Isotherms, Kinetics, and Thermodynamics of NH 4 + Adsorption in Raw Liquid Manure by Using Natural Chabazite Zeolite-Rich Tu ﬀ

: The search for safer and sustainable management of animal manure is a global and topical challenge, in particular for the reduction of nitrogen (N) content. The use of natural adsorbents as zeolite-rich tu ﬀ s is recognized as a valid method to recover N, in the form of ammonium (NH 4 + ), from animal manure. While the scientiﬁc literature is rich in studies performed on synthetic solutions and using clinoptilolite zeolites as adsorbent, it lacks information concerning adsorption in real liquid manure and using other types of zeolite-rich tu ﬀ s (e.g., chabazite). This work aims at exploring the NH 4 + adsorption process from raw liquid swine manure, using a chabazite-rich zeolite tu ﬀ as adsorbent. The e ﬀ ects of temperature, contact time, and grain size have been assessed. kinetic models, and thermodynamic parameters have been investigated. Harkins-Jura isotherm correlates well with the observed data, in accordance with the formation of an adsorption multilayer. Kinetic data have been explained by intraparticle di ﬀ usion and pseudo-second-order models. In conclusion, the natural chabazite tu ﬀ has proven to be a valid material for NH 4 + adsorption from raw liquid swine manure. In particular, to reach the highest adsorption capacities and adsorption rates, it is recommended to use it at a ﬁne particle size and with dosages < 6 %.


Introduction
The intensification of agricultural activities to meet the increasing demand for food and agricultural products is leading to rapid soil degradation and severe environmental problems like GHG emissions and water pollution. The Food and Agriculture Organization of the United Nations (FAO) has declared that "to satisfy the expected food and feed demand, it will require a substantial increase of global food production of 70 percent by 2050, involving an additional quantity of nearly 1 billion tons of cereals and 200 million tons of meat" [1]. Intensive farming brings huge quantities of chemical and organic fertilizers in the soil every year to improve productivity, but this massive amount of nutrients are inefficiently exploited by plants and they are largely lost in the environment [2,3]. The need to improve fertilizer use efficiency (FUE) thus represents one of the major challenges for the upcoming years and it is essential for achieving more sustainable agriculture.
Another global challenge that we are forced to face in the immediate future is the increasing demand for meat, which is rising according to the economic growth of countries like South America, India, and China. As a direct consequence of increased meat demand, large amounts of zootechnical Water 2020, 12, 2944 2 of 16 wastewaters rich in nitrogen (N) and phosphorous (P) are produced every year and often used as organic fertilizer, with a strong impact on climate and environment [4][5][6]. The environmental pollution resulting from the release of large quantities of nutrients in the soil, water, and atmospheric compartments is generically termed "nutrient pollution". It affects the quality of soil, underground and surface waters, their ecosystems, the climate (due to the emissions of N-based GHG and harmful gases such as N 2 O, NH 3, and NO x ), the human health, and the economy [7][8][9].
It is thus mandatory to develop proper management practices that aim at reducing the nutrient load of zootechnical wastewaters before application in the soil to improve the FUE and reduce nutrient pollution.
A valid methodology for the reduction and recycling of N consists of the so-called "Integrated Zeolitite Cycle" (IZC). The IZC promotes the use of natural materials as zeolite-rich tuffs (ZRT) in agricultural contexts, as agent for the removal of ammonium ions (NH 4 + ) dissolved in animal liquid manure, and their subsequent use as soil amendments [10][11][12]. ZRT are volcanic rocks containing more than 50% of zeolite minerals [13]. Zeolites are aluminosilicate minerals with an open 3D-structure formed by linked tetrahedra of [SiO 4 ] 4− and [AlO 4 ] 5− , which constitute their primary building units. The replacement of Si 4+ by Al 3+ induces a negative charge in the zeolite framework, which is compensated by the presence of extra-framework cations (counterions). These cations can be exchanged by other cationic species present in the surrounding aqueous solution [14,15]. This process, called ion-exchange, is mainly governed by charge neutrality and by diffusion dynamics [16]. In addition to cations, large quantities of water molecules surrounding these ions (so-called hydration spheres) can also enter the pore structure, allowing zeolites great hydration and dehydration capacity. Many studies published in recent years have shown how the application of ZRT in the soil brings important positive effects like the increase of FUE and the reduction of gaseous and leaching N losses [17][18][19][20][21]. Within natural zeolites, clinoptilolite is one of the most abundant and studied and, thanks to its adsorption and ion exchange properties, it finds application in numerous contexts such as water and wastewater treatment, agriculture [22], and the medical field [23]. Another important type of zeolite, however abundant and distributed throughout the world, is chabasite, which is not yet sufficiently studied and used, although it represents a valid alternative to the better-known clinoptilolite. Due to its high cation exchange capacity (CEC), chabasite has an excellent potential for applications like water and wastewater treatment, even greater than clinoptilolite (theoretical CEC of clinoptilolites varies between 2.0 and 2.6 meq gram −1 , while CEC of chabazite is generally between 2.5 and 4.7 meq gram −1 [24]).
Moreover, while adsorption of NH 4 + has been largely investigated in synthetic solutions (especially (NH 4 ) 2 CO 3 and NH 4 Cl) [25][26][27][28][29][30][31][32] and, to a limited extent, also in anaerobic digestates (using NaCl-modified clinoptilolite) [33], as of today there are no studies that provide a detailed characterization of NH 4 + adsorption (isotherms, kinetics, and thermodynamics) in real animal liquid manure by using chabazite ZRT. Wasielewski et al. [26] proposed a possible guideline for the determination of NH 4 + adsorption processes from high concentrated wastewaters by clinoptilolite ZRT. In this paper, we present a series of experiments in which we followed a similar protocol to characterize the isotherms, kinetics, and thermodynamics of NH 4 + adsorption using a chabazite ZRT in real animal liquid manure.
The experiments included the evaluation of temperature, contact time, and particle size effects.
Both CHAµ and CHAg were dried at 105 • C for 24 h to eliminate the gravimetric water before the beginning of the experiments.
Liquid pig manure was obtained from a pig farm located near Rovigo (Italy). Immediately after sampling, the liquid manure was centrifuged at 4000 rpm for 8 min to eliminate the coarser fraction. The supernatant was collected to obtain the liquid phase to be tested in the experiments (centrifuged swine manure, CSM). Initial CSM pH and [NH 4 + ] were 8.07 ± 0.03 and 3140 ± 45 mg L −1 , respectively (measured in 4 replicates; see Section 2.2 for analytical techniques used).

Analytical Techniques
[NH 4 + ] was measured in a dilution ratio of 1:20 CSM/Milli-Q water, using an Ion-Selective Electrode (ISE) Orion 95-12. Solution pH was measured using an Orion 9102BNWP pH-meter. Both ISE and the pH-meter were connected to an Orion 4star pH-ISE benchtop (Thermo Fisher Scientific, Waltham, MA, USA).

Isotherms
Equilibrium experiments aimed at evaluating the Isotherm models for CHAµ and CHAg at three different temperatures (13,20, and 37 • C).
Different quantities of CHA (0.5, 1, 1.5, 3, 5, 8, and 12 g) were mixed with 50 mL of CSM inside closed plastic bottles (50 mL) in three replicates and stirred with an orbital shaker at 200 rpm for 20 h to reach the equilibrium condition. Many studies have reported that NH 4 + sorption by zeolites is affected by pH without significant differences in the range 2-8 and with an immediate decrease at pH > 9 [35,36]. In real conditions it is preferable not to control the pH using chemical buffers added to the wastewater and, since pH barely varied between 8.07 and 8.48 from the beginning of the experiment to the equilibrium conditions, we decided to neglect the pH effects and not to buffer the CSM. The possible air stripping effects and/or adsorption onto plastic parts of the bottles were taken into account in the experiments, providing blanks with only CSM and without the addition of zeolite. After 20 h of shaking, the samples (CSM + CHA and blanks) were centrifuged at 4000 rpm for 8 min to separate the solid phase from the liquid. NH 4 + equilibrium adsorption capacity (q e , mg g −1 ) was determined in the supernatant by Equation (1) [26]: where C 0 (mg L −1 ) is the initial NH 4 + concentration, C b (mg L −1 ) is the NH 4 + concentration in blanks after 20 h, C e (mg L −1 ) is the concentration at equilibrium, V (L) is the volume of CSM, and m (g) is the mass of the sorbent.

Kinetics
The aim of the kinetic experiments is the determination of NH 4 + sorption kinetic models for CHAµ and CHAg at a temperature of 20 • C. A specific quantity of CHA (0.2 g per mg NH 4 + -N L −1 ; Water 2020, 12, 2944 4 of 16 123 g, as indicated by Wasielewski et al. [26]) was added at 0.5 L of CSM and mixed at a constant temperature of 20 • C at a speed of 400 rpm for 420 min. An aliquot of 10 mL was taken at periodic intervals (5,10,20,30,45,60,120,180,270,360, and 420 min) and immediately centrifuged at 4000 rpm for 4 min to separate the solid from the liquid fraction and stop the sorption processes. The batch volume was continuously reduced due to sampling, but it can be assumed that no changes in the ratio of sorbent mass to the volume of CSM occurred because of the homogeneity of the mixture [26]. Experiments were carried out in triplicate and a batch without zeolite (blank) was also included to evaluate air stripping effects. [NH 4 + ] at time t (C t , mg L −1 ) and pH were measured in a dilution ratio of 1:20 with Milli-Q water. The time-dependent NH 4 + adsorption capacity (q t , mg g −1 ) was calculated by Equation (1) replacing q e and C e with q t and C t , respectively. The evaluation of q e is important in kinetic analyzes to test the validity of the kinetic models applied [37], thus we have considered that a "near-equilibrium" condition was achieved at 420 min from the beginning of the experiment. It is therefore assumed that q t,420 q e .

Equilibrium Isotherms Modelling
The adsorption data were fitted with six different models using the software R Studio [38] with the packages PUPAIM [39] and SorptionAnalysis [40]. Within all the tested equations (Harkins-Jura, Freundlich, Langmuir, Temkin, Fritz-Schlunder, and Dubinin-Radushkevich) we selected the three models that have shown the best correlation with the experimental data, based on R 2 and p-values. The best models were Harkins-Jura, Freundlich, and Langmuir.

Harkins-Jura Isotherm
Harkins-Jura isotherm has been originally proposed for explaining the adsorption of gas molecules, but it has been extended also to liquid-solid systems [41]. It assumes the possibility of multilayer adsorption on the surface of adsorbents having a heterogeneous pore distribution [42]. It has been applied also for a ZRT to describe the adsorption of α, β, and γ-picoline from an aqueous solution [43]. The linear form of the Harkins-Jura model may be expressed by Equation (2) [44]: where q e is the equilibrium adsorption capacity (mg g −1 ), C e is the equilibrium concentration of the sorbate in the liquid phase (mg L −1 ), and α and β are constants, in particular, α is the intercept and β is the slope which is linked to the specific surface area (S) by Equation (3) [41]: where q is a constant dependent on the nature of the adsorbate, R is the universal gas constant, T is temperature and N is the Avogadro number.

Freundlich Isotherm
The Freundlich isotherm is an empirical model that can be used to explain the equilibrium relation between the sorbent and the sorbate for heterogeneous surfaces and in the case of multilayer adsorption [45]. It has been widely used in gas adsorption and environmental soil chemistry [46]. According to Freundlich, the equilibrium adsorption capacity q e (mg g −1 ) can be calculated by Equation (4): Water 2020, 12, 2944 where K F is the Freundlich constant (L g −1 ), C e is the equilibrium concentration (mg L −1 ) and n is constant at a given temperature and it is dependent on the nature of the adsorbate and the adsorbent. A linear form of this expression is given, e.g., by [47] (Equation (5)):

Langmuir Isotherm
The Langmuir model [48] assumes that only one layer of the adsorbate is formed (monolayer assumption) and that the energetic properties of the adsorption sites are equivalent. Due to the formation of a monolayer, the Langmuir model provides a "flat" region which permits the determination of the maximum adsorption capacity q max (mg g −1 ) (Equation (6)): where q e is the equilibrium adsorption capacity (mg g −1 ), K L is the Langmuir constant (L mg −1 ) and C e is the concentration at equilibrium (mg L −1 ). A linear form of this expression is given, e.g., by Equation (7) [26]:

Kinetic Models
Adsorption involves multiple processes as (i) diffusion across the liquid phase near the solid surfaces, (ii) diffusion through the pore structure of the sorbent (Intraparticle Diffusion, ID), and physical and chemical bonding on the solid surfaces [49].
Kinetic data were analyzed using the Pseudo-First-Order, Pseudo-Second-Order, Intraparticle Diffusion, and Elovich equations. As pointed out by [37], for kinetic investigations it is appropriate to take into account only data sufficiently far from equilibrium, and for this reason only data with a fractional uptake F(t) < 85% were considered. F(t) was calculated by Equation (8) [37]:

Pseudo-First-Order
The Pseudo-First-Order model (PFO), proposed by [50] can be described in its linear form by Equation (9) [51]: where q e and q t are the equilibrium adsorption capacity and the adsorption capacity at time t (mg g −1 ); in particular (q e −q t ) has been called "driving force" [52] and is proportional to the available fraction of active sites. t is the contact time (min) and k 1 is the PFO rate constant (min −1 ). If kinetic data are explainable with the PFO model, the plot of ln(q e −q t ) against t describes a straight line with a slope equal to −k 1 /2.303 and an intercept equal to ln(q e ) [53].

Pseudo-Second-Order
The Pseudo-Second-Order equation (PSO) can be expressed in linear form by Equation (10) [54]: where t is time (min), q t is the time-dependent adsorption capacity (mg g −1 ), q e is the equilibrium sorption capacity (mg g −1 ) and h is the initial adsorption rate (mg g −1 min −1 ).
The PSO rate constant k 2 is obtainable by Equation (11) [54]: All the parameters are experimentally determinable from the slope and the intercept of plot t/q t against t [55-57].

Intra-Particle Diffusion
The intra-particle diffusion (ID) equation describes a diffusion-controlled process [58,59] using Equation (12) [26]: where K ID is the intra-particle diffusion rate constant. Plotting q t against t 0.5 gives a linear correlation where the intercept C is proportional to the thickness of the boundary layer [57], and the slope is equal to K ID . If C 0, it can be assumed that sole intra-particle diffusion occurs [26]. If the experimental data shows the presence of two or more separate regions, a multistage diffusion process is present where the first step represents the external surface adsorption and/or macropore diffusion [57].

Elovich Kinetic Model
The Elovich equation was historically applied to determine the kinetics in the chemisorption of gases onto heterogeneous solids [52,60]; starting twenty years ago, the Elovich model has been applied to describe the adsorption process of different pollutants from aqueous solutions [61,62]; in 2004, Cortés and Martinez [63] applied this model on natural zeolites, to describe the sorption kinetics of cadmium (II) from solution. The model can be described by Equation (13) [53]: where q t is the time-dependent sorption capacity, a and α are constants, and, in particular, α corresponds to the initial adsorption rate. A linear form is given by Equation (14) [54]: Using the dimensionless Elovich model (Equation (15)) it is possible to calculate R E which is an approaching-equilibrium parameter representing the velocity of the system to arrive at equilibrium conditions [64]: where t ref is the longest operating time in the adsorption process (min) and q ref is the amount of adsorption at time t = t ref (mg g −1 ).
The thermodynamic equilibrium constant (K e ) is the ratio of q e against C e when C e tends to zero (Equation (16)) and it is possible to obtain by plotting q e /C e against C e and extrapolating the value of the intercept at C e = 0 [65]: Analyzing the variation of K e with temperature, it is possible to obtain the change in standard enthalpy (∆H, J mol −1 ) and the change in standard entropy (∆S, J K −1 mol −1 ) through the application of the van 't Hoff isochore (Equation (17)) [27]: where R is the universal gas constant (J K −1 mol −1 ) and T is the temperature (K). ∆H and ∆S may be obtained by the linear regression of ln(K e ) against 1/T, whose slope is equal to −∆H/R and its intercept is equal to ∆S/R) [26]. It is important to note that ∆H and ∆S are independent of temperature. The Gibbs free surface energy change (∆G, J mol −1 ), was then determined by the application of two approaches: Equation (18) and the Gibbs-Helmholtz equation (Equation (19)). The values obtained by the two methods were slightly different and these differences were due to the previous linear regression steps.

Isotherms
The plots of q e against C e are reported in Figure 1. All the parameters of Harkins-Jura, Freundlich, and Langmuir isotherms are reported in Table 1.
Analyzing the variation of Ke with temperature, it is possible to obtain the change in standard enthalpy (ΔH, J mol −1 ) and the change in standard entropy (ΔS, J K −1 mol −1 ) through the application of the van 't Hoff isochore (Equation (17)) [27]: where R is the universal gas constant (J K −1 mol −1 ) and T is the temperature (K). ΔH and ΔS may be obtained by the linear regression of ln(Ke) against 1/T, whose slope is equal to −ΔH/R and its intercept is equal to ΔS/R) [26]. It is important to note that ΔH and ΔS are independent of temperature.
The Gibbs free surface energy change (ΔG, J mol −1 ), was then determined by the application of two approaches: Equation (18) and the Gibbs-Helmholtz equation (Equation (19)). The values obtained by the two methods were slightly different and these differences were due to the previous linear regression steps.

Harkins-Jura Freundlich Langmuir
CHAµ The shape of the curves in the first region of the graphs indicates that, as more exchange sites are occupied by NH 4 + , it becomes increasingly difficult for other NH 4 + in solution to find and substitute exchangeable counterions. The presence of a semi-flat region, located in the middle of the graphs, means that a saturation condition is beginning to occur associated with the formation of an adsorption monolayer but, since the end of the curve rises again, it demonstrates a renewed availability of exchange sites for NH 4 + adsorption [66]. This behavior was observed for both CHAµ and CHAg and it starts approximately when 3 g of ZRT was added to 50 mL of CSM (6 wt%). The formation of more than one adsorption layer is not in agreement with the Langmuir monolayer assumption [44] because the Langmuir model assumes the existence of a horizontal asymptote that determines the maximum adsorption capacity, q max . R 2 values have in general shown worse correlations for Langmuir compared to the other isotherm models.
The Freundlich model is commonly utilized to explain adsorption for heterogeneous materials. n is a heterogeneity parameter that, if higher than 0, indicates surface heterogeneity [67]. For all the isotherms investigated in CHAµ and CHAg, n is greater than 0 demonstrating the heterogeneous nature of the adsorption surfaces. It is likely to expect a certain degree of inhomogeneity in the adsorbent because the used ZRT is a natural material with significative differences both in particle size and in its mineralogy (see Section 2.1). Freundlich isotherms assume an asymptotic maximum, without reaching a maximum adsorption capacity (q max ), as for the Langmuir model, but the isotherms in Figure 1 do not tend to linearize in the right portion of the graph, suggesting that the Freundlich equation cannot explain in this case the experimental observations.
The applicability of Harkins-Jura is demonstrated by obtaining straight lines in the plot In(C e ) against 1/q e 2 . Within the model tested, the best R 2 values were in general obtained with the Harkins-Jura isotherm ( Figure 2, Table 1). Within the Harkins-Jura model, two distinct straight lines can be obtained, whose intersection point corresponds to the completion of the adsorption monolayer [41]. Here, two distinct lines have not been clearly observed, but the points of some isotherms, as CHAg 13 • C and CHAg 37 • C, tend to flex downward in the rightmost part of the graph ( Figure 2B). Their flexion corresponds to an equilibrium concentration C e ≈ 2700 mg L −1 , which represents a condition where the monolayer is "almost complete" and, beyond which, an adsorption multilayer is developed allowing a rapid increase in the adsorption capacity q e ( Figure 1B).
Water 2020, 12, x FOR PEER REVIEW 9 of 16 Regarding the effects of temperature on the NH4 + adsorption at equilibrium, the isotherms of CHAμ are very close to each other, indicating that there is not a significative temperature effect for CHAμ (Figure 2A). On the other hand, CHAg sorption was much more dependent on temperature ( Figure 2B) and the best adsorption performances occurred at 20 °C whereas the worst occurred at 13 °C. Therefore, from the experimental data, it seems that temperature has increasing effects on NH4 + adsorption as the particle size increases. An explanation of this phenomenon is particularly difficult to provide with the collected data, taking also into account that, to the best of the author's knowledge, CHAµ (Figure 2A). On the other hand, CHAg sorption was much more dependent on temperature ( Figure 2B) and the best adsorption performances occurred at 20 • C whereas the worst occurred at 13 • C. Therefore, from the experimental data, it seems that temperature has increasing effects on NH 4 + adsorption as the particle size increases. An explanation of this phenomenon is particularly difficult to provide with the collected data, taking also into account that, to the best of the author's knowledge, there are no scientific publications yet on how temperature affects adsorption on different particle sizes. Alshameri et al. [68] has observed ambiguous effects of temperature on NH 4 + adsorption by a natural clinoptilolite. The NH 4 + removal increased from 25 to 35 • C, but it decreased from 35 to 45 • C.
Here also the effect of temperature on CHAg is ambiguous, but it is clear that the worst adsorption capacities were reached at the lower temperature (13 • C).

Kinetics
Kinetic parameters calculated from PFO, PSO, and Elovich equations are reported in Table 2 while q t versus t, PSO, and Elovich graphs are reported in Figure 3.  The PSO model showed high R 2 values, but qe calculated (qe,2) are quite different from the measured values, thus kinetics can not be explained using the PSO equation. The Elovich model has shown a good correlation with the experimental data, in particular regarding CHAg. RE values indicate that the velocities of the systems to reach an equilibrium condition are different between the two different particle sizes. In particular, CHAg approaches equilibrium conditions more slowly than CHAμ [64]. A plausible explanation for the differences observed in adsorption velocities between the two particle sizes may relate to the structural differences derived from the grinding process that, undoubtedly, increased the specific surface area of CHAμ compared to CHAg and compromised, at least in part, the intercrystalline macroporous structure of the tuff. The grinding process which CHAμ has undergone did not destroy the porous structure of the zeolite because, even if it is a micro-sized material, the size of CHAμ was about 10 3 times larger than the average diameter of the micropores of chabazite [69]. It is instead plausible that the crushing process has exposed to the environment a larger number of openings into which NH4 + can easily enter, increasing the ion-exchange probability for a given NH4 + ion in solution and explaining CHAμ's higher adsorption rates than CHAg. . Kinetic graphics; full dots are data with F(t) < 85%, thus they have been considered in kinetic analyzes; empty dots are data with F(t) > 85%, thus they were not taken into consideration: (A) qt against t plot for CHAμ and CHAg; the curve indicates the general trend with respect to time; (B) PSO plot (t/qt against t) thinner lines are representing the trend of all data; straight regression lines are the PSO linear equations (Equation (10)); (C) Elovich plot (ln(t+t0) versus qt); straight lines represent the Elovich linear equation (Equation (14)).
Diffusion dynamics of NH4 + has shown different behaviours when comparing CHAg and CHAμ ( Figure 4); in particular, the ID plot for CHAμ has shown only a straight line with an intercept C ~ 4, Figure 3. Kinetic graphics; full dots are data with F(t) < 85%, thus they have been considered in kinetic analyzes; empty dots are data with F(t) > 85%, thus they were not taken into consideration: (A) q t against t plot for CHAµ and CHAg; the curve indicates the general trend with respect to time; (B) PSO plot (t/q t against t) thinner lines are representing the trend of all data; straight regression lines are the PSO linear equations (Equation (10)); (C) Elovich plot (ln(t+t 0 ) versus q t ); straight lines represent the Elovich linear equation (Equation (14)).
To verify the goodness of PFO and PSO models, in addition to the evaluation of R 2 , it is necessary also to make a comparison between the q e calculated by the models and the q e experimentally measured.
In kinetic experiments, a "close-to-equilibrium" condition was assumed at t = 420 min (see Section 2.3.2) and the q e measured were 8.74 and 6.37 mg g −1 for CHAµ and CHAg respectively.
The PSO model showed high R 2 values, but q e calculated (q e,2 ) are quite different from the measured values, thus kinetics can not be explained using the PSO equation. The Elovich model has shown a good correlation with the experimental data, in particular regarding CHAg. R E values indicate that the velocities of the systems to reach an equilibrium condition are different between the two different particle sizes. In particular, CHAg approaches equilibrium conditions more slowly than CHAµ [64]. A plausible explanation for the differences observed in adsorption velocities between the two particle sizes may relate to the structural differences derived from the grinding process that, undoubtedly, increased the specific surface area of CHAµ compared to CHAg and compromised, at least in part, the intercrystalline macroporous structure of the tuff. The grinding process which CHAµ has undergone did not destroy the porous structure of the zeolite because, even if it is a micro-sized material, the size of CHAµ was about 10 3 times larger than the average diameter of the micropores of chabazite [69]. It is instead plausible that the crushing process has exposed to the environment a larger number of openings into which NH 4 + can easily enter, increasing the ion-exchange probability for a given NH 4 + ion in solution and explaining CHAµ's higher adsorption rates than CHAg.
Diffusion dynamics of NH 4 + has shown different behaviours when comparing CHAg and CHAµ  In the first region of the CHAg plot ( Figure 4B), which represents about the first 60 min of contact with CSM, the intercept value is near zero (C = 0.17), demonstrating that the adsorption was mainly governed by ID process. During the first hour, external-surface adsorption and macropore diffusion occurred and a thin boundary layer has developed, as indicated by the low value of C = 0.17 which is proportional to the thickness of the boundary layer [57]. After one hour, adsorption layers thickened significantly (C = 2.24) and NH4 + penetrated more slowly inside the internal structure and the micropores.
ID plot for CHAμ ( Figure 4A) shows only a line with a not very steep slope (KID = 0.32) and similar to the slope of CHAg after the first hour of contact (KID = 0.31). The high C value (C = 3.75) indicates the formation of a thick adsorption layer. It is likely that, in this case, the first diffusion in the external surface and through the macropore structure was really fast; the experimental data has not allowed the observation of a steep line corresponding to the first minutes of contact, but it was In the first region of the CHAg plot ( Figure 4B), which represents about the first 60 min of contact with CSM, the intercept value is near zero (C = 0.17), demonstrating that the adsorption was mainly governed by ID process. During the first hour, external-surface adsorption and macropore diffusion occurred and a thin boundary layer has developed, as indicated by the low value of C = 0.17 which is proportional to the thickness of the boundary layer [57]. After one hour, adsorption layers thickened significantly (C = 2.24) and NH 4 + penetrated more slowly inside the internal structure and the micropores.
ID plot for CHAµ ( Figure 4A) shows only a line with a not very steep slope (K ID = 0.32) and similar to the slope of CHAg after the first hour of contact (K ID = 0.31). The high C value (C = 3.75) indicates the formation of a thick adsorption layer. It is likely that, in this case, the first diffusion in the external surface and through the macropore structure was really fast; the experimental data has not allowed the observation of a steep line corresponding to the first minutes of contact, but it was plausibly present before the first five minutes of contact with CSM.
ID parameters are reported in Table 3.

Thermodynamics
The thermodynamic parameters of K e , ∆G 1 , and ∆G 2 are reported in Table 4. The ∆G values obtained by Equation (18) and Equation (19) are similar, demonstrating little discrepancies between the two approaches adopted. ∆G is always negative, indicating that NH 4 + adsorption was a spontaneous process for all the sizes tested and for all the working temperatures. NH 4 + adsorption by CHAµ is thermodynamically favored rather than CHAg, as indicated by its general lowest values of ∆G.
Temperature has a positive effect on ∆G which at higher temperatures reaches the lowest values. adsorption and desorption (represented by q e and C e respectively in Equation (16)) is shifted towards the adsorption process. The grain size of the adsorbent affected K e , indeed CHAµ has shown greater values than CHAg, meaning that the micro-sized ZRT has favored the adsorption more than the granular one. This consideration is also supported by q e against C e graphs (see Figure 1, Section 3.1), where it can be seen that the best performances have been achieved by CHAµ instead of CHAg. The values of ∆H and ∆S are reported in Table 5. ∆S were positive, indicating that the randomness in the solid-liquid interface increased, reflecting a good affinity between the sorbent and the sorbate and a condition that favors the occurrence of the adsorption processes [70]. ∆H is positive for both CHAµ and CHAg indicating that NH 4 + adsorption was an endothermic process, with significative higher values for CHAg. Endothermy is also supported by the Freundlich constant K F that increased with increasing temperature (see Table 1, Section 3.1) [71]. While many authors have observed exothermic conditions for NH 4 + adsorption onto ZRT (∆H < 0) [27,29,72], others have calculated positive values of ∆H [26,57]. In all these studies, the nature of the employed materials (the type of ZRT and type of the liquid phase) varies significantly and this may results in differences in the adsorption processes, thus explaining this variability in the thermodynamic parameters.

Conclusions
In this work, the adsorption of ammonium ions from a raw liquid swine manure by a chabazite zeolite-rich tuff was characterized. The equilibrium curve was of L3 type following the isotherms classification by Giles et al. [66], suggesting that a multilayer adsorption condition has occurred. Due to the multilayer formation, the maximum adsorption capacities were obtained using low dosages of adsorbent (<6 wt%). A clear temperature effect was not observed for the micronized zeolite tuff while the coarser particle size showed poorer performance at lower temperatures. Particle size was an important aspect that influenced both the velocity of adsorption, the equilibrium conditions, and the thermodynamic. Intraparticle diffusion had a major control on the overall adsorption rate. Zeolites are microporous selective ion exchangers, thus diffusion of the counterions (both the adsorbed and the desorbed ones) is an essential process that controls and limits the ion exchange. Generally, the highest adsorption capacities and adsorption rates were achieved using the micronized zeolite-rich tuff.
The outcomes of this work highlighted the complexity of sorption mechanisms in raw liquid animal manure and proved that the use of chabazite zeolite-rich tuff is a valid technology for the recycling of N. Funding: We kindly thank the Emilia Romagna Region for the PhD grant inherent to the research project "Innovative geomaterials for the reduction of nitrogen load in livestock and industrial wastewater", specified by Deliberation n • . 769 of 21/05/2018, B area) "Human resources for intelligent specialization".