MOLECULAR FORCES AND THEIR ELECTRIC NATURE¹

B. V. Il’in.

The sphere of action of molecular forces is extraordinarily broad and embraces processes both of inanimate and of living (i.e., highly organized) nature.

It is necessary first of all to make some explanations concerning the term “molecular forces” itself. On the basis of a whole series of generally known works, the “molecule,” according to modern views, is not such an isolated, separate system as it was in the old physics.

We know, on the basis of purely experimental material (X-ray analysis), that a solid crystal of common salt consists not of NaCl molecules, but of charged atoms Na⁺ and Cl⁻ (Fig. 1). When it is a question of the forces that determine the hardness of a solid body and hinder its rupture, modern physics sees them not in the interactions of neutral molecules with one another, but in the attractions between the charged elements of the crystal lattice (atoms, electrons).²

Fig. 1.

We know that in solutions (on the basis of the phenomena of electrical conductivity) the ultimate basic elements are not molecules, but charged atoms (ions).³ Therefore, when we speak of “molecu-

¹ The present article is a brief excerpt from a book by the author, prepared for publication under the same title. In view of the fact that the range of phenomena in which the action of molecular forces is manifested is extraordinarily broad, we must of necessity narrow our theme and shall deal below with questions in one way or another connected with our own investigations in this field.

² See, for example, M. Born, The Structure of Matter. Moscow, 1922. M. Born, Atomtheorie des festen Zustandes. Berlin, 1923.

³ Works by Ghosh, Debye, Hückel, and others advance the view that molecules in solutions are dissociated not partially, as this should seem

molecular forces,” then it is more correct to understand by this term not “forces of interaction between molecules,” but forces acting in the space occupied by matter and having this matter as the source of their origin1).

It should, however, be said that in a whole series of cases (van der Waals forces, adsorption) molecules, as such, interact with one another, and then, from the electrical point of view, one may regard them as dipoles, quadrupoles, etc. In our investigations in molecular physics we are studying precisely molecular fields of the latter type, so that in this case we may also use the old content of the concept of “molecular forces,” as “forces of interaction between molecules.”

Over the last two decades molecular physics has traversed a long path rich in successes. One of the important moments of this path should be considered the establishment of a close connection, on the one hand, with the electronic theory, and on the other—with physical chemistry and with the science of colloids (colloidology).

The endeavor to reduce all the forces of nature to electrical ones found the liveliest response among scientists working on problems of molecular physics, and led to results that at first glance seemed incredible, but later proved to be correct. The electrification of the forces of nature provides a coherent theoretical basis for the edifice of those rich experimental successes of which we are witnesses.

These theoretical foundations make it possible gradually to introduce a strict systematic order into that very often raw, undeveloped material, far from theoretical clarity, which we have in the phenomena of molecular physics, physical chemistry, and especially colloidology2.

I.

Debye is responsible for a series of works on the electrification of the molecular field. I shall dwell on his interesting investigations into the electrical nature of the forces of cohesion in gases and the forces of surface tension of pure liquids1.

Let us suppose that a molecule consists of positive and negative charges situated at an unchanging distance from one another (a solid, rigid dipole, Fig. 2). Owing to the disordered thermal motion, the molecules are oriented uniformly in all directions;

Fig. 2.                Fig. 3.

therefore a rigid dipole in the field of other rigid dipoles experiences, on the average, no attraction whatever. The situation is quite different if we regard the molecule-dipole as a not quite rigid system. Then one molecule, in the electric field \(E\) of another, acquires an electric moment proportional to \(E\). An interaction arises between the two molecules, which is nothing other than van der Waals attraction. Debye shows that whatever the position of these interacting dipoles with respect to one another, they attract each other (Fig. 3). If the dipoles are in position I, then the principal interaction (if the dipoles were rigid) would be repulsive. But since the dipoles are not rigid, under the action of the field force \(E\) on the non-rigidly bound (mobile) charges in the dipoles, these charges are displaced in such a way that their mutual distance, and consequently the electric moments, decrease. This diminishes the repulsion; in other words, an additional attraction is superimposed on the principal action (repulsion). If the dipoles are in position II, then the principal action between them is attraction. The field force displaces the charges in the dipoles so that the electric moments increase. From this the attraction becomes still greater: upon the principal action (attraction) there is superimposed an additional—again—attraction. Every position of the dipoles can be reduced to the two considered, and therefore, when with a disordered distribution of dipoles in a gas the principal action disappears, the additional action, being always

unilateral (attraction) remains for all possible orientations of the dipoles. This additional attraction is the van der Waals cohesion. The potential energy of a molecule inside a gas consisting of such non-rigid dipoles is proportional to \(E^2\).

If \(\theta\) is the electric moment of inertia, then

\[ \theta = \eta \cdot s^2, \]

where \(\eta\) is the magnitude of each of the two charges of the dipole molecule, and \(s\) is a segment whose magnitude characterizes the mutual distances of the electric charges. Therefore the internal potential energy of the gas is equal to

\[ \frac{6\pi}{5}\,\frac{a\theta^2}{d^5}\cdot N^2, \]

where \(d\) is the diameter of the molecule, \(N\) is the number of molecules in 1 gram-molecule, and \(\alpha\) is the polarization coefficient.

The attraction constant “\(a\)” in the van der Waals equation

\[ \left(p+\frac{a}{v^2}\right)(v-b=RT) \]

also represents the internal potential energy of the gas. Therefore

\[ a=\frac{6\pi}{5}\,\frac{a\theta^2}{d^5}\cdot N^2. \]

Calculation on the basis of this formula for a whole series of gases gave Debye, for \(\theta\), quantities of the order of \(3\cdot 10^{-26}\) to \(60\cdot 10^{-26}\), i.e. quite acceptable values. It is interesting to point out here the polemic between Debye and Keesom, who indicates the greater probability of a quadrupole model for the molecule of certain gases than of a dipole one1.

Debye, in a simple and ingenious way, connects the theory of van der Waals cohesive forces just considered with the electrical theory of surface tension. If the attraction between molecules is determined by the polarization of a molecule (a non-rigid dipole) in the electric field \(E\) of other molecules, then the surface tension arising from the fact that at the surface of a liquid there is a surface layer of molecules, for which attracting liquid molecules are situated only on one side (the inner side), is determined by the course of the square of the electric force \(E^2\) in passing from the inner layers of the liquid

onto the surface. The total potential energy of a liquid possessing a free surface \(S\) is composed of two parts: the first—the volume potential energy, equal, as for a gas, to

\[ \frac{6\pi}{5}\,\frac{a\theta^{2}}{d^{5}}\cdot n^{2}\cdot V, \]

where \(V\) is the volume; the second part—the surface potential energy—is equal to

\[ \frac{3\pi}{8}\,\frac{a\theta^{2}}{d^{4}}\,n^{2}\cdot S. \]

The coefficient multiplying the surface area is the surface tension of the liquid, \(\sigma\). Thus

\[ \sigma=\frac{3\pi}{8}\,a\cdot\frac{\theta^{2}}{d^{4}}\cdot n^{2}. \]

From the relation

\[ \frac{\sigma}{a}=\frac{5}{16}\,d\left(\frac{n}{N}\right)^{2} \]

one can calculate \(\sigma\). The values of \(\sigma\) calculated for various liquids have the same trend as those observed experimentally, but prove to be somewhat smaller than the observed ones.

II.

As is clear from the preceding, a molecule in an electric field may be regarded as an electric polarization dipole possessing a definite electric moment \(\tau=d\cdot\eta\), where \(\eta\) is the magnitude of the positive and negative charges of which this dipole consists, and \(d\) is the distance between them1.

On the other hand, once the forces holding the atoms and molecules of a crystal in their definite positions and imparting to the crystal its

hardness, as Born showed, is of electrical origin, then in the space occupied by matter there is a field of electric forces, extending also into the space near the surface of the solid (and even liquid) body. Of course, this electric field diminishes in intensity with distance from the surface. The field strength of the electric field \(E\) is a decreasing function of the distance from the surface \(r\) (see Fig. 4).

Fig. 4.

Thus the surface of a body possesses an electrical surface energy, having the classical expression:

\[ u = S \int_{0}^{\infty} \frac{\varepsilon E^{2}}{8\pi}\,dr, \]

where \(u\) is the electric-field strength, \(\varepsilon\) is the dielectric constant of the surrounding gas, \(S\) is the magnitude of the surface.

It is clear that a dipole molecule, entering the electric field at the surface of a body, is oriented toward attraction and is attracted. This phenomenon is called gas adsorption, if the solid body (coal, mica, glass, etc.) attracts gas molecules.

If, however, a solid body (powdered coal, quartz, sand) attracts liquid molecules, then we are dealing with a new phenomenon—wetting of powders by a liquid; but in the nature of the acting forces the attraction is determined by the same electric field strength \(E\) at the surface of the solid body.

Finally, there is also possible such a case when we are dealing with a field of electric forces on the surface of a solution of a substance active with respect to surface tension. The introduction of negligible quantities, for example, of oleic acid into water sharply lowers the surface tension of water, bringing it down from the maximum value corresponding to the surface tension of pure water, \(73 \frac{\mathrm{erg}}{\mathrm{cm}^{2}}\), to the surface tension of oleic acid itself, \(27 \frac{\mathrm{erg}}{\mathrm{cm}^{2}}\). According to Gibbs, this phenomenon is explained by the densification of oleic acid on the surface of the solution (adsorption), and therefore it bears the name of Gibbs adsorption.

According to our conceptions, all these phenomena—gas adsorption, wetting, lowering of surface tension by active substances—

—thus are phenomena of the same order and are explained by the attraction of dipole molecules in the electric field of the surface1.

The study of the surface attraction field is also of special interest in comparison with the investigation of the internal attraction field, since, owing to the relative weakness of the surface field, the screening action of the first attracted (adsorbed) layer of molecules is not so sharply manifested; therefore, in adsorption phenomena we have a case convenient for studying the variation of the intensity of molecular forces with distance and, in general, the topography of the molecular field.

That adsorption (surface) bonds are small in comparison, for example, with chemical bonds (the internal attraction field) follows from a comparison of the heats of adsorption and the thermal effects of chemical reactions. These thermal effects are equivalent, respectively, to adsorption and “chemical” potentials, i.e., in the final analysis they determine the intensity of the corresponding attraction field. It is known that the thermal effects of chemical reactions reach hundreds of thousands of calories per gram-molecule, whereas heats of adsorption have an order of magnitude of only several thousand calories per gram-molecule.

For a strong attraction field, the first row of attracted molecules absorbs all the attraction bonds of the attracting surface, so that none of these bonds remains for the molecules standing behind it. The field of the attracting surface is screened by the first layer of attracted molecules. As a crude analogy one may imagine a negatively charged dielectric, to the surface of which positive ions are attracted. Then the first layer of attracted positive ions neutralizes the action of the negative field of the dielectric, and the ions standing behind it no longer experience attraction. The field of attraction by the negative surface of the dielectric is neutralized; the field is screened by the first layer.

If the field strength at the surface of the dielectric is small, then thermal motion disrupts the rows of the first layer of attracted ions, and some of them, acquiring considerable velocity, break the bond with the surface. Gaps are formed in the first layer, through which the freed lines of force of the dielectric surface seep through and capture ions standing behind the first layer. The weaker the field of the surface and the higher the temperature, the easier it is for thermal motion to disrupt the rows of the first layer and liberate—

...break the bonds for the ions standing behind. For this it is evidently necessary that

\[ u_0 < \frac{mv^2}{2}, \]

where \(u_0\) is the attraction potential, and \(\frac{mv^2}{2}\) is the kinetic energy of the “detaching” ion. It is clear that the weaker the attraction (in particular adsorption) field and the higher the temperature, the greater is the thickness of the layer \(r_0\) in which ions or molecules are found that still experience the action of the external surface field. For a strong attraction field and a low temperature, however, already the first layer of ions or molecules attracted by the surface takes upon itself all the bonds, and thus the thickness of the layer may be equal to the diameter of an ion or molecule (\(10^{-8}\) cm).

Fig. 5.

The explanation given here shows in what sense one should understand the assertion—paradoxical at first glance—that for a strong field the thickness of the layer \(r_0\) is smaller than \(r_0\) for a weak field. Moreover, it is clear that when we say: “the intensity of the strong field decreases with the distance \(r\) from the attracting surface more rapidly than the intensity of the weak field,” we have in mind the intensity of the “loaded” field, i.e., of the field in which attracted ions or molecules are already present.

For such a loaded field the curve of density decrease with distance in adsorption (curve II, Fig. 5) is less steep than, for example, in the cases of the internal attraction field considered by Born (curve I). Born, in studying the molecular field of solid crystals, may, on the basis of the considerations stated above, restrict himself only to the interaction of neighboring elements of the crystal lattice.

III.

The ideas presented above concerning the electrical nature of molecular forces make it possible to obtain, first of all, fundamental

equations of the attraction field of a surface for the case of gas adsorption and to extend their application also to all related phenomena. Such an extension of certain theoretical concepts, obtained for some one domain of phenomena, to another domain has, besides general theoretical value, also a very important significance, in that it makes it possible in this new domain of phenomena to use, for theoretical calculations, those quantities which in the first domain were experimentally indeterminate.

If the surface of a solid body in vacuum possesses the surface energy

\[ u_1=S\int_0^{r_0}\frac{E_0^2}{8\pi}\,dr, \]

then when the body is immersed in a gas with dielectric constant \(\varepsilon\) (upon adsorption), the surface energy will decrease and acquire the new value

\[ u_2=S\int_0^{r_0}\frac{\varepsilon E^2}{8\pi}\,dr. \]

The loss in potential surface energy of the body when it is immersed in a gas, \(u_1-u_2\), occurs because the gas is attracted. During adsorption, work is expended by internal forces, which must be compensated in the reverse process—the liberation of the surface from the gas. Then it would already be necessary to expend the work of external forces, the work of detaching molecules from the surface of the adsorbent. This work is analogous to the latent heat of sublimation or evaporation. Just as in the condensation of vapor the heat of evaporation is released, equivalent to the work of attractive forces, so also in the adsorption of a gas the heat of adsorption is released, equivalent to the work of adsorption forces.

To avoid misunderstandings, it should be noted that the solid body/gas system before adsorption of the gas has a greater potential energy than after adsorption, so that the work performed by the forces of attraction in drawing molecules in during adsorption gives not a plus for the energy of the adsorbent/gas system, but a minus, since this work is performed not by forces external with respect to this system, but by its own internal forces. By the law of conservation of energy, this minus, this loss of energy caused by the work of the internal forces of the system itself, must be compensated by the appearance of energy outside. This compensation is precisely the heat released during adsorption.

Therefore we may write:

\[ Q=u_1-u_2 \]

or

\[ Q=fr, \]

where \(f\) is the force acting on one gram-molecule of gas, and \(r\) is the path over which the force \(f\) does work during adsorption1.

Let us expand the first relation.

\[ Q=u_1-u_2 =S\int_0^{r_0}\frac{E_0^2}{8\pi}\,dr -S\int_0^{r_0}\frac{\varepsilon E^2}{8\pi}\,dr = \]

\[ =S\int_0^{r_0}\frac{E_0^2}{8\pi}\,dr -S\int_0^{r_0}\frac{E_0^2}{\varepsilon\cdot 8\pi}\,dr =S\int_0^{r_0}\frac{E_0^2}{8\pi}\left(1-\frac1\varepsilon\right)\,dr. \]

It can be shown, by transforming the integrand, that if \(Q\) is the heat of adsorption of one gram-molecule of gas, then

\[ Q=\frac{E_0^2}{8\pi}\frac{\varepsilon_0-1}{\varepsilon\cdot N_0}, \]

where \(N_0\) is the number of gram-molecules of gas in \(1\ \mathrm{cm}^3\) at \(0^\circ\mathrm{C}\) and \(76\ \mathrm{cm}\) Hg, \(\varepsilon_0\) is the value of the dielectric constant of the gas at \(0^\circ\mathrm{C}\) and \(76\ \mathrm{cm}\) Hg, and \(\varepsilon\) is the value of the dielectric constant in the adsorption layer. Obviously, we must arrive at the same result if we start from the second relation. Nevertheless, we present this calculation, since it gives some new concrete conceptions.

The heat of adsorption \(Q\) is obtained experimentally in such a way that the quantity of heat in calories, obtained during adsorption, is divided by the number of gram-molecules of gas adsorbed upon the liberation of this heat. Therefore the empirically given \(Q\) is the mean of a consecutive series of heats liberated during the absorption of successive portions of gas:

\[ Q=\frac{S\displaystyle\int_0^{r_0} f n\,dr}{S\displaystyle\int_0^{r_0} n\,dr} =\frac12 f r_0, \]

where \(r_0\) is the thickness of the layer, and \(n\) is the concentration in the layer at distance \(r\).

It remains now only to calculate the force \(f\). If the molecule of the adsorbed gas, in a first approximation, is an electric dipole with moment \(\tau=d\cdot \eta'\), then the force acting on this molecule is

\[ F=\frac{e_1\eta'}{r^\nu} -\frac{e_1\eta'}{(r+d)^\nu} =\frac{e_1\nu\tau}{r^{\nu+1}}, \]

where

\[ \frac{c_1}{r^\nu}=E_0 \]

is the intensity of the electric field of the adsorbent in a vacuum,

\(r\) is the distance of the molecule from the surface of the adsorbent.

Since \(F\) is the force acting on one molecule, \(f\), the force acting on a gram-molecule, will be:

\[ f=F\cdot N_A=\frac{c_1 \nu \tau}{r^{\nu+1}}\cdot N_A, \]

where \(N_A\) is Avogadro’s number.

It remains to calculate the magnitude of the electric moment \(\tau=d\cdot \eta'\).

If the field intensity between the plates of a condenser in a vacuum is equal to \(E_0\), then, by introducing gases between them, we cause the dipole molecules to arrange themselves in the direction of the field, but in such a way that their positive ends are turned toward the negatively charged plate of the condenser, and their negative ends—conversely. Such an arrangement of the molecules diminishes the free charges on the plates, and therefore the electric-field intensity in the condenser with the gas, \(E\), is smaller and is equal to

\[ E=E_0-4\pi\sigma', \]

where \(\sigma'=N_L d\eta'=N_L\cdot \tau\), and \(N_L\) is Loschmidt’s number.

On the other hand,

\[ E=\frac{E_0}{\varepsilon}. \]

Hence

\[ \tau=\frac{E_0}{4\pi N_L}\cdot \frac{\varepsilon_0-1}{\varepsilon}. \]

Substituting this value of \(\tau\) into the expression for the force \(f\), we obtain

\[ f=\frac{\nu}{\varepsilon\cdot r_0}\frac{E_0^2}{4\pi}(\varepsilon_0-1)N_0. \]

And consequently

\[ Q=\frac{1}{2}fr_0=\nu\frac{E_0^2}{8\pi}\frac{\varepsilon_0-1}{\varepsilon\cdot N_0}; \]

that is, the former expression for \(Q\), but only with the multiplier \(\nu\).

The equation given above,

\[ Q=\frac{E_0^2}{8\pi}\frac{\varepsilon_0-1}{\varepsilon\cdot N_0}, \]

may be called the first fundamental equation of adsorption.

Using it, one can calculate the magnitude of the electric moment of the adsorbed molecule,

\[ \tau=\frac{E_0}{4\pi N_L}\frac{\varepsilon_0-1}{\varepsilon}, \]

since \(E_0\) is determined from the first fundamental equation of adsorption by the heat of adsorption \(Q\). The table below shows that the values I obtained for \(\tau=d\cdot\eta'\) from adsorption agree with the values for \(\tau\) obtained by various authors from other data. From this agreement it is clear that, if the view of a molecule as a system of positive and negative charges, polarized into an electric dipole in a molecular field, is perhaps only a rough approximation, nevertheless such a “rough” approximation makes it possible to connect the phenomena listed here with one another, since also quantitatively the magnitude of the electric moment \(\tau\) in all cases proves to be of the same order and, moreover, quite physically admissible \((d<10^{-8}\ \text{cm})\).

TABLE.

Electric moment \(\tau\) and \(d=\dfrac{\tau}{\eta}\) from various data.

The second fundamental equation of adsorption gives an expression for the quantity of adsorbed gas (for the adsorption capacity).

The gas above the adsorbing surface is distributed like the air of the earth’s atmosphere above the earth’s surface. As is known, the density of air is greatest at the surface of the earth and gradually decreases with distance from the surface. In exactly the same way, the adsorbed gas is strongly condensed at the adsorbing surface, concentrating in a thin layer of molecular dimensions. The quantity of adsorbed gas (the adsorption capacity) \(A\) is therefore expressed as

\[ A=S\int_{0}^{r_0}(n-n_0)\,dr, \]

where \(S\) is the magnitude of the adsorbing surface, \(r_0\) is the thickness of the adsorption film, and \(n\) is the gas density, decreasing with distance from the surface. Hence one may obtain, for low temperatures,

\[ A = S r_0 n_0 e^{\frac{Q}{RT}} \]

and for high temperatures

\[ A = S r_0 n_0 \frac{RT}{Q+RT}\left(e^{\frac{Q+RT}{RT}}-1\right), \]

i.e. the second fundamental equation of adsorption. It makes it possible to determine the thickness of the adsorption layer \(r_0\), which turns out to be of the order of \(10^{-8}\) to \(10^{-7}\) cm. Together with the first fundamental equation of adsorption, it also makes it possible to find the value of the surface energy (surface tension) of a solid body in vacuo.

Indeed, the density of the surface energy of a solid body in vacuo is

\[ \frac{u_0}{S}=\frac{E_0^2}{8\pi}\cdot r_0 \]

therefore, for low temperatures,

\[ \frac{u_0}{S}=\frac{A}{S}\frac{Q\cdot N_0}{\varepsilon_0-1}\frac{1}{n_0}e^{-\frac{Q}{RT}}. \]

This formula gives, for \(\frac{u_0}{S}\) of coal, a value of the order of \(1000\ \frac{\mathrm{erg}}{\mathrm{cm}^2}\), and for mica,

\[ \frac{u_0}{S}\sim 700\ \frac{\mathrm{erg}}{\mathrm{cm}^2}. \]

IV.

We have shown that the heat of adsorption \(Q\) is equivalent to the difference of the surface energies of the adsorbent in vacuo and in the gas,

\[ Q=u_1-u_2. \]

Since the energy of the surface of a solid body or liquid is defined by the surface tension, then, in a first approximation,

\[ \frac{u_1-u_2}{S} \]

may be replaced by the difference of the surface tensions \(\sigma_1-\sigma_2\), where \(\sigma_1\) is the surface tension for the surface layer without the adsorbed substance, and \(\sigma_2\) is the surface tension with the adsorbed substance.

Since gas adsorption is analogous to Gibbs adsorption, i.e. to the concentration of an active substance on the surface of solutions, of active

in the sense of surface tension, then it is quite natural and legitimate both to transfer the laws of gas adsorption to the phenomena of the Gibbs effect and, conversely, to apply the Gibbs equation, the fundamental relation for surface-active solutions, to gas adsorption.

Gibbs showed thermodynamically that the decrease in the surface tension of an active solution is due to the transition of the active substance to the surface, and derived the following relation, connecting the decrease of surface tension, \(-\dfrac{\partial \sigma}{\partial c}\), with the surface density of the dissolved active substance:

\[ -\frac{\partial \sigma}{\partial c}=\frac{1}{c}RT\Gamma. \]

On the other hand, if, following Langmuir, one takes his adsorption-isotherm equation, i.e. the relation connecting the amount of adsorbed substance \(\Gamma\) with the pressure or concentration \(c\),

\[ \Gamma=\frac{\Gamma_{\infty}\cdot c}{c+a}, \]

substitutes it into the Gibbs equation and integrates the latter, then one obtains no longer a differential but a finite relation between \(\sigma\) and \(c\).

\[ \sigma(0)-\sigma(c)=b\log_{10}(ac+1). \]

This relation shows how the surface tension of the solution changes with increasing concentration of the dissolved active substance.

It is remarkable that this equation was found purely empirically by Shishkovsky; it bears his name.

Of the three equations (Gibbs, Langmuir, and Shishkovsky), only two are independent; the third is a consequence of the first two. If so, then the constants of the Shishkovsky equation \(b\) and \(a\) can be expressed through the constants of the Gibbs and Langmuir equations.

Indeed, differentiating the Shishkovsky equation,

\[ -\frac{\partial \sigma}{\partial c}=\frac{b\cdot a\cdot 0.434}{ac+1} \]

and substituting in place of \(-\dfrac{\partial \sigma}{\partial c}\), from the Gibbs equation, \(\dfrac{1}{c}RT\Gamma\), we obtain

\[ \Gamma=\frac{0.434\,\dfrac{b}{RT}\cdot c}{c+\dfrac{1}{a}}, \]

i.e. the equation of the Langmuir isotherm. Comparing the constants of this equation with the constants of the previously written equation of the Langmuir isotherm, we obtain

\[ \Gamma_{\infty}=0.434\,\frac{b}{RT}\quad \text{and}\quad a=\frac{1}{a'}. \]

The latter relations were also used by Langmuir to calculate the quantity of adsorbed molecules \(\Gamma_{\infty}\) of fatty acids in the phenomena of lowering of the surface tension of aqueous solutions of these acids, since in this case it was possible to determine \(b\) from the experimental course of the change of \(\sigma\) with concentration \(c\), and it was not possible to find \(\Gamma\) experimentally.

Langmuir thus obtained the interesting result that the acids of the fatty series, when dissolved in water, at the limiting concentration of the solution are arranged on the surface of the solution in a thin layer, and, if it is assumed that the concentration of the fatty acid in the surface layer is equal to the density of the pure fatty acid, then the layer thickness calculated on this assumption turns out to be monomolecular \((10^{-8}\ \text{cm})\).

I have expressed the proposition \(^{1}\) that on the basis of the Gibbs equation it is possible to connect with one another the phenomena of adsorption and surface tension at the interface of any contacting phases: gas and solid body (gaseous adsorption), gas and solution (surface tension of active solutions, surface tension at the boundary between mercury and vapors of benzene, alcohol), solid body and solution.

It was clarified, moreover, \(^{2}\) the conditions necessary and sufficient for a given substance to possess activity, i.e. to be distributed nonuniformly (according to the Gibbs equation) between the surface and the bulk. A necessary condition for a dissolved substance to strongly change the surface tension is a considerable difference between the surface tension of this substance and the surface tension of the solvent, and hence also a correspondingly large difference in dielectric constants. This is a necessary condition, but not a sufficient one.

The second condition: the dissolved substance must have a surface tension smaller than the surface tension of the solvent, since only under this condition, for example, do molecules of butyric acid, even at small concentrations, pass in excess to the surface and

\(^{1}\) B. Il’in. Adsorption u. Oberflächenenergie an der Trennungsgrenze verschiedener Phasen. Phys. ZS. 26, 497 (1925).

\(^{2}\) Б. Ильин. Неспецифичность адсорбции. Журнал Прикладн. Физики, 2, issue 3—4, p. 251 (1925).

thereby reducing the surface tension of the solution. The experimental material obtained by my collaborator P. A. Rebinder1 fully confirms these considerations.

The generalization I have proposed—the extension of the equations of Gibbs, Langmuir, and Shishkovsky to all cases of surface phenomena at the interface of any contacting phases—leads to rather substantial and interesting results in the particular case of gas adsorption.

If to Langmuir’s works one adds Iredale’s investigations, which showed that the equations of Gibbs and Shishkovsky quite satisfactorily express the lowering of surface tension at the mercury–vapor interface, then it becomes clear that these equations are equally well applicable to the lowering of surface tension both at the solution–gas interface and at the liquid–vapor interface; i.e., it is entirely immaterial whence the active substance enters the boundary layer—from the liquid phase (for the solution–gas case) or from the gaseous phase (for the liquid–vapor case). This result makes quite natural and inevitable the further extension, which I give, of the application of the Gibbs and Shishkovsky equations to the phenomena of change of surface tension at the solid–gas interface during gas adsorption.

As has already been shown, in this case the difference between the surface tensions of the adsorbent in vacuum and in a gas at pressure \(c\) is

\[ \sigma(0)-\sigma(c)=\frac{Q}{S_1}, \]

where \(Q\) is the heat of adsorption on \(1\) g of charcoal having surface \(S_1\). And consequently

\[ \frac{Q}{S}= b \log_{10}(ac+1). \]

The Figs. 6 and 7 given here, in which the solid lines are theoretical curves and the points are experimental points, show good agreement with experiment for the adsorption of gases and vapors.

Moreover, the constants of the equation \(b\) and \(a\) may be compared, on the basis of the data of the above relations, with \(\Gamma_\infty\) and \(\alpha\) obtained from adsorption isotherms. This comparison confirms the theory. In contrast to the case analyzed by Langmuir, here both \(b\) and \(a\), and \(\Gamma_\infty\) and \(\alpha\), can be calculated independently of one another, and the agreement of these data is the best proof of the validity of the generalizations we have made. I shall allow myself to make one more remark. The tension of the molecular field \(E\) and the surface energy

\[ \frac{u}{S}=\frac{E^2}{8\pi}r_0, \]

in our opinion, determines the hardness of the crystal, and therefore a considerable decrease of \(\frac{u}{S}\) upon adsorption of a gas must cause a corresponding lowering of the hardness.

V.

The data presented above on the common character of all cases of the distribution of a substance between the surface and the bulk at the interface of any two contacting phases, and especially the last result concerning the possibility of applying the equation of Shishkovsky to the determination of the dependence of the heat of adsorption of a gas on its pressure, inevitably suggest the hypothesis of the common nature of the forces acting in these phenomena.

Fig. 6.

Fig. 7.

Since a whole series of the results cited above convinces us of the electrical origin of the forces of gas adsorption, it must be thought that the forces acting in the phenomena of the surface tension of solutions (Gibbs adsorption) and in the phenomena of wetting are of the same nature.

In the adsorption of a gas by the surface of a solid body, in the space above the adsorbing surface there is a field of electric forces, under the action of which the gas molecules (electric dipoles) are attracted to the surface of the solid body.

But how is one to explain that, in solutions of an active substance, the molecules of the dissolved substance pass from the solution to the surface, displacing from there molecules of the solvent and overcoming the forces of surf—

…of the (internal) pressure, which, on the contrary, tend to remove them from the surface, to draw them into the solution? I give here the explanation I have proposed1. Let us consider a particular case—the solution of one of the fatty acids in water. A molecule of a fatty acid possesses a smaller electric moment $\tau_2$ than a water molecule with electric moment $\tau_1$, since the dielectric constant of fatty acids (about 3) is less than the dielectric constant of water (81).

It should be noted that here we are speaking of the electric moment $\tau = d \cdot \eta$, whereas the geometrical dimensions of a fatty-acid molecule, which has the form of a chain, may be greater than the geometrical dimensions of a water molecule (see Fig. 8).

Fig. 8.

Water molecules situated beneath the surface layer draw into the solution the molecules of water and of fatty acid that are on the surface (this is the surface normal pressure). This attraction for a water molecule is equal to $A \cdot \tau_1$, and for a molecule of fatty acid to $A \cdot \tau_2$, where $A$ is a coefficient of proportionality; $A\tau_1 > A\tau_2$, since $\tau_1 > \tau_2$.

Consequently, water molecules are drawn into the solution with a greater force than molecules of fatty acid, and therefore an excess of fatty-acid molecules remains on the surface of the solution; on the surface of the solution there is obtained an excess, a condensation of fatty acid—Gibbs adsorption, if by adsorption one conditionally means any condensation, even that caused by a competition of forces, as here. Turning to the phenomena of wetting, I shall point to the work of my collaborator V. V. Tarasov2, who applied the ideas developed above concerning the electric nature of adsorption forces to the wetting of powders.

He obtains the following rule of wetting:

\[ \frac{Q'}{Q''}=\frac{\varepsilon''\varepsilon'-1}{\varepsilon'\varepsilon''-1}, \]

where $Q'$ and $Q''$ are the heats of wetting of one and the same powder by two different liquids with dielectric constants $\varepsilon'$ and $\varepsilon''$.

Experiment indeed confirms the existence of a parallelism between the quantities $Q$ and $\varepsilon$.

VI.

The electrical theory of the molecular field developed here has the advantage that it often makes it possible to carry theoretical calculations through to the end, and to calculate all the necessary constants, when without electrical conceptions this cannot be done.

It turns out, for example, that by means of such calculations the surface energy of carbon is obtained as a quantity equal to \(1000 \frac{\mathrm{erg}}{\mathrm{cm}^{2}}\). If this result is connected with the experimentally determined quantity of gas absorbed by carbon, then one can calculate the magnitude of the surface possessed by the carbon we have taken, and to which the absorbed gas adheres and is adsorbed.

Such a calculation gives, for \(1\ \mathrm{g}\) of carbon, a surface of \(10\ \mathrm{m}^{2}\). Only this enormous surface accounts for the great absorptive capacity of carbon. \(1\ \mathrm{g}\) of solid glass, for example, absorbs ten million times less gas. But if one calculates the amount of absorbed gas falling on \(1\ \mathrm{cm}^{2}\) of carbon and of glass, the resulting quantities differ little from one another. This unexpected result, which is a consequence of the electrical theory of molecular forces, compels us radically to revise the tables of the distribution of various bodies according to their ability to absorb gases. A fact of great technical significance, it should in any case be taken into account in posing and solving the question of the “best universal absorbent” and of methods for preparing such an absorbent, which, as is known, play a major role in gas warfare and defense.1

The chemical treatment of carbon, the activation of carbon, since it increases in the same way the absorption (adsorption) of all gases, reduces to a change in the porosity of the carbon and also, of course, in known cases to a change in the magnitude of its surface force of attraction. An increase in the surface (porosity) of the absorbent can also be achieved by simple grinding (for example, in a colloid mill). Since chemical treatment and grinding can also be applied to other bodies (sand, glass, etc.), the question may be raised of replacing, for example, carbon in gas masks by other materials that are cheaper or more convenient in their properties—an issue of technical significance in the practice of gas work.

One cannot fail to dwell on another factor determining the absorbing capacity of one or another gas absorbent. This is the magnitude of the molecular attraction at the surface of the absorbent—

under the action of which gas molecules are attracted and held inside the absorbent on the surfaces of its pores.

Our investigations of this question, as is clear from the foregoing, have shown that these forces of attraction are electrical, and that they are closely connected with the dielectric constant of the absorbed (adsorbed) gas.

We established a quantitative law according to which the amount of gas absorbed is the greater, the greater is its dielectric constant. The experimental data fully confirmed this law, which, it goes without saying, is also of purely practical significance, since it makes it possible to seek strongly absorbed gases not blindly, at random, but among gases with a large dielectric constant.

Closely adjoining these questions developed by us are such technically important problems as the strengthening of materials. As is known, the treatment of metals and other materials, both chemical and physicochemical (change in the carbon content in iron in the formation of cast iron, steel, hardening, tempering of metals, forging), greatly changes the technical properties of materials: hardness, elasticity, plasticity, brittleness, electrical resistance, and surface properties.

Clarifying the nature of the forces that determine these properties of technical materials is of primary practical importance for production technology, since it makes it possible artificially, at will, to influence the change of these properties in the desired direction. If it were possible, for example, to impart to wood the hardness and strength of steel, this would undoubtedly bring about a major revolution in technology.

On the basis of electrical conceptions of the crystalline structure of a solid body, solid bodies—for example, rock salt—consist of positive and negative ions arranged in chessboard order. The forces of attraction between these ions determine the hardness of the solid body, its resistance to rupture. If we know the charges carried by the ions and the distance between them in the solid body (these data are supplied by experiment), then we can calculate the resistance to rupture1. Such a calculation gives, for rock salt, a value of approximately \(300\ \frac{\mathrm{kg}}{\mathrm{mm}^{2}}\). In reality, a crystal of common salt breaks under a load approximately 500 times smaller.

This result brought to the fore the question of increasing strength, of strengthening solid bodies, and a series of experimental investigations in this field has appeared (the works of Academician Ioffe and his collaborators, the German scientist Polanyi, and others), wh—

Molecular Forces and Their Electrical Nature

which tend to remove the obstacles that prevent the attraction between ions from manifesting itself in full measure1.

It is obvious that the very formulation of this problem of strength became possible only with a theoretical calculation of the magnitude of strength from the standpoint of electrical conceptions.

The magnitude of surface molecular attraction thus connects these phenomena of strength with other related phenomena (temperature radiation, photoeffect)2.

But the action of molecular forces is not limited to the phenomena considered above. It is extremely varied. Changes of states of aggregation, processes of condensation (liquefaction), surface tension, capillarity and wetting, processes of ignition of powders3, absorption and distribution4 of gases, liquids, and solutions, sensitization in photography5, electrical conductivity6, viscosity, swelling, allotropy, precipitation (coagulation) of suspensions, emulsions, and colloidal solutions—this is the broad group of processes in which the action of molecular forces is manifested. The electrification of these forces, i.e., in other words, the reduction of them to electrical attractions, makes it possible to render the problem of calculating the magnitudes of the interactions entirely definite; to carry this calculation through to the end, so that in the final answer there are no indefinite, unknown constants.

The field of problems covered by the investigations of myself and my collaborators consists precisely in the systematic and consistent carrying out of the electrical interpretation of all the above-mentioned processes and in the experimental verification of the laws thus obtained.

In addition to those already indicated, one may cite a large number of technically important applications in this field. It is beyond doubt, for example, that in the gas industry the stability of a gas cloud, its mobility, the influence upon it of atmospheric factors, and much else are by no means determined solely by its chemical composition, but depend to a considerable degree on its physical properties, which are ultimately conditioned

play of electric forces and, first of all, connected with the formation of ions, which are centers of condensation1.

Finally, our attention is drawn to a quite special new field of phenomena: “the physics and chemistry of colloids.” This field, which not so long ago was merely a small chapter of physical chemistry, has now developed into a broad, promising new branch of knowledge, which almost every day brings new, often unexpected results in the most diverse directions. A colloidal solution differs from a true solution in that the suspended particles in it may be of the most varied sizes, beginning with molecules (this corresponds to a true solution) and approaching particles visible under the microscope (in the so-called emulsions—for example milk, or suspensions—for example smoke).

At first glance it seems incomprehensible why such large particles, colliding with one another, do not stick together into large clumps and do not fall to the bottom as a precipitate.

It turns out that here, too, the explanation should be sought in the action of molecular forces at the surface; moreover, in many cases these particles prove to be electrically charged, carrying an electric charge. The fact that this electric charge is of one sign (for example, positive) is the reason why these particles do not stick together. Here the simple electrical repulsion of like charges is at work.

In other cases the matter is not so simple, but here too the explanation can be reduced to the surface molecular field.

Colloids interested me and my co-workers from this point of view as well. On the basis of what has been said above, if some substance is added to a colloidal solution or emulsion which is attracted (adsorbed) to the surface of our particle, then the magnitude of the molecular forces on the surface of the particles will immediately change. This change, generally speaking, may be in two directions: the attraction between the particles either increases or decreases.

In the first case the particles stick together, form flakes, and fall out as a precipitate. In the second case, on the contrary, the colloidal solution or emulsion becomes unusually stable. The technical significance of this is obvious, for example, for the preparation of homogenized products. An emulsion, upon the addition of a negligible quantity of such a stabilizing agent, becomes almost completely non-coagulating. It should be emphasized that this capacity for non-coagulation is acquired with comparatively small doses of the stabilizing agent.

From our point of view, this is as it should be, if one recalls what was said above: that all adsorption is confined to an exceedingly thin layer of active substance on the surface (only on the surface), and for this substance, by volume, very little is needed.

The opposite effect—the action of an active agent in the sense of precipitating suspended particles of a solution or suspension—is technically important for the processes of purifying water in water-supply systems, etc.

In this case the phenomena of precipitation, the removal of harmful undesirable impurities, can be explained very simply. If the particles of a solution or suspension are charged with electricity of one sign, then the force preventing their sticking together is the mutual repulsion of their electric charges, for example, positive ones. If you add an electrolyte solution, then ions of the opposite sign (negative) are attracted to the particles and neutralize their charges (negative charges destroy the action of positive ones). As a result, the particles of the solution or suspension are deprived of their charge, and the force preventing their sticking together disappears. Flocs are formed, and the harmful undesirable impurities settle out.

I have dwelt only on some technical applications of this highly promising science of colloids. Colloids play a major role in a whole series of technical industries,^1 in the phenomena of catalysis,^2 and in the artificial fabrication of a number of technical materials.

In conclusion, one cannot fail to dwell on one more extremely important question connected with the phenomena of adsorption and the doctrine of colloids. The tissue of a living organism possesses a colloidal structure. And all those processes that proceed in living tissue, both normal and pathological, are governed by the same laws of which we have spoken here. It is clear that knowledge of these laws will make it possible to explain many enigmatic phenomena in the living organism, to predict the course of vital processes and, at will, to delay them or give them another direction (treatment of diseases).

So vast and so promising, in both the purely scientific and the applied respects, is the field of phenomena of molecular physics.

^1 It should be noted the work of our compatriot M. A. Il’inskii, “On the Adsorption of Solid Bodies by Solids,” which is very important for dyeing technology (it turns out that in many cases dense suspensions of dyes give a much greater and more durable coloration than weak ones, and not the reverse, as was formerly thought).

^2 It is possible that in a whole series of cases catalysis is conditioned by adsorption on the surface of the catalyst and by the accompanying rise in temperature, which at the first moment of adsorption may be very considerable. As the works of Prof. N. D. Zelinskii and Prof. N. A. Shilov show, the attraction field of adsorption may be capable of causing a loosening and even a rupture of molecular bonds—dissociation. An attempt at a theoretical and quantitative determination of the magnitude of this effect is the work of my collaborators B. F. Rozanov and N. A. Shishakov on calculating the association constant from the adsorption isotherm.

1. See the monograph by Gibbs, Clouds and Smokes. B. Ilyin, “On the causes of ionization oscillations in the lower layers of the atmosphere and the strength of radio reception,” Telegraphy and Telephony without Wires, No. 21, 1923. ↩↩↩↩↩↩↩↩↩↩↩↩

2. For example, the works of Langmuir. ↩↩↩

3. For example, the data obtained by me on the magnitude of surface energy and the magnitude of the adsorbing surface were used in the work of L. Wöhler u. M. Rabinowitsch, Kalorimetrische Oberflächenbestimmung verglimmender Oxyde. Kolloid-Zt. 38, 111 (1926). ↩

4. The relations derived by me gave good agreement with experiment in the work on distribution between two solvents by C. A. Voznesensky. Zt. phys. Ch. 104, 46 (1923). ↩

5. P. V. Shmakov, at my suggestion, applied adsorption conceptions to the phenomena of sensitization. Journal of Applied Physics, 1, issues 1–4 (1924). ↩

6. See, for example, the works of my collaborator S. V. Gorbachev. Proceedings of the Main Chemical-Pharmaceutical Institute, issue 12, published by the Scientific-Technical Department of the Supreme Council of National Economy, No. 105 (1925). ↩