# How to properly model a mechanochemical reaction of barium titanate and copper(II) complexes?

I would like to understand, in terms of chemical kinetics, how I could equate the reaction rate between $$\ce{BaTiO3}$$ and copper(II) complexes under ultrasound effect.

Examples in literature would be great!

• What do you mean equate the reaction rate between? Force will generally reduce reaction barriers involving bond stretching. However, it can be quite a tricky relationship! For example, we have found that by putting a radical on a polymer causes delocalization of the HOMO, therefore the force isn't efficiently directed along the orbital like it is for the non-radical C-C bonding orbital. Mar 31, 2020 at 0:50
• Could I write such a reaction between BaTiO3 and Copper(II) complexes as: CuIIX2/L + BaTiO3 -> CuIX/L + X- ? Where X is a halogen and L a ligand. Mar 31, 2020 at 12:49

Reaction rates can be calculated from the Arrhenius equation $$k=Ae^{E_a/RT}$$ where $$E_a$$ is the activation energy found at the transition state.

Please check out the Reference 1 for calculating transition states under force. Following is an excerpt from the paper (Ref.1):

As a force is delivered to the mechanophore, the energy provided by the work can be quantified by $$\Delta E =−F\Delta x$$ where $$\Delta E$$ is the change in energy, $$F$$ is the amount of force applied, and $$\Delta x$$ is the change in distance over which the force is applied ($$\Delta x$$ in the examples of this article will correspond to the distance between the two atoms where the tensile force is applied…

We have recently developed a python version of the code.

Force can also be added along bonds to simulate ultrasound and we have some work in preparation showing this for polymers. Essentially ultrasound creates bubbles which pop and drag the polymer in opposite directions.

References:

1. Allison G. Roessler, Paul M. Zimmerman, “Examining the Ways to Bend and Break Reaction Pathways Using Mechanochemistry,” J. Phys. Chem. C 2018, 122(12), 6996-7004 (https://doi.org/10.1021/acs.jpcc.8b00467).
• I found an article (doi.org/10.1002/ceat.200401905) that Arrhenius equation could be rewrite as k = (g*(1 + dW)^f)*e^(Ea/RT), where W is the ultrasound power, but I don't know if this equation is common in sonochemistry, it is? Mar 31, 2020 at 12:39
• Awesome find! I'll check it out and let you know but I've never seen that used before. Also I edited my answer for clarity Mar 31, 2020 at 15:42