Nuclear magnetic resonance study of alkane conformational statistics

Abstract

NMR spectra of ethane, propane, and n-butane as solutes in the nematic liquid crystals 4-n-pentyl-4(')-cyanobiphenyl (5CB) and Merck ZLI 1132 (1132) are investigated over a wide temperature range. The ratios of dipolar couplings of ethane to propane are constant over the entire temperature range. Assuming that this constancy applies to the butane conformers facilitates the separation of probability from order parameter. This separation allows the investigation of conformational distribution without the need of invoking any model for the anisotropic intermolecular potential. The results give an order matrix that is consistent with that predicted from model potentials that describe the orientational potential in terms of short-range size and shape effects. The isotropic intermolecular potential contribution to the trans-gauche energy difference E(tg) is found to be temperature dependent with the values and variation in agreement with that found when the same results are analyzed using the chord model for anisotropic interactions [A. C. J. Weber and E. E. Burnell, Chem. Phys. Lett. 506, 196 (2011)]. The fit obtained for 9 spectra in 5CB (63 dipolar couplings) has an RMS difference between experimental and calculated dipolar couplings of 2.7 Hz, while that for the 16 spectra in 1132 (112 couplings) is 6.2 Hz; this excellent fit with nine adjustable parameters suggests that the assumption of equal temperature dependencies of the order parameters for ethane, propane, and each conformer of butane is correct. Also the fit parameters (E(tg) and the methyl angle increase) obtained for 1132 and 5CB agree. The results indicate that the chord model, which was designed to treat hydrocarbon chains, is indeed the model of choice for these chains. The temperature variation of E(tg) provides a challenge for theoreticians. Finally, even better fits to the experimental dipolar couplings are obtained when the energy in the Boltzmann factor is used for scaling ethane to butane results. However, in this case the values obtained for E(tg) differ between 1132 and 5CB.

A model-free temperature-dependent conformational study of n-pentane in nematic liquid crystals

“…25 Here, we introduce a similar temperature dependence for the n-pentane energy parameters. For the tg conformer, we use…”

“…As we have shown in the case of n-butane in a nematic environment 25 and in liquid crystals that exhibit both nematic and smectic A phases, 26 this leads to additional information that enables us to separate p n and S n k l . The analysis depends on the observation that the anisotropic energy parameters that describe the orientational ordering scale from ethane to propane and, assuming that this scaling also applies to n-butane, have expedited analysis of the dipolar couplings that were obtained from the NMR spectra.…”

“…33 Another way of treating the n-pentane conformational problem is by using a continuous intramolecular potential, U iso int, n (φ 1 , φ 2 ); this treatment (using continuous probability distributions) was recently used in NMR studies on n-butane. 25,26,34,35 To do this for n-pentane, the internal energy was calculated in 15 • increments of φ 1 and φ 2 while keeping all other structural parameters fixed to those of the major conformer that exists at the bottom of the local (or global in the case of tt) energy well (see Figure 3 for potential energy plotted as a function of φ 1 and φ 2 ). These energy wells, calculated for the n-pentane molecule isolated in the gas phase, are affected by the environment in the anisotropic liquid phase in which the solute is dissolved.…”

“…Particularly interesting is that the value of E ′ tg (of order −2 cal K −1 ) is consistent with the value found for n-butane in an earlier study. 25 Second, we do separate fits (shown in Table II) to the 16 spectra of n-pentane in 1132 and to the 6 spectra of n-pentane in 5CB.…”

“…25 With n-pentane, we choose to sum over each dihedral angle between −45 • and +45 • (from the well minimum) in 7 steps of 15 • each. For the four independent wells, this involves 4 × 7 × 7 = 196 calculations that must be performed in the minimization routine.…”