Limitation of determination of surface fractal dimension using N2 adsorption isotherms and modified Frenkel-Halsey-Hill theory

Surface fractal dimensions, D-S, of smooth and corrugated bovine serum albumin particles were obtained from N-2 adsorption isotherms using modified Frenkel-Halsey-Hill (FHH) theory. It was found that for different particles, the correct D-S values depended on the number of adsorbed layers, n. For corrugated particles, when 1 :! n :S 10, the value of D-S 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 D-S (2.12) only for 1.0 +/- 0.5 less than or equal to n less than or equal to 2.0 +/- 0.5 (i.e., around monolayer coverage). Determination of D-S 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 D-S 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 D-S. To ensure reliable determination of D-S, it is therefore recommended to determine DS only around monolayer coverage.