Communication is an easier problem. One idea that can be made to work is electroquasistatic coupling, where each particle has an ``antenna'' electrode that is capacitively coupled to similar antenna electrodes on neighboring particles.
We have done a preliminary study of a system using an antenna built on the metal-2 layer in a CMOS process, and found that this does not work well. The antenna was guarded on metal-1 to decrease the effect of the capacitance from the antenna electrode to the substrate. The guard electrode was driven by a CMOS op amp. We did a preliminary layout of such a scheme, and we simulated it with SPICE. We also built a scale model to make it easy to probe the fringing fields. Assuming that the computing elements were arranged on a surface with spacing similar to the size of the elements, we could obtain capacitive couplings between adjacent antennas on the order of a few hundredths of a picofarad. The guard electrode had a capacitance to the substrate of a few hundred picofarads. The op amp had to charge this rather large capacitance. The numbers worked out so that we could not expect communications speeds much faster than 100 kbaud.
We can get much better performance if we relax the constraint that the antenna is planar, built in the CMOS process. For example, one can ``unfold'' the antenna up out of the chip. A similar but perhaps easier implementation is to remove the silicon substrate under the antenna structure to reduce the parasitic capacitance. Even simpler, one can bond an antenna wire to each particle. With this kind of coupling, and with good power sources, we can expect to attain communication speeds among neighboring particles in the tens of megabaud range.
One could imagine using radio communication schemes that do not depend upon the coupling capacitance between the transmitting and receiving antennas. However, for such a scheme to work, we must run at much higher frequencies. In addition, communication schemes based on radio are not very local, leading to severe interference problems unless complex schemes for sharing channels, such as large directional antennas, or spread spectrum, are used (See  for more about this idea).