Molecular Acoustics

a branch of physical acoustics in which the properties of matter and the kinetics of molecular processes are studied by acoustic methods. The main methods of molecular acoustics are the measurement of the speed of sound and sound absorption and of the dependence of these quantities on various physical parameters, such as the frequency of the sound wave, the temperature, and the pressure. Gases, liquids, polymers, solids, and plasma may be studied using methods of molecular acoustics.

The development of molecular acoustics as an independent branch began in the 1930’s, when it was established that dispersion of the velocity of sound takes place in many substances during the propagation of sound waves in them and that the absorption of sound is not described by the classical law, according to which the coefficient of absorption is proportional to the square of the frequency. These anomalies were explained on the basis of the study of relaxation processes, which made it possible to correlate certain properties of matter at the molecular level, and also a number of kinetic characteristics of molecular processes, with such macroscopic quantities as the speed and absorption of sound.

Such characteristics of matter as compressibility, the specific heat ratio, and the elastic properties of a solid can be determined from the speed of sound, and the values of shear viscosity, second viscosity, and relaxation time can be determined from the absorption of sound. In gases the parameters that characterize the interaction of gas molecules during collisions are determined by measuring the speed of sound and its temperature dependence. In a liquid, the accuracy of the model used may be assessed and the interaction energy of the molecules determined in many cases by calculating the speed of sound on the basis of a given model of the liquid and comparing the results of the calculation with experimental data. The speed of sound is affected by the peculiarities of molecular structure, the force of molecular interaction, and the packing density of the molecules. For example, an increase in the packing density of molecules, the appearance of hydrogen bonds, and polymerization lead to an increase in the speed of sound, whereas the introduction of heavy atoms into the molecule leads to a decrease.

In the presence of relaxation processes, the energy of translational motion of molecules, which they receive in the sound wave, is redistributed into internal degrees of freedom. In the process, dispersion of the velocity of sound appears, and the dependence of the product of the coefficient of absorption and wavelength on frequency has a maximum at a certain frequency, called the relaxation frequency. The extent of dispersion of the velocity of sound and the value of the coefficient of absorption depend on precisely which degrees of freedom are excited by the action of the sound wave, and the relaxation frequency, which is equal to the inverse of the relaxation time, is related to the rate of energy exchange among the degrees of freedom. Thus, an assessment of the character of molecular processes and a determination of the process that makes the main contribution to relaxation can be made by measuring the speed of sound and the absorption as a function of frequency and by determining the relaxation time. These methods may be used to study the excitation of the oscillatory and rotational degrees of freedom of molecules in gases and liquids, processes of molecular collision in mixtures of various gases, establishment of equilibrium during chemical reactions, rearrangement of the molecular structure in liquids, processes of shear relaxation in highly viscous liquids and polymers, and various processes of the interaction of sound with elementary excitations in solids.

The analysis of acoustic data is usually more difficult for liquids than for gases, since the relaxation region here generally lies at higher frequencies, which require more complex measurements. The entire set of relaxation processes with a broad range of relaxation times may contribute to absorption and dispersion in highly viscous liquids, polymers, and certain other substances. Since the relaxation time depends on temperature and pressure, the relaxation region may be shifted in frequency by changing these parameters. For example, in a gas an increase in gas pressure is equivalent to a decrease in frequency. This may be used conveniently in measuring the speed and absorption of sound if the relaxation frequency under normal conditions lies within the range of frequencies that is difficult to study experimentally. The study of the temperature dependences of the speed and absorption of sound makes it possible to separate the contributions of various relaxation processes.

Ultrasound is usually used for research in molecular acoustics. In gases the range of frequencies is 10⁴-10⁵ hertz (Hz), and in liquids and solids, 10⁵-10⁸ Hz. This results both from the great development of radiation technology and ultrasonic techniques and the high precision of measurements in this frequency range and from the fact that work at lower frequencies would require very large volumes of the substance under study, whereas at higher frequencies the absorption of sound becomes so great that many acoustical methods become inapplicable.