NANO/MESO/MACROPOROUS MATERIALS CHARACTERIZATION AFFECTED BY EXPERIMENTAL CONDITIONS AND FEATURES OF THE USED METHODS

The aim of this study was to analyze a set of methods: adsorption, X-ray, microscopic, cryoporometry, relaxometry, and thermoporometry used to investigate the morphological and textural characteristics of materials being in vacuum, or gaseous or liquid dispersion media, as well the interfacial phenomena basic for the used approaches. Techniques used in the studies should be divided into eight groups: (i) adsorption-desorption of lowmolecular weight probe compounds (N2, Ar, etc.); (ii) adsorption or confinement of lowor high-molecular weight compounds in pores (voids) of solid particles being in liquid media; (iii) small angle X-ray scattering (SAXS) or small angle neutron scattering (SANS); (iv) quantitative analysis of images recorded using microscopic methods (TEM, SEM, AFM), etc.; (v) thermoporometry based on differential scanning calorimetry (DSC) with decreasing-increasing temperature utilizing melting thermograms; (vi) cryoporometry based on low-temperature 1H NMR spectroscopy giving the dependence of signal intensity on temperature; (vii) relaxometry based on NMR spectroscopy dealing with transverse relaxation time vs. temperature; and (viii) relaxometry based on thermally stimulated depolarization current (TSDC) measurements related to dipolar and dc relaxations. Each method could be characterized by systematic errors caused by many factors. However, the use of a set of the aforementioned methods in parallel can allow one to elucidate the reasons and level of these systematic errors that is of importance for correct characterization of the materials studied. Thus, the larger the number of methods used in parallel, the more comprehensive the morphological and textural characterization of the adsorbents.


INTRODUCTION
Experimental data on the morphological and textural characteristics could give direct (first group, e.g. microscopic methods) or indirect (second group, e.g., adsorption, SAXS, cryoporometry, relaxometry, thermoporometry) information on the characteristics and properties of materials studied. For the second group, additional treatment, using some approaches, equations, models, transformation, etc., of the data is needed to obtain expected information. For example, information on adsorption, desorption, melting, and evaporation of adsorbates is indirect for the textural characterization of adsorbents. Additionally, the results could include both random and systematic errors [1][2][3][4] reducing possibility to obtain maximum adequate characteristics of the materials from indirect information. Therefore, experimental results based on indirect information need additional tests to reduce the systematic errors, e.g., using the data based on direct information or several methods from the second group. Comparison of the treated data of several methods of both groups on the same characteristics can provide the most reliable description of the materials since the systematic errors could be more accurately estimated and eliminated. The textural characteristics of porous or disperse materials could be analyzed using nitrogen (argon, carbon dioxide or other probes) adsorption-desorption isotherms, small angle X-ray (or neutron) scattering (SAXS or SANS), cryoporometry based on nuclear magnetic resonance (NMR) spectroscopy ( 1 H signal intensity vs. temperature), relaxometry based on NMR transverse relaxation time (T2) vs. temperature (T) or thermally stimulated depolarization current (TSDC) caused by dipolar relaxation of polar bonds and atomic groups vs. T, thermoporometry based on differential scanning calorimetry (DSC) and thermogravimetry (TG) vs. T. These methods can give mainly indirect information on the materials under very different conditions (low and high temperatures, vacuum or liquid dispersion media, low and high pressures, etc.) which can also affect the characteristics of the materials [5][6][7][8][9][10][11][12][13][14][15][16] but allow one to understand the behavior of the materials being under different conditions. The textural characterization of the materials is possible using the aforementioned methods because the behavior of adsorbates confined in pores depends on both pore sizes and temperature, as well pressure (or concentration in liquid dispersion media) [5,6,16] that, however, can result in systematic errors. Note that random errors are always present in any experimental measurements [1][2][3][4] that can be estimated using a set of measurements and statistical treatment of the results, but systematic errors analyses need several methods under different conditions. There are several addition factors affecting indirect information such as (i) changes in the material characteristics due to (or during) measurements; (ii) the presence several phases (or admixtures) characterized by different dependences on the changes in measurement conditions (temperature, pressure or concentration, sample prehistory, etc.); (iii) nonuniform distribution of components in complex systems; (iv) medium effects (e.g. swelling); and (v) incorrect or inadequate models and methods used in the analyses of the experimental data [1][2][3][4][17][18][19][20][21][22][23][24][25][26][27][28]. As a whole, it is of importance to analyze the differences in the characteristics determined using different indirect methods taking into account the measurement conditions. These analyses give useful information on the effects of different factors in various experimental techniques that is a way to understand the reasons of the systematic errors, which could be ignored if the characterization is based only on one method. Therefore, the aim of this work was to elucidate some effects of measurement conditions and certain sources of the systematic errors in determination of the material characteristics based on indirect and direct experimental data for highly disperse fumed oxides, various porous silicas (precipitated, ordered mesoporous silicas and silica gels), porous polymers, activated carbons, and nanostructured composites.
ADSORPTION Typically, to estimate the textural characteristics of samples degassed at increased temperature (350-470 K for several hours), low-temperature (77.4 K) nitrogen (or argon) adsorption-desorption isotherms could be recorded using an adsorption analyzer. The specific surface area (S BET ) is calculated (using the adsorption isotherms) according to the BET method [5], which, however, has some disadvantages causing some systematic errors [5,6,16,17]. For example, the S BET value depends strongly on the pressure range used (Fig. 1) due to (i) unfinished monolayer adsorption at low p/p 0,max values or started multilayer adsorption at larger p/p 0,max values and these changes could depend on the types of both adsorbent and adsorbate; (ii) changes in an occupied area of a surface by a probe (nitrogen) molecule depending on pore sizes and structure of a solid surface (e.g. content of hydroxyls or other surface functionalities affecting orientation of adsorbed N 2 molecules), etc. Additionally, the dependence is stronger for adsorbents with narrower pores (Fig. 1). Therefore, the specific surface area of adsorbents could be estimated using not only the adsorption method but also SAXS, cryoporometry, etc., which, however, can generate other systematic errors. The total pore volume (V p ) could be evaluated from the nitrogen adsorption at p/p 0  0.98-0.99, where p and p 0 are the equilibrium and saturation pressure of nitrogen at 77.4 K, respectively [6]. However, if an adsorbent possesses macropores, especially broad ones, the V p value can be strongly underestimated. For example, loose powders with fumed oxides of metals or metalloid (FMO) composed of nonporous nanoparticles (NPNP) (3-120 nm in size depending on the FMO types) forming aggregates (< 1 m in size) and agglomerates of aggregates (> 1 m) are characterized by a low bulk density  b = 0.04-0.15 g/cm 3 [7,8,16]. The low bulk density corresponds to a very large empty volume in the loose powders V em = 1/ b -1/ 0 (e.g. 24.5 cm 3 /g for A-300 at  0 = 2.2 g/cm 3 and  b = 0.04 g/cm 3 ), which is greater by 10-20 times than the V p values of FMO because nitrogen cannot completely fill macropores due to very weak interactions with distant pore walls (NPNP surface) [5,6,16]. Additionally, for "soft" (e.g. polymeric) adsorbents, adsorption of nitrogen fluid can lead to swelling that results in open hysteresis loops. Upon the adsorption of liquids (e.g. water) more strongly interacting with adsorbents, even solid adsorbents such as fumed silica can demonstrate slow swelling of nanoparticles [6][7][8][9]16]. There are the opposite effects upon strong heating of FMO because removal of intact water and surface hydroxyls leads to a decrease of NPNP sizes (S BET increases) and then NPNP sintering results in a decrease in the S BET value. All these effects related to prehistory of samples can change the final results, and sometimes these results could seem unexpected.
The nitrogen adsorption-desorption isotherms could be used to compute the pore size distributions (PSD, differential f V (R) ~ dV p /dR and f S (R) ~ dS/dR) using various approaches. These approaches could include various systematic errors caused by an inappropriate model of pores (e.g. cylindrical pores poorly modelling voids between NPNP in aggregates of FMO), inappropriate parameters of solids (e.g. parameters of carbons poorly describing polymeric adsorbents), etc. Therefore, for materials with a complex topology of pores or/and composed of several different phases (e.g. FMO and polymers or carbons, etc.), firm (Micromeritics, Quantachrome, etc.) software can give incorrect results with systematic errors. Better results could be obtained using a complex pore model with slit-shaped (S) and cylindrical (C) pores and voids (V) between spherical nanoparticles (SCV method) with the corresponding parameters for the different phases [17,28]. Additionally, the chemical structure of a solid surface (e.g. hydroxyls or other functionalities) can affect the interactions (and orientation, i.e., effective area of a surface occupied by a molecule) of dinitrogen or other probe molecules with a surface. The SCV method with a self-consistent regularization (SCR) procedure [17] allows one to consider the presence of several phases since the parameters of several types of surfaces (e.g. silica, alumina, titania, carbon, carbohydrate polymers, etc.) could be simultaneously used with an appropriate pore model for each component. The use of the SCR procedure gives information on contributions (weight coefficients) of different pore types and different components into the total porosity and specific surface area [17,28]. As a whole, the model errors remain upon the use of the SCV/SCR method because the texture of any adsorbent is not strongly ordered (pores can have very complex shape), there is a surface roughness, etc. However, the SCV/SCR method reduces the systematic errors appearing upon the application of the firm software for complex materials.
For better view of the PSD at large values of R, the differential PSD with respect to the pore volume [17]. The f V (R) and f S (R) functions could be also used to calculate contributions of nanopores into the total pore volume and specific surface area (V nano and S nano at radius in the range 0.35 nm < R < 1 nm), mesopores (V meso and S meso at 1 nm < R < 25 nm), and macropores (V macro and S macro at 25 nm < R < 100 nm) [17]. Clear, an incorrect PSD results in incorrect values of the textural characteristics.
The average values of the pore radii could be determined with respect to the pore volume (X = V) and the specific surface area (X = S), respectively, as the corresponding moments of the distribution functions max max min min Additionally, f S (R) could be used to estimate the deviation (w) of the pore shape from the model using [29] max min / ( ) 1 where R max and R min are the maximal and minimal pore radii, respectively. The S * nano , S * meso and S * macro values could be corrected by multiplication by (w+1) that gives S * (w+1) = S sum = S nano + S meso + S macro = S BET . The effective w value (w ef ) can be estimated with equation However, the reliability of the w values depends on the reliability of both S BET and PSD.
The PSD functions could be also calculated using various Density Functional Theory (DFT) methods such as nonlocal DFT (NLDFT), quenched solid DFT (QSDFT), 2D-NLDFT, etc. (present in firm (Micromeritics, Quatachrome, etc.) software) or DFT version with overall equation [17,30] where W is the adsorption, where v M the liquid molar volume,  f the fluid density in occupied pores,  m the density of the multi-layered adsorbate in pores, r k the radius of pores occupied at the pressure p,  ss is the collision diameter of the surface atoms. To calculate the density of a gaseous adsorbate (nitrogen) at a given pressure p, Bender equation [31] could be used. Transition from gas (subscript g) to liquid (l) or fluid in the form of multi-layered adsorbate in pores (m) can be linked to the corresponding fugacity f where E is the interaction energy of an adsorbate molecule with the pore walls and neighboring molecules calculated with the Lennard-Jones potentials. Thus, advantages of the SCV/SCR method are the possibilities to estimate (i) contributions of several phases of complex materials into the textural characteristics; (ii) adequate PSD of complex adsorbents; (iii) both PSD and particle size distribution (PaSD); (iv) errors of the model used that could correspond to a surface roughness of adsorbents [17,28].
To describe better the porosity of various adsorbents, an additional regularizer could be derived with maximum entropy principle [32] applied to the distribution function f(R) that can be written as N-dimension vector (N is the number of the grid points for f) [32]. This procedure was used [27] to modify the CONTIN algorithm [33] (CONTIN/MEM-j where j denotes the order of ) ( f p j   ) and applied to study different silicas [27].
Any mechanical action on FMO results in certain changes in the textural characteristics of soft powders [16,34]. However, mechanochemical activation (MCA in a ball-mill for several hours) of wetted nanosilica weakly affects the PaSD of NPNP (Fig. 2), but the structure of secondary particles (NPNP aggregates and agglomerates) strongly changes due to compaction of the powder that is well seen in changes in the PSD (Fig. 3). These changes increase with increasing MCA time that result in enhancement of the bulk density with decreasing pore volume V p at t MCA = 6 h. However, the V p value increases at t MCA = 1 h on the initial stage of the compaction, despite the value of V em monotonically decreases from 21.8 cm 3 /g (initial A-300) to 4.2 cm 3 /g (t MCA = 1 h) and 2.08 cm 3 /g (6 h), but the inequality V em > V p remains true. Note that the IPSD with DFT (model of voids between silica NPNP) and NLDFT (cylindrical pores in silica) quantitatively differ, but they are qualitatively similar since both show an increase in IPSD intensity with no shift of the main peaks at treatment time t MCA = 1 h and a shift of the main peaks toward smaller R values and a decrease in PSD intensity at R > 10 nm at t MCA = 6 h (Fig. 3).
Various measurements could be carried out at low temperatures and during these experiments water or other liquids could be adsorbed and frozen at lower temperatures T < T fr in pores of the materials studied than those in the case of free bulk liquids.
The effects of freezing of water (and other liquids, e.g. acetone) confined in pores of different materials can result in changes in the textural characteristics (Figs. 4 and 5) [16,35], and these changes differ from the swelling results because the latter change the structure of the pore walls, but the former leads to increase in the pore volume and specific surface area (this is rather similar to the burn-off effects during activation of carbons). For some porous polymers, the effects are very strong (Fig. 4 a, b), but for others, they could be much smaller (Fig. 4 c). A similar enhancement of the porosity upon water freezing is observed for activated carbons (Fig. 5). Thus, these effects depend on the types of adsorbents (chemical structure, cross-linking degree, character of interactions between adsorbent and adsorbate) and adsorbate type (e.g. structural changes in water upon freezing with increasing sizes of ice crystallites causing huge disjoining pressure up to 2000 atm). This ice pressure can lead to destroying of core-shell nanoparticles (50-200 nm) of complex FMO, but smaller silica NPNP keep integrity under high pressure by ice crystallites in thick-wall stainless steel cryoreactors [19,22]. Thus, the use of the adsorption methods to characterize the textural features of adsorbents has not only certain advantages but also several disadvantages and systematic errors caused by (i) the effects of adsorbate (fluid) on the adsorbent texture (e.g. due to swelling or freezing); (ii) dependences of an occupied area and shape of a probe molecule on pore size and shape, as well on pressure; (iii) partially non-equilibrium conditions; (iv) partial accessibility of long, curved, narrow pores for adsorbate molecules; (v) as well model and equation errors. Therefore, parallel measurements using various methods to analyze the textural and morphological characteristics are very desirable. Among these methods the most appropriate and reliable results could be provided by SAXS and high-resolution TEM (HRTEM) methods. However, additional mathematic treatments of the corresponding data should be done [16][17][18][19][20].  SMALL-ANGLE X-RAY SCATTERING The differential PSD functions f(r) based on the SAXS data could be calculated using Fredholm integral equation of the first kind for scattering intensity I(q) [36]   max min 2 2 sin cos ( ) where C is a constant, q = 4sin()/ the scattering vector value,  is the scattering angle,  is the wavelength of incident X-ray, V(r) is the volume of a pore with radius r (proportional to r 3 ), and f(r)dr represents the probability of having pores with radius r to r + dr. The values of r min (= /q max ) and r max (= /q min ) correspond to lower and upper limits of the resolvable real space due to instrument resolution. This equation could be solved using the CONTIN algorithm [33]. The f(r) function could be converted into incremental PSD (IPSD) (r i ) = (f(r i+1 ) + f V (r i ))(r i+1  r i )/2 for better view of the PSD at larger r values (similar to the PSD based on the adsorption data). The main advantage of the SAXS method upon the textural characterization [16,[36][37][38][39] is that all open and closed pores could be analyzed in contrast to the adsorption methods giving the characteristics only of pores accessible for probe molecules (Figs. 6 and 7); therefore, practically always S SAXS > S BET (Figs. [6][7][8]. Comparison of the SAXS and adsorption PSD, as well the S SAXS and S BET values, allows one a deeper insight into the textural features of the materials studied under various conditions. Additionally, the SAXS data could be used to compute the PaSD for particles of different shapes [37].  7)) and NLDFT methods (some details were described elsewhere [38]) To calculate the particle size distribution (PaSD) functions based on the SAXS data [39], several models of particles (e.g. spherical, cylindrical, lamellar ones and various blends of them [37]) could be used. For spherical particles, integral equation similar to Eq. (7) could be written as follows where C is a constant, r is the radius of particles, f(r) is the distribution function (differential PaSD), and P(r) is the form factor for spherical particles [39] (the kernel of the integral equation): The PaSD with respect to the volume of particles (as abundance in vol %) could be calculated as follows is the first-order Bessel function, V = πr 2 H is the cylinder volume, and C is a constant [39]. For lamellar particles [39] max min ( ) ( , ) ( ) where L is the lamellar thickness, and the prefactor (1/q 2 ) is the so-called Lorentz factor required to randomize the orientation of the lamellar particle and 2 2 sin( / 2) ( , ) ( / ) ( /2) qL P q L L q qL . In the case of complex systems, several models with various blends of spherical, cylindrical and lamellar particles could be used with certain weight coefficients.
For a complex model of particles, the integral equation includes three terms [37]   qr qr qr f r dr qr where I(q) is the X-ray scattering intensity, q = 4sin()/ is the scattering vector value, 2 is the scattering angle,  is the wavelength of incident X-ray, R is the radius of particles, H and R are the length and radius of cylinders, L is the lamellar thickness, f(r), f(L), and f(H) are the distribution functions, J 1 (x) is the first-order Bessel function, c x are the weight coefficients calculated, as well f(x) functions, using a selfconsistent regularization procedure [17] to solve Eq. (12). For example, Fig. 8 shows changes in the PaSD function (calculated with Eq. (12) using the SCR procedure) upon carbonization of resorcinol-formaldehyde resin bound to bentonite particles. These changes show that particle (polymer phase) carbonization results not only in diminution of the particles (e.g. at r < 7 nm) but also in certain consolidation of them (at r = 8-15 nm and r > 30 nm).
The chord size distribution, G(h) as a geometrical statistic description of a multiphase medium, could be calculated from the SAXS data [40, 41] where K is the Porod constant (corresponding to scattering intensity I(q) ~ Kq 4 in the Porod range). The specific surface area from the SAXS data could be calculated (in m 2 /g) using equation 4 SAXS 10 (1 ) where  =  a / 0 is the solid fraction of adsorbent, The Q value is sensitive to the range used on integration of Eq. (15) (since experimental q values are measured between the q min and q max values different from 0 and ). Therefore, the invariant value Q could be calculated using equation [42] max min 2 max where b is a constant determined using equation valid in the Porod range.
The G(h) curves (Fig. 9) show that carbonization of resorcinol-formaldehyde resin bound to bentonite particles results in diminution of the thickness of pore walls over the total range. The carbonization results in a decrease in the value of S BET (160 m 2 /g  122 m 2 /g) due to consolidation of particles that causes an increase in a part of closed pores since the S SAXS value increases (194 m 2 /g  211 m 2 /g) during the carbonization (Fig. 9). Thus, the SAXS method gives useful information on global textural changes in the materials that significantly completes the adsorption data. Note that the SAXS data treatments described above were successfully used for carbon, silica, and polymeric materials in comparison with the results of various methods used to analyze the nitrogen adsorption data [37,38,[43][44][45] or analysis of microscopic images. Additional not only morphological but also textural quantitative characteristics could be derived from adsorption and SAXS data, as well from TEM and SEM images.

HIGH-RESOLUTION TRANSITION ELECTRON MICROSCOPY (HRTEM)
TEM and SEM images (Fig. 10) could be used to calculate both PSD [16,28] and PaSD (Figs. 2 and 11 a) functions. However, this needs certain methods (computer programs) for image treatment using, e.g., such software as ImageJ [46] (with a granulometry plugin), Fiji [47] (with a local thickness plugin) or others [48]. The quantitative analyses of microscopic images have certain advantages and disadvantages described in detail elsewhere [48]. The advantages are due to practically direct quantitative information on the particulate morphology and texture of the materials studied that can be compared with the results based on indirect information based, e.g. on the adsorption and SAXS data. The disadvantages of the approaches are due to certain problems of quantitative analysis of images, especially pore walls and pore sizes, with a certain ambiguity of their representation on gray-scale images [48]. Figure 10 shows images of fresh A-300 and aged (about 15 years) A-500. The latter lost the surface area from 492 m 2 /g (fresh) to 331 m 2 /g (aged). This effect is caused by enhanced aggregation of NPNP (comp. Figs. 10 a-d and  10 e, f) that results in significant changes in the nitrogen adsorption-desorption isotherm (Fig. 11 a) and PSD (Fig. 11 b). These textural changes over the total range of pores (voids between NPNP) are similar (but slightly different) to those observed after the mechanical compaction of the FMO powders described above. Thus, FMO based on amorphous silica or other amorphous silicas (which are a hard-moving liquid), e.g. silica gels, are aged-time-sensitive materials. This time-dependent aggregation effect is of importance from a practical point of view.

QUASI-ELASTIC LIGHT SCATTERING
The characteristics of such highly disperse materials as FMO depend strongly on the dispersion media properties because of several factors: (i) surface charging, (ii) NPNP swelling, (iii) colloidal stability and aggregation instability and others [16][17][18][19][20][49][50][51]. Electrophoretic mobility and secondary particle size distribution (SPSD) investigations could be performed using such apparatus based on the quasi-elastic light scattering (QELS) (photon correlation spectroscopy, static light scattering, or dynamic light scattering) method as a Zetasizer 3000 (Malvern Instruments). Deionized distilled water and FMO samples (1-30 g per dm 3 of the water) could be utilized to prepare suspensions sonicated for several min using an ultrasonic disperser (e.g. Sonicator Misonix, power 500 W and frequency 22 kHz). The pH values could be adjusted by addition of 0.1 M HCl or NaOH solutions, and the salinity could be changed by addition of NaCl, NaClO 4 , etc. The electrophoretic behavior and the SPSD with respect to the intensity of scattered light (SPDS I ) and particle number (SPDS N ) of FMO in the aqueous suspensions were described in detail elsewhere [16,18,49,50]. According to the Smoluchowski theory [51], there is a linear relationship between the electrophoretic mobility U e (QELS measured) and the  potential: U e =, where  is a constant for a thin electrical double layer (EDL) at a >> 1 (where a denotes the particle radius, and  is the Debye-Huckel parameter). For a thick EDL (a < 1), e.g., at pH close to the isoelectric point (IEP), the equation with the Henry correction factor is more appropriate U e = 2 /(3), where  is the dielectric permittivity; and  is the viscosity of the liquid [51]. For FMO dispersions in the aqueous media, aggregation of NPNP is always characteristic [49,50]. However, sometimes the first peak of SPSD (Fig. 12 a,  curve 4) corresponds to NPNP. The hydrodynamic diameter of NPNP could be 5-20 % larger than the geometric one due to the presence of an immobile layer in EDL of liquid/bound counter ions depending on pH, IEP, salinity, etc. Other peaks in the SPSD correspond to NPNP aggregates and aggregates/agglomerates (Fig. 12 b). Note that QELS PaSD peak of NPNP corresponds to smaller sizes than that estimated from TEM image and nitrogen adsorption data because there were different A-300 samples with 330 m 2 /g (QELS) and 294 m 2 /g (TEM, nitrogen adsorption). Thus, the QELS method could be used to estimate the aggregation of FMO particles in liquid dispersion media depending on conditions of the measurements. This FMO behavior can affect the results of the NMR cryoporometry and relaxometry investigations of the suspensions.

NMR CRYOPOROMETRY
The confined space effects play an important role for liquid adsorbates or dispersion media (e.g. water, etc.) especially at temperatures lower than freezing temperature of bulk liquid that can be utilized in various methods to estimate the textural characteristics on the base of the temperature behavior of liquids confined in pores [16,18,19,[52][53][54]. Water can be frozen in narrower pores (or voids between nanoparticles) at lower temperatures as described by the GibbsThomson (GT) relation for the freezing point depression for liquids confined in cylindrical pores at radius R [16,[52][53][54] , , where T m (R) is the melting temperature of ice in cylindrical pores of radius R, T m, the bulk melting temperature, H f the bulk enthalpy of fusion,  the density of the solid,  sl the energy of solidliquid interaction, and k GT is the GibbsThomson constant (k GT = 40-90 K nm for various FMO, porous oxides (silica gels), polymers, carbons, etc.). Eq. (18) could be used to determine the cluster size distributions (CSD) (f V (R) = dV uw (R)/dR) of water unfrozen at T < 273 K [16] and bound to disperse or porous solids wetted or located in the aqueous suspensions.
Eq. (18) can be transformed into Eq. (19) for two (or more if their signals could be separated in total spectra deconvoluted) immiscible liquids (e.g. water and benzene characterized by different 1 H NMR signals [16,27]) with consideration for their amounts in a mixture and their temperaturedependent signal intensity (obtained on deconvolution of the total signal) Integration of the f V (R) and f S (R) functions at R < 1 nm, 1 nm < R < 25 nm, and 25 nm < R < 100 nm gives the volume and specific surface area of nano-, meso-and macropores, respectively, filled by unfrozen liquid. The specific surface area (S uw ) of adsorbents in contact with bound water (assuming for simplicity that the density of unfrozen bound water  uw = 1 g/cm 3 where R min and R max are the minimal and maximal radii of pores filled by unfrozen water, respectively. In the case of calculations of the structural characteristics of nanopores (R < 1 nm), mesopores (1 nm < R < 25 nm) and macropores (R > 25 nm), the R min and R max values are the boundary R values for the corresponding pore types (including R min = 0.2 nm for nanopores).
The uw uw C  / max value should be replaced by the corresponding values of the volumes of nanopores, mesopores, or macropores [16]. The average melting temperature <T m > could be calculated using formula related to the ratio of the first and zero moments of the distribution function [20] 0 0 min min where T 0 = 273.15 K, and T min is the temperature corresponding to C uw = 0. Fig. 13 shows the f(R) functions for the aqueous suspensions of A-300 at different concentrations of silica in comparison to the N 2 adsorption PSD (V/SCR). The value of C A-300 = 12.3 wt. % is close to that causing complete structurization (clusterization) of the dispersion [16]. Therefore, changes in the f(R) curves are non-monotonic with increasing C A300 value due to different structurization of the dispersion vs. A-300 concentration. The NMR cryoporometry gives useful information on the behavior of bound water depending not only on the silica (water) content, but also on the A-300 treatment (e.g. MCA) effects (Fig. 14). A strong increase in the content of water from h = 3 g/g (wetted powder) to 40.7 g/g (suspension) results in a relative decrease in the content of strongly bound water forming small clusters in narrow voids because in the suspension, the average distance between NPNP can strongly increase (due to electrostatic repulsion interactions). The MCA compaction of A-300 results in a relative increase in contribution of small clusters (R < 2 nm) because contribution of narrow voids increases (Figs. 3 and 14). An enhancement in the MCA compaction resulting in a greater  b value (from 0.22 to 0.39 g/cm 3 ) slightly affects the distribution of unfrozen water clusters in wetted samples over the total size range (Fig. 14) because the PSD changes too (Fig. 3), but the water content is not enough to strongly change the NPNP aggregation that observed in the aqueous suspensions. Thus, NMR cryoporometry gives information not only on the textural characteristics of the materials being in different dispersion media but also on the temperature behavior of unfrozen liquids confined in different pores. Similar information could be obtained using the DSC thermoporometry method based on the GibbsThomson relation for the melting point depression for liquids confined in pores.

DSC THERMOPOROMETRY
Melting DSC curves of bound water (ice) [55][56][57][58] can be used to calculate the pore sizes filled by this water as follows: where T m and T m0 are the melting temperatures of confined and bulk water, respectively. The pore size distribution dV/dR can be calculated from the DSC melting curves of bound ice where dq/dt, , , m and H(T) are the DSC heat flow, the water density, the heating rate, the sample mass and the melting enthalpy of ice, respectively. The H values as a function of temperature for water can be estimated as follows [55][56][57][58] The Gibbs-Thomson equation applied to DSC melting thermograms allows one to accurate calculate the PSD for silica gels (with the model of cylindrical pores since the errors of this model are relatively small for silica gels [16,17]) using melting curves at T < T f , i.e. using the lowtemperature DSC peaks [60]. Melting curves of n-decane at T < 243 K could be used to calculate the PSD for silicas with the GT equation R = k GT /(T 0,m -T m ) for cylindrical pore radius at k GT = 64.6 K nm, where T 0,m and T m were the melting temperatures for pure bulk crystallites and confined in pores of radius R, respectively. For the freezing point depression of n-decane confined in pores (voids), these calculations resulted in the PSD similar to the NLDFT PSD [28]. For water as a probe, there are certain differences between nitrogen adsorption PSD and DSC PSD for different silicas (Fig. 15) that is due to several factors: (i) water can be layer-by-layer frozen in mesopores and macropores; (ii) ice (having a larger volume than liquid water) can affects the PSD; (iii) model errors caused by the difference between model pore shape (e.g. cylindrical) and real one (e.g. voids between NPNP). However, qualitative changes in the DSC PSD and adsorption PSD are similar upon the MCA compaction of A-300 (Fig. 15 a). The DSC thermoporometry [16,28,[55][56][57][58][59][60], as well thermogravimetry porometry [28,61] could be used for the characterization of the behavior of adsorbates at low and high temperatures that gives additional information on the confined space effects important on practical applications of the materials under different conditions. Note that the confined space effects can be observed not only for unfrozen liquids but also for frozen ones using the TSDC method [62]. TSDC RELAXOMETRY Thermally stimulated (de)polarization current (TSDC) method could be used to analyze the confined space effects for frozen polar liquids (e.g. water  ice) bound to various disperse or porous solids even at low their content, i.e., diluted aqueous suspensions could be studied due to high sensitivity of the TSDC method measuring low depolarization currents at 10 15 -10 7 A [62]. The tablets (diameter 30 mm, thickness 1 mm) with frozen studied materials differently hydrated (hydration h = 0.03-99 gram of water per gram of a dry material) could be polarized by the electrostatic field at the intensity F p = 0.1-0.5 MV/m at 260-265 K then cooled to 80-90 K with the field still applied and heated without the field to 265-270 K at a various heating rate (e.g.  = 0.05 K/s). The current (I) evolving due to sample depolarization could be recorded by an electrometer over the 10 15 -10 7 A range. Relative mean errors for measured TSDC are relatively small  I = 5 %,  T = 2 K for temperature,   = 5 % for the temperature change rate [62].
The temperature range on the TSDC measurements is much broader (80-270 K) than that on the 1 H NMR measurements (180-290 K) because the dipolar relaxation (TSDC) observed at T < 200-220 K is linked to the polar bond rotations or molecular fragment relaxation (observed in confined ice) which cannot be registered in the 1 H NMR spectra (of static samples with narrow bandwidth of 20 kHz [16]) of mobile low-molecular molecules (water, benzene, acetone, etc.) that appears only at higher temperatures. However, the temperature ranges of the throughout conductivity (dc relaxation in TSDC) and the molecular mobility ( 1 H NMR) are relatively close but not the same [16,62] because the dc relaxation requires the throughout percolation of ions in the samples from one electrode to another, but the molecular mobility reflected in the 1 H NMR spectra can be due to local (cluster) mobility of bound or bulk water (from individual molecules, clusters, nanodomains to bulk water with elevating temperature). Therefore, the dc relaxation in TSDC is observed at slightly higher temperature than the 1 H NMR spectra of unfrozen clusters of confined water [16,62]. Size distributions of pores (nitrogen adsorption/desorption treated with SCV/SCR method) and water clusters located in voids between silica NPNP in aggregates located in frozen aqueous suspensions of A-50, A-300, and A-500 (TSDC/GT method) at 7 wt. % (some details were described elsewhere [16,62]) Similar to the 1 H NMR cryoporometry results for the A-300 suspensions (Fig. 13) the water cluster distributions based the TSDC data ( Fig. 16) demonstrate nonmonotonic changes in the nanostructured clusters (R < 1 nm) and mesostructured clusters and domains (R = 1-5 nm) with increasing concentration of silica in the aqueous suspensions. However, for different nanosilicas such as A-50 (S BET = 52 m 2 /g), A-300 (294 m 2 /g), and A-500 (492 m 2 /g), there are practically monotonic changes in the cluster sizes and their contributions (Fig. 17) because the smaller the NPNP size, the stronger the aggregation of NPNP affecting the TSDC spectra of confined water (ice). Note that integral GT equation based on the TSDC relaxation vs. temperature (similar to integral GT equation (20) for NMR cryoporometry but with a certain dependence of k GT on T [16,62]) gives the f(R) function close to the N 2 PSD than that calculated using nonintegral equation (Fig. 18). Thus, the TSDC relaxation data could be used for additional characterization of confined liquids at T < T f when only dipolar relaxation of bonds and certain atomic fragments is observed in ice (i.e. with no the molecular mobility for confined unfrozen liquids observed in the NMR cryoporometry or DSC thermoporometry). TSDC relaxometry characterized by certain advantages and disadvantages, as well other described methods, gives additional information allowing one a deeper insight into the interfacial phenomena and more complete characterization of the materials in different conditions.

CONCLUSION
The present study deals with analyses of a set of methods used to investigate the morphological and textural characteristics of nano/meso/macroporous materials being in various dispersion media, as well the interfacial phenomena basic for various approaches in the characterization of materials. There are several ways in these studies: (i) adsorption-desorption of low-molecular weight probe compounds (N 2 , Ar, etc.); (ii) adsorption or confinement of low-or high-molecular weight compounds in pores (voids) of solid particles being in liquid media; (iii) small angle X-ray scattering (SAXS); (iv) quantitative analysis of images recorded using various microscopic methods; (v) thermoporometry based on differential scanning calorimetry (DSC) with decreasing-increasing temperature using melting thermograms; (vi) cryoporometry based on low-temperature 1 H NMR spectroscopy giving the dependence of signal intensity of a mobile phase vs. temperature; (vii) relaxometry based on NMR spectroscopy with transverse relaxation time vs. temperature; and (viii) relaxometry based on thermally stimulated depolarization current (TSDC) measurements. Each method could be characterized by certain systematic errors. However, the use of several aforementioned methods in parallel can allow one to elucidate the reasons and level of systematic errors that is on importance for correct characterization of the materials studied. Thus, the larger the number of in parallel used methods, the more comprehensive the morphological and textural characterization of the adsorbents.