Frank R. Meeks

Statistical mechanics of Ar2+ in an inductively coupled plasma

Abstract In the mass spectrum of an argon inductively coupled plasma (ICP), there is a peak due to the presence of the argon dimer ion, Ar 2 + . Using elementary statistical mechanics, an attempt is made to elucidate the mechanism responsible for this ions presence in the ICP, The assumption of local thermodynamic equilibrium (LTE) in the ICP leads to three possible mechanisms that could be responsible for the presence of the argon dimer ion, however, the results of the calculations show that only one of the mechanisms agrees with experiment. The experimental measurements of the number density ratio of Ar 2 + to Ar + , against which the theoretical values are compared, were taken using inductively coupled plasma mass spectrometry (ICP-MS),

Measurements of inductively coupled plasma temperatures: comparison of N2+ rotational temperatures with optical pyrometry

Inductively coupled plasma (ICP) temperatures were measured using both N2+ spectral line intensity and optical pyrometry. The forward power output of the r.f. generator was varied between 0.75 and 2.00 kW in increments of 0.25 kW. Dry nitrogen was introduced into the plasma through the central gas (carrier gas) inlet at a flow rate of 0.5 dm3 min–1. A pyrolytic graphite probe with a melting-point of 3900 K was positioned 15 mm above the load coil in the centre of the plasma. The temperatures measured with the pyrometer were between 1700 and 2200 K for the power outputs mentioned above. The temperatures calculated from the slopes of the Boltzmann distribution plot (spectral line intensity versus the quantum numbers) are comparable to the pyrometric readings. Results obtained by the optical pyrometry method show that the ICP temperature is linearly dependent on the forward power of the r.f. generator.

Determination of the solubility product of CuS in a gel employing the liesegang phenomenon

Abstract The solubility product of CuS in a 3% agar gel has been determined by a technique involving the formation of Liesegang bands. Aqueous solutions of copper (II) and sulfide ions are allowed to diffuse towards one another from opposite ends of a length of gel. The rate of growth of the first (and only) band is followed chemically, and the time corresponding to zero moles of CuS after beginning of diffusion is determined by a simple extrapolation. This value, along with the band position, is substituted into an appropriate solution of Ficks Second Law for each diffusion species, and the concentration product is formed. The value is within the range of values for the Ksp, of CuS in water as reported in the literature. Assumptions are discuseed, as are limitations and generality of the method.

Some properties of the concentration product in counterdiffusion

Abstract By maximization of the concentration product of two species counterdiffusing through a medium, two approximations (one a function of time) are obtained for the position of the first Liesegang band. The expressions converge to the same value when the ratio of diffusion coefficients is unity. An expression of the Morse-Pierce form, relating band position to the square root of time after beginning of diffusion, is obtained as a straightforward result of the maximization. Physical significance of the derived quantities is discussed, and their range of validity is investigated.

Electron number density in a slightly ionized gas (argon inductively coupled plasma)

Abstract An equation defning the electron number density, ne in an argon inductively coupled plasma (ICP) regarded as a slightly ionized gas, is derived in terms of the thennodynamic temperature and the electronic chemical potential of the parent species in the ionization. The ICP is not regarded as being in a state of local thennodynamic equilibrium, but instead is considered to be an example of a thennodynamic steady state. The derivation requires nothing more advanced than elementary statistical thermodynamics, and the result is compared in detail with the Saha relation. It is shown that the new equation requires thermodynamic temperatures much lower than those from the Saha relation, and other areas of atomic emission spectroscopy to which the basic formulation is applicable are indicated

Interaction of various ions with a lead chromate ionic membrane

Abstract Lead chromate Liesegang rings in an agar gel exhibit membrane-like characteristics by selectively accumulating potassium and calcium ions at the ring but allowing sodium, magnesium, and a wide number of other inorganic ions to diffuse through freely. A hypothesis is presented relating this phenomenon to the oxygen coordination of excess chromate ions present in the ring; implications to biological membranes are discussed. Measurements were made on the structure of the lead chromate rings and on the diffusional characteristics of a wide number of inorganic ions in agar gel.

The counterdiffusion of lead and chromate in agar gel

Abstract Measurements on the counterdiffusion of Pb ++ and CrO 4 − in agar gel were made by atomic absorption spectrophotometry. The diffusion equation was applied to calculate diffusion parameters of the system, and the results were compared with experimental observations. The significance of CrO 4 − accumulation at the first PbCrO 4 ring is discussed in terms of the permeability of the precipitate of PbCrO 4 to diffusing ions.

More efficient ion transport for inductively coupled plasma mass spectrometry

Abstract A modification of the ion-lens system in an inductively coupled plasma mass spectrometer has been studied in an attempt to improve the ion transport efficiency. The modification consists of the placement of a metal rod down the axis of the lens-stack. The rod is suspended in place via a ceramic insulator inserted through the photon stop. A negative potential is applied to the rod to help focus the positively charged ions into the quadrupole. Prior to the implementation of this modification, a simple model was developed to determine if the voltages required would be practical. The resulting simulated ion trajectories showed that focusing occurs with applied voltages on the order of −10 V, which was approximately the optimal voltage found experimentally. The experimental data presented show that, with the modification, the limits of detection for 15 elements (m/z ranging from 24 through 238) improved by factors ranging from two to ten times over those of the unmodified instrument

Counterdiffusion and interaction of barium and sulfate ions in a gel

Abstract The conditions of precipitation and rate of growth of a BaSO 4 precipitate in a 1.5% agar gel were determined by a method involving the formation of Liesegang bands in a counterdiffusional system. In several experiments diffusion and precipitation were allowed to proceed for times ranging from several hours to two days after the appearance of the first BaSO 4 band. The values obtained for a calculated quantity c /Δt , which was directly related to the zeroth-order rate constant for the growth of the band, indicated that the growth of the band is diffusion-controlled rather than reaction-controlled. Data from experiments in which the gel was removed several hours prior to the appearance of the first BaSO 4 band revealed that barium ions and sulfate ions began to interact several hours before the appearance of the first band. The flux derivative ratios, calculated from the data obtained in these experiments, imply that the BaSO 4 precipitation is diffusion-controlled. The BaCl 2 and Na 2 SO 4 diffusion coefficients were determined in noncounterdiffusional systems.