Activated Adsorption on Semiconductors

F. F. Vol’kenshtein

Introduction

The present article is devoted to several questions in the theory of adsorption. We shall be concerned with the mechanism of so-called “activated” adsorption.

Here we shall restrict ourselves to the qualitative side of the matter. The reader interested in the mathematical questions should turn to the original works cited in the text.

In the present article we consider systems that are, to a certain extent, simplified in comparison with those real systems with which the physicochemist deals in practical work. This is inevitable in constructing a quantitative theory. Here the investigator encounters a dilemma: either to remain within the circle of real systems and altogether renounce a quantitative theory, or to construct a theory on more or less schematized and simplified models.

However, even in the idealized cases considered in this article, the principal features of the phenomenon are revealed, and in the least veiled and complicated form. Disclosure of the physical nature of the phenomenon, of its elementary (microscopic) mechanism, is in general made possible only with a certain schematization of the problem.

First of all, it is necessary to define what is meant by “activated” adsorption and to formulate what, properly speaking, the task of the theory consists in. What should be required of a theory that claims to be called the “theory of activated adsorption”?

There exist, as is known, various types of adsorption. First of all, chemical adsorption must be distinguished from physical adsorption. On the other hand, so-called activated adsorption must be distinguished from ordinary nonactivated adsorption.

The terms chemical adsorption and activated adsorption are often identified. Let us note at once that there are insufficient grounds for this. Chemical adsorption and activated adsorption are, generally speaking, not one and the same thing.

1. PHYSICAL AND CHEMICAL ADSORPTION

Let us first of all dwell on the concepts of physical and chemical adsorption.

A molecule adsorbed on the surface of a solid body may be held on the surface by forces of various types.

These may be forces of electrostatic nature. These include van der Waals forces, forces of electrostatic polarization, and forces of electric image. In this case we speak of physical adsorption.

If, however, the forces responsible for adsorption are of a chemical nature (forces of the exchange type), then we are dealing with so-called chemical adsorption.

Chemical adsorption, in contrast to physical adsorption, is characterized by a considerably greater heat of adsorption and, at the same time, by a considerably smaller equilibrium distance (the distance between the adsorbed molecule and the surface of the adsorbent).

In theoretical consideration, physical and chemical adsorption require essentially different approaches to the problem.

In the case of physical adsorption, the adsorbed molecule and the adsorbent may be regarded as two independent systems. The action of the adsorbent on the adsorbate may be treated as a weak perturbation. The problem can be solved within the framework of perturbation theory.

In the case of chemical adsorption, the adsorbed molecule and the lattice form a single quantum-mechanical system. They must be considered as a whole. In this case adsorption is a chemical combination of the molecule with the crystal. The problem can no longer be solved by the methods of perturbation theory.

2. ACTIVATED ADSORPTION

Let us now turn to the concept of activated adsorption. We shall call by this name any adsorption that requires activation energy. Adsorption that proceeds without activation energy we shall call normal.

As has already been said, activated adsorption and chemical adsorption are not necessarily one and the same. The frequently observed confusion of these two terms should be regarded as incorrect.

Not every chemical adsorption is activated adsorption, i.e., requires activation energy. Chemical adsorption in some cases may also proceed without activation energy.

On the other hand, activated adsorption does not always indicate the chemical nature of the adsorption forces. The presence of an activation barrier is not a necessary indication of chemical adsorption. Such a barrier may occur in some cases also in physical adsorption1.

In other words, the absence or presence of an activation energy in adsorption by itself says nothing about the nature of the adsorption forces.

Activated adsorption differs from normal adsorption in the character of its kinetics.

In normal adsorption the rate of adsorption falls (and rather slowly) as the temperature is raised. The higher the temperature, the more slowly adsorption proceeds.

In the case of activated adsorption, on the contrary, the rate of adsorption rises sharply with temperature. Heating accelerates adsorption.

At the beginning of the adsorption process, so long as the surface coverage is small and desorption may be neglected in comparison with adsorption, we have for the rate of adsorption the following expression, obtained from elementary theory:

$$ \frac{dN}{dt} = N_0\eta\alpha p. \tag{1} $$

Here \(N\) is the number of adsorbed molecules, \(N_0\) is the number of adsorption centers (per unit surface), \(p\) is the gas pressure; the coefficient \(\alpha\) has the form

$$ \alpha = \frac{\sigma}{\sqrt{2\pi MkT}} = \frac{\alpha_0}{\sqrt{kT}}, \tag{2} $$

where \(M\) is the mass of the adsorbed molecule, \(\sigma\) is its effective cross section, \(T\) is the absolute temperature, and \(k\) is Boltzmann’s constant.

The factor \(\eta\) in (1) is the probability that a gas molecule, arriving from the gas at an adsorption center on the surface, will become fixed on it.

Normal and activated adsorption differ in the form of the coefficient \(\eta\) in formula (1).

In normal adsorption the coefficient \(\eta\) is regarded as constant (not depending on temperature). It is usually assumed that

$$ \eta = 1. $$

In the case of activated adsorption, however, we have:

$$ \eta = e^{-\varepsilon/kT}, \tag{3} $$

where \(\varepsilon\) is the activation energy.

The appearance of the exponential factor (3) is characteristic of activated adsorption.

It is precisely the presence of such an exponential factor in the kinetic formula (1), and not ideas about one or another nature of the adsorption forces, that is the criterion of so-called activated adsorption.

To explain the origin of this factor—this is the task of the theory of activated adsorption.

How, then, is the origin of this multiplier usually explained? Usually it is explained by introducing the concept of a potential barrier on the adsorption curve.

In Fig. 1, adsorption curves are shown schematically, expressing the energy of the system \(W\) as a function of the distance \(r\) between the surface and the adsorbed molecule.

Fig. 1, \(a\) refers to normal adsorption. Fig. 1, \(b\) corresponds to activated adsorption. The height of the barrier is the activation energy \(\varepsilon\).

The role of the barrier amounts to this: it blocks access to the surface for all molecules whose energy is sufficiently small. Only those gas molecules incident on the surface are adsorbed whose kinetic energy (in the direction normal to the surface) exceeds the height of the barrier.

Fig. 1.

There arises, however, the question: what is the origin of the potential barrier on the adsorption curve?

The appearance of such a barrier may be caused by various reasons.

Thus, for example, an activation barrier arises in the case when adsorption of a gas molecule is accompanied by its dissociation into separate atoms or radicals. This was shown by Lennard-Jones\(^2\).

The barrier may also arise for other reasons.

Let us note, however, that the concept of a potential barrier on the adsorption curve, blocking access of slow molecules to the surface, is not indispensable for explaining activated adsorption.

A theory of activated adsorption can also be constructed without the concept of a potential barrier. The appearance of the multiplier (3) in the kinetic formula (1) may be due to certain specific properties of the adsorption centers themselves. We shall see this below.

We shall not construct any hypotheses about the origin of the exponential multiplier (3). We shall pose the problem differently. Bu-

thereby investigating, without predetermining the results, the mechanism of chemical adsorption.

If, as a result of solving this problem, the exponential factor (3) appears in the kinetic formula (1), then this will only mean that we have entered the region of activated adsorption.

We shall see that in certain cases this will indeed be so.

3. CHEMICAL ADSORPTION AS A ONE-ELECTRON BOND

In order to simplify the calculation (and to make it possible), it is necessary to choose the system in an appropriate way.

We shall consider a monovalent atom as the adsorbate. We shall denote it by the symbol \(A\). As the adsorbent we shall consider an ionic crystal constructed of singly charged ions \(M^{+}\) and \(R^{-}\) (\(M\) is the symbol of a metal, \(R\) the symbol of a metalloid). These ions will be treated as point charges.

In such a model we are dealing with a one-electron problem. The single electron is the valence electron of the atom \(A\).

As long as the atom \(A\) is sufficiently far from the surface of the crystal, our electron is the property of this atom (Fig. 2, \(a\)).

If, however, the atom \(A\) is placed on the surface, then its electron no longer belongs to it alone. Strictly speaking, it belongs to the whole system as a whole.

The calculation shows\(^{3}\) that the valence electron of the atom \(A\) is thereby drawn, to a greater or lesser degree, from the atom \(A\) into the lattice. In other words, the electron cloud surrounding the positive core of the atom \(A\) and possessing, in the case of an isolated atom, spherical symmetry, now proves to be deformed and to some extent drawn into the lattice.

Fig. 2.

This drawing of the electron cloud into the lattice is what gives rise to the bond between the adsorbed atom \(A\) and the crystal. Thus, the bond is formed at the expense of the valence electron of the atom \(A\). We obtain a bond of the same type as in the molecular ion \(H_2^{+}\). It is a one-electron bond (Fig. 2, \(b\)).

It can be shown that the strength of the bond of atom \(A\) with the surface depends on how strongly the valence electron of atom \(A\) is drawn into the lattice. The stronger the attraction, the stronger the bond.

What, then, determines the degree of attraction? It is determined by the nature of atom \(A\) and by the nature of the lattice.

Other conditions being equal, it depends on how different the ionization potentials are of the adsorbed atom \(A\) and of the metallic atom \(M\) that forms part of the lattice (what is meant is the ionization potential of atom \(M\) taken in the isolated state).

In some cases such a one-electron bond with the lattice proves to be very weak.

Let us ask: what will happen in this case, i.e., in the case when the one-electron bond is so weak that adsorption due to such a bond practically does not take place?

In this case the free electrons of the crystalline lattice itself may come to the rescue, those free electrons which form the electron gas that is necessarily present, in one concentration or another, in every crystal. We are speaking of electrons moving in the so-called surface conduction band. In other words, we are speaking of a two-dimensional electron gas on the surface of the crystal.

The concentration of this gas increases sharply with temperature. It can be artificially changed (increased or decreased) by acting in one way or another on the crystal: for example, by introducing foreign impurities into the crystal, by creating in it certain microscopic defects, or by subjecting it to illumination.

The presence of such free electrons on the surface of the crystal was ignored in the preceding calculation. Nevertheless, these electrons, belonging to the domain of the lattice itself, play their role in the phenomena of adsorption.

Their role proves decisive in those cases when one-electron adsorption practically does not occur because of the weak one-electron bond. In this case adsorption can take place only through the participation of a free electron of the lattice itself.

4. CHEMICAL ADSORPTION AS A TWO-ELECTRON BOND

Let us once again consider the same model with which we dealt in the preceding calculation: a monovalent atom \(A\) and a crystalline lattice built of ions \(M^{+}\) and \(R^{-}\), which we treat as point charges. Let us now suppose that there is a free electron on the surface of the crystal.

We now have a two-electron problem: the first electron is the valence electron of atom \(A\); the second electron is a free electron belonging to the lattice.

What does it mean for there to be a free electron on the surface of a crystal? What does it mean when we say that an electron is contained in the surface conduction band?

It means that an electron sits on one of the surface ions \(M+\). In other words, it means that one of the ions \(M+\) of the surface layer of the lattice has been neutralized (turned into a neutral atom \(M\)) (Fig. 2, в).

When we say that a free electron moves in the surface conduction band, this means that the electron jumps from one ion \(M+\) to a neighboring ion \(M+\) of the surface layer of the lattice and thus wanders over the surface of the crystal. In other words, this means that the neutral state of the atom \(M\) wanders over the surface, being transferred from one ion \(M+\) to the neighboring ion \(M+\).

Fig. 3.

Let us imagine that atom \(A\), together with its valence electron, is brought close to the surface of the crystal. The question is how the second electron (the free electron of the lattice) will behave in this case.

It can be shown\(^5\) that atom \(A\), when placed on the surface of the crystal, creates for the free electron of the lattice a local level. This level lies below the surface conduction band, as shown in Fig. 3. It plays the role of a “sticking” level for the free electron.

The free electron may then either remain in the conduction band or fall out of the conduction band onto the local level.

In the first case, when the lattice electron continues to remain free, no bond is formed between atom \(A\) and the crystal. Atom \(A\) will not be retained on the surface. (We are now ignoring the one-electron bond due to the valence electron of atom \(A\). In other words, we are considering the case in which such a one-electron bond is so weak that it may be neglected altogether.)

If, however, the lattice electron falls out of the conduction band onto the local level (as is shown schematically by the heavy arrow in Fig. 3), this means that the electron ceases to be free and becomes localized on the surface of the crystal near the place where atom \(A\) sits. Atom \(A\) thus plays the role of a “trap” for the free electron.

At the same time, between atom \(A\) and the lattice there is formed, as can be shown, a rather strong two-electron bond. Two electrons participate in this bond: the valence electron of atom \(A\) and the electron

of the crystal lattice itself, borrowed from the family of free electrons.

The lattice electron and atom \(A\) are then bound by exchange forces. These exchange forces are, in the present case, the adsorption forces holding atom \(A\) on the surface and, at the same time, holding the lattice electron near atom \(A\). We obtain a bond of the same type as in the \(H_2\) molecule. The spins of both electrons participating in the game are antiparallel.

The strength of the bond depends on how deeply beneath the conduction band the local level \(A\) is situated. The lower the level is situated (the greater \(v\) in Fig. 3, \(a\)), the stronger the bond and the stronger the localization of the lattice electron.

Other things being equal, the position of the local level depends on the distance between atom \(A\) and the surface of the crystal. As atom \(A\) moves away, the local level in Fig. 3 is pulled up toward the band (\(v\) decreases); the exchange bond of atom \(A\) with the lattice is thereby weakened, and the lattice electron sitting on level \(A\) is gradually delocalized (i.e., its wave function becomes more and more smeared out).

In the limit, when atom \(A\) is infinitely removed from the surface, the local level is drawn into the band. The electron sitting on it is thus raised into the conduction band, i.e., completely delocalized, and thereby returned to the family of free electrons.

All this can be retold in the pictorial language of models. Let us imagine that atom \(A\) falls onto the surface of the crystal, as shown in Fig. 2, \(a\). A free lattice electron remains aside, without entering into a bond with atom \(A\). In this case adsorption does not occur.

Let us now imagine that atom \(A\), falling onto the surface, meets a free lattice electron, as depicted in Fig. 2, \(c\). In this case the atom binds with the lattice electron and becomes adsorbed. Atom \(A\) is fixed on the surface, while the free lattice electron is fixed near the atom. We obtain a two-electron bond (see Fig. 2, \(d\)).

5. ADSORPTION CENTERS

Thus, a free lattice electron acts as an adsorption center. Otherwise, the adsorption center is a neutral atom \(M\), present among the ions \(M^+\) of the surface layer.

The adsorption of atom \(A\) on such a center leads to the localization of this “wandering” center and means the formation of a quasimolecule \(AM\) with the two-electron bond characteristic of it.

In other words, an electron in the surface conduction band may be treated as a free (unsaturated) valence,

Indeed, the ion \(M^+\) has a closed electron shell, whereas the atom \(M\) contains, in addition to the closed shell, one unpaired electron.

On the other hand, the monovalent electropositive atom \(A\) also has one unpaired electron, i.e., an unsaturated valence. Adsorption is a process leading to the saturation of valences.

This mechanism, quantitatively calculated for a monovalent electropositive atom \(A\), can be generalized to the case of any atom or molecule.

If a molecule possesses an unsaturated valence (for example, is a radical), then this valence is saturated as a result of adsorption. A saturated bond with the surface is formed by attracting a free electron of the lattice. This is shown in Fig. 4, \(a\).

Fig. 4.

Before adsorption  Adsorption

If, however, all bonds in the molecule are saturated, then upon adsorption of such a molecule one bond within it is broken. Here we have a switching of bonds. Indeed, an additional ...

electron (a free electron of the lattice), representing a free valence (and for precisely this reason playing the role of an adsorption center).

A rupture of valence within a molecule leads to dissociation of the molecule, as shown in Fig. 4, b, or to a weakening of the bonds between individual atoms (or groups of atoms) that make up the molecule, as shown in Fig. 4, c.

In the first case (Fig. 4, b), as a result of adsorption the gas phase is enriched with radicals (atoms or molecules with unsaturated valences), which can react with one another or bind to the surface.

In the second case (Fig. 4, c) a molecule which, in the free state, possessed saturated valences, in the adsorbed state acquires a free valence (becomes reactive).

In both cases, of course, one valence, which remained unsaturated before adsorption, remains unsaturated after the act of adsorption as well. The adsorption reaction amounts to the fact that this free valence is transferred from one atom to another atom (or group of atoms) participating in the process.

The presence of such a free valence on the surface of the crystal is a necessary (though not always sufficient) condition for the adsorption reaction to proceed. As we have seen, the role of this free valence is performed by a lattice electron (an electron belonging to the surface conduction band).

6. PROPERTIES OF ADSORPTION CENTERS

The conception of adsorption centers as free electrons of the crystal compels us to ascribe to these centers a number of specific properties. Let us enumerate some of these properties:

1) Free adsorption centers are not localized on the surface of the crystal, but wander over the surface.

When, however, an adsorption center takes on a gas molecule, it becomes fixed on the surface. Adsorption at an adsorption center leads to localization of this center.

2) The number of adsorption centers does not remain constant, but increases as the temperature is raised. This, as we shall see below, is reflected both in the kinetics of adsorption and in the adsorption equilibrium.

3) By acting on the lattice with external factors, one can artificially change the concentration of adsorption centers.

Thus, introducing into the crystal a foreign impurity of donor type increases the concentration of adsorption centers, whereas an impurity of acceptor type decreases this concentration.

The concentration of adsorption centers may also be increased by illuminating the surface with light of the corresponding frequencies.

This leads to the fact that the adsorption capacity turns out to depend on extraneous impurity in the crystal, and also may change under the action of illumination.

The concentration of the electron gas in the lattice of an ionic crystal under ordinary conditions is very small. In other words, the concentration of adsorption centers on the surface of the crystal should be considered negligibly small.

Hence, it would seem, the surface can take up only a negligible number of gas molecules (a very small coverage of the surface).

This, however, is not so. It can easily be shown5 that, as the surface is filled, ever new adsorption centers arise. The supply of free adsorption centers is exhausted very slowly owing to the appearance of new centers on the surface. Therefore the number of adsorbed molecules may substantially exceed the initial number of adsorption centers.

Let us denote by \(N\) the number of adsorbed molecules (per unit surface), by \(n\) the concentration of free electrons in the surface conduction band, and by \(n'\) the concentration of free holes in the surface normal band.

If the surface of the crystal is regarded as ideal (i.e., devoid of any structural defects) and electrically neutral, then

\[ n'=n+N. \]

This condition is the condition of charge conservation.

It can be shown that under equilibrium conditions we shall have:

\[ \left. \begin{aligned} n&=\frac{1}{2}\left\{\sqrt{N^{2}+4n_{0}^{2}}-N\right\},\\ n'&=\frac{1}{2}\left\{\sqrt{N^{2}+4n_{0}^{2}}+N\right\}, \end{aligned} \right\} \tag{4} \]

where \(n_{0}\) is the concentration of the electron (or hole) gas in the case of a clean surface (i.e., in the absence of adsorbed molecules on the surface, when \(N=0\)).

Obviously, \(n_{0}\) increases exponentially with temperature. We have for \(n_{0}\):

\[ n_{0}=C_{0}kT e^{-\frac{u}{2kT}}, \tag{5} \]

where \(u\) is the width of the forbidden interval between the surface normal band and the surface conduction band. In other words, \(u\) is the work of formation, on the surface of the crystal, of a pair: free electron + free hole.

Formulas (4) give the dependence of the equilibrium concentrations of the electron and hole gases on the number of molecules adsorbed on the surface.

Obviously, \(n\) is at the same time the number of free adsorption centers, and \(n'\) is the total number of adsorption centers (free + occupied) per unit surface area.

The dependences \(n = n(N)\) and \(n' = n'(N)\) are shown in Fig. 5 (the lower and upper curves, respectively). We see that the total number of adsorption centers \(n'\) increases as the surface is filled, i.e., as \(N\) grows, while the number of free centers \(n\) slowly decreases. Thus, on the surface there is always a certain reserve of free adsorption centers capable of accepting gas molecules.

Fig. 5.

The dotted straight line in Fig. 5 expresses the law of decrease of the number of free adsorption centers with filling according to the usual theory, in which the total number of centers is assumed constant. Adsorption ceases when all centers are occupied \((N = n_0)\).

In our case, however, as we see, the number of adsorbed molecules \(N\) can substantially exceed the initial number of adsorption centers \(n_0\).

7. DIFFERENTIAL HEAT OF ADSORPTION

The concentration of adsorption centers, as we see, changes with filling. As a consequence, the differential heat of adsorption, which we shall denote by \(Q\), also turns out to depend on the filling, i.e., on \(N\).

By definition, the differential heat of adsorption is the derivative (taken with the opposite sign) of the total energy of the system \(W\) with respect to \(N\):

\[ Q = -\frac{dW}{dN}. \tag{6} \]

The creation of each adsorption center requires an expenditure of energy \(u\); on the other hand, when each gas molecule is bound to an adsorption center, an energy \(q\) is released. Thus, taking as zero the energy of the system in the absence of adsorbed molecules, we shall have:

\[ W = u(n' - n_0) - qN. \]

Substituting here (4), we shall have, according to (6):

\[ Q = q - \frac{u}{2}\left\{1 + \frac{N}{\sqrt{N^2 + 4n_0^2}}\right\}. \tag{7} \]

The dependence of \(Q\) on \(N\) (according to formula (7)) is shown in Fig. 6. We see that the differential heat of adsorption decreases as the surface is filled.

The decrease of the differential heat with filling is often observed in reality. This fact does not fit into the elementary Langmuir theory of adsorption.

It is usually explained by introducing the notion of heterogeneity of the adsorbent surface or of repulsive forces between adsorbed molecules.

In our case the surface is assumed to be homogeneous (adsorption centers of only one kind!) and the interaction between molecules is ignored. The dependence of \(Q\) on \(N\) in the case considered by us is due to the fact that the total number of adsorption centers \(n'\) does not remain constant, but increases as \(N\) increases. The adsorption centers on the surface of the crystal are treated as a kind of two-dimensional gas, whose concentration increases together with the increase of \(N\), and whose change in energy is taken into account in calculating the differential heat of adsorption.

Fig. 6.

We see that taking account of surface heterogeneity or taking account of repulsive forces between adsorbed molecules are not the only possible causes determining the dependence of \(Q\) on \(N\), as is usually believed.

8. KINETICS OF ADSORPTION

Let us now turn to the kinetics of adsorption.

We shall neglect desorption in comparison with adsorption. This can be done as long as the filling of the surface is small, i.e., at the beginning of the adsorption process. Under this condition we return to formula (1).

Let us put \(\eta = 1\) in this formula, which means the absence of a potential barrier on the adsorption curve (see Fig. 1, a). In formula (1), \(N_0\) is the concentration of adsorption centers. We must put \(N_0 = n\), where \(n\) is the concentration of free electrons in the surface conduction band. Formula (1) can then be rewritten in the following form:

\[ \frac{dN}{dt} = n a p . \tag{8} \]

If adsorption proceeds sufficiently slowly, while electronic equilibrium in the lattice is established sufficiently rapidly, so that electronic equilibrium may be regarded as being maintained at any moment during the adsorption process, then \(n\) is a function of \(N\) according to (4).

Substituting (5) into (4), and then (4) into (8), and integrating, we obtain:

\[ N= \begin{cases} C_0\sqrt{kT}\,e^{-\frac{u}{2kT}}a_0pt, & \text{for } N\ll 2n_0,\\[6pt] C_0(kT)^{1/4}e^{-\frac{u}{2kT}}\sqrt{2a_0pt}, & \text{for } N\gg 2n_0. \end{cases} \tag{9} \]

For not very small coverages (when \(N\gg 2n_0\)) we thus arrive at the Benkhem law (with exponent \(1/2\)), which is often observed in reality and is usually regarded as evidence of surface inhomogeneity. (In our case the surface is homogeneous!)

We see (cf. (9)) that heating does not retard, but, on the contrary, substantially accelerates the adsorption process. We obtain kinetics typical of so-called activated adsorption with activation energy \(\varepsilon=\frac{1}{2}u\).*)

The appearance of the exponential factor (3) in the kinetic formulas (9) is due not to a potential barrier on the adsorption curve (which is absent), but is connected with the fact that the concentration of adsorption centers increases exponentially with temperature.

In the usual theories of activated adsorption, which deal with a potential barrier near the surface of the crystal, the number of gas molecules striking the surface increases proportionally to the factor (3), whereas the number of adsorption centers accepting these molecules remains unchanged.

In our case, on the contrary, the number of accepting centers increases with temperature proportionally to the factor (3), whereas the number of incident molecules remains practically constant.

9. ADSORPTION ISOTHERM

In the case of adsorption equilibrium we have:

\[ \begin{gathered} N_0\eta ap=\beta N,\\ \text{where}\\ \beta=\beta_0e^{-\frac{q}{kT}}. \end{gathered} \tag{10} \]

*) If, in addition to the two-electron bond, one takes into account the one-electron bond, i.e. carries out the calculation in a better approximation, then for the activation energy we obtain \(\varepsilon=\frac{1}{2}(u-v)\).

The term on the left-hand side of equation (10) represents the number of molecules adsorbed per unit time on a unit surface. The term on the right-hand side of (10) is the number of molecules desorbed per unit time from a unit surface.

Putting in (10) \(N_0=n\) and \(\gamma=1\), we shall have:

\[ N=n\frac{\alpha}{\beta}p, \tag{11} \]

whence, substituting (4) into (11) and solving (11) with respect to \(N\):

\[ \left. \begin{array}{ll} N=n_0\dfrac{\alpha}{\beta}p & \text{for } N \ll 2n_0,\\[6pt] N=n_0\sqrt{\dfrac{\alpha}{\beta}p} & \text{for } N \gg 2n_0. \end{array} \right\} \tag{12} \]

We thus obtain the Henry isotherm, which, upon further filling of the surface, passes into the Freundlich isotherm with exponent \(1/2\).

Let us note that the Freundlich isotherm, which is often observed experimentally, is usually regarded as evidence of surface inhomogeneity, or as evidence of the presence of repulsive forces between adsorbed molecules. The Freundlich isotherm with exponent \(1/2\) can also be obtained, as is known, from the assumption that the adsorbing molecule dissociates at the moment of adsorption.

In our case, however, the surface is assumed to be homogeneous, interaction between adsorbed molecules is ignored, and the possibility of dissociation during adsorption is not taken into account.

The law \(N\sim\sqrt{p}\) has an entirely different origin here. It is due to the increase in the number of adsorption centers that occurs as the surface is filled.

10. THE INFLUENCE OF ILLUMINATION ON ADSORPTION

Let us now consider the influence of illumination on adsorption.

Suppose that the crystal is illuminated by light of such frequencies as transfer electrons from the surface normal band into the surface conduction band. The light thereby creates additional adsorption centers.

By maintaining the illumination, we thereby maintain an increased concentration of adsorption centers on the surface of the crystal. In this way, illumination of the crystal will affect both the adsorption equilibrium and the kinetics of adsorption.

It can be shown\(^6\) that illumination should increase the adsorption capacity of the crystal.

A similar effect has been observed by many authors. For example, by Kurbatov\(^7\), Lux, Bodart, and Rensom\(^8\), Hedvall and Nord\(^9\),

which studied the adsorption of various molecules on various semiconductors. Upon illumination, a significant increase in the adsorptive capacity of the adsorbent was observed, as was revealed by a fall of the pressure in the adsorption volume.

Usually this effect is explained on the basis of the assumption of the dissociation of adsorbed molecules under the action of light (photodissociation).

In our case this effect is not connected with the dissociation mechanism. It is caused by an increase in the number of adsorption centers under the influence of illumination.

It is noteworthy, as follows from the experiments of Hudgell and Nord, that the increase in adsorptive capacity is observed upon illumination precisely by those frequencies which are photoelectrically active. The maximum sensitivity with respect to adsorption properties coincides with the maximum of the internal photoeffect.

From the standpoint of the theory of photodissociation this circumstance remains incomprehensible.

If the role of illumination reduces to photodissociation of adsorbed molecules, then illumination should not affect the kinetics of adsorption. It can affect only the equilibrium.

According to our mechanism, however, an effect on the kinetics should occur. Illumination should lead to an acceleration of adsorption.

It would be of interest to investigate experimentally the influence of illumination not on the equilibrium, but on the kinetics of adsorption. This, as far as the author knows, has not yet been done.

11. THE ROLE OF IMPURITIES IN ADSORPTION

Until now we have regarded the crystal lattice as ideal, i.e., as devoid of any defects or impurities.

Let us now consider the case in which the adsorbing crystal contains a foreign impurity on its surface.

The introduction of an impurity changes the concentration of electron and hole gas in the crystal; in other words, it changes the concentration of adsorption centers. Thus the impurity influences both the kinetics of adsorption and the adsorption equilibrium.

Here one must distinguish impurities of the acceptor and donor types. Impurities of these two different types play opposite roles.

An acceptor impurity decreases the concentration of electron gas and increases the concentration of hole gas. A donor impurity acts in the opposite way.

It can be shown that an acceptor impurity retards adsorption, whereas a donor impurity accelerates adsorption. In this case the kinetic law remains the same.

L. Ya. Margolis \(^{10}\) came to a similar conclusion on the basis of her experiments. She investigated the adsorption of oxygen

on magnesium chromite. The introduction of SiO$_2$ additives decreased the rate of adsorption, but did not change the kinetic law. (Margolis’ data fit the Benham law with an exponent close to ${}^{1}/_{2}$.)

Let us now turn to equilibrium.

An acceptor-type impurity should decrease the adsorption capacity of the crystal. A donor impurity, on the contrary, should lead to an increase in the adsorption capacity.

This is in agreement with the observations of Hdwalla and Nord$^{9}$. These authors investigated the adsorption capacity of various HgS samples differing in stoichiometric composition. They found that the adsorption capacity of the crystal (other conditions being equal) is the greater, the more strongly its stoichiometry is disturbed (the more excess stoichiometric metal it contains).

The influence of impurities on the adsorption capacity was also noted by Luiks, Bodart, and Rens$^{8}$.

It would be of interest to investigate experimentally the influence of impurities on the basic regularities of activated adsorption. Possibly this could provide a key to understanding the phenomenon of catalyst modification.

CONCLUSION

In conclusion it should be noted that the electronic mechanism of activated adsorption considered in this article is, of course, not the only possible mechanism of activated adsorption.

In particular, this mechanism, developed here as applied to adsorbents that are ionic crystals, cannot be directly transferred to metals.

In general, it seems unlikely that everything we group under the name “activated adsorption” would always be governed by one and the same universal mechanism, operating everywhere and in all cases.

In the complex and intricate phenomena of adsorption, the electronic mechanism may find its place among other possible and actually operating mechanisms.

There is also no doubt that conditions are possible under which precisely the electronic mechanism may prove to be the leading one and may determine the basic regularities of adsorption.

In the present article a system has been considered that is to a certain extent schematized, representing an idealization of what the physical chemist actually deals with.

However, the essential aspect of the matter, the mechanism of the phenomenon, is manifested most clearly precisely in schematized models, which alone can be calculated quantitatively.

The essence of the matter lies in those fundamentally new ideas and concepts to which we come in the theory of adsorption as a result of the quantum-mechanical formulation of the problem.

References

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