Picosecond dynamics and molecular aggregation from vibrational dephasing in the fluid phases of some 4-n-alkyl-4′-cyanobiphenyl liquid crystals

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Abstract
We describe the temperature dependence of the inhomogeneously broadened CN Raman profile I(ω) at ωc ∼2230 cm−1 of the title compounds (n=1, 6, 8, 9, 11, 12) in their isotropic liquid phase and solutions (CHCl3, CCl4) by simulating the oscillator amplitude correlation function by a vibrational equilibrium renewal process in terms of random fluctuations of the oscillator transition frequency ω(t)=ωc +ω1(t) about its central value ωc. To this effect, the autocorrelation function of the frequency shift ω1(t) is expressed as a probability density function (PDF) F̂(t) of recurrence times of the stochastic motional narrowing events in the local environment of the CN oscillators. System‐related physical meaning and satisfactory data fit is obtained if F̂(t) is understood as an expansion in terms of parallel, independent exponential relaxation processes with characteristic times τ that are distributed by a PDF ρα(τ)=〈τ〉h(τ)/τ, where α is the dispersion parameter of the extended exponential and 〈τ〉 the expectation of τ. Width and ranges of h(τ) show strong molecule–molecule clustering, possibly indicating a trend with alkyl chain length. At temperatures just above the mesophase–liquid‐phase transition, the range of the prevalent relaxation times τ in the local environment of the CN oscillators is of the order of 1–4 ps. Only at temperatures near 570 K or by high dilution in the solvents are the inter‐ and intracluster forces sufficiently diminished to approximate those of ordinary fluids. We consider our method to give a realistic description of the dynamics of types of macroscopically isotropic fluids where, nevertheless, the shape, size, and polarity of their molecules lead to a degree of aggregation that weakens the identity and the influence of constituent members. The temporary structure of the macroscopically isotropic fluids in the liquid‐crystal systems is best understood by admitting a significant presence of randomly distributed local regions of dynamic nematicity, causing temperature‐dependent relaxation pathways over 10–50 Å distances.