Energy, force, and stiffness
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 …
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
