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.