Limitation of Determination of Surface Fractal Dimension Using N₂ Adsorption Isotherms and Modified Frenkel−Halsey−Hill Theory

Abstract

Surface fractal dimensions, D S, 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 D S values depended on the number of adsorbed layers, n. For corrugated particles, when 1 ≤ n ≤ 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 ≤ n ≤ 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 D S only around monolayer coverage.

How Much Particle Surface Corrugation Is Sufficient to Improve Aerosol Performance of Powders?

“…This method has been described in detail elsewhere (9)(10)(11)(12). Briefly, particles are subjected to a light source, resulting in the scattering of light at different angles with reference to the incident light beam.…”

Evaluación de las propiedades físicas de dos rocas carbonáticas usadas como material de construcción actual e histórico en Andalucía Oriental, España

“…Para los casos estudiados el valor de δ fue siempre superior a la unidad, pudiéndose utilizar la expresión A = D S -3. Para que la determinación de D S sea comparable entre distintas muestras es necesario utilizar una adsorción cercana a la monocapa (33). Por tanto, para calcular la pendiente (A) en el gráfico Ln(V) vs Ln[Ln(P/P 0 ) se utilizó exclusivamente un rango de presión que comprendiese un núme-ro de capas adsorbidas cercana a la unidad.…”

“…Given that in the cases studied the value of δ was consistently greater than one, the expression A = D S -3 could be used. Single layer, or close to single layer, adsorption is required for the value of D S found to be comparable among different samples (33). Consequently, the range of pressures used to calculate slope (A) in the Ln(V) vs Ln[Ln(P/P 0 )] graph was limited to values that ensured that the number of layers adsorbed was close to one.…”

Current Development in the Evaluation Methods of Pulmonary Drug Delivery System

“…The surface roughness of the particles is evaluated by this method and the scanned image is quantified by image analysis software. The degree of surface corrugation can also be expressed by surface fractal dimension determined by a light scattering method [12][13][14] . A real-time aerodynamic measurement of particles ranging from 0.5 to 20 microns with high resolution was done using the Aerodynamic Particle Sizer® 3321.…”

“…Qualitative surface analysis is done by Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS). It uses image spectral data (surface chemical mapping based on mass fragment analysis) of the sample powder to provide RayleighGans-Debye (RGD) scattering theory that explains the structure of each single particle in an aggregate [14] .…”