Multi-nuclear (1H, 2H, and 19F) magnetic resonance spectroscopy techniques as functions of temperature and pressure were applied to the study of selectively deuterated 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide (EMIM TFSA) ionic liquid isotopologues and related ionic liquids. For EMIM TFSA, temperature-dependent 2H T1 data indicate stronger electric field gradients in the alkyl chain region compared to the imidazolium ring. Most significantly, the pressure dependences of the EMIM and TFSA self-diffusion coefficients revealed that the displacements of the cations and anions are independent, with diffusion of the TFSA anions being slowed much more by increasing pressure than for the EMIM cations, as shown by their respective activation volumes (28.8 ± 2.5 cm3/mol for TFSA vs. 14.6 ± 1.3 cm3/mol for EMIM). Increasing pressure may lower the mobility of the TFSA anion by hindering its interconversion between trans and cis conformers, a process that is coupled to diffusion according to published molecular dynamics simulations. Measured activation volumes (ΔV‡) for ion self-diffusion in EMIM bis(fluoromethylsulfonyl)amide and EMIM tetrafluoroborate support this hypothesis. In addition, 2H T1 data suggests increased ordering with increasing pressure, with two T1 regimes observed for the MD3 and D2 isotopologues between 0.1–100 and 100–250 MPa respectively. The activation volumes for T1 were 21 and 25 (0–100 MPa) and 11 and 12 (100–250 MPa) cm3/mol for the MD3 and D2 isotopologues, respectively.
A general method is presented to calculate from first principles the full set of third-order elastic constants of a material of arbitrary symmetry. The method here illustrated relies on a plane-wave density functional theory scheme to calculate the Cauchy stress, and numerical differentiation of the second Piola-Kirchhoff stress tensor to evaluate the elastic constants. It is shown that finite difference formulas lead to a cancellation of the finite basis set errors, whereas simple solutions are proposed to eliminate numerical errors arising from the use of Fourier interpolation techniques. Applications to diamond, silicon, aluminum, magnesium, graphene, and a graphane conformer give results in excellent agreement with both experiments and previous calculations based on fitting energy density curves, demonstrating both accuracy and generality of our new methodology to investigate nonlinear elastic behaviors of materials.
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