Universal Langmuir and Fractal Analysis of High-Resolution Adsorption Isotherms of Argon and Nitrogen on Macroporous Silica

Abstract

<p>High-resolution isotherms of argon and nitrogen adsorption on macroporous silica have been simulated with universal Langmuir and fractal models. A four-parameter, fractal universal Langmuir equation is a good fit to the data at low pressures. Standard Gibbs energy changes calculated from equilibrium adsorption coefficients show a series of broad peaks that indicate adsorbate structural transformations as a function of pressure and coverage. The Freundlich equation or mean fractal model is also a good fit to isotherms at low pressures. Pressure-varying fractals are accurate fits to the data. Fractal exponents provide information on adsorbate coverage and surface access. Broad peaks in pressure-varying exponents are indicators of adsorbate structure. From adsorptive gas amounts, mean and pressure-varying fractal exponents provide details of adsorbate fractal dimensions and surface roughness. Both Ar and N2 adsorption cause increases in mean surface roughness when compared with pure silica. Surface roughness fluctuations from pressure-dependent adsorptive gas fractal dimensions are associated with adsorbate structure. At one trough, the surface is smooth and is linked to close-packed Ar or N₂. For Ar adsorption at 87 K, this structure is a complete monolayer (1.00(4)), while for Ar (77 K), 1.15(4) layers and for N₂ (87 K), 2.02(10) layers. The universal Langmuir specific area of the silica is 10.1(4) m² g⁻¹. Pressure- and coverage-dependent adsorbate structures range from filling defects and holes on the surface to cluster formation to adsorbed Ar or N₂ evenly distributed or packed across the surface. The Ar (87 K) isotherm is most sensitive to adsorbate structural transformations.</p>