On the Relationship Between the Dielectric Strength of Gases and Liquids and Their Physicochemical Properties

A. A. Vorob’ev and A. F. Kalganov

Electrical breakdown of dielectrics occurs at the expense of the energy of the electric field. It is of interest to study the dependence of the energy expended on breakdown on the chemical composition of the dielectric. For solid dielectrics, a coincidence has been found between the energy lost during breakdown and the lattice energy referred to the destroyed volume [1], which indicates a connection between the energy expended by the field during breakdown and the dielectric strength.

The dielectric strength of gaseous and liquid dielectrics is also connected with their energy characteristics. This is evidenced by the comparisons, presented below, of the dielectric strength of gases and liquids with their physicochemical properties.

Gases

Electrical breakdown of gaseous dielectrics is explained by the theory of impact ionization. Considering the ionization process in a gas, one would naturally expect an increase in the dielectric strength of gases with increasing ionization potential and with increasing bond energy of the atoms in the molecule. Comparison of the ionization potential and the dissociation energy of molecules with the dielectric strength of the corresponding gases having the same number of atoms in the molecule did not reveal such a dependence [2, 3]. It was shown that for gases whose molecules have the same number of atoms, the dielectric strength is, on average, proportional to the molecular weight [3]. G. M. Kovalenko [2] obtained an increasing dependence of the voltage of certain diatomic gases on the critical temperature and on the distance between the nuclei of the atoms in the molecule, and a decreasing dependence on the electron mean free path in the gas. V. M. Gokhberg and E. Ya. Zandberg [4] obtained, for the groups of gases they investigated, an increasing dependence of dielectric strength on refraction.

For a more complete clarification of the connection between the dielectric strength of gases and their physicochemical properties, we compared the dielectric strength of six groups of gases \((\mathrm{H}_2, \mathrm{O}_2, \mathrm{N}_2, \mathrm{Cl}_2, \mathrm{Br}_2, \mathrm{J}_2; \mathrm{HCl}, \mathrm{HBr}, \mathrm{HJ}; \mathrm{CH}_3\mathrm{OH}, \mathrm{C}_2\mathrm{H}_5\mathrm{OH}; \mathrm{CH}_3\mathrm{Cl}, \mathrm{CH}_3\mathrm{Br}, \mathrm{CH}_3\mathrm{J}; \mathrm{C}_2\mathrm{H}_5\mathrm{Cl}, \mathrm{C}_2\mathrm{H}_5\mathrm{Br}, \mathrm{C}_2\mathrm{H}_5\mathrm{J}; \mathrm{C}_5\mathrm{H}_{12}, \mathrm{C}_6\mathrm{H}_{14})\) [2—6] with the following characteristics: molecular weight \(M\), density \(\rho\), thermodynamic (isobaric) potential \(\Delta Z\), dipole moment \(\mu\), mean polarizability \(\alpha\), molecular dissociation energy \(D\), ionization potential \(U_i\), reciprocal of the distance between nuclei of atoms in the molecule \(\frac{1}{r}\), molecular diameter \(d\), molar refraction \(P\), critical temperature \(T_{\mathrm{cr}}\), coefficients of the van der Waals equation \(a\) and \(b\), molar heat capacity \(C_p\), melting temperatures \(T_{\mathrm{m}}\) and boil-

Table 1

\(^1\) The constants \(a\) and \(b\) were calculated for the volume occupied by \(1/22416\) mole at a pressure of 1 atm and \(0^\circ\)C.

of boiling \(T_{\text{boil}}\), the heats of fusion \(Q_{\text{melt}}\) and vaporization \(Q_{\text{vap}}\) of the solid and liquid phases, respectively (Table 1).

Figure 1 graphically depicts the relation between the dielectric strength of one group of gases (HCl, HBr, HJ) and some of the characteristics indicated above. As can be seen from the graph, a larger value of the characteristics that determine the intermolecular bonding forces in the gas (density, polarizability, etc.) corresponds also to a larger value of the dielectric strength of the gas. Conversely, a larger value of the characteristics that determine the intramolecular bonding forces (thermodynamic potential, dissociation energy, etc.) corresponds to a smaller value of the dielectric strength of the gas. In this connection it should be borne in mind that the more negative the value of the thermodynamic potential \(\Delta Z\), the more stable the chemical compound.

Fig. 1. Dependence of the dielectric strength of the gases HCl, HBr, and HJ on the dipole moment \(\mu\), thermodynamic potential \(\Delta Z\), dissociation energy of the molecule \(D\), ionization potential \(U_i\), density \(\rho\), molecular weight \(M\), reciprocal distance between atomic nuclei in the molecule \(1/r\), and electronic polarizability \(\alpha\).

For all other groups of gases, analogous relationships have been found between the dielectric strength of the gases and their intermolecular and intramolecular characteristics.

The results obtained give grounds for considering that electrical breakdown of gases is associated with overcoming the intermolecular bonding forces in the gas.

It is of interest to estimate the relation between dielectric strength and the energy of intermolecular (van der Waals) interaction for some single gas. We chose carbon dioxide gas, \(\mathrm{CO_2}\), for which the dependence of dielectric strength on density is known over a wide range of densities [7].

Figure 2 gives the dependences of the dielectric strength \(E\) and of the square root of the energy of intermolecular interaction \(\sqrt{W}\) on the density \(\rho\) for \(\mathrm{CO_2}\).

As is seen from Fig. 2, at not very high gas densities the dependences \(E_{\mathrm{br}}=f_1(\rho)\) and \(\sqrt{W}=f_2(\rho)\) run parallel. At densities tens of times greater than the density of \(\mathrm{CO}_2\) under normal conditions, \(E_{\mathrm{br}}\) increases more slowly than \(\sqrt{W}\), and the curves diverge. The following circumstances must be taken into account: the energy \(W\) was calculated by us from the formula \(W=C\rho^2\), where \(C\) is a constant quantity that includes the van der Waals coefficients \(a\) and \(b\), which are also regarded as constant. In reality, however, the coefficients \(a\) and \(b\) decrease as the gas density increases. In addition, the formula \(W=C\rho^2\) takes into account only the attraction of molecules, whereas at high densities (pressures) repulsive forces begin to manifest themselves, reducing the total interaction energy. Finally, at high densities association of gas molecules is possible. All this should reduce the increase in the energy of intermolecular interaction in a gas as its density increases.

Fig. 2. 1. Dependence of the electrical strength of \(\mathrm{CO}_2\) on density. The distance between spherical electrodes of diameter \(6.35\ \mathrm{mm}\) was \(0.19\ \mathrm{mm}\). 2. Energy of van der Waals interaction as a function of density, according to the formula

\[ \sqrt{W}=\sqrt{C\rho} \]

in relative units.

The relation between the energy of intermolecular interaction and electrical strength is also revealed in the fact that, upon transition of \(\mathrm{CO}_2\) from the gaseous to the liquid state, at the same density of both phases, the electrical strength does not change [7]. No change in electrical strength is observed either when the temperature of gaseous \(\mathrm{CO}_2\) is changed in the interval from 25 to \(55^\circ\mathrm{C}\), and of liquid \(\mathrm{CO}_2\) from 25 to \(35^\circ\mathrm{C}\), at unchanged density. Conversely, a change in the temperature of a free gas causes a change in its density and electrical strength [8]. Thus, both for a single gas and for individual groups of gases of the same chemical structure, a larger value of the energy of intermolecular interaction corresponds to a larger value of electrical strength.

Liquid Dielectrics

There is no single mechanism for the breakdown of liquid dielectrics. A regular connection between electrical strength and the physicochemical nature of a liquid dielectric has likewise not yet been established. The electrical strength of liquid dielectrics of technical purification is ...

several hundred kV/cm [9]. This is explained by the fact that the breakdown of technical liquid dielectrics is determined not so much by their chemical nature as by secondary phenomena accompanying breakdown.

Recently, higher (>1 MV/cm) values of the measured electric strength have been obtained, approaching the electric strength of solid dielectrics [10, 11]. Crowe et al. [11] obtained a linear dependence of the electric strength of the homologous series of aliphatic hydrocarbons on density. As can be seen, the electric strength of the indicated liquid hydrocarbons proved to be connected with their physicochemical nature.

Fig. 3. Dependence of the electric strength of aliphatic hydrocarbons on the thermodynamic potential \(\Delta Z\), viscosity \(\nu\), boiling point \(T_{\text{boil}}\), molecular weight \(M\), heat of vaporization \(Q_{\text{vap}}\), density \(\rho\), and surface tension \(\gamma\).

We compared the electric strength of liquid hydrocarbons also with other physicochemical properties. In Fig. 3 are presented the dependences of electric strength on the heat of vaporization \(Q_{\text{vap}}\), boiling point \(T_{\text{boil}}\), surface tension \(\gamma\), viscosity \(\nu\), molecular weight \(M\), and thermodynamic potential \(\Delta Z\). The dependence of \(E_{\text{br}}\) on density \(\rho\), as obtained by Crowe et al., is also given there. As can be seen from Fig. 3, with an increase in the thermodynamic potential \(\Delta Z\), which characterizes the strength of a chemical compound, the electric strength decreases. With an increase in the other characteristics, the electric strength increases. The increase in electric strength with an increase in these characteristics, which determine the forces of bonding between gas molecules, is apparently a consequence of the fact that electrical breakdown in liquid dielectrics, just as in gases, is connected with overcoming intermolecular forces.

Indeed, the final stage of electrical breakdown of liquid dielectrics is the formation, between the electrodes, of a channel filled with dielectric vapor. Evaporation of the liquid, as is known, is connected with the rupture of intermolecular bonds without destruction of the molecules. It follows

one should therefore expect an increase in the dielectric strength of liquid dielectrics with increasing boiling point of the liquid, heat of vaporization, surface tension, density, and other quantities characterizing intermolecular bonds. This is also observed from the experimental data (Fig. 3).

Let us note that lowering the boiling point of a liquid by reducing the pressure should not affect the dielectric strength, since, in the presence of enormous surface-tension forces, a change in the external pressure will not substantially change the bonding forces between molecules. Indeed, in [12, 13] it is shown that, for degassed toluene and xylene, the dielectric strength does not depend on the external pressure.

It may be supposed that, in the general case, the process of breakdown of liquids begins with the overcoming of intermolecular bonds, which are weaker than intramolecular ones; subsequently, as the energy concentration in the discharge channel increases, destruction of intramolecular bonds may also occur.

Conclusion

An analysis of experimental and theoretical data on the dielectric strength and physicochemical properties of gaseous and liquid dielectrics indicates the existence of a definite relationship between the dielectric strength and the physicochemical properties of the dielectrics under consideration.

The dielectric strength is greater for those gases and liquids that are characterized by large values of the physicochemical quantities determining the intermolecular bonds in the gas and liquid—in the general case, by the energy of intermolecular interaction.

References

1. Vorob’ev A. A. and Kalganov A. F. Proceedings of the Conference on Dielectrics in Tomsk, 1955.
2. Kovalenko G. M. ZhTF, 10, 1014, 1940.
3. Bonch-Bruevich A. M., Glinkina M. V., and Gokhberg B. M. ZhETF, 10, 171, 1940.
4. Gokhberg B. M. and Zandberg E. Ya. ZhTF, 12, 65, 1942.
5. Gokhberg B. M. and Zandberg E. Ya. DAN SSSR, 53, 515, 1946.
6. Bachinskii A. I. et al. Handbook of Physics. Uchpedgiz, p. 164, 1951.
7. D. R. Young, J. Appl. Phys. 21, 222, 1950.
8. Vorob’ev A. A. High-Voltage Engineering. Gosenergoizdat, p. 129, 1945.
9. Vol’kenshtein F. F. Breakdown of Liquid Dielectrics. ONTI, 1934.
10. W. D. Edwards, J. Chem. Phys. 20, 753, 1952.
11. R. W. Crowe, J. K. Bragg, A. H. Sharbaugh, J. Appl. Phys. 25, 392, 1954.
12. Val’ter A. F. and Chelyustkina O. V. ZhTF, 6, 1900, 1936.
13. Val’ter A. F. and Inge L. D. ZhTF, 1, 745, 1931.

Tomsk Polytechnic Institute