A three-parameter equation was obtained in the BET theory framework taking into account the correction suggested by the authors. This equation allows the description of adsorption isotherms in the range of polylayer adsorption as well as in the range of cluster formation. This equation was demonstrated as true for a number of adsorption systems in the relative pressure range 0.05 ≤ x ≤ 0.97 for nitrogen, benzene and water vapour.

Some methods of defining certain features that characterize polymolecular sorption of water vapor by polymers are discussed: the fractal dimension, through the Frenkel-Halsey-Hill formalism; BET; the sorption film area, through the Kiselev equation and the differential function of pore surface distribution. In the framework of the BET theory, a new approach is proposed to define the surface fractal dimension of polymer sorbents, which is based on finding the number of the polylayers. The proposed method is compared with the existing ones. The proposed definition of the surface fractal dimension allowed to derive a three-parameter sorption isotherm equation, which takes into consideration the sorbent fractal properties in the domain of the relative change of water vapor pressure, is 0.05 e x e 0.95.

A three-dimensional array of ∼55 nm diameter InGaAsN : Sb quantum dots (QDs) was nonlithographically fabricated starting with a MBE-grown InGaAsN : Sb/GaAs multiple quantum well wafer. The nonlithographic fabrication process relies on the use of a highly ordered nanopore alumina membrane for lateral patterning followed by a reactive ion etching. The dot size uniformity, spatial ordering and three-dimensional packing density are among the best reported so far. Nondestructive Raman scattering was employed to assess the material quality of the samples. While photoluminescence study points towards a moderately increased role of nonradiative transitions in the fabricated QD arrays, the dots show a relatively high emission intensity at room temperature, suggesting improved operation of long wavelength optical devices. Likely mechanisms contributing to the PL increase and the observed ∼50 meV red shift in the emission peak position are discussed. This study might be of great importance for engineering well controllable, ultra-high density, three-dimensionally arranged QD arrays for active optical devices.

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