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Related Concept Videos

π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to...
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π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds01:14

π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds

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In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as...
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.0K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
2.0K
Inductive Effects on Chemical Shift: Overview01:27

Inductive Effects on Chemical Shift: Overview

1.3K
The protons in unsubstituted alkanes are strongly shielded with chemical shifts below 1.8 ppm. Methine, methylene, and methyl protons appear at approximately 1.7, 1.2 and 0.7 ppm, while the proton signal from methane appears at 0.23 ppm. An electronegative substituent, such as chlorine, withdraws the electron density from the protons, increasing their chemical shift. Progressive substitution of the hydrogens in methane by chlorine shifts the proton signals increasingly downfield, to 3.05 ppm in...
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Updated: Sep 16, 2025

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities
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High-Order Anharmonicities Shape Phonon Hydrodynamic Effects in Graphene.

Jordi Tur-Prats1, Zherui Han2, Albert Beardo1

  • 1Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain.

Nano Letters
|July 10, 2025
PubMed
Summary
This summary is machine-generated.

Four-phonon interactions significantly limit phonon hydrodynamics in graphene, challenging previous assumptions. This finding impacts understanding of thermal conductivity and collective phonon behavior in 2D materials.

Keywords:
four-phonon interactionsgraphenephonon hydrodynamicsphonon viscositysecond sound

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Nanotechnology

Background:

  • Graphene was predicted to exhibit prominent phonon hydrodynamic phenomena at low temperatures.
  • Higher-order phonon interactions, particularly four-phonon interactions, act as a resistive channel reducing thermal conductivity.

Purpose of the Study:

  • To investigate the conditioning role of four-phonon interactions on hydrodynamic effects in graphene.
  • To re-evaluate the adequacy of the collective limit assumption for phonon hydrodynamics.
  • To determine key hydrodynamic parameters under full anharmonicity.

Main Methods:

  • Theoretical analysis of phonon-electron interactions.
  • Calculation of hydrodynamic parameters (nonlocal length, heat flux relaxation time).
  • Critical review of existing theoretical models and experimental conditions.

Main Results:

  • Four-phonon interactions severely condition the occurrence of hydrodynamic effects in graphene.
  • The collective limit assumption is inadequate for describing graphene's hydrodynamic transport.
  • Key hydrodynamic parameters are significantly reduced when considering full anharmonicity.

Conclusions:

  • Four-phonon interactions are crucial for understanding phonon hydrodynamics in graphene.
  • Previous predictions on collective phonon behavior and hydrodynamics require critical re-evaluation.
  • The study provides insights into observable implications for experimental configurations.