SURFACE CHEMISTRY *

Irving Langmuir, Schenectady, USA

The phenomenon of adsorption has long been known and has attracted the attention of investigators.

Thus, James Dewar found that charcoal cooled in liquid air is capable of absorbing very large quantities of such gases as oxygen and nitrogen. It was known that this is a surface phenomenon, dependent on the extremely high degree of subdivision of the charcoal. The fact that soap lowers the surface tension of water depends on the presence of a higher concentration of soap molecules in the surface layer than in the solution.

Willard Gibbs proved thermodynamically that there is a general relation between surface adsorption, the lowering of surface tension, and the concentration of the solution. The equation he derived may be written in the form:

\[ \frac{dF}{d(\ln p)}=\sigma kT, \tag{1} \]

where \(p\) is the partial pressure of the vapor of the adsorbed substance in equilibrium with the surface of the liquid, or the partial osmotic pressure of the substance dissolved in the liquid; \(\sigma\) is the number of molecules adsorbed on the surface per unit area; \(T\) is the absolute temperature; \(k\) is the Boltzmann constant, \(1.37\cdot 10^{-16}\) erg degree\(^{-1}\); and \(F\) is a quantity that may be called the force causing spreading, and is given by the equation:

\[ F=\gamma_0-\gamma, \tag{2} \]

where \(\gamma_0\) is the surface tension of the pure solvent (in dyn/cm), and \(\gamma\) is the surface tension of the solution.

The form of the Gibbs equation given by equation (1), thermodynami-

* This article is an address delivered on the occasion of receiving the Nobel Prize in Stockholm, December 14, 1932. In it Langmuir summarizes the results of his investigations and his present views in this field, mentioning only incidentally the work of other authors. Published in Chemical Reviews, 13, 147, 1933.

theoretically valid under the condition that the film is in equilibrium with two bulk phases and that the ideal-gas law

\[ p = nkT \tag{3} \]

is applicable to the bulk phases.

Up to 1910 many different theories of adsorption had been proposed, but none of them could be regarded as particularly successful. Most of these theories considered the increase in the concentration of the adsorbed substance near the surface as a phenomenon analogous to the retention of the earth’s atmosphere by the gravitational attraction of the earth. Thus the adsorbed gas was regarded as something like an atmosphere in miniature, extending a short distance from the solid substance. In general, these theories were capable of explaining only the qualitative aspect of gas adsorption on solids. Most of the available information about adsorption was empirical in character. Even the Gibbs law had not been experimentally verified.

When in 1909 I began work in an industrial research laboratory,¹˒² I found that the high-vacuum technique developed in the manufacture of incandescent lamps, especially after the introduction of the lamp with a tungsten filament, was considerably ahead of the technique used in university laboratories. This new technique opened broad possibilities for the investigation of chemical reactions on surfaces, as well as of the physical properties of surfaces, under strictly defined conditions. I decided to investigate the effect produced by introducing very small quantities of various gases into a lamp with a tungsten filament, evacuated to a high vacuum. A McLeod manometer, making it possible to measure pressures down to \(10^{-8}\) atm, permits one to observe the disappearance of a quantity of gas smaller than \(0.1\ \mathrm{mm}^3\), measured at atmospheric pressure. The use of a tungsten filament has the advantage that the latter can be heated in a high vacuum to temperatures above \(3000^\circ\ \mathrm{K}\), so that any impurities can be removed from it by evaporation. Very important advantages are also the ease and accuracy with which any desired temperature can be attained and measured.

When a heated body, such as a filament, comes into contact with a gas at atmospheric pressure in a glass lamp, the explanation of the observed phenomena of interaction between the filament and the gas is greatly complicated by convection currents and by the uncertain distribution of temperature in the gas.

Meanwhile, if the gas is under a pressure of 100 bars,* the mean free path of the molecules is many times greater than the diameter of an ordinary tungsten filament. Thus each mole-

* The bar, or unit of pressure in the CGS system, \(1\ \mathrm{dyne}/\mathrm{cm}^{2}\), is almost exactly equal to \(10^{-6}\) atm.

where, after striking the filament, since the moment of its last collision it has undergone so many collisions with other molecules that the effective temperature of the gas in contact with the filament may be taken as equal to the temperature of the bulb. Thus the disturbing influence of convection currents is completely eliminated, and the rate at which the gas molecules reach the surface of the filament can be calculated according to the laws of the kinetic theory of gases.

This theory leads to the equation:

\[ \mu=\frac{p}{(2\pi m k T)^{1/2}}, \tag{4} \]

where \(\mu\) is the rate of arrival of gas molecules, expressed in molecules cm\(^{-2}\) sec\(^{-1}\), and \(m\) is the mass of a molecule. Substituting numerical values, we obtain:

\[ \mu=2.65\cdot 10^{19}\,p\sqrt{MT}, \tag{5} \]

where \(M\) is the molecular weight of the gas (taking \(O=16\)), and \(p\) is expressed in bars. By using filaments of small size and bulbs of large size, it was possible experimentally to measure rates of disappearance of gas (clean up) so great that each molecule striking the filament disappeared. Under ordinary conditions, however, the clean-up rates were considerably smaller than this theoretical maximum. It was thus possible to determine the fraction of all incident molecules that reacted upon striking the filament.

In this direction I began a systematic investigation of the action of such gases as oxygen, hydrogen, nitrogen, carbon monoxide, etc., and of their mixtures on tungsten, carbon, molybdenum, and platinum filaments. In what follows I shall mention only those of these experiments that contributed to clarifying the question of the phenomenon of adsorption.

Disappearance of Hydrogen\(^3\)

When a tungsten filament is heated to \(1500^\circ\)K in an atmosphere of hydrogen at a pressure of about 20 bars, the hydrogen disappears, and the pressure falls with time, as shown by curve \(I\) in Fig. 1. The pressure drops to a very low value in the course of 10–20 min. When hydrogen is added, the clean-up rate is somewhat slowed, and the pressure decreases according to curve \(II\). Although analysis shows that the residual gas is pure hydrogen, the “clean-up” gradually ceases.

It was found that, in the case of a bulb with two filaments, ignition of the second filament does not restore the former clean-up rate. This proves that the disappearing gas is not absorbed by the filament itself. If the bulb is kept in liquid air, the total amount of clean-up increases. These investigations show that the disappearing hydrogen is adsorbed by the inner surface of the lamp-

the filament, but the latter is capable of adsorbing only a limited amount of hydrogen. This hydrogen adsorbed on the glass is capable of reacting with oxygen at room temperature after the filament has been cooled. Consequently, the adsorbed hydrogen is in a chemically extremely active state. Finally, it was shown that a heated tungsten filament dissociates ^{4,5,6,7,8} a small part of the hydrogen molecules reaching it into atoms, and that these latter, owing to their unsaturated chemical nature, show a tendency to be adsorbed on glass. However, these hydrogen atoms are capable of reacting with one another and forming molecules. If one adopts this point of view, then it proves impossible to retain on the glass an amount of hydrogen greater than that which is necessary for forming a layer one atom thick.

Fig. 1. Clean-up of hydrogen and oxygen by means of a tungsten filament.

Adsorption increases when the bulb is cooled in liquid air. In these experiments the maximum amount of hydrogen adsorbed on the glass reached \(0.03\ \mathrm{mm}^3/\mathrm{cm}^2\), measured as molecular hydrogen at atmospheric pressure. This corresponds to \(\sigma = 1.15 \cdot 10^{15}\) hydrogen atoms per \(1\ \mathrm{cm}^2\), which is equal to the number of spheres of diameter \(2.8\ \text{\AA}\)* that can be arranged on \(1\ \mathrm{cm}^2\) in a close-packed hexagonal lattice. The distance between adsorbed atoms is, in all probability, determined by the arrangement of the atoms in the underlying glass, forming “elementary sites” in which atoms can be accommodated. Thus—

* Atomic and molecular distances are given in Angstrom units \(10^{-8}\ \mathrm{cm}\), which below will be denoted by \(\text{\AA}\).

Thus, if the average diameter of the glass atoms can be taken as \(2.8\ \text{Å}\), then the observed maximum amount of adsorbed hydrogen agrees well with that which may be expected in a monatomic film. If the surface of glass, saturated with atomic hydrogen at the temperature of liquid air, is heated to room temperature, then part of the hydrogen leaves the surface in the form of molecular hydrogen; the remaining hydrogen can be removed by heating to a temperature of \(300^\circ\text{K}\). Since the adsorbed hydrogen atoms, on coming into contact, probably react to form molecular hydrogen, our experiments indicate that the mobility of adatoms* along the surface at room temperature is very small.

It has been shown that atomic hydrogen can diffuse over large distances through glass tubes at room temperature (but not at the temperature of liquid air) and reduces metallic oxides\(^9\), such as, for example, \(\mathrm{WO_3}\), \(\mathrm{CuO}\), \(\mathrm{Fe_2O_3}\), \(\mathrm{ZnO}\), or \(\mathrm{PtO_2}\), and also dissolves in platinum to a degree sufficient to increase its resistance\(^ {10}\). At room temperature it reacts with phosphorus, forming \(\mathrm{PH_3}\)\(^3\).

Oxygen Films on Tungsten

When a tungsten filament is heated in oxygen to \(1500^\circ\text{K}\) or higher at very low pressures, such as, for example, \(100\) bars or less, the oxygen combines\(^ {11}\) with the tungsten, forming the oxide \(\mathrm{WO_3}\), which at these temperatures evaporates from the filament at the same rate at which it is formed, and the surface of the filament apparently remains clean. At temperatures below \(2200^\circ\text{K}\), the presence of extremely small amounts of oxygen (\(10^{-6}\) mm) lowers the electron emission from a tungsten filament to values amounting to from \(10^{-2}\) to \(10^{-5}\) of the emission from pure tungsten, depending on the temperature at which the emission measurement was made.

This change in the properties of the surface must depend on the presence of a film containing oxygen. If the temperature of the filament is high, for example \(2000^\circ\text{K}\) or higher, then the emission returns to the normal emission from tungsten as soon as the oxygen has been completely consumed or removed by introducing a “getter” into the bulb, for example magnesium vapor. If, however, the temperature of the filament is not above \(1500^\circ\text{K}\), then the complete removal of oxygen from the gas phase, even by introducing cesium vapor as a getter, is unable to destroy the oxygen film on tungsten after it has formed. This means that at \(1500^\circ\text{K}\) no appreciable evaporation of oxygen from such a film takes place. Measurements, pro-

* This term for denoting adsorbed atoms was proposed by Becker. (J. A. Becker, Trans. Am. Electrochem. Soc. 55, 153, 1929.)

conducted at higher temperatures show that about half of the adsorbed oxygen evaporates in the course of 27 min at \(1860^\circ\text{K}\) and in the course of 20 sec at \(2070^\circ\text{K}\) \({}^{12}\). From the temperature coefficient for this rate of evaporation one may conclude that, to remove half of the film by evaporation at \(1500^\circ\text{K}\), 3 years would be required, and that the heat of evaporation is a quantity of the order of 160 large calories per gram-atom.

This heat of evaporation is much higher than the heat of dissociation of oxygen into atoms, so that here we have direct evidence that the forces holding oxygen on the surface of tungsten may be placed on a par with the strongest of the chemical forces known to us. This gives grounds for assuming that the oxygen film, which so greatly lowers the electron emission from tungsten, consists of a single layer of oxygen atoms in chemical combination with the tungsten atoms lying beneath them.

It turns out that the electron emission from a tungsten filament in the presence of oxygen at temperatures below \(1500^\circ\text{K}\) does not depend on the pressure of oxygen, provided the latter exceeds \(10^{-3}\) bar. This must mean that the surface is practically entirely covered with oxygen and that an increase in the oxygen pressure does not increase the thickness of the layer, which consists of a single row of atoms.

Curve III in Fig. 1 shows how the pressure of oxygen in the bulb decreases with time if the tungsten filament is maintained at a temperature of \(1500^\circ\text{K}\). The rate of disappearance of oxygen is proportional to the oxygen pressure, and no fatigue effect is observed, such as was observed in the clean-up of hydrogen.

Interaction of oxygen with hydrogen in contact with a tungsten filament

Mixtures of hydrogen and oxygen at low pressures in a bulb with a tungsten filament behave in a very strange manner (see ref. 13, p. 2271; ref. 14 and ref. 15, p. 608). Typical results obtained with filaments at a temperature of \(1500^\circ\text{K}\) are shown by curves IV and V of Fig. 1. These curves were obtained with a mixture of three parts hydrogen and five parts oxygen. When the filament was heated, the gas disappeared at exactly the same rate as in the case of curve III with only five parts oxygen present. In approximately 15 min practically all the oxygen disappeared. This was confirmed by analysis of the residual gas, which proved to be pure hydrogen. However, this hydrogen does not decompose in the usual way into atoms and does not disappear as a result of adsorption on the glass walls, as shown by curve I; the pressure remains constant for approximately 24 min, after which the pressure begins to fall sharply, as curve V shows.

Meanwhile this curve V is identical with curve I, characteristic of

clean-up of hydrogen in the absence of oxygen. Repeated experiments with different amounts of oxygen and hydrogen show that hydrogen does not interfere with the clean-up of oxygen, but that an exceedingly small amount of oxygen, of the order of \(10^{-3}\) bars, completely stops the dissociation of hydrogen into atoms by a tungsten filament at \(1500^\circ\mathrm{K}\). Thus oxygen acts as a catalytic poison. Such experiments can serve for the precise analysis of mixtures of oxygen and hydrogen.

The fact that a monatomic oxygen film on tungsten does not react with hydrogen at \(1500^\circ\mathrm{K}\) is striking confirmation that oxygen is in a state very different from gaseous oxygen. However, the results confirm our conclusion, according to which the film consists of oxygen atoms chemically saturated by the tungsten atoms with which they are in contact.

Taking into account that the evaporation of an oxygen film on tungsten at \(1500^\circ\mathrm{K}\) requires not less than a year, one cannot fail to note the fact that in the presence of hydrogen the clean-up of hydrogen begins suddenly. Since curve \(V\) coincides exactly with the lower part of curve \(I\), then, apparently, as soon as hydrogen begins to dissociate, the oxygen suddenly disappears completely from the surface; in other words, hydrogen can remove monatomic oxygen films from the surface of tungsten if the amount of oxygen on the surface is less than a certain amount. This, in all probability, means that adsorbed oxygen molecules cannot react directly with hydrogen atoms, but can react with hydrogen atoms adsorbed on the nearby tungsten surface.

Thorium on Tungsten \(^{16}\)

When a tungsten filament made from tungsten oxide containing about \(1\%\) thorium oxide, \(\mathrm{ThO_2}\), is heated to a temperature of \(2800^\circ\mathrm{K}\) or higher, a very small part of the thorium oxide is reduced to metallic thorium. The thorium oxide is contained in the filament in the form of tiny spherical particles distributed throughout the volume of the tungsten crystals, and not at the boundaries between the crystals. If the filament is then heated for several minutes to a temperature of from \(1900\) to \(2000^\circ\mathrm{K}\), the metallic thorium formed at higher temperatures slowly diffuses within the crystalline grains to the crystal boundaries, then rapidly diffuses along these boundaries to the surface of the filament, and then spreads over the surface of the filament by surface migration and forms on it a monatomic film consisting of adsorbed thorium atoms. At \(2000^\circ\mathrm{K}\) the rate of evaporation of thorium from the filament is so small that, on the latter, an amount of thorium soon accumulates sufficient to form an almost continuous monatomic film. When the temperature is raised to \(2200^\circ\mathrm{K}\)

or 2400° K the rate of evaporation of thorium from the surface increases so much more rapidly than the rate at which thorium arrives from within by diffusion that the surface concentration falls considerably.

These changes in the thorium content in the adsorbed film can be investigated by measuring the electron emission of the filament, carried out at a standard low temperature; the latter is set so low that neither diffusion to the surface nor evaporation from the surface produces noticeable changes in the adsorbed film. A convenient temperature proved to be 1500° K. At this temperature the presence of adsorbed thorium on the surface can increase the electron emission by \(10^5\) times in comparison with that from a pure tungsten surface.

Similar experiments make it possible to investigate the electrical properties of surface films containing known quantities of thorium. Starting from the assumption that each thorium atom on the surface acts as a dipole possessing a definite dipole moment, it can be shown that the logarithm of the electron emission should increase linearly with increasing number of thorium atoms on the surface. Experiments have shown that, for low thorium concentrations, this relation is approximately justified.

There are several indications that the thickness of the adsorbed thorium film formed by diffusion from within never exceeds one atom.

Interaction of Carbon Dioxide with Carbon Filaments

If a carbon filament is heated to a temperature exceeding 1700° K in the presence of carbon dioxide at low pressure, then from each molecule of carbon dioxide one molecule of carbon monoxide is liberated (see ref. 2, p. 1154). If this carbon monoxide is pumped out of the bulb and the filament is then heated to 2300° K, a volume of carbon monoxide is slowly liberated equal to that originally formed from the dioxide. This proves that each molecule of carbon dioxide which comes into contact with and reacts with the filament gives up to the latter one oxygen atom and thus forms a molecule of carbon monoxide. The oxygen atoms transferred in this way to the filament form a monatomic film covering the surface, consisting of oxygen atoms chemically joined, in all probability by double bonds, to the carbon atoms with which they are in contact. This film adsorbed on the filament is very stable at 1700° K. Heating to 2300° K, however, destroys the film, not as a result of evaporation of oxygen atoms, but because of rupture of the bonds between the carbon atoms bound to the oxygen and the carbon atoms lying beneath them, with which they are in contact. Thus the oxygen disappears in the form of carbon monoxide.

We see that, from this point of view, the adsorbed film on the carbon filament may be regarded as consisting of adsorbed oxygen, or else as an adsorbed film consisting of oriented molecules of carbon monoxide or carbonyl radicals, chemically bound by their carbon atoms to the carbon atoms of the filament lying beneath them. It is to be expected that the properties of the adsorbed film will prove to be quite different if it consists of carbon monoxide molecules bound to the underlying surface by means of their oxygen atoms. Thus these experiments led to the idea that the properties of adsorbed films generally depend on the orientation of molecules or radicals in the film. The author of the present article believed (in 1915) that confirmation of such an orientation could be found in data on the surface tension of pure liquids.

Surface Energy of Pure Liquids17,18

If a prism of liquid with a cross-section equal to \(1\ \mathrm{cm}^2\) is divided into two parts by an imaginary plane perpendicular to the axis of the prism, and the two parts of the liquid are then separated from one another, the surface of the liquid increases by \(2\ \mathrm{cm}^2\). The total energy per \(1\ \mathrm{cm}^2\), theoretically required in order to bring about this separation, may be called the total surface energy \(\gamma_0\). The latter is related to the free surface energy \(\gamma\), which is equivalent to the surface tension of the liquid, by the relation

\[ \gamma_0=\gamma-T\frac{d\gamma}{dT}. \]

Thus the surface energy \(\gamma_0\) can be measured by measuring the surface tension. This quantity (\(\gamma\)) represents the excess potential energy of the molecules forming the surface of the liquid (per \(1\ \mathrm{cm}^2\)), as compared with that which they possess while inside the liquid.

In Table 1 are given data for several substances, serving to illustrate the relationships19,20 between the orientation of molecules and other properties of liquids. The latent heat of vaporization, which, according to Trouton’s rule, is proportional to the absolute boiling point \(T_b\), is a measure of the energy required to transfer molecules from the inner layers of the liquid into the vapor phase. We have already seen that the surface energy \(\gamma_0\) is the energy per unit area required for the formation of a surface.

The molecular volume \(V\) given in this table is the volume of the liquid divided by the number of molecules. The molecular surface \(S\) is the surface of a sphere having volume \(V\). The exceedingly low values of the heat of vaporization \(\lambda\) per molecule for helium and hydrogen indicate that the forces by which these molecules…

act on their neighbors are unusually small. This is in full agreement with the great stability of the electron pair forming the \(K\) electron shell and providing the covalent bond. The diameters of the helium atom and the hydrogen molecule, given by kinetic theory on the basis of viscosity measurements, namely 1.9 and \(2.4\,\text{Å}\), correspond to sizes of only 3.6 and \(7.2\,\text{Å}^3\), which are very small in comparison with the volumes occupied by them in the liquid. Such a loose structure of the liquid also indicates the weakness of the attractive forces acting between these molecules.

Surface properties of molecules

Substance	\(V\), volume, \(\text{Å}^3\)	\(S\), surface, \(\text{Å}^2\)	\(T_B\), boiling point, \({}^{\circ}\mathrm{K}\)	\(\lambda\), heat of evaporation, \(\mathrm{erg}\cdot 10^{-14}\)	\(\lambda/S\), \(\mathrm{erg}\cdot\mathrm{cm}^{-2}\)	\(\gamma_0\), \(\mathrm{erg}\cdot\mathrm{cm}^{-2}\)
He	52	68	4.3	0.24	0.35	0.59
H—H	47	63	20.5	1.67	2.7	5.4
H—OH	30	48	373	67	140	118
A	47	63	88	11.3	18	35.3
\(\mathrm{CH}_4\)	64	78	112	16.3	21	—
\(n\)-\(\mathrm{C}_7\mathrm{H}_{18}\)	266	200	398	56	28	50.7
\(n\)-\(\mathrm{C}_8\mathrm{H}_{17}\mathrm{OH}\)	260	198	467	82	41.5	50.7

Replacement of one of the hydrogen atoms in the hydrogen molecule by the hydroxyl radical, as a result of which water is obtained, leads to a decrease of the value of \(V\) from 47 to 30, which indicates considerable forces acting between hydroxyl groups and compressing the liquid. The best measure of these forces is the increase of \(\lambda\) by a factor of forty, from 1.67 to 67. The surface energy \(\gamma_0\) has increased twenty-fourfold. The data for argon illustrate the properties of an atom having a completed electron shell, or octet. The fact that, despite the much larger electron configuration (with a diameter equal to 2.9 according to kinetic theory), the volume per molecule in the liquid remains the same as for hydrogen shows that the force field around the molecule is much greater than in the case of hydrogen or helium. The heat of evaporation per unit area \(\dfrac{\lambda}{S}\) is a very convenient measure of the intensity of this field. For hydrogen, helium, and argon the latter is approximately equal to half the surface energy \(\gamma_0\).

The data for methane show that for this molecule the value \(\dfrac{\lambda}{S}\) is approximately the same as for argon. This molecule possesses a complete octet, which has shared electron pairs with the hydrogen atoms. Apparently, the presence of hydrogen atoms does not introduce noticeable changes into the force field; the funda-

the result is an increase in molecular volume, the consequence of which is an increase in \(\lambda\) and in the boiling point \(T_B\), almost proportional to the growth of \(S\).

The values of \(\dfrac{\lambda}{S}\) for saturated aliphatic hydrocarbons above propane are practically constant and equal to 28. The same constancy is also seen for the surface energy \(\gamma_0\). The data for octane in Table 1 are typical. Thus the surfaces of the molecules of the higher saturated hydrocarbons are very similar to the surfaces of argon atoms, the effect of chain formation manifesting itself mainly in an increase of \(\dfrac{\lambda}{S}\) from 18 to 28.

The constancy of \(\dfrac{\lambda}{S}\) is also an indication that the molecules of the higher hydrocarbons have an approximately spherical shape. The latter is quite sufficiently explained by the known flexibility of the chain and by the reduction of surface energy owing to the more compact form.

The last line of the table illustrates the effect, in the data for normal octyl alcohol, of replacing one hydrogen atom in octane by a hydroxyl radical. A large decrease in \(V\) is observed, parallel to a similar decrease for water, with the difference that in the present case the decrease in volume is considerably smaller, since each OH group in the liquid cannot be near many other OH groups. The best proof of the large force field around the OH group is the increase in the value of \(\lambda\) by 26 units. The fact that this increase is not even half of that observed in the transition from \(H_2\) to \(H_2O\) shows that the OH group in the molecule of octyl alcohol vapor is capable of hiding, at least partly, in the approximately spherical molecule.

Despite the considerable increase of \(\lambda\) and \(\dfrac{\lambda}{S}\) in octyl alcohol, the surface energy \(\gamma_0\) remains the same as for octane. This can be explained by the orientation of molecules in the surface layer. The large attractive forces with which the hydroxyl groups act are the reason why the latter are drawn into the interior of the liquid. Thermal motion tends to oppose this tendency. According to Boltzmann’s equation, the relative distribution of molecules between two regions possessing different energies is measured by

\[ e^{\frac{W}{kT}}, \]

where \(W\) is the difference of the energy of a molecule in the two states. Comparing the values of \(\lambda\) for octane and octyl alcohol, one must acknowledge that the energy required to transfer one OH group from the hydrocarbon environment into the free state must be at least \(26 \cdot 10^{-14}\) ergs. The energy corresponding to \(kT\) at room temperature is approximately

$4 \cdot 10^{-14}$ ergs. Since $W$ thus proves to be more than 6.5 times greater, we may conclude that almost all molecules (with the exception of $e^{-6.5} = 10^{-3}$) at the surface of octane will be oriented so as to prevent the hydroxyl groups from reaching the surface.

It now becomes clear to us why the surface energy of octyl alcohol is the same as that of octane. Above we saw that $\gamma_0$ can be determined by means of the energy required to divide a prism into two parts. We may imagine that this division takes place in two steps. The molecules on opposite sides of the imaginary plane separating the two parts may first be oriented so that the hydroxyl groups are turned to the sides opposite this plane, and only the hydrocarbon parts of the molecule are in contact with the plane. Then these two parts of the liquid prove to be separated by this surface, which requires the same amount of energy as pure octane. Thus, owing to the orientation of the molecules, $\gamma_0$ in this case differs from that in octane apparently only by the small amount of energy necessary for rotating the molecules within the liquid.

Returning again to Table 1, we see that comparison of $\dfrac{\lambda}{S}$ with $\gamma_0$ gives us a measure of the orientation effect. In general, for molecules with homogeneous force fields, $\dfrac{\lambda}{S}$ is equal to from 0.5 to 0.55 of the value of $\gamma_0$.

However, when one part of the molecular surface has a considerably weaker force field than the other parts, the surface of the liquid consists chiefly or entirely of the least active parts, so that $\gamma_0$ turns out to be below normal. Thus, for octyl alcohol $\dfrac{\lambda}{S}$ is equal to $0.82\,\gamma_0$, whereas for water it is equal to 1.18, which indicates that the water molecule is very asymmetric and strongly oriented at the surface.

For the present these examples will suffice. In a paper published in 1916, I showed that this theory is generally applicable to the surface tension of organic liquids, including the case of substituted benzene derivatives, where the value of $\gamma_0$ depends to a considerable extent on the relative positions of the substituting groups. Somewhat later Harkins and his co-workers investigated in this way a large number of organic substances and conclusively proved the significance of molecular orientation in the surface layer of liquids consisting of asymmetric molecules.

Oil Films on Water18,21.

A pure saturated liquid hydrocarbon, when placed on water, remains on the surface in the form of a drop or globule, which does not affect the surface tension of the surrounding water. On the contrary, if onto the surface of pure water ...

place an insoluble fatty or oily substance, such as, for example, an ordinary vegetable or animal oil, it spreads almost instantaneously over the surface of the water in the form of a thin film. If the movements of the surface are made visible by sprinkling it with talc powder, it turns out that, with a limited quantity of oil, the film spreads only until it covers a certain area, or, at any rate in the case when the area exceeds a certain value, the oil has no effect on the surface tension of the water. A comparison of various insoluble organic substances showed that the tendency to spread depends on the presence in the organic molecule of certain active groups or radicals which tend to increase the solubility of organic substances in water. For example, pentane \(C_5H_{12}\) is practically insoluble in water, whereas amyl alcohol \(C_5H_{11}OH\) is relatively soluble. Thus hydroxyl groups in organic molecules act upon the hydroxyl groups of water molecules with a considerable attractive force, which is manifested in an increase of solubility. In a similar way, the carboxyl group \(COOH\) considerably increases the solubility in water of the lower fatty acids in comparison with the corresponding hydrocarbons.

Hydrocarbons having a large molecular weight, such as, for example, \(C_{18}H_{38}\), are extremely insoluble in water. If a carboxyl group replaces the \(CH_3\) group at the end of the chain, then only one end of the molecule tends to dissolve in water, while the remaining part retains the insolubility of hydrocarbons. Spreading over the surface of the water, molecules of this kind can bring their carboxyl groups into contact with the water without separating from one another.

The oily film thus formed must consist of a single layer of molecules, compactly arranged on the surface layer of the water. If the quantity of fatty acid is too large for that limited region over which it can spread, then, owing to the tendency of the carboxyl groups to come into contact with the water, the molecules prove to be arranged so closely on the surface that they stand in rows almost vertically. Thus the area occupied by each molecule is determined by the cross-section of the hydrocarbon chain, or, if the head of the chain is wider, by the cross-section of the latter. The thickness of the film, on the other hand, is determined by the length of the hydrocarbon chain.

By dissolving definite parts by weight of liquid or solid oily or fatty substances in a volatile solvent, for example in hexane, and placing known quantities of these dilute solutions on the surface of water, we can transfer to the latter a definite number of molecules. The oily film may be confined to a definite part of the surface of the water in a long narrow trough by means of a floating strip of paper lying on the water across the trough. By measuring the forces acting on the strip of paper, one can

directly measure, in dynes per centimeter, the force \(F\) causing spreading with which an oil film, having a given number of oil molecules per \(1 \text{ cm}^2\) of area, acts. We shall denote this surface concentration by the symbol \(\sigma\). Measurements similar to those described above, by means of which \(F\) can be expressed as a function of \(\sigma\) and \(T\), give us a two-dimensional equation of state of an oil film, exactly corresponding to the three-dimensional equation of state characterizing ordinary gases and liquids. Indeed, in these experiments the movable strip of paper corresponds to the piston compressing gas in a cylinder.

Oil films observed on water may exist as two-dimensional solids, liquids, or gases. A film of stearic acid \(\mathrm{C}_{17}\mathrm{H}_{35}\mathrm{COOH}\) on water is a solid. When such a film is compressed by a force equal to \(10 \text{ dyn}/\text{cm}\), acting on a strip of paper, then these properties of a solid become evident if the surface is sprinkled with talc powder and the action of air currents directed at this surface is observed. The talc particles do not move freely over the surface. Being displaced by a strong wind, after the latter ceases they return to their places, thereby proving the rigidity and elasticity of the surface characteristic of solids. Other substances, such as, for example, cetyl alcohol or oleic acid, give liquid films, as is evident from the fact that on them talc particles move freely under the action of weak forces produced by the wind.

By slightly increasing the area available for these films of saturated fatty acids, we find that the spreading force falls almost to zero. This proves that these films act not as two-dimensional gases, but rather as two-dimensional liquids possessing an immeasurably small two-dimensional vapor pressure. However, in the case of myristic acid\({}^{22}\) a definite two-dimensional vapor pressure is observed, equal to approximately \(0.2 \text{ dyn}/\text{cm}^2\).

Lower fatty acids give typical “gaseous” films which, however, cannot be investigated by the method described above, since they are so readily soluble in water that they pass into solution under the influence of the forces originating from the movable barrier.

Adsorbed Films on Solutions\({}^{18,21}\)

The method described above for studying the properties of oil films on the surface of water is not applicable in cases where the film is soluble or volatile. In such cases the measurements must be carried out in the presence of saturated vapor or a saturated solution. The Gibbs equation [equation (1)] gives us the possibility of determining the relation between the quantity adsorbed on the surface of a solution and the force \(F\) causing spreading, as a function of the partial pressure \(p\) of the vapors of the adsorbed substance above the liquid or of the partial osmotic pres-

of the pressure \(p\) of the dissolved substance in the underlying solution. Experimentally, \(F\) can be measured as the decrease in the surface tension of the pure liquid caused by the presence of the dissolved substance. By integrating this equation, using the experimentally obtained values of \(F\), one can obtain the equation of state of a two-dimensional film, irrespective of whether the latter is gaseous, liquid, or solid.

For cases of very high or very low surface concentration, the Gibbs equation assumes simple limiting forms. At very low concentrations the molecules in adsorbed films are situated so far apart from one another that the forces acting between them cannot be detected. Under such conditions the surface concentration \(\sigma\) will be proportional to the volume concentration, which, in turn, is proportional to \(p\). If equation (1) is solved on the assumption that \(\sigma\) is proportional to \(p\), we find that it leads to the following equation of state:

\[ F=\sigma kT, \tag{6} \]

which is the two-dimensional analogue of equation (3), the equation of state of an ideal gas, and may therefore be called the equation of state of an ideal two-dimensional gas.

The forces acting between adsorbed molecules tend to modify this equation. The two-dimensional analogue of the van der Waals equation may be written in the form:

\[ F=\frac{\sigma kT}{\left(1-\frac{\sigma}{\sigma_1}\right)}+a\sigma^2. \tag{7} \]

where \(a\) and \(\sigma_1\) are constants.

When the gas or liquid phase has a relatively high concentration, the concentration of molecules in the adsorbed film tends to increase to the limiting value \(\sigma_1\), corresponding to a continuous monomolecular adsorbed film, similar to those which we observed in the study of oil films on water. Although such films possess surface elasticity, i.e. are compressible, nevertheless the forces required to compress liquid and solid films are so much greater than those required to compress a gaseous film that surface compressibility may be neglected in the first approximation; thus we may regard \(\sigma_1\) as an approximately constant quantity, i.e. independent of \(p\) and \(F\). Making this substitution in equation (1) and integrating, we obtain the following equation, which should be applicable in cases of concentrated surface films:

\[ F=\sigma_1 kT \ln \left(\frac{p}{p_0}\right). \tag{8} \]

These two limiting equations are in complete agreement with the general relations found by Traube \(^{23}\). In equation (8), \(p_0\) is a constant of integration, the value of which is not

can be found from the Gibbs equation. Using the Boltzmann equation, we can estimate the changes in the energy \(\lambda\) expended in transferring a molecule from the gaseous or liquid phase into the surface phase. Thus we have:

\[ \frac{\Gamma}{p}=\mathrm{const}\ e^{\frac{\lambda}{kT}}. \tag{9} \]

Traube found that, for molecules of aliphatic compounds having different lengths of hydrocarbon chains, the ratio \(\frac{\Gamma}{p}\) for dilute solutions (which should be proportional to \(\left(\frac{p}{\sigma}\right)\)) increases approximately threefold with the addition of each new \(CH_2\) group. Interpreting this in accordance with the Gibbs and Boltzmann equations, we arrive at the conclusion that the energy \(\lambda\) expended in the adsorption of these molecules increases linearly with the length of the chain. This means that each \(CH_2\) group in the molecule must be similarly situated in the surface film. In other words, in these dilute films, where there is much free water surface, the hydrocarbon chains must lie flat on the surface. In concentrated films, in which \(\sigma\) is a constant quantity, so that equation (8) is applicable to them, there is no free water surface, and the molecules must therefore be arranged on the surface in an almost upright position.

The cases given by equations (6) and (8) are only limiting cases, and the complete equation of state for the whole series from dilute to concentrated films must be more complex, since it must include the intermediate states between that in which the molecules lie flat on the surface and that in which they are in an almost upright position. The experimental difficulties of exact measurements of the surface tension of solutions are so great that, on the question of the equation of state of these adsorbed films on solutions, little has been done in comparison with the great work that has been carried out by Adam[^22] and others on equations of state of films of insoluble substances on water.

It is obvious that molecules in adsorbed films on liquids can move freely over the surface of the liquid, of course only insofar as the film itself does not possess the properties of a solid body.

Adsorbed films on solids

Adsorbed films on solids may exist in three states corresponding to two-dimensional gases, liquids, and solids. However, in this case we encounter a new factor that was absent in the case of adsorbed films on liquids. The forces with which the solid lying beneath them acts on the adsorbed atoms or molecules tend to hold the molecules in definite positions, determined by

lattice of a solid body. Thus we must regard the solid surface as a kind of chessboard containing definite numbers of definitely arranged elementary sites \(^{13,24}\), each of which is capable of holding an adsorbed molecule. Consequently, for the displacement of a molecule from one elementary site to another there is apparently required something analogous to an activation energy; only molecules possessing sufficient kinetic energy to overcome the potential barrier can jump from one elementary site to another \(^{25}\). On this basis we must expect that the surface mobility falls at low temperatures. The logarithm of the rate of these motions, or the coefficient of surface diffusion, should vary linearly as a function of the reciprocal absolute temperature, and the slope of this curve should be proportional to the activation energy.

In general, the coefficient of surface diffusion increases with increasing \(\sigma\), since the ability of “adatoms” to pass through the potential barrier is determined not only by the thermal motion of the molecules, but also depends on \(\dfrac{dF}{d\sigma}\), since differences in the value of \(F\) over the surface increase the mobility.

Thus we may assume that, in general, adatoms on solids move over the surface by jumping from one elementary site to another. If the adatoms move almost independently of one another, so that they freely pass to all free parts of the surface, adsorbed films may be regarded as a two-dimensional gas, notwithstanding the fact that the atoms tend to occupy definite positions. Such films form a two-dimensional crystalline gas, and its crystalline character is imparted to it by the lattice lying beneath it. If attractive forces exist between the adatoms, sufficient to form from them a definite two-dimensional condensed phase that is in equilibrium with a two-dimensional vapor phase, then we are obviously dealing likewise with a two-dimensional liquid or solid. In the case of high mobility this condensed film may possess properties characteristic of liquids; at low temperature and in the absence of mobility the conditions will be analogous to those for a two-dimensional glass. A two-dimensional solid, analogous to the ordinary three-dimensional one, can exist only on the condition that the forces acting between the adatoms can hinder their sliding with respect to one another.

THEORY EXPLAINING ADSORPTION ON SOLIDS BY CONDENSATION AND EVAPORATION

If the molecules of a gas in contact with a solid body strike its surface one at a time, they may either condense or rebound from the solid body, as in elastic reflection. The condensing molecules may subseq—

SURFACE CHEMISTRY

…to evaporate. Numerous theoretical and experimental data show that true reflection of molecules under these conditions is rather a deviation from the norm, although specular reflection of molecular beams from certain crystalline surfaces shows that the latter is possible in some cases. However, in the overwhelming majority of cases the observed phenomena show that a large fraction of the incident molecules, before evaporating, condenses on the surface and reaches thermal equilibrium with it[^26][^27]. For hydrogen and helium, accommodation coefficients considerably smaller than unity have been found. They usually refer to gases striking solids at temperatures at which the rate of evaporation may be taken so high that the lifetime of the condensed molecule will be of the order of \(10^{-13}\) sec., i.e. approximately equal to the time required for the molecule to execute one thermal vibration on the surface. Under such conditions there is nothing surprising in the fact that thermal equilibrium proves unattained.

If the rate at which molecules fall on the surface is equal to \(\mu\), as follows from equation (4), and the rate of their evaporation is \(\nu\) (molecules \(\mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\)), then the rate at which they accumulate on the surface is expressed by the equation:

\[ \frac{d\sigma}{dt}=\alpha\mu-\nu, \tag{10} \]

where the condensation coefficient \(\alpha\) is in most cases equal to unity, but never exceeds unity. The evaporation rate \(\nu\) generally depends on the temperature and on the surface concentration \(\sigma\). It is self-evident that it also depends on the nature of the solid surface on which adsorption occurs. If the surface is strictly homogeneous, then \(\nu\) may be a function of \(\sigma\) and \(T\) only for the given surface; but cases are possible in which different parts of the surface act on adatoms with different forces; in such cases \(\nu\) and \(\sigma\) may not be the same over the entire surface.

In the stationary state, when \(\sigma\) does not change with time, the basic condition that must be satisfied is

\[ \alpha\mu=\nu. \tag{11} \]

Dividing the evaporation rate \(\nu\) by \(\sigma\)—the number of atoms per \(1\ \mathrm{cm}^{2}\)—we obtain the mean probability per second for evaporation of an individual atom. Thus the reciprocal value of this ratio, \(\tau\), represents the mean lifetime of an adatom on the surface. Hence we have:

\[ \tau=\frac{\sigma}{\nu}. \tag{12} \]

Thus the time interval between condensation and evaporation of adatoms may be regarded as the fundamental cause of adsorption of gases on solid surfaces.

In general, \(\nu\) should increase rapidly with increasing temperature, as is observed for the vapor pressure of a substance. Thus the logarithm of \(\nu\) should increase approximately linearly as a function of the reciprocal of the absolute temperature; the slope of this curve is proportional to the heat of evaporation and serves as a measure of the magnitude of the forces holding the adatoms on the surface. Thus \(\nu\) is approximately expressed by an equation of the form

\[ \nu=\text{const}\ e^{-\frac{\lambda}{kT}}, \tag{13} \]

where \(\lambda\) is a measure of the energy required to remove an adatom from the surface. The fact that \(\nu\) varies within wide limits for different substances is explained chiefly by changes in \(\lambda\), and not by differences\({}^{28}\) in the constant multiplier in equation (13). This is indicated by such approximate rules as Trouton’s law.

The forces between atoms and molecules act normally over short distances\({}^{27,29}\), so that the forces acting on an adatom, which determine the magnitude of \(\lambda\) and, consequently, \(\nu\), depend mainly on the atoms with which each given adatom is in contact. If the gas pressure is increased or the temperature is lowered, so that \(\sigma\) increases so much that in the first layer in contact with the solid there is no room left for additional molecules, a further increase of \(\sigma\) must entail an increase in the number of atoms in the second layer. And since these atoms in the second layer cannot be in contact with the solid surface on which the initial adsorption occurs, for these atoms \(\lambda_2\) must differ from the value \(\lambda_1\), valid for atoms in the first layer. Since \(\lambda\) occurs in the exponent of equation (13), a comparatively small change in \(\lambda\) is sufficient to produce a considerable difference in the magnitude of \(\nu\).

Thus, when the adsorbed substance is not approximately identical in its properties with the substance on which adsorption occurs, we must expect that the values of \(\nu\) for atoms in the first and in the second layers will differ considerably from one another. Naturally, two cases may arise: \(\nu_2\) may be greater or less than \(\nu_1\) (see ref. 28, pp. 2811 and 2815).

Case 1:

\[ \nu_2<\nu_1. \]

If \(\nu_2\) is less than \(\nu_1\), then the atoms of the second layer are held by the atoms of the first layer with greater force than the latter are held by the atoms of the solid lying beneath it. Therefore the atoms of the first layer show a tendency to form clusters on which the second, third layer, etc. begin to form long before the entire first layer is covered\({}^{27}\). Such phenomena are not rare. For example, when mercury, cadmium, or iodine evaporate in a vacuum and are then con-

condense on the surface of the glass at a not very low temperature, then separate crystals of the condensed substances form on the glass. This is a direct indication that these atoms act upon one another with greater force than upon the glass lying beneath them. If the glass surface is maintained at so high a temperature that these nuclei cannot form, then it will appear that this surface reflects all atoms incident upon it, since the latter evaporate from the glass surface much more rapidly than from the surface of cadmium at the same temperature. Similar observations were made by Wood, who tried to explain them by a high reflection coefficient. He believed that the experiments indicate that mercury molecules incident at low pressures upon a cold glass surface are completely reflected at temperatures above \(-90^\circ\mathrm{C}\) and completely condense at lower temperatures.

From our present point of view, such a critical temperature has nothing in common with true reflection, but depends on the fact that the given flux of mercury or cadmium atoms has a definite temperature below which the evaporation of individual atoms cannot occur rapidly enough to prevent the formation of a monoatomic film, as a result of which further evaporation ceases at these low temperatures.

The experiments prove with complete convincingness that mercury atoms condense at all temperatures, but that under favorable temperature conditions individual atoms again evaporate from the glass at comparatively low temperatures.

It is therefore evident that cases in which \(\nu_2\) is less than \(\nu_1\) are characterized by the growth of crystals from nuclei and lead to the formation not of monomolecular films, but rather of separate crystalline particles.

Case 2:

\[ \nu_2 > \nu_1. \]

In this case, with a slow increase in pressure or decrease in temperature, \(\sigma\) increases until a monomolecular layer is formed; however, for the formation of a second layer a considerable increase in temperature or decrease in pressure is required. Therefore, under the most varied experimental conditions, this leads to the formation of layers whose thickness does not exceed one molecule. Consequently, the second case is characterized by typical adsorbed films.

Adsorption Isotherms

The fundamental equation determining the amount of substance adsorbed on a solid surface is equation (11). To express this in a definite form relating the pressure of the external gas \(p\) to the surface concentration \(\sigma\), it is sufficient

to have exactly the possibility of expressing \(\alpha\) and \(\nu\) as functions of \(\sigma\) and \(T\). The functional dependence of \(\nu\) on \(\sigma\) depends not only on the forces caused by the solid body lying beneath them, but also on the forces acting between the adatoms. Further, we must remember that the incident molecules, corresponding to \(\mu\), do not all at once fall on elementary areas on the bare surface, but that many of them first fall on places already occupied by adatoms. One of the important aspects of the problem of the adsorption isotherm is the manner in which these incident atoms find a place for themselves in the first layer. Many atoms may be forced temporarily to occupy places in the second layer, from which they can then either evaporate at a much greater rate than from the first layer, or move about until they find places for themselves in the first layer.

Under these conditions it is natural to make the simplest assumptions and then to check whether the equations derived from them can find application.^24 Thus, if the adatoms do not act on one another with an appreciable force, then we may assume that the lifetime of each of them does not depend on the presence of other atoms on the surface. Hence, proceeding from equation (12), \(\nu\) is proportional to \(\sigma\).

Instead of the surface concentration \(\sigma\), it is often more convenient to deal with the fraction of the surface covered, expressed by the equation:

\[ \theta=\frac{\sigma}{\sigma_1}, \tag{14} \]

where \(\sigma_1\) is the surface concentration of a continuous monomolecular film. Thus we may put

\[ \nu=\nu_1\theta, \tag{15} \]

where \(\nu_1\) represents the rate of evaporation from a completely covered surface.

When atoms falling on the surface land on a part not occupied by other adatoms, we may assume that the fraction \(\alpha_0\) of them condenses. The uncovered fraction of the surface may be represented by \(1-\theta\). Therefore the number of incident atoms immediately entering the first layer may be put equal to \(\alpha_0(1-\theta)\mu\). The fate of the other incident atoms, namely those which at first fall on adsorbed atoms, depends on many factors, some of which will be considered below. A very simple, though not very probable, assumption is that all these atoms evaporate again so rapidly that they do not have time to find places for themselves in the first layer. Proceeding from these assumptions, we find:

\[ \alpha\mu=\alpha_0(1-\theta)\mu. \tag{16} \]

Substituting this equation and equation (15) into equation (11) and solving for \(\theta\), we find the following simple adsorption isotherm:

\[ \theta=\frac{\alpha_0\mu}{\nu_1+\alpha_0\mu}. \tag{17} \]

It turned out that this equation is applicable with a quite sufficient degree of accuracy to an exceedingly large number of cases of adsorption on plane surfaces. Of course, taking into account the nature of the simplifying assumptions admitted in deriving this equation, it should not be regarded as a general equation for the adsorption isotherm. It proves especially applicable in those cases where adsorption occurs only on elementary areas separated from one another so far that the adatoms located on them exert no forces on one another. This may serve as a justification of the assumption made in equation (15). It seems quite probable that in this case condensation may also occur according to equation (16), since, if the given area is occupied, the probability of which is proportional to \(\theta\), then the incident atom cannot simply slip onto the neighboring elementary area, but must fall on areas where the forces retaining it are so weak that it evaporates before it can move to some other free elementary area. These assumptions lead us to an equation similar to equation (17), with the sole difference that the value of \(\theta\) and of the coefficient \(a_0\) are somewhat modified.

Recent experiments have shown that mobility plays an important role in the mechanism of condensation\({}^{30}\). Namely, it may be supposed that in most cases an incident molecule striking an already covered surface travels a noticeable distance before finding a place for itself in the first layer. Of course, if the surface is homogeneous, i.e., all its parts are accessible for adsorption, it can hardly be considered that an incident molecule striking an isolated adsorbed molecule is, even temporarily, in the second layer. Such an atom will find a place for itself in the first layer before there is a chance for it to rebound or evaporate from the surface. An atom cannot be, even temporarily, in the second layer if it is not supported by at least three, and more often four, atoms in the layer lying beneath it. Even in the absence of mobility, the probability that an incident atom can occupy a place in the second layer would be proportional to \(\theta^n\), where \(n\) is equal to at least 3 or 4. At a very high rate of evaporation one may expect these atoms to evaporate before they find a place for themselves in the first layer. On this basis the rate of arrival of atoms into the first layer must be expressed not by equation (16), but by the following expression:

\[ \alpha_\mu = a_0 (1 - \theta^n)\mu. \tag{18} \]

To determine the plausibility of these conclusions, several experiments were carried out. The bottom of the boat was covered with steel balls (0.96 cm in diameter), closely packed in a square lattice and fixed in these positions. Thus a surface was obtained possessing many features of a crystalline surface, with the steel balls corresponding to individual

atoms. When other small spheres of the same size were dropped onto the surface, the latter occupied definite elementary sites, each being in contact with four spheres lying beneath it. The number of such elementary sites (apart from the correction for edge positions) was equal to the number of fixed spheres (the zero layer). A large number of spheres, sufficient to cover a fraction $\theta$ of the available sites, was placed on the tray (in the first layer), the tray being shaken in order to ensure a random arrangement. Then a small number of additional spheres was dropped onto the surface from a height of 5 cm, and the number of spheres that entered the second layer was counted. It turned out that the probability $P$ that a given falling sphere would occupy a position in the second layer is expressed quite accurately by the formula:

\[ P=\theta^{4.5}. \tag{19} \]

Thus the fraction of falling spheres that found a place in the first layer proved to be equal to $1-\theta^{4.5}$. Comparison of this quantity with equation (18) gives the value $n=4.5$. The fact that $n$ is greater than four—the number of underlying atoms—is apparently explained by the kinetic energy of the spheres, which causes some of them to roll out of the position they initially occupied.

Applying these results to adsorption, we may expect that, in cases where $\theta$ is not very close to unity, all atoms falling on the surface should occupy places in the first layer, without any possibility of evaporation or reflection, even if the rate of evaporation from the second layer is very high.

Effect of the Forces Acting between Adatoms[^28]

The fact that two adatoms cannot simultaneously occupy one and the same elementary site must mean that they act on one another with repulsive forces. In the equation of state of adsorbed atoms this is expressed by a factor similar to $1-\theta$ in the denominator of the first term on the right-hand side of equation (7). This means that, as $\theta$ approaches unity, the force producing spreading tends to increase without bound. Combining this equation of state with the Gibbs equation and putting $\alpha=1$, we obtain the following equation for the adsorption isotherm:

\[ \ln \frac{\nu}{\theta}=\ln \frac{1}{1-\theta}+\frac{1}{1-\theta}+\mathrm{const}. \tag{20} \]

From this we see that the rate of evaporation must increase without bound as $\theta$ approaches unity. This is precisely the effect which, in typical cases of adsorbed films on liquids or solids, limits the amount of material to that contained in a monomolecular layer.

In characteristic cases of adsorption, the forces holding adatoms

on the surface, usually much greater forces acting between adatoms. If this were not so, then we would normally be dealing with cases in which \(\nu_2\) would be less than \(\nu_1\), so that we would obtain not adsorbed films, but crystalline embryos. The result of these large forces originating from the underlying surface is the polarization of the adatoms. If the latter all belong to one species, then, as a consequence of what has been said above, they tend to become identically oriented dipoles, repelling one another with a force varying inversely as the fourth power of the distance between them. We may also have attractive forces of the van der Waals type, but the latter will vary with a much higher power of the distance. Dipole forces will act over much greater distances than other forces. Knowledge of these factors, which in all probability are of great importance in most cases of adsorption, may best be attained by a detailed investigation of some example that permits quantitative determination of all the factors. For this purpose I chose the case of adsorption of cesium vapor on tungsten, since in this case we can measure with great accuracy the surface concentration \(\sigma\), as well as the rates of evaporation \(\nu\) of atoms, ions, and electrons\(^{30}\). In this way we can express these values \(\nu_a\), \(\nu_p\), and \(\nu_e\) as functions of \(\theta\) and \(T\). These measurements allow us to determine not only the forces acting between the atoms, but also the electrical properties of the adsorbed films.

Cesium Films on Tungsten

The ionization potential of cesium is \(3.9\ \mathrm{V}\), i.e., lower than that of any other element. The heat of evaporation of electrons from tungsten corresponds to \(4.6\ \mathrm{V}\). Thus the energy required to detach an electron from a cesium atom is \(0.7\ \mathrm{V}\) less than the energy required to detach an electron from metallic tungsten. Therefore there is nothing surprising in the fact that experiments show\(^{31,32}\) that every cesium atom striking a tungsten filament at high temperature loses its electron and leaves the surface as a cesium ion. The electric current thus issuing from the tungsten filament is a measure of the number of cesium atoms striking the filament. Since currents of \(10^{-17}\ \mathrm{A}\) can be measured with an electrometer, it thus becomes possible to determine cesium-vapor pressures so weak that only hundreds of cesium atoms per second reach the surface of the filament.

The disappearance of cesium ions from the surface of tungsten is an evaporation phenomenon. If the temperature is approximately \(1100^\circ\mathrm{K}\) or lower, then the rate of evaporation of ions may be so low that it begins to lag behind the rate at which atoms arrive at the surface, so that an accumulation of adsorbed cesium on the surface results. Indeed, the rate of eva-

the desorption of adsorbed cesium from the surface at a thousand degrees is approximately equal to the rate of evaporation of metallic cesium at room temperature (300° K). Thus, according to Trouton’s rule, we may expect that cesium adatoms possess a rate of evaporation exceeding, approximately threefold, the rate of evaporation of cesium itself.

We may expect such a magnitude of the forces acting between cesium atoms and the tungsten lying beneath them as a result of the fact that cesium, being near the surface of tungsten, tends to lose its electron. Thus the positively charged cesium atom induces, in the conducting surface of tungsten, a negative charge acting on the ion with an attractive force (image force) equal to \(\frac{e^2}{4x^2}\), where \(x\) is the distance of the ion from the surface. The magnitude of this image force is sufficiently large to explain the large forces retaining cesium on tungsten.

If we have a filament coated with thorium and subject it to the heat treatment necessary to cover its surface with a continuous monoatomic film of thorium, then the rate of evaporation of electrons falls to 3 V, which is 0.9 V lower than the ionization potential of cesium. In agreement with this fact, experiments show that cesium atoms are not converted into ions under the action of an activated filament coated with thorium, and also that cesium shows no tendency to adsorb on the filament.

If, in the case of a filament of pure tungsten in the presence of cesium vapor, the temperature is maintained sufficiently low for the formation of an adsorbed film of cesium, then the positively charged adatoms, which cause a positive contact potential relative to pure tungsten, lower the heat of evaporation of electrons. If such a quantity of cesium accumulates on the surface that the heat of evaporation falls considerably below 3.9 V, then the filament loses its tendency to take away from the arriving cesium atoms their electrons and to convert them into ions. This means that, as the fraction \(\theta\) of the surface covered by cesium atoms, \(\nu_p\), increases, the rate of evaporation of ions becomes very small.

At temperatures of about 700° K in the presence of cesium vapor saturated at room temperature (pressure about \(10^{-9}\) atm), \(\theta\) increases approximately to 0.7, and the heat of evaporation by this time decreases to such an extent that the electron emission increases by a factor of \(10^{22}\) in comparison with the emission from pure tungsten at the same temperature.

During the last three years Dr. Taylor and I have carried out a detailed investigation\(^{28,30}\) of the rates of evaporation of atoms, ions, and electrons from these cesium films on tungsten as functions of \(\theta\) and \(T\). For the purpose of measuring \(\theta\), a method was developed for determining the number \(\sigma\) of adsorbed atoms per \(1\ \mathrm{cm}^2\) of the tungsten surface. Two methods were developed. When \(\theta\) is less than 0.08, sudden heat-

Annealing or over-annealing the filament at temperatures above \(1300^\circ K\) forces all cesium adatoms to leave the filament in the form of ions, so that the ballistic deflection of the galvanometer gives directly the value of \(\sigma\). The second method, applicable at any values of \(\sigma\) (even in cases corresponding to monatomic layers), involves the evaporation of adatoms in the form of atoms in the presence of a retarding field that delays the escape of ions. This beam of atoms falls on a neighboring parallel tungsten filament, heated to a temperature above \(1300^\circ K\), which these atoms leave in the form of ions. Thus the ballistic current impulse from this second filament serves for measuring \(\sigma\) on the first filament. We have called the latter method of measuring \(\sigma\) the two-filament method.

Measurements of \(\sigma\) showed that, with increasing cesium pressure or with decreasing filament temperature, \(\sigma\) increases up to a certain limiting value \(\sigma_1\), equal to \(4.8 \cdot 10^{14}\) atoms per \(1\ \mathrm{cm}^2\) of apparent filament surface. A study of the crystalline structure of tungsten showed that the surface lattice of the surfaces etched by evaporation contains \(1.425 \cdot 10^{15}\) atoms per \(1\ \mathrm{cm}^2\). Since the diameter of cesium atoms is almost exactly twice the diameter of tungsten, and since adatoms, under the influence of the large forces with which tungsten acts on them, show a tendency to occupy definite elementary areas on the surface, we conclude that the maximum number of cesium adatoms is equal to one fourth of the number of tungsten atoms and that therefore the true value of \(\sigma_1\) is \(3.563 \cdot 10^{14}\) atoms per \(1\ \mathrm{cm}^2\). Comparing this value with the observed or apparent value of \(\sigma_1\), it turns out that the true surface of the tungsten filament is equal to 1.347 of the apparent surface; the reason for this difference is a slight etching of the filament surface as a result of evaporation at high temperatures.

The study of transition states, during which \(\theta\) increases or decreases with time, has conclusively shown that the phenomena of condensation and evaporation proceed independently of one another, with condensation depending on \(\mu\), while evaporation \(v\) is exclusively a function of only \(\theta\) and \(T\) and does not depend on the method of formation of the film.

Experiments show that, within the limits of experimental error (about \(0.5\%\)), the condensation coefficient \(\alpha\) is always equal to unity, even in those cases when \(\theta\) reaches the value 0.98. This proves that the incident atoms, which under these conditions must almost all fall on adatoms, can slide off them into the second layer until they find places for themselves in the first layer. However, experiments show that at every instant the number of atoms in the second layer is extremely small, of the order of \(10^{-7}\). The atoms in the second layer possess very high surface mobility.

The evaporation rate of atoms \(v_a\) at any temperature increases extremely rapidly with increasing \(\theta\). Thus, at \(1000^\circ K\), an increase of \(\theta\) from 0.1 to 0.9 causes an increase of \(v_a\) by \(10^{11}\) times. This

indicates the presence of very considerable repulsive forces between adatoms, which is in full agreement with the fact that the latter tend to become positively charged, as is indicated by the effect of the film on the increase of the electron emission. It proved possible to develop this dependence between \(\nu_a\) and \(\nu_e\) into a quantitative theory.

A separate cesium adatom on the surface of tungsten may be regarded as an ion held on the metal by means of its image force. Thus the image force and the ion form a dipole possessing an electric moment \(M\), and oriented with its axis perpendicular to the surface. Owing to the strong electric fields near the ion while it is adsorbed on the surface, we must expect the conduction electrons to be drawn toward the ion, so that the dipole moment must be considerably smaller than could be calculated for a cesium ion situated at a distance of its radius from an ideal metallic surface. Indeed, the experimental values for \(M\) proved to be equal to \(16.2 \cdot 10^{-18}\), whereas, according to calculations, they should have been equal to \(25 \cdot 10^{-18}\) for a spherical cesium ion in contact with an ideal conducting plane.

The force acting between two such dipole-adions is given by the equation:

\[ f=\frac{3}{2}\frac{M^2}{r^4}, \tag{21} \]

where \(r\) is the distance between the adions.

Now we can construct the equation of state of adsorbed cesium films, taking these forces into account by means of the Clausius virial equation, which for surfaces assumes the form:

\[ F=\sigma kT+\frac{1}{4}\sigma \sum (rf), \tag{22} \]

where the summation must be extended over all adatoms acting on any other adatom. The forces \(f\) may be of two kinds: first, forces acting at large distances and corresponding to the dipole repulsion of equation (21), and then forces acting at short distances, which act between atoms in contact and prevent the simultaneous occupation of one elementary site by two atoms. These forces acting at short distances may be taken into account by dividing the right-hand side of equation (6) by \((1-\theta)\), as was already done in equation (7). Thus, by integration it was possible to derive a general equation of state for adsorbed atoms repelling one another as dipoles. This is the following equation:

\[ F=\frac{\sigma kT}{1-\theta}+3.34\sigma^{3/2}M^2+1.53\cdot10^{-5}\sigma^2T\,M' l, \tag{23} \]

where \(I\) is an integral whose numerical value can never exceed 0.89 and which can be found from tables and curves from the values of \(M, \sigma\), and \(\sigma_1\).

The spreading force \(F\), calculated in this way, cannot be measured directly for a solid surface, but it can be related to the evaporation rate \(\nu_a\) by means of the Gibbs equation:

\[ \frac{dF}{d\ln \nu_a}=\sigma kT. \tag{24} \]

By substituting into this equation the value of \(F\) from equation (23), we can calculate \(\nu_a\) as a function of \(M\). In practice we reversed this process. For certain experimentally obtained values of \(\nu_a\) as functions of \(\sigma\) and \(T\), we calculated \(F\) by means of equation (24), and from it, by means of equation (23), obtained \(M\). These values of \(M\) proved to be functions of \(\sigma\), but not to be in any noticeable dependence on \(T\), although, incidentally, the form of equation (23) indicates a certain dependence.

This theory can be tested, since the values of \(M\) obtained from \(\nu_a\) can be compared with the values of \(M\) obtained from the contact potential, which, in turn, can be obtained from measurements of \(\nu_e\). The contact potential \(V\) of a surface covered with an adsorbed film, in comparison with the surface of the pure metal, is given by the equation:

\[ V=2\pi\sigma M. \tag{25} \]

In addition, the electron emission \(\nu_e\) is related to the contact potential \(V\) by the Boltzmann equation:

\[ \frac{\nu_e}{\nu_w}=e^{\frac{Ve}{kT}}, \tag{26} \]

where \(\nu_w\) is the electron emission from pure tungsten at the same temperature. The solid curve in Fig. 2 gives the values of \(V\) calculated by means of equation (25) from \(M\), determined in turn by means of \(\nu_e\). The points marked by circles indicate the values of \(V\) obtained from \(\nu_e\) by means of equation (26).

The values of \(V\) obtained by these two independent methods coincide almost completely for \(\theta<0.5\). The deviations observed at higher values of \(\theta\) apparently indicate that, for higher values of \(\theta\), the forces acting at short distances are somewhat greater than those given by the factor \(1-\theta\)—the denominator of the first term of the right-hand side of equation (23). Calculations show that for the value \(\theta=0.75\) the part of the spreading force that depends on forces acting at short distances is in fact 45% higher than that given by the first term of the right-hand side of equation (23).

It is also possible to calculate the contact potential from data concerning \(\nu_p\)—the rate of evaporation of ions from the surface.

The values \(v_a\), \(v_e\), and \(v_p\) must stand in such relations to one another that the concentrations of atoms, electrons, and ions in the vapor phase near the filament, as given by them, do not contradict the requirements of thermodynamics for equilibrium between these particles. Thus we may set:

\[ \frac{n_e n_p}{n_a}=K, \tag{27} \]

where \(K\) is the equilibrium constant, which can be determined from the ionization potential according to Saha’s equation. Then, combining with the Boltzmann and Dushman equations for electron emission from tungsten, we obtain:

Fig. 2. Contact potential of a cesium film on tungsten in comparison with pure tungsten.

\[ \ln(2v_p)=\ln v_a+\frac{e}{kT}\left(V_w-V_i-V\right), \tag{28} \]

where \(V_i\) is the ionization potential of cesium, and \(V_w\) is the heat of evaporation of electrons from tungsten. The values of the contact potential \(V\), calculated in this way from \(v_p\), are indicated in Fig. 2 by squares. These points lie on the curve obtained from \(v_a\).

The agreement of the values of \(V\) obtained by means of the three methods described above shows that our theory gives a complete explanation of the electrical and chemical properties of moderately diluted cesium films on tungsten. It also proves that the surface of these tungsten filaments was essentially homogeneous, so that the probability of evaporation of each atom or adion did not depend on the position of the atoms on the surface and was determined exclusively by the value of \(\sigma\) at that point.

However, experiments have shown that this conclusion, although valid for more than 99% of the entire surface, is not of universal applicability. Deviations at very low values of \(\theta\) indicate that about 0.5% of the surface consists of what may be called active sites, which adsorb cesium much more strongly than the rest of the surface; thus, on these areas the heat of evaporation is 37% higher than that for atoms on the normal part of the surface. Experiments have also shown that adsorption on this part of the surface is described by a simple type of adsorption isotherm, expressed by equation (17). This means that atoms adsorbed on the active areas do not act upon one another with appreciable forces. Evidently the active sites consist of separate elementary areas distributed over the surface, in all probability near grain boundaries or on steps in the faces of the crystal. The change in the dipole moment \(M\) as a function of \(\sigma\) occurs as a result of the depolarizing action of neighboring dipoles. The electric fields caused by these dipoles can be calculated by integration, just as was done in calculating \(F\), and are of the order of \(5 \cdot 10^7\ \mathrm{V\!\cdot cm^{-1}}\).

If a tungsten filament is heated to approximately \(1100^\circ\mathrm{K}\) in cesium vapor in the presence of an accelerating field that draws ions from the surface, then we may have two coexisting surface phases. For one of them \(\theta\) will be approximately equal to 0.15, while for the other it will be very close to zero. Atoms falling on the less concentrated phase evaporate as ions, whereas those falling on the concentrated phase evaporate as atoms. At a definite temperature and a given cesium pressure the phase boundary is absolutely stable and immobile. With a slight increase in temperature the phase boundary gradually moves in the direction of the concentrated phase, so that the entire filament gradually becomes bare; lowering the temperature causes the whole surface to be covered by the concentrated phase. A detailed analysis of the mechanism at the boundary between the phases, including diffusion from one phase into the other, makes it possible to measure the coefficient of surface diffusion \(D\). The results showed that

\[ \log D = -0.70 - \frac{3060}{T}. \]

From the temperature coefficient \(D\) it can be calculated that the activation energy of surface diffusion is approximately \(0.6\ \mathrm{V}\). This means that between each two elementary areas there exist potential barriers of height \(0.6\ \mathrm{V}\), over which the adatoms must jump before beginning to move over the surface.

The experimental methods used by us in the above-described investigations of cesium films on tungsten are distinguished by great accuracy and high sensitivity and, increas-

which, it seems, may open a broad field for a detailed study of adsorption phenomena. Dr. Taylor and I are continuing our work in this area. We intend to carry out exact comparisons of the properties of adsorbed films of cesium, rubidium, and potassium. We have developed a method for introducing definite small quantities of oxygen by diffusion through a heated silver tube. In this way a known number of oxygen atoms can be placed on the surface of a tungsten filament, forming negative dipoles. The latter attract positive cesium dipoles, which tend to form clusters around them, producing a kind of two-dimensional colloidal distribution of cesium. We hope, through a detailed study of such systems, to investigate the effects not only of repulsive but also of attractive forces acting between adatoms. Experiments are also now being carried out to study the adsorption of cesium on a tungsten surface containing a known number of adsorbed thorium atoms.

The methods described, in combination with the method based on the spreading of oil films on water, make it possible to determine the equation of state of two-dimensional gases with the same degree of accuracy as for three-dimensional gases, but with the advantage that in this case the conditions are especially favorable for determining the mechanism of all the processes that play a role here.

Types of Adsorption

The classical kinetic theory of gases, as applied by Sutherland in the study of viscosity and by van der Waals in the study of the continuity of the transition from gas to liquid, led to the recognition of the action of attractive forces between molecules at large distances and of powerful repulsive forces between molecules at short distances. Chemists have long known that especially large attractive and repulsive forces are associated with the chemical bond between neighboring molecules, which they represent in the form of a valence bond (primary valence), and that weaker forces, which they call forces of secondary valence, usually correspond to other types of chemical bonding. Physicists have investigated the forces acting between charged particles, such as ions and dipoles, and in recent times have discovered exchange forces, which can best be explained with the aid of quantum mechanics.

In the structure of matter there can be no fundamental distinction between chemical and physical forces; usually a force is called chemical while chemists study it, and then that same force is called physical after physicists find an explanation for it. Usually, likewise, there is no hard boundary between attractive and repulsive forces and between the various kinds of repulsive and attractive forces. However, recognition of the distinction between the types of forces that maintain equi-

... substances of matter, proves convenient in classifying natural phenomena. Thus, from a qualitative point of view, we can distinguish the following types of forces[^29].

1. Coulomb forces, acting between ions or ions and electrons and varying in proportion to

\[ \frac{1}{r^2}, \]

where \(r\) is the distance between the ions. The best examples of such forces are encountered in salt-like substances.

1. Forces acting between dipoles, varying as

\[ \frac{1}{r^4} \]

and depending on the orientation of the dipoles.

1. Valence forces, associated with the sharing of electrons between atoms.

2. Attractive van der Waals forces, depending on the mutual polarizability of molecules. It is usually considered that these forces vary as

\[ \frac{1}{r^7}. \]

1. Repulsive forces, arising as a consequence of the mutual impenetrability of closed electron shells. It is precisely these forces that, in the first instance, determine the effective area of repelling molecules in kinetic theory. Born and Mayer[^33] found that the potential energy of these repulsive forces acting between two closed shells is given by the equation:

\[ A e^{\frac{r_1+r_2-r}{r_0}}, \]

where \(r_1\) and \(r_2\) are the effective radii of the two shells, \(r_0\) is a universal constant equal to \(0.435\ \text{\AA}\), and \(A\) is also a universal constant. This means that the repulsive force of this type, acting between two atoms, can be expressed as a function of the distance between the surfaces of the atoms, and this function is almost the same for all atoms (or molecules) possessing closed shells, independently of their electric charge. From consideration of certain other properties of solids and liquids, I had already earlier come to the conclusion that (ref. 20, pp. 529–531) repulsive forces should be regarded as “surface forces, which must be expressed as functions of the distances between the surfaces of atoms (established by electron orbits), and not by means of the distances between the centers of atoms.” Consideration of van der Waals forces showed that for them as well “the intensities of the fields around various nonpolar molecules, when considered as surface forces, are practically identical.”

The fact that, according to Born and Mayer, these repulsive forces decrease to the value

\[ \frac{1}{e} \]

with an increase in the distance...

between atoms by \(0.435 \,\text{Å}\), indicates that they have a very small range of action.

1. Electronic pressures. The force that balances the Coulomb attraction of electrons and ions in alkali metals and, apparently, also in other metals, owes its origin to the pressure of the Fermi electron gas.

Since all these forces may manifest themselves both at the surface and within solids and liquids, they must take part in adsorption phenomena. There must exist different types of adsorption corresponding to different types of forces that hold atoms or molecules on a surface. Let us consider a few examples.

Cesium on tungsten. Cesium ions are held on the underlying metal by Coulomb attractive forces (in this case—a modified image force). The corresponding repulsive forces, which hold the ion at a certain distance from the surface (and thereby determine the dipole moment \(M\)), are caused by the gradient of the pressure of the Fermi electron gas extending beyond the lattice of tungsten atoms. The forces acting between cesium adatoms are typical dipole-repulsion forces.

Oxygen on tungsten or carbon. The attractive forces are, in all probability, typical valence forces. That these are not ordinary Coulomb forces, like those acting in cesium adsorption, becomes clear from considering the relation between the contact potential and the heat of evaporation of the adatoms. A cesium film producing the maximum effect on electron emission \((\theta = 0.67)\) has a contact potential equal to \(+3.0\ \mathrm{V}\) relative to tungsten, while the heat of evaporation of the adatoms corresponds to \(1.9\) electron-volts. In the case of an oxygen film obtained by contact of a tungsten filament at \(1600^\circ\mathrm{K}\) with oxygen at low pressures, the contact potential relative to tungsten at a temperature of \(1600^\circ\mathrm{K}\) is equal to \(1.6\ \mathrm{V}\), but the heat of evaporation is approximately \(7\ \mathrm{V}\).

The adsorption of oxygen, hydrogen, and carbon monoxide by platinum\({}^{36}\) is also an example of adsorption depending on forces of principal valence.

Oil films on water. In these cases the attractive forces that cause the active heads of the molecules to spread over the surface are chiefly the dipole forces acting between the heads and the water molecules, with some participation of van der Waals forces. Above the heads lies the hydrocarbon phase, in which van der Waals forces and the repulsive forces acting between closed shells predominate.

Nonpolar gases on glass. The adsorption of such gases,

as nitrogen, argon, etc., with glass or mica at low temperatures is determined by typical van der Waals forces[^24].

Activated Adsorption

Owing to the existence of different types of adsorption, the same gas can be adsorbed by a given surface in several different ways. At sufficiently low temperatures, only van der Waals forces alone are sufficient for adsorption (van der Waals adsorption). At higher temperatures, molecules on the surface may undergo chemical changes and thus be held by valence forces. In such cases the heat of adsorption is much higher than that corresponding to van der Waals adsorption. The only reason why such adsorption does not occur at low temperatures is that, in this case, the rate of the chemical reaction may be too small. Since each such reaction is associated with an activation energy, Taylor[^34] proposed the term activated adsorption for adsorption connected with such chemical changes.

In some cases, as, for example, in the adsorption of cesium atoms on tungsten, adsorption is associated with the transfer of only one atom and therefore can occur at very low temperatures, so that there is no need for activation and only one type of adsorption is observed.

The distinction between van der Waals and activated adsorption was noted by the author in 1918 (ref. 24, pp. 1399–1400) and illustrated by examples of the adsorption of carbon monoxide and oxygen by platinum. At the temperature of liquid air and with a clean platinum surface in contact with carbon monoxide, at a pressure equal to 16 bars, the surface concentration \(\sigma\) of adsorbed carbon monoxide was equal to \(3.9 \cdot 10^{14}\) molecules cm\(^{-2}\), but upon gradual heating of the platinum to \(20^\circ\text{C}\), \(\sigma\) fell to \(1.4 \cdot 10^{14}\). We concluded that “at the temperature of liquid air platinum adsorbs carbon monoxide in approximately the same manner as glass, i.e., by means of secondary-valence forces. With a moderate rise in temperature this gas is liberated, but at approximately room temperature the reaction rate becomes sufficient for the reaction (principal valence) of platinum with carbon monoxide and the formation of a more strongly adsorbed film.”

In a discussion of the mechanism of hydrogen dissociation on tungsten filaments in 1916, the author[^7] considered the possibility of the existence of adsorbed hydrogen on the surface in two forms, and also that the rate of interaction between these two forms may determine the rate of production of atomic

hydrogen. The mathematical formulation then given is applicable to many cases of activated adsorption.

In recent years Taylor and his collaborators have discovered many cases of activated adsorption[^34] and have shown their great importance for understanding contact catalysis. The rate of the activation reaction was measured; it is very often low, even at temperatures of several hundred degrees, and the activation energy was calculated. Other investigators have tried to find an explanation for these slow surface reactions in the assumption that the adsorbed gas dissolves in the substance lying beneath it, or in its slow penetration into cracks or capillary spaces.

That this cannot be a general explanation has been proved by certain experiments[^35] which Dr. Blodgett and I carried out on the thermal accommodation coefficient of hydrogen in contact with tungsten. At temperatures from 200 to 600°K a stable adsorbed film of hydrogen is formed on tungsten, giving an accommodation coefficient \(\alpha\) approximately equal to 0.22. With increasing temperature this film slowly changes into a much more stable film, characterized by the value \(\alpha = 0.14\). The rate of the reaction is such that the formation of the stable film requires several minutes at 600°K and a small fraction of a second at 900°K, which indicates an activation energy of the order of at least 20 \(b.\) cal for each molecule. Since the accommodation coefficient is a purely surface property, these experiments prove that the hydrogen films are in both cases monatomic films, which in all probability represent two kinds of chemical bonding by valence forces. There is no doubt that at liquid-air temperatures a clean tungsten surface would also show van der Waals adsorption of hydrogen. This would thus be a third kind of hydrogen adsorbed film on tungsten.

Catalytic Action of Surfaces

A monatomic oxygen film on tungsten at 1500°K acts as a catalytic poison for all reactions which under other conditions would take place in contact with a tungsten surface[^15]. Thus, the dissociation of hydrogen into atoms at 1500°K is suspended in the presence of traces of oxygen, as is the decomposition of ammonia, methane, and cyanogen. The action of oxygen consists in covering the surface, so that another gas cannot come into contact with the tungsten surface.

In a similar way, hydrogen and carbon monoxide act as catalytic poisons on platinum surfaces[^36]. The rate of combination of carbon monoxide with oxygen in contact with platinum is directly proportional to the pressure of oxygen and inversely proportional to the pressure of carbon monoxide. The rate of the reaction depends on the fraction of the po-

of the platinum surface not covered by adsorbed carbon monoxide molecules. Oxygen molecules, which can be adsorbed on these free sites of the platinum surface, can thus react with adjacent adsorbed carbon monoxide molecules.

In numerous cases studied, the catalytic action of a surface on a gas reaction is caused precisely by such interaction between molecules adsorbed on neighboring elementary areas on the surface. On this basis one can develop\(^{7, 13, 36}\) a “law of mass action” for the rate of surface reactions, by means of which the observed reaction rates can be explained quantitatively. It has been noted\(^{15}\) that reactions of this kind depend extremely strongly on the actual distance between atoms on the surface of the catalyst. Thus, for many surfaces, we have only a comparatively small fraction of the surface on which the reaction can proceed with extraordinary rapidity, whereas over the greater part of the surface it proceeds at a negligible rate. Sherman and Eyring\(^{37}\) have recently given a quantum-mechanical explanation of the importance of distances between atoms in the catalyst.

The presence of a second layer of adsorbed atoms or molecules, even if it covers only an insignificant fraction of the surface, is often of great importance for the mechanism of gas reactions caused by a surface catalyst.

Thus, in the oxidation of a heated tungsten filament in oxygen at low pressures, with formation of \(WO_3\), the oxygen molecules striking the surface, already almost completely covered with a monatomic film of oxygen atoms, condense and for an instant exist in a second adsorbed layer (cf. 29, p. 473). Although the rate of evaporation from this second layer is so great that the surface concentration is very low, the adsorbed atoms or molecules of this layer move freely over the surface and thus fill holes in the first layer, formed by the evaporation of \(WO_3\) molecules, much sooner than would be possible under other conditions. These atoms of the second layer can also interact with atoms of the first layer and with the tungsten lying beneath them, forming \(WO_3\) molecules that leave the surface.

References

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