Dynamics of nuclear spins in unexplored arenas

概要

学位論文の要約
題目

Dynamics of nuclear spins in unexplored arenas
（未踏領域の原子核スピンダイナミクス）

氏名

王 雨 (Wang Yu)

序論

Nuclear spin diffusion suppresses the local difference of polarization by
transporting the polarization of one spin to more distant nuclear spins and obeys the
general diffusion equation 𝜕𝑝⁄𝜕𝑡 = 𝐷∆𝑝, where 𝐷 is the diffusion coefficient and 𝑝
is the nuclear polarization. 𝐷 has been calculated in high-temperature approximation
where 𝑝 ≪ 1. In the first part of this thesis, we propose a correction 1/√1 − 𝑝̅ 2 to the
diffusion coefficient 𝐷 as a result of extending the Lowe-Gade formula to
low-temperature case. We will also show how this correction can be observed
experimentally.
In the second part of this thesis, we study Cross Polarization (CP) proceeding in a
different arena, which is realized through simultaneous nutations around a pair of
orthogonal axes of the source spins at frequencies 𝜔1𝐼 and 𝜔2𝐼 . In DOuble NUTaion
Cross Polarization (DONUT CP), frequency mixing is achieved through generating the
sum and difference frequencies 𝜔1𝐼 ± 𝜔2𝐼 , resulting different Hartmann-Hahn
matching conditions. The experimental results also exhibit some interesting
characteristics that can lead to further studies on this topic.
１．Speedup of nuclear spin diffusion in hyperpolarized solids
Dynamic Nuclear Polarization (DNP) is a powerful technique to enhance the NMR
signal by transferring the electron spin polarization to the nearby nuclei, leading to an
inhomogeneous profile of nuclear spin polarization. This local difference of polarization
distribution is suppressed by spin diffusion that transports the polarization to more
distant nuclear spins and obeys the general diffusion equation 𝜕𝑝⁄𝜕𝑡 = 𝐷∆𝑝, where 𝐷
is the diffusion coefficient and 𝑝 is the nuclear polarization. The spin diffusion
equation has been derived and the diffusion coefficient 𝐷 has been calculated in

high-temperature approximation, where the nuclear spin polarization 𝑝 ≪ 1. It is
obvious that 𝐷 obtained in this way may not be sufficient to describe the spin diffusion
in a hyperpolarized system where 𝑝 can be close to unity.
We propose a correction to the coefficient of nuclear spin diffusion by a factor
̅ is the average nuclear spin polarization. The correction, derived
1/√1 − 𝑝̅ 2 , where 𝑝

by extending the Lowe-Gade theory to low-temperature cases, implies that
transportation of nuclear magnetization through nuclear spin diffusion accelerates when
the system is hyperpolarized, whereas for low polarization the correction factor
approaches unity and the diffusion coefficient coincides with the conventional diffusion
coefficient valid in the high-temperature limit. The proposed scaling of the nuclear spin
diffusion coefficient can lead to observable effects in the buildup of nuclear polarization
by dynamic nuclear polarization.
２. Double nutation cross polarization between heteronuclear spins in solids
Cross Polarization (CP) is another widely-used tool to enhance the NMR signal of
nuclei (13C,

15

N...) with low gyromagnetic ratio, utilizing the polarization of abundant

spin such as proton. So far, numerous variants of CP have been developed in order to
improve its performance.
In this work, we study transfer of magnetization from one nuclear spin species to
another in solid-state nuclear magnetic resonance by cross polarization (CP) employing
the radiofrequency irradiation that causes simultaneous nutations around a pair of
orthogonal axes. Under such DOuble NUTation (DONUT), polarization transfer
undergoes in an unexplored arena of what we refer to as the nutation frame, which
represents the interaction frame with respect to the Hamiltonian that drives nutation.
The effect of DONUT is to develop either the zero-quantum or double-quantum secular
component of the heteronuclear dipolar interaction, causing flip-flop or flop-flop
exchange of the spin states. We demonstrate DONUT CP in polycrystalline adamantane,
glycine, and histidine, also examining folding of the CP spectrum under magic angle
spinning as well as the buildup behavior of the magnetization in comparison with the
conventional CP scheme. In addition, we put forth a concept of spin relaxation in the
nutation frame, which is a straightforward extension of the well-known concept of spin
relaxation in the rotating frame. ...