The validity of the rotational isomeric state model for short alkyl chains with large substituents: A maximum entropy analysis of the 1H dipolar couplings within the trimethylene group of a liquid crystal molecule

Abstract

Deuterium decoupled proton spectra of the chain region of a partially deuteriated liquid crystal have been taken. The liquid crystal is a trimethylene chain with perdeuteriated cyanobiphenyloxy groups on either end: 1,3-bis(4,4′-cyanobiphenyloxy-d8) propane (BCBO3-d16). The spectra have been analyzed to give the dipolar couplings within the propyl chain at various temperatures in the nematic phase of the liquid crystal. These couplings are the most sensitive measurements of molecular flexibility that have yet been taken of an alkyl chain in a pure liquid crystal molecule and give a unique insight into rotational potentials of the flexible component essential to a liquid crystal molecule. The couplings have been analyzed using a maximum entropy method designed for a two-rotor system; in our case the two C–C bonds in the propyl chain. The analysis was also performed by adding to the data set the deuterium quadrupolar splittings of the chain hydrogen atoms, previously measured on the same molecule but deuteriated in the chain. The method picks out the flattest distribution consistent with the data. This also happens to be the most likely distribution given only the data used in the analysis and no other constraints. The results for BCBO3-d16 show a probability maximum for a partially eclipsed conformation (twisted approximately 86° in opposite directions about each C–C bond from the all-trans conformation), a smaller maximum for the all-trans conformation itself, and no significant probability for any of the gauche conformations. The possible motions, that are suggested by these results, therefore, are concerted librations (±86°) between the all-trans position and the partially eclipsed conformations, and full (360°) rotations. These results are in stark contrast to the assumptions made in the rotational isomeric state (RIS) model that the probability distribution can be well approximated by constraining the molecules to exist only in trans and/or gauche states with fast isomerization between such states. In fact the analysis rules out a rotational isomeric state distribution altogether, since our data could not be reproduced by restricting the distribution in this way. Instead it is shown that other distributions are not only possible, but also more likely than any kind of constrained trans–gauche model.