Difference between revisions of "Energy, force, and stiffness"

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Energy, force, and stiffness. These are derivatives of each other. <br>  
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Energy, force, and stiffness. <br>
Or, the other way around, antiderviatives.
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These are derivatives of each other like so:.<br>  
 
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* stiffness * path = force --force * path = energy
* stiffness * path = force - and - force * path = energy
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* energy per path = force - and - force / path = stiffness
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Thus we have:
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* Integration: stiffness => force => energy
 
* Integration: stiffness => force => energy
 +
 +
Or, the other way around, antiderviatives. Thus we have:
 +
* energy / path = force --- force / path = stiffness
 
* Differentiation: energy => force => stiffness
 
* Differentiation: energy => force => stiffness
  
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== Further related topics ==
 
== Further related topics ==
  
* Historically caused focus on energies and frequencies
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There's a historically caused focus on frequencies (and proportional energies) rather than forces (and stiffnesses)
* Comparison of all three properties for gaining a better intuitive feel
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Frequencies is what was first accessible to experiment via optical spectroscopy.
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And energies and frequencies associated with interatomic bonds are still usually easier to directly measure to this day (state 2020). <br>
 +
See main article: [[Energies and frequencies]]
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Bond enthalpy tables can be easily found but bond maximum tensile strength tables are not available just as there are no tables for bond stiffnesses.
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{{wikitodo|add image of a bond enthalpy table}}
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 +
Comparison of all three properties  
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* a bonds total energy (enthalpy)
 +
* a bonds maximum tensile stress
 +
* a bonds maximum stiffness
 +
energy for gaining a better [[intuitive feel]]
 +
 
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== Related ==
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* [[Covalent bond]]
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* [[Van der Waals force]]

Revision as of 10:25, 10 September 2020

This article is a stub. It needs to be expanded.

Energy, force, and stiffness.
These are derivatives of each other like so:.

  • stiffness * path = force --- force * path = energy
  • Integration: stiffness => force => energy

Or, the other way around, antiderviatives. Thus we have:

  • energy / path = force --- force / path = stiffness
  • Differentiation: energy => force => stiffness

Models for chemical bonds

There are several models approximating the behaviour of chemical bonds in a mass and spring model.

  • Lennard Jones Potential

These is by far not as accurate as quantum mechanical modelling, but depending on the problem at hand this can more than suffice.

From this energy curve a force curve and a stiffness curved can be derived by taking the first and second spacial derivative. Note that in 3D this would give a force vector field and a stiffness tensor field.

From the original and the derive curves special values can be read out.

Special values

  • total bond energy (equivalent to bonds toughness)
  • Absolute tensile strength
  • point of highest stiffness
  • there are some more …

Further related topics

There's a historically caused focus on frequencies (and proportional energies) rather than forces (and stiffnesses) Frequencies is what was first accessible to experiment via optical spectroscopy. And energies and frequencies associated with interatomic bonds are still usually easier to directly measure to this day (state 2020).
See main article: Energies and frequencies

Bond enthalpy tables can be easily found but bond maximum tensile strength tables are not available just as there are no tables for bond stiffnesses. (wiki-TODO: add image of a bond enthalpy table)

Comparison of all three properties

  • a bonds total energy (enthalpy)
  • a bonds maximum tensile stress
  • a bonds maximum stiffness

energy for gaining a better intuitive feel

Related