Approximate multipole coefficients of RF ion traps as functions of aperture size

In this study we present approximate analytical expressions for estimating the variation in multipole expansion coefficients as a function of the size of the apertures in the electrodes in axially symmetric (3D) and two-dimensional (2D) ion trap ion traps. Following the approach adopted in our earlier studies which focused on the role of apertures to fields within the traps, here too, the analytical expression we develop is a sum of two terms, A(n,noAperiure), the multipole expansion coefficient for a trap with no apertures and A(n,dueToAperture), the multipole expansion coefficient contributed by the aperture. A(n,noAperture) has been obtained numerically and A(n,dueToAperture) is obtained from the n th derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A(2) to A(12), estimated by our analytical expressions, were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap dimension. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be largely in the range of 10-15%. The leading multipole expansion coefficient, A(2), however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and the LIT for large aperture sizes. (C) 2010 Elsevier B.V. All rights reserved.

Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant Xi,or X i/Xj are presented. The expression for In γsolvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.

Transfer of F- in the reaction of SF6- with SOF4: Implications for SOF4 production in corona discharges

The temperature (T) and electric field-to-gas pressure (E/P) dependences of the rate coefficientk for the reaction SF 6 � +SOF4rarrSOF 5 � +SF5 have been measured. ForT<270>k approaches a constant of 2.1×10�9 cm3/s, and for 433>T>270 K,k decreases withT according tok (cm3/s)=0.124 exp [�3.3 lnT(K)]. ForE/Pk has a constant value of about 2.5×10�10 cm3/s, and for 130 V/cm·torr>E/P>60 V/cm·torr, the rate is approximately given byk (cm3/s)sim7.0×10�10 exp (�0.022E/P). The measured rate coefficient is used to estimate the influence of this reaction on SOF4 production from negative, point-plane, glow-type corona discharges in gas mixtures containing SF6 and at least trace amounts of O2 and H2O. A chemical kinetics model of the ion-drift region in the discharge gap is used to fit experimental data on SOF4 yields assuming that the SF 6 � +SOF4 reaction is the predominant SOF4 loss mechanism. It is found that the contribution of this reaction to SOF4 destruction falls considerably below the estimated maximum effect assuming that SF 6 � is the predominant charge carrier which reacts only with SOF4. The results of this analysis suggest that SF 6 � is efficiently deactivated by other reactions, and the influence of SF 6 � +SOF4 on SOF4 production is not necessarily more significant than that of other slower secondary processes such as gas-phase hydrolysis