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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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 π orbitals.
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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,...
The Colloidal State01:29

The Colloidal State

The formation of a colloidal system is exemplified by an aqueous solution containing Cl− ions is introduced to another containing Ag+ ions, resulting in the precipitation of solid AgCl as extremely tiny crystals. Instead of settling out as a filterable precipitate, these crystals remain suspended in the liquid, showcasing a colloidal system.A colloidal system involves colloidal particles within the approximate range of 1 to 1000 nm in at least one dimension, dispersed in a medium called the...
Noncovalent Attractions in Biomolecules02:35

Noncovalent Attractions in Biomolecules

Noncovalent attractions are associations within and between molecules that influence the shape and structural stability of complexes. These interactions differ from covalent bonding in that they do not involve sharing of electrons.
Four types of noncovalent interactions are hydrogen bonds, van der Waals forces, ionic bonds, and hydrophobic interactions.
Hydrogen bonding results from the electrostatic attraction of a hydrogen atom covalently bonded to a strong-electronegative atom like oxygen,...
Noncovalent Attractions in Biomolecules02:35

Noncovalent Attractions in Biomolecules

Noncovalent attractions are associations within and between molecules that influence the shape and structural stability of complexes. These interactions differ from covalent bonding in that they do not involve sharing of electrons.
Four types of noncovalent interactions are hydrogen bonds, van der Waals forces, ionic bonds, and hydrophobic interactions.
Hydrogen bonding results from the electrostatic attraction of a hydrogen atom covalently bonded to a strong-electronegative atom like oxygen,...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

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.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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Updated: Jul 15, 2026

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures
08:53

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

Published on: October 9, 2012

Low-temperature ultrafast mobility in systems with long-range repulsive interactions: Pb/Si(111).

M Yakes1, M Hupalo, M A Zaluska-Kotur

  • 1Department of Physics, Iowa State University, Ames, IA 50011, USA.

Physical Review Letters
|May 16, 2007
PubMed
Summary

Numerous Pb/Si(111) phases, predicted by theory, were observed at low temperatures. Theoretical calculations of collective diffusion coefficient D(c) explain this phenomenon, showing sharp maxima for stable phases.

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Area of Science:

  • Surface Science
  • Condensed Matter Physics
  • Materials Science

Background:

  • Systems with long-range repulsive interactions theoretically predict numerous phases.
  • Experimental realization of these phases was recently observed in Pb/Si(111).
  • These phases were grown at low temperatures (approx. 40 K) over macroscopic distances.

Purpose of the Study:

  • To explain the unusual observation of numerous stable phases in Pb/Si(111) at low temperatures.
  • To investigate the role of collective diffusion in the formation of these phases.
  • To correlate theoretical predictions with experimental findings.

Main Methods:

  • Theoretical calculations of the collective diffusion coefficient D(c).
  • Analysis of D(c) dependence on coverage (c).
  • Comparison of theoretical results with experimental data for Pb/Si(111).

Main Results:

  • Collective diffusion coefficient D(c) exhibits sharp maxima at low temperatures.
  • These maxima occur at specific, rational coverage values (theta=p/q), corresponding to stable phases.
  • The theoretical findings align with the experimental observation of numerous phases in Pb/Si(111).

Conclusions:

  • The formation of numerous stable phases in Pb/Si(111) at low temperatures is explained by collective diffusion.
  • Sharp maxima in D(c) at low temperatures are crucial for the growth of these ordered phases.
  • Theoretical models accurately predict and explain experimental observations in complex surface systems.