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

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.

Intra- and intermolecular interactions in mesogenic cyano compounds

“…On the other hand, it was reported that vibration frequencies of alkyl chains and aromatic rings showed signiÐcant changes in Sm A, nematic, and isotropic liquid in the cases of polymeric20,21 and discotic22 liquid crystals, reÑecting the changes of intermolecular interactions with temperature rise. Comparing with these cases, it was con-Ðrmed that the change of the CN environments is very small ; dimers formed by the CN groups in the mesophases are stable and still exist in isotropic liquid states, as was found for nCB by Rothschild et al 23 Furthermore, it is found that the frequencies in mesophases are almost the same for each series : 2227.05 ^0.18 cm~1 and 2225.97 ^0.14 cm~1, on average, for nCB and nOCB, respectively, and 2230.3 ^0.3 and 2231.8 ^0.2 cm~1, on average, for CPnOB and nOPCB (except for 6OPCB), respectively. The di †erence between nCB and nOCB is 1.1 cm~1 in mesophases, larger than that for molecules in solutions (0.5 cm~1).…”

Raman Spectroscopic Studies of Liquid Phase Ordering and Dynamics for Solutions of ME6N Liquid Crystal: The Approach to Simple Molecule Behavior at High Dilutions

“…Very limited results are reported in the literature on the effect of dilution on the dispersion parameter and then on the rate of achievement, by dilution, of the simple liquid condition. Rothschild determined values of α falling in the range 0.5−0.7 for CCl 4 solutions at x = 0.02 of n- CB (i.e., 4- n -alkyl-4′-cyanobiphenyl) liquid crystals with n (the carbon number of the alkyl chain) equal to 8, 9, and 12 . Incidentally, the n -independence of α for this family suggests the extension of the above result to n = 6.…”

“…Rothschild determined values of α falling in the range 0.5−0.7 for CCl 4 solutions at x = 0.02 of n- CB (i.e., 4- n -alkyl-4′-cyanobiphenyl) liquid crystals with n (the carbon number of the alkyl chain) equal to 8, 9, and 12 . Incidentally, the n -independence of α for this family suggests the extension of the above result to n = 6. The values of α found for n -CB ( α = 0.5−0.7) are remarkably lower than that (α = 0.93) we have obtained for ME6N ( n = 6) in the CCl 4 solution at approximately the same concentration ( x = 0.03).…”

“…In complex liquids the perturbation relaxation F ( t ) is, to some extent, altered by the dynamical processes of formation/disruption of aggregates. In the approach formulated by Rothschild and co-workers, − these are taken into account by modeling the perturbation relaxation with a non-Markovian process, and explicitly in the form of a stretched exponential F̂ ( t ) = ⟨ ω 1 ( t ) ω 1 ( 0 ) ⟩ ⟨ | normalω 1 false( 0 false) | 2 ⟩ = exp ( − t / τ 0 ) α …”

“…The approach formulated by Rothschild and co-workers, successfully applied to a wide range of complex liquids, − has provided a general framework for the interpretation of the vibrational correlation functions observed in liquids with local, short-lived order, by assuming for the perturbation decay a stretched exponential function: exp−( t /τ 0 ) α . This model represents a generalization of that formulated earlier , based on the assumption of a single exponential function for the perturbation decay.…”