Textural characteristics of composite adsorbents analyzed with density functional theory and self-consistent regularization procedure

Abstract

Highly disperse or porous complex and hybrid materials and nanocomposites characterized by the presence of several phases, nonuniform particulate morphology, and complicated porosity with contributions of pores of various shapes are widely used in various applications in industry and medicine. Accurate determination of their textural characteristics is of importance from a practical point of view because these characteristics play an important role in practically all applications of the materials. The aim of this study, to solve the mentioned task, is to develop a selfconsistent regularization (SCR) procedure applied to integral adsorption equations based on complex models with slit-shaped and cylindrical pores and voids between spherical particles packed in random aggregates (SCV model) for two or three types of components (such as activated carbon, carbon black, silica gel, and fumed silica) in composites, mechanically treated, with application of the density functional theory (DFT) method. The pore size distribution (PSD) functions calculated using the DFT SCV/SCR method are compared to the PSD calculated for the same materials with the SCV/SCR method based on the modified BET/Kelvin equations (MND method) previously developed. The DFT SCV/SCR method works better than the latter since it gives smaller model errors and better describes the PSD functions of composite components alone. The DFT SCV/SCR method could be used to study the textural characteristics of various complex and hybrid materials and composites which are characterized by a nonuniform porosity. It should be noted that the PSD functions of similar complex adsorbents are difficult to be calculated using standard approaches distributed with firm software due to restriction on the type of material (typically one) and the absence of SCR.

Polymer Adsorbents vs. Functionalized Oxides and Carbons: Particulate Morphology and Textural and SurfaceCharacteristics

“…Additionally, complex and hybrid systems with PVA/AC, fumed silica/PDMS, etc., are described here mainly concerning the morphological and textural characteristics. All these materials can be considered as representatives of various classes of simple and complex adsorbents and polymer fillers described in detail elsewhere [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 28 , 31 , 32 , 54 , 55 , 56 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 89 , 90 , 91 ]. Some details on the materials used here are given in the Supplementary Materials file.…”

“…Note that firm software used with various adsorption analyzers is oriented on such simple materials as silica or carbon, i.e., the treatment results with this software are rather incorrect for complex and hybrid composites. Therefore, to increase the reliability and validity of the characterization of complex systems, several experimental and theoretical methods should be used in parallel with software, including models for complex materials [ 28 , 32 , 54 , 89 , 90 , 91 ], and this aspect is analyzed here in detail.…”

“…There are several adsorbent classes with different textural features. Therefore, it is difficult to accurately describe their various blends using firm software [ 87 , 89 , 90 ]. There are (i) synthetic highly disperse oxides (fumed silica, alumina, titania, binary and ternary fumed oxides) composed of spherical-like nonporous nanoparticles (NPNP); (ii) natural nanostructured oxides (clays, zeolites) with a complex shape of pores; (iii) porous oxides (silica gels, ordered mesoporous silicas, complex oxides) mainly with cylindrical pores, but with certain deviations and surface roughness; (iv) carbons (chars, activated carbons, graphene, graphene oxide, exfoliated graphite, nanotubes, carbon blacks, fullerites), which can have not only slit-shaped pores but also spherical, cylindrical, wedge-shaped and other pores; (v) polymers (1D, 2D, 3D hydrophobic and hydrophilic, functionalized, synthetic and natural) with complicated and tortuous pore networks; (vi) metal–organic framework structures with complex pore shapes; (vii) complex and hybrid systems with components of different kinds or classes [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 28 , 32 ].…”

“…In this work, some aspects of relatively comprehensive characterization of individual and complex, unmodified and functionalized materials with oxides, carbons, and polymers are analyzed to show the possibilities of parallel applications of several experimental methods with the treatment of the data with simple regularization/functional minimization or more complex self-consistent regularization procedures [ 87 , 89 , 90 , 91 , 92 ] and other applied mathematics and computational methods. Note that some experimental methods, which complement each other well, can give different pictures on the same materials.…”

“…For composites, various models, including different pore shapes for different components, e.g., for carbon/nanooxides, polymer/nanooxides, polymer/carbons, etc. (described here), are much better than any simple model (from firm software) for any individual material as a component of composites because it poorly describes other components with different textures [ 87 , 89 , 90 ]. Unfortunately, the simplified approach for textural characterization of composites based on the firm adsorption methods with firm software is typically used.…”