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

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 N 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 N. 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 N (87 K), 2.02(10) layers. The universal Langmuir specific area of the silica is 10.1(4) m g. Pressure- and coverage-dependent adsorbate structures range from filling defects and holes on the surface to cluster formation to adsorbed Ar or N evenly distributed or packed across the surface. The Ar (87 K) isotherm is most sensitive to adsorbate structural transformations.