Vacuum thermochromatography. Diffusion approximation, evaluation of desorption energy

The recent report (I. Zvara Vacuum thermochromatography: physical principles and Monte Carlo simulation 2014 Report JINR E6-2014-1, Dubna) concerned Monte Carlo (MC) approach to understanding the vacuum thermochromatography in cylindrical columns by simulating migration histories of a great many molecules. Their paths consist of random variable steps, each of them being followed by adsorption for a random time. The same problem is considered here using the diffusion approximation to random walks. The appropriate diffusion equation is for the fraction of the total retention time spent by the adsorbate 'in flight'; it monotonously decreases with time and distance. Meanwhile, the related fraction due to the adsorption time rapidly grows with the inverse temperature and so with distance. The product of the two factors yields a peaking distribution, which well fits that from the MC simulation. Like the latter, the diffusion approach does not yield any explicit formula for the peak as a function of the experimental variables. Yet, we did find such a formula in a semi-theoretical way, when aiming at the two factors' structure. It accurately enough fits the MC profiles, provides much faster calculations than the two above tools, and is reasonably versatile in accounting for many possible variables. It, for example, greatly enhances accurate evaluation of the experimental data with very poor statistics, like those met in the VTC studies of the heaviest known elements. The here illustrated Bayesian approach to the latter problem requires calculation of the peaks for many desorption energies to find the prior likelihoods of the particular experimental data. This gives the posterior probability density and so the credible intervals of required levels for the sought for energy values. Considered are also peculiarities of treating the VTC data when the column has a non-linear temperature profile, non-circular cross section, or heterogeneous surface. (author)