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Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

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The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance from a fixed...
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Planar tetracoordinate carbon in extended systems.

Pattath D Pancharatna1, Miguel Angel Méndez-Rojas, Gabriel Merino

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA.

Journal of the American Chemical Society
|November 19, 2004
PubMed
Summary

Researchers explored extending a novel carbon system, C(5)(2-), into polymers. They found that coordination through terminal carbons is favored, leading to potential new materials like C(5)M(x).

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Area of Science:

  • Theoretical Chemistry
  • Materials Science
  • Solid-State Chemistry

Background:

  • A novel planar tetracoordinate carbon system, C(5)(2-), has been proposed.
  • This unique structure offers potential for extension into extended networks.

Purpose of the Study:

  • To investigate the potential for extending the C(5)(2-) unit into one, two, and three-dimensional systems.
  • To explore the polymerization of C(5)(2-) in the presence of countercations.

Main Methods:

  • Analysis of the electronic structure of C(5)(2-).
  • Computational examination and geometry optimization of dimers (e.g., C(10)Li(3-), C(10)Li(4)) and trimers (C(15)Li(6)).
  • Band structure calculations and energetic evaluations for potential polymeric systems.

Main Results:

  • Coordination through terminal carbons is identified as the preferred mode in oligomers and polymers.
  • Several plausible stoichiometries for C(5)M(x) systems (where M = Li, Be, Pt, Zn) were identified.
  • Electronic and structural reasonableness of these potential polymeric materials were assessed.

Conclusions:

  • The C(5)(2-) unit can be extended into polymeric structures.
  • The study provides a foundation for designing novel carbon-based materials with tunable electronic properties.