Pretransitional behavior of viscoelastic parameters at the nematic to twist-bend nematic phase transition in flexible n-mers

We report dynamic light scattering measurements of the orientational (Frank) elastic constants and associated viscosities among a homologous series of a liquid crystalline dimer, trimer, and tetramer exhibiting a uniaxial nematic (N) to twist-bend nematic (N-TB) phase transition. The elastic constants for director splay (K-11), twist (K-22) and bend (K-33) exhibit the relations K-11 > K-22 > K-33 and K-11/K-22 > 2 over the bulk of the N phase. Their behavior near the N-N-TB transition shows dependency on the parity of the number (n) of the rigid mesomorphic units in the flexible n-mers. Namely, the bend constant K-33 in the dimer and tetramer turns upward and starts increasing close to the transition, following a monotonic decrease through most of the N phases. In contrast, K-33 for the trimer flattens off just above the transition and shows no pretransitional enhancement. The twist constant K-22 increases pretransitionally in both even and odd n-mers, but more weakly so in the trimer, while K-11 increases steadily on cooling without evidence of pretransitional behavior in any n-mer. The viscosities associated with pure splay, twist-dominated twist-bend, and pure bend fluctuations in the N phase are comparable in magnitude to those of rod-like monomers. All three viscosities increase with decreasing temperature, but the bend viscosity in particular grows sharply near the N-N-TB transition. The N-N-TB pretransitional behavior is shown to be in qualitative agreement with the predictions of a coarse-grained theory, which models the N-TB phase as a "pseudo-layered" structure with the symmetry (but not the mass density wave) of a smectic-A* phase.