In effect, therefore, the particles of the disperse phase each carry an
electric charge of the same nature, and as similarly charged bodies
repel one another, the particles of the disperse phase will tend to
separate and to occupy a bigger volume. It is the author's opinion that
this repulsion of similarly charged particles is the cause of the
swelling of gelatine. The amount of charge and force--tending to
swell--is due possibly to several ionic adsorptions, which may be
considered to operate independently, and the power of repulsion is
determined by the nett charge, which in the case of a "positive colloid"
is positive, and in the case of a "negative colloid" is negative. As
ions possess different electric charges, the charge on the disperse
phase is subject to the valency rule.
Now the repulsive force between two similar and similarly charged bodies
is proportional to the amount of charge and is inversely proportional to
the square of the distance between them. The amount of charge on a
colloid particle will be determined by the dispersity--best signified by
the specific surface (s)--and by the operation of the adsorption law
y = mac^(1/n)
The distance between the particles varies with the degree
of swelling, and is determined by the cube root of the volume of the gel
(_v_). Hence if F be the force tending to make the gelatine swell, we
may write
F = Q/(d^2) = (sy)/v^(2/3)
Now with all electrolytes, even with water, we have both positively and
negatively charged ions, and y is consequently determined by the
difference in the amounts adsorbed. Hence in the case of an electrolyte
with an equal number of oppositely charged ions
y = ma{1}c^(1/n{1}) - ma{2}c^(1/n{2}), where a{1}, a{2}, and
n{1}, n{2}, are the appropriate constants for the particular ions
concerned. Hence at constant temperature, pressure, etc., we may write
F = [ sm( a{1}c^(1/n{1}) - a{2}c^(1/n{2}) ) ] / v^(2/3)
The force tending to make a piece of gelatine swell is proportional to
its mass, which is perhaps fairly obvious. The swelling force is also an
inverse function of the volume of the gel, and as swelling proceeds
therefore the force tending to swell further decreases. The force
tending to swell is proportional to the specific surface of the disperse
phase, other factors being constant. To illustrate this one has only to
imagine that one particle of the disperse phase be split into two
particles each carrying half the original charge. It is clear that a new
repulsive force becomes operative, which did not before influence the
swelling, and that the distance between the particles is halved. In the
swelling of gelatine, however, we may consider the dispersity constant
for constant temperature, and if we consider unit mass we see that the
force causing swelling depends upon the operation of the adsorption law
and upon the degree to which the gel is already swollen.
Public-domain text, read in full here on John Shaqi.
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