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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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

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

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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 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.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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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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¹H NMR Signal Multiplicity: Splitting Patterns01:13

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
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Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons
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The effective coupling coefficient for a completed PIN-PMN-PT array.

D N Stephens1, R Wodnicki2, R Chen2

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Summary
This summary is machine-generated.

This study introduces closed-form expressions for calculating the electromechanical coupling coefficient (EMCC) in medical ultrasound transducer arrays. The new method offers a more accurate and efficient way to determine EMCC, crucial for transducer performance.

Keywords:
Electromechanical coupling coefficientKLM modelPIN-PMN-PTSingle crystal

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Area of Science:

  • Materials Science
  • Acoustics
  • Electrical Engineering

Background:

  • Accurate computation of the electromechanical coupling coefficient (EMCC) is vital for optimizing medical ultrasound transducer array performance.
  • Existing methods for EMCC calculation can be complex and time-consuming, especially for fully assembled arrays.

Purpose of the Study:

  • To develop and validate closed-form expressions for directly computing the EMCC of a fully assembled medical ultrasound transducer array.
  • To compare the accuracy and efficiency of the new method against established models.

Main Methods:

  • Measurement of complex electrical impedance spectra for a 1-3 composite array before and after thermal stress.
  • Application of the Levenberg-Marquardt non-linear regression algorithm (LMA) to validate EMCC predictions.
  • Utilizing closed-form expressions for direct EMCC calculation.

Main Results:

  • The developed closed-form expressions for EMCC show good agreement with the KLM model-based LMA.
  • The new method exhibits approximately one-tenth the error compared to formulas for flat, unloaded transducers.
  • Thermal stress (160°C for 15 min) induced changes in EMCC (-4.9%), clamped dielectric constant (-11%), and effective transducer longitudinal velocity (-2.5%).

Conclusions:

  • The novel closed-form expressions provide an accurate and efficient means for calculating the EMCC of assembled medical ultrasound transducer arrays.
  • This method offers significant advantages in terms of error reduction and computational simplicity.
  • Understanding the impact of thermal variations on EMCC is crucial for transducer reliability.