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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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Spin–Spin Coupling Constant: Overview01:08

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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NMR Spectroscopy: Spin–Spin Coupling01:08

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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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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Two coupled, driven Ising spin systems working as an engine.

Debarshi Basu1, Joydip Nandi1, A M Jayannavar2,3

  • 1Department of Physics, Indian Institute of Technology, Delhi, Hauz Khas 110016, New Delhi, India.

Physical Review. E
|June 17, 2017
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Summary
This summary is machine-generated.

This study explores microscale heat engines using Ising spins. Fluctuations in efficiency and performance are significant, with broad probability distributions and power-law tails, impacting engine reliability.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Miniaturized heat engines are a key research area, often using colloidal particles or bacterial baths.
  • Micron-sized systems experience large thermal fluctuations, making average thermodynamic quantities less meaningful.
  • Traditional microengine models adapt Carnot or Stirling cycles, involving isothermal and adiabatic processes.

Purpose of the Study:

  • To investigate a novel prototype microengine model using two classical Ising spins.
  • To analyze the performance and reliability of this spin-based engine/refrigerator.
  • To understand the role of fluctuations in efficiency and coefficient of performance (COP).

Main Methods:

  • Utilizing a system of two classical Ising spins driven by time-dependent, phase-shifted magnetic fields.
  • Simultaneously exposing the spins to two heat reservoirs at different temperatures.
  • Numerically calculating and analyzing the full probability distributions of efficiency and COP.

Main Results:

  • Engine/refrigerator performance is determined by the phase difference between the driving magnetic fields.
  • Fluctuations in efficiency and COP are found to dominate their mean values.
  • Probability distributions for efficiency and COP are broad, exhibiting power-law tails.

Conclusions:

  • The Ising spin model offers a new paradigm for studying microscale heat engines.
  • The broad, power-law-tailed distributions highlight the significant impact of fluctuations on performance.
  • Understanding these fluctuations is crucial for assessing the reliability of microengines.