Stochastic−Dispersive Theory of Chromatography

Abstract

The stochastic model of chromatography has been combined with mobile-phase dispersion. With the combined model, both the effect of slow mass transfer or adsorption-desorption kinetics and dispersion on the band profile can be characterized. The stochastic model of chromatography is addressed with the characteristic function method. The moments of the peaks are calculated analytically for homogeneous and heterogeneous surfaces. It is shown that even in cases when the characteristic function cannot be calculated in closed form, the moments of the peak, and therefore the retention time, the number of theoretical plates, the peak asymmetry, can be calculated with simple expressions. Therefore, a full description of the chromatographic peak is available for homogeneous and any heterogeneous surfaces provided that the distribution of the sorption energies is known.

Experimental validation of the stochastic theory of size-exclusion chromatography: Retention on single and coupled columns

“…According to Eq. (27), it seems possible to estimate c~ from the experimentally observed dependence of band broadening on KsEc, and thus to get some insight into the intimate mechanism of selectivity in SEC. Unfortunately, this is not the case.…”

“…Indeed, the differences in the standard deviation between extreme values of c~ (0 and 1) on the basis of the GEC model is modest. Furthermore, this effect is, in practice, leveled off by the moving zone contribution to band broadening, so that the peak standard deviation is obtained by combining Eqs (27) and (29): Figure 3. It is seen that the effect ofc~ is modest.…”

“…This requires the precise and accurate determination of KSEC, i, which is the key quantity appearing in Eqs. (25), (27), (28), (31). Such a task presents difficulties as other retention mechanisms can interfere with SE, such as HDC and interaction with the pore surfaces.…”

“…The stochastic theory foresees peak splitting in two possible cases: i) in a monopore column, near the exclusion limit, when the size of the macromolecules is similar to that of the pores, a fraction of them do not visit the pore structure and give origin to a spike, ii) on a column with two types of pores, of different dimension and relative amount, which behaves as an heterogeneous column [26]. These primary peak splitting effects convolute with other Original band-broadening phenomena and can thus be either partially or completely obscured [27]. The fact that peak splitting always appears well before the exclusion limit specified by the producer can be explained by the presence of a mesopore structure beside the main monopore structure of the SEC column.…”

Stochastic simulation of reactive separations in capillary electrophoresis

“…Stochastic models use the statistical behavior of individual molecules to develop probability distribution functions, from which zone profiles and statistical moments are generated. These models have been extended to Monte Carlo and random walk applications [46][47][48]. Another stochastic method applies fundamental equations of motion to individual molecules and follows the trajectories of the individual molecules through the system [49][50][51][52][53][54].…”