Molecular Spectral Analysis

V. M. Chulanovsky

Introduction

The topic to which the present article is devoted is extensive. Descriptions of works in which methods of molecular spectral analysis are used fill the pages of journals on analytical chemistry in various languages. The situation is worse with reviews and monographs, but even their number and scope testify to the great topical importance and variety of the methods of molecular spectroscopy and to the broad possibilities for their use in the national economy.

In this article only a brief outline can be given of what molecular spectral analysis is at the present time and what the possibilities are for its use in various cases. For more detailed acquaintance I must refer the reader to the monographs and reviews available in Russian[^1].

The need for new, more effective methods of analysis has arisen mainly in connection with the intensive development, over the last two or three decades, of the mass production of materials with special properties. The old methods of analysis, by means of which an idea was formed of the degree of purity and of the qualitative and quantitative composition of semifinished products and the finished product, often proved insufficient. Particularly acute has been the need for methods by means of which it is possible to determine not so much the elemental composition of the molecules of the substance under investigation as their form, the presence in them of certain structural elements, or the character of those more complex formations which arise, for example, during polymerization. Various branches of production of complex organic substances are interested in such methods of molecular analysis. To an ever greater extent they are also becoming necessary in the laboratory of the biologist or the physician.

Chemical methods of analysis, whose main basis is the ability of a substance to enter into reactions characteristic of it, often prove insufficiently selective. Thus, in the produc-

...in the composition of gasolines, it is impossible by chemical methods to distinguish two isomers of paraffin hydrocarbons with one side chain, differing only in the point of branching. In the analysis of a mixture of paraffin hydrocarbons by chemical methods only a more or less rough group analysis is possible. With the aid of spectral analysis such a problem is solved unambiguously and, moreover, by comparatively simple means. In other cases the exact meaning of the results of chemical analysis is not known and is to some extent conventional. Its meaning can be revealed by means of more selective spectral analysis. Usually spectral analysis requires considerably less time (hours, and sometimes minutes), and in a properly equipped laboratory it is always cheaper. Very often one or another combination of both methods is the most advantageous.

In the spectral methods of analysis use is made of the interaction of a substance, characteristic for it, with light. By their nature these methods are related to chemical ones. In both cases the matter concerns the action of either another substance or a light wave on the system of electrons and positively charged nuclei forming the molecule. In spectroscopy these interactions lead to an exchange of energy between the molecule and the light wave, as a result of which the reserve of internal energy of the molecule changes by the amount \(E_2-E_1\), if \(E_2\) and \(E_1\) refer to the initial and final states of the molecule. Molecular spectral analysis is possible only in those cases when such an exchange does not lead to destruction of the molecule itself: to its ionization or dissociation. Such cases of destruction of the molecule occur very often and may be noted by the appearance in the absorption spectrum of a continuous band, having no structure and unsuitable for analytical purposes, or by the spectra of the products of destruction of the molecule.

The characteristic of a spectrum determining the possibility of qualitative analysis is the set of proper frequencies inherent in the given molecule:

\[ \tilde{\nu}=\frac{E_2-E_1}{h}, \tag{1} \]

or of wave numbers:

\[ \nu=\frac{1}{\lambda_{\mathrm{cm}}}=\frac{E_2-E_1}{hc}. \tag{1a} \]

The letter \(h\) denotes Planck’s constant, \(c\) the velocity of light. By \(E\) are denoted the values of the total energy of the molecule in different energy states. The character of the change of energy states determines the character and the position, on the scale of wave numbers (or wavelengths), of the lines or bands.

Spectra obtained as a result of changes only of the rotational state of a free molecule require the least energy for their excitation. They lie in the very far...

in the infrared region, within limits from several tenths to several tens of reciprocal centimeters (in the wavelength region from several centimeters to fractions of a millimeter). This region has become accessible to investigation only very recently, as a result of the latest advances in radio engineering, and is the subject of rapidly developing radiospectroscopy. For analytical purposes this region at present is of only limited interest.

From rotational spectra one can determine the rotational constant, which depends on the moment of inertia of the molecule \((I = mr^2)\), and by this means the molecule can also be determined. This is not a very selective characteristic of it, and the analytical problem can be solved more easily and more broadly by other spectral methods. Radiospectroscopy can be of interest to the spectroscopist-analyst only in those cases in which its enormous resolving power can be used, for example, for determining the isotopic composition of molecules.

At present, vibrational spectra are of the greatest interest for analytical purposes. The region of vibrations used in practice is bounded, on the one hand, by several hundreds and, on the other, by ten thousand reciprocal centimeters. The wave numbers of electronic spectra, obtained upon excitation of the electron shell of the molecule, are measured in tens of thousands of reciprocal centimeters.

For analytical purposes both absorption spectra in various regions of the spectrum and emission spectra or spectra of combination scattering of light are used. An electric discharge for obtaining emission spectra can be used only for work with diatomic molecules. Polyatomic molecules, as a rule, are destroyed in it. Flames also give spectra of the decomposition products of polyatomic molecules; therefore the spectral study of flames may be of interest primarily for investigation of the combustion process itself.

Below, only the use of one emission method—the luminescence method—will be discussed.

ABSORPTION METHODS OF MOLECULAR SPECTRAL ANALYSIS

A) Lambert–Beer Law

Absorption methods, for a number of reasons that will become clear from what follows, possess the widest field of application, and at present they should be regarded as the principal ones.

The basis of all absorption methods is the Lambert–Beer law

\[ I_\nu = I_{0\nu} e^{-k_\nu C d}, \tag{2} \]

where \(I_\nu\) is the magnitude of the monochromatic radiation flux that has passed through the absorbing layer, corrected for reflection at its boundaries, \(I_{0\nu}\) is the magnitude of the radiation flux incident on the first boundary of the substance, \(k_\nu\) is a quantity characteristic of the substance and called the absorption coefficient,* \(C\) is the concentration, and \(d\) is the thickness of the absorbing layer. This law presupposes strict monochromaticity of the radiation. If the deviations from monochromaticity are not large and the value of \(k_\nu\) in the region of these deviations changes little, then the Lambert–Beer law is still applicable, but already for the mean values of \(I_\nu\), \(I_{0\nu}\), and \(k_\nu\). In those cases where these conditions are not satisfied sufficiently rigorously, apparent deviations from this law are observed, which, when not very large, can be taken into account.

Real deviations from the Lambert–Beer law occur in those cases where, with a change in concentration, the very nature of the absorbing substance changes. An excessive increase in concentration sometimes leads to the formation of more complex complexes. Conversely, when it is decreased, in a number of cases decomposition into ions may occur as a consequence of electrolytic dissociation.

When the concentration of a substance is increased, the exponent at \(e\) in expression (2), or the quantity \(\ln \dfrac{I_{0\nu}}{I_\nu}=D\), called the optical density, increases proportionally to it. Quantitative analysis from absorption spectra is based on measurement of this quantity \(D\). For a mixture of several absorbing substances or for their solution in a nonabsorbing solvent, the corresponding formulas will have the form

\[ I_\nu = I_{0\nu} e^{-\Sigma k_{\nu_i} C_i d} \]

and

\[ D=\ln \frac{I_{0\nu}}{I_\nu}=\sum k_{\nu_i} C_i d. \]

To find the concentrations \(C_i\) of all absorbing components, it is necessary to know, for them, \(k_{\nu_i}\) and the common value \(d\), and to make measurements at \(n\) points of the spectrum, where \(n\) is the number of components. The concentrations \(C_i\) are ultimately found by solving the system of equations

\[ D^{(l)} = d \sum_{i=1}^{n} C_i k_{\nu_i}^{(l)}. \]

* For practical purposes this equation is often written in another form:

\[ I_\nu = I_{0\nu} 10^{-\chi_\nu C d}. \tag{2a} \]

In this case \(\chi_\nu\) is called the extinction coefficient.

V. M. CHULANOVSKY

For the simple case of a solution in a nonabsorbing solvent of two absorbing substances \(a\) and \(b\) with overlapping absorption spectra, this system has the form*)

\[ \begin{aligned} D_{\nu_1} &= C_a k_{\nu_1}^{(a)} + C_b k_{\nu_1}^{(b)},\\ D_{\nu_2} &= C_a k_{\nu_2}^{(a)} + C_b k_{\nu_2}^{(b)}, \end{aligned} \tag{3} \]

whence

\[ C_a = \frac{ D_{\nu_1} k_{\nu_2}^{(b)} - D_{\nu_2} k_{\nu_1}^{(b)} }{ k_{\nu_1}^{(a)} k_{\nu_2}^{(b)} - k_{\nu_2}^{(a)} k_{\nu_1}^{(b)} }, \]

\[ C_b = \frac{ D_{\nu_2} k_{\nu_1}^{(a)} - D_{\nu_1} k_{\nu_2}^{(a)} }{ k_{\nu_2}^{(b)} k_{\nu_1}^{(a)} - k_{\nu_1}^{(b)} k_{\nu_2}^{(a)} }. \tag{4} \]

Expressions for the concentration have the same form also when the number of components is larger. From the system of equations written above it is not difficult to see that the errors in determining the various \(D\) and \(k\) have the smaller effect on the determination of \(C_a\) and \(C_b\), the smaller are the second terms in the numerator and denominator of equation (4) in comparison with the first terms, i.e., the more \(k_{\nu_1}^{(a)}\) predominates over \(k_{\nu_1}^{(b)}\) at \(\nu_1\), and \(k_{\nu_2}^{(b)}\) over \(k_{\nu_2}^{(a)}\) at \(\nu_2\).

Fig. 1. Scheme of overlap of two absorption bands.

Figure 1 shows a comparatively simple case of overlap of the absorption bands of two absorbing substances \(a\) and \(b\). The vertical parallel lines mark narrow spectral regions cut out by the monochromator and used for the analysis. As is evident from the figure, the conditions for the most accurate determination of \(C_a\) and \(C_b\)

*) For simplicity of reasoning it is assumed that \(d = 1\).

are not strictly tied to the exact choice of \(\nu_1\) and \(\nu_2\) at which the analysis is carried out. With equal success they can be chosen otherwise, within fairly broad limits.

If the matter concerned only the accuracy of finding the concentrations from equations (4), then it would be possible to work not only with wide slits, but even to dispense with the spectrograph altogether, replacing it by a differential absorptiometer in which coarse monochromatization in different parts of the spectrum is achieved by light filters.

This would mean a great simplification of the work and the use of apparatus much cheaper and more familiar to the chemist. For the case shown in the figure, two light filters would be quite satisfactory, their transmission regions being indicated by the dotted curves.

An obstacle to such a transition to simpler apparatus is the fact that, in the absence of monochromatization, the Lambert–Beer law cannot be used. It must be replaced by the integral formula

\[ I=\int I_\nu\,d\nu=\int I_{0\nu} e^{-c_i k_{\nu i} d}\,d\nu . \tag{5} \]

However, it can be shown that, for a small amount of absorption—which can always be achieved by dilution in the absorbing solvent or by reducing the thickness of the absorbing layer—the determination of concentrations can likewise be reduced to the solution of a system of linear equations, and that the condition for the accuracy of determining the individual concentrations is also determined by the extent to which, with one filter, the absorption of one of the components is greater than the absorption of the other, while with another filter the absorption of the second component is large relative to the first.\(^1\)

Methods employing integral absorption have high sensitivity and are of special interest in the detection or quantitative measurement of very small impurities whose qualitative composition is known.

At present the principal method of absorption analysis is the spectral method, in which the absorption of monochromatic beams of light is determined separately.

The basis of qualitative analysis is the presence of bands characteristic of a substance or of individual structural elements of its molecule.

Quantitative absorption analysis is based on measuring the magnitude of absorption—or, better, optical density—at specified values of \(\nu\) as a function of concentration. The accuracy of measuring the amount of absorbing substance depends on the magnitude of its absorption. At low concentration the absorption is also small and, consequently, the errors in measuring absorption will be comparable with the measured magnitude of absorption. At very large absorp-

the amount of light that has passed through the absorbing layer will be small. Since the primary measured quantity is this amount of light, the error in its measurement will also be comparable with its magnitude. The absorption will again be determined inaccurately. It is not difficult to show that small changes in the absorption curve, determined by the presence of an absorbing substance, appear most distinctly, and the determination of the amount of substance itself can be made with the greatest accuracy, when the magnitude of the flux \(I_\nu\) is from 25 to 50% of \(I_{0\nu}\).

B) Analysis by spectra in the visible and ultraviolet regions

The possibility of using ultraviolet and visible absorption spectra for analytical purposes was understood and employed earlier than all others; the technique of working with them is the simplest and has long been known.

Absorption in the visible and ultraviolet regions of the spectrum is associated with the transition of the electron shell of a molecule into an excited state or with its destruction as a result of ionization or dissociation. Excitation of the electron shells of polyatomic molecules that do not have multiple bonds almost always leads to the appearance of continuous spectra, i.e. is associated with destruction of the molecule. Much more rarely, broadened spectra with weakly expressed maxima are observed in this case, which are also unsuitable for analytical purposes. Only in diatomic molecules with a single bond are they discrete. Thus, absorption methods in the visible and ultraviolet parts of the spectrum cannot be used for the analysis of saturated chain or cyclic hydrocarbons or their derivatives, although the need for such analyses is very great, for example, in the production of synthetic gasolines or of the intermediates from which they are obtained.

At present these methods are used for the analysis of substances whose molecules contain one or several multiple, usually double, bonds. They have found especially wide application in the analysis of aromatic hydrocarbons or their derivatives and of dyes.

Thus, the structural element of a molecule that determines the discreteness of its absorption spectrum is the multiple bond.

If absorption occurs in a sufficiently rarefied gas, whose molecules may be regarded as not interacting with one another, then the electronic transition associated with absorption is accompanied by various changes in the vibrational and rotational states of the molecule. In a liquid, the character of the motion of the molecule as a whole changes, and the separation of the band into individual lines

(rotational structure of the band) disappears. The spectrum consists of a series of comparatively narrow bands corresponding to various changes in the vibrational state of the molecules. In more complex molecules these bands merge, and one broader band is formed, sometimes extending over several hundred angstroms and possessing an internal structure. In both cases the selectivity is sufficiently good for analytical purposes.

The group of atoms (near a multiple bond) that determines the discrete absorption is called a chromophore. In the case of chain molecules one most often has to deal with ethylenic \((\mathrm{C}=\mathrm{C})\) and carbonyl \((\mathrm{C}=\mathrm{O})\) chromophores. The characteristic wavelength in the first case is about \(1800\,\text{Å}\), in the second—about \(2800\,\text{Å}\). However, absorption is characteristic not only of those two atoms which are connected by a double bond, but to some extent also of their immediate environment. Thus, for example, in the case of an ethylenic bond the absorption of the groups \(\mathrm{H_2C}=\mathrm{CH}-\), \(-\mathrm{HC}=\mathrm{CH}-\), or

\[ \begin{array}{c} \mathrm{CH_3}\backslash \\ \mathrm{CH_3}/ \end{array} \mathrm{C}=\mathrm{CH}- \]

although it lies approximately in the same spectral region, nevertheless differs considerably in its character and somewhat in its wavelength.

Chromophoric groups, if they are located close to one another, for example in adjacent or conjugated positions, influence one another. As a result the spectrum changes its appearance and, as a rule, is shifted into the long-wavelength region. Sometimes this circumstance can be used to facilitate analytical work. Thus, in determining the degree of unsaturation of fatty acids, whose molecules have several ethylenic double bonds separated from one another and therefore not interacting, the absorption spectrum is observed, as in the case of a single double bond, in the far ultraviolet. In this spectral region the quartz optics of the spectrograph, the gelatin of the photographic plate, and even the air itself (more precisely, the oxygen of the air) become opaque. For ordinary analytical work this region of the spectrum is practically not used. By subjecting fatty acids to the action of an alcoholic alkali solution at a temperature of \(180^\circ\mathrm{C}\), the separated ethylenic bonds can be converted into the conjugated position. In this case, with two double bonds, the absorption maximum shifts to \(2340\,\text{Å}\), and the work becomes comparatively simple.^10 With a larger number of double bonds in the conjugated position, the absorption spectrum shifts still farther into the long-wavelength region.

The most favorable object for analytical work in the ultraviolet is aromatic compounds. The absorption spectrum of benzene, toluene, xylenes, and other benzene derivatives, as well as the spectra of more complex aromatic hydrocarbo-

carbons: naphthalene, anthracene, etc., in the form of a pure liquid or solution, consists of a small number of narrow bands conveniently located in the near ultraviolet region of the spectrum.

Analysis for the detection of aromatics is very sensitive. In a layer of solution about 50 mm thick, it is still possible to detect 0.005% of benzene or toluene.

The spectral method of determining aromatic hydrocarbons is successfully applied in the most varied cases, both in the production of these hydrocarbons and in those cases where they interfere or are harmful, for example traces of naphthalene and heavier aromatics in illuminating gas, the detection of benzene vapors in the air of workshops when working with rubber, etc.

In the food industry, molecular spectral analysis in the ultraviolet is used not only in the production of edible fats, but also in their enrichment with vitamins: analysis for ascorbic acid, carotenes, etc. In the case of carotenes it is easy to carry out an analysis for their total amount. It is considerably more difficult to separate α-, β-, and γ-carotenes, which differ only in the character of the terminal units of a long chain with nine conjugated bonds.

Analysis by electronic absorption bands is especially convenient in application to dyes, since in this case it can be carried out in the visible region of the spectrum.

Recently this type of analysis has found application also in solving more complex chemical and biochemical problems: in the analysis of mixtures of alkaloids, in the production of penicillin, and even in the study of the protein components of healthy and diseased tissue of the animal organism. More detailed acquaintance with these works may be obtained from review articles^2,1,11,12.

Within the scope of the present article it is impossible to speak either of the apparatus or of particular analytical methods. For this one must turn to the sources indicated above.

I shall confine myself only to the remark that the methods of visual and photographic spectrophotometry are gradually yielding to methods of photoelectric recording, which are more accurate, faster, and more convenient. The most suitable instrument for this purpose is the SF-1 spectrophotometer, manufactured by domestic industry *).

B) Analysis by infrared absorption spectra

In the infrared region of the spectrum, analytical work is carried out in the wavelength range of approximately 1 to 15 μ. In this region there are located, for the most part, absorption bands corresponding to fundamental vibrations and their first overtones.

*) See the article by S. A. Khrshanovskii^2.

The number of vibrations determining these bands depends on the complexity of the molecule. It does not exceed \(3N-5\) for a linear molecule and \(3N-6\) for a three-dimensional one, if \(N\) denotes the number of atoms forming the molecule. Usually the number of distinct vibrations is smaller, since some of them have the same frequency and the corresponding bands overlap.

Vibrational spectra differ from electronic spectra above all in their universality. When a molecule is excited as a result of the absorption of light, it does not decompose, and therefore the absorption has a selective character. The process by which the absorbed energy is transformed into heat occurs in this case in one way or another and in practice is not an obstacle to the operation of the spectroscopist.

Since the absorption coefficients of the characteristic bands in the region of the fundamental frequencies are very large, very thin layers must be used for analytical work. Under these conditions even products obtained from coal or tars can be successfully investigated in the infrared region. A slight turbidity, which scatters light and interferes with work in the ultraviolet and even in the near infrared region, ceases to be an obstacle in the region of the medium frequencies of the fundamental vibrations. Vibrational spectra are simpler than electronic spectra.

The rotational structure of absorption bands in a gas, which interferes with analysis in the case of light molecules, ceases to be an obstacle for gases whose molecules contain not fewer than four carbon atoms.

The elasticity of the gas in this case must exceed several tens of millimeters of mercury[^13][^14]. In a liquid, the spectra retain sufficient selectivity for analysis and consist partly of separated and partly of overlapping bands. Complication of the spectrum is often obtained as a result of the superposition, on the fundamental absorption bands, of overtones or combination bands, the wave number of which is equal to the sum or difference of the wave numbers of the elementary bands.

Sometimes the spectrum is complicated by the formation of combination bands produced as a result of the interaction of an intramolecular vibration with the vibration of molecules of the liquid relative to one another. Such bands appear most clearly in the case of hydrogen bonding.

The excitation of the vibrational state upon absorption of light differs favorably from electronic excitation also in that, in this case, the activity of the molecule is increased to a lesser degree.

The wave number corresponding to the vibration of a diatomic molecule is highly characteristic of it, since it depends on the most important parameters determining its structure—

meters: on its reduced mass \(\mu\)* and on the force constant \(f\):

\[ \nu=\frac{1}{2\pi c}\sqrt{\frac{f}{\mu}}, \tag{6} \]

where \(c\) is the speed of light. In a polyatomic molecule capable of various vibrations, all the atoms of the molecule take part in each of the vibrations. However, in different vibrations they do not all participate to the same extent. In those cases where the molecule contains a group of atoms differing from the others in mass and in bond strength \((f)\), and where its frequency is incommensurable with the frequencies of the other vibrations, there necessarily occurs such a vibration in which primarily the atoms of this group take part. The participation of the remaining atoms of the molecule in this vibration is small. This is the case, for example, with the O—H group in alcohols, with the C=O group in carboxylic acids, with the C—H group in chloroform \((\mathrm{CHCl}_3)\) or bromoform \((\mathrm{CHBr}_3)\), with the \(\mathrm{CH}_3\) group in methyl chloride \((\mathrm{CH}_3\mathrm{Cl})\), and so on. In these cases the vibration is characteristic of the group and can be observed in molecules of various structures, provided that this group is present in them. The wave number of such a vibration and the intensity of the corresponding absorption band may be used as an analytical indication both for detecting definite groups of atoms and for determining the multiplicity of the bonds between them in various substances. Table I gives the wave numbers for a number of characteristic groups of atoms in the molecule.

A much more complete list of characteristic vibrations may be found at the end of the second volume of the book by M. V. Vol’kenshtein, M. A. El’yashevich, and B. I. Stepanov[^15]. The complete set of vibrations is characteristic of the entire molecule and may serve for its unambiguous identification.

Identical and closely situated structural elements of a molecule, for example two C—C groups in the chain of a paraffin hydrocarbon, interact with one another. As a result, instead of one band characteristic of the C—C group in a diatomic molecule, in this case two bands are observed, one with a somewhat lower and the other with a higher frequency. The greater the number of identical and mutually bonded groups, the more complex the spectrum determined by them. A change in the mutual arrangement of the C—C elements upon branching of the molecule leads to a change in the form of the spectrum. On the basis of an analysis of a large amount of experimental material, B. I. Stepanov1 developed in detail a scheme by which, from the observed position in the spectrum and

* The reduced mass \(\mu\) depends on the masses of both nuclei \(m_1\) and \(m_2\) as follows:

\[ \frac{1}{\mu}=\frac{1}{m_1}+\frac{1}{m_2}. \]

MOLECULAR SPECTRAL ANALYSIS

Table I

from the intensities of a number of bands to judge the character and position of branching in the molecule of the paraffin hydrocarbon being determined.

The analytical possibilities of infrared spectroscopy are very broad. In the present article I shall confine myself to considering only a few typical examples.

For analytical work with absorption spectra in the infrared region, the so-called two-beam scheme$^{1}$ is being used more and more often; it makes it possible to determine directly the value of $\dfrac{I}{I_0}$, or even $\ln \dfrac{I_0}{I}$ or $\lg \dfrac{I_0}{I}$. This circumstance speeds up and facilitates the process of measurement and, to an even greater extent, the recalculation of experimental data. Such a method of work is especially convenient when the solvent itself has absorption bands in the measured region that interfere with observation*).

*) In the infrared region of the spectrum it is much more difficult, and often simply impossible, to find a solvent that is completely transparent in the region of the spectrum of interest to the investigator.

Figure 2 shows an example of such a recording. In the upper part of the figure is given the recording of the percentage transmission of a mixture of acetone with catechol, whose absorption spectra overlap. The middle curve corresponds to the transmission of pure acetone, which in this case is regarded as the solvent. In the lower part of the figure is shown the differential curve, during the obtaining of which the same mixture of catechol in acetone was placed in one light beam, and pure acetone in the other.

Fig. 2. Automatic recording of the spectral transmission curve (in percent) for a mixture of acetone with catechol and for pure acetone.

in acetone, and in the other—pure acetone. In the difference curve, recorded directly in this case, no traces of the acetone spectrum remained. It characterizes only catechol.

As was said above, in analyzing a mixture consisting of \(n\) components, it is necessary to select such \(n\) points in the spectrum, at each of which the absorption of one component would be, as far as possible, large in comparison with the absorption of the other components (the key wavelength for determining the given component).

At these \(n\) points of the spectrum the optical density is determined. The rest of the matter reduces to solving a system of \(n\) equations for the concentrations of the individual components. With a good setup—

... analysis can be performed with great accuracy. Tables II and III give two examples of such an analysis.

Table II

Analysis of a seven-component mixture in the vapor state¹³

Table III

Analysis of a five-component liquid mixture

It is often necessary to deal with mixtures in which the absorption curves \((k_\nu)\) of some of the components intersect at a single point. By using measurements of the optical density at this point, these components can be determined in total.

Specific difficulties in quantitative determination arise in those cases where the individual substances to be determined in the mixture cannot be obtained in pure form. This is the case, for example, in the polymerization of rubbers, which may proceed by various paths. In this case model substances are used, i.e., simpler substances that can be obtained individually and that contain the same characteristic groups as the rubber forms being determined.

Thus, in diene polymers the following arrangements of neighboring atoms about the double bond are possible:

\[ \begin{array}{ccc} \begin{array}{c} \mathrm{H}\qquad\qquad \mathrm{H}\\ \ \backslash\qquad\ /\ \\ \mathrm{C}=\mathrm{C}\\ /\qquad\backslash\\ {-}\mathrm{CH}_2\qquad \mathrm{CH}_2{-}\\[4pt] \text{cis 1-4 form} \end{array} & \begin{array}{c} \mathrm{CH}_2\backslash\\ \qquad \mathrm{CH}{-}\\ \mathrm{H}{-}\mathrm{C}\\ \qquad\ \Vert\\ \qquad \mathrm{CH}\\ \mathrm{H}\\[4pt] \text{1-2 form} \end{array} & \begin{array}{c} \qquad\qquad \mathrm{H}\\ \qquad\qquad |\\ \mathrm{CH}_2\backslash\qquad \mathrm{C}\\ \qquad\qquad \mathrm{C}\ \Vert\qquad \backslash \mathrm{CH}_2 /\\ \qquad\qquad |\\ \qquad\qquad \mathrm{H}\\[4pt] \text{trans 1-4 form.} \end{array} \end{array} \]

Natural rubber consists almost entirely of the cis 1,4-form, balata of the trans 1,4-form. Synthetic rubber is a mixture of all three forms. Analysis is necessary in order to select those polymerization conditions under which the rubber acquires the best technical properties.

The three forms indicated above occur in various olefins. To each of these forms in different olefins there corresponds its own band with an almost constant absorption coefficient1.

Thus, for

The same bands are also encountered in diene rubbers. Assuming that the same absorption coefficient corresponds to them, one can, using its values obtained for olefins, reliably carry out the analysis of rubbers.

A special place in the analytical use of infrared spectroscopy should be assigned to XH groups, in which X may denote an atom of oxygen, carbon, nitrogen, a halogen, or some other atom. Owing to the small mass and dimensions of the hydrogen atom entering into XH groups, the wave numbers characteristic of their bands occupy the most short-wavelength region of the infrared spectrum, approximately from 2700 to 4000 reciprocal centimeters (\(\lambda\) from 3.6 to \(2.5\mu\)). Of the other fundamental vibrations, only overtones and combination bands fall into this region, and their absorption is considerably weaker. For practical purposes not only these bands are used, but also their overtones, lying in an even shorter-wavelength region of the spectrum. Work in the region in which the bands of XH groups or their overtones are found is considerably simpler than in the longer-wavelength region. First, in this spectral region the source gives more light, and it is easier to combat parasitic radiation. Second, almost down to \(3.5\mu\) one can use quartz optics, which also provides great convenience. In contrast to rock salt, used for the more distant spectral region, quartz is not hygroscopic, is chemically stable, and is easily worked. Moreover, in the near infrared region the thermoelement can be replaced by a more sensitive photoelement.

The possibilities of analysis by means of XH groups are more limited, but nevertheless in a number of cases such analysis proves quite profitable.

Thus, for example, it may sometimes be of interest to determine the number of hydroxyl groups \((\mathrm{OH})\) not bound into complexes by hydrogen bonding. Spectroscopically free hydroxyl, giving

well-defined narrow band near 3600 cm\(^{-1}\), is easily distinguished from the bound one, since upon formation of a complex through a hydrogen bond the spectrum is a broad band shifted from 3600 cm\(^{-1}\) toward smaller wave numbers (longer wavelengths). Especially often, for analysis one has to use absorption spectra associated with vibrations of CH groups. These groups may occur in various combinations:

\[ \mathrm{C{-}CH_3},\quad \begin{array}{c} \mathrm{C}\\[-0.2em] \diagdown\\[-0.2em] \mathrm{CH_2}\\[-0.2em] \diagup\\[-0.2em] \mathrm{C} \end{array},\quad \mathrm{C{=}CH_2},\quad \begin{array}{c} \mathrm{C}\\[-0.2em] \diagdown\\[-0.2em] \mathrm{C{-}C{-}H}\\[-0.2em] \diagup\\[-0.2em] \mathrm{C} \end{array} \quad \text{and} \quad \begin{array}{c} \mathrm{C{\equiv}C{-}H}\\[-0.2em] |\\[-0.2em] \mathrm{C} \end{array} \]

In the thirties, when the still primitive technique of infrared spectroscopy in the longer-wavelength region did not permit analytical applications, analysis by CH groups was used to determine the degree of branching of paraffin hydrocarbons in the production of aviation gasolines. The analysis was based on the fact that the absorption band characteristic of CH\(_3\) groups is shifted toward shorter wavelengths relative to the CH\(_2\) band.

And indeed, by means of such a method one can determine, for an unknown paraffin hydrocarbon, the relative number of CH\(_3\) and CH\(_2\) groups. For rough determinations this method can also be applied in analyzing not very broad fractions of mixtures of paraffin hydrocarbons.

The reasons that hindered the further development of this method for analyzing mixtures of paraffin hydrocarbons are that the CH\(_2\) and CH\(_3\) bands partially overlap and somewhat change their appearance for different isomers.

Considerably greater prospects are offered by determining the degree of unsaturation of hydrocarbon chains by the group \(=\)CH\(_2\), whose spectrum has sufficiently well isolated peaks. The absorption band characteristic of this group was used by M. G. Batishcheva and A. N. Mironov\(^2\) to determine the degree of unsaturation of esters of unsaturated fatty acids in cottonseed oil at various stages of its hydrogenation, or as a result of its oxidation or polymerization. In Figs. 3 and 4 the curves \(I_0/I\) are given for these cases.

Analysis by the absorption spectra of the groups —CH\(_2\)— and \(=\)CH\(_2\) was used by M. P. Burgova and A. A. Korotkov\(^ {21}\) to determine the nature of branching in rubber obtained by polymerization of the divinyl molecule

\[ \mathrm{CH_2{=}CH{-}CH{=}CH_2}. \]

Fig. 3. Absorption curves \((I_0/I)\) of sunflower oil at different stages of hydrogenation: 1 — original oil, 2 — hydrogenated for 20 minutes, 3 — hydrogenated for 30 minutes, 4 — hydrogenated for 40 minutes; layer thickness 1 mm. Curves 1a and 2a correspond to a layer thickness of 0.152 mm.

Fig. 4. Absorption curves of sunflower oil: 1 — original, 2 — oxidized, 3 — polymerized.

In the cell of 1,4-divinyl,

\[ -\mathrm{CH_2-CH=CH-CH_2}- \]

there are two groups \(-\mathrm{CH_2}-\).

In the cell of 1,2-divinyl there is one group \(-\mathrm{CH_2}-\) and one \(=\mathrm{CH_2}\)

\[ \begin{array}{c} -\mathrm{CH_2-CH}-\\ \phantom{-\mathrm{CH_2}}\vert\\ \mathrm{CH}\\ \Vert\\ \mathrm{CH_2} \end{array} \]

The absorption bands of these groups are well separated from one another

\[ (\nu_{-\mathrm{CH_2}-}=2919\ \mathrm{cm}^{-1}, \]

\[ \nu_{=\mathrm{CH_2}}=3075\ \mathrm{cm}^{-1}) \]

and from other CH bands. The authors showed that it is more advantageous to carry out the analysis not on the fundamental tones, but on the first overtones, since in rubbers they are better isolated. The positions of these bands in Figs. 5 and 6 are indicated by arrows. For quantitative determinations, the absorption coefficients of these groups were used

Fig. 5. Spectral absorption curve of divinyl rubber (solution in \(\mathrm{CCl_4}\)) at the fundamental tone.

Fig. 6. Spectral absorption curve of divinyl rubber (solution in \(\mathrm{CCl_4}\)) at the first overtone.

in various individual substances, for which they are sufficiently constant.

Undeservedly forgotten, after a not very successful beginning in application to mixtures of paraffin hydrocarbons, the field of absorption analysis on overtones of CH vibrations may, in a number of cases, prove very useful.

ANALYSIS BY SPECTRA OF COMBINATION SCATTERING OF LIGHT

Methods of analysis by means of combination scattering of light began to be used for analytical purposes earlier than the methods of infrared absorption spectroscopy, and the Soviet reader is better acquainted with them\(^{7,5,1,2}\); I shall therefore confine myself to a more concise exposition.

When the sample under study is illuminated with monochromatic light (far from the absorption bands), a light quantum \(h\nu\), acting on a molecule of the substance, may lose part of its energy \(h\nu_{\mathrm{v}}\) in exciting intramolecular motion. The quantum \(h\nu_{\mathrm{n}}\) changed in this way is accessible to observation. In rarer cases, a quantum \(h\nu_{\mathrm{v}}\) may be added to the light quantum \(h\nu\). Thus, in combination scattering of light, the observer can detect, with the aid of a spectral instrument, not only unchanged quanta \(h\nu\), but also quanta decreased or increased through exchange with intramolecular motion:

\[ h\nu_{\mathrm{n}} = h\nu \mp h\nu_{\mathrm{v}}. \tag{7} \]

Cancelling \(h\) and passing to wave numbers \(\nu\), we obtain:

\[ \nu_{\mathrm{n}} = \nu \mp \nu_{\mathrm{v}}. \]

The wave number corresponding to a change in the rotational or vibrational state can be obtained as the difference between the wave numbers of the incident monochromatic light and the wave number observed in the combination scattering of light.

An important property of such a process of light scattering for analytical purposes is the very small probability of energy exchange of the light wave simultaneously with two different types of motion, for example vibrational and rotational, or with two different vibrations. This circumstance leads to the fact that in the spectrum of combination scattering of light there are almost no lines of the type \(\nu_{\mathrm{v}_1} \pm \nu_{\mathrm{v}_2}\), and the spectrum becomes more selective.

This great selectivity of the spectra of combination scattering of light makes them especially suitable for qualitative analysis of multicomponent mixtures.

In quantitative analysis various difficulties arise, stemming chiefly from the low brightness of the spectra of combination scattering of light, with which various other kinds of radiation easily compete, reaching the photographic

plates: 1) fluorescence of negligible fluorescing impurities not removed during purification, 2) scattering, with unchanged wavelength, of the weak glow with a continuous spectrum from the mercury arc that is usually used to illuminate the sample, 3) stray light with unchanged wavelength, scattered by slight turbidity in the sample or by surfaces and defects of the optical system, etc. Nevertheless, combination scattering of light is now being successfully used not only for qualitative, but also for precise quantitative analysis of mixtures. Very recently, successful attempts have been made to replace the photographic plate by an electron photomultiplier. Work with such a receiver of radiant energy not only eliminates the laborious and, in the case under consideration, not very accurate procedure of photographic photometry, but also makes the measuring process itself more accurate, rapid, and simple.

The field in which combination scattering of light has been used for analysis is narrower than the field of application of absorption methods in the infrared spectra. It is limited by the requirements that the sample should not absorb near the exciting line, should not fluoresce, should not change under the influence of excessively bright illumination, and should not contain scattering suspensions.

Despite the fact that spectroscopy of combination scattering of light has been applied in the study of a very large number of the most diverse compounds, for analytical purposes it has been used chiefly in the case of various mixtures of not very heavy hydrocarbons.

This type of analysis has found its best application in the production of synthetic gasolines. Soviet physicist-spectroscopists occupy an honorable place in this field.

It may be hoped that the use of so-called additional filters and special illumination[^1] will make this method suitable also for everyday work with solutions of polymerizing unsaturated hydrocarbons. Such solutions are always turbid, and the usual working procedure is insufficient here; the need for such a selective, although not very sensitive, analysis, which the method described is, is very great in the production of synthetic rubbers and other polymerization products.

LUMINESCENCE ANALYSIS

The luminescence method is the only emission method used in the molecular analysis of complex compounds. Luminescence, i.e. the glowing of a body, may occur under the influence of various factors: a chemical reaction, the action of a beam of cathode rays, or illumination. We shall

one has in mind only the latter case. However, when excited by light, luminescence may have a different character and, accordingly, is called phosphorescence or fluorescence. Formerly these two kinds of luminescence were distinguished only by the duration of their afterglow. As is known, in fluorescence the afterglow ceases more rapidly, although converse cases are also known. For analytical purposes the phenomenon of fluorescence is of incomparably greater importance, and in the present article I shall speak only of it. In the case of fluorescence the process of luminescence may be regarded as the direct return (accompanied by luminescence) of the excited electron shell of the molecule to its initial state.

Analysis based on the phenomenon of fluorescence has very high sensitivity.

It is more sensitive than all other spectral methods. However, its selectivity in most cases is low, and most often luminescence analysis is carried out without spectral resolution.

In Russian there are fairly complete manuals^17,18 on luminescence analysis, and the task of the present section is mainly to compare the luminescence method with other spectral methods.

A number of properties of the phenomenon of fluorescence determine its analytical possibilities.

1. The phenomenon of fluorescence takes place in the electron shell of molecules and therefore does not depend on temperature.

2. It obeys Stokes’ law, according to which the absorption of quanta of greater magnitude (shorter-wavelength) is accompanied by the emission of smaller quanta (the fluorescence spectrum is located in the longer-wavelength region). Violation of this law can occur only at the expense of other sources of energy.

3. The appearance of the fluorescence spectrum does not depend on the absorbed wavelength, provided only that it does not go beyond the limits of the absorption band.

4. In many cases of fluorescence, the relative position of the absorption and emission bands obeys Levshin’s rule: if on the ordinate axis one plots, for the absorption band, its absorption coefficient, and for fluorescence, the number of quanta emitted expressed in conventional units, then one curve is the mirror reflection of the other.

For analysis it is especially important that, first, the fluorescence spectrum is characteristic of the substance and, second, that one can find such a spectral region in which the phenomenon of fluorescence is not complicated by absorption of the emitted light, i.e., the total amount of emitted light is proportional to the number of radiating centers.

Unfortunately, there is another cause that complicates the phenomenon and consists in the partial exchange of absorbed light energy, before it is emitted, into other degrees of freedom. The quenching of fluorescence as a result of this exchange depends both on the nature of the solvent and on the concentration of the fluorescing substance itself. Finally, an obstacle to analysis, to some extent, is the unusually high sensitivity of luminescence analysis (for example, for the determination of cerium or terbium it amounts to \(10^{-8}\,\mathrm{g/ml}\)). A quite negligible impurity of a foreign fluorescing substance is sufficient for its glow to affect the observed spectrum.

The methods of luminescence analysis are most widely used for identifying or detecting objects. In this case one usually uses spectrally unresolved light and, in fact, the phenomenon of luminescence itself: the range of colors perceived by the eye is simply expanded.

In this direction of work the field of application of fluorescence is extraordinarily broad. By the character and color of the luminescence one can distinguish an imitation from a genuine article. In the food industry it can be used to determine the freshness of products; in agriculture, to determine the germination capacity of grain or its contamination with weeds; in factory production—for sorting and rejection; in biology and medicine—to distinguish diseased tissue of a living organism from healthy tissue, to detect bacteria, and so on. Many other examples could be given.

As an exciting light source, a mercury arc is used, enclosed in black uviol glass, which transmits the light of the bright mercury line \(3650\,\text{\AA}\) and eliminates visible light. Qualitative spectral analysis, even with spectral decomposition, is nevertheless usually not very selective and therefore is used chiefly to determine the presence or absence of a single component. If there are several fluorescing components, then it is advantageous to combine luminescence analysis with chromatographic analysis. First the components should be separated on a suitable adsorbing substance, and then, extracting them with the appropriate solvents, analyzed in turn.

Fluorescence analysis can be used only in those cases when, upon absorption of light, the molecules are excited to new discrete electronic levels; therefore, in the case of organic substances, as also in absorption analysis in the ultraviolet, fluorescence analysis is used when multiple bonds are present in the molecules. For the reasons indicated above, in quantitative analysis one has to overcome a number of difficulties, and therefore the simplest method of quantitative analysis is analysis by means of standards.

V. M. Chulanovskii

ANALYSIS BY MASS SPECTRA

The methods of molecular spectral analysis should also include analysis by mass spectra, despite the fact that in this case the matter is not a measurement of the amount of radiation emitted or absorbed that is characteristic of the molecule of a substance, but rather a measurement of the number of ions of different mass produced when molecules collide with electrons accelerated by a field.

The problems, methods of processing observations, and even the processes themselves that occur with the molecules of the substance being analyzed are related in the two cases. The very possibility of analysis by mass spectra2 is determined by the fact that, when molecules of a substance collide with electrons, the character of the decomposition of the molecules into ions, within broad limits, does not depend on the velocity of the incident electron, but is determined by the nature and structure of the molecule. The ions formed in the analytical chamber are separated by means of magnetic and electric fields2.

Analysis by mass spectra is carried out mainly on mixtures of not very heavy paraffinic and aromatic hydrocarbons and is performed in the gas phase.

By means of this method such gases as hydrogen, oxygen, and others are also readily detected. With great difficulty analysis is performed on more active substances that are readily adsorbed on the walls of the instrument: olefins, water, amines, alcohols, and others. However, in this respect definite successes have recently been achieved.

The value of the method of analysis by mass spectra lies in its very high accuracy and in the possibility of determining, in a mixture, even those components that remain unnoticed in infrared spectra.

With modern apparatus, the analysis is simple and takes little time.

Analysis by mass spectra is advantageously combined with analysis by infrared absorption spectra, which possesses far greater universality.

CITED LITERATURE

1. V. M. Chulanovskii, Introduction to Molecular Spectral Analysis. Gostekhizdat, 1950.
2. Conference on Molecular Spectral Analysis. (Collection of reports delivered at the conference.) Bulletin of Leningrad University No. 3, p. 1—178 (1950).
3. V. Ts. Williams, Apparatus and technique of infrared spectrometry. UFN 37, 183 (1949).
4. F. Veigert, Optical Methods in Chemistry. Gostekhizdat, 1934.
5. M. M. Sushchinskii, Zav. lab. 14, 1077 (1948).

1. M. V. Vol'kenshtein, Advances in Chemistry 8, no. 7 (1939).
2. G. S. Landsberg, Combinational scattering of light and its significance for chemical problems. Advances in Chemistry 1, 464 (1932).
3. A. N. Terenin, Absorption spectra of electrolyte solutions. Uspekhi 18, 1 (1937).
4. V. P. Dailey, Analyt. Chem. 21, 540 (1949).
5. K. S. Popov, L. A. Grauerman and L. G. Karantsevich, Application of ultraviolet spectrophotometry to the study of fats. Bulletin of Leningrad University No. 3, 87 (1950).
6. E. Miller Elmer, Quantitative Biological Spectroscopy, vol. 1. Burges Publ. Corp. 1940.
7. R. Brode Wallace, Chemical Spectroscopy, John Willy a. sons, 1943.
8. N. Coggensholl, Analyt. Chem. 22, 381 (1950).
9. Thornton Vernon and Herald Annette. Analyt. Chem. 26, 9 (1948).
10. M. V. Vol'kenshtein, M. A. El'yashevich and B. I. Stepanov, Molecular vibrations. Gostekhizdat, 1949.
11. Robert R. Hampton, Analyt. Chem. 21, 923 (1949).
12. M. A. Konstantinova-Shlezinger, Luminescence analysis. Publishing House of the Academy of Sciences of the USSR, 1948.
13. P. Pringsheim and M. Vogel, Luminescence of liquids and solids. I. L., 1948.
14. V. M. Chulanovskii, Molecular analysis by mass spectra, Zav. lab. 5, 566 (1950).
15. R. Harrison, Lord and Loofbourow, Practical Spectroscopy. I. L., 1950.
16. M. P. Burgova and A. A. Korotkov, Izvestiya of the Academy of Sciences of the USSR, Physical Series 14, 452 (1950).

1. Reference number as printed on the page. ↩↩

2. Reference marker as printed on the page. ↩↩