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Related Concept Videos

Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
696
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Author Spotlight: Exploring Intrinsically Disordered Protein Dynamics Through NMR Relaxation Experiments
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NMR Relaxation by Redfield equation in a spin system I=7/2.

A Consuelo-Leal1, A G Araujo-Ferreira1, E Lucas-Oliveira1

  • 1Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, São Paulo, Brazil.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|March 2, 2023
PubMed
Summary

This study analytically solves the Redfield master equation for spin I=7/2 nuclear systems. The method accurately models cesium-133 nuclear spin dynamics in liquid crystals and is adaptable for other nuclei.

Keywords:
Lyotropic liquid crystalRedfield theoryRelaxationSpin dynamics

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • The Redfield master equation is crucial for describing relaxation processes in quantum systems.
  • Understanding nuclear spin dynamics in complex environments like liquid crystals is vital for advanced NMR applications.
  • Cesium-133 (133Cs) nuclei in liquid crystals present a unique system for studying spin dynamics.

Purpose of the Study:

  • To analytically solve the Redfield master equation for a nuclear system with spin I=7/2.
  • To compute density matrix elements using an irreducible tensor operator basis.
  • To accurately model the longitudinal and transverse magnetization dynamics of 133Cs nuclei.

Main Methods:

  • Analytical solution of the Redfield master equation.
  • Utilizing the irreducible tensor operator basis for computation.
  • Numerical procedures for generating accurate mathematical expressions.
  • Experimental monitoring of 133Cs nuclear magnetization dynamics in a lyotropic liquid crystal.

Main Results:

  • Derived accurate analytical solutions for the density matrix elements.
  • Generated precise mathematical expressions for nuclear spin dynamics.
  • Successfully modeled the experimental longitudinal and transverse magnetization dynamics of 133Cs.
  • Demonstrated the high accuracy of the theoretical approach.

Conclusions:

  • The analytical solution of the Redfield master equation provides a robust framework for understanding nuclear spin dynamics.
  • The developed methodology accurately predicts experimental observations for 133Cs nuclei.
  • This approach is versatile and can be readily extended to other nuclear spin systems.