Ultrasonic dispersion in halo-methane vapours

The velocity of ultrasonic waves has been measured in the vapours of methyl fluoride, chloride, bromide and iodide, methylene fluoride and chloride, fluoroform and chloroform, carbon tetrafluoride and carbon tetrachloride, at frequencies 200, 566, 1192 and 4000 kc/s, pressures ranging from 0·25 to 2 atm, and temperature 100°C. Dispersion, or incipient dispersion, occurs in all cases. Each dispersion zone observed corresponds to a single relaxation time, involving disappearance of the whole of the molecular vibrational energy. On the assumption that vibrational energy is taken up via the mode of lowest frequency, a simple functional relation is found to exist between the frequency of this mode and the probability of vibrational energy being acquired in collision. The theoretical significance of this is discussed. The paper includes second virial coefficient data for all the vapours investigated.

Download Full-text

Ultrasonic dispersion in halo-ethylene vapours

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1955.0237 ◽

1955 ◽

Vol 232 (1191) ◽

pp. 537-547 ◽

Cited By ~ 19

Keyword(s):

Virial Coefficient ◽

Vinylidene Fluoride ◽

Vibrational Energy ◽

Relaxation Times ◽

Second Virial Coefficient ◽

Ultrasonic Waves ◽

Ultrasonic Dispersion ◽

Infra Red ◽

Acoustic Interferometer ◽

Inactive Mode

The velocity and absorption of ultrasonic waves have been measured by acoustic interferometer in the vapours of vinyl fluoride, chloride, bromide and iodide, vinylidene fluoride, cis -dichloro-ethylene, trans -dichloro-ethylene, trichloro-ethylene and tetrafluoro-ethylene at 100° C and for values of f|p ranging from 100 kc s -1 atm -1 to 15 Mc s ~1 atm~1. All show dispersion or incipient dispersion, and single relaxation times appear to control the whole of the molecular vibrational energy in each case. The results are correlated with previous results for halo-methane vapours and for other polyatomic molecules. The conclusion is drawn that vibrational activation enters a molecule via the mode of lowest frequency. The probability of excitation of that mode in collision is a function both of its frequency and of the intensity of its infra-red activity. In most cases a strongly infra-red active mode is very much more easily excited by collision than an inactive mode of the same frequency. The paper includes second virial coefficient data for all the vapours investigated.

Download Full-text

Ultrasonic dispersion in gaseous sulphur dioxide

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1957.0204 ◽

1957 ◽

Vol 243 (1232) ◽

pp. 78-83 ◽

Cited By ~ 45

Keyword(s):

Relaxation Time ◽

Sulphur Dioxide ◽

Major Part ◽

Vibrational Energy ◽

Vibrational Mode ◽

Relaxation Times ◽

Ultrasonic Waves ◽

Ultrasonic Frequency ◽

Ultrasonic Dispersion ◽

Dispersion Zone

The velocity of ultrasonic waves has been measured in gaseous sulphur dioxide at 20, 102 and 200° C for values of f/p ranging from 200 kcs -1 atm -1 to 7 Mcs -1 atm -1 . ( f is the ultrasonic frequency, p the pressure.) Dispersion involving the major part of the vibrational specific heat was found at all temperatures. Each dispersion zone corresponds to two distinct relaxation times differing by a factor of ten. The lower relaxation time corresponds with activation of the lowest (519 cm -1 ) vibrational mode, the higher to activation of the remainder of the vibrational energy. The conditions giving rise to a double relaxation process are discussed.

Download Full-text

The second virial coefficients of mixed polar vapours

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0033 ◽

1959 ◽

Vol 249 (1258) ◽

pp. 414-426 ◽

Cited By ~ 21

Keyword(s):

Methyl Acetate ◽

Virial Coefficient ◽

Methyl Formate ◽

Second Virial Coefficient ◽

Virial Coefficients ◽

Ethyl Formate ◽

Carbonyl Oxygen ◽

Second Virial Coefficients ◽

Theoretical Significance ◽

Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

Download Full-text

Ultrasonic dispersion in organic vapours

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1950.0185 ◽

1950 ◽

Vol 204 (1078) ◽

pp. 424-434 ◽

Cited By ~ 22

Keyword(s):

Molecular Structure ◽

High Temperatures ◽

Diethyl Ether ◽

Methyl Alcohol ◽

Vibrational Energy ◽

Low Frequency ◽

Polyatomic Molecules ◽

Ultrasonic Waves ◽

Ultrasonic Dispersion ◽

Internal Rotations

The velocity of ultrasonic waves has been measured in a series of organic vapours at frequencies 566, 1192 and 4000 kc./sec., temperatures 20 and 100° C, and pressures ranging from 0.25 to 4 atm. Ultrasonic dispersion was found with benzene, cyclopropane and ethane. No dispersion was found with propane, n -hexane, cyclohexane, cyclohexene, ethylchloride, chloroform, acetonitrile, acetaldehyde, acetone, diethyl ether and methyl alcohol. The mechanism and rate of the activation of vibrational energy by intermolecular collisions are discussed in relation to molecular structure. It is concluded that, for polyatomic molecules in general, there is little hindrance to the interconversion of translational and vibrational energy, especially at high temperatures. Slow interconversion, leading to ultrasonic dispersion, only occurs with small or rigid molecules, where internal rotations or vibrations of low frequency are absent. Interchange of vibrational energy between the different modes within the molecule is usually very rapid.

Download Full-text

The transfer of vibrational energy between molecules

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1964.0240 ◽

1964 ◽

Vol 282 (1390) ◽

pp. 380-389 ◽

Cited By ~ 16

Keyword(s):

Vibrational Energy ◽

General Pattern ◽

Relaxation Times ◽

Quantum Mechanical ◽

Ultrasonic Dispersion ◽

Quantum Mechanical Theory ◽

Dispersion Zone ◽

Double Dispersion ◽

Made In ◽

Linear Concentration

Ultrasonic dispersion measurements have been made in mixtures of SF 6 + CHClF 2 , extending over the whole concentration range. All mixtures showed a single dispersion zone corresponding to relaxation of the whole of the vibrational energy of both components, with approximately quadratic dependence of reciprocal relaxation time on molar concentration. A quantitative interpretation is based on the assumption that the vibrational energy of the whole system is maintained in continuous equilibrium by rapid near-resonant transfer of vibrational energy between the 344 cm -1 mode of SF 6 and the 369 cm -1 mode of CHClF 2 . The collision number for this transfer is estimated as Z AB ~ 50, which is lower than the collision numbers for homomolecular deactivation of SF 6 (Z 10 = 1005) and CHClF 2 (Z 10 = 122). This behaviour is contrasted with that of mixtures previously investigated, which showed double dispersion with linear concentration dependence of reciprocal relaxation times. A quantitative reinterpretation of these is based on the assumption of a near-resonant vibration-vibration transfer, with a rate intermediate between the homomolecular deactivation rates of the two pure components. Values of Z AB ranging from 5 to 110 are estimated for these systems. The significance of the available values of Z AB for vibration-vibration transfer is discussed, and their general pattern, in relation to the vibrational frequencies of the exchanging modes, is shown to be in accord with the quantum-mechanical theory of Schwartz, Slawsky & Herzfeld.

Download Full-text

Numerical studies of the second virial coefficient asymptotic expressions at low temperatures for the Morse intermolecular potential

Journal de Chimie Physique ◽

10.1051/jcp/1990871187 ◽

1990 ◽

Vol 87 ◽

pp. 1187-1188

Author(s):

H Guérin

Keyword(s):

Low Temperatures ◽

Virial Coefficient ◽

Second Virial Coefficient ◽

Intermolecular Potential ◽

Numerical Studies ◽

Asymptotic Expressions

Download Full-text

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19951641 ◽

1995 ◽

Vol 60 (10) ◽

pp. 1641-1652 ◽

Cited By ~ 2

Author(s):

Henri C. Benoît ◽

Claude Strazielle

Keyword(s):

Approximation Theory ◽

Random Phase Approximation ◽

Virial Coefficient ◽

Random Phase ◽

Second Virial Coefficient ◽

Solvent Mixture ◽

Gyration Radius ◽

Thermodynamic Quantities ◽

Phase Approximation ◽

Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

Download Full-text