In practice, however, the predicted bridging may not happen, because
thermodynamic equilibrium is not reached. When two particles meet by
Brownian motion, they will be close together for, say, 1 ms, and it will
probably take a far longer time for the adsorbed layers to attain an
equilibrium conformation (cf. Section 10.4). Hence the dispersion will
appear stable. On the other hand, if the particles stay together for a long
time, for instance because they are sedimented, bridging may occur in the
long run. This has been observed in some systems, but the author is unaware
of an unequivocal example involving adsorbed proteins.
Anyway, bridging by adsorbed polymers will often depend on the
history of the system. Consider a dispersion of small solid particles that tend
to aggregate. To stabilize the suspension, an adsorbing polymer is added
that can give a maximum surface excessGplateauof 6 mg?m^2. If the specific
particle surface areaAis 1 m^2 per ml and 3 mg of a suitable surfactant
polymer is added per ml, aGvalue of at most 3 mg per m^2 can result. This
value is on the low side, but the particles are nevertheless stabilized;
apparently, polymer chains stick out far enough into the solvent to cause
steric repulsion. Assume now that to 1 ml of the suspension 6 mg of polymer
is added and that subsequently 1 ml of suspension without polymer is added.
FIGURE12.8 Various modes of bridging two colloidal particles. Situation (c) can
only occur for emulsion drops (or possibly gas bubbles) and (d) generally for solid
particles. Not to scale: the number of polymer molecules involved in situations (a)
and (b) would be very much larger than depicted.