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Is there a possible theoretical effect of mechanical vibration on the stability of organic molecules. E.g. some medicines degrade if they are not stored in a fridge, is there a theoretical foundation that suggests that low frequency vibrations might have the same effect?

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What do you mean by "low frequency vibrations"? The term "extemely low frequency" is used to describe earthquake type frequencies (3-30 Hz, give or take), whereas "low frequency" is used to describe frequencies in the 30kHz - 300 kHz range. If you mean "low frequency" as defined in the previous sentence, then yes, that frequency range of vibration is known to have chemical effects. The process involves the formation and collapse of bubbles (cavitation) in the solution. High temperatures and pressures can be generated during the bubble formation and collapse process. The typical lab apparatus can homogenize samples, produce catalytic effects by cleaning metal surfaces or increasing phase transfer, disrupt cells, and break some (weak?) chemical bonds. This reference reports,"Ligand-metal bond cleavage in transition metal complexes to give coordinatively unsaturated species or modified complexes as well as complete strip off of ligands to produce amorphous metals disrupture of the solvent structure altering the solvation of reactants Sonolysis of molecules (homolytic fragmentation to radicals, rupture of polymers, generation of excited states, cell disrupture)."

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