Molecular theory of dielectric relaxation in nematic dimers

Abstract

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.

Molecular dynamics of a binary mixture of twist-bend nematic liquid crystal dimers studied by dielectric spectroscopy

“…Equation 331 (2) entails the emergence of an additional lower-frequency 332 relaxation mode. Both low-frequency processes are related to 333 the individual flip-flop motions of the units, and dielectric 334 strengths are determined by equilibrium population their of 335 the conformers [30,34]. Experimental results for FFO9OCB 336 clearly confirm [30] such model's prediction.…”

“…In 31 this phase, formed by achiral molecules, the director exhibits 32 periodic twist and bend deformations forming a conical helix 33 having doubly degenerate domains of opposite handedness. 34 Although initially described for dimers of the CBnCB family, 35 the discovery of a low temperature nematic phase boosted 36 research in the area, and a number of materials combining 37 different mesogenic units linked by chains have been identified 38 which exhibit the N TB phase [16][17][18] and its chiral counterpart 39 [19,20]. It is now recognized that molecular curvature plays 40 a crucial role in stabilizing the twist-bend nematic phase.…”

“…Experimental results for FFO9OCB 336 clearly confirm [30] such model's prediction. Accordingly, 337 we associate the three dielectric relaxations observed for the 338 mixture to (i) a superposition of the precessional motion 339 of the dipolar groups around the director and the rotation 340 around the long axis at the high-frequency branch of the 341 spectrum (m 2 ) and (ii) the end-over-end reorientation of the 342 dipolar groups parallel to the director at low frequencies (m 1L 343 and m 1H ) [34]. It is evident that the mixture shows a behavior 344 resembling that of nonsymmetric dimers, with the appearance 345 of a third dielectric mode at low frequencies, that in this case 346 results from the fluorinated group reorientations.…”

“…298 Note that reorientations (end-over-end processes) of the con-299 nected dipolar groups are considered to be individual, but not 300 independent, because of the correlation imposed by the flexible 301 spacer and accounted for by the conformational distribution 302 through the detailed balance equation P eq T k [34], where P eq T and P eq C are the equilibrium populations of the 304 trans and cis configurations, respectively. Whole molecular 305 reorientation is excluded, since the energy barrier for the 306 simultaneous rotation of both units is too high and results 307 in a nonsignificant transition rate [34]. As order increases, 308 calculation showed that the four wells become deeper but the 309 barriers are still much smaller for the individual flip-flops than 310 for the whole molecular reorientation.…”

Short-range correlations seen in the nematic phase of bent-core liquid crystals by dielectric and electro-optic studies

“…However, such a change accompanies a change in the bent angle θ V and a change in the molecular dipole moment. Such a behavior is normally observed in liquid-crystalline dimers consisting of two rigid meosogenic groups linked by a flexible alkyl chain [20]. But a conformational change should also affect the birefringence, and this is not observed here.…”