## 2 Materials and Methods
### Phosphorus Adsorption Experiments  
Experiments on phosphorus adsorption and desorption were conducted in laboratory conditions (in triplicate). Portions of 2.0 g of fresh bottom deposits were put into test tubes and prepared P solutions in lake water (25 cm\({}^{3}\)) in rising concentrations (0.00; 0.15; 0.30; 0.60; 1.20; 2.40; 4.80; 9.60 mg P dm\({}^{-3}\)) were poured into tubes, adding 2 drops of CHCl\({}_{3}\) protected samples from bacterial activity [9; 24]. After 24 h equilibration (at 20 \({}^{\circ}\)C), samples were centrifuged, and the supernatant was filtered through 0.45 \(\upmu\)m pore filters before analysis. SRP in the supernatant was analyzed using the molybdenum blue method (Merck spectrophotometer). The adsorbed phosphorus was calculated as the difference between the initial and final phosphorus concentration (mg) per 1 kg of sediment DW.  
Desorption of P was assessed after 24 h equilibration of samples with previously adsorbed P using lake water (without P). Calculations were made according to the method described by [25; 26] (Figure 4).  
The estimation of P adsorption parameters was conducted using Freundlich, BET, and Freundlich-Langmuir models using the non-linear estimation method (Statistica 13.5). As a measure of fitting experimental data to the tested model, the R\({}^{2}\) coefficient was used. Langmuir and double Langmuir models were also tested, but they showed a very weak fit to experimental results, and obtained results were omitted in the presented analysis.  
Used adsorption models equations:  
(a) Freundlich model equation [27]:  
\[S=K_{f}*C^{\frac{1}{n}} \tag{1}\]  
where:  
\(S\)--phosphorus amount adsorbed by bottom sediment (mg P kg\({}^{-1}\) DW), a sum of \"native\" adsorbed P (S\({}_{0}\)) and P adsorbed during experiment (\(S\)')  
\(C\)--final concentration of phosphorus concentration after 24 h equilibration (mg dm\({}^{-3}\));  
\(K_{f}\)--Freundlich model constant (dm\({}^{3}\) kg\({}^{-1}\));  
\(1/n\)--constant describing heterogeneity of adsorption.  
The EPC\({}_{0}\) (phosphorus equilibrium concentration) parameter was calculated using the Freundlich model. This value was corrected taking into account the amount of desorbed P (-S\({}_{0}\)) for initial P concentration 0 mg P dm\({}^{-3}\)[28]:  
Figure 4: Scheme of P adsorption experiment procedure.  
\[\text{S}=\left(K_{f}*C^{\frac{1}{n}}\right)-S_{0} \tag{2}\]  
The change of Gibbs free energy (kJ mol\({}^{-1}\)) was calculated with the formula [29]:  
\[-\Delta Gads=RTlnK_{d} \tag{3}\]  
where:  
\(K_{d}\)--division coefficient [dm\({}^{3}\) kg\({}^{-1}\)];  
\(R\)--gas constant [J mol\({}^{-1}\) K\({}^{-1}\)];  
\(T\)--temperature [K].  
(b) BET adsorption model, which describes multilayer adsorption [30]:  
\[S=\frac{S_{BET}*k_{BET}*C}{\left(C_{s}-C\right)*\left[1+\left(k_{BET}-1\right)* \frac{C}{C_{s}}\right]} \tag{4}\]  
where:  
\(C\), \(S\)--as it was in the equation [1];  
\(S_{BET}\)--maximum adsorption capacity of sediment, which corresponds to the monolayer, [mg kg\({}^{-1}\) DW];  
\(k_{BET}\)--BET model constant [dm\({}^{3}\) mg\({}^{-1}\)];  
\(C_{s}\)--concentration of saturation of adsorbate monolayer [mg dm\({}^{-3}\)].  
(c) General Langmuir-Freundlich adsorption model [31]:  
\[S=S_{FL}\frac{\left(k_{FL}*C\right)^{a}}{1+\left(k_{FL}*C\right)^{a}} \tag{5}\]  
where:  
\(S\), \(C\)--as it was in previous equations  
\(S_{FL}\)--maximum adsorption capacity [mg kg\({}^{-1}\) DW]  
\(k_{FL}\)--Langmuir-Freundlich constant [dm\({}^{3}\) mg\({}^{-1}\)]  
\(\alpha\)--heterogeneity factor