Mass dispersion

All MC-ICPMS instruments are equipped with a multiple Faraday collector array oriented perpendicular to the optic axis, enabling the simultaneous static or multi-static measurement of up to twelve ion beams. Most instruments use Faraday cups mounted on motorized detector carriers that can be adjusted independently to alter the mass dispersion and obtain coincident ion beams, as is the approach adopted for MC-TIMS measurement. However, some instruments instead employ a fixed collector array and zoom optics to achieve the required mass dispersion and peak coincidences (e.g., Belshaw et al. 1998). 

Figure 8. Schematic outline of a second-generation MC-ICPMS instrument (Nu Instalments Nu Plasma), equipped with a multiple-Faraday collector block for the simultaneous measurement of up to 12 ion beams, and three electron multipliers (one operating at high-abundance sensitivity) for simultaneous low-intensity isotope measurement. This instmment uses zoom optics to obtain the required mass dispersion and peak coincidences in place of motorized detector carriers. [Used with permission of Nu Instruments Ltd.]...

ToF analysers are able to provide simultaneous detection of all masses of the same polarity. In principle, the mass range is not limited. Time-of-flight mass analysis is more than an alternative method of mass dispersion it has several special qualities which makes it particularly well suited for applications in a number of important areas of mass spectrometry. These qualities are fast response time, compatibility with pulsed ionisation events (producing a complete spectrum for each event) ability to produce a snapshot of the contents of the source volume on the millisecond time-scale ability to produce thousands of spectra per second and the high fraction of the mass analysis cycle during which sample ions can be generated or collected. 

Figure 4.6. Illustrating the principle of the TOF mass analyser, showing a longitudinal cross-section of the flight tube and demonstrating mass dispersion.

The principal use of Eq. (173) is in conjunction with a similar heat dispersion equation. Unfortunately, a system of coupled nonlinear partial differential equations then has to be solved, which is very difficult even with the aid of computers. In the oxidation of sulfur dioxide. Hall and Smith (HI) found relatively good agreement between theory and experiment near the center of the reactor. Their calculations were based on the heat-dispersion equation, and they did not take detailed mass dispersion into account. Baron (B2) later solved the mass and heat dispersion equations simultaneously by a novel graphical method, and found better agreement between his calculations and the data of Hall and Smith. 

Amundson (A5) discussed the analytical solution of the heat dispersion equations for a packed bed chemical reactor. The form of the differential equations is, of course, similar to the mass dispersion equations for certain cases. A wealth of analytical methods and results are presented for various types of boundary conditions. 

For packed bed reactors, Carberry and Wendel (1963), Hlavacek and Marek (1966), and Carberry and Butt (1975) report that axial dispersion effects are negligible if the reactor length is sufficient. These and other researchers (Young and Finlayson, 1973 Mears, 1976) have developed criteria based on the reactor length for conditions where axial dispersion can safely be neglected. The criterion shown in Table V is a classic criterion for neglecting axial mass dispersion. The works by Young and Finlayson (1973) and Mears (1976) provide more detailed criteria to predict when axial dispersion is unimportant in nonisothermal packed bed reactors. 

Instrumental developments (e.g., of sector field instruments with multiple ion collection, introduced in 1992, or the insertion of collision and reaction cells in order to reduce disturbing isobaric interferences), the progress in applications for ultratrace analysis, also in combination with on line hyphenated separation techniques (HPLC, CE), especially routine capability as well as decreasing price and user friendly maintenance mean that sales are increasing by 10 % every year. To improve the analytical performance of ICP mass spectrometers for precise isotope ratio measurements (e.g., for geochronology or for the study of fine isotope variation in nature) powerful instrumentation with high mass dispersion and multiple ion collector systems instead of single ion collection are commercially available on the analytical market. 

The conditions presented above have been formulated for the case that the values of the Peclet numbers for heat and mass dispersion in a bed are indentical. However, recent experimental research on axial heat dispersion in packed beds has indicated that the values of the Peclet number for heat transfer may be different from those for mass transfer (48). Fortunately, the aforementioned conditions are still valid, however, the critical values of B and Pe as well as the bounds Dan,in and Da x are dependent on the ratio q = PeH/PeM. From the theoretical results may be inferred that for highly exothermic reactions multiple steady states may... 

Here we have denoted y conversion, 0 Frank-Kameneckii dimensionless temperature, Da Damkohler number, Pe Peclet number for axial mass dispersion, Pe Peclet number for Sxial heat dispersion, Y dimensionless activation energy, B dimensionless adiabatic temperature rise, 3 dimensionless cooling parameter, 6 temperature of the cooling medium, A mass capacity, AT heat capacity. 

DL = axial mass dispersion coefficient, pf = fluid density, g/cm3... 

In summary, current observations indicate that most circumstellar gas mass disperses quickly on a timescale similar to (or maybe even shorter than) the dustclearing timescale. Significant progress in this field is expected to occur in the next years with the launch of the Herschel Space Observatory. In particular, the... 

Commercial reactors are non isothermal and often adiabatic. In a noniso-thermal gas-liquid reactor, along with the mass dispersions in each phase, the corresponding heat dispersions are also required. Normally, the gas and liquid at any given axial position are assumed to be at the same temperature. Thus, in contrast to the case of mass, only a single heat-balance equation (and corresponding heat-dispersion coefficient) is needed. Under turbulent flow conditions (such as in the bubble-column reactor) the Peclet number for the heat dispersion is often assumed to be approximately equal to the Peclet number for the mass dispersion in a slow-moving liquid phase. 

Figure 8.20. Mass dispersion for nuclear reactions of protons with nuclides of medium mass. Example reaction of protons of various energies with copper (according to J. M. Miller, J. Hudis, Annu, Rev. Sci. 9, 159 (1959)).

Roughly matches a maximum in yield stress of 11.7-19.9 mass% dispersions. 

Roughly matches maximum in yield stress of a 17% (by mass) dispersion. 

IEP shifts to high pH in 0.1 M NaCI. Viscosity and yield stress in 18 mass% dispersions peak at IEP. 

Matches the maximum in settling rate and in yield value of 20 mass% dispersion. 

Unwashed sample had negative potentials at pH 3-11, except for two positive values observed at pH = 6. The numerical values of two lEPs reported in [360] are based on arbitrary interpolation. IEP roughly matches a maximum in viscosity of 38 mass% dispersion. 

The Gq axes in Figures 4 and 5 in [1986] have incorrect labels. The corrected figures are in the erratum. The maximum in the viscosity of 38 mass% dispersion matches the IEP. 

Matches a maximum in yield stress of 16.3 mass% dispersion however, in 19.8% dispersion, yield stress did not show a clear maximum. 

Matches maximum in yield stress of 37.5 mass% dispersion only value, data points not reported. 

Maximum in viscosity and yield stress of 61.1% by mass dispersion at pH 6. 

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