(57d) Chemical Swarming

Nano- and micro-scale
objects can undergo autonomous motion owing to chemical activity at their
surfaces – so-called catalytic nanomotors.  A surface chemical reaction creates local
concentration gradients of the reactant (the fuel) and product species and, as
these species diffuse in an attempt to re-establish equilibrium, they entrain
the motor causing it to move.  A
single chemically active particle acts as a source (or sink) creating a reactant
concentration disturbance that decays as 1/r, where r is the distance from the
active particle.  A second particle will,
in general, undergo normal diffusiophoresis in the concentration gradient created
by the first particle.  For particles
that move down the concentration gradient two sink particles will attract each
other, while two source particles will repel each other.  (A source and a sink particle will not
move relative to one another.)  Thus,
a collection of source particles will tend repel each other and drift apart,
while sink particles will attract each other and tend to 'collapse' into a
dense clump – they 'swarm.'  However,
if fuel is supplied uniformly at the rate at which it is consumed by the active
particles a 'chemically neutral' steady sate can be achieved in which the active
particles exhibit Debye-like screening and phase behaviors analogous to those
of a one-component plasma.