Polarized Luminescence

P. P. Feofilov

In the development of spectroscopy, the transition from the study of only scalar characteristics of radiation—frequency and intensity—to their investigation together with the vector properties of radiation, which find expression in the state of polarization of the emitted light, is quite natural. The importance is well known that was attached to the study of the polarization of the components of the Zeeman splitting of spectral lines in a magnetic field for the theory of atomic spectra, and to the study of the polarization of the lines of combination scattering for the theory of molecular vibrations. At the same time, in the theory of the electronic spectra of complex organic molecules, interest in which is steadily increasing, attention to questions of the anisotropy of absorption and emission was, until recently, clearly insufficient. The reason for this lies in the fact that only comparatively recently, chiefly thanks to the work of Soviet investigators and, first of all, Academician S. I. Vavilov, have the possibilities become clear that the study of polarized luminescence—an expression of this anisotropy—offers for investigating both the structure of the absorbing and emitting molecular systems themselves and the behavior of molecules in the surrounding medium. For a long time, the attention of investigators of polarized luminescence was centered on the regularities of the behavior of molecules in a medium; as a result of experimental and theoretical studies it proved possible to clarify a number of questions connected with the Brownian rotational motion of molecules in solutions and, more broadly, with the problem of the liquid state; it proved possible to discover and investigate a specific intermolecular interaction leading to the transfer of the energy of electronic excitation from one molecule to another. Later, the significance became clear that the study of polarized luminescence can acquire as a method for investigating the structure of the elementary systems that determine the absorption and emission of light by complex molecules. Here, by comparatively simple means, it is possible to obtain

information on the details of the structure of molecules, which are difficult to investigate by other methods. This direction in the study of polarized luminescence appears to be the most promising.

1. POLARIZATION OF LUMINESCENCE AS AN EXPRESSION OF THE ANISOTROPY OF MOLECULES

The light of luminescence emitted by an isotropic body, for example by a fluorescing solution, may in some cases prove to be partially polarized. This phenomenon was discovered in 1920 by F. Weigert[^1], who showed that if the excitation of luminescence is produced by light polarized in a certain plane, then the luminescence light sometimes proves to be partially polarized in the same plane. S. I. Vavilov and V. L. Levshin[^2] showed that the luminescence light may prove to be partially polarized also under excitation by natural light; it is only necessary that the distribution of the exciting light vector in the plane perpendicular to the line of observation be anisotropic.

The very fact of the existence of polarization of luminescence already indicates that the distribution of excited molecules in an isotropic luminescent medium proves to be anisotropic, i.e., that the exciting light is absorbed predominantly by molecules having a definite orientation relative to the exciting light vector. This proposition is, however, a fairly trivial consequence of the basic concepts of the theory of absorption and emission of light. The process of absorption of light corresponds to the transition of a molecule from some ground state, possessing a definite dipole (in the general case, multipole) moment, to an energy state corresponding to a greater electronic energy and possessing another dipole (multipole) moment. Thus, the process of absorption of light corresponds to a quite definite change of the dipole moment of the molecule. A corresponding change of the dipole moment also occurs in the reverse transition from the excited state to the ground state, accompanied by the emission of light. It is obvious that these changes of the electronic moments of the molecule can be represented by certain vector quantities. Thus, quite naturally, the theory of absorption and emission of light includes the concept of elementary molecular oscillators, which plays an extremely important role in the interpretation of the phenomena of polarized luminescence. The principal characteristics of elementary oscillators are their frequency, determined by the change in the energy of the molecule in the corresponding electronic transition, and their orientation relative to the elements forming the molecule, characterized by a vector quantity—the change in the electronic dipole moment of the molecule. The third principal characteristic of elementary emitters—their

POLARIZED LUMINESCENCE

multiplicity—we shall not touch upon it for the time being, considering the most widespread case, when the absorption and emission of light are connected with a change in the electric dipole moment.

The probability of absorption of light of a given state of polarization by a molecule having a definite spatial orientation, in other words, the probability of excitation of an elementary oscillator oriented in a definite way, will be determined entirely by the relative orientation of the exciting light vector and the axis of the oscillator. The presence of such anisotropic absorption of light by the molecules and anisotropy of the spatial distribution of the exciting vector are, obviously, a necessary and sufficient condition for the anisotropic distribution of excited molecules. If, during the time the molecule remains in the excited state, the anisotropy of the distribution of the excited molecules is not lost, and if the mutual orientation of the absorbing and emitting oscillators of the molecule is not random, then, in the general case, the radiation will be distributed anisotropically in space, and the luminescence light observed in definite directions will be partially polarized.

Fig. 1.

In the simplest case, when absorption and emission of light correspond to transitions between the same electronic levels (resonance fluorescence), the absorbing and emitting oscillators, obviously, coincide in direction. It is not difficult to calculate what degree of polarization may be expected in this case. Let the exciting linearly polarized light propagate along the direction \(x\) (Fig. 1), the electric vector of the exciting light being vertical. If the elementary oscillators are electric dipoles, then the probability of excitation of oscillators whose axes make an angle \(\alpha\) with the vertical will be proportional to \(\cos^{2}\alpha\). In the elementary solid angle there will be excited (to within a normalizing factor) \(\cos^{2}\alpha \sin\alpha\, d\alpha\, d\varphi\) oscillators. If the emitting oscillators coincide in direction with the absorbing ones, then the amplitudes of the vertical electric oscillations in the radiation field will be proportional to \(\cos^{2}\alpha \sin\alpha\, d\alpha\, d\varphi \cos\alpha\), and the corresponding intensities of the luminescence light

\[ dz = \cos^{2}\alpha \sin\alpha\, d\alpha\, d\varphi \cos^{2}\alpha . \]

Integration over the sphere gives

\[ I_{z}=8\int_{0}^{\frac{\pi}{2}}\int_{0}^{\frac{\pi}{2}}\cos^{4}\alpha \sin\alpha\, d\alpha\, d\varphi=\frac{4}{5}\pi . \]

The intensities of the horizontal light oscillations are, respectively,

\[ I_x(=I_y)=8\int_0^{\frac{\pi}{2}}\int_0^{\frac{\pi}{2}}\cos^2\alpha\sin^3\alpha\cos^2\varphi\,d\alpha\,d\varphi =\frac{4}{15}\pi. \]

If the degree of polarization is determined, as is usually done, by the expression

\[ P=\frac{I_z-I_x}{I_z+I_x}\quad(\text{observation along }y), \]

then

\[ P=\frac{\frac{4}{5}\pi-\frac{4}{15}\pi}{\frac{4}{5}\pi+\frac{4}{15}\pi} =\frac{1}{2}=50\%. \]

The degree of polarization of the luminescence of complex organic dyes observed experimentally usually does not reach this limiting value. This is explained, first, by the presence of depolarizing factors and, second, by circumstances connected with the structural properties of the luminescing systems, which will be discussed in the following paragraphs. In most cases, however, if depolarization is eliminated and excitation is produced by light of a wavelength corresponding to the long-wavelength absorption band of the dye, it is possible to obtain values of the degree of polarization approaching the theoretical value. Thus, to a first approximation, the long-wavelength absorption band and the luminescence band may be described by oscillators that coincide in direction, i.e., they correspond to transitions between the same electronic levels. The difference in the spectral position of these bands (the Stokes shift) is due to the fact that these transitions occur between different levels within the energy bands into which the electronic levels of complex molecules in solutions split.

This simplest model of a luminescing center has proved sufficient to explain the totality of all phenomena connected with depolarization due to the rotational Brownian motion of molecules and with the depolarization observed when the concentration of the luminescing substance in solution is increased.

2. OBSERVATION AND MEASUREMENT OF POLARIZED LUMINESCENCE

The most widespread visual methods for measuring partial polarization of light are Cornu’s polarimeter method and Savart’s polariscopic method with a compensating plate. Cornu’s polarimeter, based on comparing the intensity of light beams obtained when the investigated partially polarized light is passed through a ...

light through a Wollaston prism, convenient for measuring large degrees of polarization, is of little use for measuring polarized luminescence, where one often has to deal with small degrees of polarization. The Savart polariscope proves considerably more convenient; in order to obtain quantitative data it must be equipped with a compensating stack of glass plates. The Savart polariscope consists essentially of a Savart plate viewed through a Nicol analyzer. The Savart plate consists of two plane-parallel plates of a uniaxial crystal (quartz, Iceland spar), cut at an angle of \(45^\circ\) to the optical axis and cemented so that their axes are mutually perpendicular. The plane of polarization of the analyzer makes an angle of \(45^\circ\) with the principal sections of the plate. When a source of partially polarized light is viewed through this system, one can see in the field of view a system of interference fringes, sharp at large values of the degree of polarization and disappearing if the source gives unpolarized light. For quantitative measurement of the degree of polarization, in front of the Savart plate there is placed a stack of 3–4 glass plates, rotating about a vertical axis (when measuring positive values of the degree of polarization). Since on passing through the stack the light becomes partially polarized, and more strongly the more obliquely it falls on it, by rotating the stack one can attain a position in which the polarization introduced by the stack is equal in magnitude and opposite in sign to the polarization of the source, and the fringes in the field of view disappear. The dependence of the degree of polarization of the light that has passed through the stack on the angle of rotation of the stack can be calculated on the basis of Fresnel’s formulas; however, the calculated formulas give a dependence that differs rather strongly from that observed experimentally, even when multiple reflection of light in the stack is taken into account\(^{3,4}\). Therefore calibration of the stack by a source giving light with a known degree of polarization is far more reliable.

For measuring the degree of polarization of light in separate spectral regions one may use, as S. I. Vavilov\(^{5}\) showed, the well-known König–Martens spectrophotometer. Recently attempts have been made to develop an objective method for measuring the degree of polarization.

A typical arrangement for measuring the degree of polarization of luminescence is shown in Fig. 2. Here \(S\) is the source of exciting light, \(F_1\) and \(F_2\) are crossed light filters, \(P\) is the polarizer, \(C\) is the cell with the solution under investigation, and \(Sv\) is the Savart polariscope.

If the excitation is produced by monochromatic light obtained with the aid of a monochromator, then as the polarizer it is very convenient to use a crystal of Iceland spar, placing it directly at the exit slit of the monochromator. For excitation one of the beams emerging from the crystal is used; the second beam, polarized in the perpendicular plane, is screened off.

In this way it is possible to obtain polarized ultraviolet rays down to 2000 Å.

It should be noted that in a number of cases (for example, when the luminescence is weak, while its degree of polarization is large) it is expedient to produce excitation with natural light, observing the luminescence in a direction perpendicular to the exciting ray. The transition from the polarization values measured under excitation by natural light \((P_n)\) to the values obtained under polarized excitation \((P_p)\) can be made by means of the formula obtained by S. I. Vavilov and V. L. Levshin\({}^2\)

\[ P_p=\frac{2P_n}{1+P_n}. \]

Fig. 2. Diagram of the apparatus for measuring the degree of polarization of luminescence.

If the task of the investigation does not include the study of depolarization of luminescence (see below, §§ 3 and 4), then one tries to avoid it by using viscous and sufficiently dilute solutions. Usually, to eliminate rotational depolarization it is sufficient to have a viscosity of several poises. A very convenient solvent in this respect for the investigation of polarized luminescence is anhydrous glycerin. The concentration of the luminescent substance in the solution must be less than the concentration at which depolarization begins. Usually this is \(10^{-4}\)—\(10^{-5}\,\text{g}/\text{cm}^3\).

3. ROTATIONAL DEPOLARIZATION AND SOME QUESTIONS OF THE THEORY OF THE LIQUID STATE

Excited molecules located in a liquid solution are subject to Brownian rotational motion, which tends to destroy the initial anisotropy of the distribution of excited molecules. If, during the time of the excited state, the molecules have time to rotate, then, owing to the randomness of these rotations, the distribution of excited molecules at the moment of emission will be completely isotropic, and the luminescence will be completely depolarized. The presence of rotational depolarization was one of the reasons that delayed the discovery of polarized luminescence of solutions. The relaxation time of molecules proves to be commensurable with the duration of the excited state only in sufficiently viscous solu-

racks. It is obvious that rotational depolarization must be determined, on the one hand, by parameters characterizing the luminescing molecule itself: the lifetime of the excited state \(\tau\) and the molecular volume \(v\), and, on the other hand, by parameters characterizing the medium: the viscosity \(\eta\) and the temperature \(T\). An experimental investigation of the dependence of the degree of polarization on these parameters, carried out already in the very first works on polarized luminescence (\(^{2,6,7}\), etc.), enabled V. L. Levshin\(^{8}\) and later F. Perrin\(^{7,9}\) to give a quantitative theory of rotational depolarization. Especially convenient for comparison with experiment is the expression obtained by Perrin:

\[ \frac{1}{P}=\frac{1}{P_0}+\left(\frac{1}{P_0}-\frac{1}{3}\right)\frac{kT}{v\eta}\tau, \]

where \(P\) is the observed polarization, and \(P_0\) is the limiting value of the polarization observed in the absence of rotational depolarization \((\eta\to\infty,\ \tau\to0)\). The quantity \(P_0\) was introduced by Perrin as an empirical constant; below (§ 5) we shall try to state some considerations concerning its physical meaning. It follows from Perrin’s formula that the degree of polarization is the greater the lower the temperature (weaker Brownian motion), the larger the size of the molecule, the higher the viscosity of the solution, and the shorter the lifetime of the excited state. Perrin’s formula has repeatedly been subjected to experimental verification and has invariably been confirmed both with respect to the correctness of the functional dependences and with respect to the correctness of the parameter values obtained with its aid (\(^{9,4}\), etc.; we exclude the work of S. Mitra\(^{10}\), who incorrectly interpreted the experimental facts he observed and came, as was shown by us\(^{11}\), to absurd conclusions). As an example, Fig. 3 gives the dependence of the reciprocal values of the degree of polarization on the reciprocal values of the viscosity for a solution of fluorescein in glycerin.

Fig. 3. Change in the polarization of a glycerin solution of fluorescein upon heating.

Measurements of the degree of polarization while varying the viscosity or temperature give a simple method for determining the lifetime of the excited state from the slope of the experimental straight lines

\[ \frac{1}{P}=f\!\left(\frac{1}{\eta}\right) \quad\text{or}\quad \frac{1}{P}=f\!\left(\frac{T}{\eta}\right). \]

In doing so, it must be sufficiently

precisely cautious, since often an increase in temperature leads to quenching of luminescence, accompanied by a shortening of \(\tau\). The values of \(\tau\) obtained from Perrin’s formula agree rather well with the values of the mean decay time of the emission measured directly by means of fluorometric devices.

The formula given for rotational depolarization provides yet another convenient method for determining \(\tau\). As is known, the addition of certain substances (quenchers) to a luminescing solution causes a decrease in the light yield \(\rho\), in a number of cases a strictly proportional change in \(\tau\) (for quenching of luminescence see, e.g., \(^{12}\)):

\[ \frac{\rho}{\rho_0}=\frac{\tau}{\tau_0}. \]

Introducing this expression into Perrin’s formula, one can obtain the law of change of the degree of polarization under quenching:

\[ \frac{1}{P}=\frac{1}{P_0}+\left(\frac{1}{P_0}-\frac{1}{3}\right)\frac{kT}{v\eta}\,\tau_0\,\frac{\rho}{\rho_0}. \]

Indeed, when luminescence is quenched, an increase in polarization is observed, and the latter tends to the same limiting value \(\mathcal P_0\) as when the viscosity is increased. The validity of the last formula has been verified for many cases of quenching (\(^{4,12}\), etc.). The values of \(\tau\) obtained from the slope of the straight lines

\[ \frac{1}{P}=f\left(\frac{\rho}{\rho_0}\right), \]

agree well with the values obtained by varying the viscosity.

The values of the viscosity \(\eta\) at which values of \(\tau\) are obtained that coincide with the fluorometric ones correspond to the molar viscosity measured by the usual viscometric methods. This by no means trivial result indicates that the equations of Brownian motion, formulated on the basis of the classical hydrodynamic equations for sufficiently large particles in an ideal (structureless) liquid, prove applicable to objects whose dimensions are comparable with, or in any case only slightly exceed, the dimensions of the particles forming the viscous medium. The formula of rotational depolarization was specially tested by us for particularly small luminescing molecules of sodium salicylate, whose dimensions only slightly exceed those of the glycerin molecules that served as solvent; it turned out that, at least in order of magnitude, the values of microscopic viscosity coincide with the values of molar viscosity, since the obtained values of \(\tau\) agree well with the fluorometric measurements of M. D. Galanina*).

*) In this connection, however, it should be borne in mind that in the usual methods for determining molecular volume (for example, in the diffusion method) one is also required to know the value of the molecular viscosity, and therefore, in order to decide the question of agreement or disagreement between macro- and microviscosity, it is neces-

Investigation of polarized luminescence makes it possible to distinguish cases in which the microscopic viscosity differs sharply from the molar—viscometric—viscosity. Such, for example, are cases of colloidal systems (gelatin). The macroscopic viscosity of such a medium may be very large, whereas the polarization of the luminescence of a substance introduced into it may prove insignificant, since it may be determined by a low-viscosity solvent filling the gaps between individual colloidal particles. Thus, polarized luminescence may serve as a convenient and sensitive indicator of microviscosity.

4. CONCENTRATION DEPOLARIZATION AND INTERMOLECULAR EXCHANGE OF EXCITATION ENERGY

The depolarizing effect of increasing the concentration of a luminescent substance in solution was discovered almost simultaneously by a number of authors \(^{13,14,15}\) in viscous solutions of luminescent dyes. Over a considerable range of concentrations the polarization remains unchanged, and then, at concentrations of the order of \(10^{-4}\)—\(10^{-3}\ \mathrm{g/cm^3}\), begins to fall rapidly, tending to zero at concentrations of the order of \(10^{-2}\ \mathrm{g/cm^3}\) (Fig. 4). The intermolecular distances at which the phenomenon takes place exceed the kinetic radii of the molecules by several times (appreciable depolarization is already observed at distances \(\sim 10^{-6}\ \mathrm{cm}\)), so that the phenomenon cannot be explained as the result of collisions. The course of the curves of concentration depolarization is described rather well by the empirical formula \(^{11}\)

\[ \frac{1}{P}=\frac{1}{P_0}+\left(\frac{1}{P_0}-\frac{1}{3}\right)\frac{kT}{v\eta}\tau+Ac, \]

where the first two terms on the right-hand side represent Perrin’s formula.

Fig. 4. Concentration depolarization and concentration quenching of fluorescein in glycerin.

Like the depolarization caused by Brownian rotational motion of molecules, concentration depolarization is determined by the ratio of the mean lifetime of the excited state to the time of depolarization. However, in this case the lifetime of the excited state also depends on the concentration, owing to the possibility of nonradiative transfer of excitation energy between molecules. In order to describe concentration depolarization quantitatively, one must have independent data on the molecular volume; in the case where solvation of the luminescent molecules by solvent molecules is absent, the molecular volume can be calculated from interatomic distances or from the volume of the substance in the solid state.

is determined by processes occurring throughout the entire time the molecule remains in the excited state. This was established in the investigation of the polarization of luminescence of quenched solutions, which showed that, upon quenching, along with rotational depolarization, concentration depolarization is also eliminated11 (Fig. 5). As quenching is intensified, the degree of polarization increases, tending toward the same limiting value as when rotational depolarization is eliminated. The dependence of \(\frac{1}{P}\) on \(\tau\) is close to linear, so that the empirical formula for depolarization can be rewritten in the form:

\[ \frac{1}{P}=\frac{1}{P_{0}}+\left[\left(\frac{1}{P_{0}}-\frac{1}{3}\right)\frac{kT}{v\eta}+A'c\right]\tau . \]

The same result was also obtained when the duration of the excited state was shortened as a result of temperature quenching of luminescence. Interesting results obtained in this case for rhodamine \(B\) are shown in Fig. 6. When solutions of this dye are heated, its luminescence weakens as a result of quenching by the solvent16.

Fig. 5. Change in the degree of polarization upon quenching. Fluorescein in glycerin.

Fig. 6. Change in the polarization of rhodamine \(B\) upon heating.

Thus, when rhodamine solutions are heated, the degree of polarization, first, decreases as a result of the intensification of rotational depolarization due to the decrease in viscosity and the intensification of Brownian motion and, second, increases owing to the decrease in rotational depolarization, and at high concentrations also concentration depolarization, as a result of the shortening of the duration of the excited state. At low concentrations one may expect the degree of polarization to decrease with temperature; at high concentrations, the second factor begins to exert the decisive influence—incre-

POLARIZED LUMINESCENCE

increase in the degree of polarization. This is precisely the character of the experimental curves obtained.

Establishing a connection between the phenomenon of concentration depolarization and the duration of the excited state makes it possible to explain the “anomalous” character of depolarization curves in the case of certain acridine dyes (Fig. 7). For these dyes, at a concentration of about \(10^{-2}\ \mathrm{g/cm^3}\), depolarization slows down, the polarization passes through a minimum, and begins to increase with a further increase in concentration. As a joint consideration of the curves of concentration depolarization and concentration quenching (the decrease in the yield of luminescence with increasing concentration) shows, the slowing of the fall in polarization and its subsequent increase lie in the region of considerable concentration quenching. The latter, as also quenching by foreign quenchers, is accompanied by an approximately proportional shortening of \(\tau\). If the curve of concentration quenching (= shortening of \(\tau\)) is sufficiently steep, then the development of concentration depolarization does not keep pace with its decrease as a result of the shortening of \(\tau\), and the curve \(P=f(c)\) assumes a form similar to that shown in Fig. 7.

Fig. 7. Concentration depolarization and concentration quenching of trypaflavine in glycerin.

The dependence of the processes determining concentration depolarization on time, and the fact that significant depolarization exists at distances many times exceeding the kinetic radii, served as a strong argument in favor of theories explaining the phenomenon from the standpoint of resonant transfer of excitation energy from excited molecules to unexcited ones.

The first attempt to explain the phenomenon of concentration depolarization by transfer of excitation energy as a consequence of quantum-mechanical resonance was made by F. Perrin1. The possibility of such transfer follows from the basic conceptions of quantum mechanics. Describing a system consisting of two identical particles (for example, molecules), one of which is in an excited state and the other in the normal state, and fixing at a certain moment the excitation energy on a definite molecule, we may assert that at any other moment of time the system will be found in the same state only if there is no interaction between the elements of the system. If, however, the particles interact with one another, even weakly, then we are not able to

indicate a priori where the excitation energy is located at a given moment; we are entitled to speak only of the probability of one state or another. Generally speaking, these probabilities will be functions of time, so that if the system is specified at some moment of time, one can speak of the probability of its transition to another state during a given interval of time.

The consideration of this problem in the general theory of perturbations leads to equations for probability amplitudes that are quite analogous to the equations obtained in the classical theory of oscillations for oscillating pendulums, which makes it possible to illustrate the processes occurring here by a clear mechanical model. In this model, the amplitudes of the oscillations of the pendulums correspond to the probability amplitudes of the states, and the energies of the pendulums correspond to the probabilities themselves. If the system under consideration is degenerate, i.e. if the energy required for excitation is the same for both particles—which is certainly the case in the case considered here of identical particles—then the mechanical analogue will be two pendulums with equal natural frequencies of oscillation. When there is coupling between such pendulums, the well-known phenomenon of mechanical resonance occurs: the oscillations of one pendulum will be transmitted to the other, and an exchange of energy will take place between them, the transmission frequency being determined by the magnitude of the coupling between the pendulums. In exactly the same way, in quantum-mechanical resonance there will be an exchange of probabilities between states: the probability of one state will increase at the expense of the other. Of course, the exchange of probabilities of states must not be identified with an exchange of excitation energy; the transfer of probability occurs continuously, whereas the excitation energy can be associated only with one or another element of the system.

If the excitation energy is ultimately emitted in the form of a light quantum, then the acts of energy transfer can be judged by observing the polarization of the emitted light. It is not difficult to see that such a transfer of energy must act in a depolarizing manner. Indeed, as a result of the transfer, the excitation energy will fall upon molecules with oscillator orientations different from those which they had in the primarily excited molecule, which will, of course, reduce the predominant orientation of the oscillators.

An exact solution of the microscopic problem of the transfer of excitation energy in dye solutions is hardly possible, owing to the absence of concrete ideas about the mechanism of the interaction that leads to resonant energy exchange, and owing to the large number of complicating circumstances (fluctuations of concentration, relative motion of molecules, the perturbing action of the solvent, the unclear relation of the interaction energy to the mutual orientation of the molecular oscillators, etc.). It is hardly possible

to regard F. Perrin’s attempt, undertaken by him in this direction, as successful1. As a result of taking into account the perturbing action of the solvent, he arrives at a quadratic dependence of \(1/P\) on concentration, which is not confirmed by experiment. In calculating the asymptotic values of the interaction energy, Perrin treats this interaction as the interaction of dipoles whose moments are determined by the excitation energy. This leads the author to a dependence of the probability on the third power of the wavelength of the fluorescence light, likewise inconsistent with the experimental data.

It is possible, however, to construct a phenomenological theory of the phenomenon, proceeding from the most general ideas about resonant transfer of excitation energy and without specifying the “microscopic” meaning of the constants entering into the expressions. This problem was solved in recent years by S. I. Vavilov, who developed a general theory of the influence of concentration on luminescence[^18]. Assuming a certain a priori probability of transfer of excitation energy and taking into account the loss of anisotropy in the distribution of excited molecules during such transfer, S. I. Vavilov obtained expressions fully consistent with the empirical dependences of polarization on the concentration of the luminescent substance and on the duration of the excited state. S. I. Vavilov’s theory is internally self-consistent, since the constants appearing in it are common to the three expressions describing the dependence on concentration of the three principal characteristics of luminescence: yield, polarization, and duration of the excited state.

A comprehensive experimental verification of S. I. Vavilov’s theory and of its consequences was recently carried out by M. D. Galanin and F. M. Pekerman[^19].

A direct experimental proof that the process determining concentration depolarization develops in time is provided by the change in the degree of polarization observed as the luminescence decays. It is obvious that light emitted at later stages of the afterglow process must be more strongly depolarized, since the corresponding quanta are emitted predominantly by molecules excited not directly by the light, but having received excitation energy from neighboring molecules[^20]. Indeed, experiments by A. N. Sevchenko[^21] and M. D. Galanin[^22] revealed a decrease in polarization as the luminescence decays (Fig. 8). At the same time, in crystals, where all luminescent centers are oriented in the same way and transfers of energy are not accompanied by a loss of anisotropy, no depolarization is observed as the luminescence decays.

If the kinetic aspect of the problem of concentration depolarization may be considered completely solved by S. I. Vavilov’s theory and by the experiments of a number of authors, we can say only very little about the concrete conditions under which reso-

molecular interaction. In this respect, the observation of F. M. Pekerman^23 is extremely interesting; in a number of examples it establishes an unambiguous connection between concentration phenomena (concentration quenching, concentration depolarization, and the shortening of $\tau$ as the concentration increases) and the degree of overlap of the absorption and luminescence spectra. The superposition of spectra proves to be a necessary condition for concentration phenomena—a necessary condition for the possibility of resonant transfer of excitation energy. The physical meaning of this regularity is not yet entirely clear.

Fig. 8. Decrease in the degree of polarization of uranium-glass luminescence as the glow decays. (Two glass samples.)

It should be noted that the notions of resonant transfer of excitation energy, which entered the theory of luminescence through quantum mechanics, are in essence contained, as S. I. Vavilov^19 recently pointed out, already in classical physics. An oscillating electric dipole, modeling in classical optics an elementary radiator, must inevitably induce oscillations in the surrounding dipoles at rest, as a result of which the latter must also become radiators. The magnitude of the inductive interaction must, evidently, increase with increasing concentration and with the time during which the unexcited molecule remains near the excited one.

5. POLARIZATION OF LUMINESCENCE AND THE STRUCTURE OF MOLECULES

The subject of investigation in the study of polarized luminescence may be not only the behavior of molecules in the medium being studied, as we have seen in the preceding sections, by the depolarization of the glow, but also certain details of the structure of molecules—namely, the nature and arrangement of the elementary electronic oscillators that determine the absorption and emission of light. Studying polarized luminescence in order to obtain information about molecular oscillators, we encounter three principal characteristics of it: 1) polarization diagrams, i.e., diagrams indicating the spatial distribution of the polarization of luminescence; 2) polarization spectra, i.e., curves determining the dependence of the observed polarization on the wavelength of the exciting light; and 3) limiting values.

degree of polarization, i.e., the values observed at the maximum of the polarization spectrum when all known depolarizing factors have been eliminated. Consideration of these characteristics shows2 that polarization diagrams make it possible to establish (in most cases unambiguously) the nature of the elementary emitters—their multipolarity; that polarization spectra make it possible to establish the relative arrangement of the elementary oscillators of the molecule which determine the emission and absorption of light of different wavelengths; and that, finally, the study of limiting values of polarization makes it possible to express definite judgments concerning the symmetry of the structure of molecules.

A. The Nature of Elementary Emitters and Polarization Diagrams

The case considered above, in which the elementary molecular oscillators are electric dipoles, is the most widespread, but by no means the only possible one.

Fig. 9. Spatial distribution of radiation.
\(d_e\)—electric dipole, \(q_e\)—quadrupole, \(d_m\)—magnetic dipole.

The electromagnetic theory of radiation indicates that, in the periodic motion of charges, alongside the ordinary radiation of an electric dipole—determined in the classical theory by a harmonic change of the electric dipole moment—radiation of higher multipoles may be observed, first of all that of the electric quadrupole and the magnetic dipole3. These radiations also represent spherical electromagnetic waves, but with a different character of the spatial distribution of the radiation (Fig. 9). If, in the case of an electric dipole, the amplitudes of the waves emitted in some direction making an angle \(\alpha\) with the axis of the oscillator are proportional to \(\sin \alpha\), then in the case of quadrupole radiation these amplitudes vary as \(\sin 2\alpha\), i.e., radiation is not observed either along the axis of the emitter or in the perpendicular direction. A model representation of a quadrupole emitter may be obtained by considering two parallel dipoles oscillating with equal frequency and opposite phases and situated at a distance—

of a medium significantly smaller than the length of the emitted wave. In the case of a magnetic dipole, the spatial distribution of the radiation does not differ from the distribution of the radiation of an electric dipole if the axis of the latter is replaced by the axis of the magnetic dipole; the plane of polarization of the radiation will be rotated by \(90^\circ\). The radiation intensity of second-order multipoles (electric quadrupoles and magnetic dipoles) is approximately a million times smaller than the intensity of electric dipole radiations. The relatively small probability of transitions corresponding to the radiation of higher multipoles determines the fact that the duration of these radiations considerably exceeds the duration of ordinary dipole radiations. If the latter is approximately \(10^{-8}\)—\(10^{-9}\) sec., then the duration of quadrupole and magnetic dipole radiations reaches \(10^{-2}\)—\(10^{-3}\) sec.

Real emitters may, generally speaking, represent an arbitrary superposition of different multipoles; however, usually the symmetry of the motion of charges in real systems leads to the fact that practically significant is some one term in the expansion of the electromagnetic field created by moving charges. Most often this is the term corresponding to electric dipole radiation; however, for example, in the case of luminescence of the rare earths we not infrequently encounter elementary emitters of the quadrupole or magnetic-dipole type. By determining the multipolarity of a given elementary emitter, we can form a fuller conception of the mechanism of the process under investigation and of the structure of the object under study.

The experimental determination of the multipolarity of radiation in the case of atomic spectra can be carried out by observing the Zeeman splitting of spectral lines in a magnetic field. This method is not applicable, however, to the radiation of complex molecules having a diffuse spectrum. The lifetime of the excited state also does not always prove to be an unambiguous characteristic of the multipolarity of emitters, since the often observed increased duration of afterglow testifies only to the nonspontaneous character of the radiation (forced dipole transitions from metastable states, recombination radiation).

A partial experimental solution of the question of the multipolarity of elementary acts in complex systems is provided by the classical works of Wiener[^26], Drude and Nernst[^27], and others with standing light waves. In these experiments the maximum action of light on photographic layers, fluorescent films, and photoelectric indicators was observed at the places of the antinodes of the electric vector of the light wave. These experiments, simple in conception and rather complicated technically, played an extremely important role in their time in resolving the much-discussed question of “light-

...of the electromagnetic field vector. They proved with what seemed to be conclusive persuasiveness that the active—“light”—vector is the electric vector. It is obvious, however, that the unambiguity of the results of these experiments is due to the fact that all the indicators used (photographic plates, luminescent substances in the experiments of Drude and Nernst, sulfur scattering particles in Zehnder’s experiments^28, photoelectric layers in the experiments of Ives and Fry^29) are systems in which the absorption (scattering) of light is associated with a change of the electric dipole (or, in the general case, multipole) moment. It is further obvious that the question of the acting vector “in general” is devoid of meaning and cannot be considered apart from the system subjected to the action of light. Thus, for example, one may suppose that if the experiments of Drude and Nernst had been carried out with luminescent substances in which the absorption of light is effected by magnetic dipoles, their results would have been reversed—the luminescence would have been brighter at the places of the antinodes of the magnetic vector of the standing light wave. Experiments with standing waves thus make it possible to draw conclusions about the electric or magnetic character of the absorbing (scattering) system.

An unambiguous and quite general feature characterizing the multipolarity of an emitter is, as we have seen, the anisotropy of the spatial distribution of the radiation. The features of the spatial distribution derived for elementary monochromatic emitters must remain valid, at any rate, for the individual elements of complex radiation; and since, apparently, the factors that determine the diffuse character of molecular spectra do not substantially affect the quantities determining the electronic moments of the molecule, the study of the anisotropy of radiation becomes a quite universal method for determining the multipolarity of emitters.

The anisotropy of the spatial distribution of radiation must manifest itself first of all in the pattern of the interference field of the emitter. In 1932 S. I. Vavilov^30 published the results of a calculation of the interference pattern that should be observed upon interference of beams emitted by a dipole emitter at large angles to one another, and the results of an experimental verification of these calculations^31. Later he himself^32, and also Halpern and Lerman^33, calculated the interference fields for a quadrupole, a magnetic dipole, and other more complicated cases. It turned out that the spatial distribution of the visibility of the interference fringes is quite distinctive for emitters of different multipolarity and permits them to be distinguished. Using the method of wide-angle interference, Fried and Weissman^34 were able to prove that some luminescence lines of rare earths in solution represent radiation of magnetic dipoles.

The interference method thus makes it possible to express certain judgments about the multipolarity of the emitting system. A more complete characterization is given by the method of determining multipolarity from the polarization of photoluminescence, proposed in 1940 by S. I. Vavilov[^35]. This method, which makes it possible simultaneously to determine the multipolarity of both the emitting and the absorbing systems, consists in studying polarization diagrams, i.e., the dependence of the observed polarization of luminescence on the direction of observation and on the position of the electric vector of the exciting light. S. I. Vavilov calculated polarization diagrams for four possible combinations of electric dipoles and quadrupoles and showed that, in all the cases calculated, they differ sharply from one another and are a sensitive indicator of the nature of the oscillators. From the experimental point of view it is most convenient to vary the angles: \(\chi\)—the angle between the direction of the exciting beam and the direction of observation, and \(\eta\)—the deviation of the electric vector of the exciting light from the vertical. The polarization diagrams calculated by S. I. Vavilov are given in the first four columns in Fig. 10. These diagrams were calculated for the case \(P = 1/2\), characterizing parallel oscillators and often realized under long-wave excitation. The characteristic nature of the polarization diagrams is somewhat diminished if the limiting value of the degree of polarization proves to be substantially smaller than the theoretical limiting value \(1/2\)[^36]. Investigation by the method of polarization diagrams has proved the dipole character of the luminescence of organic dyes (both short-lived and long-lived)[^36] and of uranium glass[^21].

In a completely analogous way, polarization diagrams can also be constructed for the case of a magnetic dipole[^37]. As we have indicated, the spatial distribution of the radiation in this case does not differ from the distribution of the radiation of an electric dipole, if the axis of the latter is replaced by the axis of the magnetic dipole. However, the plane of polarization of the radiation will be rotated by \(90^\circ\). The probability of excitation of a magnetic dipole depends on the mutual direction of the dipole axis and the magnetic vector of the exciting light in the same way as the probability of excitation of an electric dipole depends on the mutual direction of the dipole axis and the electric vector of the exciting light. Polarization diagrams constructed on the basis of these simple concepts of the anisotropy of the magnetic dipole are given in the last three columns in Fig. 10. As consideration of the polarization diagrams shows, in the case where the observed degree of polarization of luminescence is close to \(1/2\), the nature of the multipolarity of both the absorbing and the emitting systems can be established quite unambiguously. If, however, the observed value of the degree of polarization does not exceed \(1/3\) in absolute magnitude, then an unambiguous conclusion can be drawn only about the absorbing system.

Fig. 10. Polarization diagrams of dipole and quadrupole radiation. \(\vec e\) — electric dipole, \(\vec q\) — quadrupole, \(\vec m\) — magnetic dipole; solid lines — the emitting oscillator is parallel to the absorbing one; dashed lines — the emitting oscillator is perpendicular to the absorbing one.

The emitting oscillator may be either an electric or a magnetic dipole (cf. the cases \(\vec e \to \vec e\) and \(\vec e \to \vec m\)). Such an indeterminacy occurs in the case of luminescence of uranyl compounds, which is of considerable interest. As is known, the relatively long duration of the glow of these compounds (\(\sim 10^{-4}\) sec.) with an exponential character of decay, indicating the spontaneity of the process, gives grounds for supposing that in this case we are dealing with the radiation of magnetic dipoles. The polarization diagrams of the luminescence of uranyl glass, however, have the form characteristic of the radiation of electric dipoles \(^{21}\). At the same time, from Fig. 10 it is seen that the case of parallel electric dipoles is indistinguishable from the case in which the emitting magnetic dipole is perpendicular to the absorbing electric dipole, if the observed polarization does not exceed \(1/3\). The maximum value of the polarization of the luminescence of uranyl glass, observed by A. N. Sevchenko, is about 0.29. Thus, the possibility is not excluded that the emitter in the case of uranyl compounds is a magnetic dipole. Against this possibility speak the orientation experiments with wide-angle interference carried out by us. From these experiments it follows that the radiation of uranyl compounds, like absorption, can be described by electric dipoles.

A definitive answer concerning the nature of the elementary emitters in the case of luminescence of uranyl compounds will be obtained if a uranyl glass is found for which the degree of polarization of luminescence will exceed \(1/3\) at the maximum of the polarization spectrum. This, however, will not only fail to remove, but, on the contrary, will deepen the contradiction between the dipole character of the luminescence of uranyl compounds and the exponential character of the decay at the relatively long afterglow duration.

B. Polarization spectra and the relative arrangement of molecular oscillators

The dependence of the observed degree of polarization of luminescence on the wavelength of the exciting light already attracted interest in the first works on polarized luminescence. V. L. Levshin \(^{38}\), in 1924, exciting luminescence by various regions of the visible spectrum, noticed some decrease in the degree of polarization with decreasing wavelength in the case of rhodamine B and magdala red. For fluorescein and rhoduline red, in the interval investigated, the dependence was absent. P. Pringsheim \(^{39}\), having advanced somewhat further along the spectrum, found a slight decrease of polarization in these, as well as in a number of other dyes. However, only after the work of S. I. Vavilov \(^{40}\), who extended the observations to the entire ultraviolet region of the spectrum and discovered very sharp and characteristic changes in the degree of polarization, can we speak of polarization spectra as a new charac-

...characteristic of the luminescent substance. Several papers following the work of S. I. Vavilov merely confirmed its results, without providing any fundamentally new data \(^{41}\).

The quasiperiodic dependence discovered by S. I. Vavilov cannot be interpreted as a depolarization that is a consequence of a decrease in the anisotropy of the molecule or of a weakening of the connection between the absorbing and emitting systems of the molecule. Against such an assumption is evidenced at least by the existence, upon excitation by light of certain wavelengths, of negative polarization. A change in the sign of the polarization (i.e., a rotation of the plane of preferential vibrations by \(90^\circ\)) requires, for its explanation, the assumption that the emitting oscillator has, at certain wavelengths of the exciting light, a spatial orientation differing from the orientation of the absorbing oscillator. This change in the direction of the oscillator may be interpreted either dynamically—as a rotation of the oscillator, during the lifetime of the excited state, through some angle \(\alpha\), determined by the magnitude of the absorbed quantum—or statically—from the point of view of separate oscillators of absorption and emission forming with one another some angle \(\alpha\) \(^{42}\). It is obvious that, formally, both representations must lead to an identical expression. This expression,

\[ P=\frac{3\cos^2\alpha-1}{\cos^2\alpha+3}, \]

does indeed correctly determine the limits of the observed polarization values \(\left(+\tfrac12 \geq P \geq -\tfrac13\right)\). In individual cases the polarization approaches its lower limit; it follows that the emitting oscillator may form with the absorbing oscillator angles approaching a right angle.

Although the hypotheses expressed are not entirely equivalent from the physical standpoint, the final choice between them could be made only on the basis of additional data. Such data, making it possible to make an unambiguous choice, were obtained in experiments with anisotropic cellophane films dyed with luminescent dyes \(^{43,44}\). Dye molecules adsorbed by the fibers of cellophane are partially oriented, which is manifested in the dichroism of the dyed films and in the fact that the luminescence of the adsorbed molecules is partially polarized even for an isotropic distribution of the exciting light in the plane perpendicular to the direction of observation, for example, under excitation by natural light and observation along the exciting beam. In isotropic media the luminescence observed under these conditions is, of course, unpolarized. The degree of polarization of the observed glow depends strongly on the nature of the dye and may reach \(20\text{–}25\%\). It is extremely significant here that this polarization—so-called “spontaneous polarization”—is completely independent of the wavelength

waves of the exciting light, whereas the polarization of the luminescence of the same films, excited by polarized light, changes with wavelength in the same way as in isotropic media (Fig. 11). This result, paradoxical at first glance, has an extremely simple meaning: it indicates that the degree of orientation of the emitting oscillators, which determines the magnitude of the “spontaneous polarization,” does not depend on the wavelength of the exciting light, i.e., that the emitting oscillator retains its direction relative to the axes of the molecule. In other words, it is sufficient to assign to the molecule an emitting oscillator having a quite definite orientation relative to the axes of the molecule. It follows inevitably from this that the oscillators corresponding to the absorption of light of different wavelengths must, in general, have different orientations. This circumstance alone is already sufficient for an unambiguous choice between the hypotheses mentioned above. The correctness of the static hypothesis—the hypothesis of separate oscillators—is finally confirmed, and fundamentally new results are obtained concerning the orientation of molecules, by observations of the dichroism of films with partially oriented molecules. If the absorption of light of different wavelengths corresponds to the excitation of oscillators having different orientations relative to the molecular axes, then the dichroism of the medium, determined by the absorption coefficients \(k_1\) and \(k_2\), corresponding to two mutually perpendicular polarized components of the incident light, as

Fig. 11. Polarization of luminescence of partially oriented molecules as a function of the wavelength of the exciting light (benzoflavin). \(P_p\)—excitation by polarized light; \(P_n\)—excitation by natural light (“spontaneous polarization”).

\[ D=\frac{k_1-k_2}{k_1+k_2}, \]

must undergo changes with wavelength. Without anticipating the spectral course of the dichroism, one may nevertheless assert that it will be connected in some way with the polarization spectrum of the same substance, since the latter also expresses the different orientation of oscillators corresponding to absorption of different wavelengths. Indeed, measurements of dichroism show that its spectral course is quite analogous to the course of the polarization spectra of the corresponding substances (Fig. 12).

It is not difficult to show that this coincidence acquires a simple meaning if one assumes that the orientation occurs in such a way that the emitting oscillator is oriented, or, what is the same, the oscillator,

corresponding to long-wavelength absorption. We indicated above that these oscillators may, to a first approximation, be regarded as coincident in direction, since the degree of polarization under long-wavelength excitation is close to \(1/2\) for most dyes. Indeed, suppose that at a certain wavelength the polarization is negative; this means that the oscillator corresponding to the absorption of light of this wavelength is perpendicular to, or at any rate forms a considerable angle with, the emitting oscillator (the oscillator of long-wavelength absorption). Then, for this wavelength, the sign of the dichroism will also be opposite to the sign of the dichroism in the region of the long-wavelength absorption band, and so on.

Consideration of other possible cases of molecular orientation shows \(^{43}\) that, for a given polarization spectrum, the most diverse forms of curves expressing the spectral course of dichroism are possible (Fig. 13). Thus, although the connection between polarization spectra and dichroism spectra is quite obvious, their qualitative agreement is by no means trivial, but testifies to a quite definite character of molecular orientation. As we shall see below, a joint analysis of these spectra does indeed make it possible to establish the character of molecular orientation in an anisotropic medium.

Fig. 12. Polarization spectra \((P_n)\) and dichroism spectra \((D)\).

Thus, polarization spectra are an expression of the spatial relations between molecular

oscillators responsible for the absorption of light of various wavelengths, an expression of the spectral course of the absorption anisotropy of the molecule. Establishing the connection between the orientation of electronic vibrations and the structural elements of molecules is highly relevant at the present time, in view of the intensified development of theories linking the optical properties of compounds, in particular their color, with the structure of molecules. The study of the orientation of electronic vibrations relative to molecular

Fig. 13. Dependence of the spectral course of dichroism on the character of molecular orientation (schematic).

axes is often associated with the undertaking of investigations of extraordinary experimental difficulty, which, nevertheless, often yield only limited results (the work of W. Kuhn and collaborators45, S. Nikitin46, and others). The method of polarization spectra, being incomparably simpler and more exact, yields considerably more than, for example, Kuhn’s very complicated and very inaccurate experiments.

Clarification of the nature of polarization spectra made it possible consciously to approach the consideration of the spectra of various chemical compounds. Since polarization spectra are an expression of the anisotropy of absorption of molecules, it was of interest to compare them with absorption spectra. This comparison immediately made it possible to establish an unambiguous correspondence between particular spectra. It turned out that each separate band in the absorption spectrum of a luminescent dye is characterized by its own value of polarization, i.e., that each separate band may be described by a separate oscillator. In Fig. 14 a comparison is made

polarization spectra and the absorption spectra of a number of dyes of different chemical structure. This correspondence can be traced especially clearly in the relatively simple spectra of acridine, azine, and oxyfluorone (fluorescein) dyes. The spectra of rhodamines are more complex: a larger number of absorption bands here corresponds to a more complex structure of the polarization spectra. Because the individual bands in the absorption spectrum overlap one another, the transition from one value of the degree of polarization to another occurs not abruptly but continuously, which explains the smoothness of the curves expressing the spectral dependence of the degree of polarization.

The structure of the polarization spectrum may undergo sharp changes when the concentration of hydrogen ions in the medium is changed (Fig. 15). These changes are quite natural, since the electronic configuration of the dye ion differs from the configuration of the corresponding undissociated base, and, when the substance passes into the ionic state and back, a sharp change in its optical properties, in particular its absorption spectra, often occurs.

The spectra shown in Fig. 14 indicate that the polarization spectra of dyes of different chemical structure have many common features, apparently connected with the similarity of the electronic configuration of those elements of the molecules that determine the color of the luminescent compounds. Thus, in all cases the polarization hardly changes its magnitude within the limits of the main absorption band of the dye, only decreasing somewhat toward shorter wavelengths; it then falls sharply, often assuming negative values, then rises again and passes through a maximum in the short-wave ultraviolet region (250–270 mμ).

However, despite this general similarity, the polarization spectrum of each individual compound is quite distinctive and can undoubtedly be used as a new, additional characteristic in solving analytical problems. Thus, for example, in solving one of the fundamental problems of luminescence analysis—the problem of establishing the identity of two substances—the polarization spectrum may prove to be a considerably more characteristic property of a luminescent substance than the emission spectrum, which is often insufficiently characteristic, or the absorption spectrum, which may be distorted by extraneous substances present in the mixture under study.

Solving the problem of the relative arrangement of oscillators in a molecule is only the first stage in the investigation of molecular structure by means of polarization spectra. The next step must be the establishment of the absolute orientation of the absorbing oscillators relative to the axes of the molecule, and the establishment of the connection between electronic vibrations and the structural elements of the molecule. This problem is most closely connected with the problem of color.

Fluorescein (Hantzsch)

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\); \(c=10^{-5}\,\mathrm{g/cm^3}\), \(c=10^{-3}\,\mathrm{g/cm^3}\).

Chemical label: \(2\mathrm{Na}^+\).

Rhodamine B extra (I. G. Farbenindustrie)

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\); \(p_{\parallel}\), \(p_{\perp}\).

Chemical labels: \((\mathrm{C}_2\mathrm{H}_5)_2\mathrm{N}\), \(\mathrm{N}(\mathrm{C}_2\mathrm{H}_5)_2\), \(\mathrm{COOH}\), \(\mathrm{Cl}\).

Eosin (Meister Lucius)

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\).

Chemical labels: \(\mathrm{Br}\), \(2\mathrm{Na}^+\).

Perylenetetracarboxylic acid tetra-sodium salt (PI)

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\); \(p_{\parallel}\), \(p_{\perp}\).

Chemical labels: \(\mathrm{NaOOC}\), \(\mathrm{COONa}\).

Esculin (Merck)

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\); \(p_{\parallel}\).

Chemical labels: \(\mathrm{C}_6\mathrm{H}_4\mathrm{O}\), \(\mathrm{HO}\).

Sodium salicylate

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\); \(p_{\parallel}\), \(p_{\perp}\).

Chemical labels: \(\mathrm{OH}\), \(\mathrm{COONa}\).

Thiamine hydrochloride (Merck)

Labels in the graph: \(p\%\), \(\lambda\,m\mu\), \(K\); \(p_{\parallel}\), \(p_{\perp}\).

Figure 14. Polarization spectra and absorption spectra of some luminescent dyes.

organic compounds and at the present time cannot yet be considered solved. Here we first encounter the necessity of reconciling purely physical ideas about elementary oscillators with the chemists’ established ideas about the structure of molecules. Strictly speaking, this problem could be solved if we were able to calculate, from a given arrangement of atoms,

Fig. 15. Polarization spectra and absorption spectra of acridine orange in acidic and alkaline media.

the dipole moments of a molecule in its various electronic states. The complexity of the structure of luminescent molecules, however, permits this calculation to be carried out only in a limited number of cases. Therefore we are forced to resort to the aid of certain qualitative considerations, often abandoning strictness of reasoning. We cannot, of course, picture the absorption and emission of light as the result of oscillatory motions of charges—the consistent application of purely classical ideas proves impossible—but certain ideas from the old oscillator theories of color may be borrowed. Without specifying

physical meaning of these representations and, combining them with the concepts of the modern resonance theory of color, one may try to compare the directions of the oscillators with the direction of “displacement” of the charges of the molecule in the transition from one resonance structure to another^44.

Thus, in a number of cases it may be assumed that, in compounds with a sharply expressed anisotropy of structure, as organic dyes often are, the direction of the “principal” oscillator describing the long-wave absorption and emission band is determined by the final position of the charges in the resonating structures responsible for the appearance of color. In the case of typical dyes with two auxochromic groups, such a direction will be the line joining the auxochromes. For example, in the case of symmetric structures of the type

[resonance scheme of a symmetric dye: auxochrome \(A\) at the left and \(A^+\) at the right, with \(B\) above the central ring, in resonance with the structure having \(A^+\) at the left and \(A\) at the right, with \(B\) above the central ring]

which are often encountered among luminescent dyes, the principal oscillator may be regarded as arranged horizontally along the line \(A—A\). The orientation of the shorter-wave absorption oscillators can be determined with less certainty. Short-wave absorption is apparently determined by the “local resonance” of individual elements of the molecule. The absorption band observed for most dyes and located in the short-wave ultraviolet region \((250—270\ \mathrm{m}\mu)\) may be associated with the resonance of the benzene ring. In dyes of the indicated type, the degree of polarization upon excitation in this region is close to the degree of polarization observed upon excitation in the region of the “principal”—long-wave—band, which makes it possible to regard the oscillator corresponding to absorption by the benzene ring as also arranged horizontally. Some acridine dyes possess a distinct polarization spectrum; these dyes have asymmetrically located auxochromes, for example, dyes with “active” groups (the groups \(\mathrm{NH_2}—\), \(\mathrm{OH}—\), etc.) in the 9-position: 9-aminoacridine (I), acridone (II), acrichine, etc.

[structural formula of 9-aminoacridine, with \(\mathrm{NH_2}\) substituent; labeled \((I)\)] \[ (I) \] [structural formula of acridone, with \(\mathrm{O}\) above \(\mathrm{C}\) and \(\mathrm{N}\!-\!\mathrm{H}\) in the ring; labeled \((II)\)] \[ (II) \]

In these compounds the polarization under short-wave excitation is negative, i.e. the short-wave oscillator is oriented perpendicular (or almost perpendicular) to the “principal” one. The “spontaneous” polarization of the luminescence of cellophane films colored with these dyes is negative, while the dichroism follows a course sharply different from that of the polarization spectrum. The totality of these observations makes it possible to suppose that, unlike the case of typical luminescent dyes, the “principal” oscillator, determined by the position of the auxochromes, is here oriented vertically, whereas the orientation of the short-wave oscillator, determined by the “skeleton” of the molecule—the benzene rings—remains unchanged. The orientation of the molecules on cellophane is apparently also determined by the acridine “skeleton” of the molecule. Fig. 16 explains, using acridine as an example, the relationships that occur here.

Fig. 16. Absorption, polarization, and dichroism spectra.

In these examples one can see how a joint analysis of polarization spectra, dichroism spectra, and absorption spectra makes it possible to understand the picture of the spatial relationship of molecular oscillators in complex organic compounds. However, up to now the discussion has been concerned not so much with solving specific structural problems by means of polarization spectra as with establishing certain general principles and substantiating the possibility of using polarization measurements to elucidate the “optical architecture” of the molecule. Since the question has until now been posed in such a rather general form, all the experiments performed served chiefly to test the hypotheses advanced and to illustrate individual conclusions. To the extent that the basic principles prove to be correct, we may proceed to attempts to solve individual

of concrete problems and to the refinement and detailing of various conclusions.

At the end of the next section we shall give some examples of the application of polarization spectra to the solution of concrete problems.

V. Limiting polarization of luminescence and molecular symmetry

As we have already indicated, the limitingly high values of the degree of polarization of luminescence, observed when all known depolarizing factors are eliminated and when luminescence is excited in the longest-wavelength band of the absorption spectrum, by no means always prove to be sufficiently close to the limiting value predicted by a theory based on the notion of linear absorbing and emitting oscillators coinciding in direction. In individual cases, especially in the case of compounds with a relatively simple molecular structure, the deviations from the limiting theoretical value are very large. As Pringsheim and Vogel showed^47, in the case where the solvent is a mixture of several components, the polarization may be determined not by the macroscopic viscosity of the solution, but by the mobility of the dye molecule in a shell of solvating molecules of one or another component of the solvent. Cases are possible in which the reason for the smallness of the observed polarization is solvation of the luminescing molecule by molecules of the low-viscosity component of the solvent. However, the limiting polarization is often small even in solid solutions, where rotations of molecules are practically impossible. In these cases we are undoubtedly dealing with intramolecular properties of the luminescing substance.

It can be shown that a sharp difference of the observed degree of polarization from the theoretical one is an inevitable consequence of peculiarities in the structure of luminescing molecules, in particular, a consequence of their symmetric structure^48. Indeed, a planar molecule having an axis of symmetry of order \(n\), perpendicular to the plane of the molecule, and absorbing light whose electric vector is located in the plane of the molecule (for example, a benzene molecule, which has an axis of symmetry of order 6), must with equal probability absorb light with an electric vector located in certain \(n\) directions lying in the plane of the molecule. We have no need to specify the actual direction of the absorbing oscillators; it is sufficient only to assume that the probability of absorption will be a periodic function with period \(\frac{2\pi}{n}\). Naturally, one should suppose that the excited molecule preserves its symmetry, i.e., after a certain time required for rearrangement, the molecule

can, with equal probability, emit light by means of one of the \(n\) oscillators situated in the plane of the molecule and forming with one another angles equal to \(\dfrac{2\pi}{n}\). Using the analogy with asymmetric molecules of organic dyes, one may suppose that the directions of the absorbing and emitting oscillators coincide (we are speaking of light absorption in the longest-wavelength absorption band and of emission in the luminescence band conjugate with it); however, this is not obligatory, and the emitting oscillators may turn out to be rotated through some angle in the plane of the molecule relative to the absorbing oscillators.

Simple calculations show that in this case the polarization observed upon excitation by linearly polarized light is equal to

\[ P= \frac{\displaystyle \sum_{k=0}^{n-1}\left(3\cos^{2}\alpha_k-1\right)} {\displaystyle \sum_{k=0}^{n-1}\left(\cos^{2}\alpha_k+3\right)} = \begin{cases} \dfrac{1}{2}, & \text{for } n \leq 1,\\[4pt] \dfrac{1}{7}, & \text{for } n > 2. \end{cases} \]

Thus, if a planar molecule has an axis of symmetry of the third order or higher, then, independently of the degree of symmetry, the limiting polarization of photoluminescence cannot exceed \(1/7\). Asymmetric molecules and molecules having symmetry of the second order, in full agreement with experiment, may have a higher degree of polarization, approaching \(1/2\).

The study of the polarized ultraviolet luminescence of a series of benzene derivatives (see Table 1) shows\(^{48}\) that for benzene (symmetry of the sixth order) and mesitylene (symmetry of the third order) the polarization, in accordance with the considerations set forth above, does not exceed \(1/7\). The same holds in the case of toluene. Apparently, the introduction of a methyl group has little effect on the symmetry of the electronic cloud of the nucleus. Less obvious, but nevertheless also naturally explicable, is the small value of the polarization in the case of phenol and aniline. The presence of a considerable dipole moment in these compounds indicates a significant weight of intramolecular-ionized structures with positively charged oxygen or nitrogen and an electron located in the ring. In this case the following structures are possible:

[shown: resonance structures of aniline with \(+\mathrm{NH}_2\) and charge displacement in the benzene ring]

(similarly for phenol).

As is seen, the electron cloud in the ring has symmetry of the third order, i.e. the luminescence of this cloud determined by excitation must have a low degree of polarization. If the luminescence were determined by a transition from an intramolecular ionic structure to a neutral one and back, then the oscillator determining it would be unique, and a high degree of polarization could be expected. In compounds with two strongly polar groups (hydroquinone, resorcinol, p-phenylenediamine) the degree of polarization is substantially higher.

In these compounds the weight of structures with charges on both oxygen or nitrogen atoms is large, and the third-order symmetry for the electron cloud of the ring is disturbed. For example, resonance is possible

with symmetry of the second order. It is difficult to say definitely how the oscillator determining the long-wave absorption is arranged here; however, there is no doubt that the predominant directions are the line connecting the substituents and the line perpendicular to it. The change in the symmetry of the electron cloud of the ring has led to a sharp change in the degree of polarization.

Table 1

Polarization of the luminescence of benzene derivatives

Compound	$P_0$ %	Compound	$P_0$ %
Benzene	7.7	Pyrogallol	17.5
Toluene	5.8	Phloroglucinol	does not fluoresce
Mesitylene	8.75	Aniline	12.0
Phenol	5.7	p-Phenylenediamine	32.0
Hydroquinone	29.6	Diphenylamine	15.8
Resorcinol	27.3

The smallness of the polarization in the case of diphenylamine, whose molecule as a whole has symmetry of the second order, is apparently explained by the fact that the luminescence is determined by processes occurring

within one aromatic ring whose electronic structure is analogous to the structure of the ring in the case of aniline^48.

Cases are not rare in which, for sufficiently complex molecules, the limiting polarization observed upon excitation of luminescence in the main absorption band has values intermediate between the limiting values established above, \(1/7\) and \(1/2\). Thus, for example, in the case of acridine and its derivatives the limiting polarization has values from 17 to 40% (see Table II). The degree of polarization of anthracene and of some of its derivatives, of certain derivatives of phthalimide and of many other compounds is also substantially below 50%.

Table II

Limiting polarization of acridine and its derivatives

Compound	\(P_0\)%	\(\alpha^\circ\)	Compound	\(P_0\)%	\(\alpha^\circ\)
Acridine	17.1	76	9-aminoacridine	26.3	56
Acridinium	18.2	73	3-aminoacridine	40.0	34
Acridone	25.0	58	3,6-diaminoacridine	40.0	34

To explain this circumstance one might make use of the same model that served to explain the nature of the polarization spectra, i.e., assume that even upon excitation in the region of the main absorption band the oscillators absorbing and emitting light form a certain angle with one another. Such an assumption, however, is unlikely; the comparatively small distance between the spectral position of the emission band and that of the “main” absorption band (an energy difference approximately equal to the energy of vibrational quanta) indicates that the process of absorption of light and the process of emission correspond to a transition between the same electronic levels, but in opposite directions. Consequently, the changes of the dipole electronic moments (vectors!) in both processes coincide in direction, differing in sign. The fact that these transitions take place, on the average, from different vibrational levels can hardly substantially affect the direction of these vectors. One might also try to explain intermediate values of the limiting polarization by introducing the concept of ellipticity of the molecular oscillators^49; however, attempts to detect ellipticity of luminescence light (S. I. Vavilov, F. Perrin) have not yielded positive results.

More plausible is the explanation that can be given to the phenomenon by relating the magnitude of the limiting polarization to the symmetry of the molecule^24. Above we considered the case of planar molecules,

having an axis of symmetry perpendicular to the plane of the molecule. Let us now imagine a planar molecule having a second-order axis of symmetry lying in the plane of the molecule. Obviously, in this case, if only the absorbing oscillator does not coincide in direction with the axis of symmetry and is not perpendicular to it, the molecule absorbs, with equal maximum probability, light whose directions of vibration coincide with two certain directions in the molecule forming angles equal to \(\frac{\alpha}{2}\) with the axis of symmetry. Preserving the earlier and, apparently, sufficiently plausible assumption that the molecule retains its symmetry also in the excited state, we may assume that emission can take place with equal probability both through an oscillator coinciding in direction with the absorbing one and through an oscillator symmetric to it, forming with the absorbing one an angle equal to \(\alpha\). It is not difficult to show that in this case the observed degree of polarization will be equal to

\[ P=\frac{3\cos^2\alpha+1}{\cos^2\alpha+7}, \]

i.e. it may assume any values from \(1/2\) (\(\alpha=0\) or \(\pi\)—the oscillator coincides with the axis of symmetry or is perpendicular to it) to \(1/7\) \(\left(\alpha=\frac{\pi}{2}\right.\)—the oscillators form an angle \(\frac{\pi}{4}\) with the axis of symmetry, i.e. the molecule, with respect to electronic vibrations, has a center of symmetry of the fourth order).

The values of the angles \(\alpha\) for acridine derivatives, calculated on the basis of this formula and given in Table II, are placed in the last column of the same table. It would, however, be erroneous to compare these quantities with any directions in the molecule determined by the positions of individual groups. We indicated above that, although the transitions corresponding to long-wavelength absorption and luminescence occur between the same electronic levels, the vibrational states upon excitation and upon emission may be different. The dipole moments of a molecule in an excited vibrational state may differ somewhat from the dipole moments of the resting molecule (regardless of whether it is excited or unexcited). This difference may be characterized by some small vector quantity. Then, in characterizing the vector properties of a real state with excited vibrational levels, we are compelled to specify not simply the direction of the dipole moment, but a bundle of directions (both for the ground and for the excited electronic state). Correspondingly, the directions of the emitting and absorbing oscillators can likewise be specified only with a certain limited accuracy—the connection of the oscillators with the molecule as it were loses its rigidity; the degree of anisotropy of the molecule, and consequently also the degree of

of polarization of luminescence decreases. This circumstance evidently accounts for the fact that, even in the case of completely anisotropic molecules, the degree of polarization does not reach the limiting theoretical value. (It also possibly explains the slight decrease in the degree of polarization with decreasing wavelength of the exciting light within the main absorption band, first found by V. L. Levshin.) Thus, the obtained values of the angles are somewhat exaggerated, and comparing them with the angles between bonds in the molecule is hardly meaningful.

Peculiar phenomena can be observed in the case of dyes having a structure close to symmetric, namely, in the case of triphenylmethane dyes. Their general structural formula has the form:

Here \(A_1\), \(A_2\), and \(A_3\) are auxochromes capable of accepting charge. In liquid solutions these dyes do not fluoresce, which is apparently connected with the fact that their structure permits rotation around the chain of conjugated bonds connecting the auxochromes and determining the color—the presence of an absorption band in the visible part of the spectrum[^50]. In solid media, where the possibility of such rotation is practically eliminated, triphenylmethane dyes begin to luminesce rather brightly.

Whereas for all previously studied dyes, asymmetric or having symmetry no higher than second order, the limiting polarization practically did not change when the wavelength of the exciting light was varied within the long-wavelength absorption band, for triphenylmethane dyes with three auxochromes (fuchsin, parafuchsin, methyl violet, crystal violet, etc.) the degree of polarization changes sharply when the wavelength of the exciting light is varied within this absorption band (Fig. 17, a). Upon excitation in the long-wavelength part of the band, the degree of polarization has the same magnitude as in most asymmetric dyes—about 40–45%. As the wavelength decreases, the degree of polarization falls sharply and, upon excitation in the short-wavelength part of the absorption band, assumes negative values (absolute values about 5–7%). Triphenylmethane dy-

dyes with two auxochromes (alkaline phenolphthalein and malachite green) behave quite analogously to the previously investigated asymmetric dyes (Fig. 17, b)51.

The specific form of the polarization spectrum of triphenylmethane dyes with three auxochromes makes it possible to assert that the oscillators which determine absorption in the short-wavelength part of the main band are situated here quite differently from the oscillators

Fig. 17. Absorption spectra and polarization spectra of triphenylmethane dyes: a — fuchsin (3 auxochromes), b — malachite green (2 auxochromes).

Fig. 18. Arrangement of oscillators and scheme of the energy levels of a molecule of a triphenylmethane dye with three auxochromes.

of the more long-wavelength absorption and the emitting oscillators parallel to them. Thus, the main absorption band of symmetric and nearly symmetric triphenylmethane dyes is complex and can be modeled only with the aid of two linear oscillators having somewhat different frequencies and oriented in different ways relative to the axes of the molecule. It is quite natural to try to explain these phenomena by assuming that, in the case of a certain asymmetry of the molecule (for example, if one auxochrome differs somewhat from the other two), the frequencies of the electronic vibrations along the lines connecting the auxochromes and determining, as

one may think, the directions of the absorbing oscillators differ somewhat from one another. This difference may be small and may appear in the form of a subsidiary maximum on the short-wave side of the principal absorption band, corresponding in its long-wave part to the excitation of the oscillator having the lowest frequency. In the process of rearrangement of the molecule following the act of absorption, the oscillations are transferred to this oscillator, regardless of which of the oscillators was excited (Fig. 18). Upon excitation in the long-wave part of the absorption band, the absorbing and emitting oscillators coincide in direction, and the polarization may be close to \(^{1}/_{2}\). With more short-wave excitation, on the contrary, oscillators directed at an angle of \(60^\circ\) to the emitting one will be excited, and the polarization, according to the Levshin—Perrin formula,

\[ p_{\alpha}=\frac{3\cos^{2}\alpha-1}{\cos^{2}\alpha+3}=-\frac{1}{13}\quad \text{for}\quad \alpha=60^\circ . \]

Indeed, the subsidiary maximum is expressed quite distinctly in all dyes with three auxochromes. The values of negative polarization observed under short-wave excitation are close to the theoretical ones.

In the case of dyes which, according to the structural formula assigned to them, possess a completely symmetrical structure (parafuchsin, crystal violet), one would expect, as we saw above, a degree of polarization not exceeding \(^{1}/_{7}\) and not changing in the spectral interval investigated. However, the absorption spectra and polarization spectra of these dyes have exactly the same character as the spectra of dyes having a somewhat asymmetric structure. One may think that this is connected with the nonequivalence of the auxochromes of the molecule in solution, due to the fact that the salt-forming anion is bound predominantly to one of the auxochromes.

Thus, analysis of the polarization spectra makes it possible, among other things, to put forward a supposition concerning the nature of the subsidiary maxima in the absorption spectra of triphenylmethane dyes. Similar maxima are also observed in other dyes, and their nature, which apparently may be different, has repeatedly been discussed.

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1. 17. ↩↩