Blanc's Law Research Articles

AC Conduction Rule for a Gaseous Mixture

The AC conduction rule for ions in a binary gaseous mixture is derived using the Langevin model for charged particle transport in an oscillating electric field. The complex mobility \\dotµ=µr+jµi of the ion obeys simple sum rules expressed only in terms of mobilities at the source frequencies ω=0 and ∞. Specifically, µr and µi at high ω vary almost linearly with the portion of the mixture as do µr-1 and || µi|| -1/2 at low ω according to Blanc's law.

Measurements of electron drift velocities and positive ion mobilities for gases containing CF 4 II

Measurements of electron drift velocities and positive ion mobilities for gases containing CF 4 have been made. Our previous paper described the results on electron drift velocities for gas mixtures containing CF 4 and hydrocarbon, and ion mobility results for gas mixtures of CF 4 + hydrocarbon, Ar + C 2H 6 and Ar + C 3H 8. The present paper is the second and final paper of the series. It describes the results on electron drift velocities for the gas mixtures; Ar + CF 4 + hydrocarbon, where hydrocarbon is CH 4 or C 2H 6 or C 3H 8 or iso-C 4H 10. The fraction of each gas component was changed systematically for each set of gas mixtures, and the electron drift velocity was measured as a function of the applied drift field between 0.2 and 2.5 kV/cm. Indications were found for relatively large electron drift velocities, even for low electric fields, with better saturation properties than was the case for the gas mixtures of CF 4 + hydrocarbon previously measured. Positive ion mobility was measured for several kinds of gas mixtures; Ar + hydrocarbon, CF 4 + hydrocarbon and Ar + CF 4 + hydrocarbon. Since ion currents and their arrival times were actually measured, the word “positive ion” does not necessarily mean a specific kind of ions but rather a group of ion clusters. The positive ion mobilities were deduced from this measurement under the assumption that Blanc's law was valid. A consistent picture was obtained within this approximation.

Heavy ions in mixtures of light gases: Fokker-Planck equation and its solution

The Fokker-Planck equation for heavy ions moving in a mixture of light neutral gases in electric and (static) magnetic fields is explicitly given. A general procedure to obtain exact stationary and non-stationary solutions, both for constant and time-dependent electric fields, is outlined, and the results relative to the most interesting and common physical situations are explicitly reported. The obtained formulas formally coincide with the corresponding ones valid for heavy ions in a single light gas. Consequently, all the properties of the solutions relevant to heavy ions in a single light gas hold also for heavy ions in any multicomponent light-gas mixture. In the framework of the theory based on the Fokker-Planck equation, it is shown that additive properties (as regards the contributions of the single mixture components) can be found for the reciprocal of the ion mobility (Blanc's law) in dc electric fields and, in part, for the ion drift velocity inhigh-frequency ac electric fields. Finally, the limits of validity of the solutions of the Fokker-Planck equation are discussed.

Thermal mobilities of electrons in binary rare gas mixtures

The mobility of electrons in binary mixtures of the inert gases is calculated versus mole fraction for different electric field strengths. The deviations from the linear variation of the reciprocal of the mobility of the mixture with mole fraction, that is from Blanc's law, is determined and interpreted in detail. Very large deviations from the linear behaviour were calculated for several binary mixtures at specific electric field strengths, in particular for HeXe mixtures. An interesting effect was observed whereby the electron mobility in HeXe mixtures, for particular compositions and electric field strength could be greater than in pure He or less than in pure Xe. The results of this study suggest that the experimental measurements of the electron mobility in these mixtures could be used to refine the electron-atom momentum transfer cross sections.

Negative ion drift velocities in mixtures of methane and sulphur hexafluoride

The velocities of negative ions drifting in mixtures of methane and sulphur hexafluoride have been measured. Measurements were made as a function of gas composition, reduced electric field strength between 3 and 185 Td, and total gas pressure in the range 100-600 Torr at 300K. The data indicate that SF6- (SF6) ions are the dominant ion in all of the gas mixtures studied. Extrapolation of the data using Blanc's Law was used to determine the velocity of sulphur hexafluoride ions drifting in pure methane.

The Application of Blanc's Law to the Determination of the Diffusion Coefficients for Thermal Electrons in Gases

Blanc's law is exactly applicable when the momentum transfer cross sections for electrons in each constituent of a gas mixture have the same energy dependence in the relevant energy range. This condition is rarely satisfied even for thermal energies. In this paper the magnitude of the errors arising from the applications of Blanc's law is examined for some cases where the condition is strongly violated, and a procedure developed for obtaining useful data from its application even under these circumstances.

The Determination of the Diffusion Coefficient for Thermal Electrons in Water Vapour by the Use of a Modified Blanc's Law Procedure

The Cavalieri electron density technique has been used to measure the diffusion coefficient for thermal electrons in water vapour. When analysed by a straightforward application of Blanc's law to determine the diffusion coefficient for water vapour, the normalized coefficient ND showed an anomalous pressure dependence. The application of a modified procedure, in which these data were corrected using a calculated correction factor, removed the anomalous dependence and gave data which are in agreement with previously published data.

A method to calculate mobilities of ions in gas mixtures

A method for calculating mobilities in gas mixtures is described. The method is based upon an assumption that the momentum transfer cross sections of ions in a gas mixture and those in pure component gases are the same if mean relative velocities of ions and gas atoms/molecules are equal. Deviations from Blanc's law of the calculated reciprocal mobilities agree well with experimental values for K+ ions in mixtures of He+Ne, Ne+Ar and H2+N2 and with those for Li+ ions in mixtures of H2+N2.

Mobilities of positive ions in some gas mixtures used in proportional and drift chambers

We have measured the mobility of positive ions in several gas mixtures frequently used in proportional and drift chambers, namely Ar-(OCH3 )2CH2, Ar-(OCH3)2CH 2-IsoC4H10, Ar-CH4, and Ar-CO 2. In all gas mixtures considered, Blanc's law of positive ion mobility has been verified, except for a very small methylal concentration in argon-isobutane-methylal. The law permits the calculation of ion mobility in any mixture of the gases considered.

The mobility of potassium ions in gas mixtures

The reduced mobility of K+ ions in He, Ne, Ar, H2 and N2 and in mixtures of He-Ne, Ne-Ar and H2-N2 has been measured at 293 K over the range 20<or=E/N(Td)<or=100 using the Bradbury-Nielsen time-of-flight technique. A theory has been developed which predicts the deviations from Blanc's Law in situations where only elastic scattering occurs. The measured deviations in mixtures of He-Ne and Ne-Ar are in good qualitative agreement with the predictions of this theory. In H2-N2 mixtures the measured deviations are of opposite sign and differ in magnitude from the predictions of the recent theory of Mason and Hahn (1972). The measured values of the reduced mobility of the ions in the pure gases are estimated to be in error by less than +or-2% over the whole range of E/N and the errors in the measured deviations from Blanc's Law are considered to be less than +or-0.4%.

Mobility of Ions in Gas Mixtures

A formula for the mobility of ions in a mixture of neutral gases is obtained as a generalization of an expression previously derived from the Boltzmann equation for ions in a pure gas (Kumar aitd Robson 1973). It is shown that Blanc's law holds only for very specialized situations. Using interaction potentials obtained in a previous work (Robson and Kumar 1973), the mobilities of K + ions in helium-neon mixtures have been calculated and the deviations from Blanc's law are discussed.

Composition Dependence of Ion Diffusion Coefficients in Gas Mixtures at Arbitrary Field Strengths

Expressions for the diffusion coefficient of ions in gas mixtures are obtained from momentum-transfer theory, and are given in terms of the diffusion coefficients and drift velocities of the ions in the pure component gases. Blanc's law holds exactly at all field strengths if the mean free time between collisions is independent of velocity (Maxwell model), but otherwise there may be either positive or negative deviations from Blanc's law at high fields. Such deviations are of comparable magnitude for the diffusion coefficients and the mobility, but are not identical. Specific cases of inverse-power potentials are treated in further detail, and some numerical examples are given for rigid-sphere interactions.

Ion Drift Velocities in Gaseous Mixtures at Arbitrary Field Strengths

A momentum-transfer theory is used to obtain an expression for the drift velocity of an ion in a multicomponent gas mixture. This is combined with an approximate calculation of the partition of the ion energy in the mixture to yield a formula for the drift velocity in terms of the drift velocities in the pure component gases. Positive deviations from Blanc's law at high fields are predicted, of magnitudes that should be easily measured experimentally.

1180. Kinetic-theory deviations from Blanc's law of ion mobilities: S I Sandler and E A Mason, J Chem Phys, 48 (7), 1 st April 1968, 2873–2875

1180. Kinetic-theory deviations from Blanc's law of ion mobilities: S I Sandler and E A Mason, J Chem Phys, 48 (7), 1 st April 1968, 2873–2875

Kinetic-Theory Deviations from Blanc's Law of Ion Mobilities

Ion mobilities in gas mixtures are investigated by rigorous kinetic theory. It is shown that the Einstein relation between mobility and diffusion coefficient is exact in higher approximations, contrary to previous conjectures, and an explicit expression for the deviations from Blanc's law for ions in a binary gas mixture is obtained in second Chapman–Enskog approximation. Numerical calculations show that deviations from Blanc's law are usually small, as expected, but that systems with large deviations are possible. The results apply generally to any tracer diffusion, and are not limited to ions.

Drift velocity of electrons and ions in dry and humid air and in water vapour

The avalanche current resulting from the release of a short (30 nsec) pulse of photoelectrons (5 × 104) at the cathode of a uniform field gap (5 cm) is observed experimentally. By this technique the drift velocities of electrons (v-) and of positive ions (v+) are measured. In dry air in the range E/p = 50-100 v cm-1 torr-1 at temperature 20 °c, v- = 256 × 103 E/p + 5 × 106 and in water vapour in the range E/p = 55-85 v cm-1 torr-1 at 20 °c, v- = 255 × 103 E/p + 8.9 × 106, with units cm sec-1 and v cm-1 torr-1. The values of v- obtained for dry air fit the values calculated by Heylen and are higher than those measured with the magnetic-deflection method by Townsend and Tizard. The mobility of positive ions in dry air, which is constant in the range E/p = 45-70 v cm-1 torr-1 and is equal to 2.2 × 103 cm2 v-1 sec-1 (at 1 torr and at 20 °c), gradually decreases at higher E/p values. In water vapour the mobility of positive ions was constant over the measured range E/p = 50-90 v cm-1 torr-1 and is equal to 0.61 × 103 cm2 v-1 sec-1 (at 20 °c and at 1 torr). In humid air the value of mobility is lower than the value calculated from Blanc's law. This suggests a clustering of ions.

New Method for Measuring the Rates of Ionic Transport and Loss. I. Mobility of NO+

N${\mathrm{O}}^{+}$ ions are produced between parallel electrodes by photoionization, using the Kr resonance line at 1236 \AA{}. Rectangular voltage pulses, separated by a variable time interval, are applied to the electrodes. The transient current, as charges are swept out of the collection region, is displayed on an oscilloscope and recorded photographically; from this curve the mobility of the charge carriers may be deduced. Experimental values for the mobility of N${\mathrm{O}}^{+}$ in He, Ar, ${\mathrm{N}}_{2}$, and ${\mathrm{H}}_{2}$ at 20\ifmmode^\circ\else\textdegree\fi{}C and 760 mm Hg are: 19.1\ifmmode\pm\else\textpm\fi{}2.4, 3.7\ifmmode\pm\else\textpm\fi{}0.2, 3.3\ifmmode\pm\else\textpm\fi{}0.2, and 16.3\ifmmode\pm\else\textpm\fi{}1.2 ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{V}}^{\ensuremath{-}1}$, respectively. The mobility of N${\mathrm{O}}^{+}$ in He-${\mathrm{N}}_{2}$ mixtures obeys Blanc's law, thus indicating negligible complexing of N${\mathrm{O}}^{+}$ with ${\mathrm{N}}_{2}$ or He. The integrated transient current is related to the total charge in the collection region at the initiation of collection; the rate of growth of ion density as the time interval between pulses is increased indicates the predominant ion loss process and its rate. In these experiments, the integrated current is consistent with ion loss by diffusion, with $D=\frac{\mathrm{KkT}}{e}$, where $K$ is the experimental ion mobility. The transient current shape, the role of space charge, and the initial charge distribution have been treated theoretically.

Temperature Dependence of Ionic Mobilities in Gas Mixtures

An ion mobility tube has been used to investigate the mobilities of various ions in helium—neon mixtures at gas temperatures of 77°, 195°, and 300°K. From plots of reciprocal mobility vs fractional concentration of the gases in the mixture which exhibit the linear dependence predicted by Blanc's law, it is possible to trace the mobility of a given ion, e.g., He+, from its parent gas (helium) value, through the mixtures, to its value in the ``foreign'' gas (neon). In this way we have determined the thermal-energy mobilities of the various ions under conditions where the ion—atom interaction changes markedly (e.g., from predominantly charge transfer to polarization interaction). In addition, a search was made for the effects of (HeNe)+, previously postulated to account for deviations from Blanc's law in 300°K studies. No effects clearly attributable to (HeNe)+ ions have been observed.

Blanc's Law—Ion Mobilities in Helium-Neon Mixtures

The mobilities of ions of near thermal energies are measured in helium-neon mixtures using a drift velocity apparatus. These studies permit the investigation of ion motion in gases, e.g., ${\mathrm{He}}^{+}$ in Ne, under conditions where the charge transfer interaction is negligible compared to polarization attraction and short-range repulsion between ion and atom. In addition, the measurements provide a test of Blanc's empirical law, $\frac{1}{\ensuremath{\mu}}=\frac{{f}_{1}}{{\ensuremath{\mu}}_{1}}+\frac{{f}_{2}}{{\ensuremath{\mu}}_{2}}$, which relates the mobility $\ensuremath{\mu}$ in a binary mixture to the pure gas mobilities ${\ensuremath{\mu}}_{1}$ and ${\ensuremath{\mu}}_{2}$ and to the fractional gas concentrations ${f}_{1}$ and ${f}_{2}$. A theoretical treatment developed by Holstein is presented which shows that deviations from Blanc's law are limited to a few percent. The mobilities of ${\mathrm{He}}^{+}$, ${\mathrm{He}}_{2}^{+}$, and ${\mathrm{Ne}}_{2}^{+}$ ions are found to obey accurately Blanc's law. However, the ${\mathrm{Ne}}^{+}$ ion curve deviates markedly from the law. These deviations are explained in terms of the formation of moderately stable ${(\mathrm{He}\mathrm{Ne})}^{+}$ ions from ${\mathrm{Ne}}^{+}$. Finally, the observed mobilities of ${\mathrm{He}}_{2}^{+}$ in Ne and ${\mathrm{Ne}}_{2}^{+}$ in He are found to agree with the predictions of polarization theory.

The Clustering of Ions and the Mobilities in Gaseous Mixtures

It is shown by direct analysis that the deviations from Blanc's law for mobilities of ions in mixtures of gases observed when a strongly polarizable gas is mixed with one less polarizable cannot be ascribed to a statistical clustering effect as proposed by Loeb. Analysis involving the assumption that the ion undergoes labile clustering of the simplest type indicates that the observed results can be completely accounted for within the realms of simple theory. Thus assuming that the active gas can attach a single molecule to the ion and that this attachment molecule may be detached with different probabilities by collisions with the two types of gas molecules leads to an equation for the resultant mobilities which will cover practically all cases observed. The forces assumed can be dielectric but may also be secondary valence or van der Waals' forces. It is indicated how, with appropriate experimental procedures possible under modern techniques, most of the constants required for the solution of the equation can be directly determined or computed.