Energy, force, and stiffness
From apm
Energy, force, and stiffness. These are derivatives of each other.
Or, the other way around, antiderviatives.
- stiffness * path = force - and - force * path = energy
- energy per path = force - and - force / path = stiffness
Thus we have:
- Integration: stiffness => force => energy
- 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 …
- Historically caused focus on energies and frequencies
- Comparison of all three properties for gaining a better intuitive feel
