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Related Concept Videos

Continuous Charge Distributions01:17

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Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
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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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Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
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The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.
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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Charge Renormalization for Ellipsoidal Macroions.

YongSeok Jho1,2, Jonathan Landy3, P A Pincus4

  • 1Asia-Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790-784, South Korea.

ACS Macro Letters
|May 21, 2022
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Summary
This summary is machine-generated.

Counterion condensation around ellipsoidal macroions creates a quasi-equipotential surface. This resistance to deformation suggests a balance of forces influencing macroion shape transitions.

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Area of Science:

  • Physical Chemistry
  • Soft Matter Physics
  • Colloid Science

Background:

  • Counterion condensation is crucial for understanding macroion behavior in solutions.
  • Ellipsoidal macroions model diverse systems like liquid crystals and vesicles.
  • Previous studies on spherical macroions suggested deformation preferences.

Purpose of the Study:

  • To investigate counterion condensation on ellipsoidal macroions.
  • To derive analytic estimates for critical valence in the weak screening limit.
  • To explore the implications of condensation for macroion shape stability.

Main Methods:

  • Analytical modeling of counterion distribution around ellipsoids.
  • Application of Alexander et al.'s procedure for critical valence estimation.
  • Comparison with spherical macroion deformation behavior.

Main Results:

  • Unrestricted ion motion establishes a quasi-equipotential surface on ellipsoids.
  • Accurate analytic estimates for critical valence of general ellipsoids were obtained.
  • Eccentric ellipsoids exhibit higher critical valence than spheres of equal volume.

Conclusions:

  • Counterion condensation resists macroion deformation, favoring spherical shapes.
  • This force opposes linear effects that might favor flattening.
  • The interplay of these forces could modify macroion shape transition dynamics.