Diverse conventional wastewater treatments, have been used in recent years for mitigation of water pollution caused by a vast gamma of environmentally undesirable and potentially toxic elements. The adsorption onto solid adsorbents has been the most employed technology, due to low cost and ease operation [1] . A wide variety of natural and synthetic solid adsorbents with different chemical, structural, and surface characteristics have been extensively studied in terms of their adsorption behavior [2] [3] . The surface properties of the adsorbents impact on the removing of toxics elements, nuclear or not, from aqueous media [4] and surface area, zero charge point, hydroxyl groups and porosity are among these key properties; however, the fractal dimension (roughness) as superficial property of solids has been little studied for adsorption purposes. So, this pioneering study allows looking for a new and important approach on this interesting surface property of solid adsorbents.

Roughness can be understood as the set of atomic irregularities of a surface, and the value of the fractal dimension parameter (D_f) is closely related to the roughness profile of a powder material. The roughness of the surface is due to the presence of uniform size pores or to distribution of larger pore size [5] . Measurements of this parameter are achieved by diverse methods, N₂ physisorption on powders is one of them. Values of D_f below 2 indicate regularity and smoothness of surfaces, whereas values close to 3 reveal irregular or rough surfaces [6] . Many determinations of fractal dimension (D_f) studies have been carried out involving the heterogeneity of the structural geometry of solid surfaces [7] - [11] ; particularly, fractal dimension of building materials has gained attention recently [12] - [16] . The surface fractal dimension values are useful for understanding several physicochemical processes (adsorption, adhesion, surface diffusion and catalyst) because the structural heterogeneity of solids affects their interaction with other substances [17] [18] . Contreras-Ruiz et al. (2016) [18] determined D_f of TiO₂-Hydrotalcite composites and these mesoporous materials were in the intermediate roughness range (2.11 ≤ D_f ≤ 2.47). Vilchis-Granados et al. (2013) [19] examined the surface fractal dimensions (D_f) and textural properties of three different alkaline-earth hydroxyapatites. They found that the D_f values for these materials range from 0.7 to 2.3 and reported a linear correlation between the surface hydroxyl group content and the surface fractal dimensions. On other hand, some studies included a relationship between D_f dimensions of adsorbent materials and adsorption mechanism regarding aqueous decontamination [19] [20] .

The oxyhydroxides of the present study occur in soils, rocks, and sediments [21] where they are crystalline in nature; but when synthesized the crystallinity depends upon the preparation method [22] . Recently these compounds have shown being a considerable promise in environmental remediation, due to their chemical, surface, and structural properties [22] . Structurally, boehmite (γ-AlOOH) consists of Al(O,OH)₆ octahedral layers [22] . Goethite (α-FeOOH) is one of the most common oxyhydroxide and the structure includes FeO₆ octahedral units liked by corners, edges, or faces, so forming different structural arrays that remain even in amorphous state [23] . Manganite (γ-MnOOH) is composed of octahedral units of Mn³⁺O₆ that are edge and corner-shared forming a 1 × 1 tunnel in which hydrogen atoms reside [24] . The synthetic oxyhydroxides have a variety of technical applications, to mention a few, in pigments, electrochemical reactions, electrochromic materials, lithium batteries, and catalysis [25] . Adsorption capacities of these oxyhydroxides have also been studied regarding decontamination of aqueous solutions [26] - [28] and resulted in good adsorbents due to their high surface areas, surface reactivity, resistance to high temperature and radiation, structural flexibility, and relatively low cost.

The aim of this study was to evaluate the properties of the oxyhydroxides boehmite, goethite, and manganite, synthesized from different processing methods. Techniques such as XRD. SEM-EDS, FTIR, TGA-DSC, potentiometry, and N₂ physisorption isotherms allowed determining data on surface area, mean pore diameter, total pore volume, surface hydroxyl groups, zero point of charge, grain size, purity, thermo-stability, crystallinity, and surface fractal dimension. The relationship between that last parameter and the hydroxyl group content of these materials was explored.

The XRD patterns of the synthesized oxyhydroxides are shown in ( Figure 1 ). The boehmite powder synthesized by the sol-gel method presents peaks associated with the amorphous phase of γ-AlOOH (JCPDS card 21-1307); this result agrees with those found elsewhere [22] [34] . On the contrary, hydrolysis and oxidizing methods used for goethite and manganite, respectively, resulted in crystalline phases. The goethite diffractogram ( Figure 1 ) showed the phase of α-FeOOH (JCPDS card 81-0462) in agreement with Brigante et al. 2010 [35] , and Granados-Correa et al. 2011 [27] . Figure 1 showed as well the manganite diffractogram, corresponding to the phase of the γ-MnOOH (JCPDS card 41-1379), resulting like that reported by Chen et al. 2009 [36] .

Figure 2 shows the micrographs at 100x of the synthesized oxyhydroxides. The boehmite powder ( Figure 2(a) ) consists of irregular, smooth-surfaced grains with particle sizes between 10 and 200 μm. Goethite powder ( Figure 2(b) ), appears as irregular, large, and agglomerated particles, each grain of which is composed of very porous and fine particles of about 40 to 500 μm in size. The SEM examination of manganite powders ( Figure 2(c) ) showed flakes of irregular sharpness with a wide range of sizes, from 30 to 400 μm. EDX analysis of the oxyhydroxides revealed the presence of the characteristic metal of each material: in boehmite 29% Al, in goethite 61% Fe, and in manganite 65% Mn. The aluminum percentage of the synthesized boehmite is lower than expected by its chemical formula (45%). Alternatively, the experimental values of the metallic content of the two last materials are near to those of goethite and manganite (63% and 62% for iron and manganese, respectively). These differences may be imputed by synthesis methods.

Figure 3 shows the FTIR spectra of the oxyhydroxides; all of them show a strong band at around 3400 cm⁻¹ related to the stretching vibration of H₂O molecules or to the surface OH groups and additionally a band around 1600 cm⁻¹ is due to the OH groups [37] . The main bands of boehmite ( Figure 3(a) ) at 611 and 482 cm⁻¹, are attributed to the reflection in the angular plane OH-Al=O, while the band at 1072 cm⁻¹ corresponds to symmetric and asymmetric bending of AlOH [38] . For goethite ( Figure 3(b) ), the major bands are at 399 and 635 cm⁻¹, caused by Fe-O and Fe-O-OH bonds and in addition the bands at 796, and 839 cm^-1 correspond to OH⁻ groups [37] . Manganite spectrum ( Figure 3(c) ) shows peaks at 364, 447, 489, and 594 cm⁻¹ of the Mn-O vibrations [39] , the absorption band at around 2100 cm⁻¹ and those around 1000 cm⁻¹ - 1200 cm⁻¹ can be attributed to O-H modes, like γ-OH, δ-2-OH, and δ-1-OH [21] .

The goethite TGA curve ( Figure 4(b) ) shows a 1.48% weight loss between 10 to 160˚C due to the physical desorption of water and a second one (6.78%) upon heating to 160˚C. A third weight loss occurs at a temperature range of 350˚C - 540˚C due to the loss of structural hydroxyl groups [43] . The DSC curve ( Figure 4(b) ) shows several endothermic peaks. The first ones at 255.9 and 286.2˚C are due to dehydration and the conversion of goethite (α-Fe³⁺O (OH)) into hematite ((Fe³⁺)₂O₃) [44] , the following peak, above 400˚C, indicated the evolution from hematite to magnetite (Fe₃O₄) [45] . The manganite powder TGA curve ( Figure 4(c) ) presented four significant weight loss steps. The first one was small (about 1.4%) and occurred at 50˚C - 150˚C because of the surface water desorption [46] . The second one was observed between 160˚C - 340˚C (endothermic peak at 274.89˚C), indicating the structural conversion of Mn³⁺O (OH) into MnO₂. The third weight loss at 500˚C - 590˚C (endothermic peak at 437˚C) is associated to the MnO₂ conversion into Mn₂O₃ [47] . Finally, the exothermic peak at 550˚C is due to a transition from Mn₂O₃ to well-crystallized α-MnO₂.

The zero point of charge of the as-synthesized materials were 9.2 for boehmite, 12.4 for goethite, and 2.2 for manganite, respectively. When the material is in an aqueous solution of pH = pH_zpc the charge of its surface is neutral; but if the pH > pH_zpc the surface is negatively charged and on the contrary, it is positively charged if pH < pH_zpc. Therefore, this parameter describes the variations in electric charge that are responsible for the interaction between the material surface and the ions present in aqueous solution and so designates the electrostatic affinity to anions or cations depending on the pH of the solution [48] . According to the results, boehmite and goethite will have affinity through the anion adsorption [49] [50] . In contrast, manganite is suitable for cation adsorption [51] . The results of the surface hydroxyl group content for the as-prepared materials ( Table 1 ) show that goethite has the highest amount of hydroxyl groups per gram of material (1.7 meq OH⁻/g), whereas the values for boehmite and manganite were 1.16 and 0.855 meq OH⁻/g, respectively. The content of the hydroxyl group is considered as surface active sites for attracting ions in aqueous solution; thus, goethite has a large possibility of ion attraction on its surface.

Figure 5 shows the N₂ adsorption-desorption isotherms of the oxyhydroxides at 77 K. According to the International Union of Pure and Applied Chemistry (IUPAC), these materials presented type IV isotherms with hysteresis loop characteristic of mesoporous materials. The hysteresis of boehmite is larger than those corresponding to goethite and manganite. In general, these isotherm types are usually associated with materials in which monolayer-multilayer retention can occur.

Values of BET surface areas, mean pore diameters, and total pore volumes are in Table 1 . These values are within those previously reported for materials synthesized in similar conditions than the present ones [52] ; differences among the oxyhydroxides depend on the specific experimental conditions, like reaction times and temperature [27] . Values of the BET surface areas are bigger than 100 m²/g indicating that the oxyhydroxides are not highly crystalline [53] . According to the mean pore diameters, these materials may be classified as mesoporous (2nm < size < 50 nm); interestingly, the values of goethite and manganite are very close, which may be due to the similarity of their methods of synthesis.

Data of a N₂ adsorption-desorption isotherms at 77 K were used to obtain the adsorbed volume (V), the relative pressure (P_o/P), and V_m values by means of the following equation (1):

$\frac{P}{V\left(Po-P\right)}=\frac{1}{V_{m}C}+\frac{C-1}{V_{m}C}\left(\frac{P}{P_o}\right)$ (1)

Values of the slope and the ordinate of a linear fit of data ( Figures 6(a)-(c) ) allow calculate V_m ( Table 1 ). The corresponding to boehmite is higher than those to goethite and manganite. Next, Surface fractal dimensions D_f were calculated by the following equation (2) [6] .

$\ln \left(\frac{V}{V_m}\right)=cons\tan t+\frac{D_f-3}{3}\left[\ln \left(\ln \left(P_o/P\right)\right)\right]$ (2)

A plot of ln(V/V_m) as a function of ln(ln (P_o/P), in a certain range ( Figures 6(d)-(f) ) gives a straight line and based on the slope the surface fractal dimension D_f was calculated. The values of the surface fractal dimensions of boehmite, goethite and manganite are in Table 1 . The magnitude of D_f may be used for the surface description of a material [54] and is associated with the surface active sites and with the functional groups like hydroxyl among others that are available for chemical, physical, or mechanical interaction with anions or cations in aqueous solutions [55] . Data of Table 1 reveals that the surface geometry of these oxyhydroxides are rather smooth at a molecular scale [56] , i.e. their surfaces present scarce roughness.

Figure 7 displays a plot of hydroxyl group content as a function of the surface fractal dimensions, where linearity is observed. Ismail and Pfeifer (1994) [55] proposed a linear correlation between these parameters and the results obtained corroborate that proposal. The correlation between the active sites of a material directly depends on its roughness; the greater is this, the greater is the accessibility to the active sites. That property is very interesting in various processes, adsorption among others.

In this study, boehmite, goethite, and manganite powders were successfully synthesized, having different structural, morphological, and textural characteristics. XRD patterns revealed that goethite, and manganite were of crystalline structure and boehmite was rather amorphous. These differences were then attributable to the preparation methods; those synthesized by chemical reactions were crystalline, while the sol-gel method resulted in a rather amorphous compound. TGA-DSC curves indicated that these oxyhydroxides undergo structural changes associated, initially with dehydroxylation into the range from 100˚C to 300˚C and thereafter to phase conversions between 400˚C and 600˚C. SEM-EDX showed that the as-prepared oxyhydroxide materials have particles of sizes between 10 to 400 μm. N₂ physisorption measurements and N₂ adsorption-desorption isotherms demonstrated that the materials are fine mesoporous powders with high BET surface areas (380, 413, and 188 m²/g for boehmite, goethite, and manganite, respectively). Surface fractal dimensions showed that these materials were in the range from 1.4 to 1.7, indicating that their surfaces are lightly rough; the uniformity or dissimilarity of pore sizes depends on the grade of surface irregularity of the material. Interestingly the surface hydroxyl group content linearly correlated with the surface fractal dimensions. From which it is inferred that the greater the fractal dimension, and therefore the roughness of the material, the greater the possibility that the OH⁻ groups will be found on the surface. According to the zero point of charge concept, boehmite, and goethite have affinity for anions in aqueous media, whereas manganite, which showed a low value (pH_zpc = 2.2) may have preference for cations. Therefore, the results indicate that the obtained materials possess different physicochemical characteristics for be used as effective adsorbents of contaminants in aqueous media.

The authors acknowledge the financial support of ININ (Project QU-001), and the technical assistance of Iris Zoet López-Malpica and Elvia Moreno-Morales.