On the variation of Differential Polarizability in polarized Raman Scattering measurements

Jones et al recently developed a framework to measure P$_{2}$ and P$_{4}$ using PRS.\footnote{W. J. Jones, et al., ``On the determination of order parameters for homogeneous and twisted nematic liquid crystals from Raman spectroscopy'' \textit{Journal of Molecular Structure}, \textbf{708}, 145-163 (2004).} The method requires the measurement of the angular dependence of the depolarization ratio. While the agreement of the results of P$_{2}$ and P$_{4}$ with theory is satisfactory there are some aspects to the methodology that need further scrutiny. The differential polarizability ratio (r) is used as a fitting parameter to the depolarization profile. The value of r so calculated from the method of Jones et al. has a sharp discontinuity at the phase transition from the nematic to the istropic phase (T$_{\mathrm{NI}})$ and also the variation of r in the nematic phase is not well understood. Further we show that when values of the r as obtained by data fitting are used in the expression of the original method of Jen et al, the values of P$_{2}$ and P$_{4}$ are in excellent agreement with theoretical predictions, rising the premise that a better understanding of the variation of r needs to be developed more accurate experiments using PRS.