Molecular Jumps within the Fast Motion Limit: The Influence of Unequally Populated Sites on ²H-solid State NMR Lineshapes

Fast Dynamics and Conformations of Polymer in a Conformational Disordered Crystal Characterized by 1H−13C WISE NMR

“…In addition, two-site jump motions due to a conformational transition also reduce the dipolar interaction and can be analyzed to give solutions for different populations in the two sites. ,, The population ratios of 78 and 22 for two conformations were applied at β 1 = 60° and β 2 = 300°, respectively, obtained in the former SS-NMR work . Then, δ̅ and η̅ are described by a function of the jump angle, α, as follows: true normalδ false̅ -0.2em = normalδ ( 1 4 + 3 4 cos 2 α + 0.44 sin 2 α ) 1em and 1em true normalη false̅ -0.2em = 3 true( 1 − cos 2 nobreak.25em normalα + 0.44 .25em sin 2 nobreak.25em normalα true) true( 1 + 3 cos 2 nobreak.25em normalα + 0.44 .25em sin 2 nobreak.25em normalα true) …”

“…At the fast motion limit (τ c ≫1/δ, where τ c is correlation time), the angular dependence of the NMR frequency becomes true normalω false̅ false( normalΘ , normalΨ false) -0.2em = 1 2 0.2em true normalδ false̅ false[ 3 .25em cos 2 nobreak.25em normalΘ − 1 − true normalη false̅ .25em sin 2 nobreak.25em normalΘ .25em cos false( 2 normalΨ false) false] where δ̅ and η̅ are the averaged anisotropy and averaged asymmetry parameter, respectively, and (Θ, Ψ) are the polar angles of B 0 in the averaged principal axes. δ̅ and η̅ depend on the dynamic geometry as well as the population of the different sites involved in the dynamic process. ,, …”

“…δ h and η h depend on the dynamic geometry as well as the population of the different sites involved in the dynamic process. 12,20,21…”

Molecular dynamics in solid polymers

“…For motional rates kZ1/(2t c ) of the order of the chemical-shift anisotropy parameter d CSA , the powder spectrum changes considerably with t c , making it possible to estimate this parameter from the line shapes. In the fast exchange regime, t c !2p/d CSA , the spectrum also is a powder pattern, but with distinct interaction parameters ( h and d) that depend on the amplitude of the dynamic process [20]. Nevertheless, there are some intrinsic difficulties in obtaining such information from CSA line shapes: (a) a small deviation in the size and orientation of the CSA tensor can produce significant changes in the average spectrum; (b) different types of motion can produce identical line shapes; (c) a knowledge of the orientation of the CSA tensor in a welldefined molecular reference frame is required for the calculation of the spectra; (d) for the case of 13 C NMR, which is the most common nucleus for studying organic systems, line shape analysis can only be done for systems with only one or a small number of different chemical sites, or requires 13 C isotopic labeling at selected molecular sites.…”

Deuterium NMR studies of guest motions in urea inclusion compounds of 1,6-dibromohexane with analytical evaluation of spectra in the fast motion limit

“…In the fast-motion limit, the averaged field gradient tensor is the sum of the field gradient tensors the deuterium nucleus experiences during its motion, weighted by the corresponding fractional site populations. (The idea of unequal populations on 'H NMR [28,29] and 2H NMR [29][30][31][32][33] has been investigated previously.) The simplest motional process that can yield all possible 2 H NMR lineshapes is a three-site jump between sites 1, 2, and 3 ( Fig.…”