Some of the Parameters Affecting Knudsen Effusion. IV. Monte Carlo Calculations of Effusion Probabilities and Flux Gradients for Knudsen Cells

Abstract

Data are presented for effusion probabilities and cell-wall flux gradients calculated dynamically by means of Monte Carlo computer studies. Typical effusion cell dimensions were programmed for both knife-edged and Clausing orifices; all calculations apply to a flat sample. The influence of the size and the length-to-radius ratio of the orifice and the effects of different condensation coefficients are described. An analytical expression relating the equilibrium sample flux to the flux at steady state has been derived. It is shown that for a given cell design, the ratio of these fluxes is constant and independent of the nature of the vaporizing species. Because the Monte Carlo method requires no mathematical approximations or simplifying assumptions, results analogous to real cell behavior are to be expected. Comparison of these results with the treatment derived by Motzfeldt shows that his formula is applicable and quite accurate over a wide range of experimentally encountered conditions. 7 J. W. Ward and M. V. Fraser, "Study of Some of the Parameters Affecting Knudsen Effusion. VI. Monte Carlo Analyses of Channel Orifices," J. Cbem. Phys. (to be published).

High-temperature mass spectrometry: Instrumental techniques, ionization cross-sections, pressure measurements, and thermodynamic data (IUPAC Technical Report)

“…The measured pressure then depends on the ratio f = aC/A and on the conductance of the cell [59,60], (7) where α is the evaporation coefficient [61] of the effusing species, W Α the Clausing factor of the inner cell body, p m the measured pressure, and p eq the equilibrium pressure. This relation was confirmed by Monte-Carlo calculations [62]. It is to be stressed that upon using eq.…”

Vapor pressures, mass spectra, magnetic susceptibilities, and thermodynamics of some phthalocyanine compounds

“…Carlson et al (3,4) have discussed the inconsistencies and approximations involved in deriving Equation 4, and have shown that it applies rigorously only to the case of a spherical cell with negligible rate of effusion. Ward and Fraser (23) have shown by Monte Carlo simulation of the real effusion process that, despite the inconsistencies, Equation 4 should give Pobsd correct within 1% for cells of the present geometry and a's on the order of 0.01. Carlson et al (3,4) have also observed that a's obtained via Equation 4 may be spurious, because nonequilibrium effects such as temperature gradients and surface depletion may result from the use of large orifices.…”

Monte Carlo simulation of a Knudsen effusion mass spectrometer sampling system

“…As noted, many investigators have written Monte Carlo codes to simulate Knudsen flow. [12][13][14][15][16][17][18][19] Molecule-molecule collisions are minimal and hence the linear trajectory of each molecule can be traced individually until it either exits the upper orifice or goes out of the beam before that. The details of the code are discussed in the companion report to this paper.…”

“…[12] Since then, many investigators have further extended this Monte Carlo approach. [12][13][14][15][16][17][18][19] Today, because of the wide availability of high-speed desktop computers with multicore processors, Monte Carlo simulation is one of the easiest and most flexible ways to describe Knudsen flow.…”