Transitions between liquid crystalline phases investigated by dielectric and infra-red spectroscopies

The liquid crystalline 11OS5 compound, forming the nematic phase and a few smectic phases, is investigated by broadband dielectric spectroscopy and infra-red spectroscopy. The dielectric relaxation times, ionic conductivity, and positions of infra-red absorption bands corresponding to selected intra-molecular vibrations are determined as a function of temperature in the range from isotropic liquid to a crystal phase. The correlation coefficient matrix and k-means cluster analysis of infra-red spectra are tested for detection of phase transitions. The density-functional theory calculations are carried out for interpretation of experimental infra-red spectra. The performance of various basis sets and exchange-correlation functionals is compared, including both agreement of scaled calculated band positions with experimental values and computational time. The inter-molecular interactions in the crystal phase are inferred from the experimental IR spectra and density-functional theory calculations for dimers in head-to-head and head-to-tail configurations. The experimental temperature dependence of the C=O stretching band suggests that the head-to-tail configuration in a crystal phase is more likely. A significant slowing down of the flip-flop relaxation process is observed at the transition between the smectic C and hexagonal smectic X phases.

💡 Research Summary

The paper presents a comprehensive study of the liquid‑crystalline compound 11OS5 (4‑pentylphenyl‑4′‑undecyloxythiobenzoate) using broadband dielectric spectroscopy (BDS) and Fourier‑transform infrared (FT‑IR) spectroscopy across the full temperature range from the isotropic liquid to the crystalline phase. The authors first map the phase sequence (Iso → N → SmA → SmC → SmX → Cr) by cooling the sample at 5 K min⁻¹ and recording dielectric spectra from 0.1 Hz to 10 MHz. By fitting the complex permittivity with a Cole‑Cole model plus conductivity and electrode‑polarization terms, two relaxation processes are identified. The low‑frequency process (Maxwell‑Wagner‑Sillars) shows a dielectric strength Δε≈5.9, distribution parameter α≈0.11 and an activation energy of ~79 kJ mol⁻¹. The high‑frequency “s‑process” corresponds to flip‑flop rotations of the molecules around their short axis, with Δε≈0.11, α≈0.01 and Ea≈94 kJ mol⁻¹. At the SmC → SmX transition the relaxation time of the s‑process increases by a factor of 46, its dielectric strength drops to 0.07 and the activation energy rises to 144 kJ mol⁻¹, indicating a strong restriction of molecular rotation due to the emergence of long‑range positional order. Ionic conductivity follows an Arrhenius behaviour with Ea≈97 kJ mol⁻¹ and shows a modest decrease on entering the SmX phase.

In parallel, FT‑IR spectra are recorded in reflection (room‑temperature crystal) and transmission (on cooling). The authors calculate theoretical IR spectra of an isolated 11OS5 molecule using density‑functional theory (Gaussian 16) with several basis sets (def2SVP, def2SVPP, def2TZVP, def2TZVPP, 6‑31+G(d), 6‑311+G(dp)) and two dispersion‑corrected functionals (B3LYP‑D3(BJ) and BLYP‑D3(BJ)). Scaling factors σ are determined separately for three wavenumber regions (<1000 cm⁻¹, 1000‑2000 cm⁻¹, >2000 cm⁻¹). The best overall agreement (RMSD ≈ 11.6 cm⁻¹) is obtained with the triple‑ζ def2TZVPP basis set combined with B3LYP‑D3(BJ), but this calculation requires 157 h of CPU time. Comparable accuracy (RMSD ≈ 12 cm⁻¹) is achieved with the smaller def2TZVP/B3LYP‑D3(BJ) (86 h) and with the medium‑size 6‑31+G(d)/B3LYP‑D3(BJ) (18 h), demonstrating a favorable trade‑off between precision and computational cost. BLYP‑D3(BJ) generally underestimates high‑frequency bands.

To detect subtle spectral changes associated with phase transitions, three analytical tools are applied to the temperature‑dependent IR data: (1) a correlation‑coefficient matrix, (2) k‑means clustering (Euclidean distance), and (3) tracking of selected band positions. The correlation matrix clearly separates the isotropic‑nematic region (373–357 K) from the smectic‑crystalline region (≤338 K). k‑means clustering yields four distinct clusters, with a pronounced shift at the SmC → SmX transition. The most informative band is the carbonyl stretching mode (ν(C=O) ≈ 1720 cm⁻¹); its peak shifts by 2–3 cm⁻¹ to lower wavenumbers when the system passes from SmC to SmX. This shift is interpreted through DFT calculations on dimers arranged in head‑to‑head and head‑to‑tail configurations. The experimental trend matches the head‑to‑tail dimer model, suggesting that in the crystal phase molecules preferentially adopt a head‑to‑tail packing, which influences the C=O vibrational environment.

Overall, the combined dielectric and infrared approaches provide complementary insight: dielectric spectroscopy readily detects major transitions (Iso → N, N → SmA, SmC → SmX) via abrupt changes in dielectric dispersion, while the SmA → SmC transition is too subtle for BDS alone but becomes evident in the IR correlation and clustering analyses. The dramatic slowing of the flip‑flop relaxation at SmC → SmX reflects the onset of a more rigid, hexagonal smectic lattice, corroborated by the concurrent shift of the carbonyl band. The systematic evaluation of DFT methods offers practical guidance for future spectroscopic modeling of liquid‑crystalline molecules. The study demonstrates that multi‑modal spectroscopy, supported by robust statistical analysis and quantum‑chemical calculations, is a powerful strategy for elucidating complex phase behavior in liquid crystals, with implications for the design of advanced display materials, sensors, and other applications where precise control of mesophase transitions is essential.