Abstract
Molecular diffusion in nanoporous materials can be understood as series of dynamic hopping or exchange motions of molecules between different discrete sites. Exchange NMR offers the spectral resolution to distinguish between these different sites, based on isotropic and anisotropic NMR interactions that manifest differences in the local chemical or structural environments of molecules at different sites or their local orientations. Such interactions facilitate the observation of distinct adsorption environments and provide insights on the number and distributions of distinct types of environments and the geometries and motional correlation times of local hopping events between different sites. The temporal range accessible by exchange NMR is governed by the time required for the observation of the NMR signal (< 1 ms) and the return of the nuclear magnetic polarization to thermal equilibrium (typically several seconds). Over such timescales, this permits slow molecular exchange processes between local environments to be probed in great quantitative detail. The resulting insights on dynamic exchange or hopping of atoms, molecules, or ions in nanoporous solids provide a basis for understanding processes that occur over longer length and time scale, which ultimately account for their macroscopic diffusion properties.
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Abbreviations
- B :
-
Magnetic-flux density, in Tesla or kg s−2 A−1
- \(R^{EIS}\) :
-
Ratio of integrated centerband and sideband peak areas
- B 0 :
-
Stationary main magnetic-flux density in z-direction, Tesla
- \({R}_{\rm {fe}}\) :
-
\({R}^{EIS}\)In the full exchange limit
- \({C}_{n}\) :
-
nth order autocorrelation function
- \(S\left(\omega \right)\) :
-
Spectral intensity
- D :
-
Diffusion coefficient, in m2 s−1
- T 1 :
-
Longitudinal (spin–lattice) relaxation time, s
- \({E}_{a}\) :
-
Activation energy, Joules mol−1
- T 2 :
-
Transverse (spin–spin) relaxation time, s
- \({E}^{*}\) :
-
Transition state energy, Joules mol−1
- t n :
-
Time domain in the nth dimension, s
- \({F}_{n}\) :
-
Free energy associated with n xenon atoms in a cage, J mol−1
- t :
-
Time, s
- f n :
-
Frequency domain in the nth dimension, rad s−1
- T :
-
Absolute temperature, K
- \(\Delta F\) :
-
Separation energy, Joules
- \({\tau }_{n}\) :
-
Correlation time of exchange process n, s
- \({k}_{0}\) :
-
Pre-exponential factor associated with an mth-order exchange process, molm s−1
- \({t}_{\rm {mix}}\) :
-
Mixing time, s
- \({k}_{\rm {n}}\) :
-
Rate coefficient associated with an mth-order exchange process n, molm s−1
- \({\nu }_{\rm {MAS}}\) :
-
Magic angle spinning frequency, Hz
- \({k}_{\rm {B}}\) :
-
Boltzmann’s constant, J K−1
- \({\nu }_{\rm {aniso}}\) :
-
Frequency of the anisotropic NMR interaction, Hz
- \({k}_{\rm {eff}}\) :
-
Effective rate coefficient with an mth-order exchange process, molm s−1
- \({\omega }_{n}\) :
-
Angular frequency of the nth component, rad s−1
- \({k}_{\rm {micr}}\) :
-
Microscopic rate coefficient with an mth-order exchange process, molm s−1
- \({\omega }^{(n)}\) :
-
Angular frequency associated with a cage containing n atoms
- \({k}_{\rm {SD}}\) :
-
Spin diffusion rate coefficient, s−1
- \({\varvec{\Pi}}\) :
-
Magnetization exchange matrix
- L :
-
Characteristic length, m
- \({\Pi }_{n,m}\) :
-
Magnetization exchange matrix element
- \(\mathbf{M}\) :
-
Normalized spectral intensity matrix at time
- \(\lambda\) :
-
Decay rate, s−1
- \({M}_{n,m}\) :
-
Normalized spectral intensity matrix element
- \({\omega }_{0}\) :
-
Larmor frequency, rad s−1
- \(P\left(n\right)\) :
-
Probability for a cage to have an occupancy of n atoms
- \(\theta , \phi\) :
-
Polar angles, radians
- \({P}_{n}\) :
-
nth-order Legendre polynomial
- \(\eta\) :
-
Asymmetry parameter in the Haeberlen convention
- \(\mathbf{R}\) :
-
Atomic (e.g., Xe) exchange matrix
- \(\delta\) :
-
Reduced chemical shift anisotropy in the Haeberlen convention, Hz MHz−1 (ppm)
- \({R}_{n,m}\) :
-
Atomic exchange matrix element
- \({\delta }_{iso}\) :
-
Isotropic chemical shift, Hz MHz−1 (ppm)
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Selter, P., Schmithorst, M.B. & Chmelka, B.F. Hopping dynamics and diffusion of atoms, molecules, and ions in nanoporous solids by exchange NMR spectroscopy. Adsorption 27, 857–874 (2021). https://doi.org/10.1007/s10450-021-00318-8
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DOI: https://doi.org/10.1007/s10450-021-00318-8