Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Rigid tetracatenar liquid crystals derived from 1,10-phenanthroline

Tetracatenar liquid crystals were obtained by substituting the 1,10-phenanthroline central core unit at the 3- and 8-positions by extended, rigid acetylene moieties, equipped at the termini with two alkoxy chains of various lengths (n = 6, 8, 10, 12, 14). The liquid crystals exhibit a rich mesomorphism including smectic C, cubic, hexagonal and rectangular columnar phases, depending on the alkoxy chain length. The corresponding rhenium(I) complexes containing the bulky [ReBr(CO)₃] fragment are not liquid-crystalline. The ligands and rhenium(I) complexes were investigated by scanning tunneling microscopy (STM). Both the ligands and the rhenium(I) complexes can be self-assembled into monolayers at the TCB–graphite and octanoic acid–graphite interfaces. The ligands and rhenium(I) complexes are luminescent.

1-butyl-3-methylimidazolium 3,5-dinitro-1,2,4-triazolate: a novel ionic liquid containing a rigid, planar energetic anion

The novel ionic liquid, 1-butyl-3-methylimidazolium 3,5-dinitro-1,2,4-triazolate has been synthesized and exhibits an unexpectedly low melting point (35 degreesC) considering the size and shape of the rigid, planar anion; analogous tetraalkylammonium salts (methyl, ethyl and n-butyl) have also been prepared and the tetraethylammonium example was characterized by single crystal X-ray diffraction.