LIGHT SCATTERING, RAYLEIGH EQUATION AND ITS ANALYSIS

TABLE OF CONTENTS

INTRODUCTION

The heterogeneity of disperse systems is the cause of their optical inhomogeneity and causes a change in the direction of light, electron, ion and other rays on the interfacial surfaces, as well as uneven absorption or transmission of rays by substances of the conjugate phases of the disperse system. All this is the reason for the appearance of a number of specific optical phenomena inherent only in colloidal systems. The difference between the optical properties of colloidal systems and the properties of homogeneous media has led to the creation of a number of optical methods for studying disperse systems, which are widely used to study the composition and structure of phases, the properties of interfacial surfaces, the dispersion of the system, as well as the nature, composition, and structure of surface layers.

Theoretical foundations of optical phenomena characteristic of dispersed systems, and optical methods for their study should be studied using textbooks , a list of which is given in the list of references . This manual provides only a brief theoretical introduction.

The main part of the publication is devoted to the practical part of the section “optical properties of disperse systems” of the course of colloidal chemistry and contains a detailed description of the laboratory work on the topic with practical recommendations for its implementation, processing of the obtained data and compiling a report. Before starting work, it is necessary to read and accept for strict implementation the safety rules that are given at the beginning of the description of the laboratory work and are in addition to the general briefing given to students at the beginning of the semester.

Mastering the practical part should begin only after studying the theory. For theoretical preparation on the topic, below is a plan for a theoretical colloquium . At the end of the manual is an application , which is an auxiliary material useful for self-control: control questions and tasks .

PLAN OF THE THEORETICAL COLLOQUIUM

1. General characteristics of optical phenomena.

2. The phenomenon of light scattering. Tyndall effect. Influence of particle sizes on the shape of the scattering indicatrix (Mie diagram).

3. Rayleigh equation and its analysis.

4. Light scattering by conductive spherical particles.

5. Light absorption. Bouguer – Lambert – Beer equation. Optical density of the solution, light transmission, relative absorption.

6. Optical methods for studying colloidal systems: (fundamental foundations of the method, its capabilities and applicability limits):

a) light and electron microscopy;

b) ultramicroscopy;

c) turbidimetry;

d) nephelometry; determination of the molar mass of macromolecules.

7. Coloring of colloidal systems.

8. Laboratory work. Determination of particle sizes of disperse systems by turbidimetric method:

a) Principal optical scheme of the photoelectric colorimeter;

b) Determining the particle size of dispersed systems that obey the Rayleigh equation;

c) Determination of particle sizes of dispersed systems that do not obey the Rayleigh equation, the Geller method.

9. Self-preparation for control questions and tasks in the application.

BIBLIOGRAPHY

1. Frolov Yu.G. Course of colloid chemistry. M., Chemistry, 1982, pp. 245-267.

2. Boyutsky S.S. Course of colloid chemistry. M., Chemistry, 1975, p. 33-53

3. Friedrichsberg D.A. Course of colloid chemistry. L., Chemistry, 1984, pp. 38-44.

4. Laboratory work and problems in colloidal chemistry.- Under. ed. SOUTH. Frolova and A.S. Grodsky. M., Chemistry, 1986, pp. 111-117.

5. Calculations and problems in colloidal chemistry. Ed. V.I. Baranova. M., Higher. school, s. 254-260.

THEORETICAL PART

LIGHT SCATTERING, RAYLEIGH EQUATION AND ITS ANALYSIS

When a beam of light falls on a dispersed system, it can be transmitted or refracted, as well as reflected , scattered or absorbed by particles of the dispersed phase. The passage of light is characteristic of transparent homogeneous media. Reflection – for microheterogeneous and coarsely dispersed systems with particle sizes exceeding the wavelength of incident light (0.4 – 0.7 microns), and manifests itself in the form of turbidity of suspensions, emulsions and aerosols. For colloidal systems with a particle radius less than the wavelength of the incident light, the phenomena of light scattering (opalescence) and its absorption (absorption) are characteristic.

The theory of light scattering for spherical particles that do not conduct electric current was developed by Rayleigh .

Dispersed systems with particle sizes smaller than the wavelength of light scatter light in all directions. In this case, each point of inhomogeneity becomes a source of secondary electromagnetic oscillations with a frequency equal to the frequency of the incident light wave ( diffraction ). The particle is thus an induced dipole equal to the product of the polarizability of the particle α and the electric field strength E:

Р = α E (1)

The scattered light intensity is determined by the quantities included in equation (1). The polarizability of a particle α is proportional to its volume V, and the intensity of light scattering is proportional to the square of the polarizability and, consequently, the square of the volume of the particle. Thus, as the particle size increases, the scattering intensity increases. The polarizability is also affected by the difference between the refractive indices of the dispersed phase n and the dispersion medium n 0 .

The electric field strength E characterizes the density of the energy flux of the supplying light (its intensity) and is proportional to the square of the amplitude of the wave emitted by the electric dipole (particle of the dispersed phase). And since the amplitude of the wave is proportional to the square of the frequency of the dipole oscillations, the scattered light intensity J p is proportional to the frequency of the dipole oscillations to the fourth power or inversely proportional to the wavelength λ to the fourth power.

If the incident light is not polarized, then the intensity of the scattered light depends on the direction of propagation of the radiation: J p is proportional to (1+cos 2 Θ), where Θ is the angle between the directions of the incident and scattered light (scattering angle).

Thus, the intensity of the scattered light is different in different directions, while the scattered light is partially polarized. Scattering and polarization of light by a particle in all directions is characterized by the Mie vector diagram (Fig. 1). The arrow indicates the direction of the incident beam. The unshaded area corresponds to the intensity of unpolarized light, the shaded area corresponds to the polarized part.

As can be seen from the diagram, the scattered light is not polarized in the direction of the incident beam and at an angle of 180°. The maximum polarized light is scattered at an angle of 90° to the incident beam.

Rayleigh’s theory is applicable to dilute colloidal solutions, so the possibility of secondary scattering is not taken into account, and the scattered light intensity is proportional to the number of particles per unit volume, ν.

The Rayleigh equation for the intensity of light J p , scattered by a unit volume of a disperse system with spherical particles that do not conduct electric current, with a radius much smaller than the wavelength of the incident light (r ≤ 0.1λ), at a distance R from the particles, in a direction that makes an angle Θ with the direction of the incident beam, has the form:

J p = (2)

where

F= (3)

J 0 is the intensity of the incident light;

ν is the number of particles of the dispersed phase per unit volume (partial concentration);

and – respectively, the refractive index of the substance of the dispersed phase and the dispersion medium;

is the volume of one particle.

a) b)

Fig.1. Mie diagrams characterizing the scattering and polarization of light by spherical particles that do not conduct electric current:

a) small; b) a large particle

Let us consider the effect of various parameters on the scattered light intensity in accordance with the Rayleigh equation.

1. Equation (2) is applicable in the absence of light absorption , for “white” non-metallic sols.

2. The area of strict applicability of the equation is limited by the condition where r is the radius of particles of the dispersed phase. For the visible part of the spectrum this corresponds to the values of the radius r < (2÷4) x10 -6 cm. Dependence from r is used to determine the particle sizes of dispersed systems. Exceeding the specified particle sizes and approaching them to the values leads to a decrease in the exponent at in the Rayleigh equation from 4 to 2.8. The lower bound of the exponent corresponds to the values of r when the phenomenon of scattering is replaced by the reflection of light . When the value of the exponent at becomes less than 4, Rayleigh’s law ceases to be observed and empirical methods are used to determine the particle radius. The most common of these is the Heller method discussed below.

3. The dependence of the intensity of scattered light on the concentration of particles is used to determine the concentration (in the absence of multiple scattering).

4. According to the Rayleigh equation, the higher the dispersion of particles, the less scattering. Approximation of particle sizes to molecular leads to the disappearance of opalescence.

5. is inversely proportional to λ 4 , i.e. when a white light beam passes through a colloidal solution, it is mainly short waves that scatter ; blue region of the spectrum. This is manifested in the bluish color of colloidal systems when viewed from the side. When examining a cell with a colloidal solution in transmitted light, i.e. when the light source in relation to the observer is behind the cuvette, the solution has an orange-red tint. This pattern explains the use of blue for blackout and red for signaling. The blue color of the sky is also due to opalescence, the scattering of short waves of solar radiation by the Earth’s atmosphere. At sunrise and sunset, we observe light passing through the atmosphere, so we perceive the sky as colored in orange-red tones.

6. The difference between the refractive indices of a particle and a medium is very small for solutions of macromolecular compounds and some emulsions. Light scattering for such systems is small (according to equation (2)).

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