**3. Results**

#### *3.1. Efficiency of P Desorption*

The efficiency of the desorption solutions showed in particular that the lower concentration of 5 mM led to a higher P release than the corresponding higher concentration of 50 mM for each reaction solution (Table 3). For the lower concentration of 50 mM, the efficiency of the desorption solutions ranked according to the following order: KCl > KNO3 > Mal > His. This order changed for the 50 mM concentration treatment to KCl > Mal > His > KNO3, where KCl also showed the highest P desorption efficiency.


**Table 3.** Total P desorption after 336 h by using desorption solutions KCl, KNO3, histidine (His), and malic acid (Mal).

For the concentration of 5 mM, goethite showed the highest P desorption in the range from 70.4 to 81.0%, followed by gibbsite with P desorption in the range from 50.7 to 42.6%. The poorly crystalline ferrihydrite had lower desorption values in the range from 11.8 to 1.9% compared to the crystalline goethite. Within the group of the amorphous Fe-Al-hydroxide mixtures, the pure hydroxides of Fe and Al had higher desorption with values in the range from 27.6 to 13.5% for 1 Fe: 0 Al, and from 23.2 to 19.7% for 0 Fe: 1 Al than the binary composites. P desorption was lowest at the balanced mixture ratio for 1 Fe: 1 Al in the range from 2.5 to 5.2%, and increased either with increasing Fe or Al amount. In total, more P was desorbed from the crystalline hydroxides than from the amorphous hydroxides.

If P desorption was related to the specific surface area, gibbsite had a higher desorption amount than goethite, because the specific surface area of goethite was substantially larger than that of gibbsite, which is why less P was ad- and desorbed from the goethite surface. Similar was observed for the hydroxide mixtures. While e.g., 1 Fe: 0 Al and 1 Fe: 5 Al had similar amounts of P desorption in%, especially for the organic treatment, the desorption amount related to the specific surface area was much lower for the pure amorphous Fehydroxide compared to the mixture due to the highly different surface area and hence, the amount of ad- and desorbed P per m2.

### *3.2. Kinetics of P Desorption*

The curves of the P desorption kinetics showed that the fast initial desorption step occurred during the first 48 h for all used reaction solutions (Figures 1 and 2). While for goethite and gibbsite, after 48 h equilibrium was nearly reached using KCl and KNO3, desorption was still ongoing for ferrihydrite and the Fe-Al-hydroxide mixtures (Figure 1). Similar was observed for Mal and His, whereby it can be seen that P desorption from goethite and gibbsite continued using Mal (Figure 2).

**Figure 1.** Kinetics of P desorption from (**A**) goethite, (**B**) gibbsite, (**C**) ferrihydrite, (**D**) 1 Fe: 0 Al, (**E**) 5 Fe: 1 Al, (**F**) 1 Fe: 1 Al, (**G**) 1 Fe: 5 Al, (**H**) 0 Fe: 1 Al with KCl and KNO3 at concentrations of 5 mM and 50 mM.

**Figure 2.** Kinetics of P desorption from (**A**) goethite, (**B**) gibbsite, (**C**) ferrihydrite, (**D**) 1 Fe: 0 Al, (**E**) 5 Fe: 1 Al, (**F**) 1 Fe: 1 Al, (**G**) 1 Fe: 5 Al, (**H**) 0 Fe: 1 Al with histidine and malic acid at concentrations of 5 mM and 50 mM.

The coefficients of determination for the applied kinetic models showed that desorption kinetics fitted best with the Elovich equation (mean R<sup>2</sup> = 0.93) (Table 4), followed by the exponential function (mean R<sup>2</sup> = 0.91) (Table 5), and the parabolic function (mean R<sup>2</sup> = 0.83) (Table 6). Only ferrihydrite had the best fit with the Parabolic equation (mean R<sup>2</sup> = 0.89), followed by the exponential function (mean R2 = 0.87), and the Elovich equation (mean R<sup>2</sup> = 0.80). However, it is necessary to evaluate the results of the kinetic models as well as their calculated kinetic parameters (Tables 4–6) for each hydroxide separately. For goethite and gibbsite, the Elovich equation had the best fit, followed by the exponential function. In addition, the kinetic parameters obtained showed mainly a higher initial P release (α, a) and a lower P release over time (β, b). The Mal desorption treatments of goethite and the applied Elovich function showed a lower initial P release and a higher P release over time. However, noticeable were the α-values, which were overestimated compared to the actual desorption amounts. As already mentioned, for ferrihydrite the best fit was obtained by application of the exponential function. For ferrihydrite, the initial P release was lower than the release over time. By using the Elovich equation certainly, β was higher than α, where an overestimation of α for the His treatment was concluded as well. The amorphous Fe- and Al-hydroxide mixtures had the best fit with the Elovich equation, followed by the Exponential equation. For the pure amorphous Fe-hydroxide, the Fe-dominated mixtures, and the mixture with equal amounts of Fe and Al, the initial P release values α and a were lower than the release over time values β and b. The values for the mixture with predominant Al amount indicated a greater initial release of P.


**Table 4.** Coefficients of determination (R2), standard error (S.E.), and calculated kinetic parameters for the Elovich equation used to describe the kinetic release of P after 336 h desorption time.


**Table 4.** *Cont.*

\* *p* = 0.059.

**Table 5.** Coefficients of determination (R2), standard error (S.E.), and calculated kinetic parameters for the exponential function used to describe the kinetic release of P after 336 h desorption time.



**Table 5.** *Cont.*

**Table 6.** Coefficients of determination (R2), standard error (S.E.), and calculated kinetic parameters for the parabolic function used to describe the kinetic release of P after 336 h desorption time.


#### *3.3. Dissolved Elemental Composition during P Desorption*

With regard to possible release mechanisms of P from the investigated hydroxides, the concentrations of dissolved total Fe, Al, Cl, N, as well as C were measured in the reaction solution during and after desorption experiments. Since anion exchange is the dominating mechanism during P desorption, an increase of Cl− and NO3 − could be observable. The concentrations of total Cl and N showed despite some variation a decreasing trend. The correlation of the change of dissolved total Cl and N with the concentration of dissolved P in the sample solution showed no clear relationship (Figure 3C,D).

**Figure 3.** Correlation between desorbed P and the change of (**A**) dissolved total Fe + Al for KCl, (**B**) dissolved total Fe + Al for KNO3, (**C**) dissolved total Cl for KCl, and (**D**) dissolved total N for KNO3 in the sample solution for all hydroxides and each desorption time step.

The concentration of dissolved total Fe and Al (separately Fe or Al for the sole hydroxides, sum of Fe and Al for the hydroxide-mixtures) showed enrichment in the sample solution during P desorption, however, the values had a high variation and no distinct correlation with the amount of desorbed P for the inorganic treatment (Figure 3A,B). While the KCl treatment with the lower 5 mM concentration had higher concentrations of dissolved total Fe and Al, the opposite was observed for KNO3. The same missing correlations of Fe, Al, and P were observed for the organic desorption treatments, whereas the concentration of dissolved Fe and Al increased in the sample solution as well. The Mal treatment showed higher concentrations of dissolved total Fe and Al than His (Figure 4A,B).

**Figure 4.** Correlation between desorbed P and the change of (**A**) dissolved total Fe + Al for histidine, (**B**) dissolved total Fe + Al for malic acid, (**C**) dissolved total C for histidine, and (**D**) dissolved total C for malic acid in the sample solution for all hydroxides and each desorption time step.

In addition, for desorption using organic constituents, total C was measured in the sample solution, and the difference from the initial total C concentration (240 mg L−<sup>1</sup> for Mal and 3400 mg L−<sup>1</sup> for His, respectively) to total C in the sample solution was calculated. Again, no clear relationship to the amount of desorbed P was observed, whereas the C concentration tended to decrease (Figure 4C,D).
