In the swelling of (say) one gram of gelatine to its maximum, both the
contractile force of surface tension and the expanding force of
electrical repulsion are in operation. At the commencement the latter is
much the greater force--hence the rapid imbibition. Both these forces
decrease in magnitude as the swelling proceeds, but the force tending to
swell decreases at a more rapid rate, and the time comes when it has
decreased to the precise value of the force tending to resist swelling.
At this point equilibrium is established and the maximum swelling
attained. Obviously this maximum will in many cases be determined
largely by the value of a{1}c^(1/n{1}) - a{2}c^(1/n{2}).
This factor, therefore, demands particular consideration.
Now, unfortunately, the adsorption law constants for the different ions
have not yet been numerically determined, so that we are still somewhat
in the dark as to the operation of ionic adsorptions. It is
possible, however, to form conclusions of a qualitative or relative
order, and these are such as to throw much light upon the question at
issue. In the first place, we know that in general the various ions are
not usually very widely different in the extent to which they are liable
to be adsorbed. If this were otherwise, the valency rule would hardly
operate so well in endosmosis, kataphoresis, and precipitation. In
consequence we must expect the differences between the ions to appear in
small rather than in large concentrations, the amounts adsorbed being
under those conditions more affected by changes in the volume
concentration. At the larger concentrations, therefore, the value of
a{1}c^(1/n{1}) - a{2}c^(1/n{2}) is small, and the force causing
swelling often tends to zero.
There are, however, noticeable differences at lower concentrations. Thus
we know that if a substance be primarily a positive colloid, it will
absorb kations more readily than anions. As gelatine falls into this
class, we may therefore conclude that usually a{1} > a{2}. Further,
it often happens that very adsorbable substances are less affected by
concentration changes, and in the case under consideration, therefore,
we should expect that n{1} > n{2}. Moreover, we know that the hydrion
and hydroxyl ion are much more readily adsorbed than other ions, _i.e._
have a large value for _a_. Hence in the case of gelatine we expect that
a{1}c^(1/n{1}) - a{2}c^(1/n{2}) will have a comparatively large
value when one of the ions is H+ or OH-. Also we know that organic
anions are usually much more strongly adsorbed than inorganic anions,
and hence that in such cases a{1} is more nearly approached by the
value of a{2}. It should be emphasized perhaps, at this point, that
these various considerations are not based upon any facts relating to
the phenomena of imbibition in gels, or in gelatine in particular, but
are based upon the behaviour of colloids in endosmosis, kataphoresis,
electrolytic precipitation, adsorption, etc.
[Illustration: FIG. 1.]
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