An overall pore distribution was attained using non-local density function theory (NLDFT). Using NLDFT on N2 adsorption isotherm at 77 K resulted in a pore size above 12 A, but if the same is applied on CO2 adsorption isotherm at 273 K, pore size below 12 A is obtained. Overall distribution is achieved by combining both of them and large micropore widths in 14.7 and 18.5A (this implies that carbon narrow micropore widths in regions of 3.5, 4.8, 5.2 and 8.2 A). However, there was no significant mesopore contribution noticed during the analysis of pore size distribution. The pore volume of carbon in total is the 0.412cm3/g, and overall size of the particle ranged from few microns to few hundred microns. Scanning microscopic electron images are illustrated in various magnification levels. These images verified that carbon has different sizes of macroporosity consisting 1-10um and 500-699nm.

Figure 2(c) confirmed the existence of a sorted array of the main porous units of approximately 1um width. These pores are important in developing kinetics of adsorption. Probably, the pores were created by the action of KOH or P (C6H5)3 or both. Figure 3 shows thermogravimetric for carbon in the nitrogen atmosphere. It lost around 60% of its mass up to the 10000C Level, and the greater part of these masses could be oxygen and phosphorous functionality. The loss is mostly observed in 800 to 10000C region. One carbon contains approximately 0.9 0.3 at percentage phosphorous. The two deconvoluted peaks appear at energy levels of 132.20 eV and 133.78 eV, which are slightly lower than 132.51 eV and 134.25 eV as seen in literature. These higher energy peaks are attributed to the high oxidation states of phosphorous 39, iii, iv while lower energy peaks are mostly attributed to abound of phosphorous formed on the carbon surface. Therefore, XPS detected C-P-O as the only phosphorus functionality. The virtually lower content of phosphorous found in the carbon matrix is also common in literature, compared to other heteroatoms since it was measured using XPS,, NOTEREF _Ref347862973 \h \* MERGEFORMAT 39, NOTEREF _Ref347915659 \h \* MERGEFORMAT 41 its quantity varied around 0.26 to 1.84 at.%. The remaining significant contributions evidently originated from carbon and oxygen. Different carbon functionalities that were present in the systems include; C- sp2, C-sp3, C-O/C-N and C=O/COOH/O-C=O and had quantitative contributions in ranges of 68.5, 7.8, 1.0 and 0.8 %, respectively. Key oxygen functionalists were C-O/OH/N=O with a quantitative contribution of 10.1 at. % and C-O-H which had a quantitative contribution of 4.1%. Oxygen functionality was derived on the carbon surface from both KOH and original carbon precursor during activation together with other elements such as Na, K, and traces of Mg. Potassium apparently originated from KOH while the other elements most likely came from porcelain boat during carbonization process. An XPS analysis was also carried on neodymium (Nd), and dysprosium (Dy) adsorbed carbons.

Recovery

Neodymium (Nd), dysprosium (Dy) and iron (ferric, Fe3+) equilibrium adsorption in an aqueous stage were done together with their corresponding nitrate salts with a maximum concentration of 500 ppm (corresponding molarity: Nd: 2.42 mM, Dy: 2.15 mM, Fe: 6.26 mM). Figure 5 illustrates equilibrium adsorption isotherms of the metals while iron adsorption isotherm is magnified in the inset of the same figure. It can also be observed that Nd and Dy displayed similar adsorption behavior including their overall adsorption capacity, which was 335.5 mg/g for Nd and 344.6 mg/g, for Dy (corresponding to 3.46 and 3.96 mmol/g for Nd and Dy, respectively). These two demonstrated a very linear adsorption behavior (Henrys law type behavior). Iron adsorption was however very low. Its adsorption isotherm displayed a linear nature up to 300 ppm then a relatively sharper rise to about 47.6 mg/g. When the overall uptake of iron is compared to Nd and Dy, it remained one order of magnitude lower.

The equilibrium adsorption of Nd and Dy is observed to be higher than that of many adsorbents described in the literature. These values are orders of magnitude that are greater in some cases. Neodymium adsorption was as high as ca. 300 mg/g in magnetic nano-hydroxyapatite at an equilibrium concentration of 200 ppm (Naser et al.). Used impregnated organophosphorus resulted in Nd absorption of 4.96 mg/g together with a composite of silica-based urea-formaldehyde. The carboxylic acid-functionalized porous aromatic structure illustrated the Nd adsorption uptake of more than 2mmol/g. As reported by Moriwaki et al., an equilibrium uptake of Nd and Dy was not more than ca. 3 mmol/g in freeze-dried microbial strains and the adsorption was 50-80 mg/g in both DTPA and EDTA-functionalized chitosan biopolymers. A marked mesoporous silica demonstrated Dy uptake of 22.33 mmol/g. As reported in literature other phosphorous functionalized materials showed Dy uptake of 40-52 mg/g.

The three equations mentioned below were used to model the equilibrium adsorption isotherm. In these models, qe is adsorption amount (mg/g), and Ce is the initial concentration of the metal solution (ppm). According to the linearity of isotherms, the first evident model is Henrys law isotherm, which is given by;Where K is a constant in Henrys law, and it is calculated by the linear regression of qe versus Ce data, via the origin.A Freundlich isotherm model is given by;Whereby, k and n are constants of the model and can be calculated by linear regression of ln (qe) versus ln (Ce). am, b and n are Sips constants and they are calculated by using solver technique.

Where am, b and n are Sips constants and they are calculated using solver technique.

Table 1 gives isothermic constants for Nd and Dy The kinetics of a typical earth adsorption was examined by analyzing the adsorption amounts of Nd and Dy for 500-ppm concentration only and in the interval of 30 sec, 2 min, 15 min, 40 min, 1 hr, 2 hrs, 3 hrs and 4 hrs as illustrated in figure 6. An observation was made that Nd and Dy showed different kinetic behavior. Dy adsorption was rather quick completing over 67 % of total adsorption in 2 mins only, while rest of the adsorption took 4 hours to complete. Adsorption of Nd was however quite sluggish, taking about an hour to complete 67 % of total adsorption and rest of the adsorption took place within the remaining 3 hours. Amusingly, total adsorption quantity of both metals remained same. This supports the equilibrium adsorption study as shown in figure 5. Both rapid adsorption of Dy and sluggish adsorption of Nd can also be observed in different past studies discussed in this article.

The metal adsorption method on permeable adsorbents takes place in four stages;Bulk diffusion-this involves migration of metal ions from bulk of the solution to the propinquity of carbon

(b) Diffusion of metal ions in the boundary layer on the carbons surface

(c) Intra-particle diffusion- transportation of metal ions from the surface of carbon to the pores

(d) Chemical adsorption at the active sites of carbon. Intra-particle diffusion can be represented as:

Where (qt) is the amount adsorbed at a given time (t). (Kid) is the intra-particle pace constant (mg g-1min-1/2). Intra-particle diffusion acts as the single limiting step if a linear regression of Qt versus t1/2 passes through the origin. For Nd alone, this type of linear regression passes through the origin, giving rise to a Kid value of 24 mg g-1min-1/2 (R2 value of 0.93). It is noted that the slow intra-particle diffusion might be the primary reason for slow diffusion of Nd.

The pseudo first order rate equation is provided by:

Where k1 represents a rate constant of pseudo first order, and it is calculated by a linear regression of against t plot.

Alternatively, pseudo second order rate constant is given by:

Where k2 is a rate constant of the pseudo second order can be calculated by linear regression of against t plot. It is also observed that rate constant of the pseudo first order fits accurately with R2 value ~0.90-0.91. Nonetheless, pseudo-second order rate equation fits perfectly well both Dy and Nd with R2> 0.99. Table 2 demonstrates both the rate constants for Nd and Dy. Besides, micropore diffusion in an adsorbent matter can be modeled using the following equation,

Where is mass adsorbed during time t and is the final adsorption amount is intra-crystalline diffusivity in micro-pores and is an equivalent crystal radius. is also known as the diffusive time constant and can be determined by the linear regression of versus t. The diffusive time constant of Nd is 0.70x10-5 s-1 while that of Dy is 1.01x10-5 s-1, rapid kinetics of Dy is apparently supported by its faster diffusive time constant.

PH values of 2, 4 and 6.1 (Nd) or 6.6 (Dy) were used to investigate the dependence of solution PH on the adsorption of Nd and Dy the results are displayed in figure 7. The solutions were fixed at the strength of 500 ppm on the metal and regulations on PH were performed by adding suitable amounts of 36 M HCl to the solution. The pH values of 6.1 (for Nd) and 6.6 (for Dy) were attained by directly mixing metal salts without any additional adjustments. The results implied that dependency of both Nd and Dy adsorption on solution pH is irrelevant. Such a trend presents an outstanding advantage of these adsorbents over other adsorbents previously described in the literature since most of them revealed lower adsorption at lower pH NOTEREF _Ref346897841 \h \* MERGEFORMAT 13, NOTEREF _Ref347941711 \h \* MERGEFORMAT 33, NOTEREF _Ref346976927 \h \* MERGEFORMAT 25, NOTEREF _Ref348292895 \h \* MERGEFORMAT 26. These values lie between ca. 6000 to 679 mL/g for Dy and 1223 to 215 mL/g for Nd. Due to low the adsorption, distribution coefficients for Fe are within 187 to 126 mL/g within the same original concentration. One order of magnitude difference in allocation of coefficients between Fe and Nd or Dy signifies the possible separation between them. Distribution coefficient values of Nd and Dy are higher compared to those reports available in the literature, especially at lower pH. Kd values for Nd and Dy were ca. 175 and 25 mL/g in imprinted mesoporous silica. These values were about 500 to 900 for Nd and Dy in microbial strain-based adsorbents. In DTPA chitosan-based sorbents, the maximum Kd values for Nd and Dy reached about 10,000, but when PH dropped below 2, it rapidly fell below 1000. Adsorption consistency, irrespective of solution pH for adsorbents, however, suggests a much higher distribution coefficient at low pH levels. The Kd value for Nd at high pH was reported to be higher than ca. 30,000 mL/g In carboxylic acid functionalized porous aromatic framework, but it also fell below 20 at a pH lower than 2. In a surface customized porous silica KIT-6, the distribution coefficients for Nd and Dy in the combination of REEs were reported to range from 4000 to 4500 mL/g.

The enhancement factor can be defined, as the ratio of moles of the preferred component in the adsorbed stage over moles a same component in the remaining solution after adsorption at equilibrium. This enrichment factor is, therefore, a function of initial concentration of the metals (REEs). As described in figure 9(a), it is evident that the highest enrichment factors are achieved at the lowest concentration of 50 ppm with values of 6300 for Nd and 11800 for Dy. At the high concentration, enrichment factors drop and remain at a stable value of 670 for both Nd and Dy.

The selective nature of component 1 over component 2 is defined as,

Where component 1 is the preferred adsorbent while component 2 is non-preferred adsorbate, x and y are adsorbed and bulk phase concentration in moles at equilibrium. Ideal Adsorbed Solution T...

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