Systematic analysis of the nitrogen adsorption-desorption isotherms recorded for a series of microporousmesoporous amorphous aluminosilicates using classical methods
Understanding the porous structure of microporousmesoporous materials is very important for developing useful scientific concepts and principles in materials science, surface science, heterogeneous catalysis, adsorption and related technological applications. Amorphous aluminosilicates are of particular interest in this sense because it is relatively simple to design them with diverse porous structures comprising micro, meso, and even macropores. In this work, we took advantage of the latter and developed a systematic and in-depth analysis of the results of nitrogen physisorption tests at 77 K performed over a series of microporousmesoporous amorphous aluminosilicates and of the characterization of their texture by classical models to estimate surface area and porosity. The strategy for the analysis consisted hysteresis loops. Overall, the present study can thus be said to make two contributions: (i) it proposes a systematic methodology for analyzing both the raw data and the textural properties calculated by classical methods both derived from nitrogen physisorption experiments. (ii) It presents useful new insights on the texture of microporousmesoporous materials.
<!>Introduction<!>Nitrogen physisorption measurements.<!>Assessment of porosity, surface area, and fractal dimension.<!>Hysteresis loops.<!>Surface area and type of porosity. Table<!>Characterization of porosity.<!>Material code<!>ASAP18<!>NiMo/ASAP18<!>ASAP28<!>NiMo/ASAP38<!>NiMo/ASAP48<!>Material code<!>ASAP26<!>NiMo/ASAP26<!>NiMo/ASAP28<!>ASAP36<!>NiMo/ASAP36<!>ASAP38<!>ASAP48<!>Material code<!>ASA095**<!>Material code<!>ASAR075*<!>ASAR566*<!>Material code<!>ASAR568<!>NiMo/ASAR568<!>ASAR586<!>NiMo/ASAR586<!>ASAR588<!>NiMo/ASAR588<!>Material code<!>ASA075<!>NiMo/ASA075<!>ASA085<!>NiMo/ASA085<!>Conclusions
<p>of making a thorough description of the features showed by the recorded nitrogen isotherms, first. As a result, a proposal for considering two new types of isotherms, types I(c) and IV(c), and five new types of hysteresis loops, H1(b), H2(c), H3(b), H3(c), and H4(b), in addition to the standard IUPAC classification. These new categories stemmed from the microporousmesoporous nature of the materials and from the presence of strong network effects. The previous analysis helped interpreting and judging the results of the calculations made with classical methods to assess the texture of the materials; namely, their BET surface area, tplot microporosity, BJH mesopore size distribution, and fractal dimension. The performed analyses allowed establishing that the relative percentage of microporosity of the materials can be correlated to the physisorption energy as described qualitatively by the CBET constant. Concerning mesopore size distributions, it was found that the BJH method remains to be very valuable for describing the porous structure of the materials particularly if the results obtained with both branches of the isotherms are considered. Finally, it was shown that the fractal dimension can complement the analysis of the porous structure of microporousmesoporous materials if the latter are compared considering the features of their isotherms and of their</p><!><p>The physical adsorption of nitrogen (physisorption) at cryogenic temperatures (most often at 77 K; the boiling point of nitrogen) is the most used technique for characterizing the texture; i.e., surface area and porosity, of nanoporous materials. As narrated by Sing 1,2 , the technique dates back to the beginning of the 20 th century and its use for estimating the surface area of porous solids was adopted during the 1930s following the development of theoretical models by Langmuir 3 and Brunauer, Emmet, and Teller 4 for explaining the adsorption of gases and vapors over solids. Further advances during the late 1940s 5 and early 1950s 6 led to the development of methods that apply the Kelvin equation for estimating the pore size distribution of solids where capillary condensation occurs during the nitrogen physisorption tests. This type of pores were later named mesopores and their size ranges between 2.0 and 50.0 nm. 7 Further studies by Dubinin and his group 8 established the basis for studying pores smaller than 2.0 nm. All the above efforts and many other more [9][10][11][12][13][14] provided researchers with a relatively complete set of tools (classical models) to analyze physisorption isotherms in order to estimate the surface area and porosity of materials. Furthermore, the very rapid development of molecular level calculations by the density functional theory during the 1990s has led to more modern models for assessing texture in nanoporous materials. 15,16 However, the access and number of the latter models is still very limited because of the complex calculations that need to be carried out and because their accuracy strongly depends on the particular chemistry of each type of adsorbent. Consequently, classic models 1,[17][18][19][20][21][22] are still the most used in the field because their usefulness triumphs their strong shortcomings. Proof of this is that all modern equipment comes provided with automated software that allows to comfortably do estimations of surface area and porosity with classic models with a couple of clicks.</p><p>However, comfortability in science often comes at the expense of critical thinking. Nowadays, scores of scientific reports routinely report nitrogen physisorption data and the textural properties thereafter derived without an in-depth analysis of the recorded data or criticism of the results obtained after applying the models for assessing texture. Furthermore, there is an unhealthy trend to omit the experimental details of the test, even though clear recommendations have been published in several books, 11,[23][24][25][26] reviews, [27][28][29][30] IUPAC reports, 7,31 and some in international standards. 32 In this contribution, a critical assessment of the nitrogen adsorption-desorption isotherms of a series of materials based on amorphous silica-aluminas and of the data thereof derived to characterize their texture is done. Namely, a set of amorphous silica-aluminas were tested in nitrogen physisorption experiments before and after loading them with nickel and molybdenum oxide by wet impregnation. 33,34 These materials are normally applied for hydroprocessing reactions. [35][36][37] The paper fulfills two purposes. First, providing practical guidance on how to qualitatively analyze the data measured during nitrogen physisorption tests; i.e., the recorded isotherms and on how to put this data in the service of interpreting and judging the results of the calculations of surface area and porosity made via classic methods. Second, it is demonstrated that the above method of analysis fruitfully leads to better interpretation and advances in the knowledge of the structure of nanoporous materials. The strategies for analysis presented in the paper seem particularly handy when dealing with materials that exhibit both micropores and mesopores; a type of materials often found in many scientific and industrial applications. 19,35,36,[38][39][40][41][42][43][44][45][46][47][48] 2. Experimental and analytical methods 2.1 Analyzed materials. The analyzed amorphous silica-aluminas were synthesized by three variations of the sol-gel method; namely, sol-gel via hydrolysis in acidic medium (ASA), 42 a sol-gel method where polyethylene glycol (ASAP) 43 was used as a template, and another where a so-called gel skeletal reinforcing solution (ASAR) composed of tetraethylorthosilicate (TEOS) and 2-propanol was employed for the synthesis. Further impregnation of a Ni-MoOx phase was made to these amorphous silica-aluminas (NiMo) whose primary application was the refining of heavy crude oil cuts. 44,45 Specific details for the synthesis of the materials are reported by Coconubo 36 and Duarte. 35 For the purposes of the current work, the materials were branded as ASA###, ASAP##, ASAR###, and NiMo/ASA###, NiMo/ASAP##, and NiMo/ASAR###. Where, # was an internal code assigned to each material. A total of 34 materials; 17 amorphous silica-aluminas and their 17 impregnated amorphous silica-aluminas counterparts were analyzed in the present study.</p><!><p>Nitrogen physisorption isotherms were recorded at 77 K with a 3Flex instrument from Micromeritics. Prior to measurements, samples of the materials whose weight was between ca. 0.1000 and 0.2000 g were put in an outgassing unit operated under vacuum (~0.05 mbar) at 573 K for one night. Equilibrium adsorption isotherms were recorded within a relative pressure, P/P0, range between ~2.0×10 -3 and ~0.998 using 10 s equilibration intervals.</p><!><p>The nature and characteristics of the porous network of the materials was qualitatively assessed from the shape of the recorded isotherms and from the shape of the corresponding hysteresis loops considering IUPAC recommendations 31,49 and other literature works. 19,29,30,[49][50][51][52][53] Afterwards, the surface area of the materials was assessed by the Brunauer-Emmet-Teller (BET) method 4 applying the so-called Rouquerol consistency criteria. 17 The contribution of microporosity to the surface area of the materials was assessed with the t-plot method 54 and applying the Harkins and Jura reference isotherm. 9,10 This method proved to produce the most satisfactory results for fitting the recorded isotherms. Calculations for assessing the micropore size distribution of the materials were not made because of the restricted lower P/P0 limit used during the physisorption tests. On the other hand, mesopore size distributions were estimated with the Barret-Joyner-Halenda (BJH) method 6 using the Harkins and Jura standard isotherm 10 with the Faas correction. The latter employs the concept of thickness of an adsorbed layer in a circular pore versus the simple application of thickness on a flat surface. All of the above calculations were done with the MicroActive® software provided with the 3Flex apparatus.</p><p>Finally, the fractal dimension of the materials was estimated in an attempt to analyze the complexity of their porous network. 55 Four methods were tested for this purpose; the Pfeifer et al. 56,57 adaptation of the Frenkel-Halsey-Hill method, the thermodynamic method proposed by Neimark, 55,58 the Wang and Li method, 59 and the Sandoval et al. method. 60 Among these four, only the results obtained with the method by Sandoval et al. 60 will be presented in the paper since the other three either sometimes produced values of the fractal dimension without physical sense; namely, fractal dimensions larger than 3 or did not showed an adequate linear fit of the data (see Supporting Information, Figure S3 and Table S1). All these calculations were made by setting-up an Excel workbook where conventional numerical methods were used for fitting the data. 61 1 and 2 represent the different types of N2 physisorption isotherms recorded for the studied materials while Table 1 describes the characteristics of all the isotherms recorded for this work. The full set of isotherms are shown in Figure S1 of the Supplementary Information. To explain the notes presented in Table 1, it is important to recall the classification of isotherms made by IUPAC in its most recent technical report. 31 For the sake of brevity, we will refer only to the isotherms akin to those found in the present work; namely, types I and II, and subtype IV(a). We apologize with the expert reader who is already well acquainted with this information. IUPAC's type I isotherms are exhibited by solids constituted by micropores. These isotherms are completely reversible; i.e., they do not show hysteresis, they are concave to the relative pressure axis, and, after micropore filling, 8 the amount of adsorbate reaches a limiting value up to the highest P/P0 value measured during the experiment. There are two subtypes of the type I isotherm. Subtype I(a) exhibits a very steep initial increase in the amount of adsorbed N2 at the P/P0 range defined for micropore filling; which is between 0.005 and ~0.050 according to Bardestani et al. 29 Such a phenomenon is attributed to the strong interaction between the adsorbate and the walls of pores whose width is ca. 1.0 nm. 31 When the width of the micropores is larger than the aforementioned value and up to ca. 2.5 nm, the initial increase in the amount of adsorbed N2 is lower and a more pronounced change in curvature is found hence producing the subtype I(b) isotherm in IUPAC's system. 31 However, in general, IUPAC 31 has not defined a typical range for the amount of nitrogen that is adsorbed by microporous materials. IUPAC's type II isotherms are also completely reversible and have an S-shape; i.e., they are concave to the P/P0 axis in the low relative pressure region followed by a semi-linear section, and, finally, they become convex to the axis at the high relative pressure region of the isotherm. Near P/P0 = 1.0, the amount of adsorbed N2 can increase "without limit" according to IUPAC. 31 The S-shape of the isotherm behavior is attributed to unrestricted monolayer-multilayer adsorption after the initial completion of the theoretical/statistical monolayer 4 of adsorbate but the unlimited adsorption of N2 near P/P0 = 1.0 is not explained in IUPAC's report. 31 Typically, nonporous and macroporous (i.e., materials whose pores are larger than 50 nm 31 ) show IUPAC's type II isotherms but the S-shape of this isotherm is basically the same as that of IUPAC's type IV isotherms. Finally, the shape of IUPAC's subtype IV(a) isotherms is similar to that of type II, but they show irreversibility as manifested by their distinct hysteresis loops in the relative pressure region after P/P0 ~ 0.4. For tests made with N2 at 77 K, it is said that hysteresis is produced by capillary condensation in mesopores whose width is wider than ca. 4.0 nm. 31 After hysteresis, type IV(a) isotherms normally show a saturation plateau of variable length; including some cases where a mere inflection point is found. 31 Considering the above, Table 1 summarizes the classification made for the recorded isotherms. They were classified in three types; namely, type I(c) for 12 out of the 34 materials, type IV(a) for 10 out of the 34 materials, and type IV(c) for 12 out of the 34 materials. Among the latter, types I(c) and IV(c) are categories proposed in this work. The proposed type I(c) isotherm is a combination of IUPAC's types I(b), II, and IV(a) isotherms which indicates that the material has both micropores and mesopores. It is somehow surprising that the literature has not made a formal proposal for classifying these isotherms apart even though classic papers such as the one by Shull et al. 5 already presented cases such as the ones found in this work. In addition, Schneider 52 admitted that "adsorption isotherms of real porous material represent usually a combination of these [IUPAC standard] types". Furthermore, the recent update of IUPAC's technical report on the physisorption of gases 31 only considered fully reversible isotherms for microporous materials hence excluding a particular category for microporous-mesoporous materials showing irreversibility due to capillary condensation-evaporation phenomena in mesopores. The latter, despite the humongous number of materials that follow into this category such as some amorphous silica-aluminas, 5 molecular organic frameworks 46,47,62,63 , and zeolites both classic such as ZSM-5 64,65 and hierarchical ones. 39,40  The other proposed category is type IV(c). In this instance, though the isotherm could be classified as a type IV(a), the fact that it displays unlimited adsorption at P/P0 > 0.7 makes it inadequate to classify it as such, in our opinion. Furthermore, type IV(c) isotherms found herein may also show multiple inflection points instead of the plateau that is characteristic of IUPAC's type IV isotherms. Isotherms with unlimited adsorption are normally associated with unfilled macropores 31 or with materials formed by non-rigid aggregates of platy particles. 66 So far, IUPAC does not consider this feature of the isotherm within its classification for the type of isotherm but rather as a feature of the so-called H3 hysteresis loop (more on this below). The association of this behavior to the platy nature of the particles of the porous solid agrees with what is known for mesoporous oxides such as -Al2O3 67 and parent aluminum containing mixed oxides. 68,69 Multiple inflection points at P/P0 > 0.7 are also commonly observed when the accumulation of extraneous materials over mesopore mouths takes place; e.g., carbonaceous residua over fluid catalytic cracking catalysts. 68 Herein, the catalysts NiMo/ASA095 and NiMo/ASAR065 were the ones that displayed such type of behavior. Therefore, it is reasonable to assume that the impregnated metals accumulated either on the mouths or inside the mesopores of the corresponding amorphous aluminosilicates.</p><!><p>Concerning the hysteresis loops found for the studied materials, Table 1, two materials were considered to have IUPAC's H1 loop, six showed a mixture of IUPAC types H1 and H3, two showed a mixture of H2(a) and H4 loops, five showed IUPAC type H3 loops, twelve showed a variation of the H3 loop, and another twelve showed a variation of the H4 loop. Therefore, all except the IUPAC type H5 hysteresis loop 31 were identified in the tested materials. Several of the recorded loops were either variations (strong variations in some cases -Figures 1, 2, and S1) or mixtures of the IUPAC's loops. Consequently, we propose five new categories for hysteresis loops; namely, H1(b), H2(c), H3(b), H3(c), and H4(b), while the standard H1, H3, and H4 IUPAC loops may now be called H1(a), H3(a), and H4(a) loops, respectively.</p><p>Concerning the hysteresis loops found for the studied materials, Table 1, two materials were considered to have IUPAC's H1 loop, six showed a mixture of IUPAC types H1 and H3, two showed a mixture of H2(a) and H4 loops, five showed IUPAC type H3 loops, twelve showed a variation of the H3 loop, and another twelve showed a variation of the H4 loop. Therefore, all except the IUPAC type H5 hysteresis loop 31 were identified in the tested materials. Several of the recorded loops were either variations (strong variations in some cases -Figures 1, 2, and S1) or mixtures of the IUPAC's loops. Consequently, we propose five new categories for hysteresis loops; namely, H1(b), H2(c), H3(b), H3(c), and H4(b), while the standard H1, H3, and H4 IUPAC loops may now be called H1(a), H3(a), and H4(a) loops, respectively.</p><p>The proposed type H1(b) is a mixture of IUPAC's H1 and H3 types making a bean pod shape with an intermediate inflection point between P/P0 ~ 0.50 -0.75, Figures 1a) and S1h) -S1l). IUPAC 31,70 assigns H1 hysteresis to loops whose raise in the amount of physisorbed nitrogen is steep and that are given by well-ordered mesopore networks with pore shapes that may either be tubular or ink-bottle. For the latter, the neck width is near the same as the pore cavity. Meanwhile, IUPAC characterizes H3 loops as those produced either by non-rigid platy particles or by a pore network comprising macropores which are not filled by condensed nitrogen during the measurement.</p><p>The proposed H2(c) loop was a mixture of IUPAC's type H2(a) and H3 whose shape resembled an inclined mound, Figures 2a) and S1f). According to IUPAC, 31 H2(a) loops are produced when either the pore network has necks that may induce cavitation or pore blocking/percolation during desorption since such phenomena may cause a characteristic steep drop in the amount of nitrogen desorbed from the sample during the test. Considering the combination of the aforementioned features of H2(a) and H3 loops, it seems more adequate to add a new category, H2(c), for the loops found for the materials featured in Figures 2a) and S1f).</p><p>Both the proposed H3(b) and H3(c) loops distinguished themselves by displaying an empanada like shape before the closure of the hysteresis loop, Figures 1b), 1d), and S1a) -S1e). The differences between H3(b) and H3(c) were the location of the inflection point after the empanada feature of the loop and a longer semi-linear section for the adsorption branch of the materials showing the latter loop, compare Figures 1d) and  Finally, the proposal of the H4(b) loop responds to the fact that IUPAC H4 loops are represented with an adsorption branch that reaches a very extended plateau after micropore filling. 31 Conversely, the materials that showed the H4(b) loop, Figures 2b) and S1r) -S1w) had very pronounced downward concavity in regards to the P/P0 axis without ever reaching a plateau during the measurements. 2 shows the values of the BET surface area (SABET), CBET parameter, microporous surface area (Micro-SA), the so-called external, -i.e., mesoporous plus macroporous-surface area, (Exter-SA), the percentage of microporous surface area (ξ = %Micro-SA), the types of isotherm and hysteresis loop, as in agreement with the classification discussed above and summarized in Table 1, and a classification of the porosity of the materials. The latter was done according to the following criteria: if ξ ≤ 10%, the material was classified as mesoporous, if 10% < ξ ≤ 40%, the material was classified as microporous-mesoporous with mesoporosity being prevalent, if 40% < ξ ≤ 60%, the material was classified as microporous-mesoporous, if 60% < ξ ≤ 90%, the material was classified as microporous-mesoporous with microporosity being dominant, and, if ξ ≥ 90% the material was classified as microporous.</p><!><p>According to the collected data, the following observations were made: (i) ~44.1% of the materials were mesoporous; ~32.4% of the materials were microporous-mesoporous with the mesoporosity being prevalent; ~11.8% of the materials were microporous-mesoporous with no dominant type of porosity; the same percentage of materials as above were microporous-mesoporous with microporosity being prevalent; and, finally, the remaining (1/34) ~2.9% of the materials were microporous. (ii) The classification for the type of isotherm proposed in Table 1 was coherent with the classification of porosity made in Table 2. Therefore, the materials whose isotherms were classified either as IV(a) or IV(c) showed a prevalence of mesoporosity. Meanwhile, the materials whose isotherms were classified as I(c) showed well developed microporosity; namely, they were microporous or microporousmesoporous materials where either no prevalent type of porosity was found or microporosity was dominant.</p><p>Table 2. Surface area calculations; total (SABET), microporous (Micro-SA), and external (Exter-SA) for the studied materials. All surface areas are expressed in m 2 /g. *Values estimated using the t-plot method with the Harkins and Jura standard isotherm. 54 ** Calculated as: ξ = 100×(Micro-SA/( Micro-SA + Exter-SA). *** As in agreement with the classification proposed in Table 1. **** Meso = mostly mesoporous (ξ ≤ 10), micro-MESO = microporous-mesoporous material where mesoporosity is dominant (10 < ξ ≤ 40), micro-meso = microporous-mesoporous material (40 < ξ ≤ 60), MICRO-Meso = microporousmesoporous material where microporosity is dominant (60 < ξ ≤ 90), and Micro = mostly microporous material (ξ > 90). Besides the above, it was interesting to analyze the correlation between the micropore surface area of the materials and the so-called CBET constant. In this sense, trying to directly correlate these two parameters proved fruitless, 𝑑 . This correlation is mathematically complex since it is an exponential function that includes four parameters. However, it can be pointed out that this type of equations are rather characteristic of transport processes. 71 In general, one may consider that the correlation between CBET and ξ is composed of a semi-linear part and of an exponential part, Figure 3, with the former comprising data up to ξ ≈ 20%, where the CBET values were between 74 and 133. , 4 where, E1 = is the heat of adsorption of the first statistical layer of adsorbate, EL is the heat of liquefaction of the adsorptive, R the universal gas constant (≈ 1.9872 cal×K -1 ×mol -1 ), and T is the temperature of the physisorption test (77 K, herein), one may assess how the BET apparent energy of adsorption (E App ads = (E1 -EL)) was statistically distributed for the studied samples. To do this, we made an Averaged Shifted Histogram 72 of the data using the app available in the website: https://maverick.chem.ualberta.ca/plot/ash, Figure 4. Accordingly, as a random variable, E App ads was better described by a platykurtic (i.e., short-tailed -kurtosis < 3-) distribution with positive skewness (~ 1.56). Hence, considering the information presented in Figures 3 and 4, one may assume that the higher the percentage of microporosity of the materials, the stronger the interaction between the adsorbate and the adsorbent was. Furthermore, as earlier mentioned, the relationship between these parameters seems to be related to transport processes.</p><!><p>Transport processes depend strongly on pore size distributions, of course. 73 Herein, porosity was assessed only for the mesoporous range since data for P/P0 < 1×10 -3 was not available. As announced in the Experimental section, the analysis of mesoporosity was done with the BJH method 6 using the Harkins and Jura standard isotherm 10 with the Faas correction. For the analysis, both the adsorption and the desorption branches of the isotherms were considered for performing the calculation of the pore size distributions, Figures 5 to 12. These figures included not only the produced pore size distributions but also a zoom of the region of the corresponding isotherms where the hysteresis loops closed. The latter was used to analyze the probable influence of the so-called tensile strength effect 22,74 on the distributions estimated from the desorption branch of the isotherm. Considering the number of materials that were tested and the classification of their isotherms and hysteresis loops, Tables 1 and 2, it was more practical to tabulate the observations made on the estimated pore size distributions from each branch of the adsorption isotherm for the families of materials that showed the same kind of isotherms and hysteresis loops, Tables 3 to 8.</p><p>In general, all pore size distributions from the type I(c) isotherms, Figures 5 and 6, and those from the IV(a) type of isotherm with H2(c) hysteresis, Figure 9, showed a peak due to the tensile strength effect at 3.68 ± 0.04 nm (t-Student 95% confidence interval with 13 degrees of freedom) in the pore size distributions derived from the desorption branch of the isotherms, Figures 5 and 6. The latter value is very similar to the 3.8 nm value reported by Groen et al. 22 The tensile strength effect is associated to a sudden closure of the hysteresis loop between 0.41 ≤ P/P0 ≤ 0.48. 22 It arises when the network of mesopores has an stochastic nature and it is to some extent interconnected which causes the so-called network effects leading to cavitation during the desorption of the nitrogen adsorptive. 22 In practice, as seen in Figures 5 and 6, this often generates a tall and sharp peak in the distribution estimated from the desorption branch of the isotherm. The artifact then consists on considering that this peak is indicative of the fact that the mesoporosity of the material is dominated by a family of pores whose pore size is very narrow; a fact that is not corroborated by the distribution of pore sizes derived from the adsorption branch of the isotherm. A contrast between the two pore size distributions rather indicates that the network of mesopores includes pores of the size associated to the tensile strength effect but these pores are not particularly remarkable within the pore size distribution. Instead, as evidenced by the results featured in Figures 5  and 6, the distribution of sizes for the mesoporous network of the examined microporousmesoporous materials may span the whole range of mesoporosity. On the other hand, regardless of the branch of the isotherm considered for the calculations, the curves for pore size distribution for the materials with the type I(c) isotherm were characterized by a monotonic decrease which is a mathematic consequence of the fact that the rate of change of the amount of adsorbed nitrogen constantly decreased as a function of the width of the pores.         The pore size distributions estimated from the desorption branch of the isotherm for materials with IV(a) isotherms with H1(b) hysteresis loops, Figure 8, also showed strong differences with those calculated from the adsorption branch. Particularly, the pore size distributions estimated from the desorption branch were bimodal while those calculated from the adsorption branch had high symmetry around a central point; in other words, they can be represented by a Gaussian curve from which statistical normal distributions stem. In addition, the distributions derived from the adsorption branch of the isotherms always indicated that the relative number of pores of sizes larger than 10.0 nm was higher than those predicted by the distributions derived from the desorption branch. The bimodality of the pore size distributions obtained from the desorption branch hints to the strong influence of pore network effects related to cavitation by the tensile strength effect; this time occurring at P/P0 ≈ 0.5, and also maybe to percolation effects. In the case of the type IV(a) isotherms with H1(a) hysteresis, Figure 7, no peaks associated to network effects were found for the pore size distributions calculated from the desorption branch of the isotherms. Instead, a single broad and left skewed peak was found for these materials with both the adsorption and the desorption branches of the isotherm. The corresponding distributions showed that these materials mostly had large mesopores with widths larger than 13 nm.</p><p>Table 3. Description of the mesopore size distribution from the materials exhibiting a I(c) isotherm with H4(a) hysteresis loop. Distributions were calculated from the adsorption and desorption branches of the isotherms by the BJH method 6 with the Harkins and Jura standard isotherm 10 and the Faas correction.</p><!><p>Adsorption pore size distribution Desorption pore size distribution</p><!><p>The curve markedly decreased in the beginning. Afterwards, the curve was almost flat with a very broad shoulder at 6.7 nm.</p><p>The curve markedly decreased in the beginning. The only peak of the distribution was the TSE peak at 3.9 nm. It was very sharp.</p><!><p>The curve markedly decreased in the beginning. Afterwards, it was almost flat with two very broad shoulders at 8.4 and 31.9 nm.</p><p>The curve markedly decreased in the beginning. The only very sharp peak of the distribution was the TSE peak at 3.7 nm. A very broad shoulder appeared at 31.9 nm.</p><!><p>The curve decreased monotonically with a hitch at 2.8 nm and shoulder at 3.6 nm.</p><p>The curve had a semi-monotonic decreasing trend broken by the very sharp TSE peak at 3.6 nm.</p><!><p>The curve decreased monotonically and had a very broad shoulder at 8.3 nm.</p><p>The curve had a semi-monotonic decreasing trend broken by the very sharp TSE peak at 3.5 nm.</p><!><p>The curve was almost flat. It had a wide and not very tall peak at 5.3 nm and a shoulder at 27.8 nm.</p><p>The distribution was almost flat with a very slight decrease in the beginning. The TSE peak was very sharp, and it was centered at 3.7 nm. A very broad shoulder appeared at 15.1 nm.</p><p>Table 4. Description of the mesopore size distribution from the materials exhibiting a I(c) isotherm with H4(b) hysteresis loop. Distributions were calculated from the adsorption and desorption branches of the isotherms by the BJH method 6 with the Harkins and Jura standard isotherm 10 and the Faas correction.</p><!><p>Adsorption pore size distribution Desorption pore size distribution</p><!><p>The curve decreased monotonically and had a shallow and very broad shoulder at 4.6 nm.</p><p>The curve had a semi-monotonic decreasing trend broken by the very sharp TSE peak at 3.9 nm followed by a shallow and broad shoulder at 13.4 nm.</p><!><p>The curve decreased monotonically and had a shallow and very broad shoulder at 6.0 nm.</p><p>The curve had a semi-monotonic decreasing trend broken by the very sharp TSE peak at 3.8 nm followed by a shallow and broad shoulder at 13.3 nm.</p><!><p>The curve was flat in the beginning. Then, it dropped monotonically at 3.8 nm.</p><p>The curve was flat in the beginning and then the very sharp TSE peak appeared at 3.6 nm.</p><!><p>The curve decreased monotonically and had a very shallow and broad shoulder at 4.2 nm.</p><p>The curve had a semi-monotonic decreasing trend broken by the very sharp TSE peak at 3.8 nm.</p><!><p>The curve decreased monotonically and had a shallow and very broad shoulder at 5.4 nm.</p><p>The curve had a semi-monotonic decreasing trend broken by the very sharp TSE peak at 3.7 nm. A shallow and very broad shoulder appeared at 13.3 nm.</p><!><p>The curve decreased strongly and monotonically. It had a very shallow and broad shoulder at 3.8 nm.</p><p>The curve decreased strongly and had a semi-monotonic trend broken by the very sharp TSE peak at 3.5 nm.</p><!><p>The curve was almost flat. It had a very shallow peak at 2.2 nm followed by less shallow one at 5.3 nm. It ended with a shoulder at 27.8 nm.</p><p>The curve very slightly decreased before the appearance of the TSE peak at 3.7 nm. Afterwards, it showed a broad shoulder at 15.1 nm.</p><p>Table 5. Description of the mesopore size distribution from the materials exhibiting a IV(a) isotherm with H1(a) hysteresis loop (marked with *), a IV(a) isotherm with H2(c) hysteresis loop (materials marked with **), and a IV(c) isotherm with H3(c) hysteresis loop. Distributions were calculated from the adsorption and desorption branches of the isotherms by the BJH method 6 with the Harkins and Jura standard isotherm 10 and the Faas correction.</p><!><p>Adsorption pore size distribution Desorption pore size distribution ASAR085* Monotonic increasing and strongly skewed to the left distribution with incomplete peak at 20.5 nm.</p><p>Monotonically increasing and strongly skewed to the left distribution with a well-defined broad peak at 17.2 nm.</p><p>NiMo/ASAR085*</p><p>The curve was flat in the beginning. Then, it showed a strongly skewed to the left incomplete peak at 20.7 nm.</p><p>The curve was flat in the beginning. Then, it showed a strongly skewed to the left peak with a shoulder at 8.1 nm and a maximum at 13.5 nm.</p><p>NiMo/ASA050** Distribution with high symmetry around the center which was located at 5.3 nm.</p><p>The distribution was skewed to the right with a very sharp TSE peak at 3.4 nm.</p><!><p>The curve was skewed to the left and centered at 5.2 nm.</p><p>The distribution was skewed to the left with a very sharp TSE peak at 3.7 nm. It showed a shallow and broad peak at 8.8 nm.</p><p>NiMo/ASA095***</p><p>The distribution showed two relatively symmetric broad and well separated peaks. The tallest was at 29.0 nm and the other was located at 4.0 nm. Peaks were separated by a deep valley near 9.3 nm.</p><p>A sharp TSE peak at 3.4 nm followed by realtively smaller and broader peak at 16.1 nm. The valley between the peaks was deep and around 5.5 nm. Both peaks showed weak skewness to the left.</p><p>NiMo/ASAR065***</p><p>The curve increased monotonically and showed a broad peak at 4.3 nm followed by an inflection point at 20.5 nm.</p><p>The curve increased monotonically and showed the TSE peak at 3.4 nm.</p><p>A second very broad peak was composed of a shoulder at 9.2 nm, a maximum at 16.2 nm, and a hitch at 23.0 nm. Table 6. Description of the mesopore size distribution from the materials exhibiting a IV(c) isotherm with H3(a) hysteresis loop. Distributions were calculated from the adsorption and desorption branches of the isotherms by the BJH method 6 with the Harkins and Jura standard isotherm 10 and the Faas correction.</p><!><p>Adsorption pore size distribution Desorption pore size distribution ASAR065*</p><p>The curve increased monotonically and showed a very broad and relatively shallow peak at 5.7 nm. Afterwards, it showed an inflection point at 21.1 nm.</p><p>The curve increased monotonically and showed the TSE peak as a bump at 3.4 nm. The latter was followed by a skewed to the left broad peak at 6.4 nm. The curve then showed a very wide peak at 16.8 nm.</p><!><p>The curve started flat and showed a single incomplete and very broad peak that had a hitch at 4.7 nm, a shoulder at 7.9 nm, and a maximum at 29.7 nm.</p><p>The curve started flat and then showed two peaks. The first peak showed a shoulder at 7.3 nm followed by its maximum at 13.7 nm. The second peak was incomplete, skewed to the left, and relatively narrow with a pointy maximum at 29.5 nm. There was a small valley between the two peaks.</p><p>NiMo/ASAR075* The curved showed a shallow hitch at 2.8 nm. Then, a very broad peak, incomplete, and skewed to the left peak appeared with a maximum at 29.5 nm.</p><p>The curve slightly decreased in the beginning. Then, a broad incomplete peak appeared showing a flat shoulder at 10.8 nm and a pointy maximum at 22.2 nm.</p><!><p>The curve resembled a mountain with a short plateau at 10.5 nm and a point summit at 21.1 nm.</p><p>The curver resembled a chain of three mountains with the sharp TSE peak at 4.7 nm and a second pointy peak at 9.3 nm. The summit was at 17.0 nm.</p><p>NiMo/ASAR566*</p><p>The curve showed a single incomplete and very broad peak with a shoulder at 7.1 nm and a maximum at 21.1 nm.</p><p>The curve resembled a mountain chain with the TSE peak at 5.1 nm, a short plateau at 9.4 nm, and a pointy summit at 16.9 nm.</p><p>Table 7. Description of the mesopore size distribution from the materials exhibiting a IV(a) isotherm with H1(b) hysteresis loop. Distributions were calculated from the adsorption and desorption branches of the isotherms by the BJH method 6 with the Harkins and Jura standard isotherm 10 and the Faas correction.</p><!><p>Adsorption pore size distribution Desorption pore size distribution</p><!><p>The distribution showed a single, relatively symmetric, and very broad peak with a shallow sag at 2.9 nm, a hitch at 5.6 nm, a summit at 7.9 nm, and a shoulder at 15.8 nm.</p><p>The distribution showed two relatively symmetric peaks separated by a valley. The first and tallest peak showed its maximum at 4.8 nm, while the second peak had its summit at 9.5 nm.</p><!><p>The distribution showed a single, symmetric and very broad peak with a maximum at 9.1 nm and a shallow shoulder at 12.7 nm.</p><p>The distribution showed two symmetric peaks of approximately the size height and separated by a valley. The first peak showed its maximum at 5.1 nm, while the second had its summit at 9.4 nm.</p><!><p>The distribution showed a single and very broad peak with a maximum at 7.0 nm and a shallow shoulder at 12.7 nm.</p><p>The distribution showed two peaks. The first and tallest was the TSE peak at 4.4 nm and the second at 9.5 nm.</p><!><p>The distribution showed a single, symmetric and very broad peak with a maximum at 8.0 nm.</p><p>The distribution showed two symmetric peaks of approximately the same size height and separated by a valley. The first peak was the TSE at 4.8 nm and the second was at 9.2 nm.</p><!><p>The distribution showed a single, relatively symmetric, and very broad peak with a maximum at 7.0 nm and a shallow shoulder at 12.7 nm.</p><p>The distribution showed two relatively symmetric peaks separated by a valley. The first and tallest peak was the TSE at 4.7 nm and the second was at 8.3 nm.</p><!><p>The distribution showed a single, relatively symmetric and very broad peak with a maximum at 7.9 nm and a shoulder at 12.8 nm.</p><p>The distribution showed two relatively symmetric peaks of approximately the same height and separated by a valley. The first and tallest peak was the TSE at 4.4 nm and the second was at 9.2 nm.</p><p>Table 8. Description of the mesopore size distribution from the materials exhibiting a IV(c) isotherm with H3(b) hysteresis loop. Distributions were calculated from the adsorption and desorption branches of the isotherms by the BJH method 6 with the Harkins and Jura standard isotherm 10 and the Faas correction.</p><!><p>Adsorption pore size distribution Desorption pore size distribution ASA050 Very broad and skewed to the left with shoulder at 3.6 nm, main peak at 6.0 nm, and shoulder at 31.0 nm.</p><p>Very sharp TSE peak at 3.4 nm followed by smaller narrow peak at 4.0 nm. The peaks show weak skewness.</p><!><p>The curve decreased slightly in the beginning. The distribution was very broad and skewed to the left with one main peak at 9.2 nm and shoulder at 29.9 nm.</p><p>The curve slightly decreased in the beginning.</p><p>There was a sharp TSE peak at 3.6 nm followed by taller wide peak at 5.7 nm and very wide shoulder at 29.9 nm. Peaks were skewed to the left.</p><!><p>The distribution showed two broad peaks. The tallest was at 10.9 nm and the other was the broadest and it was located at 52.0 nm. Peaks were separated by a shallow valley. The second peak was strongly skewed to the left.</p><p>Small TSE peak (hitch) at 3.5 nm followed by tallest broad peak 7.7 nm and then by a smaller broader peak at 32.3 nm. The peaks were well separated by a valley. The second peak showed the strongest skewness to the left.</p><!><p>The distribution showed a single very broad, semi-symmetric peak at 7.1 nm followed by a smaller shoulder at 15.9 nm</p><p>The curve showed a very slight decrease in the beginning. The TSE peak appeared as a flat shoulder at 3.7 nm followed by a weakly skewed peak at 4.7 nm and then by a very broad peak at 13.5 nm. The two main peaks were separated by a very shallow valley.</p><!><p>Very broad and weakly skewed distribution. The main peak appears at 9.2 nm followed by a strong shoulder 29.6 nm.</p><p>Very broad distribution. TSE appears at 3.5 nm as a shoulder of the tallest peak whose maximum is at 5.6 nm. The latter is weakly skewed and is followed by another shoulder at 6.9 nm which is almost at the same height as the top of the distribution. The smallest peak appears at 16.1 nm and is separated by shallow valley from the main peak.</p><p>Concerning the pore size distributions for those materials showing IV(c) type isotherms, Figures 10 to 12, though network effects were found to influence the distributions calculated from the desorption branch of the isotherms, in this case, the shapes of the curves found from the adsorption branch showed better resemblance to those from the desorption branch. Hence, pore size distributions from both branches of the isotherm were multimodal. The findings described above demonstrated the complexity of the pore networks that amorphous aluminosilicates can develop. Another metric that may help analyzing such a complexity is the fractal dimension. Herein, plotting the fractal dimension as a function of the BET surface area, Figure S4 and the percentage of microporosity, Figure S5, of the studied materials led to no apparent correlations. Therefore, it was decided to analyze how the fractal dimension behaved when considering the different types of isotherms and hysteresis loops showed by the tested amorphous aluminosilicates. Figure 13 presents boxplots for the fractal dimension as function of the type of hysteresis loop and isotherm. It was found that the fractal dimension tended to increase for those hysteresis loops that represented more complex pore networks from materials showing type I(c) and IV(a) isotherms. Meanwhile, the opposite seemed to be true for those materials with a type IV(c) isotherm. At present, no further conclusions can be drawn from the current measurements.</p><!><p>This paper presented a systematic analysis of the nitrogen physisorption data measured for a series amorphous aluminosilicates. The analysis started with an ample description of the features of the recorded isotherms. This was made with the purpose of identifying the nature of the porous networks of the materials. To do this, the isotherms and hysteresis loops recorded for the different materials were classified following IUPAC recommendations. However, it was found that several materials could not be described by the standard isotherms and hysteresis loops of the IUPAC classification. Therefore, two new types of isotherms, types I(c) and IV(c), and five new types of hysteresis loops, H1(b), H2(c), H3(b), H3(c), and H4(b), were proposed to better describe these materials. The need for these classifications stemmed from the microporousmesoporous nature of the materials and from the presence of strong network effects. The exercise of describing and classifying the isotherms helped interpreting and judging the results of the calculations made with classic methods to assess the texture of the materials; namely, their total surface area by the BET method, microporous surface area by the t-plot method, mesopore size distribution by the BJH method, and fractal dimension by the method proposed by Sandoval et al. 60 From these results, it was possible to establish the following: (i) for microporousmesoporous materials, there is an exponential type correlation between the physisorption energy (herein indirectly and qualitatively assessed with the CBET constant) and the relative percentage of microporosity. (ii) A better assessment of the mesopore size distributions derived from the BJH method is done by comparing the results obtained with both branches of the isotherms and when systematically classifying the recorded isotherms before. (iii) The fractal dimension is a useful complementary descriptor of the complexity of the porous network of the material as long as the classification of the materials is based on the corresponding types of isotherms and hysteresis loops guide the analysis.</p>