODEs, namely the fold, the period-doubling (or flip) bifurcation, and the torus (or Neimark–Sacker) bifurcation. In the fold and flip cases we append one scalar equation to the standard periodic BVP that defines the periodic solution; in the torus case four scalar equations are appended. Evaluation of these scalar equations and their derivatives requires the solution of linear BVPs, whose sparsity structure (after discretization) is identical to that of the linearization of the periodic BVP. Therefore the calculations can be done using existing numerical linear algebra techniques, such as those implemented in the software AUTO and COLSYS

Charge transport through image charged stabilized states in a single molecule single electron transistor device

The present paper gives an elaborate theoretical description of a new molecular charge transport mechanism applying to a single molecule trapped between two macroscopic electrodes in a solid state device. It is shown by a Hubbard type model of the electronic and electrostatic interactions, that the close proximity of metal electrodes may allow electrons to tunnel from the electrode directly into a very localized image charge stabilized states on the molecule. Due to this mechanism, an exceptionally large number of redox states may be visited within an energy scale which would normally not allow the molecular HOMO-LUMO gap to be transversed. With a reasonable set of parameters, a good fit to recent experimental values may be obtained. The theoretical model is furthermore used to search for the physical boundaries of this effect, and it is found that a rather narrow geometrical space is available for the new mechanism to be effective: In the specific case of oligophenylenevinylene molecules recently explored in such devices several atoms in the terminal benzene rings need to be at van der Waal's distance to the electrode in order for the mechanism to be effective. The model predicts, that chemisorption of the terminal benzene rings too gold electrodes will impede the image charge effect very significantly because the molecule is pushed away from the electrode by the covalent thiol-gold bond.Comment: 9 pages, 5 figue