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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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Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, and solubilities (miscibilities) of substances. Molar mass, molecular shape, and polarity affect the strength of different intermolecular forces, which influence the magnitude of physical properties across a family of molecules.
Temporary attractive forces like dispersion are present in all molecules, whether they are polar or nonpolar. They...
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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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¹H NMR: Complex Splitting01:13

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A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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Molecular Orbital Theory II03:51

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Molecular Orbital Energy Diagrams
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Sharp interface limit of a two-time scale phase field model of a binary mixture.

V G Lebedev1,2, V E Ankudinov2, N V Kropotin3

  • 1Udmurt Federal Research Center UB RAS, 426067 Izhevsk, Russia.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|January 31, 2025
PubMed
Summary
This summary is machine-generated.

This review explores hyperbolic phase field models for analyzing phase transformations, particularly solidification. It demonstrates mapping these models to the sharp interface limit, revealing insights into non-equilibrium effects like solute trapping during solidification.

Keywords:
Stefan problemdiffusionless solidificationfast phase transitionphase fieldphase interfacesolute trapping

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Area of Science:

  • Materials Science and Engineering
  • Thermodynamics and Physical Chemistry
  • Computational Materials Science

Background:

  • Phase field methodology offers analytical flexibility and thermodynamic consistency for studying phase equilibria and transformations.
  • Hyperbolic phase field models are crucial for analyzing both slow and fast phase transformations.
  • Understanding solidification processes, especially in metastable liquids and binary mixtures, is vital for materials design.

Purpose of the Study:

  • To review hyperbolic phase field models applicable to slow and fast phase transformations.
  • To analyze the reduction of diffuse interfaces to sharp interfaces using solidification of metastable liquid as an example.
  • To investigate non-equilibrium effects and the transition between diffusion-limited and diffusionless solidification.

Main Methods:

  • Asymptotic analysis of hyperbolic phase field models for binary mixtures with diffuse interfaces.
  • Mapping hyperbolic phase field models to the hyperbolic Stefan problem in the sharp interface limit.
  • Utilizing common tangent construction to analyze non-equilibrium phenomena.

Main Results:

  • The hyperbolic phase field model can be accurately mapped to the hyperbolic Stefan problem under sharp interface conditions.
  • Non-equilibrium effects, such as solute trapping, can be analyzed using this framework.
  • The complete transition from diffusion-limited to diffusionless solidification at finite interface velocities is elucidated.

Conclusions:

  • Hyperbolic phase field models provide a robust framework for analyzing complex solidification phenomena, including non-equilibrium effects.
  • The sharp interface limit offers a valuable simplification for theoretical and computational analysis.
  • The findings align with and provide theoretical underpinnings for experimental observations in solidification science.