Challenges in Pulsed-Field Gradient Nuclear Magnetic Resonance on Magnetically Heterogeneous Interfaces: Sequence and Field-Dependent Apparent Diffusion Coefficients
It is well known that the internal gradient (gi) that exists within pores haunts the diffusion coefficient (D) as measured by the pulsed-field gradient (PFG) nuclear magnetic resonance (NMR). Several PFG-NMR methods developed to determine accurate D were not successful. Then, the steady-state diffusion coefficient (Dapp,∞) for the cation [C4mim]+ of [C4mim][Tf2N] [1-butyl-3-methylimidazolium][bis(trifluoromethylsulfonyl)imde] ionic liquid confined in ordered mesoporous carbon (OMC) was determined by comparing Dapp,∞ obtained from 1H PFG-NMR performed with three different stimulated echo sequences: STE, alternating pulsed-field gradient (APFG), and magic pulsed-field gradient (MPFG) under the two external magnetic field strengths, B0 = 9.4 and 14.1 T. The measured Dapp,∞, which is an order of magnitude smaller than D of bulk [C4mim][Tf2N], is in good agreement between APFG and MPFG in both B0 = 9.4 and 14.1 T. However, the strong gi artifact, which caused apparent diffusion coefficient (Dapp), depending strongly and weakly on B0 and temperature, respectively, in diffusion time-dependent Dapp, Dapp(Δ), obtained from a sequence with monopolar gradients (STE), was suppressed by using sequences employing bipolar gradients (APFG and MPFG) in the region of steady-state diffusion. However, the incompletely suppressed gi artifact resulting in the different behaviors of the early part of Dapp(Δ) between the sequences leads to α ≈ 0.6 and 0.9 in MPFG and APFG, respectively, in the relationship between mean-squared displacement and diffusion time: ⟨z(t)2⟩ = 2Dtα, where α = 0.5 and 1 for one-dimensional single-file diffusion and 3D bulk diffusion, respectively. The above observations clearly show that the diffusion behavior of ions/molecules within the pores and pore structure, such as the surface-to-volume ratio (Dapp(Δ)=D0[1−49πSVD0Δ]) and tortuosity (T ≡ D0/Dapp,∞), is possible to be misunderstood, especially in systems with a non-negligible gi. This work demonstrates that it may be necessary to test several PFG sequences under multiple external magnetic fields for the correct determination of the diffusion behavior of ions or molecules in the pores with a larger internal gradient, gi.
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