Molecular theory of dielectric relaxation in nematic dimers.

This paper reports a theory for the dielectric relaxation of dimeric mesogenic molecules in a nematic liquid crystal phase. Liquid crystal dimers consist of two mesogenic groups linked by a flexible chain. Recent experimental studies [D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez, and M. A. Perez Jubindo, J. Chem. Phys. 115, 8681 (2001)] of the dielectric properties of polar liquid crystal dimers have found unexpected results for both the static (low frequency) and variable frequency dielectric response of these materials. The theory developed in this paper provides a quantitative model with which to understand the observed experimental results. The mean-square dipole moments of alpha,omega-bis[(4-cyanobiphenyl-4'-yl]alkanes in a nematic phase have been calculated using both the rotational isomeric state model and a full torsional potential for the carbon-carbon bonds of the flexible chain. The orienting effect of the nematic phase is taken into account by a parametrized potential of mean torque acting on the mesogenic groups and the segments in the flexible chain. Results of calculations using the full torsional potential are in excellent agreement with experimental results for comparable systems. The probability density p(eq)(beta(A),beta(B)) for the orientation of the mesogenic groups (A,B) along the nematic director is also calculated. The resultant potential of mean torque is a surface characterized by four deep energy wells or sites equivalent to alignment of the terminal groups A and B approximately parallel and antiparallel to the director; of course, the reversal of the director leads to equivalent sites. This potential energy surface provides the basis for a kinetic model of dielectric relaxation in nematic dimers. Solution of the Fokker-Planck equation corresponding to this four-site model gives the time dependence of the site populations, and hence the time-correlation functions for the total dipole moment along the director. In this model the end-over-end rotation of the molecule, corresponding to simultaneous reversal of both mesogenic groups, is excluded because the activation energy is too large. Results are presented for a number of cases, in which a dipole is located on one or both of the mesogenic groups, and additionally where the groups differ in size. For the latter, under particular conditions, the correlation function exhibits a biexponential decay, which corresponds to two low frequency absorptions in the dielectric spectrum. This is exactly what has been observed for nonsymmetric nematic dimers having different groups terminating a flexible chain. Experimental results over a range of temperature for the nonsymmetric dimer alpha-[(4-cyanobiphenyl)-4'-yloxy]-omega-(4-decylanilinebenzylidene-4'-oxy)nonane can be fitted precisely to the theory, which provides new insight into the orientational and conformational dynamics of molecules in ordered liquid crystalline phases.

Cranklike conformational transitions in polyethylene.

Molecular dynamics simulations of a variety of polymeric systems provide the evidence for two different kinds of conformational transitions: independent single bond transitions and cranklike transitions (or correlated bond transitions). While single bond transitions can be rationalized according to standard theories of activated processes controlled by the saddle point crossing, a more complex description is required for the other type of transitions. In a recent work devoted to the analysis of the simplified chain model with three rotors [B. Nigro and G. J. Moro, J. Phys. Chem. B 106, 7365 (2002)], a theory has been proposed for cranklike transitions represented as a kinetic process between equilibrium states differing by two torsional angles (i.e., two bond transitions). Moreover their rate coefficients were estimated on the basis of a local expansion about the bifurcation of the separatrices departing from the potential function maximum. In the present work the same theory is applied to a model for long alkyl chains in solution, in order to rationalize the behavior of cranklike transitions in polyethylene and to recognize the molecular features controlling them. We obtain probabilities of occurrence of cranklike transitions in substantial agreement with simulation results. Furthermore, the theory is capable of explaining the dependence of the rate on the separation between the two reactive bonds, as well as the dependence on the conformational state of the starting configuration. In particular, selection rules for next-to-nearest neighbor transitions are recovered from the shape of the separatrices and the location of the corresponding bifurcations.