Generalized variables make it possible to reveal the nuances of the structure of porous materials and divide samples into their series with similar properties (Titelman, L. AMPC 2021, vol. 11, No. 11). Adsorbents for gas storage have a unique set of variables that can be combined: textural and mechanical properties of the adsorbent, preparation conditions, pressure and temperature of gas during storage and delivery. Taking gas pressure and mechanical strength as forces, textural properties as displacements, we obtained the energies of gas and sorbent as generalized variables. The interrelationships between them and the storage capacity for metal-organic frameworks, porous organic polymers and activated carbons were studied. Due to the variety of sorbents and the attracting effect of micropore walls on gas adsorption, the previously proposed average thickness of the probing gas layer is useful as estimation of the pore size. Its effect on adsorbent capacity was tested. The ratio of the gas layer to the kinetic diameter of the molecule gives the packing of molecules inside the pores and makes it possible to represent the pore model. Excessive surface area results in too small pores, repulsive forces and reduced capacitance. Sometimes the gas energy correlates better with the residual adsorption uptake than with the total or delivery capacity. Compared to texture parameters, the proposed generalized variables correlate better with sorbent capacity.

In the multifactorial preparation of porous materials, the simultaneous/sequential influence of a number of technological variables changes the individual parameters of the texture of the material (surface area, volume, pore size, etc.) to different values and with increase or decrease.Generalized parameters (GPs) combine these changes; new dependencies arise.GPs behave like the dimensionless similarity numbers known in science and technology (Reynolds, etc.).They split the data (phenomena) into series with similar properties, reveal special patterns and structural nuances.New GPs proposed.The average pore size is presented as the product of two GPs: the dimentionless shape factor F and pore width of unknown shape (reciprocal of the volumetric surface).Using F, for example, the SBA-15 dataset (D.Zhao, Science 1998) was split into 3 series of samples differing in synthesis temperatures, unit cell parameters, intra-wall pore volumes, pore lengths, and the ratios of wall thickness to pore size.A surprising phenomenon was discovered one of the copolymers acts in a similar way to high temperatures.The standard deviation (STD, %) of the texture parameter in the series is its serial GP.The surface topography (micropore volume per m 2 ) is proposed; it eliminates fluctuation in material density and has a lower STD than cm 3 /g.Examples of the use of GPs for silica, carbon, alumina and catalysts are given.A correlation has been shown between the efficiency of some catalytic reactions (adsorption) and GPs.GPs provide new information about materials and open up new research challenges.

There are insufficient parameters to explain the appearance of microporosity in porous materials. One of the parameters associated with micropores is the generalized pore shape factor F, which includes, as special cases, the known slit, circular and spherical model pore shapes. F covers the shapes between the slit (F = 2000) and spherical (F = 6000), as well as beyond. For the intermediate shape, one can estimate proportions of model motifs. The transition of the shape from one model to another is accompanied by the appearance of micropores (or vice versa); corresponding dependencies are given. Nanotechnologies, such as self-assembly of ordered mesoporous materials (OMMs), the production of carbon OMMs as replicas of silica matrixes, supercapacitors made of carbon nanofibres (CNF), a hybrid CNF/MWCNT for use in lithium-ion batteries, carbon xerogels with Ni additive for storage of H2, catalysis and others are discussed; they cover materials with F in the range 1,100 ÷ 32,600. A pore surface length index Lsi is proposed for any pore shape; it supplements the generalized parameters causing stresses, deformations and micropores. Using F and Lsi, it was discovered, that activated carbon, obtained as a replica of non-circular matrix of silica, behaves like a compressed spring, which, after removal of silica, expands and its pores become circular. A concept of molecular sieving based on the shape of molecules is proposed and demonstrated by the example of lipase immobilization. Application of the proposed parameters improves understanding of many published and new results.

This work is a continuation of our previously published work (Titelman in J Porous Mater 19:1–13, 2012), where generalized variables for the synthesis of porous materials were proposed: processing X and structural Y. X represents the route of the entire production process and covers the complete set of individual variables, both quantitative and qualitative. This paper proposes a concept of equivalent X-s, that is, routes leading to equal values of the property of interest. Examples of equivalent X are given. The most economical route can be chosen. Y = Vw/Vp (the ratio of the apparent volume of the walls to the total volume of open pores) is the structural parameter of the ordered mesoporous materials (OMMs), more sensitive than the wall thickness. For OMMs a formula is proposed for estimating Vw; this is the product of the total surface area SBET and the wall thickness t. Now the Y covers all parameters of OMM. Excluding the volume Vsk of the skeleton from Vw, we obtain the volume Viw of inaccessible intrawall pores; the size effect (Vradman et al. in Microporous Mesoporous Mater 93:313–317, 2006) on Viw was discovered. The specific length of the adsorbate body Lv proposed in Titelman (2012) is supplemented by the length of the surface area of the adsorbent Ls and the equation relating the hydraulic diameter Dh to the average pore diameter Dp is obtained. The known Dh = 4Vp/SBET is equal to Dp, only if Lv = Ls. Dh is considered as a diameter of pores with smooth walls, and Ls/Lv—as a roughness factor. Application of the proposed parameters gives a new insight of many published results. Presentation of equivalent processing variables (routs); roughness factor as result of new derivation of hydraulic pore diameter and size effect on intrawall void space.

An equation connecting a generalized overall structural property Y with a generalized processing variable X was proposed to monitor the structural evolution of porous materials. The equation PVp = const (P—mechanical strength, Vp—pore volume) suggested previously for granulated catalysts (Titelman 1989) was transformed into a generalized function for any porous material Y = f(X). Y is considered to be internal energy (work) establishing a conjugate pair of force/displacement, both are generalized. This was obtained in the form of a pore-to-wall volume ratio. For ordered mesoporous materials, this ratio was reduced to a ratio of pore to wall cross-sectional areas and further to a ratio of pore diameter to wall thickness. An additional type of Y is the ratio of the cross-sectional area of the pore shell to that of struts. X is any processing variable of synthesis and post-synthesis treatment of the material (quantitative, non-quantitative and a set of single variables). For X, a method of ranking X by Y was used. Large amounts of published data were recalculated, and typical sections of Y = f(X) (constant, linear, etc.) in different X ranges were found. Obtained dependencies allow for the monitoring of both collective and individual effects of independent variables on Y, discovering energetic-wise equal and similar states of material, controlling material stability, selecting optimal sample, correcting some published data and notably expanding on the information obtained from regular adsorption measurements.

It was established that partial combustion of carbon constituting the walls of multiwall carbon nanotubes (MWCNTs) catalyzed by previously deposited CaCO3 nanoparticles converts parallel graphene layers in a multiwall structure to aggregates formed by nano-onions with a diameter of 5–12 nm. The areas with positive curvature of graphene layers on the external surface of air-etched MWCNTs played the role of docking stations for nickel nanoparticles inserted by sonochemical deposition after removal of the CaCO3. The nickel nanoparticles were located exclusively at the tops of the onions. Formation of nanoscale curvature at the MWCNT support surfaces decreased the average size of Ni nanocrystals at similar loading of 50–60 wt% from 8 to 2 nm. Partial catalytic combustion did not change the concentration of surface carbonyl groups measured by titration, which attributes the observed phenomena directly to the corrugation of the MWCNT surfaces. The catalytic tests revealed a significant increase of catalytic activity of supported Ni catalyst due to corrugating of the external surface of the MWCNT support. After oxidative etching of the MWCNTs, the rate of chloroacetophenone hydrogenation measured with a Ni–MWCNT catalyst increased by a factor of 2 without change in selectivity yielding chlorophenylethanol as the main product.

Magnetic properties of compacted La0.8Ca0.2MnO3 manganite nanoparticles with average particle size of 18 and 70 nm and Curie temperatures T-C approximate to 231 K and T-C approximate to 261 K, respectively, have been investigated. The relative volume of the ferromagnetic phase has been estimated to be 52% for ensembles of 18 nm particles and 92% for 70 nm particles. It was found that applied hydrostatic pressure enhances T-C of La0.8Ca0.2MnO3 nanoparticles at a rate dT(C)/dP approximate to 1.8-1.9 K/kbar, independently on the average particle size. Pronounced irreversibility of magnetization below T-irr approximate to 208 K and strong frequency dependent ac susceptibility below T-C for smaller 18 nm particles have been observed. 18 nm particles have also shown aging and memory effects in zero-field-cooled (ZFC) and field-cooled magnetization. These features indicate the appearance of spin-glass-like state, partially reminiscent the behavior of La1-xCaxMnO3 crystals, doped below the percolation threshold x < x(C)=0.225. In contrast, ensembles of larger 70 nm particles have shown insignificant irreversibility of magnetization only and no frequency dependence of ac susceptibility, similarly to the behavior of La1- xCaxMnO3 crystals with x > x(C). The temperature of the ZFC magnetization maximum for 18 nm particles decreases with increasing magnetic field and forms a critical line with an exponent 1.89 +/- 0.56. The results suggest that superspin-glass features in ensembles of interacting 18 nm particles appear along with superferromagnetic-like features.

Magnetic and transport properties of La0.8Ca0.2MnO3 nanoparticles with average size of 18 nm and Curie temperature T C≈231 K have been studied. Pronounced irreversibility of magnetization below T irr≈208 K has been observed. Studied particles have shown memory effects in zero-field-cooled and field-cooled magnetization. The resistivity has a semiconducting character at 150<T<300 K and exhibits relaxation and memory effects below the Curie temperature. The results suggest that superspin-glass features in ensembles of interacting 18 nm La0.8Ca0.2MnO3 particles appear along with superferromagnetic-like features.

Transport and magnetic properties of LaMnO3+δ nanoparticles with average size of 18 nm have been investigated. The ensemble of nanoparticles exhibits a paramagnetic to ferromagnetic (FM) transition at TC∼246 K, while the spontaneous magnetization disappears at T≈270 K. It was found that the blocking temperature lies slightly below TC. The temperature dependence of the resistivity shows a metal–insulator transition at T≈192 K and low-temperature upturn at T<50 K. The transport at low temperatures is controlled by the charging energy and spin-dependent tunnelling through grain boundaries. The low temperature I–V characteristics are well described by indirect tunnelling model while at higher temperatures both direct and resonant tunnelling dominates.

Magnetic properties of electron-doped La0.2Ca0.8MnO3 manganite nanoparticles with average particle size ranging from 15 to 37 nm, prepared by the glycine-nitrate method, have been investigated in temperature range 5-300 K and in magnetic fields up to 90 kOe. A monotonous enhancement of weak ferromagnetism linked to the reduction in the particle size was observed for all nanoparticles. Magnetic hysteresis loops also indicate size-dependent exchange bias effect displayed by horizontal and vertical shifts in field-cooled processes. The magnetization data reveal two ferromagnetic components: first one appears at T similar to 200 K and may be attributed to surface magnetization and second one appears as a result of spin canting of antiferromagnetic core or is developed at some interfaces inside nanoparticles. Time evolution of magnetization recorded in magnetic fields after the field cooling to low temperatures exhibits a very noisy behavior that may be caused by formation of collective state of nanoparticles with no clear tendency to reach equilibrium state. Magnetic properties of the nanoparticle samples are compared with those of the bulk La0.2Ca0.8MnO3.

Magnetic and structural properties of nanocrystalline low-doped La0.8Ca0.2CoO3 cobaltites with particle size of 8, 13, 23, and 50 nm, prepared by the glycine-nitrate method, were investigated in temperature range 5–320 K, magnetic field up to 50 kOe and under hydrostatic pressure up to 10 kbar. With particle downsizing, a noticeable expansion of unit cell, with concomitant changes in the rhombohedral structure toward the cubic one was observed. It was found that the increased surface-disorder effect strongly suppresses the ferromagnetic state in La0.8Ca0.2CoO3 nanoparticles leading to a decrease, by factor of about 2, both in spontaneous magnetization, MS, and Curie temperature, TC, when particle’s size decreases from 23 to 8 nm. The effective magnetic moment μeff was found also to decrease distinctly due to the strong interdependence between Co–O–Co interactions and Co spin state. The size-induced magnetic disorder drives the La0.8Ca0.2CoO3 nanoparticles to a dominant glassy behavior for 8 nm particles. This is evidenced by the fact that the freezing temperature varies with magnetic field in a strict conformity with the de Almeida–Thouless law for spin glasses and also by the observation of characteristic slowing down in the spin dynamics. The applied pressure suppresses TC, MS, and coercive field HC, like it is observed for bulk La0.8Ca0.2CoO3. Nevertheless, in nanoparticles the pressure effect on TC is noticeably stronger, while HC diminishes with pressure much slower then in bulk material.

Magnetic properties of electron-doped La1/3Ca2/3MnO3 manganite nanoparticles with average particle size ranging from 12 to 42 nm, prepared by the glycine-nitrate method, have been investigated in temperature range 5–300 K and in magnetic fields up to 90 kOe. Reduction in the particle size suppresses antiferromagnetism and decreases the Néel temperature. In contrast to bulk crystals, the charge ordering does not occur in all studied nanoparticles, while a weak ferromagnetism appears above 200 K. Low temperature magnetic hysteresis loops indicate upon exchange bias effect displayed by horizontal and vertical shifts in field cooled processes. The spontaneous and remanent magnetization at low temperature shows a relatively complex variation with particle size. The size-induced structural/magnetic disorder drives the La1/3Ca2/3MnO3 nanoparticles to a pronounced glassy behavior for the smallest 12 nm particles, as evidenced by large difference between zero field cooled and field cooled magnetization, frequency dependent ac-susceptibility, as well as characteristic slowing down in the spin dynamics. Time evolution of magnetization recorded in magnetic fields after field cooling to low temperatures exhibits pronounced relaxation and a very noisy behavior that may be caused by formation of some collective states. Magnetic properties of the nanoparticle samples are compared with those of La0.2Ca0.8MnO3 nanoparticles. These results shed some light on the coupling between charges and spin degrees of freedom in antiferromagnetic manganite nanoparticles.

The effect of SBA-15 microporosity on the crystal size of TiO2 was investigated employing SBA-15 materials with high (SBA-15-HM) and low (SBA-15-LM) microporosities (14.2% and 4.7% of microporous volume, respectively). TiO2 phase was incorporated inside SBA-15 using internal hydrolysis method over a wide range of loadings (7–63wt%). At all loadings, TiO2 inside SBA-15 pores was in the form of anatase nanocrystals as found in characteristic Raman spectra. The crystal size of TiO2 anatase phase was determined by Raman spectroscopy using a correlation between Raman peak position and peak width and TiO2 crystal size. The correlation was established based on the set of unsupported TiO2 samples with the crystals size in the range 5–120nm (BET and XRD). Using this correlation, it was found that the crystal size of TiO2 inside SBA-15 with high microporosity was lower than inside SBA-15 with low microporosity. This is a direct proof of the effect of wall microporosity on the dispersion of TiO2 inside SBA-15. Due to the higher TiO2 dispersion, TiO2/SBA-15-HM adsorbed more vanadia than TiO2/SBA-15-LM at the same TiO2 loadings. As a result, V2O5/TiO2/SBA-15-HM displayed higher activity than V2O5/TiO2/SBA-15-LM in NO SCR with ammonia.

The formation of polycrystalline tin oxide nanoparticles (NP) and nanowires was investigated using nanocasting approach included solid–liquid strategy for insertion of SnCl2 precursor and SBA-15 silica as a hard template. HR-TEM and XRD revealed that during the thermal treatment in air 5nm tin oxide NP with well defined Cassiterite structure were formed inside the SBA-15 matrix mesopores at 250°C. After air calcination at 700°C the NP assembled inside the SBA-15 mesopores as polycrystalline nanorods with different orientation of atomic layers in jointed nanocrystals. It was found that the structure silanols of silica matrix play a vital role in creating the tin oxide NP at low temperature. The pure tin chloride heated in air at 250°C did not react with oxygen to yield tin oxide. Tin oxide NP were also formed during the thermal treatment of the tin chloride loaded SBA-15 in helium atmosphere at 250°C. Hence, it is well evident that silanols present in the silica matrix not only increase the wetting of tin chloride over the surface of SBA-15 favoring its penetration to the matrix pores, but also react with hydrated tin chloride according to the proposed scheme to give tin oxide inside the mesopores. It was confirmed by XRD, N2-adsorption, TGA-DSC and FTIR spectra. This phenomenon was further corroborated by detecting the inhibition of SnO2 NP formation at 250°C after inserting the tin precursor to SBA-15 with reduced silanols concentration partially grafted with tin chloride.

Magnetic properties of compacted 50 nm CaMnO3-delta (CMO) nanoparticles have been investigated. Measurements of ac-susceptibility exhibit upon cooling two magnetic transitions at T similar to 270 K accompanied by a small spontaneous magnetic moment and a para-antiferromagnetic (AFM) transition at T-N similar to 120 K, observed previously in bulk CMO. Asymmetric magnetization hysteresis loops observed in applied magnetic fields H <= 90 kOe are attributed to an exchange coupling between the antiferromagnetic core and the ferromagnetic (FM) shell of the CMO nanoparticles. This work provides the observation of exchange bias effect in manganite nanoparticles with inverted AFM-core-FM-shell structure, as compared to the typical FM-core-AFM-shell. Effects of surface and exchange anisotropy are also discussed.

Magnetic and structural properties of nanocrystalline LaCoO 3 with particle size ranging from 25 to 38 nm, prepared by the citrate method, were investigated. All nanoparticles exhibit ferromagnetism below T C ≈ 85 K. It was found that the unit-cell volume increases monotonically with decreasing particle size and ferromagnetic (FM) moment increases simultaneously with lattice expansion, whereas T C remains nearly unchanged. It appears that both magnetic and structural properties of LaCoO 3 nanoparticles are size-dependent due to the surface effect. On the other hand, an applied pressure suppresses strongly the FM phase leading to its disappearance at ∼11 kbar. Remarkably, the T C does not change visibly under pressure. Our data reveal that the ferromagnetism in LaCoO 3 nanoparticles, likely related to the intermediate-spin (IS) Co 3+ state, is simply controlled by the unit-cell volume. Within this scenario, the FM coupled IS states appear/disappear with expanding/compressing the lattice and/or Co–O bonds.

Magnetic properties of nanocrystalline LaCoO3 with particle size of 25, 30, 32, and 38 nm, prepared by the citrate method, were investigated in temperature range 2-320 K, magnetic field up to 50 kOe, and under hydrostatic pressure up to 11 kbar. All nanoparticles exhibit weak ferromagnetism below T-C approximate to 85 K, in agreement with recent observation on LaCoO3 particles and tensile thin films. It was found that with decreasing particle size, i.e., with increasing the surface to volume ratio, the unit-cell volume increases monotonically due to the surface effect. The ferromagnetic moment increases as well, simultaneously with lattice expansion, whereas T-C remains nearly unchanged. On the other hand, an applied hydrostatic pressure suppresses strongly the ferromagnetic phase leading to its full disappearance at 10 kbar, while the T-C does not change visibly under pressure. It appears that the ferromagnetism in LaCoO3 nanoparticles is controlled by the unit-cell volume. This clear correlation suggests that the nature of ferromagnetic ground state of LaCoO3 is likely related to orbitally ordered Jahn-Teller active Co3+ ions with intermediate-spin (IS) state, which may persist in the expanded lattice at low temperatures. A robust orbital order presumed among the IS Co3+ species can explain the very stable T-C observed for LaCoO3 samples prepared under different conditions: single crystal powders, nanoparticles, and thin films.