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 ma.s.s, 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 ill.u.s.trate 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 ma.s.s 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.

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, kataph.o.r.esis, 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 cla.s.s, 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, kataph.o.r.esis, electrolytic precipitation, adsorption, etc.

[Ill.u.s.tration: FIG. 1.]

Now if we select a few simple figures which are in accord with the above considerations, we can examine the value of the factor a{1}c^(1/n{1}) - a{2}c^(1/n{2}) in a purely ill.u.s.trative and typical way, and at any rate form some idea as to the manner in which it is likely to vary. The figures might be:--

Ion. | _n_. | _a_.

-------------------------+---------+--------- Hydrion _or_ hydroxylion | 20 | 10 Kation of a metal | 15 | 7 Organic anion | 10 | 8 Inorganic anion | 6 | 6

For the sake of simplicity we can a.s.sume that these ions are all monovalent. The ions adsorbed by unit ma.s.s will then be 10c^(1/20), etc. If these hypothetical adsorption isotherms be plotted as usual we get the fairly typical curves shown in Fig. 1.

Now in practice there are always two of these ions, each giving its own specific effect in opposite senses, and the difference ( a{1}c^(1/n{1}) - a{2}c^(1/n{2}) ) represents the nett charge adsorbed. Hence we have the following combinations:--

Inorganic acid 10c^(1/20) - 6c^(1/6)

Organic acid 10c^(1/20) - 8c^(1/10)

Alkali 10c^(1/20) - 7c^(1/15)

Inorganic salt 7c^(1/15) - 6c^(1/6)

If we plot these values of nett adsorption against the concentration we obtain the curves shown in Fig. 2.

[Ill.u.s.tration: FIG. 2.]

On the a.s.sumption that the nett charge adsorbed is the dominant factor in determining the maximum swelling at equilibrium, one must therefore regard the curves of Fig. 2 as representing the changes in volume of the swollen gel as the concentration is increased. Now in _type_ these curves correspond to those obtained by experiment from hydrochloric acid, acetic acid, caustic soda, and common salt. The maximum swelling with hydrochloric acid increases rapidly with the concentration at first and then rapidly decreases, though not at such a great rate. The swelling with acetic acid increases less rapidly and to a less maximum, but decreases more slowly. With common salt there is a slight swelling followed by contraction. Caustic soda gives a rapid increase in volume at first, afterwards much less so, and finally yields an exceedingly slow decrease. The correspondence of these facts with the type-curves inevitably suggests that the phenomenon of swelling might be accounted for, in part at least, along these lines.

Of course it is not likely that the simple figures selected for the ill.u.s.tration of the argument are either relatively or absolutely correct. Thus we know that the adsorption curve for hydrions and hydroxylions are not likely to be quite identical, as a.s.sumed above. As gelatin is primarily slightly positive, it is probable that the values of _a_ and of _n_ for hydrion adsorption will be relatively slightly greater. The relative values supposed, however, are near enough to ill.u.s.trate the contention that the type of the maximum volume curve can be explained on this a.s.sumption of different adsorption isotherms for each of the ions.

If the remarks on the compression of the continuous phase be recalled, it will be obvious that in the present paragraphs we have been giving the question of equilibrium-volume a rather one-sided consideration. The volume of the gel when equilibrium is established may be determined in type by the nett charge adsorbed by the disperse phase, but it will be modified also by the lyotrope influence of the particular substance on the continuous phase. When gelatine swells in solutions the influences on both phases are always in operation, and either upon occasion may become predominant. In the case of neutral organic substances, such as cane-sugar, the lyotrope influence is the determining factor. In the case of neutral salts the predominant influence is decided by the place occupied by the salts in the lyotrope series. If at either end of the series the lyotrope influence is uppermost and the effect of ionic adsorptions is practically swamped. Thus sodium sulphate and sodium iodide hinder and promote imbibition respectively as could be expected from their strong lyotrope power. On the other hand, in the case of sodium chloride, which has comparatively feeble lyotrope influence, the relatively different adsorptions of its ions comes to the fore. With acids and alkalies the relatively large adsorption of the hydrion and hydroxylion causes this to be the predominant influence, but we must concede the possibility that purely lyotrope influences may be at work in some cases, and especially at the greater concentrations. Indeed, it is sometimes a difficult problem to decide whether an increase or decrease in swelling is due to lyotrope or adsorptive influence, but, broadly speaking, we can expect strong lyotrope effects at either end of the series and also at large concentrations, and we can expect strong adsorptive effects in dilute solutions, in the middle of the lyotrope series and in the case of alkalies and acids.

For much of the above explanation of the nature and behaviour of gelatine, the author must himself take responsibility, and in this section he has freely quoted from his own papers upon the subject (see References). He claims that his view of a gelatine gel as involving a network of compressed water, liable to modification by lyotrope influence upon the continuous phase and by ionic adsorptions of the disperse phase, is most in harmony with the recent advances in our knowledge of colloids; that much of the theory is a necessary corollary of those discoveries; and also that he has found this view to be a sound guide in practice, both in tanning and in gelatine manufacture.

Many other theories have been advanced, but most are generalizations over too limited a field, and from experiments with only a few substances, and show little or no correlation with the wider facts of colloid behaviour. That of Procter, for example, discards altogether the idea of a two-phased structure of the gel as an "unproved and rather gratuitous a.s.sumption," dismisses surface tension considerations as "more complicated and less verified," and adsorption as "wholly empirical," whilst it ignores lyotrope influence and the a.n.a.logy with agar gels completely. Procter's theory applies mainly to the swelling of gelatine by acids, which swelling he considers to be due to the osmotic pressure of the anion of a highly ionizable salt formed by the chemical combination of the acid with gelatine. On this a.s.sumption, mathematical considerations show that the electric charge on the gelatine is given by the expression z = sqrt(4ex + e^2), where z = the amount of ion taken up, x the concentration of the surrounding solution, and e the excess concentration of diffusible ions in the jelly.

The property of gelatine and glue which is chiefly used in cla.s.sifying them into grades of different commercial value, is the strength of the jelly obtained as compared with any arbitrary standard gelatine. An enormous number of other physical tests have been devised, but none are nearly so simple or so reliable. Gelatine is unfortunately very liable to hydrolysis even by water, and long before any amido-acids, etc., have appeared there is a change to a not greatly hydrolyzed product (sometimes called [beta] gelatine) which has lost the power of setting to an elastic gel. It is thus the lyophile nature which has been altered, and the fall in elasticity corresponds to the fall in power of compressing water, which is proportional to the concentration of [alpha]

gelatine. Now the elasticity of a gelatine gel varies as the square of the concentration. Hence if one so arranges the concentrations of standard and unknown samples that gels of equal elasticity are obtained, the concentration of [alpha] gelatine is the same in both gels, and the _relative_ amounts of [alpha] gelatine in the original samples are inversely proportional to the weights used to give gels of equal elasticity. The "strength" of a gelatine or glue is therefore usually stated as the number of grams of a standard gelatine which will yield a gel with elasticity equal to that from 100 grams of the gelatine or glue being tested. Elasticity is matched by lightly pressing with the finger-tips.

It is also possible to grade samples of gelatine and glue by the estimation of "peptones," whose amount indicates the degree of hydrolysis. Nitrogen is estimated by Kjeldahl's method in the sample and in the precipitate obtained by saturating a solution with zinc sulphate.

The difference is calculated as peptones by multiplying by 5.33. Trotman and Hackford say that the results are in the same sequence as those of the finger test. The method, however, is much more laborious than the "finger test."

Gelatine is also graded according to the results of bleaching and clarifying, but with quite arbitrary standards, largely determined by the fancy of the customer.

Chemical a.n.a.lyses, involving estimations of ash, lime, fat, acid, water, insoluble matter, and poisonous metals, _e.g._ a.r.s.enic, copper, zinc and lead, are of value for special cases according to the destiny of the goods. Special physical tests, such as "breaking strain" and "foam test," are also of some little value in special cases.

REFERENCES.

"The Chemistry of Colloids," W. W. Taylor. 1915.

"Handbook of Colloid Chemistry," W. Ostwald. 1919.

"Chemistry of Colloids," Zsigmondy and Spear. 1918.

"Introduction to the Chemistry and Physics of Colloids," E.

Hatschek.

"Surface Tension and Surface Energy," Willows and Hatschek.

"Chemistry of Colloids," V. Poschl.

"Grundzuge d. Dispersoid Chemie," von Weimarn.

"The Lyotrope Series and the Theory of Tanning," Bennett, J.S.L.T.C., 1917, p. 130.

"The Swelling of Gelatine," Bennett, J.S.L.T.C, 1918, p. 40.

"The Swelling of Gelatine," Procter, _J.C.S. Trans._, 1914, =105=, 313; and _Koll. Chem. Beihefts_, 1911, =2=, 234.

"The Swelling of Gelatinous Tissues," Procter, J.S.C.I., April 16, 1916.

"Summary of Procter's Views, and Bibliography," Collegium (London), p. 3, 1917.

"Lyotrope Influence and Adsorption in the theory of wet work,"

Bennett, J.S.T.C., 1920, p. 75.