Inelastic neutron scattering spectra of the longitudinal acoustic modes of the normal alkanes from pentane to pentacosane

The inelastic neutron scattering spectra of the polycrystalline n-alkanes, 5<n<25, have been obtained at ∼25 K. At this temperature the n-alkane molecules are extended in their all-trans configuration. The spectral region from 200 to 600 cm^-1 is reported with emphasis on the higher frequency longitudinal acoustic modes (LAM). These modes are identified by their nominal translational symmetry eigenvector, κ. A complete assignment of experimental frequencies out to κ≈0.7 is presented for the first time. This assignment is consistent with the known optical data and ab initia Hartree-Fock and DFT calculations. On the basis of these theoretical results, the lower frequency, higher κ LAM modes are also assigned. The LAM sequences exhibit bandhead behavior, i.e., a maximum frequency value, υ_max, at some value of κ. The maximum frequency is consistently found at κ_max=0.36±0.01 [cf. polyethylene (PE), κ_max=0.34] for all chain lengths but the value of the maximum frequency, υ_max, increases roughly linearly with n for n>7. At about n = 21 it reaches the value found for PE, 525 cm^-1. This variation in frequency with chain length for the same nominal value of κ and also the full set of calculated DFT LAM results is compared with the expectations of a simple zig-zag bead bending model.