INVESTIGATION OF THE HYDROGEN BOND BY SPECTROSCOPIC METHODS

V. I. Malyshev

INTRODUCTION

Very soon after the discovery of the combination scattering of light and the study of the basic laws of this phenomenon, G. S. Landsberg began to regard this new phenomenon as a method of investigation that made it possible to solve various physical and chemical problems. In his article “Combination Scattering of Light and Its Significance for Chemical Problems,” published in 1932 in the journal Uspekhi Khimii[^1], G. S. Landsberg, along with questions connected with the determination of the natural vibrations and the study of molecular structure, also points out the possibility of applying combination scattering of light to the study of intermolecular interactions. He writes that, when the aggregate state changes, “a certain broadening of lines was found in condensed phases, occurring, probably, as a result of intermolecular interactions.” And further: “the possibility is not excluded of applying the method described (the method of combination scattering.—V. M.) to the investigation of the question of the association of dipole molecules.”

Already in one of the first experimental works, carried out in 1934 under the direction of G. S. Landsberg, the method of combination scattering was applied precisely for the purpose of studying the phenomena of association of dipole molecules in solutions.

Beginning in 1932 and up to the last days of his life, G. S. Landsberg attached very great importance to the question of studying intermolecular interactions by spectroscopic methods, and a large part of Grigorii Samuilovich’s many years of work was devoted to experimental investigations in this direction. Moreover, in the first works of G. S. Landsberg and his pupils on the investigation of intermolecular interactions, the method of combination scattering was used chiefly, while in recent times the method of infrared absorption has also been brought to bear on these investigations; in a number of cases it has considerable advantages.

The results of these extensive and systematic investigations by G. S. Landsberg and his pupils are a valuable contribution to the study of intermolecular forces and especially to the study of the hydrogen bond.

The present article sets itself the task of giving a review of the principal works carried out by G. S. Landsberg, his pupils, and his collaborators in the direction of studying intermolecular interactions by spectroscopic methods, without, however, claiming to cover completely all the questions touched upon or to systematize all the literature.

The essence of spectroscopic methods for investigating intermolecular interactions is as follows.

As is known, the frequencies of intramolecular vibrations observed in the spectra of combination scattering and infrared absorption are determined by the masses of the atoms and by intramolecular forces, i.e., by those forces which bind the individual atoms in a molecule. Intermolecular forces acting between molecules can also exert some perturbation on the interacting molecules themselves, deforming them, altering the intramolecular forces, etc. In the general case this perturbation can change the frequency of the proper vibrations of the molecules, cause broadening of the infrared absorption lines or of the lines of combination scattering, and can also change the transition probabilities, which may be manifested in changes in the intensities of lines or in the appearance of new lines. In addition, intermolecular forces can lead to the formation of certain molecular complexes or of a quasi-crystalline structure, as a result of which the possibility arises of the appearance of new low-frequency intermolecular vibrations.

It should be noted that the study of changes occurring in the vibrational spectra of molecules when the concentration of a solution is changed or when the nature of the solvent is changed, and in the case of gases when the pressure is changed, is not only of purely physical interest, but is also extremely important for carrying out quantitative analytical work. In the presence of deviations from the linear dependence of the intensity of combination-scattering lines or of the optical density in infrared absorption spectra on concentration, the performance of quantitative analyses is considerably complicated and is possible only with the aid of calibration curves constructed from standard mixtures.

In the case of ordinary intermolecular forces—van der Waals forces, whose magnitude is much smaller than that of intramolecular forces—these perturbations are small, and therefore the changes in frequencies should likewise be insignificant. However, experimentally these changes in frequencies have been observed in many cases, especially when the state of aggregation is changed: the spectra of solids and liquids often differ noticeably from the spectra of the corresponding gases at low pressures. Changes are also observed in the spectra of some substances when they are dissolved in various solvents.

Unfortunately, many of the published works devoted to the investigation of intermolecular forces by spectroscopic methods, and especially the early works (see, for example, the reviews \(^{4,5,1}\)), do not have the character of systematic investigations, and in a number of cases merely state the fact that changes occur in the spectra when the state of aggregation is changed or upon dissolution.

In this respect, the only works that stand apart are those of Welsh and co-workers \(^{6-9}\), who systematically investigated the influence of a foreign gas at high pressures on the infrared absorption bands of a number of substances. The authors attempt to explain the observed phenomena from the standpoint of the induction interaction of molecules.

Also favorably distinguished from the majority of published works are those of G. S. Landsberg and his co-workers on the investigation of the spectra of combination scattering of solids, liquids, solutions, and vapors. These works showed that the proper choice of objects of investigation (from the point of view of the physical problem posed) and the conduct of comprehensive and systematic investigations under various conditions make it possible to draw far-reaching conclusions concerning the mechanism of the hydrogen bond, which is a special type of intermolecular force.

§ 1. HYDROGEN BONDING AND ITS SPECTROSCOPIC MANIFESTATIONS

Among substances in which a change in the frequencies of intramolecular vibrations is observed upon a change in the state of aggregation, a special place is occupied by substances whose molecules contain the hydroxyl group, O—H. These include water, alcohols, phenols, glycols, etc. In these substances, upon transition from the vapor phase to the condensed phase, sharp changes are observed in the frequency of the stretching vibration of the O—H group. These changes in the frequency of the O—H group are observed both in combination-scattering spectra and in infrared absorption spectra in the region of the fundamental tone and overtones. Thus, for example, the vibration of the O—H group in the combination-scattering spectrum of liquid water is characterized by a broad, smeared-out band about 400 cm\(^{-1}\) wide, with a maximum near 3460 cm\(^{-1}\). In the spectrum of water vapor, however, a narrow line of frequency \(\nu = 3654\) cm\(^{-1}\) is observed. Thus, the line is shifted relative to the maximum of the band by approximately 200 cm\(^{-1}\), which amounts to about 6%. Analogous phenomena are also observed for other substances containing the O—H group. It should be noted that in these substances, upon transition from the vapor phase to the liquid phase, such considerable changes in the frequencies of intramolecular vibrations are observed only for the frequency of the O—H group, whereas other frequencies, for example CH\(_2\) and CH\(_3\) in alcohols, practically do not change. From this fact one may conclude that the vibration of the O—H group is most sensitive to external intermolecular interactions and therefore can be used as an indicator of these interactions.

On the other hand, it is known (see, for example,\(^{2,3,5}\)) that substances containing the O—H group possess a number of anomalous properties: increased values of the measured molecular weight in comparison with the chemical formula, increased values of the melting and boiling temperatures, violation of Debye’s relation connecting the dielectric constant and the dipole moment of molecules, etc. These anomalies can be explained if it is assumed that relatively large intermolecular forces act between molecules containing the O—H group, leading to association of the molecules into complexes. Estimates of the magnitude of the energy necessary to break these complexes, made by various physicochemical and spectroscopic methods, give values for it from 4 to 8 kcal/mole. The magnitude of this energy is, of course, small in comparison with the energy of intramolecular bonds, which is on the average about 100 kcal/mole, but it is several times greater than the energy of ordinary van der Waals interaction, which amounts to 1–2 kcal/mole.

Thus, the sharp change in the frequency of the O—H group, manifested in a considerable shift and broadening of the line, simultaneously indicates the presence of a relatively large interaction between molecules containing the O—H group, the relatively great sensitivity of the O—H group to these interactions, and, finally, the fact that this interaction is connected with the presence of hydroxyl groups in the molecules and is realized through the interaction of these groups.

This special type of intermolecular interaction is called the hydrogen bond.

It should be noted that a hydrogen bond is formed not only between molecules containing O—H groups, but also between molecules containing F—H, N—H groups, and sometimes S—H groups\(^{2}\). And, finally, it should be pointed out that a hydrogen bond may also form between molecules of different nature, if one of the molecules contains one of the indicated groups, while the other molecule contains an oxygen atom or

nitrogen. In addition, a hydrogen bond may be formed not only between separate molecules, but also within a single molecule, if this molecule contains the groups of atoms necessary for the formation of such a bond. Therefore intermolecular and intramolecular hydrogen bonds are distinguished. The class of substances in which the formation of a hydrogen bond can occur is fairly large, and therefore its study is of great interest.

The study of the hydrogen bond can be carried out by various physical and chemical methods (see, for example, ^2). However, spectroscopic methods of investigation have a number of advantages, since they make it possible to observe a number of details inaccessible to other methods.

As has already been indicated, the hydrogen bond that leads to association of molecules causes a noticeable perturbation of the vibration of the O—H group, manifested in a shift and broadening of the frequency of this vibration. Consequently, these changes in frequency, as compared with the frequency of the O—H group of isolated molecules, are spectroscopic indications of the hydrogen bond. Since these spectroscopic indications appear both in combination-scattering spectra and in infrared absorption spectra, both methods can be used for the study of the hydrogen bond.

The number of works devoted to the study of the hydrogen bond by spectroscopic methods, and especially by infrared-absorption methods, is very large. Without setting ourselves the goal of a detailed examination of these works, as well as of works concerning the theory of the hydrogen bond, in what follows we shall confine ourselves mainly to a review of the experimental works of G. S. Landsberg and his school *).

§ 2. INVESTIGATION OF THE INFLUENCE OF DENSITY AND TEMPERATURE ON THE VIBRATION OF THE O—H GROUP

In the works of G. S. Landsberg and S. A. Ukholin ^12,^13,^14, the change in the frequency of the lines of combination scattering of the O—H group of water and methyl alcohol was investigated under a gradual increase in the temperature of the liquid, i.e., under a gradual increase in the mean distance between molecules caused by a decrease in density upon heating. These works were not limited merely to the investigation of the spectra of combination scattering of the liquid phase; the task was set of tracing the change in the frequency of the O—H group in the transition from the liquid state to the gaseous state through the critical point. Despite the great experimental difficulties associated with the low intensity of the spectra, with high pressures and high temperature, the authors succeeded in carrying out this work successfully.

The results obtained by them may be briefly formulated as follows. As the mean distance between molecules increases, caused by a decrease in density, the broad band characterizing associated molecules shifts toward higher frequencies and at the same time narrows. In water, the narrowing of the band is more considerable than in methyl alcohol, which, in the opinion of the authors (see also ^15), is connected with the more complex ^42, as compared with alcohol, structure of water, which becomes simpler as the temperature rises. In the case of water the shift of the maximum practically ends at a temperature of about \(t = 200^\circ\text{C}\), when the density of water is equal to 0.86. In this case the frequency of the maximum is equal to \(\nu \approx 3530\ \text{cm}^{-1}\), and it does not change with a further increase in temperature, including upon passage through the criti—

*) Reviews of works on the hydrogen bond may be found in ^2,^10,^11.

critical point, although the density of water changes very considerably from $\rho=0.86$ at $t=200^\circ\mathrm{C}$ to $\rho=0.33$ at the critical point. It is significant that the transition through the critical state is not accompanied by any noticeable changes in the spectrum. In the superheated-vapor stage, i.e., with a further decrease in density, a broad band is still observed in the spectrum, indicating the presence of associated molecules. And only at density $\rho=0.096$, along with the broad band of associated molecules with a maximum $\nu=3530\ \mathrm{cm}^{-1}$, does a sharp line of frequency $\nu=3645\ \mathrm{cm}^{-1}$ appear; this line is observed in the spectrum of water vapor at low pressure and characterizes the vibration of the O—H group of isolated molecules. Finally, with a further decrease in density, the band disappears and only the line of isolated molecules remains, which at very low densities becomes a doublet. The results of measuring the vibration frequencies of the O—H group are given in Table I.

Table I

Change in the frequency of the O—H group of water as a function of density and temperature

In the case of methyl alcohol, the changes observed in the combination-scattering spectrum are analogous to what occurs in the spectrum of water; only the appearance of the line of isolated molecules and the stage of coexistence of the band and the line are observed at larger density values: at $\rho=0.58$, when the substance is still in the liquid phase. This difference in the magnitude of the density is connected with the more complex structure of the alcohol molecule in comparison with the water molecule. The $\mathrm{CH}_3$ group of the alcohol seems to shield the hydroxyl group and thereby hinders the mutual orientation of the hydroxyl groups necessary for the formation of a hydrogen bond. The results of the measurements are given in Table II.

It should be noted that in the case of methyl alcohol as well, the critical point is likewise not distinguished by any changes in the form of the spectrum.

In the review paper $^{15}$ G. S. Landsberg emphasizes that in these experiments, with a continuous change in density, no continuous transition of the band of associated molecules into the line of isolated molecules is observed, and that the observed coexistence of the band and the line, separated by a finite frequency interval, indicates the presence of an equilibrium

Table II

Change in the frequency of the O—H group of methyl alcohol as a function of density and temperature

Table III

Frequency of the hydroxyl group of ethyl alcohol

Table IV

Frequency of the hydroxyl group of methyl alcohol

state between isolated and associated molecules. A change in temperature leads only to a shift of this equilibrium, but does not lead to a gradual relaxation of the bonds between associated molecules.

In the cited works \({}^{12,13,14,15}\), an estimate is also made of the influence of the mean distance between molecules on the vibrational frequency of the O—H group. In the case of water, a decrease in density from \(\rho = 1\) to \(\rho = 0.06\) leads to an increase in the mean distance from 3 Å to 8 Å, but in this interval a broad band is observed in the spectrum and, consequently, most of the molecules are in the associated state. A further increase in the mean distance leads to the appearance of isolated molecules, and at distances exceeding 10 Å all molecules are practically isolated, i.e., non-associated.

These investigations of the influence of density and temperature on the vibrational frequency of the O—H group were continued by I. A. Yakovlev \({}^{16}\) in the region of low temperatures and extended to the liquid, glassy, and crystalline states. The spectra of combination scattering of methyl alcohol were studied in the temperature interval from \(+20^\circ\)C to \(-70^\circ\)C, and of ethyl alcohol in the interval from \(+20^\circ\)C to \(-190^\circ\)C; moreover, at a temperature of \(-190^\circ\)C ethyl alcohol could be both in the glassy (supercooled) and in the crystalline state.

The results of measurements of the position of the maximum of the band of associated molecules and of its half-width are given in Tables III and IV.

The results of these investigations may be briefly formulated as follows: as the temperature is lowered, the frequency of the band maximum decreases and, at the same time, its width decreases. It is interesting to note that the transition from the liquid state to the solid state (from a supercooled liquid to the crystalline state) is not accompanied by any discontinuous changes in the spectrum; the decrease in frequency and the decrease in the band width occur during this transition continuously, in accordance with the change in density and temperature.

It should be noted that the results of the investigations by Landsberg and Ukholina \({}^{13}\) and by Yakovlev \({}^{16}\) on the dependence of the band width on temperature appear to be contradictory. Namely, in the experiments of Landsberg and Ukholina the band width decreased with increasing temperature, whereas in Yakovlev’s experiments the band width decreased with decreasing temperature. However, apparently this contradiction is only seeming, since the observed effects were caused by different factors. Already in Yakovlev’s work \({}^{16}\), and in a more definite form in the work of Landsberg and Baryshanskaya \({}^{17}\), the suggestion is made that the broadening of the O—H band is a secondary effect and is caused by fluctuations of the mutual positions of molecules connected by a hydrogen bond*). Under these assumptions, lowering the temperature should lead to a decrease in the band width, which is indeed the case in Yakovlev’s experiments, and also in the experiments of Landsberg and Baryshanskaya \({}^{17}\). In addition, the observed band may be composite as a result of the superposition of individual bands belonging to different associated complexes (see § 4, c), differing in the magnitude of the bond energy. When the temperature changes, the

*) Here and below, the interpretation of the observed phenomena is given from the standpoint of the “fluctuation” theory put forward by G. S. Landsberg, which makes it possible to explain satisfactorily all the experimental facts. A similar attempt is also made within the framework of the “predissociation” theory \({}^{11,43}\), proposed by B. I. Stepanov. Both these theories are qualitative and the available experimental facts do not provide sufficient grounds for rejecting the fluctuation theory. It is not excluded that, in reality, in the formation of a hydrogen bond both fluctuation and predissociation effects simultaneously play a role.

relative number of complexes of different types, which leads to a change in the shape, width, and position of the resultant band. In the experiments of Landsberg and U-kholin, the effect of band broadening due to an increase in temperature is, apparently, outweighed by the effect of band narrowing owing to simplification of the liquid structure, i.e., owing to a change in the relative number of different associated complexes. This supposition is confirmed in a number of works\(^{18, 19}\), including our own, on the study of the dependence of the infrared absorption spectra of alcohol solutions in neutral solvents on temperature and concentration (see below, § 4, c).

§ 3. STUDY OF THE HYDROGEN BOND IN CRYSTALS

In studies of the dependence of the combination-scattering spectra of alcohols and water on density and temperature\(^{12, 13, 16}\), it was possible to establish that density, and consequently also the value of the mean distance between molecules, has a substantial influence on the association of molecules owing to the formation of a hydrogen bond. However, the results of these studies are only qualitative in character and do not make it possible to establish more precisely those minimum distances between molecules at which the formation of a hydrogen bond occurs. In order to solve this important question, G. S. Landsberg and F. S. Baryshanskaya\(^{17}\) undertook a study of the combination-scattering spectra of a series of crystals whose molecules contain hydroxyl groups and for which, from X-ray structural data, the distances between the interacting groups—OH groups—are known. The objects of study selected were anhydrous hydroxides of the metals: LiOH, NaOH, Mg(OH)\(_2\), Ca(OH)\(_2\), Sr(OH)\(_2\), and B(OH)\(_3\). It should be noted that, from the experimental standpoint, these studies are extremely difficult, since the selected substances are finely crystalline powders, and therefore the usual methods for obtaining combination-scattering spectra are not applicable here. However, after a number of trials the authors succeeded in developing the necessary technique, called by them the diffuse-reflection method, which made it possible to obtain with confidence the combination-scattering spectra of the hydroxyl group at exposures ranging from several minutes for NaOH to several hours for B(OH)\(_3\).

The results of measurements of the frequencies of the lines of the O—H group are given in Table V.

Table V

As is evident from this table, in all the anhydrous hydroxides studied, with the exception of B(OH)\(_3\), the O—H vibration is characterized by a shar-

of which line, the frequency of which lies within the limits \(\nu=3600\)—\(3640\ \mathrm{cm}^{-1}\) (Fig. 1 *), which is close to the frequency of vapor-like water \(\nu=3645\ \mathrm{cm}^{-1}\) and alcohol \(\nu=3670\ \mathrm{cm}^{-1}\). In the spectrum of \(\mathrm{B(OH)}_{3}\), however, two considerably

Fig. 1. Spectrum of combination scattering of an \(\mathrm{Mg(OH)}_{2}\) crystal.

shifted bands are observed, \(\nu=3170\ \mathrm{cm}^{-1}\) and \(\nu=3240\ \mathrm{cm}^{-1}\), whose width is about \(100\ \mathrm{cm}^{-1}\) (Fig. 2). Thus, there is a substantial difference between the spectrum of \(\mathrm{B(OH)}_{3}\) and all the other hydroxides investigated, and on the basis of the spectroscopic criterion of the hydrogen bond adopted by us one may assert that only in \(\mathrm{B(OH)}_{3}\) crystals does the formation of a hydrogen bond occur.

If the data obtained on the form of the O—H spectrum are compared with X-ray structural data on the distance between neighboring oxygens

Fig. 2. Spectrum of combination scattering of a \(\mathrm{B(OH)}_{3}\) crystal:
\(a\)—at \(T=250^\circ\ \mathrm{K}\), \(b\)—at \(T=100^\circ\ \mathrm{K}\).

\(R_{\mathrm{OO}}\) (the second column of Table V) in the corresponding crystal, then one may come to the conclusion that a hydrogen bond is formed only in those cases when the distance between the oxygens of neighboring hydroxyls is less than \(3\ \text{Å}\). This conclusion is extremely significant.

The authors see the reason why, of all the crystals investigated, only in \(\mathrm{B(OH)}_{3}\), and also in water, the distance between oxygens is less than \(3\ \text{Å}\), in the fact that all the other crystals are ionic, and the additional electrostatic repulsion of the ions leads to an increase in the distance between hydroxyl groups and, consequently, to the absence of a hydrogen bond.

In the study of the spectra of combination scattering of aqueous solutions of a series of alkalis (\(\mathrm{NaOH}\), \(\mathrm{RbOH}\), \(\mathrm{KOH}\), and \(\mathrm{Ba(OH)}_{2}\)) it was found that in the spectrum, along with the broad band of water, there is also observed a sharp line \(\nu=3624\ \mathrm{cm}^{-1}\), belonging, apparently, to the unperturbed vibration O—H of the \((\mathrm{OH})^{-}\) ion, since the frequency of this line is close to the frequency of the line observed in crystalline hydroxides. The presence of an unperturbed O—H vibration of the \((\mathrm{OH})^{-}\) ion in aqueous solution also, pro-

* In these studies, mercury lines \(\lambda=3650\ \text{Å}\), \(\lambda=3655\ \text{Å}\), and \(\lambda=3663\ \text{Å}\) were used as the exciting line; therefore the combination lines were also triple and of the corresponding relative intensity.

probably associated with the peculiar screening action of the ion charge, which hinders the necessary favorable orientation of the hydroxyl groups of the water molecules and the ion \((\mathrm{OH})^{-}\).

In the Raman spectra of crystalline hydrates of hydroxides, i.e., hydroxides with several molecules of water of crystallization, instead of sharp lines of frequency \(\nu = 3600\text{–}3640\ \mathrm{cm}^{-1}\), somewhat broadened and shifted lines of the \(\mathrm{O—H}\) group are observed. For example, in the spectrum of anhydrous \(\mathrm{LiOH}\) the band frequency is \(\nu = 3630\ \mathrm{cm}^{-1}\), whereas in the spectrum of \(\mathrm{LiOH}\cdot \mathrm{H}_{2}\mathrm{O}\), \(\nu = 3560\ \mathrm{cm}^{-1}\); for anhydrous \(\mathrm{Sr(OH)}_{2}\), \(\nu = 3610\ \mathrm{cm}^{-1}\), whereas for \(\mathrm{Sr(OH)}_{2}\cdot 8\mathrm{H}_{2}\mathrm{O}\), \(\nu = 3495\ \mathrm{cm}^{-1}\), and in the latter case, in addition to the line \(\nu = 3495\ \mathrm{cm}^{-1}\), a broad band is also observed, belonging, probably, to the \(\mathrm{O—H}\) vibrations of the molecules of water of crystallization. Thus, the presence of molecules of water of crystallization leads to a certain perturbation of the \(\mathrm{O—H}\) vibrations of hydroxide groups, which indicates some, albeit weak, interaction of the hydrogen-bond type and also that in this case the distance between hydroxyl groups is less than \(3\ \text{Å}\). Unfortunately, the absence of reliable X-ray structural data for these crystalline hydrates does not make it possible to verify the validity of the assumption made.

Of particular interest are the studies by G. S. Landsberg and F. S. Baryshanskaya\(^{17,20}\) of the Raman spectra of various crystals (in which hydrogen bonding occurs) at different temperatures.

As has already been noted, in the experiments of I. A. Yakovlev\(^{16}\) lowering the temperature of alcohols caused a decrease in the frequency of the maximum of the \(\mathrm{O—H}\) group band and a decrease in its width. But in these experiments the substance under investigation was in the liquid phase, and lowering the temperature simultaneously led to a considerable increase in density, i.e., to a decrease in the average distance between molecules, which in turn could lead to a change in the type of association of the molecules, thereby causing a change in the frequency of the band maximum and its width. In other words, in Yakovlev’s experiments a non-pure temperature effect was observed. In the case of crystals, however, the distances between hydroxyl groups are more definite, and one cannot expect that lowering the temperature could change the type of association.

Fig. 3. Raman spectrum of a crystal of \(\mathrm{CuSO}_{4}\cdot 5\mathrm{H}_{2}\mathrm{O}\):
\(a\)—at \(T = 290^\circ\ \mathrm{K}\), \(b\)—at \(T = 100^\circ\ \mathrm{K}\).

As objects of investigation, crystals were chosen in which the \(\mathrm{O—H}\) vibration is characterized by a broad and shifted band. First of all, crystals of \(\mathrm{B(OH)}_{3}\) were studied. At a temperature of \(400^\circ\ \mathrm{K}\), in the spectrum of this substance there is observed a broad, strongly shifted band with two maxima, corresponding to two frequencies of the valence vibration of the \(\mathrm{O—H}\) group, as follows from the nature of the symmetry of the \(\mathrm{B(OH)}_{3}\) molecule. Upon lowering the temperature, the maxima of the band separate more and more distinctly, and at a temperature of \(100^\circ\ \mathrm{K}\) they turn into two sharp lines \(\nu = 3170\ \mathrm{cm}^{-1}\) and \(\nu = 3240\ \mathrm{cm}^{-1}\) (see Fig. 2).

Similar results were obtained by G. S. Landsberg and F. S. Baryshanskaya20 in investigating the spectra of crystals containing water of crystallization (Fig. 3). In these investigations a special technique was used, making it possible to vary the temperature of the specimens studied over very wide limits: from room temperature to the temperature of liquid helium (4° K). The results of the investigations are presented in Table VI.

Table VI*)

) Frequencies in cm⁻¹; accuracy ~5 cm⁻¹.
*) The line at 4° K is somewhat narrower than at 100° K.

As is seen from this table, the broad band characterizing the perturbed O—H vibrations, when the temperature is lowered to that of liquid air, breaks up into a series of individual narrow bands, the width of which in a number of cases continues to decrease upon further lowering of the temperature to that of liquid helium, while the frequency remains unchanged.

It is significant that the decrease in the width of the bands with lowering of temperature is not accompanied by a change in their frequencies; the frequencies of the lines into which the broad band splits remain shifted relative to the frequency of the unperturbed vibration of the O—H group, indicating the presence of the same perturbation as at higher temperatures. These convincing experiments enabled G. S. Landsberg and F. S. Baryshanskaya to regard the broadening of the O—H vibration line upon the formation

hydrogen bond as a secondary effect caused by fluctuation of the relative positions of interacting molecules as a result of thermal motion. The principal sign of a hydrogen bond is the shift of the frequency of the perturbed O—H vibration from the frequency of O—H of isolated molecules. The smaller the distance \(R_{OO}\) between the oxygen of the hydroxyl group of one molecule and the perturbing oxygen of another molecule, the greater the magnitude of the perturbation and the greater the shift of the O—H frequency. For example, for a crystal of \(\mathrm{B(OH)_3}\), \(R_{OO}\approx 2.7\ \text{Å}\), \(\nu=3240\ \text{cm}^{-1}\) and \(\nu=3170\ \text{cm}^{-1}\); for \(\mathrm{KH_2PO_4}\) and \(\mathrm{NH_4H_2PO_4}\), \(R_{OO}=2.54\ \text{Å}\), \(\nu=2800\ \text{cm}^{-1}\), etc.

On the other hand, the shift of the O—H frequency upon perturbation by the oxygen atom of another molecule indicates a change in the force constant of the O—H bond and a change in the equilibrium distance between the O and H atoms. If one uses Badger’s empirical relation \({}^{23}\):

\[ k_0(r_e-d_{ij})^3=1.86\cdot 10^5, \]

where \(k_0\) is the force constant, which can be found from the numerical value of the frequency of the perturbed vibration, \(r_e\) is the internuclear distance (in the present case the distance \(r_{\mathrm{O-H}}\)), and \(d_{ij}\) is a constant equal, according to Badger, to \(0.335\ \text{Å}\) for the O—H bond, then one can estimate the magnitude of \(r_{\mathrm{O-H}}\) and the change of this distance for various magnitudes of perturbation. Thus, for the unperturbed O—H vibration \((\nu=3650\ \text{cm}^{-1})\), \(r_{\mathrm{O-H}}=0.97\ \text{Å}\); for the perturbed vibration having frequency \(\nu=3200\ \text{cm}^{-1}\), \(r_{\mathrm{O-H}}=1.018\ \text{Å}\); for \(\nu=2800\ \text{cm}^{-1}\), \(R_{\mathrm{O-H}}=1.08\ \text{Å}\), etc.

The assumption of a dependence of the magnitude of the frequency shift of the perturbed vibration on the distance \(R_{OO}\) makes it possible to explain the cause of the observed splitting of the broad O—H band into a number of narrow lines upon cooling. It may be assumed that in crystals whose molecules contain several molecules of water of crystallization, the distances \(R_{OO}\) between individual hydroxyl groups and perturbing oxygen atoms are not identical, but have several different values. Then each value of \(R_{OO}\) corresponds to a definite frequency shift, and the set of values of \(R_{OO}\) determines the number of perturbed frequencies observed upon cooling.

Finally, G. S. Landsberg and F. S. Baryshanskaya also carried out other experiments \({}^{20}\), which with still greater convincingness confirm the dependence of the magnitude of the frequency shift of the perturbed O—H vibration on the distance \(R_{OO}\). These were studies of the dependence of the frequency of the perturbed O—H vibration of a crystal on the magnitude of \(R_{OO}\), when the latter changes owing to thermal expansion of the crystal. Since the coefficient of thermal expansion of crystals decreases strongly with decreasing temperature, the low-temperature region proves unsuitable for these experiments, although in this region the O—H lines are narrowest, which facilitates observation of their shift. Therefore, as the object of study, a crystal of natural hydrargillite \(\mathrm{Al(OH)_3}\) was chosen, in which already at room temperature the four observed lines of the O—H group are sufficiently narrow and have the frequencies:

\[ \nu_\alpha=3370\ \text{cm}^{-1},\quad \nu_\beta=3445\ \text{cm}^{-1},\quad \nu_\gamma=3530\ \text{cm}^{-1} \quad \text{and} \quad \nu_\delta=3624\ \text{cm}^{-1}. \]

The very values of these frequencies already allow one to suppose that the frequency \(\nu_\delta\) characterizes the unperturbed O—H vibration and, consequently, belongs to bonds for which \(R_{OO}>3\ \text{Å}\), while the remaining frequencies characterize perturbed vibrations, and for them \(R_{OO}<3\ \text{Å}\), and the lower the frequency, the smaller \(R_{OO}\). Analysis of crystallographic and X-ray structural data for the \(\mathrm{Al(OH)_3}\) crystal does indeed show that in the unit cell

of this crystal there are distances both greater than \(3\,\text{\AA}\) and less than \(3\,\text{\AA}\) (\(\sim 2.8\,\text{\AA}\)).

The Raman spectra of an \(\mathrm{Al(OH)_3}\) crystal, obtained at temperatures of \(100^\circ\), \(290^\circ\), and \(420^\circ\) K, show that the frequency \(\nu_\delta = 3624\ \mathrm{cm}^{-1}\) of the unperturbed vibration does not change with temperature. The frequency \(\nu_\gamma = 3530\ \mathrm{cm}^{-1}\) increases by approximately \(11\ \mathrm{cm}^{-1}\) when the temperature is changed from \(290^\circ\) K to \(420^\circ\) K, with practically no change in its width. The frequencies \(\nu_\alpha = 3370\ \mathrm{cm}^{-1}\) and \(\nu_\beta = 3445\ \mathrm{cm}^{-1}\), corresponding to a considerable perturbation of the O—H vibration, show noticeable broadening and an increase in frequency as the temperature is raised. Thus, unperturbed or weakly perturbed O—H vibrations are little sensitive both to a change in temperature and to a change in the distance \(R_{OO}\). Perturbed vibrations, however, characterized by a significantly shifted frequency of the O—H vibration, undergo large changes when the temperature and the distance \(R_{OO}\) are changed.

There are, however, cases in which the explanation given above for the causes of broadening of perturbed O—H vibrations is not confirmed. This applies, for example, to crystals of ferroelectrics: Rochelle salt, \(\mathrm{KH_2PO_4}\), and \(\mathrm{NH_4H_2PO_4}\). The Raman spectra of these crystals were investigated in the work of G. S. Landsberg and his collaborators \(^{20, 21, 22}\). In the spectrum of Rochelle salt at room temperature, the O—H vibration is characterized by a broad band in the region \(3200\text{--}3300\ \mathrm{cm}^{-1}\) and by three diffuse bands \(\nu = 3400\ \mathrm{cm}^{-1}\), \(\nu = 3470\ \mathrm{cm}^{-1}\), and \(\nu = 3535\ \mathrm{cm}^{-1}\). In the spectrum of \(\mathrm{KH_2PO_4}\), two broad, strongly shifted bands were found with maxima at \(\nu \approx 2800\ \mathrm{cm}^{-1}\) and \(\nu \approx 2500\ \mathrm{cm}^{-1}\), whose width is about \(350\ \mathrm{cm}^{-1}\). When the temperature is lowered to \(100^\circ\) K, the diffuse bands of Rochelle salt become narrower and turn into sharp lines with frequencies \(\nu = 3390\ \mathrm{cm}^{-1}\), \(\nu = 3455\ \mathrm{cm}^{-1}\), and \(\nu = 3530\ \mathrm{cm}^{-1}\), whereas the broad bands of both Rochelle salt and \(\mathrm{KH_2PO_4}\) practically do not change their position or width. Analogous phenomena were also observed for the \(\mathrm{NH_4H_2PO_4}\) crystal. Further lowering of the temperature of Rochelle salt to \(4^\circ\) K introduces no additional changes into the spectrum. Thus, in the case of ferroelectrics, the observed broadening of the lines of perturbed O—H vibrations cannot be explained from the standpoint of the fluctuation theory, and it is not excluded that the cause of this broadening has a different nature and is connected with the specific properties of ferroelectrics. An attempt was made to affect the O—H vibrations by polarizing the ferroelectric when an electric field was applied to the crystal. However, experiments showed \(^{21}\) that the application of an electric field to a Rochelle-salt crystal at temperatures both above and below the Curie point does not lead to any changes in the frequency spectrum of the O—H group.

§ 4. STUDY OF THE HYDROGEN BOND BY DISSOLVING SUBSTANCES CONTAINING THE O—H GROUP IN DIFFERENT SOLVENTS

Studies of the influence of density and temperature on the frequency of the O—H vibration convincingly showed that the shift of the frequency of this vibration is caused by the perturbing action of the hydroxyl groups of neighboring molecules through the formation of a hydrogen bond. On the other hand, these studies showed that the hydroxyl group is a convenient object for studying intermolecular interactions and therefore it can be used to solve the broader problem of studying intermolecular interactions, without being restricted to the interactions of identical molecules. By dissolving substances containing the O—H group in appropriate solvents, it is possible to isolate one

molecule containing O—H from another, and, by changing the nature of the solvent, to investigate the effect on the O—H vibration of the solvent molecules. Along this path there opens up the possibility of studying which features of the surrounding molecules play the principal role in such interactions.

From the foregoing it becomes evident that, in carrying out such investigations, the substance under study must be chosen so that it dissolves in as large a number as possible of different solvents and at the same time is sufficiently simple in its chemical composition. Therefore, monohydric alcohols are usually chosen as such objects of study and, first of all, the simplest of them—methyl alcohol, CH$_3$OH.

The same considerations guided G. S. Landsberg in his extensive and systematic investigations of the combination-scattering spectra of solutions, carried out by him and by the author of the present article[^24][^25][^26][^27][^28][^29].

The principal results of these investigations are presented below.

a) Investigation of solutions of methyl alcohol in neutral solvents

If the interaction between the molecules of the dissolved substance and the molecules of the solvent is small, then one may expect that, upon changing the concentration of the dissolved substance, effects will be observed close to those which were observed in experiments on changing the density of a pure substance. Indeed, in the combination-scattering spectrum of a 1% (by volume) solution of methyl alcohol CH$_3$OH in CCl$_4$, instead of the broad band with a maximum at $\nu = 3370\ \text{cm}^{-1}$ observed for the pure alcohol, there is observed a sharp line of frequency $\nu = 3647\ \text{cm}^{-1}$ and width $\sim 18\ \text{cm}^{-1}$ (Fig. 4), which in its width and position approaches the lines observed in the spectrum of vapor-phase alcohol. This

Fig. 4. Combination-scattering spectrum of pure liquid methyl alcohol (a) and a 1% solution of methyl alcohol in CCl$_4$ (b).

gives grounds to consider that the behavior of the alcohol molecules in a 1% solution in CCl$_4$ is similar to their behavior in the gaseous phase. However, the frequency of the O—H line observed in the solution differs from the frequency of the vapor line, where it has the value $\nu = 3672\ \text{cm}^{-1}$, i.e., a shift of 25 $\text{cm}^{-1}$ takes place. Evidently, this shift is the result of interaction between the alcohol molecules and the CCl$_4$ molecules.

In the spectrum of a 2% solution of CH$_3$OH in CCl$_4$ there are observed the same sharp lines, and of the same frequency, as in the spectrum of a 1% solution, but, in addition, traces are observed of a broad band which, in its position, form, and width, is close to the band of pure 100% alcohol. In the spectrum of a 5% solution the intensity of this band already becomes

significant (Fig. 5). Since the broad shifted band characterizes the perturbed O—H vibration of associated alcohol molecules, the presence in the spectrum of the 5% solution of both the line and the band indicates that in such a solution there is simultaneous coexistence of isolated alcohol molecules and molecules associated into complexes. It should be noted that in the 5% solution the “density” of the dissolved alcohol is still small \((\rho = 0.039)\) and corresponds to the density of gaseous alcohol, and that in this case there are about eight solvent molecules per one alcohol molecule. Nevertheless, even under such conditions there is already considerable association of alcohol molecules. The latter indicates that the forces of interaction between alcohol molecules are considerably greater than the forces of interaction between alcohol molecules and \(\mathrm{CCl}_4\) molecules. With a further increase in the alcohol concentration \((10—20—50\%)\), the intensity of the line decreases, while the intensity of the band increases, i.e., the equilibrium between isolated molecules and molecules associated into complexes shifts toward an increase in the number of the latter. In the 50% solution the number of alcohol molecules is twice as large as

Fig. 5. Spectrum of combination scattering of a 5% solution of methyl alcohol in \(\mathrm{CCl}_4\).

solvent molecules. However, the presence in the spectrum of this solution of a sharp line indicates that even under these conditions, when it is no longer possible to speak of the alcohol molecules being surrounded only by solvent molecules, there exist alcohol molecules in which the O—H vibration is unperturbed, i.e., nonassociated molecules. Evidently, such a situation is possible only if it is assumed that the formation of a hydrogen bond, accompanied by perturbation of the O—H vibration, occurs only for a definite mutual orientation of the interacting molecules and is not determined solely by the distance between these molecules.

It is also of interest to investigate solutions of extremely low concentrations, in which the initial stages of association of alcohol molecules are manifested. One may expect that study of these transitional stages would make it possible to obtain some information on the mechanism and forms of association of alcohol molecules. However, because of the great experimental difficulties in obtaining combination-scattering spectra of solutions of low concentrations, these investigations were carried out by us using infrared absorption spectra in the region of the fundamental vibration and of the first overtone of the vibration of the O—H group. Here it should be noted that the relative intensity of the band of the perturbed O—H vibration and of the line of the unperturbed vibration in the combination-scattering and infrared-absorption spectra of one and the same solution differ substantially. In the infrared absorption spectrum in the region of the fundamental vibration \((\sim 2.9\ \mu)\), the relative intensity of the band and of the lines of the unperturbed O—H vibrations is greater than in the combination-scattering spectrum, and greater than in the infrared absorption spectrum in the region of the first overtone \((\sim 1.5\ \mu)\).

The different relative optical activity of the unperturbed and perturbed vibrations of the O—H group in the spectra of combination scat—

data on spectra and on infrared absorption spectra and, especially, on infrared absorption spectra in the region of the fundamental vibration and overtones is of known interest, since this provides additional information on the spectroscopic manifestations of the hydrogen bond.

The investigations showed that, when the concentration of methyl alcohol in CCl₄ is decreased below 1%, substantial transformations of the band shape of the associated molecules are observed. Thus, at a concentration of the order of 0.7–0.8% (by volume) the band becomes complex; in addition to the principal maximum $\nu \simeq 3340\ \text{cm}^{-1}$, a small maximum of frequency $\nu \simeq 3500\ \text{cm}^{-1}$ is also observed. With a further decrease in concentration, the relative intensity of the maximum $\nu \simeq 3500\ \text{cm}^{-1}$, as compared with the maximum $\nu \simeq 3340\ \text{cm}^{-1}$, increases, and at concentrations $\lesssim 0.2\%$ practically only one maximum is observed, with $\nu = 3500\ \text{cm}^{-1}$, and the line of the isolated molecules $\nu = 3640\ \text{cm}^{-1}$. It should also be noted that the width of the maximum $\nu = 3500\ \text{cm}^{-1}$ is considerably smaller than the width of the maximum $\nu = 3340\ \text{cm}^{-1}$. These results*) are in complete agreement with the results[^18][^19] for ethyl alcohol.

It is unlikely that such a transformation of the band shape upon a change in concentration is connected with a change in the perturbation of the O—H vibration in the associated complexes. It is more probable that this transformation of the band shape is due to a change in the type of association. The presence of two maxima with $\nu \simeq 3340\ \text{cm}^{-1}$ and $\nu \simeq 3500\ \text{cm}^{-1}$ indicates the presence of two types of association, differing in the magnitude of the perturbation of the O—H vibration and, consequently, in the magnitude of the interaction, i.e., in the magnitude of the distance between the O—H groups. Such an interpretation is supported by studies (see also[^19]) of the dependence of the relative intensity of the observed maxima $\nu = 3340\ \text{cm}^{-1}$ and $\nu = 3500\ \text{cm}^{-1}$ on temperature. When the temperature of the solution is raised, the intensity of the maximum $\nu = 3340\ \text{cm}^{-1}$ rapidly decreases, while the intensity of the maximum $\nu = 3500\ \text{cm}^{-1}$ at first increases, and then, after the disappearance of the band $\nu = 3340\ \text{cm}^{-1}$, a further rise in temperature already leads to a decrease in the intensity of the maximum $\nu = 3500\ \text{cm}^{-1}$ and to an increase in the intensity of the monomer line $\nu = 3640\ \text{cm}^{-1}$. Thus, the effects observed when the temperature of the solution is raised are analogous to what occurs when the concentration is decreased. From the point of view of the possibility of the existence of two different types of association of alcohol molecules, the observed transformation of the band of the perturbed O—H vibrations can be explained as follows. At high concentrations and in the pure liquid one type of association predominates, characterized by the maximum $\nu = 3340\ \text{cm}^{-1}$, which masks the weaker maximum $\nu = 3500\ \text{cm}^{-1}$. When the concentration is decreased or the temperature is raised, complexes of one type dissociate and the number of complexes with the other type of association and the number of isolated molecules—monomers—increases. The relative intensity of the maxima $\nu = 3340\ \text{cm}^{-1}$ and $\nu = 3500\ \text{cm}^{-1}$, generally speaking, makes it possible to judge the relative number of complexes of both types. However, as our investigations have shown, the absence of the maximum $\nu = 3500\ \text{cm}^{-1}$ in solutions at methyl-alcohol concentrations greater than 1% still does not permit one to assert that association of one type is practically absent. The fact is that the optical activity of the maxima $\nu = 3340\ \text{cm}^{-1}$ and $\nu = 3500\ \text{cm}^{-1}$ is substantially different. Thus, if one examines[^30] the absorption spectra of solutions of alcohols in CCl₄ in the region of the first overtone, then there also the band of the perturbed O—H vibrations has two maxima, $\nu = 6745\ \text{cm}^{-1}$ and $\nu = 6265\ \text{cm}^{-1}$ (for ethyl

*) The infrared absorption spectra of solutions of methyl alcohol in CCl₄ were obtained by M. E. Movsesyan, a graduate student of the Optical Laboratory of the Physical Institute of the Academy of Sciences.

alcohol), and the less displaced maximum \(\nu=6745\ \text{cm}^{-1}\) (corresponding to the maximum \(\nu=3500\ \text{cm}^{-1}\)) is observed at considerably higher concentrations than occurs in the spectrum of the fundamental vibration. For example, in the spectrum of a 10% solution of ethyl alcohol in \(\mathrm{CCl}_4\), the intensity of the maximum \(\nu=6745\ \text{cm}^{-1}\) is only slightly less than the intensity of the maximum \(\nu=6265\ \text{cm}^{-1}\).

Thus, the two types of association of alcohol molecules differ not only in the magnitude of the interaction, which is manifested in the different magnitude of the displacement of the maxima of the perturbed vibrations of the O—H group, but also in the optical activity of the perturbed O—H vibrations in the region of the fundamental O—H vibrations and overtones. In addition, the different temperature dependence of the intensity of the observed maxima indicates different heats of formation of complexes of one type and the other.

Considerations concerning the nature of these types of interaction will be set forth below.

In addition to solutions of methyl alcohol in \(\mathrm{CCl}_4\), solutions of this alcohol were also investigated in other neutral solvents: in hexane (\(\mathrm{C}_6\mathrm{H}_{14}\)), cyclohexane (\(\mathrm{C}_6\mathrm{H}_{12}\)), and benzene (\(\mathrm{C}_6\mathrm{H}_6\)), the molecules of which do not possess a dipole moment.

In the combination-scattering spectra of 5% solutions of methyl alcohol in cyclohexane and hexane\(^{27}\) at a temperature of \(50^\circ\mathrm{C}\), a sharp line of frequency \(\nu=3653\ \text{cm}^{-1}\), with a width of about \(20\ \text{cm}^{-1}\), is observed, characterizing the O—H vibration of isolated alcohol molecules. The magnitude of the frequency of this line and its width indicate a weak interaction between the alcohol molecules and the molecules of hexane and cyclohexane, similar to that which occurs in solutions in \(\mathrm{CCl}_4\).

In the combination-scattering spectrum of solutions of methyl alcohol in benzene\(^{26}\), the line of frequency O—H of isolated alcohol molecules has frequency \(\nu=3611\ \text{cm}^{-1}\), and its width is about \(40\ \text{cm}^{-1}\). Comparison of the frequencies and widths of the lines of the O—H group in the spectra of alcohol solutions in benzene and in cyclohexane or in hexane indicates that the magnitude of the interaction between benzene and alcohol molecules is greater than between alcohol molecules and cyclohexane or hexane molecules, although the molecules of these solvents consist of the same atoms and all of them have no dipole moment. The presence of a significant interaction between \(\mathrm{CH}_3\mathrm{OH}\) and benzene molecules is also evidenced by the fact that, as the concentration of alcohol in solution is increased, the band of associated alcohol molecules appears in benzene solutions at higher (\(\sim 10\%\)) concentrations as compared with solutions in \(\mathrm{CCl}_4\) (2%). In this respect benzene molecules behave as though they possessed a dipole moment (see below).

We note that our conclusions concerning the different action of benzene molecules and cyclohexane, or hexane, on the alcohol molecule are confirmed in studies of the molecular polarization of alcohol solutions in the indicated solvents (see, for example,\(^{31}\)).

b) Investigation of the influence of the dipole moment of solvent molecules

It is of interest to clarify the role of the dipole moment of solvent molecules in the perturbation of the O—H vibration and the influence of the dipole moment on the association of alcohol molecules in solution. Answers to these questions are provided by investigations\(^{25,26}\) of the combination-scattering spectra of solutions of methyl alcohol in chloroform (\(\mathrm{CHCl}_3\)), chlorobenzene (\(\mathrm{C}_6\mathrm{H}_5\mathrm{Cl}\)), and fluorobenzene (\(\mathrm{C}_6\mathrm{H}_5\mathrm{F}\)).

In the spectrum of a 2% solution of alcohol in chloroform, as also in the spectrum of a 2% solution in \( \mathrm{CCl}_4 \), instead of a broad band there is observed a line of the \( \mathrm{O—H} \) vibration of isolated molecules; however, the frequency of this line, \( \nu = 3630\ \mathrm{cm}^{-1} \), differs from the frequency of the line in the solution in \( \mathrm{CCl}_4 \) (\( \nu = 3647\ \mathrm{cm}^{-1} \)); in addition, the line in the solution in chloroform is broader (its width is \(\sim 30\ \mathrm{cm}^{-1}\)). Thus, the presence in the chloroform molecules of a dipole moment (\(\mu = 1.15 \cdot 10^{-18}\) CGSE) is manifested only in a small shift (\(\sim 17\ \mathrm{cm}^{-1}\)) and broadening of the \( \mathrm{O—H} \) vibration line of isolated alcohol molecules.

The dipole moment of the chloroform molecule has a much greater effect on the association of alcohol molecules in solution. First, in the case of solutions in chloroform, the band of associated alcohol molecules appears in the spectrum at considerably higher concentrations than in solutions in \( \mathrm{CCl}_4 \). Therefore, if one compares spectra of solutions in \( \mathrm{CCl}_4 \) and in \( \mathrm{CHCl}_3 \) with equal alcohol concentrations, then in the solutions in \( \mathrm{CCl}_4 \) the relative intensity of the band, compared with the intensity of the line, is considerably greater than in solutions in \( \mathrm{CHCl}_3 \) (Fig. 6). Moreover,

Fig. 6. Combination-scattering spectra of a 10% solution of methyl alcohol in \( \mathrm{CCl}_4 \) (a) and in chloroform \( \mathrm{CHCl}_3 \) (b).

the maximum of the band of associated molecules in the spectrum of solutions in \( \mathrm{CHCl}_3 \) has a somewhat different frequency, \( \nu = 3417\ \mathrm{cm}^{-1} \), than the maximum of the band in solutions in \( \mathrm{CCl}_4 \) (shift \(\sim 50\ \mathrm{cm}^{-1}\)), and the width of the band in chloroform solutions is somewhat smaller. In its position the band in the spectrum of the solution in chloroform is close to the position of the band in the solution of alcohol in \( \mathrm{CCl}_4 \) at a temperature of \(65^\circ\) (see \(32\)). Consequently, the dipole moment of chloroform molecules, like an increase in temperature, shifts the equilibrium state among the different kinds of association.

Thus, the dipole moment of the solvent molecules changes only insignificantly the proper frequency of the \( \mathrm{O—H} \) vibration, but, by interacting with the dipole moment of the alcohol molecules, it hinders their mutual orientation, favorable for their association into complexes, and, in addition, apparently changes the relative number of complexes with different kinds of association.

In studying the combination-scattering spectra of solutions of methyl alcohol in chlorobenzene and fluorobenzene, the same picture was observed as in the spectra of alcohol solutions in chloroform or benzene. In the spectra of solutions of low concentrations, a broadened line of frequency \( \nu = 3630\ \mathrm{cm}^{-1} \) is clearly visible; its width and shape are approximately the same as in the spectrum of alcohol solutions in benzene, while its frequency is close to the frequency of the line observed in the spectrum of the alcohol solution in chloroform. The presence of a dipole moment in the molecules of chlorobenzene (\(\mu = 1.5 \cdot 10^{-18}\) CGSE) and fluorobenzene (\(\mu = 1.4 \cdot 10^{-18}\) CGSE) was manifested chiefly in the fact that the band of associated alcohol molecules appears at still higher concentrations (\(\sim 20\%\)) in comparison with solvents in chloroform and benzene.

Replacement of the chlorine atom by a fluorine atom in the benzene ring had no effect on the perturbing action of the solvent on the \( \mathrm{O—H} \) vibrations of the alcohol.

c) Study of alcohol solutions in solvents whose molecules contain an oxygen atom

If substances whose molecules contain an oxygen atom are taken as the solvent, then in this case the spectra show a considerably shifted broad band with a maximum frequency of about \(\nu = 3500\ \mathrm{cm}^{-1}\), which indicates an essential difference between these solvents and neutral ones. Thus, in the combination-scattering spectrum of a solution of methyl alcohol in acetone \(([\mathrm{CH}]_3\mathrm{CO})\), at concentrations of 4, 10, and 20%, a band is observed with a maximum at \(\nu = 3530\ \mathrm{cm}^{-1}\) (Fig. 7) and a width of about \(200\ \mathrm{cm}^{-1}\) \({}^{26,27}\). An analogous picture is observed in the spectra of solutions of methyl alcohol in dioxane \((\mathrm{C}_4\mathrm{H}_8\mathrm{O}_2)\), ethyl \(([\mathrm{C}_2\mathrm{H}_5]_2\mathrm{O})\) and isoamyl \(([\mathrm{C}_5\mathrm{H}_{11}]_2\mathrm{O})\) ether, although the molecules of these substances differ both in their structure and in the magnitude of their dipole moment; what is common is only the presence of an oxygen atom in these molecules.

The observed phenomenon can be explained in two different ways. It may be assumed that in such a solution there are alcohol molecules associated with one another, but, owing to the interaction of the alcohol molecules with the solvent molecules, the type of association of the alcohol molecules changes and the perturbation of the O—H vibration changes correspondingly. On the other hand, it may be assumed that there is a considerable interaction between the alcohol molecules and the solvent molecules, and that the perturbation of the O—H vibration of the alcohol molecule is effected directly by the oxygen atom of the solvent molecules, i.e., in such a solution, in addition to association of the alcohol molecules with one another, association of the alcohol molecules with the solvent molecules occurs, and in dilute solutions (as was the case in our experiments) the latter mainly takes place. The second explanation appears to us more probable. Confirmation of this interpretation may be seen in the investigation of the spectra of ternary mixtures \({}^{26,27}\). If 5% acetone is added to a 2% solution of methyl alcohol in \(\mathrm{CCl}_4\), in the spectrum of which an intense line of isolated alcohol molecules and weak traces of the band of associated alcohol molecules are observed, then in the spectrum of such a ternary mixture the intensity of the line of isolated molecules decreases sharply, and a shifted band of frequency \(\nu = 3530\ \mathrm{cm}^{-1}\) appears (Fig. 8). In its position and shape this band coincides with the band observed in the spectrum of a solution of alcohol in acetone. Thus, the appearance in the ternary mixture of a band with \(\nu = 3530\ \mathrm{cm}^{-1}\), at the expense of a decrease in the intensity of the lines of isolated molecules, clearly indicates that the perturbation of the O—H vibration in the present case is due to the interaction of alcohol molecules with acetone molecules, namely the interaction of the O—H group of the alcohol with the oxygen atom of the acetone molecule.

Fig. 7. Combination-scattering spectrum of a 10% solution of methyl alcohol in acetone.

Since the band of perturbed O—H vibrations observed in the spectrum of pure alcohol differs, in its position and width, from the band observed in the spectrum of alcohol solutions in “oxygen-containing” solvents, one may speak of two different, in magnitude,

perturbations of the O—H vibration and, consequently, about two interactions of different magnitude. In the first case the interaction of two hydroxyl groups is involved, and in the second case—the interaction of an O—H group and an oxygen atom. In accordance with such interaction mechanisms, the first type of interaction may be called a hydroxyl bond\(^{27, 28}\), and the second—a hydrogen bond. As is seen from the spectra, the hydroxyl bond is characterized by a larger displacement of the band of perturbed O—H vibrations and, consequently, by a larger interaction energy than the hydrogen bond. In the formation of a hydroxyl bond there is simultaneous interaction of both hydroxyl groups of the interacting molecules, which can occur only with a definite

Fig. 8. Microphotograms of combination-scattering spectra:
a—2% solution of methyl alcohol in CCl\(_4\), b—ternary mixture: 2% methyl alcohol and 5% acetone in CCl\(_4\).

mutual orientation of them. If such orientation of the molecules is not realized, then in this case the formation of a hydrogen bond is also possible. In the case of interaction of molecules of different nature, one of which contains a hydroxyl group and the other an oxygen atom, only a hydrogen bond can be formed. These two types of bond, as was indicated earlier, also differ in their optical activity.

Schematically these two types of bond may be represented in the form of dimers:

\[ \begin{array}{c} \begin{array}{ccc} & R & \\ & \backslash & \\ & O\!-\!H\cdots O & \langle\!\begin{array}{c} H \\ R \end{array} \end{array} \\[0.5em] \text{hydrogen bond} \end{array} \qquad \begin{array}{c} \begin{array}{ccc} & R & \\ & \backslash & \\ & O\!-\!H & \\ & \vdots & \vdots \\ & H\!-\!O & \\ & / & \\ & R & \end{array} \\[0.5em] \text{hydroxyl bond} \end{array} \]

In reality, in pure liquids and concentrated solutions, the formation of more complex complexes can apparently also take place, especially in the case of a hydrogen bond, when the formation of branched chains is possible, but the indicated dimers, differing in the character of the interaction, must enter as elements of these more complex formations.

Undoubtedly, the assumption of the formation of dimers of the hydroxyl bond meets with certain objections from the point of view of the smallness, in such a model, of the distance \(R_{OO} = 2\) Å, if for the distances \(r_{\mathrm{OH}}\) and \(r_{\mathrm{H}\cdots O}\) one takes

the same dimensions \(r_{\mathrm{OH}} \approx 1\) Å and \(r_{\mathrm{H\ldots O}} \approx 1.7\) Å that occur in the formation of a hydrogen bond when the atoms O—H…O are situated on one straight line. However, it is not excluded that in dimers of the hydroxyl bond the distance \(r_{\mathrm{H\ldots O}}\) may be different. Some confirmation of the proposed assumption may be seen in the fact that, when dimers are formed with simultaneous interaction of both hydroxyl groups, a considerable shift of the band frequency is observed, as, for example, occurs in dimers of fatty acids, in which the band is strongly displaced and has a frequency \(\nu \simeq 3000\ \mathrm{cm}^{-1}\). For alcohols this frequency is equal to \(\nu \simeq 3370\ \mathrm{cm}^{-1}\), since the dimers of the hydroxyl bond are different from the dimers of fatty acids.

With such assumptions about two types of interaction of alcohol molecules, a whole series of phenomena receives a simple interpretation. The fact that in the spectra of pure alcohols and water, and also of concentrated solutions of alcohols in neutral solvents at room temperature, the band of associated molecules has a frequency of the order \(\nu = 3370\ \mathrm{cm}^{-1}\), indicates that under these conditions the association of molecules is effected chiefly by formation of the hydroxyl bond. Direct spectroscopic determinations of the heat of the bond[^32] in concentrated solutions of alcohols also speak in favor of this; the value obtained in this case, \(\sim 13.0\ \mathrm{kcal/mol}\), is close to the heat of the bond of formic acid,[^33] equal to \(13.9\ \mathrm{kcal/mol}\).

With decreasing alcohol concentration, i.e., with increasing mean distance between alcohol molecules, the probability of formation of more ordered dimers of the hydroxyl bond decreases and, correspondingly, the number of molecules linked by a hydrogen bond and the number of isolated molecules increase, as is evidenced by the appearance in the spectrum of the line of isolated molecules \(\nu = 3640\ \mathrm{cm}^{-1}\) and of a maximum \(\nu = 3500\ \mathrm{cm}^{-1}\) in the region of the fundamental frequencies (\(\nu = 6745\ \mathrm{cm}^{-1}\) in the first overtone). The frequency of this maximum is close to the frequency of the band observed in solutions of alcohol in oxygen-containing solvents. At very low concentrations the band with maximum \(\nu = 3370\ \mathrm{cm}^{-1}\) disappears, and the remaining band with \(\nu = 3500\ \mathrm{cm}^{-1}\) indicates that association is effected only by formation of a hydrogen bond. This explains the transformation of the band of associated molecules as the alcohol concentration is decreased.

The great sensitivity of the maximum \(\nu = 3370\ \mathrm{cm}^{-1}\) of the hydroxyl bond to a change in temperature is also simply explained. Since the heat of formation of the hydroxyl bond is greater than the heat of formation of the hydrogen bond, the change in the equilibrium constant for one and the same change in temperature will be greater for the hydroxyl bond. This follows from the isochore equation

\[ \frac{d \ln k}{dT} = \frac{W}{RT^2}, \]

where \(k\) is the equilibrium constant between associated and dissociated molecules, and \(W\) is the heat of dissociation.

The effects of transformation of the band on heating, discovered in the experiments of Landsberg and Ukholin,[^13] also receive a simple interpretation from this point of view. If conditions exist in a molecule by virtue of which the freedom of orientation of the hydroxyl group is restricted, then in intermolecular interactions this must first of all show itself in hindrance to the formation of the hydroxyl bond. Indeed, in the spectrum of ortho-chlorophenol there is observed[^35] only a relatively slightly shifted band, which in its position and form coincides with the band,

observed in the spectra of solutions of alcohols in acetone, whereas in phenol and parachlorophenol a strongly shifted broad band is observed. This indicates that in orthochlorophenol, where the O—H group is connected through the interaction of dipole moments with the C—Cl group, a hydrogen bond is mainly realized, whereas in phenol and parachlorophenol it is chiefly a hydroxyl bond.

Analogous phenomena were observed by us in ethylene chlorohydrin \(^{27}\) and glycols \(^{30}\), where the band of associated molecules already in the pure liquid has two maxima corresponding to the hydrogen and hydroxyl bonds.

More direct proof of the existence of hydrogen-bond dimers and hydroxyl-bond dimers could be obtained by measuring the dipole moments of alcohol complexes in solutions of neutral solvents at those concentrations at which strong changes in the shape of the band of associated molecules are observed, since the resultant moments of these dimers differ substantially.

In addition, it is of interest to measure the rate of isotopic exchange (for example, of light and heavy alcohol) in solution at concentrations at which only the band \(\nu = 3500\ \text{cm}^{-1}\) is present in the spectrum (only hydrogen bond, exchange hindered) and when the band \(\nu = 3370\ \text{cm}^{-1}\) is intense (hydroxyl bond, exchange facilitated \(^{34}\)). If these assumptions are correct, then with small changes in concentration the rate of isotopic exchange should change markedly.

d) Investigation of solutions of alcohol in solvents whose molecules contain a nitrogen atom

In the combination-scattering spectra of a solution of methyl alcohol in pyridine \((\mathrm{C}_5\mathrm{H}_5\mathrm{N})\), at concentrations of 5–10%, a band is observed \(^{26}\) with a maximum at \(\nu \sim 3400\ \text{cm}^{-1}\), about \(200\ \text{cm}^{-1}\) wide, which in its shape resembles the band in the spectrum of a solution of alcohol in acetone, but differs in position \((\nu = 3530\ \text{cm}^{-1})\). Addition of 5% pyridine to a 2% solution of alcohol in \(\mathrm{CCl}_4\) leads to a decrease in the intensity of the line of isolated alcohol molecules and to the appearance of a band which, in its position and shape, coincides with the band observed in solutions of alcohol in pyridine. Thus, the presence of a nitrogen atom in the pyridine molecule leads to a significant perturbation of the O—H vibration of the alcohol molecule, indicating the presence of interaction between these molecules. Since the general character of the perturbation (the magnitude of the shift and the width of the band) in this case is close to that which occurs in the interaction between an alcohol molecule and a molecule containing an oxygen atom, one may speak of the formation of a hydrogen bond between the O—H group and the nitrogen atom; moreover, the magnitude of the shift of the O—H band from the position of the line in vaporous alcohol indicates that the nitrogen atom causes a stronger perturbation of the O—H vibration than the oxygen atom.

In the combination-scattering spectra of solutions of water in pyridine, and also in dioxane \(^{24}\), a picture is observed close to that observed in solutions of methyl alcohol in the same solvents. Consequently, the perturbation of the O—H vibration of water and alcohol molecules by oxygen or nitrogen atoms is approximately the same, i.e. it is determined by the properties of the O—H group and does not depend on to which molecular residue this group is attached.

§ 5. DETERMINATION OF THE HEAT OF FORMATION OF A HYDROGEN BOND BY SPECTROSCOPIC METHODS

As already indicated, when the temperature of alcohol solutions in \( \mathrm{CCl}_4 \) is changed, a change is observed in the relative intensity of the line of isolated alcohol molecules and of the band of associated molecules, indicating a shift of the thermodynamic equilibrium between the number of isolated and associated molecules (Fig. 9).

By measuring at different temperatures the intensity of the combination-scattering line (or the optical density in the absorption spectra) of the \( \mathrm{O—H} \) vibration, \( I_{\mathrm{OH}} \), which is proportional to the number of isolated molecules, and the intensity of the \( \mathrm{C—H} \) vibration line, \( I_{\mathrm{CH}} \), proportional to the total number of alcohol molecules in the solution, and, in addition, making certain assumptions concerning the applicability of the law of mass action to the given solution, one can determine the heat of formation of the hydrogen bond.

Fig. 9. Combination-scattering spectra of a 25% solution of methyl alcohol in \( \mathrm{CCl}_4 \):
\(a\)—at a temperature of \(6^\circ\mathrm{C}\), \(b\)—at a temperature of \(65^\circ\mathrm{C}\).

Thus, if in a first approximation it is assumed that the molecules in the solution are associated in the form of identical complexes, each of which consists of \(m\) molecules, then for the bimolecular reaction

\[ (\mathrm{ROH})_m \rightleftarrows (\mathrm{ROH})_1 + (\mathrm{ROH})_{m-1} \]

the law of mass action gives, for the equilibrium constant \(K\), the expression

\[ K = \frac{n_0 a^2}{V(1-a)_2}, \]

where \(\alpha\) is the degree of dissociation, \(n_0\) is the number of complexes in the absence of dissociation, and \(V\) is the volume.

Determining the values of the equilibrium constant \(K_1\) and \(K_2\) for two temperatures \(T_1\) and \(T_2\), and integrating the van ’t Hoff isochore equation

\[ \frac{\partial \ln K}{\partial T} = \frac{W}{RT^2}, \]

one can obtain the relation

\[ \frac{K_2}{K_1} \simeq e^{\frac{W}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)}, \]

which makes it possible to determine the quantity \(W\)—the heat of bond formation.

The degree of dissociation \(\alpha\), knowledge of which is necessary for calculating \(K\), can be found by measuring the relative intensity of the lines

\[ \delta = \frac{I_{\mathrm{OH}}}{I_{\mathrm{CH}}} = \frac{\beta_{\mathrm{OH}} n_0 \alpha}{\beta_{\mathrm{CH}} n} = \beta \frac{\alpha}{m}, \]

where \(\beta = \frac{\beta_{\mathrm{OH}}}{\beta_{\mathrm{CH}}}\), and \(\beta_{\mathrm{OH}}\) and \(\beta_{\mathrm{CH}}\)—

coefficients characterizing the optical activity of the O—H and C—H bonds of the molecule, \(n\) is the total number of alcohol molecules \((n=n_0 m)\). As is evident from the relation written above, in order to determine \(\alpha\) it is necessary, in addition to measuring the ratio

\[ \delta=\frac{I_{\mathrm{OH}}}{I_{\mathrm{CH}}}, \]

to know the number of molecules in the complex \(m\) and the ratio

\[ \beta=\frac{\beta_{\mathrm{OH}}}{\beta_{\mathrm{CH}}}, \]

which can be found from measurements of the relative intensity of the lines at infinite dilution \((\alpha=1,\ m=1)\): \(\delta_\infty=\beta\). In the particular case of a small degree of dissociation \(\alpha \ll 1\)*) and a small temperature interval \((T_2-T_1=10\text{—}20^\circ)\), when the quantity \(W\) may be regarded as constant, and when the average number of molecules entering the complex may also be regarded as constant, i.e., one may put \(\overline{m}_1=\overline{m}_2\), the quantity \(W\) can be calculated without great difficulty, since in this case

\[ \frac{K_2}{K_1} = \left(\frac{a_2}{a_1}\right)^2 = \left(\frac{\delta_2}{\delta_1}\right)^2 = e^{\frac{W}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)}. \]

Such determinations were carried out\(^{32}\) for a 25% solution of methyl alcohol in \(\mathrm{CCl}_4\), where the condition \(\alpha \ll 1\) is fulfilled.

The measurements were made at different temperatures of the solution in the range \(9\text{—}65^\circ\mathrm{C}\).

The measurement results are as follows:

The mean value \(W=13\ \text{kcal/mole}\) indicates that, in such a solution, apparently, most of the molecules were associated by formation of a hydroxyl bond.

More reliable results were obtained in the work of A. A. Shubina\(^{33,36}\), in which the heat of formation of a series of carboxylic acids was determined. In this case it is well known that the associated complexes are only dimers, and therefore no assumptions are required here except the constancy of \(W\) over the temperature interval.

The quantity \(W\) was determined on the basis of the results of measuring the optical density at the maximum of the absorption band of associated acid molecules at different temperatures and using the formulas written above for the law of mass action

*) In the event that the condition \(\alpha \ll 1\) is not fulfilled, determination of \(W\) can be carried out if three values \(\delta_1\), \(\delta_2\), and \(\delta_3\) are measured for three temperatures \(T_1\), \(T_2\), and \(T_3\). Then the two resulting equations make it possible to determine both the quantity \(W\) and the quantity \(\overline{m}\).

and the van’t Hoff isochore. The results of the determination are given in Table VII.

Table VII

Heat of dissociation of carboxylic acids

The results of the measurement of the heat of dissociation are in good agreement with the most reliable data obtained by other physicochemical methods.

§ 6. INVESTIGATION OF THE INFLUENCE OF THE STERIC FACTOR ON THE ASSOCIATION OF MONOHYDRIC ALCOHOLS

Experiments with solutions of alcohols in neutral solvents have convincingly shown that association of molecules through the formation of a hydrogen or hydroxyl bond can occur only with a definite mutual orientation of the hydroxyl groups. Therefore the presence of any factors that hinder sufficient approach and the necessary orientation of the hydroxyl groups must lead to a decrease in the probability of formation of an intermolecular bond and to an increase in the number of isolated (dissociated) molecules.

Already the experiments of G. S. Landsberg and S. A. Ukholin \(^{12,13}\) showed that the line of isolated molecules appears in methyl alcohol at a considerably higher density than in the case of water; the \(\mathrm{CH_3}\) group of the alcohol molecule to a certain extent screens the \(\mathrm{O—H}\) group and thereby hinders the formation of a hydrogen bond. On the basis of these ideas, one may suppose that in higher monohydric alcohols, in which the hydrocarbon part is more substantial than in methyl alcohol, the steric factor mentioned \(^{15}\) should play an even more noticeable role. It may be expected that in the liquid phase of higher alcohols, already at a comparatively low temperature, there is a certain number of dissociated molecules with an unperturbed \(\mathrm{O—H}\) vibration, and that their number is the greater, the larger the hydrocarbon part.

The investigation of the combination-scattering spectra of monohydric alcohols \(^{37}\), from ethyl \((\mathrm{C_2H_5OH})\) to octyl \((\mathrm{C_8H_{17}OH})\), fully confirmed the assumptions made.

In the spectrum of ethyl alcohol, already at a temperature of \(75^\circ\mathrm{C}\), alongside the band of associated molecules there is observed a sharp line of frequency \(\nu = 3632\ \mathrm{cm}^{-1}\), corresponding to unperturbed vibrations of the hydroxyl group. At the same time, raising the temperature from room temperature to \(75^\circ\mathrm{C}\) led to a displacement of the maximum of the band of associated molecules toward higher frequencies \((\nu \approx 3420\ \mathrm{cm}^{-1})\) and to a slight increase in its width, in accordance with the fluctuation theory.

In the spectra of propyl, butyl, hexyl, heptyl, and octyl alcohols at a temperature of \(75^\circ\mathrm{C}\), the line of isolated molecules is also observed; moreover, its relative intensity, in comparison with the intensity of the band maximum, is the greater, the greater

the hydrocarbon part of the alcohol. The frequency of the line of the isolated molecules is approximately the same for all these alcohols and lies in the interval \(\nu = 3630\)—\(3640\ \text{cm}^{-1}\). The same is true for the band of the associated molecules: the frequency of its maximum lies in the interval \(\nu = 3400\)—\(3430\ \text{cm}^{-1}\). The results of direct photometric measurement of the relative intensity of the line of the isolated molecules and the intensity of the band maximum in the spectra of the alcohols (Table VIII), obtained under identical conditions, illustrate the dependence of the ratio of the number of isolated and associated molecules on the size of the hydrocarbon part.

Table VIII

It is also of interest to estimate the effect of the degree of branching of the hydrocarbon part at one and the same number of hydrogen and carbon atoms. It may be expected that the more branched hydrocarbon part of the molecule will exert a greater shielding action. Indeed, the relative intensity of the line and band for isobutyl alcohol

\[ \left( \begin{array}{c} \mathrm{CH_3}\\[-2pt] \ \backslash\\[-2pt] \mathrm{CH}\\[-2pt] /\\[-2pt] \mathrm{CH_3} \end{array} -\mathrm{CH_2-OH} \right) \]

(see Table VIII) is greater than for normal butyl alcohol \((\mathrm{CH_3-CH_2-CH_2-CH_2-OH})\), and, consequently, the degree of dissociation of the molecules of isobutyl alcohol is also greater.

Fig. 10. Microphotogram of the combination-scattering spectrum of secondary isoamyl alcohol at \(t = 75^\circ\text{C}\).

Similarly, the position of the \( \mathrm{O-H} \) group in the hydrocarbon chain also has an effect: the relative intensity of the line in the spectrum of second-

of isoamyl alcohol

\[ \left( \begin{array}{c} \mathrm{CH}_3\\[-2mm] \mathrm{CH}_3 \end{array} \!\!>\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_3 \atop \mathrm{OH} \right) \]

is greater (see Table VIII and Figs. 10, 11) than in the spectrum of primary isoamyl alcohol

\[ \left( \begin{array}{c} \mathrm{CH}_3\\[-2mm] \mathrm{CH}_3 \end{array} \!\!>\mathrm{CH}-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{OH} \right). \]

These results of measuring the relative intensity of the line and band of butyl and isobutyl alcohols, as well as of primary and secondary isoamyl alcohols, find confirmation in the ordinarily observed lowering of the boiling point of alcohol isomers\(^2\) with an increase in the degree of dissociation (see Table IX).

Fig. 11. Microphotogram of the combination-scattering spectrum of primary isoamyl alcohol at \(t=75^\circ\)C.

Table IX

§ 7. STUDY OF THE PROCESS OF WATER-VAPOR CONDENSATION

One of the latest works carried out under the direction of G. S. Landsberg in the Optical Laboratory of the Physical Institute of the Academy of Sciences, is devoted to the study of the process of condensation of water vapor by spectroscopic methods\(^ {38}\). The formulation of the problem and the results obtained in this work are of known interest and are briefly set forth here.

The process of condensation is connected with the formation of nuclei and, in all probability, proceeds through a series of stages that are intermediate

between the vapor-like and droplet phases, especially if the medium is carefully purified of ions and dust and nuclei arise as fluctuation phenomena. The study of these intermediate stages would undoubtedly be of considerable interest for elucidating the mechanism of condensation. In the case of condensation of water vapor, such investigations could be carried out by studying changes in the frequency of the O—H vibration (for example, from infrared absorption spectra), since this vibration is sensitive to intermolecular interactions and, in particular, to the formation of a hydrogen bond, which occurs for water molecules.

In addition, the study of true absorption in the droplet phase is also of independent interest, since for small droplet sizes \((<1 \mu)\) the number of molecules concentrated in the surface layer may be relatively large compared with the total number of molecules in the drop and therefore the vibrational frequencies of these surface molecules may appear in the spectrum. This, in turn, would make it possible to study the features of intermolecular interactions in the surface layer.

Fig. 12. Transmission spectrum of water fog, obtained by the usual method. Mean droplet diameter \(4\text{–}5 \mu\). LiF prism. The arrow indicates the position of the maximum of the absorption band of a film of liquid water.

To clarify all these questions, transmission spectra of fog with various degrees of condensation were investigated. The transmission spectra were obtained with an automatic double-beam spectrophotometer[^39] in the region \(2.5\text{–}15 \mu\).

The first experiments were carried out with a jet of vapor emerging from the nozzle of a boiler at various distances from the nozzle, where the degree of condensation is different. In this case the spectrum shows only an attenuation of light due to scattering and a very intense absorption spectrum of water vapor; absorption by the droplet phase was not detected even at large distances from the nozzle.

In order to eliminate the interfering absorption bands of vapor, subsequent experiments were carried out with fog obtained by spraying water with an atomizer, and also with fog obtained from vapor but with subsequent strong cooling. Owing to the use of a double-beam illuminator, the absorption of the vapor remaining in the fog could be compensated by the absorption of vapor in the comparison beam. Under these conditions the absorption bands of vapor are absent from the spectrum; however, the absorption bands of the liquid droplet phase also do not appear. At the same time, instead of the expected absorption bands of liquid water in the region where these bands are located, the opposite phenomenon is observed—selective transparency of the fog against the background of the general attenuation of light caused by scattering (Fig. 12). The minima of transparency are located in the region \(\lambda = 2.77 \mu\) and \(5.8 \mu\), and they do not co-

coincide with the maxima of the absorption bands of liquid water ($\lambda = 2.95\ \mu$ and $\lambda = 6.02\ \mu$, respectively). A series of experiments with mists having different mean droplet diameters showed that the position of the transparency bands does not depend on the droplet size.

The existing theories of light scattering by fog for the case in which the particle sizes are comparable with the wavelength of light do not make it possible to explain the observed phenomena. (In our case the droplet diameter lay within the range $3$–$6\ \mu$.)

A number of considerations and additional experiments give grounds for assuming that the observed transparency bands owe their origin to selective scattering near an absorption band, associated with the anomalous course of the refractive index in the region of the absorption bands of liquid water, since the scattering coefficient depends on the refractive index. For the case of water, the quantity $m^2(m-1)^2$, which enters as a factor into the scattering coefficient*), changes by approximately a factor of 13 in the region of anomalous variation of the refractive index $m$, and this causes sharp changes in the attenuation of light due to scattering. These scattering effects evidently mask the true absorption in the droplets, which must also occur, since in scattering a considerable part of the light passes through the droplets.

With the aim of detecting the true absorption, integrating spheres were installed in the optical scheme of the two-beam illuminator; these made it possible to measure the integral absorption within a scattering angle of $\pm 90^\circ$ and to exclude attenuation of the beam due to scattering both in the region of anomalous variation of the refractive index and outside it.

Fig. 13. Transmission spectrum of water mist obtained with integrating spheres. Mean droplet diameter $4$–$5\ \mu$. LiF prism. The arrow at $\lambda = 2.95\ \mu$ indicates the position of the maximum of the liquid-water film; the arrow at $\lambda = 2.77\ \mu$ indicates the position of the transparency band.

The transmission spectrum of the mist obtained with integrating spheres (Fig. 13) differs substantially from the spectrum observed in the ordinary scheme. In it, attenuation of light due to scattering is already practically not manifested; the transparency band is absent, but selective attenuation of the radiation is observed, resembling the absorption band of a film of liquid water. However, the observed band differs somewhat from the absorption band of a water film: it is somewhat broader and has a different shape.

* Such a dependence is strictly fulfilled only for the case in which the particle sizes are greater than the wavelength of light (Jobst’s formula $^{40,41}$). In the present case it is applied only for a qualitative explanation.

and its maximum is shifted by approximately \(100\ \mathrm{cm}^{-1}\) toward longer wavelengths. It is possible that this difference in the shape of the bands is connected with certain scattering phenomena that have not been completely eliminated, owing to the limited integration angle of the sphere; however, it is also not excluded that this difference is caused by absorption by surface molecules, although the role of this effect cannot be significant for droplets several microns in diameter. To clarify this effect, it is proposed to carry out a number of additional experiments. But it may be asserted that in the spectrum obtained with integrating spheres there is manifested, in the main, the true absorption of water droplets, which is not observed in the usual methods of obtaining fog spectra.

Analogous phenomena are also observed in the transmission spectra of a “two-dimensional” fog obtained by depositing small water droplets on various surfaces. By varying, in this case, the distance between the cell with the fog and the entrance aperture of the integrating sphere (thereby changing the integration angle), one can observe all intermediate pictures: from an transparency band to an absorption band.

If the droplets of the “two-dimensional” fog are surrounded not by air but by a transparent solvent, for example \(\mathrm{CCl}_4\), then the scattering effects are considerably reduced and, when observed in the transmitted beam (without spheres), an absorption band of liquid water is observed in the spectrum. The same is also observed in the case of an aqueous emulsion in \(\mathrm{CCl}_4\)—a “three-dimensional” fog in \(\mathrm{CCl}_4\).

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