Principles of General Physiology

Although membranes of hydrophile colloid substances do not allow water to filter through at any perceptible rate under moderate pressures, it is possible, by the application of pressures from two to thirty atmospheres or more, to concentrate colloidal solutions and separate them from " crystalloid " admixture, by forcing the liquid phase through the membrane. This was first done by Chas. J. Martin (1896). His filter consisted of a porous clay Chamber-land candle, whose pores were filled with gelatine. This was fixed in a gun-metal case, with the nozzle projecting, and the space between the two was filled with the liquid to be filtered. A pressure of some thirty atmospheres or more, applied to the solution, caused the water and crystalloids to be driven through, while the colloids remained behind.

Bechhold (1907) modified the apparatus so that flat sheets of various membranes, differing in permeability, could be used. He also showed how to make membranes of different degrees of permeability. Some of the results obtained by this method will be referred to in Chapter V., on u Permeability of Membranes." The name of " Ultra-filter " is due to this investigator. If sand be shaken with water, and the mixture then allowed to stand, the sand rapidly falls to the bottom, leaving the water clear and free from grains. Why, then, do the particles of gold, whose density is greater than that of sand, remain suspended for an indefinite time in the colloidal state ?

It will be obvious that this is, in some way, connected with their size ; but there must also be forces active in preventing them from sticking together to form grains large enough to fall rapidly, as the following consideration will show. The larger the number of particles into which a given mass is divided, the greater the surface energy. Now, by the principle of Carnot and Clausius, the system strives to diminish this free energy, so that, unless prevented, the particles will aggregate together to form larger particles and sink.

In 1828 the botanist, Robert Brown (1828), noticed particles in microscopic preparations to be in a continuous state of rapid oscillatory motion ; the smaller the particles, the greater the amplitude of the movement. Various suggestions were made from time to time to explain this " Brownian" movement, such as inequality of temperature, electrical charge, and so forth, but none were found to stand the test of experimental investigation. One fact, which at once disposes of any hypothesis referring the movement to any external cause, is the complete independence of the direction of movement of two particles in close proximity to one another. That electrification has nothing to do with the phenomenon is shown by an experiment of Svedberg (1907). By gradual addition of an aluminium >alt to a colloidal solution of silver, he was able, owing to facts which will be explained below, to reverse the sign of the electric charge on the silver particles, thereby passing through a stage of zero charge, without in any way diminishing the extent of the Brownian movements.

It is only in recent years that it has been shown, chiefly by the work of Perrin (1908), that this movement is identical with that of the molecules of the liquid, as postulated by the kinetic theory. In order to understand the nature of the proof, which has also important bearings on the question of the real existence of molecules, a few words are necessary on the kinetic theory and on the molecular basis of chemical science. Certain difficulties in the atomic theory of Dalton, when applied to the volumes of gases taking part in reactions, were removed by accepting the law proposed by Avogadro in 1813, namely, "equal volumes of gases at the same pressure contain equal numbers of molecules." Now, if molecules have an actual existence, it follows that, in a definite volume of any gas, say one cubic millimetre, there is a certain definite number of molecules. This number which, of course, varies with temperature and pressure, is known as " Avogadro's constant," when standard temperature and pressure are taken, and is usually designated by the letter N. It has been determined by several independent methods, and the fact that the values obtained lie very near together is, in itself, powerful evidence of the truth of the assumption on which they were calculated. A short account of these methods will be found in Perrin's monograph (1910, pp. 75-93).

Further, according to the kinetic theory of gases, these molecules although very minute have a finite size, and the space occupied by the molecule, or rather by its sphere of action, is very small compared with the space unoccupied. At all temperatures above absolute zero the molecules are in ceaseless movement. Any one molecule will travel in a certain direction until it meets another one. After collision and interchange of kinetic energy, the two molecules will rebound and travel again, but with a velocity changed in direction and in magnitude, until further collisions occur. It will be seen that the kinetic energy of any individual molecule will vary from moment to moment, but will oscillate about a mean value. Similarly, the distance travelled between collisions will vary about a certain value, called the " mean free path."

It is interesting to remember that, although the first actual publication of the kinetic theory was made, independently, by Kroenig in 1856 and by Clausius in 1857, a complete development of the theory had been sent to the Royal Society in 1845 by J. J. Waterston. This paper, unfortunately, was not printed until 1892, in the Philosophical Transactions, having been found by Lord Rayleigh in the archives. Similar statements apply to liquids, with the exception that the molecules are in such close relation that the cohesive force of attraction, the quantity a of Van der Waals' equation, about which we shall have more to say later, comes into play much more powerfully, as does also the other quantity b, representing the volume of the molecules themselves. In the case of solids, this molecular movement, due to heat, must be supposed to be confined to oscillation about a mean position. The molecules of solids do not continually change their places, as is the case with gases and liquids.

Let us now fix our attention on a particular molecule in the interior of a liquid. It will be di'iven hither and thither by the impact of other molecules, upwards, downwards, and so on, occasionally taking a comparatively long journey before collision with another molecule. It can be easily shown (Perrin, 1910, p. 11) that the mean molecular kinetic energy is the same in all gases, and van't Hoff has shown that the same statement holds for dilute solutions ; so that a molecule of alcohol in solution in water has the same kinetic energy as each molecule of the water. __ Again, the molecules of sugar in solution have the same mean energy as those of the water, as also have those of any other molecule, light or heavy, in true solution. Why, then, should we not extend the conception to aggregates of molecules, in other words, tocolloidal particles 1 This is the starting point of Perrin's important work.

Consider first what will happen to a particle very large in comparison with the molecules of the liquid in which it is immersed. It will be bombarded on all sides by a large number of molecules, moving in all possible directions, whose resultant will be zero or very nearly so, and no movement will be perceptible. As the particles are imagined to become smaller and smaller, they will be hit by fewer and fewer molecules simultaneously, so that the forces acting on them will cease to be balanced, and the particles will be driven hither and thither just as the molecules of the liquid itself. There is thus every reason to suppose that their mean kinetic energy will also be identical with that of the molecules of the liquid or of any other molecule in solution.

Suppose next that, on this assumption, we proceed to calculate the constant of Avogadro from direct observation of the Brownian movement or of states of equilibrium due to its operation. -If the values arrived at agree with those obtained in other ways, the proof is practically complete that the hypothesis is a valid one. This is what Perrin (1910) has done. , Three different methods were adopted, the exact details of which will be found in his little monograph. The first method depends on the fact that, if the Brownian movement of particles is really the same as the movement of molecules in a gas, their vertical distribution in equilibrium must follow the same law as that of the atmosphere, under the influence of gravity. In order to verify this experimentally, it was necessary to prepare suspensions of particles of a uniform size and sufficiently large for the observation to be made in the depth of a cell on the stage of the microscope. The use of the microscope was

Fie. 40. BROWNIAN MOVEMENT. — Paths obtained by joining the consecutive positions of three particles of mastic at intervals of thirty seconds. They only give a feeble idea of the complexity of the real trajectories. If the positions were indicated from second to second, each of the rectilinear segments of the figure would be replaced by a polygonal contour of thirty sides, as complicated as the drawing given here. necessary in order to count the particles. Gamboge and mastic were the substances used. By a process of fractional centrifugation, preparations containing particles of a uniform size were made. From these experiments, a value of 70 •"> x 1 ()'-"-' was found for the number of molecules in 22'4 litres of a gas.

The second method was based on a formula of Einstein, giving the mean displacement of a particle in a given time in terms involving N, together with other values capable of experimental determination. The positions of an individual particle were mapped out at intervals of thirty seconds by the camera lucida on squared paper. Samples of three such tracings are given in Fig. 40. This figure will serve to give some idea of the complexity of the movements in question, but only a limited one, since it must lie remembered that, if the position of the particle had been mapped at more frequent intervals, it would have been found that between each of the positions marked, a path fully as elaborate as the whole of the figure would have to be inserted.

These figures are also instructive as showing what complexity results from the action of apparently simple and uniform forces. The mean kinetic energy of each molecule is the same as that of other molecules, and the forces to which it is exposed might be imagined to be symmetrically distributed in the body of the liquid, and yet we obtain this apparently "chaotic" variety of movement. It is unnecessary to remark that it is not really in any way " chaotic," the impression it gives us is merely due to our inadequate methods of observation. By this second method a value of N of 71 '5 x 1022 was obtained.

The third method depends on the fact that, when the dimensions of the particles are sufficiently large, many of the impacts of the water molecules will be directed more or lass tangentially, and so cause rotation of the particles, which can be observed when these contain some distinguishing mark, as an inclusion in course of their formation. A formula, also due to Einstein, gives the possibility of another determination of N, which comes out as 65 x 102'2.

If we compare these various values with the latest and most accurate measurement by Millikan (1910) (see Perrin, p. 84), by the method of electric charge on gas ions, which gives 62 x 10— with an uncertainty of only 2 per cent., we must be struck by the very close agreement, and have no hesitation in admitting the truth of the view that Brownian movement is the same thing as the molecular movement of the kinetic theory. Perrin's latest results (1911, pp. 1-2), indeed, give values still closer to the number found by Millikan.

Experiments were also made by the second method with much larger particles in 27 per cent, solution of urea in order to keep them in suspension. These gave a value for N of 78 x 1022. Considering the small number of observations made, the agreement must be regarded as satisfactory. Since the foundation of Einstein's theorem is the assumption of equal partition of kinetic energy, and the experiments showed that particles differing in diameter 60,000 times gave the same value of N, they must be looked upon as the most weighty confirmation of the hypothesis of equal partition of kinetic energy.

It should be remembered that Ramsay (1891) advocated the view that Brownian movement is due to the impacts of molecules of the liquid against the particles, and that Ramsay and Senter (British Association Reports, 1901) concluded from the fact that the density of colloidal solutions of arsenious sulphide is the same, whether measured by the hydrometer or by weighing, that the particles of the colloid hit against the hydrometer to float it with the same energy as the molecules of the water do.

It is impossible to avoid some satisfaction that further evidence is given by Perrin's experiments, that we are not compelled to be content with equations derived from energetics, since the visible particles of these experiments behave precisely like the supposed molecules of the atomic theory. The chemist may also regard his structural formulae with more satisfaction of their approximate resemblance to actual fact. Incidentally, van't Hoff s theory of solutions receives confirmation.

In connection with the illustration of the kinetic theory afforded by the Brownian movements, as pointed out above, attention may be called to the fact that theories dealing with the movement of molecules, such as the kinetic theory of gases, are essentially statistical, that is, they are not concerned with the actual energy possessed by an individual molecule at a given instant of time, but with the average of a very large number. If the energy of a single molecule at a given moment of time could be measured, it might be found to be a very long way off from the mean.

This consideration is probably that which lies at the basis of the possibility, to which Donnan has called attention, that a living organism might appear to evade the second law of energetics. If we look upon an individual organism as a molecule in respect to the world of similar organisms, it does not seem, prima facie, altogether impossible that its activities might so far differ from the mean as to contravene the laws deduced from the general mass. But, in point of fact, we do not meet with deviations of this kind. We know, for example, that if we stimulate the vagus nerve, the heart will certainly stop, except some counteracting agency, such as atropine, is present, which we can lay our finyer upon and allow for, in due order.

Although the Brownian movement is the chief cause of the permanency of the colloidal state, there are some other conditions which play a part. The density of the medium in which the particles are suspended will clearly have an effect, the greater the density, the less the effective weight of the particles, hence the greater will be the buoyant effect of the bombardment on the part of the water molecules. The presence of an electric charge will also tend to prevent aggregation, on account of mutual repulsion. If by any means a number of the particles are given opposite charges to the remainder, aggregation will naturally be brought about by mutual attraction. This question will be discussed below. That the electric charge is not the sole cause of permanent suspension is shown by the fact that it can be reduced to zero, without affecting the stability, as in the experiment of Svedberg, given on page 84 above, where the Brownian movement was unaffected.

The opposing action of mechanical surface tension and electric charge has already been indicated. Lewis (1909, 3) shows how, with a given electrical charge, at a certain definite radius of the particle, the surface energy will be at a minimum, and therefore the stability at a maximum. It will be remembered that the surface tension is tangential and the electric force radial, so that it is only the radial component of the former which is opposing the electric force. This latter, however, acts inversely as the fourth power of the diameter, while the former acts inversely as the simple diameter.

The viscosity of the external phase should also be referred to. Increase of internal friction of the medium of suspension will increase the time taken for particles to fall under the action of gravity. Interesting evidence of the gradual transition from molecules to colloidal particles is afforded by the work of Svedberg (1909, 2) on the colour of gold hydrosols. With increasing dispersion, that is, more minute subdivision, the colour of the colloidal solution of gold approximates more and more to that of a gold salt in true solution, or the colour of the gold ion, supposing the anion to be colourless. The absorption in the spectrum shifts more and more towards the ultra-violet, where gold chloride possesses a characteristic absorption. Wohler and Spengel (1910) have shown also that coarsely colloidal platinum is of a more or less violet colour, which becomes more and more like the orange colour of platinum salts as the dispersion is increased. Wo. Ostwald (1911) shows that the maximum of absorption, as a general rule, gradually passes to the shorter wave lengths as the particles become smaller, so that the colour of the solution, that is, the colour of the light transmitted, changes from blue or green to red and yellow. For further details, the reader is referred to the interesting article by the last named author.

The relationship between the dimensions of the particles and the wave length of the light absorbed obviously suggests effects of resonance, or simple relationship between the rate of vibration of the particle and that of the light absorbed. This phenomenon of resonance enables a considerable amount of energy to be accumulated from a series of periodic impulses, each of a very minute energj", and deserves a little consideration. Suppose a pendulum with a rate of vibration of one second, reckoned as the time elapsing between the passage through any position, and the next passage in the »amf. direction. If we start with such a pendulum at rest, and give it a very slight push in the plane of its vibration, and repeat this at intervals of one second, it is possible to get up a considerable amplitude of vibration ; each impulse adds its effect to that of the previous ones. Unless the interval between the periodic impulses is a multiple of the time of vibration of the pendulum, only a very small amplitude, if any at all, will be obtained, since it will only occasionally happen that the impulse is delivered in the same direction in which the pendulum is moving ; all other impulses will retard the movement, energy from the pendulum being given back to the body producing the periodic impulses.

This resonance process plays a large part in decomposition by light and, if we remember the rates of vibration of light and of molecules, we realise the possibility of considerable energy changes in comparatively short times. The rate of vibration of the light of the D line of sodium is, in fact, about 5 x 1014 per second. Resonance .also comes into play in the production of powerful high frequency electrical discharges, as used in electro-therapeutics, and in the action of the auditory apparatus, according to the theory of Helmholtz.

An instructive model to illustrate the phenomena of resonance has been designed by Burch (1913, p. 490). The fact that contact surfaces between phases are usually the seat of differences of electrical potential has been referred to in the previous chapter. It is not surprising, therefore, to find that such charges play a large part in the properties of the colloidal state. The origin of these charges is clearly, in many cases, electrolytic dissociation. Imagine a particle of silicic acid in water. This particle consists of a very great number of molecules. Silicic acid must be supposed to be not wholly insoluble in water. The outer layer of molecules will, therefore, be dissociated. H- ions will travel off, in accordance with their great mobility, while the silicate anions, probably on account of their relative insolubility, remain as a layer on the outer surface of the particle. This particle will then have the negative charges corresponding to a large number of dissociated molecules and will behave as a multivalent anion. Similar considerations will apply to all acidic substances in the colloidal state. If basic, such as aluminium hydroxide, OH' ions will be given off, leaving a multivalent cation. Substances of the kind here described are called by Hardy (1910) "electrolytic colloids" and the huge aggregate, partially dissociated, a " pseudo-ion " or, preferably, a " colloidal ion."

When such a colloidal solution is examined by the ultra-microscope, the particles are found to be of various sizes, but, if exposed to the field between oppositely charged electrodes, they all move at the same rate. The differences of potential between them and the external water phase must therefore be the same for all. It follows that the charge must be directly proportional to their size. While a true ion, of the same chemical composition, always carries the same charge, these colloidal ions carry variable charges, although the chemical nature is unaltered. If the charge be due to surface dissociation, as described, it is natural that more ions should be produced on a large surface than on a smaller one.

An interesting class of colloids is that of certain salts, which do not pass through parchment paper, but yet, according to measurements of electrical conductivity, are electrolytically dissociated in solution, except in very concentrated ones, to very nearly the same degree as salts like sodium chloride are. Dyes with a large molecular weight, such as Congo-red, belong to this class. The precise nature of their solutions is not yet clear, since the osmotic pressure is less than would be expected from their conductivity (see my work on . Congored, etc., Bayliss, 1911). Salts of proteins with a strong acid or base, such as sodium caseinogenate, or globulin hydrochloride, belong to this class.

Now, Congo-red is a sodium salt and presumably, on dissociation, Na- ions will be formed. These ions can readily pass through parchment paper, as shown by the diffusion through it of sodium chloride. But, in the presence of the colloidal anion, they are held back. How1? The answer is, by electrostatic attraction. An ion cannot leave the immediate neighbourhood of an oppositely charged ion, unless much work is done in overcoming the attraction. For this reason, the H- ions in the case of silicic acid are held in close proximity to the oppositely charged particle, forming, in fact, one component of a Helmholtz double layer. Certain important phenomena due to colloidal salts bounded by membranes are due to the same fact, as will be seen in the following chapter.

Substances like Congo-red and salts of caseinogen may be called " electrolytically dissociated " colloids, to distinguish them from the electrolytic colloids of Hardy. At the same time it may turn out that the two are essentially the same, since the large colloidal ion may really consist of aggregates of ions in both cases, although in the former, these aggregates, if present, are too small to be resolved by the ultra-microscope ; the utmost that can be seen is a faint haze.