Limitation of Determination of Surface Fractal Dimension using N2 Adsorption Isotherms and Modified Frenkel-Halsey-Hill Theory
Surface fractal dimensions, DS, of smooth and corrugated bovine serum albumin particles were obtained from N2 adsorption isotherms using modified Frenkel−Halsey−Hill (FHH) theory. It was found that for different particles, the correct DS values depended on the number of adsorbed layers, n. For corrugated particles, when 1 ≤ n ≤ 10, the value of DS is equal to 2.39, which agrees with the value obtained from light scattering (2.39 ± 0.05). Unlike the corrugated particles, the adsorption isotherm for the smooth particles generated the correct value of DS (2.12) only for 1.0 ± 0.5 ≤ n ≤ 2.0 ± 0.5 (i.e., around monolayer coverage). Determination of DS in the multilayer region (n > 2) produced a higher value than the one obtained from monolayer coverage. This was because the smooth particles were in closer contact with each other; at higher coverage the gas molecules probed the surface of the aggregates instead of the single particles. As there were fewer contact points between the corrugated particles compared to the smooth particles, this effect took place at higher coverage (pressure) causing deviation from the expected values. This finding is supported by the fact that for corrugated particles, the value of DS started to deviate at higher n and increased to 2.58 when n > 10. The use of modified FHH theory is thus limited by the number of adsorbed layers on the particles. The closer the particles come in contact, the thinner is the coverage region describing the correct DS. To ensure reliable determination of DS, it is therefore recommended to determine DS only around monolayer coverage.