All,
Interesting discussions on the resonances and I think garbageman had a good point in that for real effecient breakage of the hydrogen/oxygen bonds we will probably have to use a number of different mechanisms (electrical and/or mechanical and/or chemical).
In my profession that I do to pay the bills, I work for a company that produces piezoelectric transducers and the associated electronics to drive them. We then take these transducers, and then put them into arrays that are used in many ultrasonic applications.
The problem with trying to use piezoelectric transducers to create the 2.4 GHz frequency is that it is almost impossible (or at least probihitively expensive). Piezoelectric transducers resonate at frequencies that are dependent upon their capacitance. The capacitance is a direct relation of the physical shape of the ceramic element. There are literally hundreds of shapes (cylinders, blocks, discs, donuts, etc.). The lower you go in frequency, the larger the physical transducer size has to be. Piezoelectric transducers are also very "narrow band". This means that once you get a physical configuration of a transducer, it will resonate over a very narroe frequency. In other words, it is physically impossible to get a transducer to vibrate over a very large frequency band. They typically have a bandwidth of about 10 kHz or less. So, if we wanted a drive a transducer at 59kHz, then, because of it's physical configuration (that it is designed for) it may resonate efficiently over the range of 54kHz to 64kHz with the most efficient frequency being in the center of the band (59kHz).
Also, piezoelectric transducers are pretty inefficient. Typically their efficiency is around 45% - 65%. This might be okay if you want to heat the water
The highest frequency transducer that I have used is in the 900kHz range. This is way short of the Mhz and Ghz ranges that has been discussed.
I like the idea of vibrating the electrodes....
Open up a computer, and take off the heat sink of the CPU. Use this as the positive voltage electrode. Get another heat sink just like it for the negative voltage. Burn off the paint, and fasten wires to it. This has a lot of surface area. Now put a pulsed DC voltage on the positive terminal. Vary this frequency until you hit the resonant frequency of the heat sink. Better yet, there are Finite Element Analysis programs that will calculate the resonant frequency of any model. Put the CPU heat sink model in this package, and you now know at what frequency to drive it.
Our company also designs a lot of mechanical structures. We have to do a lot of Finite Element analysis to make sure that the resonant frequency of the shape is way out of band from what it will see in real life. If we don't do this right, then we have a "Tacoma Narrows Bridge" situation (very, very, bad for the younger audience). However, in our case, we would want to drive the structure (our electrode) at this resonant frequency. Not to the point of self destruction, but just enough to keep 'em shakin'. If, during the chemical reaction a voltage is generated, this could be modulated so that it is fed back down the electrode to keep them vibrating.
On another note...
Please be careful about using the 2.4 GHz range of frequencies. If this is put into a transmitter or amplified, it will radiate a very dangerous microwave frequency, and fry you (i.e. think of a microwave oven). I think the only safe way to use this frequency is if you turn on and off the power to the electrodes with out amplifier. I am assuming that everyone understands this.
'nuf said for now... you can all wake up now!