Modelling the Kinetics of Elements Release from a Zeolitic-Rich Tu ﬀ

: The present investigation aims at modeling the kinetics of elements (Fe, Mg, K, Ca, Na, Al, and Si) release from zeolitic-rich Phlegraean Yellow Tu ﬀ weathered by tannic acid solutions at di ﬀ erent concentration. Three equations were tested—power function, the Weber–Morris model, and the Elovich equation. Power function was revealed to be an excellent empirical equation well ﬁtted to the experimental data. Its numerical parameters were suitable predictive tools, highlighting both the intensity and modality of weathering processes. By paralleling the dissolution rates, it was possible to allow rock-sources from which elements were released during three distinct weathering stages—(i) the ﬁrst stage was dominated by biotite and amorphous weathering, (ii) the second stage also started with the breakdown of zeolite framework; and (iii) in the third stage, the whole of weathering / release process approached a steady state. Finally, these outcomes may be used to forecast the pedogenic / nutritional potential of zeolitic-rich tu ﬀ s as pedotechnical matrices in restoration design.

On the other hand, the rate of pedogenization depends on the contribution of various factors, such as time, climate, parent material, geomorphology, and organisms. The chemical-mineralogical features of soil formed in the course of pedogenesis are almost governed by the nature of rock parent material. In particular, as volcanic rocks, zeolitic-rich tuffs provide soil with both amorphous and crystalline phases, which variously support the overall soil fertility, e.g., by increasing water retention, cation exchange capacity (CEC), and potassium (a fundamental plant nutrient, along with nitrogen (i) the weathering effectiveness of the different solutions is quite proportional to the order of exponential magnitude of the TA concentration, viz. 0 < n × 10 1 µmol·L −1 n × 10 2 µmol·L −1 < n × 10 3 µmol·L −1 < n × 10 4 µmol·L −1 ; (ii) the variability of electrical conductivity and proton budget activity of rock/solutions, as well as the elements release seem to be differentiated in three distinct temporal stages, probably due to the weathering of different mineralogical phases over time.
These findings also suggested that the elements release would be strongly differentiated with reference to (i) the nature of the elements, (ii) the stage of weathering, or (iii) both of them.
From such hypothesis, the present paper aims at providing a qualitative/kinetic interpretation of the elements release processes. In particular, attention is focused on: finding kinetic models best fitting the observed, complex elements release; identifying the mineral phases involved, step by step, on elements release, with special reference to potassium taking into account its already mentioned importance as plant nutrient (vide supra).

Previous Phlegraean Yellow Tuff (PYT) Weathering Experiment
The Phlegraean Yellow Tuff (PYT) weathering experiment was widely detailed in a previous paper [30]. Here, we briefly summarize the adopted protocol.
The weathering of PYT was carried out by "discontinuous equilibrium" batch through 23 weathering treatment cycles (WTCs) (each lasting seven days) to simulate natural soil saturation/leaching cycles. Five grams of PYT were placed in polypropylene tubes with 100 mL weathering solutions at room temperature and end-over-end shaken at 60 opm for the entire duration of the experiment (196 days). After each WTC supernatants were carefully removed and quantitatively replaced by fresh weathering solutions. Ca, Mg, K, Na, Fe, Al, and Si were chosen because of their relevance in pedogenic processes. The element contents were determined by flame atomic absorption spectroscopy using a Perkin-Elmer Analyst 100 Spectrometer (Waltham, MA, USA).

Kinetic Models
Sparks [32] thoroughly revised the kinetic models to understand the mechanisms of soil chemical reactions. According to the specific aim of the present paper, the following three equations were initially tested for their suitability in modeling the element release during the whole period of weathering-power function, the Weber-Morris model, and the Elovich equation.
The power function is an empirical equation given by where Y is the concentration (mmol L −1 ) of each element in the solution at time t, whereas k (mmol L −1 days −n ) and n (dimensionless) are constants. Equation (1) has been commonly used in the past for describing the kinetics of plant nutrient release from natural materials [34,35], as well as for kinetics of minerals dissolution [36,37]. The power function has the practical advantage over other kinetic models, such as the pseudo-second order equation [38], in that it can be applied for modelling experimental conditions far from equilibrium. The higher the values of k and n, the greater is the element release rate with time. In addition, n gives information on how the release rate varies during the weathering period; as time goes on, the release rate of each element decreases (n < 1, remains constant (n = 1) or increases (n > 1), respectively. For the case where n = 0.5, Equation (1) is similar to the parabolic diffusion equation.
The Weber-Morris model [39] can be properly used when the rate of transport of the mineral components to the reactive surface sites limits the overall reaction rate [40]. If that is the case, the dissolution process is said to be diffusion controlled and the element release can be expressed as where k d (mmol L −1 days −0.5 ) is a diffusion kinetic constant and κ (mmol L −1 ) is a constant proportional to the thickness of the boundary layer [41]. Besides adsorption studies [42][43][44], the equation has been used in several minerals weathering studies to describe, for example, potassium release from phlogopite [45]; dissolution of magnesium silicates [46]; and dissolution of brucite, antigorite, and talc [47]. The Elovich equation has the following form: where a (L mmol −1 ) and b (mmol L −1 days −1 ) are constant. The Elovich equation, originally developed for gas adsorption [48], has also been used for modelling minerals dissolution. Some examples are the dissolution of phosphate rocks in acidic sandy soils [49] and of zinc silicate in ammoniacal solution [50].
As discussed below (vide infra), the preliminary step of the present investigation is the choice of the equation best fitting, element by element, the experimental data, with specific reference to the whole 161-days release process, and/or to each of the three stages in which the release process has been subdivided.
The second step aims at assessing whether the parameters of the kinetic model describing the release of a given element change from stage to stage.
The third step is the comparative analysis and interpretation of the kinetic releases of the different elements, from the perspective of assessing the involvement of different mineral phases present in the native rock.

Kinetic Modelling
As mentioned above (vide supra), the weathering of PYT was directly depending on TA concentration and that the overall elements release exhibited three distinctive stages. By way of example, Figures 1 and 2 show (i) the amount of Ca (mmol·L −1 vs. time) extracted by W and by TA solutions and (ii) the proton activity budget, respectively. In particular, solutions with similar tannic acid concentration behaved in an almost similar way, exhibiting analogous weathering efficiency. On the bases of such considerations, in the present paper, we will take into the account the element release in the following weathering solutions: W and TA 3 × 10 2 , 3 × 10 3 and 3 × 10 4 µmol·L −1 .   The release rate of each element during the whole experiment (161 days) has been fitted, time by time, by the three models considered in the present work; Table 1 shows the respective χ 2 and coefficient of determination (R 2 ).
It is evident that the power function fits the elements release very well, independently from tannic acid concentration and always showing the largest R 2 and the smallest χ 2 . Therefore, the power function has been chosen as the equation modeling the release rate of each element during the three distinct stages. In particular, the three distinct temporal stages of weathering, have been more accurately identified, with respect the previous work (Figures 1 and 2)-the first stage from the beginning to 49th day; the second stage up the 98th day, and the third stage until the end of experiment (161st day). Table 2 shows the power function parameters, including the equation coefficient k and n, calculated in the three weathering stages.
It can be noted that the k and the n parameters widely vary according to (i) the nature of the element, (ii) the tannic acid concentration in extractant solution, and (iii) the specific release stage to which the equation is fitted. In fact, the k parameter is almost less than 1 for each stage, with a few exceptions, the most appreciable of which is represented by calcium release in TA solution during the late stage. However, as explained in the Material and Methods section, the k parameter has no influence on the effective trend of the release. This, in turn, is substantially conditioned by the n parameter, which tunes the slope of the fitting curve. In this regard, the calculated n values usually are less than 1, with relevant exceptions for all considered elements, in particular during the early and middle stages. Such a variability deserves detailed case-by-case discussion.

Kinetic Analysis of the Three Weathering Stages
As expected, the synoptic comparison among the parameters calculated for the different elements and the relative release stages puts forward complex and distinct trends of elements release. For better analyze and understand such trends, the Figures 3-5 depict the release rate (r) of each element, calculated by the first derivative of the power function (Equation (1)) with respect to time: r = dY/dt = k n t n−1 (4) Environments 2020, 7, x FOR PEER REVIEW 3 of 6     Several aspects must be considered. It is appropriate to clarify that from now onward we assume that when extraction curves show similar trends, it likely implies that analogous physical-chemical release processes occurred and the same mineral phases are involved. In the first weathering stage, the release rates usually decrease during the extraction process, with some relevant exceptions including Al (Figure 3), Ca, Fe, and Mg ( Figure 4). As a matter of fact, for these elements, the n parameter of the fitting equation sometime is close to or larger than 1 (Table 2), thus implying that the release rate tends to be constant, or to increase as time goes on, respectively. In this last case, the release rate curve exhibits a "convex" shape. The "convexity" suggests a sort of "activation" of release process, which becomes more efficient as the weathering proceeds. Such an occurrence is particularly marked for Al (in TA 3 × 10 4 µmol·L −1 solution; Figure 3) and, to a lesser extent, Fe (in TA 3 × 10 3 µmol·L −1 solution; Figure 4) and Mg (in W and in TA 3 × 10 3 µmol·L −1 solution; Figure 4); for Ca, n increases along with TA concentration from 0 (water) to 3 × 10 3 µmol·L −1 , but is equal to 0.88 in TA 3 × 10 4 µmol·L −1 solution (Figure 4).
As a matter of fact, the tannic acid concentration does not affect in the same way the release of the different elements. Tannic acid, similar to humic acids, can interact with the tuff surface promoting the release/chelation of elements [51][52][53]. In the first weathering stage and in the absence of TA, the release rate of Al and K is lower than that of Ca and Na (see n values in Table 2). In contrast, at the highest concentration investigated, TA dramatically enhances the release of structural elements (especially Al), causing a partial loss of crystallinity of the tuff minerals and thus favoring the release of strongly retained exchangeable elements such as K. The charge density may have a great impact on the elements ability to be chelated by tannic acid. This is particularly evident for Na (Figure 3), which, as hydrated large monovalent cation, does not form stable chelates with tannic acid [54]. The opposite is true for Fe release (Figure 3), which is directly dependent on TA concentration, according to its well-known ability to be bound by tannic acid [55]. We must also take into account that the considered elements, or even a same element, arise from mineral phases that are either amorphous or crystalline, which in turn are differently prone to be weathered. In particular, during the first stage, it is reasonable to infer that loosely bound elements are primarily removed, such as Fe, Mg, and K prevailingly from biotite and Si, Al, Ca, and Na mainly from amorphous aluminosilicates.
The examination of the release rate during the second stage clearly highlights dramatic quali-quantitative changes in the weathering process (Figures 3-5). In fact, for each element, further changes of both rate and n parameter occur, compared to the first stage. The most remarkable variation is the wide gap discriminating the elements release in the solution with the largest TA concentration with respect to the lower concentration solutions.
Specifically, for both Si and Al the n parameter tends to increase with TA concentration of extractant solutions ( Table 2), suggesting that the release of these elements is "activated" during the second stage (Figure 3), with a possible concurrent weathering of the same mineralogical phases. Such an hypothesis can be supported by a concomitant increment of n parameter for potassium which, in 3 × 10 4 µmol·L −1 TA solution, reaches 1.37 (Table 2). In fact, in this last extractant solution, the release trend of potassium ( Figure 5) becomes more similar to those of silicon and aluminum (Figure 3), while quite differs from those of iron and magnesium. These two, in turn, still exhibit similar dissolution patterns ( Figure 4). This could indicate that, during the middle stage, potassium should arise from other sources than biotite, such as zeolites. This could be corroborated by the releases observed for calcium and sodium-also present in zeolites-that show high rates, but almost constant, with smoothed slopes quite different from those detected during the first stage ( Figure 4). These variations imply that the bulk of sodium and calcium is extracted during the first stage from amorphous (volcanic glass), but they continue to be released during the middle stage deriving also from crystalline phases, e.g., phillipsite and chabasite. Truly, the release rate curves of Na and Ca are distinct from the respective curves observed during the first stage (Figure 4), as well as from those of Si, Al, and K during the middle stage (Figures 3 and 5). This is consistent with the coexistence of amorphous and crystalline phases in PYT, which are variously weathered during the whole experiment [30].
During the late weathering stage, the dissolution rates calculated for the different elements tend to be less heterogeneous and more coherent (Figures 3-5). Specifically, the slopes are not as steep as in the previous stages, with n parameter values usually less than or close to 1. However, differences are still evident with respect to the absolute values of release rates, likely depending on the initial amount of the native elements.
For a better interpretation of the release processes during the final stage, the rates have been normalized to the amounts of the native elements. Figure 6 shows as an example the normalized release trend observed for water (a) and maximum TA concentration (b). It is obvious that all the release rates tend to become constant, with similar order of magnitude along with the TA concentration. In other words, after normalization, the release rates in the last stage are substantially dependent from the concentration of weathering solutions and from the nature of element, rather than the respective amounts of native elements. All this clearly denotes that during the last stage the weathering of every mineral phase proceeds slowly but steadily towars the definitive breakdown and transformation of the parent material. After the end of the WTC experiments (161 days), the weathering process carried out in the presence of the highest TA concentration (3 × 10 4 µmol·L −1 ) leads to a decrease in the PYT zeolites content of 73.3% (phillipsite) and of 41.1% (chabazite), accompanied by a total mass loss of 26.3%.

Conclusions
The outcomes of the present investigation inspire several remarks. From the kinetic modelling standpoint, the power function was revealed to be an excellent empirical equation fitting the experimental elements releases, which are clearly characterized by huge differences in qualitative and quantitative terms. This allowed us to gain numerical parameters that, even if empirical, are in any case suitable predictive tools. Specifically, the variability of n parameter has been consistently related to actual chemical-physical factors such as the concentration of tannic acid solutions or the nature of the considered elements. Furthermore, the huge variability of n directly focused the attention on the various (and sometimes dramatically divergent) release trends observed in the different weathering stages, thus highlighting the intensity of the weathering and the modality of element release. In turn, this accounted for the involvement of distinct mineral phases during the experiment.
By paralleling the dissolution rates of each element during the three stages, it is possible to guess the various sources from which they are released. During the first stage, Fe, Mg, and K likely arise from biotite, Ca and Na from amorphous, and Al and Si from both of them. The second stage denotes, concurrently to amorphous weathering, the early breakdown of zeolite framework, from which Al, Si, Ca, Na, and K are further released. In the third stage, the whole of weathering/release process approaches a steady state. The outcomes of the present investigation are also remarkable and convenient to forecast the behavior of pedogenic and nutritional potential of zeolitic-rich tuffs when utilized as pedotechnical matrices in restoration design.
Author Contributions: Literature searching, A.G.; writing-original draft preparation, E.G.; conception and design of the study, data analysis, writing-review and editing, S.S. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.