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Potential Due to a Polarized Object

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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...

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In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...

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When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.

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Updated: Jul 16, 2026

Hyperpolarized Xenon for NMR and MRI Applications

Hyperpolarized Xenon for NMR and MRI Applications

Published on: September 6, 2012

Comment on "Pushing the hyperpolarizability to the limit".

Greg A Wiggers¹, Rolfe G Petschek

¹Department of Physics, Case Western Reserve University, Cleveland, Ohio 44120-7900, USA.

|March 22, 2007

Summary

Maximizing electron hyperpolarizability is complex due to energy/length scaling. A new formula clarifies this, showing modulated conjugation does not guarantee large hyperpolarizability.

Area of Science:

Quantum chemistry
Computational physics

Background:

The first hyperpolarizability (beta) is crucial for nonlinear optical (NLO) materials.
Previous studies suggested modulated conjugation enhances beta, but lacked rigorous theoretical proof.

Discussion:

Energy and length scaling present significant challenges when optimizing the first hyperpolarizability of a single electron.
A simplified formula for hyperpolarizability is derived, offering clearer insights into its dependencies.
Analysis of the derived formula indicates that the claims by Zhou et al. regarding modulated conjugation leading to large hyperpolarizability are unsubstantiated.

Key Insights:

Energy/length scaling complicates the maximization of electron hyperpolarizability.
A transparent formula for the first hyperpolarizability is presented.

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The effectiveness of modulated conjugation for achieving high hyperpolarizability is questioned.

Outlook:

Further theoretical and computational studies are needed to fully understand hyperpolarizability scaling.
Development of accurate predictive models for hyperpolarizability is essential for designing novel NLO materials.
Experimental validation of theoretical predictions concerning modulated conjugation and hyperpolarizability is warranted.