Vacuum thermochromatography

In an isothermal vacuum tube, with the tracer initially concentrated at its closed end as 8(z), the random flights are reflected at z = 0 and must produce [26] a zone with a shape of the half of a symmetrical distribution (not necessarily normal). This distribution will ever broaden with time, and there cannot emerge any maximum away from the zero coordinate. In VTC such a peak does appear. The obvious reason is that the flight frequency of the molecules rapidly decreases with lower temperature, which produces a seeming flow towards the cold end of the column. 

Because of the principal absence of convective flow in VTC, it is not easy to derive the basic relations by analogy with the treatment of gas-solid chromatography processes. Help is offered by a concept of vacuum physics related to Knudsen regime - the conductance Cvc of a tube with the length lc. The quantity has dimension of the flow rate  

Eichler and Schadel [29] alternatively used tq = h/k T. It is justified in view of the real uncertainty of the two quantities. The no values for metals have been estimated through several physical approaches. Ref. [30] contains a useful compilation and comparison of the derived values. By integrating Eq. 4.57, the authors of Ref. [28] evaluated the adsorption characteristic as a function of t CT and other experimental parameters. The resulting formula is quite cumbersome, because the 

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Fig. 4.11 Vacuum thermochromatography of gold in quartz column [35]. Black bars — distribution of 192Au, solid histogram — the result of simulation. Conditions dc = 0.3 cm, /c = 100 cm, t TC = 1-2 hours, column temperature profile - see the broken line.

Chapter 4 starts with some basic equations, which relate the molecular-kinetic picture of gas-solid chromatography and the experimental data. Next come some common mathematical properties of the chromatographic peak profiles. The existing attempts to find analytical formulae for the shapes of TC peaks are subject to analysis. A mathematical model of migration of molecules down the column and its Monte Carlo realization are discussed. The zone position and profile in vacuum thermochromatography are treated as chromatographic, diffusional and simulation problems. 

Gaggeler, H., Eichler, B., Greulich, W., Herrmann, G., Trautmann, N. Vacuum-Thermochromatography of Carrier-free species. Radiochim. Acta 40, 137-143 (1986)... 

The proposed approach may also be useful in simulating thermochromatography in vacuum columns, chromathermography and other separation techniques in open columns. Moreover, repeated Monte Carlo experiments with small number of molecules serve to visualize the uncertainties imposed by poor statistics. They are very helpful in evaluating Bayesian confidence intervals for the parameters measured in the experiment performed in non-ideal conditions, when any attempt to obtain an analytical solution fails completely. This will be discussed and illustrated in Sect. 6.2. 

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