The action of an electromagnetic wave on a solution and laser sensing of the structure of a solution

In the absence of a field, gas or liquid molecules are randomly oriented in space. When the laser radiation field is turned on, they are partially oriented along the direction of the external electric field. The axis of the molecule oscillates relative to the direction of the field strength vector. Such a process is called the alignment or orientation of molecules.

The interaction of a dipole with a strong field of laser radiation leads to the rotation or oscillation of the molecular axis. In the case of a constant dipole moment of the molecule and a constant electric field, this effect is used to orient the molecules along the direction of this field. One important point to make. The behavior of ions with an odd charge in an external field is similar to the behavior of neutral polar molecules such as HC1. Although in the absence of a field ions do not have a dipole moment, a small electric field is enough for an electron to easily move to one of the protons and a constant dipole moment of a molecular hydrogen ion is formed (it is of the order of eR, where e is the electron charge, R is the internuclear distance), independent of from the field. The tendency of molecules to line up in the presence of an alternating laser field is well known in nonlinear optics [155]. The alignment of polar molecules is responsible for the so-called orientation Kerr effect, which has been intensively studied in connection with the possibility of orientation of molecules in liquids. Its essence is as follows: the initial optically isotropic medium becomes anisotropic and birefringent under the influence of a constant electric field.

Under the action of the field, the initial indicator of refraction of the medium changes. The refractive indices for linearly polarized light propagating parallel and perpendicular to the direction of the electric field vector become different. The orientational mechanism for establishing optical anisotropy determines the optical properties of the medium. The microscopic nature of the Kerr effect is that a polar molecule interacts with an external electric field and is oriented under the influence of this field so that the energy of the molecule in the field is minimal. This takes place when the dipole moment is oriented in the field. Thermal motion impedes the orientation of molecules. For this reason, the optical properties of the medium depend both on the field strength Eel and on the temperature of the medium T.

The degree of orientation of the molecules in the electric field depends on the ratio dE/kT, where dE(EJ is the Stark shift of the energy of the considered electronic state of the molecule in the electric field, which determines the field orientation (see the Stark shift in [156]).

Orientation disappears when this ratio becomes less than unity. On the contrary, thermal motion can be neglected when this ratio is much greater than unity. For example, in accordance with this relation, for a chlorine molecule, thermal motion (at room temperature) can be neglected when the laser radiation intensity is above 5 • 1012 W/cm2. Under such conditions, the task of interaction of laser radiation with molecules is simplified and instead of three- dimensional becomes flat. Indeed, the precession of the molecular axis around the direction of the electric field vector caused by thermal motion is negligible: the molecular axis oscillates only in the plane passing through the initial direction of this axis and the direction of the intensity vector.

The action of an external alternating electric field of the light frequency range on a neutral molecule is similar to the action of a constant electric field, since the orientation time of the molecule is much longer field period due to the large mass of the molecule. The effective value in this case is the average square of the field strength over a period. An exception is the case of a constant dipole moment of the molecule, since then the field perturbation is linear in the intensity of the alternating field and formal averaging over the period makes the perturbation zero. For nonpolar molecules in the light field, the optical Kerr effect takes place. It consists in the fact that atoms and molecules, initially without a constant dipole moment, acquire it under the influence of a field or, as they say, are polarized. The reason for the polarization is electrons, which tend to move in the field in the opposite direction to the electric field, while heavy positively charged nuclei are practically unshifted. In the case of molecules, the anisotropic nature of the induced polarization is due to the initial anisotropy of the structure of the molecule. Since initially the molecules in the medium (in gas or liquid) do not have a fixed orientation, as a result of electron polarization, the nonpolar medium becomes similar to the medium of polar molecules. In the formation of macroscopic anisotropy the arising polarization of molecules is directed along the electric field vector.

The Kerr optical effect is inertialess effect even for picosecond laser pulses (with a duration of the order of 10~12 s). In almost any molecular medium, the optical Kerr effect arises, which leads to a dependence of the refractive index on the laser field strength and anisotropy of this refractive index relative to the direction of polarization radiation. The task is complicated in the case of femtosecond laser pulses, since then the time to establish the polarizability of the system can be longer than the pulse duration.

In the absence of a laser radiation field, the molecules rotate due to thermal motion. The characteristic rotational quantum numbers can also be either small or large. The classical rotation energy of one diatomic molecule is kT. At room temperature, for heavy molecules, chaotic thermal rotation is classical, and for the lightest (for example, a hydrogen molecule, deuterium or their molecular ions) - quantum. Molecular orientation can occur if the molecules of the medium are able to easily rotate.

When a laser radiation field acts on neutral diatomic molecules (for example, HC1), two competing processes can take place: 1) ionization (electron emission) with the formation of a charged molecular ion (in this example, HC1+) and 2) dissociation of a neutral molecule into two neutral atoms (in this example, H and Cl) or two ions (in this example, the proton and ion Cl'). Experiments using linearly polarized light have shown that the dissociation products are detected mainly along the direction of polarization of the laser radiation.

Anisotropy in the distribution of dissociation products can be explained in one of two ways [157]: 1) molecules whose axes are perpendicular to the radiation polarization do not ionize due to the strong angular dependence of the ionization probability, 2) during the dissociation, the molecular axis is oriented along the radiation polarization vector. Angular distributions are determined by polarizability. It is much larger in molecules than in atoms, because in a molecule an electron can move from one nucleus to another under the influence of a field. The polarizability also increases with increasing internuclear distance R in the process of dissociation if charged ions form. Such a strongly polarized system has a large moment of rotation in an external electric field (if it is not already aligned with this field). Although the molecule does not have time to rotate during the ultrashort laser pulse, but it acquires a large angular momentum. This leads to a significant deviation of the trajectories of the products of dissociation and the observed angular distributions of the products of dissociation of light molecules, due to the process of orientation of these molecules. A different situation occurs in the case of heavy molecules. A typical experiment is the effect of linearly polarized laser radiation with an intensity of the order of 1015 W/cm2 on the iodine molecule. At such a high intensity, for example, the emission of three electrons takes place during a time of the order of atomic times (0.1 fs). The mechanism of emission in such a strong field corresponds to the classical collapse, when the force acting from the side of the laser field exceeds the force that holds the electrons in the molecule. As noted above, the formed molecular ion, as noted above, dissociates into two atomic ions. The Coulomb repulsion between the ions of the same name leads to very fast dissociation, in which the participation of an external laser field is no longer required. This process is called the Coulomb explosion.

It was found in experiments that most molecular ions fly out along the polarization axis of linearly polarized laser radiation. Similar angular distributions take place for the dissociation of other molecular ions formed during the ionization of molecular iodine. The obtained angular distributions are explained by the fact that the probability of multiple ionization depends on the angle between the axis of the molecule and the axis of polarization of the laser radiation. It is greatest when the directions of these axes coincide. The indicated alignment effect is weakened by the fact that the polarizability of molecules and molecular ions is anisotropic. In other words, in addition to the induced dipole moment along the axis of the molecule, there is an (albeit smaller) induced dipole moment in the transverse direction. Actually the longitudinal and transverse polarizabilities differ in one and a half to two times. Dissociation and ionization of molecules in a laser field proceed in a rather complicated way. These processes were considered in [157] as an example of the simplest hydrogen molecule H2.

The laser field cannot increase internuclear distance in a diatomic neutral molecule, consisting of identical atoms, in the form of selfcorrectness of both directions along the axis of the molecule, along which this distance could increase. Therefore, an external field first pulls out one electron from a neutral H, molecule. After ionization, a molecular hydrogen ion is formed. The second electron can freely with small internuclear distances move from one nucleus (proton) to another under the influence of the electric field of laser radiation. Since the field oscillates, the electron also easily oscillates between protons with a period equal to the period of radiation. The potential barrier between nuclei is below the energy level of this electron and weakly interferes with such oscillations. At the moment when the electron is near one of the protons, it forms a neutral system with this proton, similar to a hydrogen atom. The laser field does not act on such a neutral system, but on the other hand, it acts on the second proton left without screening, and the increase in the internuclear distance begins. After half a period of radiation, the electron appears at another proton, but the field acting on the proton, now left without screening, changed the sign. Therefore, this field ‘pushes’ the proton again in the opposite direction to the neutral atom. So, each time there is a repulsion between the charged and neutral systems.

An increase in the internuclear distance occurs to a certain critical value of Rc, at which it becomes difficult for the electron to transfer from one proton to another: the effective potential barrier between the protons begins to be interfered with. At this moment, the second electron is ionized, since a further increase in the internuclear distance becomes difficult.

The remaining protons are repelled in a Coulomb way from each other, and their total kinetic energy at infinity is 0. This is confirmed by the available experimental data. The actual critical value of the internuclear distance is three to four times greater than the equilibrium distance. For example, for a molecular ion, the equilibrium internuclear distance is Re = 10~8 cm, and the critical distance R =3.5 • 10~8 cm.

c

So, the neutral molecules can effectively interact with intense laser radiation. This interaction is due to the polarizability of the molecule. The axis of the molecule oscillates relative to the direction of the polarization vector of the laser radiation. The amplitude of the oscillations decreases during dissociation. In the case of light

H, type molecules, the alignment mechanism is completely different than for heavy type I, molecules. Effective repulsion between the intradon and the neutral hydrogen atom occurs when the axis of the molecular ion is aligned with the axis of the electric laser radiation vector. This explains the angular distribution of protons with a maximum along the axis of polarization of laser radiation for light molecules, observed experimentally.

The alignment of molecules in the field of laser radiation is stronger for higher intensities of laser radiation and lighter molecules. In the case of heavy molecules, there is no alignment, and during ionization only those molecules are selected whose axes are directed along the polarization of the laser radiation. As in plasma, any separation of charges in a salt solution in a liquid, polar dielectric leads to fluctuations in charge density. On average, over many periods of oscillation, the solution behaves as a quasi-neutral medium. Separation of polarization charges is significant only at time intervals shorter than with a time scale of charge separation t0 ~ (co0)~‘. For the spatial scale of charge separation d, we can take the distance that the solvated ion travels in time t0 during its thermal motion, i.e., d ~ (v)/co0, where (v) is the average thermal velocity of solvated ions (clusters) having mass m. On a spatial scale, larger than d, quasineutrality of the solution is observed. By definition, the dielectric constant of a continuous medium e is the ratio of the strength of the external electric field E to the strength of the weakened field inside this medium E' (dielectric). Moreover, e is always greater than 1.

In the solution, E/E' < 1. Therefore, for the solution, e < 1. Moreover, the lower the frequency of the external electric field со, (v = co/2tt), the greater the ‘swing’ of the oscillations of polarized solvated ions, that is, the amplitude of their displacements. It turns out that with decreasing со, the dielectric constant of the solution e also decreases.

Free electrons in plasma behave in the same way, which is used in the technique of plasma sounding by radio waves. In the case of plasma there is a critical value of the frequency со,, of radio waves at which the plasma dielectric constant e = 0. The value of this frequency coincides with the value of the Langmuir plasma frequency. In our case, the analog of the Langmuir frequency is the frequency of oscillations of the polarization charge in the solution volume co0.

The dielectric constant of the plasma is determined by the relation [151]

where со is the frequency of external radio emission. If this frequency is со < со,, then s < 0.

Maxwell [158] established that the refractive index of an electromagnetic wave in matter у = л/ё. For e < 0, the elec- electromagnetic waves cannot propagate in matter and must be completely reflected from it. Therefore, the plasma is an ideal reflector with respect to waves with a frequency со < cor By analogy, we can assume that the salt solution in a liquid, the polar dielectric will be a reflector for waves with a frequency

where E is the electric field in the wave.

From the point of view of physics, the divergence of the electric field vector is an indicator of the extent to which a given point in space is the source or sink of this field:

div E > 0 - the field point is the source;

div E < 0 - the field point is a sink;

div E = 0 - there are no drains and sources, or they compensate each other.

The source of the electric field is the charge, therefore, if the electromagnetic wave is laser radiation, then this charge is the charge induced by laser radiation in the volume of the solution.

In terms of electricity, matter is divided into conductors and dielectrics. The conductors are bodies in which there are free charge carriers, that is, charged particles that can freely move inside this body (for example, electrons in a metal, ions in a liquid or gas). The dielectrics are bodies in which there are no free charge carriers, i.e. there are no charged particles that could move within this dielectric. As previously shown, the salt solution in a liquid polar dielectric at the macroscale is neutral. Each ion is surrounded by solvent molecules that shield the electric field of this ion. The last expression can be rewritten as

where X is the wavelength of electromagnetic radiation, c is the speed of light in vacuum.

We will consider laser radiation as an electromagnetic wave. In this case, the wavelength of the laser radiation is equal to X, and the electric field in the laser radiation, as in an electromagnetic wave, is determined by the relation

where pc = 1207c is the free-space wave impedance(ohm, 2). The power of laser radiation, including the wavelength of laser radiation, determines the value of E (E~yfp /X) and the divergence of the electric field in the laser radiation div E.

In accordance with (3.78), it should be expected that, for fixed parameters of laser radiation, there is a threshold value of nm in the salt solution, the excess of which should cause a sharp increase in the reflection coefficient of laser radiation from the salt solution.

The cluster mass m is proportional to the third power of the cluster radius:

where rcl is the cluster radius (m); up to a constant m = a ■ r2 If we conduct experiments in which, for fixed parameters of laser radiation, the reflection coefficient of radiation from a salt solution is measured, then as the concentration increases at a certain value (let's call it critical), we should expect a sharp increase in the reflection coefficient. We denote this value as CCI1'. The corresponding value is thc".' Then the radius of the cluster, formed by the central ion of the salt in the solution can be determined from the ratio

A consequence of the Ostrogradsky-Gauss theorem is the equality V'E = — p, in which the charge density is on the right. Thus, the divergence of the electric field strength is equal to the density of

the charge induced by the field in the volume of the solution. The polarization of the solution is equivalent to the appearance of a charge with a density p' = -div p = -Vp. This is not obvious. If the polarization vector is constant, then no charge appears in the volume. Now, if the vector changes from point to point, then this is manifested in the fact that a certain fictitious charge p' appears in this volume element.

With this assumption in mind, the equation VE = — p can be

1 8o

rewritten in the form V E = — (p- V P) where p is the density of

e0

real charges, and -V • P is the density of ‘coupled’ charges, that is, fictitious charges that appear as a result of the polarization of the solution under the action of laser radiation (electromagnetic wave).

We transform the last equation, multiplying everything by e0 and carrying V • P to the left. As a result, we obtain the equation V(e0E + P) = p

'--where p is the density of real charges. Thus, VD =

p. The vector D = e0E + P is called induction of an electric field generated in the solution volume under the action of laser radiation (electromagnetic wave). Of course, the value of the divergence of the electric field in the laser radiation acting on the solution (divE) is determined not only by the laser radiation parameters, but also by the value of nm. But this issue is a subject of separate consideration.

Conclusions

A theoretical model of a salt solution in a liquid polar dielectric should take into account the presence of four carriers induced by an external periodic electric field of polarizing charges: solvated cations, solvated anions, positively and negatively polarized solvent molecules.

The action of an electromagnetic wave on a salt solution in a liquid, polar dielectric causes separation of charges and leads to density fluctuations of the polarization charge distributed in the solution volume. Moreover, the prevailing mechanism of separation of metal cations is not the interaction of an electric field with a separate solvated cation, but the collective interaction of an electric field with a polarized charge distributed in the volume.

The radii of the solvation shells of cationic aquacomplexes can be determined in the approximation of the existence of a self-consistent electric field in the solution volume. Theoretical frequency spectrum parameters of complex oscillations of solvated ions theoretically defined as the spectrum of complex vibrations of systems of interacting masses. This allows us to determine the expected values of the frequencies of the electric field at which the manifestation of the effect of the electro-induced selective drift of cationic aquacomplexes is maximized. At concentrations of metal cations of the order of units g/1 the sizes of aquacomplexes formed by metals of the third group are micrometers, and the values of the excitation frequencies of the effect are units - tens of hertz.

The theoretical estimates indicate the possibility of the formation of associate clusters from solvated ions in salt solutions in polar dielectric liquids. It is likely that the action of an external periodic electric field with different amplitudes of intensities in half-periods first causes directed motion not of individual solvated ions, but of associate clusters formed by groups of solvated ions. Then a redistribution of the total momentum of the associate between olvated ions having different inertial properties occurs. The significantly larger mass of the associate and, consequently, the larger value of the moment of inertia explains the shift in the range of manifestations of the effect of the electroinduced drift of solvated ions to lower frequencies at salt concentrations up to 10 g/I, which agrees well with the experimental results both in the case of cerium and lead nitrates, and in experiments with cerium and nickel chlorides.

 
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