A large number of data points for the vibrational relaxation time (pτv in atm sec) of simple systems have been logarithmically plotted vs (T°K)—⅓. It appears that each system is well represented by a straight line, and that most of these straight lines when extended to higher temperatures intersect near the point [pτv=10—8 atm sec, (T°K)—⅓=0.03]. Systems with a small reduced mass μ are exceptions to such a simple convergence, and in an improved scheme, the location of the convergence point is dependent on the reduced mass. Such a presentation has lead to an empirical equation correlating available measurements of vibrational relaxation times: log10(pτv)=(5.0×10−4)μ12θ43[T−13−0.015μ14]−8.00, where θ is the characteristic temperature of the oscillator in K deg. This equation reproduces the measured times within 50% for systems as diverse as N2, I2, and O2–H2. In the worst case thus far, O2–Ar near 1000°K, it is off by a factor of 5.

Systematics of Vibrational Relaxation

A new correlation of second virial coefficients of both polar and nonpolar systems is presented. It uses the Pitzer-Curl correlation for nonpolar compounds, but in a modified form. The second virial coefficient of nonhydrogen bonding compounds (ketones, acetaldehyde, acetonitrile, ethers) and weakly hydrogen bonding compounds (phenol) is fitted satisfactorily with only one additional parameter per compound, which is shown to be a strong function of the reduced dipole moment. Two parameters are needed for hydrogen bonding compounds (alcohols, water), but for alcohols, one parameter has been kept constant and the other expressed as a function of the reduced dipole moment. The extension of the correlation to mixtures is satisfactory, direct, and involves only one coefficient per binary.

An empirical correlation of second virial coefficients

In a preceding project, functional forms for “short” Helmholtz energy equations of state for typical nonpolar and weakly polar fluids and for typical polar fluids were developed using simultaneous optimization. In this work, the coefficients of these short forms for the equations of state have been fitted for the fluids acetone, carbon monoxide, carbonyl sulfide, decane, hydrogen sulfide, 2-methylbutane (isopentane), 2,2-dimethylpropane (neopentane), 2-methylpentane (isohexane), krypton, nitrous oxide, nonane, sulfur dioxide, toluene, xenon, hexafluoroethane (R-116), 1,1-dichloro-1-fluoroethane (R-141b), 1-chloro-1,1-difluoroethane (R-142b), octafluoropropane (R-218), 1,1,1,3,3-pentafluoropropane (R-245fa), and fluoromethane (R-41). The 12 coefficients of the equations of state were fitted to substance specific data sets. The results show that simultaneously optimized functional forms can be applied to other fluids out of the same class of fluids for which they were optimized without significant loss of a...

Short Fundamental Equations of State for 20 Industrial Fluids

Publisher Summary This chapter discusses molecular refractivity and polarizability. Refractive indices ( n ) of pure substances are more accurately measurable than any other optical properties. The refractive index of a substance varies with its physical state, temperature t , and wave-length λ of the light by which n is observed. The first two of these effects are attributed to the density d . The specific refraction r of a substance multiplied by the molecular weight is referred as molecular refraction. Polarizability of a particle is defined as the dipole moment induced by an electric field of unit intensity. The polarizabilities of monatomic ions and molecules are generally independent of field direction. The principal polarizabilities of molecules can be analyzed in terms of anisotropic bond polarizabilities. Polarizabilities are also responsible for the birefringence, which appears whenever the orientations of anisotropic molecules in an assemblage are derandomized or changed by any disturbing force.

Molecular Refractivity and Polarizability

A theory of homogeneous nucleation from the vapor phase is presented, which is based on an extension of Fisher’s semiphenomenological droplet model for the Gibbs free energy of formation of a cluster. This droplet model allows translational, rotational, vibrational, and configurational degrees of freedom of the cluster as well as the variation of surface tension with cluster size. By suitable choice of the three free model parameters, known nucleation theories such as the classical Becker–Doring–Zeldovich theory and others are obtained as special cases. Since, however, an ansatz for the Gibbs free energy of formation allows the construction of an equation of state for real gases below the critical point, a new method of determining the model parameters is suggested, which is based on the idea of forcing the identity of the constructed equation of state with an experimentally verified one. Thus, all free model parameters can be determined purely from well‐known handbook properties. It is shown that the new theory gives a better prediction of observed nucleation rates than the classical one.

A refined droplet approach to the problem of homogeneous nucleation from the vapor phase

The velocity of ultrasonic waves has been measured in a number of gases at 25 degrees C and for values of the ratio, ultrasonic frequency/pressure, ranging from 2 $\times $ 10$^{5}$ to 2 $\times $ 10$^{7}$ c s$^{-1}$ atm$^{-1}$. Dispersion, corresponding to a single vibrational relaxation process was shown by acetylene, CD$_{3}$Br and hexafluoro-ethane; and, to a double relaxation process, by ethane. Incipient dispersion was shown by propane, ethyl chloride, ethyl fluoride and dimethyl ether. No dispersion was shown by 1.1-difluoro-ethane, n-butane, iso-butane, neo-pentane and ammonia. Correlation of these with previous results leads to the conclusion that: (a) For molecules with a distribution of fundamental frequencies, such that there is only a small gap between the lowest and the remaining frequencies, vibrational activation enters via the lowest mode and spreads rapidly to the other modes, giving rise to a single relaxation process involving the whole of the vibrational energy. The chief factors determining the probability of excitation of the lowest mode are its frequency and the presence or absence of hydrogen atoms in the molecule. Molecules containing two or more hydrogen atoms suffer translational-vibrational energy transfer very much more easily than other molecules. Deuterium has almost the same effect as hydrogen. (b) For molecules, in which there is a large gap between the lowest and the remaining fundamental frequencies, a double relaxation process occurs. The complex energy transfer probabilities involved do not fit the same quantitative functional relation with vibrational frequency as in (a) above. (c) Torsional oscillations due to hindered internal rotation behave similarly to other fundamental modes. For molecules in which there is a large gap between the torsional frequency and the other modes (e.g. ethane) a double relaxation process occurs as in (b). Where there is no such gap, vibrational energy enters all modes via the torsional mode as in (a).

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Vibrational relaxation in gases

The compressibilities of a num ber of organic vapours have been measured at pressures up to 1 atm. and temperatures ranging from 40 to 130° C. The observed second virial coefficients are compared with values calculated from the critical data by the Berthelot equation. The results show two distinct classes of behaviour. Class I is shown by ethane, ethylene, n -hexane, cyclohexane, benzene, diethyl ether, ethyl chloride, chloroform and carbon tetrachloride, where the measured second virial coefficients are in agreement with the calculated values. Class II by acetaldehyde, acetone, acetonitrile, methyl alcohol, where the measured second virial coefficients are consistently very much higher than the calculated values. It is concluded that the vapours of polar substances for which the energy of attraction between molecules, due to dipole interaction or to hydrogen bonding, is larger than kT undergo dim erization. This view is supported by thermal conductivity data. The range of validity of the Berthelot equation for both non-polar and polar vapours is examined.

The second virial coefficients of organic vapours

Measurements have been made, at temperatures between 35 and 100 degrees C, of the viscosities and thermal conductivities of gaseous methane, ethane, ethylene, propane, propylene, cyclo-propane, n-butane, cis-2-butene, trans-2-butene, 1:3-butadiene, iso-butane, n-pentane, iso-pentane, neo-pentane, cyclo-pentane, n-hexane, neo-hexane, cyclo-hexane, benzene, n-heptane, 2:4-dimethyl-pentane, n-octane, 2:3:4-trimethyl-pentane and of carbon tetrafluoride. Viscosities were measured by observing the damping of a pendulum swinging in the vapour and by a capillary-flow viscometer. Thermal conductivities were measured by the hot-wire method. The observed values of the ratio between the transport properties are discussed in the light of the kinetic theory of gases. It is found that highly flexible molecules show systematically lower values of the ratio, k/$\eta $, than other molecules, and it is suggested that this is due to a special type of intermolecular collision, involving some degree of intercoiling of the two molecules. This view is relevant to the interpretation of recent work on the vibrational activation of the ethylene molecule by collision with other hydrocarbons, and on the kinetics of the thermal decomposition of gaseous hydrocarbons. Inferences can also be drawn about the ease of interchange of translational energy with vibrational and with rotational energy in collisions; these are discussed in relation to information obtained from ultrasonic dispersion measurements.

Transport Properties of Gaseous Hydrocarbons

The second virial coefficients of ammonia and the vapours of the primary, secondary and tertiary methylamines and ethylamines have been measured at temperatures between 20 and 130 degrees C. The results are interpreted as showing that dimerization occurs with ammonia and with the primary and secondary amines, but not with the tertiary amines. The dimerization is attributed to hydrogen bonding, and the energy of the N$\chembond{1,0} $H$\cdots $N bond is discussed.

The dimerization of ammonia and amines

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.

J. D. Lambert

Papers

Vibrational relaxation in gases

The second virial coefficients of organic vapours

Transport Properties of Gaseous Hydrocarbons

The dimerization of ammonia and amines

Ultrasonic Dispersion in Gaseous Sulphur Dioxide