Experimental and numerical validation of the effective medium theory for the B-term band broadening in 1st and 2nd generation monolithic silica columns

•Effective medium diffusion expressions have been applied to silica monoliths.•The geometrical parameters appearing in these expressions have been determined.•Validation of the expressions through numerical simulations as well as experiments.•Experiments and simulations over a very wide range of retention factors.•Intra-skeleton diffusion rates have been determined in 1st and 2nd order monoliths.

Effective medium theory (EMT) expressions for the B-term band broadening in monolithic silica columns are presented at the whole-column as well as at the mesoporous skeleton level. Given the bi-continuous nature of the monolithic medium, regular as well as inverse formulations of the EMT-expressions have been established. The established expressions were validated by applying them to a set of experimental effective diffusion (Deff)-data obtained via peak parking on a number of 1st and 2nd generation monolithic silica columns, as well as to a set of numerical diffusion simulations in a simplified monolithic column representation (tetrahedral skeleton model) with different external porosities and internal diffusion coefficients. The numerically simulated diffusion data can be very closely represented over a very broad range of zone retention factors (up to k″ = 80) using the established EMT-expressions, especially when using the inverse variant. The expressions also allow representing the experimentally measured effective diffusion data very closely. The measured Deff/Dmol-values were found to decrease significantly with increasing retention factor, in general going from about Deff/Dmol = 0.55 to 0.65 at low k″ (k″ ≅ 1.5–3.8) to Deff/Dmol = 0.25 at very high k″ (k″ ≅ 40–80). These values are significantly larger than observed in fully-porous and core–shell particles. The intra-skeleton diffusion coefficient (Dpz) was typically found to be of the order of Dpz/Dmol = 0.4, compared to Dpz/Dmol = 0.2–0.35 observed in most particle-based columns. These higher Dpz/Dmol values are the cause of the higher Deff/Dmol values observed. In addition, it also appears that the higher internal diffusion is linked to the higher porosity of the mesoporous skeleton that has a relatively open structure with relatively wide pores. The observed (weak) relation between Dpz/Dmol and the zone retention factor appears to be in good agreement with that predicted when applying the regular variant of the EMT-expression directly to the mesoporous skeleton level.