Phosphorus adsorbed by HCl desorption–activated red mud adsorbents: a molecular dynamics studys

In this study, modified red mud after phosphorus adsorption was used as the adsorbent, and HCl and deionized water were used as desorbents to desorb phosphorus. The components in the adsorbent were optimized based on density functional theory, and adsorbent and desorbent models were established. Molecular dynamics simulation was performed to determine the phosphorus concentration before and after desorption, interaction energies, radial distribution function(RDF), mean-square displacement(MSD), and diffusion coefficient. The Monte Carlo method was used to simulate the desorption isotherm, desorption site, heat of desorption, and desorption energy. Simulation results showed that deionized water could only desorb phosphorus on the adsorbent surface, and the stability of the system deteriorated upon adding HCl. HCl destroyed the ionic and hydrogen bonding between the O atoms in H2PO4 − and reactive metal and oxygen atoms in the activated red mud particles. Moreover, the van der Waals force decreased considerably. The ionic and hydrogen bonds between H2PO4 − and the surface of activated red mud particles were broken by HCl, which accelerated the desorption of phosphorus from the adsorbent surface. The interaction between HCl and phosphorus accelerated the diffusion, which decreased the adsorption capacity. Moreover, the desorption capacity increased with increasing temperature.


Introduction
Red mud, an alkaline solid, is a byproduct of alumina synthesis.It is porous and has a good particle size distribution, with an average particle size of <0.1 mm and a specific surface area of ∼10-25 m 2 /g [1], it is used as an adsorbent for phosphorus removal.As red mud contains alkaline substances, red mud adsorbent for acidic wastewater phosphorus removal has a very good effect, in the dewatering of wastewater phosphorus at the same time, neutralise the acid in the acidic wastewater, to achieve the purpose of the waste for the waste.When the red mud adsorbent adsorbs phosphate from wastewater, how to desorb and enrich the phosphorus in the adsorbent so that the adsorbent can be reused for 3-5 times is a current hot research topic.The desorption regeneration of red mud is an effective treatment method [2][3][4] because it enables efficient adsorbent regeneration and target ion recycling.HCl is used as the desorbent for the desorption of modified red mud (as the adsorbent).Zhao [5] showed that HCl achieved a high desorption efficiency of 90%; however, its use in the desorption of phosphorus from red mud was not clarified therein.Therefore, several studies were conducted to verify the use of phosphorus as a desorbent for red mud [6][7][8].
Molecular dynamics simulation uses molecular force fields and computational methods developed based on Newtonian kinematics.It is used to analyze the movement of particles in a system [9].It yields highly accurate results in determining the dynamics and thermodynamic statistics of various systems and is used for various surface characterizations [10].Tang used molecular dynamics and the radial distribution function (RDF) to determine the hydrogen bonding strength between two atoms [11].Xin used molecular dynamics to investigate the relaxation in binding energy and transient regime and revealed that SO 4 2− primarily ensures electrostatic and hydrogen bonding during the desorption of oil film on the calcite surface [12].Xu used molecular dynamics simulations to study the adsorption characteristics of water molecules on the muscovite surface [13]; however, the use of this method for studying phosphorus desorption is still in its infancy.The Monte Carlo method uses mathematical models and randomly samples inputs from the probability distribution curve.Then, the lowest feasible result is determined.Based on the storage of the mathematical model for the calculation, this simulation is repeated to obtain statistical results.This method is widely used in mathematical and statistical research.The adsorption amount, heat of adsorption, adsorption isotherm, adsorption sites, and adsorption probability density are determined using the Monte Carlo method to determine the adsorption mechanism [14], gas-solid interfacial adsorption, such as methane [15] and hydrogen [16] adsorption, and solid-liquid adsorption/desorption of water.Kim using this method to study the water adsorption mechanism of coal [17].Bahamon studied the pollutant adsorption mechanism of activated carbon using this method [18].Li studied the adsorption mechanism of phosphorus by the components of red mud [19].Square studied the adsorption of phosphate anion on Pt(1 1 1) surface using the Monte Carlo method and density functional theory [20].Wang studied the adsorption mechanism of phosphorus on calcite surface via first principles calculation [21].However, the Monte Carlo method has not been used to study the desorption of phosphorus.Surface reaction and molecular adsorption/desorption were also studied using this method [22].Microscopic molecular dynamics and Monte Carlo methods are not currently used for studying the adsorption/ desorption of phosphorus by red mud.Therefore, these methods were used herein to simulate the desorption characteristics, optimize the activation of red mud components, determine the adsorbent mass, and develop the desorbent mass model based on the distribution of adsorbent concentration before and after adsorption and desorption.Based on the results, the interaction energy, RDF, MSD, diffusion coefficient, desorption isotherm, desorption sites, heat of desorption, and desorption energy after desorption were determined at the microscopic level.

Experimental raw materials
Modified red mud, used as an adsorbent herein, was prepared using charcoal powder (Henan Xingnuo Environmental Protection Materials Co., Ltd), silica sol (Wuhan Jiye Sheng Chemical Co), and red mud (Guizhou Huajin Aluminum Co., Ltd).It contained 30% water and was dried at 50 °C for 12 h.The mixture was ground in a ball mill and sieved through a 0.075-mm sieve.The red mud mainly contained 21.94% of Fe 2 O 3 , 21.04% of Al 2 O 3 , 19.05% of SiO 2 , 17.95% of CaO, 8.96% of Na 2 O, and 11.06% of other components.Phosphorus wastewater (pH 4 and phosphorus content of 320 mg L −1 ) obtained from a phosphorus ore dressing plant in Guizhou of China was used for simulation.The mass ratio of red mud:charcoal powder: silica sol was preset as for 92:5:3 after weighing and mixing, and a granulated mixture was obtained using a disc granulator.The water-to-cement ratio was 1:2 to obtain particle sizes of 1-2 mm.The activated particles were then placed in a muffle furnace and sintered for 30 min at 700 °C.The red mud particles were mixed with phosphorus wastewater for adsorption.The phosphorus wastewater contained tailings, and the main elements were 1278.0,213.15, 401.40, 0.25, 0.02, 0.04, 66.35, and 66.35 mg L −1 of P, Ca, Mg, Al, Fe, Cr, K, and Na, respectively.Phosphorus wastewater is weakly acidic (pH 3-4) and contains phosphorus mainly as H 2 PO 4 2− , which can be diluted to the required concentration using deionized water.Then, desorption test was performed after the adsorbent was dehydrated naturally and dried at 60 °C.The phosphate in the red mud adsorbent was desorbed using 0.2 mol L −1 HCl as desorbent, and the desorption temperature was controlled to be 35 °C and the desorption time was 12 h.The phosphorus concentration in the solution was determined at the end of the experiment.More information on the preparation and testing methods of the relevant adsorbents can be found in the literature [2].

Mineral composition analysis
The adsorbents were analyzed for mineral phase composition using an x-ray diffractometer (XPert PRO MPD).
x-ray powder diffraction and Cu-target Kα diffraction were performed at 40 kV and 40 mA at a scanning speed of 2°/s and scan range of 10°-80°.The spectrum was fitted via Rietveld refinement XRD using internally doped standard samples.The calculations were performed to quantitatively analyze the composition of crystalline phases in the red mud particles.

Construction of desorption model
The mineral composition of the activated red mud was obtained via XRD, and geometry optimization of each mineral was performed using the CASTEP module.Local density approximation (LDA) and generalized gradient approximation (GGA), including LDA-CA-PZ, GGA-RPBE, GGA-PBESOL, GGA-PBE, GGA-PW91, and GGA-WC, were used to obtain the structure that best matches the experimental test lattice parameters.The mass content and specific density were obtained using the amorphous cell module for constructing the activated red mud model [19] using Forcite molecular dynamics.The adsorbent and desorbent were placed on the surface of the activated red mud model, and molecular dynamics relaxation was performed.The sorption module was used to determine the desorbent interactions in the activated red mud model based on the Monte Carlo method to investigate the microscopic mechanisms of desorption.

Calculation of desorption concentration distribution curves for adsorbents of activated red mud particles
After kinetic calculations, the target atoms were selected and analyzed along the z-axis [23].Based on the comparison of the initial distance between phosphorus and the surface of the activated red mud particles and the calculated distance, the concentration distribution of phosphorus in each direction was derived.This allowed the analysis of spatial distribution of different desorption agents to quantitatively represent the effect of desorption and the migration law of phosphorus.

Calculation of desorption interaction energy of activated red mud particles
The interaction energy can reflect the binding strength of the adsorbate and adsorbate surface, which is a measure of the interaction size of different components in a mixed system.It determines the overall system stability.A negative interaction energy implies that the adsorption state is stable and facilitates easy adsorption [24,25].A higher binding energy implies that the system is more stable with better adsorption effect; the binding energy is the negative interaction energy [26].The interaction and binding energies were calculated for the system with and without the desorbent as follows: where E total is the energy of the whole system after the action, E surface is the energy of the representative adsorbent after the action, E polymer is the energy of the adsorbent after the action, E interation is the interaction energy, and E bin is the binding energy.The magnitudes of the interaction and binding energies of the two systems were compared to determine the adsorption state of phosphorus on the surface of activated red mud particles and the effect of desorbent.

Calculation of desorption radial distribution function of activated red mud particles
By calculating the radial distribution function (RDF) between the active atoms, namely Ca, Al, Fe, and O, in the activated red mud particles and O in H 2 PO 4 − , the main appearing positions of phosphorus adsorption and desorption and intermolecular interactions.The RDF is the ratio of the area of the system at the reference particle to the average density of the system, which reflects the aggregate molecular size and internal microstructure of the system [27].By comparing r and the peak height, the mode and strength of interatomic interactions can be determined.The peaks in the RDF g(r) within 3.5 Å are mainly attributed to chemical and hydrogen bonding [28], those at 3.5-5 Å are mainly van der Waals interactions, and those at >5.0 Å are attributed to very weak van der Waals interactions.
where N is the total number of molecules, T is the total computational time (number of steps), r d is the set difference in distance, and N ∆ is the number of molecules between the r r r d  + scores.In solids, the RDF curve shows a series of clear and stable peaks due to the relatively fixed position of molecules.In liquids, where the motion of the molecules is characterized by proximal order and remote disorder, the RDF curves show clear peaks only at short distances [29].

Calculation of desorption mean-square displacement of activated red mud particles
For phosphorus in the desorption system from the starting position of the non-stop movement, the position of the phosphorus atoms at each instant is different.The particle diffusion trajectory was determined via meansquare displacement (MSD) calculations, which describe the movement of molecules in a macroscopic equilibrium state and the degree of intensity of molecular movement.Here, r t ( )  is the position of the particle at time t; then, the MSD is represented by the average of the squared particle displacements [30]: According to the statistical principle, the calculation time is lengthy because of large number of molecules.Any instant of the system can be taken as the initial time, and the calculated average value is the same.MSD can be calculated as follows: ¢ is the MSD of the molecule in the simulation time interval t, r t i 0 is the position of the molecule N at moment t , 0 i is the total number of molecules in the system, and áñ is the systematic mean value.

Calculation of adsorption/desorption diffusion coefficient of activated red mud particles
The diffusion coefficient of molecules indicate the diffusion ability of phosphorus in the liquid-solid system during adsorption by activated red mud particles.The diffusion ability depends on the substance and medium as well as the temperature and pressure.The diffusion coefficient D of liquid-solid systems can be calculated using the Einstein's relational equation [31], and the velocity correlation function (VACF) is determined using the Green-Kubo relation.The corresponding normalized velocity autocorrelation coefficient is defined as follows:  and v 0 i ( )  are the displacement and velocity vectors of the particle t moments, respectively, and áñ is the average value of the system.The periodic boundary conditions were used herein to develop a three-dimensional model, and the NVT system was selected.

Monte Carlo simulation
The Monte Carlo method is a statistically based probabilistic research method used for solving the occurrence of a certain event.Typical characteristics of the problem are created and a mathematical probabilistic model is constructed, using which a solution that is close to the problem is determined.This simulation was performed herein using the giant regular system synthesized Monte Carlo method [32].Adsorption isotherms, adsorption isothermal heat, and adsorption sites were obtained using this method.Then, microscopic analyses were  performed to obtain valuable results and microscopic details that are difficult to understand using conventional modeling.

Physical phase analysis of activated red mud particle
The prepared red mud particle adsorbents were used to adsorb the total phosphorus in recycling water continuing flotation tailings [2,33].When the initial concentration of total phosphorus was 127.8 mg•L −1 , the amount of red mud particle adsorbents was 25 g•L −1 , and the adsorption time was 14 h, and the adsorption capacity and removal rate of total phosphorus were 48.63 mg•g −1 and 95.13%, respectively.The mineral composition of activated red mud before and after adsorption was quantitatively analyzed using the Rietveld method.Figure 1 shows the XRD results.).In addition, red mud also contains a small amount of alkaline substance sodium hydroxide, chemical substances and pharmaceuticals residual in the production process, organic matter and a small amount of non-crystalline substances, due to the relatively small amount of these substances, the adsorption and desorption of red mud adsorbent has little effect, therefore, these small amounts of substances were not considered in the establishment of the model, and the effect of these small amounts of substances will be continued to focus on in future research work.

Optimization of the activated red mud components
The CASTEP module in Materials Studio was used for the geometry optimization of the model based on the density functional theory.Different exchange correlation functions were selected, and the convergence accuracy was set to Fine.The other parameters were set to default values.Table 1 shows the calculation results.When the exchange correlation function is GGA-PW91, the total energy of the bulk phase is minimized and the structure is the most stable.Therefore, the PW91 gradient correction approximation under the GGA was used.The errors of lattice parameters under this condition were <5.5%, closer to the experimental values.

Construction of desorption model for activated red mud particles
Using the amorphous cell module in the Materials studio 8.0 software, a density of 1.5 g cm −3 was selected to simulate the mass composition of activated red mud.The composition of each components was optimized as Na   boundaries.The atoms in the red mud supercell were frozen during dynamic simulation to avoid interference with the simulation results.The steepest-descent method was used for geometry optimization under the Forcite module.The steepest-descent method was used to optimize the system structure, and molecular dynamics relaxation was performed for 10 ns under the NVT regular system.Then, the results were analyzed.Subsequently, H 2 PO 4 − molecules were adsorbed on the red mud surface, and a solution layer containing 10 HCl molecules and 1000 water molecules was constructed to be placed on the surface after adsorption.For comparison, an aqueous layer containing 1000 water molecules without HCl molecules was constructed to be placed on the surface after the adsorption of phosphorus by the adsorbent.To eliminate the effect of periodic boundaries, a 2-mm-thick vacuum layer was added in the direction perpendicular to the red mud surface.Geometry optimization was performed using the Forcite module, and the system structure was optimized using the steepest-descent method.Then, molecular dynamics relaxation was performed under the NVT regular system for 10 ns, and the results were analyzed.The first 9 ns were used for system equilibrium, and 1 ns was used for analyzing the results.

Analysis of concentration distribution of phosphorus before and after desorption of desorbent
After kinetic calculations, the target atoms were selected and analyzed along the z-axis.Based on the comparison of the initial distance between phosphorus and the surface of the activated red mud particles and the calculated distance, the concentration distribution of phosphorus in each direction was derived.The z-axis concentration distribution of phosphorus before and after desorption of desorbent is shown in figure 5, it can be seen that in the initial state, the concentration distribution of phosphorus is within 90 Å, there are three large relative peaks at 0.2 Å, 48.2 Å and 91.7 Å, with relative concentrations of 4.95, 5.39 and 3.68 g c.c −1 ., respectively, and the rest of the peaks are less than 1.When HCl and deionised water were added, it was found that the relative concentration curve shifted to the right relative to the initial state with the increase of the distance, and the relative concentration decreased at 0-10 Å, and then increased after 90 Å, which indicates that the effect of HCl and deionised water on phosphorus was not significant.Both HCl and deionised water have desorption effect on phosphorus.Comparing the concentration distribution curves of the HCl system and the deionised water system, it was found that at the concentration peak of 1-10 Å, the relative concentration of phosphorus in the deionised water system decreased from 4.95 g c.c −1 .to 3.13 g c.c −1 ., while the relative concentration of phosphorus in the HCl system decreased from 4.95 to 2.58, and at the concentration peak of 40-60 Å, the concentration in the deionised water system increased from 5.39 g c.c −1 .to 6.54 g c.c −1 ., but the relative concentration in the HCl system decreased from 5.39 g c.c −1 .c .to 3.72 g c.c −1 ., after that at 78-124 Å, the relative concentration at the peak wave is >1 g/c.c. for five distributions, the desorption effect of the deionised water is the relative concentration at the peak wave is >1 g/c.c. for five distributions, the desorption effect of the deionised water is general, but the relative concentration of HCl at 124 Å reaches 4.94 g c.c −1 ., and HCl completely removes phosphorus from the red mud surface.Thus, HCl accelerates the desorption of phosphorus on the activated red mud.Thus, HCl accelerates the desorption of phosphorus on the activated red mud particle surface.

Interaction energy analysis of phosphorus desorption by desorbents
The interaction energy of the two desorption agents after desorption of phosphorus is shown in table 2, the interaction energy of the deionised water system (−427.31kJ mol −1 ) is significantly better than that of the HCl desorption agent system (−416.74kJ mol −1 ), and the binding energy of the deionised water system is larger than  that of the HCl desorption agent system, which shows that The binding energy of the deionised water system was larger than that of the HCl desorbent system, indicating that the HCl desorbent played a certain desorption effect, and the stability of the system became worse.

Analysis of radial distribution function of phosphorus desorbed by desorbents
After kinetic calculations, the active elements Ca, Al, Fe, and O and the oxygen atoms of H 2 PO 4 -on the surface of the activated red mud were set up in the analysis of the Forcite Plus module to analyse the diffusion and distribution of H 2 PO 4 − in the HCl system and the deionised water system.diffusion and distribution states in the HCl system and the deionised water system.From figures 6(a)-(d) shows the radial distribution function between the active metals, namely Ca, Al, Fe, and O in activated red mud and O in H 2 PO 4 − after desorption.
In the deionized water desorption system, O from H 2 PO 4 − and Al, Ca, and O from the activated red mud appeared at a distance of 0-3.5 Å interval of the g (r) values.Fe is in the range of 0-5 Å.The maximum g (r) peak of Ca is 0.35 in the initial state and 0.44 at 5 Å.The r-backward shift of g (r) peak increases, and the maximum g(r) peak of Al decreases from 0.85 at 4.73 Å in the initial state to 0.73 at 4.16 Å, with a decrease in the r-forward shifted g(r) peak.The g(r) peak of Fe decreases from 4.64 at 4.71 Å to 0.62 at 3.39 Å, with a more pronounced decrease in the r-forward shifted g(r) peak.The g(r) peak of O decreases from 0.67 at 5 Å to 0.55, with a decrease in the r-invariant g(r) peak.In the HCl desorption system, O from H 2 PO 4 − and Al, Ca, and O atoms from the activated red mud undergo phase separation in the 0-3.5 Å interval of the g (r) value.In the 0-5 Å interval, the maximum g (r) peak of Ca is 0.35 at 3.95 Å in the initial state and 0.26 at 4.13 Å, indicating a decrease in the r-backward shift of the g (r) peak.The maximum g(r) peak of Al decreases from 0.85 at 4.73 Å in the initial state to 0.19 at 4.81 Å, indicating a decrease in the r-forward shift of g(r) peak.The g(r) peak of Fe decreases from 4.64 at 4.71 Å to 0.26 at 4.53 Å, indicating a decrease in the r-forward shift of g(r) peak.The g(r) peak of O decreases from 0.67 at 5 Å to 0.2 at 5 Å, with a more pronounced decrease in the r-invariant g(r) peak.Thus, changes in the g(r) peak in the 0-3.5 Å interval shows that the addition of HCl destroys the ionic and hydrogen bonding between O atoms in H 2 PO 4 − and the active metal and oxygen in red mud.Contrarily, deionized water only removes Fe and slightly influences the other interatomic interactions.The change in g(r)  peak and peak position in the 5 Å interval shows that the van der Waals force is considerably reduced after the addition of HCl.This indicates that the breaking of ionic and hydrogen bonds between H 2 PO 4 − and activated red mud surface due to HCl accelerated the desorption of phosphorus from the red mud surface.

Mean-square displacement analysis of phosphorus desorption by desorbents
The micro-interfacial diffusion of phosphorus desorbed by the two desorbents was investigated via molecular dynamics simulation of the MSD curves of the activated red mud.The MSD curves were obtained by analyzing the trajectories of phosphorus in different simulated activated red mud samples using the analysis function in the Forcite module.The first 80% of the simulation time, i.e., 8,000 ps, at 288, 298, and 308 K was used to minimize the effect of statistical errors (figure 7).As seen in figure 7, the slope order of MSD different tem peratures is K 308K >K 298K >K 288K when the temperatures are 288,298,308 K, both for the deionised water system and the HCl system.This result indicates that the temperature increases the kinetic energy and movement of H 2 PO 4 − , thus increases the possibility of H 2 PO 4 − abscondding red mud absorbent.
The MSD curve of deionized water is lower, indicating that the interaction between deionized water and phosphorus inhibits the diffusion.Moreover, the interaction energy is larger and the degree of adsorption.The MSD curve of HCl is higher, indicating that its interaction with phosphorus promotes the diffusion.Moreover, the interaction energy is smaller and the degree of adsorption is poorer.Additionally, as the temperature increases, the MSD curve of HCl reaches its peak, indicating a better desorption effect.Thus, the desorption of phosphorus by HCl is a heat absorption reaction.The MSD curves of deionized water show less variation from 298 to 308 K, indicating that the desorption has reached equilibrium.

Diffusion coefficient analysis of phosphorus desorption by desorbents
MSD was used to calculate the diffusion coefficient of phosphorus in activated red mud and quantify the diffusion behavior of each component on the aggregate surface.As shown in table 3, the D of deionized water from 288 K to 308 K are 2.3143 × 10 -8 m 2 s −1 , 2.7570 × 10 -8 m 2 s −1 , and 2.7240 × 10 -8 m 2 s −1 and HCl are 2.658 × 10 -8 m 2 s −1 , 2.8690 × 10 -8 m 2 s −1 , and 3.1268 × 10 -8 m 2 s −1 respectively, the diffusion coefficient of HCl is greater than that of deionized water.Moreover, the higher the temperature, the greater the diffusion coefficient and desorption capacity of the desorbent.
3.9.Monte carlo simulation of phosphorus desorption by desorbents 3.9.1.Desorption isotherms Figure 8 shows the desorption isotherms of deionized water and HCl after desorption from 1 to 100 kPa at 288, 298, and 308 K.The adsorption amount at 1-10 kPa increased with pressure and that at 1-50 kPa increased linearly with temperature, which was favorable for desorption.The desorption amount of deionized water stabilized at 50-60 kPa and 308 K and that of HCl stabilized at 50-70 kPa and 308 K.The increase in adsorption amount with pressure for HCl is flat compared with that for deionized water.This indicates that HCl has better adsorption effect than deionized water; moreover, temperature has a greater influence on the adsorption.

Heat of adsorption after desorption of phosphorus
The effect of different desorbents on the adsorption amount at various pressures and temperatures on the heat of adsorption can be determined from table 4. The heat of adsorption is lower for HCl than that for deionized water, indicating that the former has a better desorption effect.The heat of adsorption considerably decreases with an increase in temperature.These results agree well with the results of the thermodynamics of desorption that temperature majorly influences the heat of adsorption than pressure.

Adsorption sites after phosphorus desorption
Deionized water only removes the phosphorus adsorbed on the surface of the activated red mud.Contrarily, HCl removes majority of the phosphorus content from the surface and within the activated red mud.The interception of the more obvious XYZ for the phosphorus ions at the (26.52,6.47.28.60) for microscopic analysis.As shown in figure 9 that the phosphorus adsorbed by deionized water and Ca, Fe, Al, and Si in the activated red mud have atomic distances of 5.55, 9.528, 3.86, and 5.71 Å, respectively.The atomic distance increases after the removal of Fe, the other more than the initial adsorption distance has not changed greatly.
Figure 10 shows that the atomic distances between P and Ca, Fe, Al, and Si in HCl were 10.46, 6.75, 8.27, and 4.68 Å, respectively, and the initial adsorption distances of Ca and Al considerably increased compared with those in the deionized water.These results are consistent with the molecular dynamics simulation results, indicating that HCl mainly removed phosphorus in the vicinity of Ca and Al atoms.

Energy distribution after phosphorus desorption of phosphorus
The adsorption sites and potential energy distribution after desorption are studied herein.Figures 11 and 12 show the energy distribution of phosphorus with changes in pressure for the two desorbents at 288, 298, and 308 K. Figure 10 shows that for the deionized water, the higher the temperature, the higher the energy of the main absorption peaks.At 1 kPa and 308 K, the energy of the main absorption peak is −35.7 kJ.mol −1 .The probability of 0.3 in the vicinity of the first absorption peak increases with increasing pressure and the peak of the wave increases as the pressure decreases; the second absorption peak occurs near 0. Figure 11 shows that for HCl, the higher the temperature, the higher the energy and the higher the main absorption peak.At 1 kPa and 298 K, the energy is −29.7 kJ.mol −1 for the main absorption peak.The probability of 0.4 in the vicinity of the first absorption peak increases with increasing pressure, and the wave peak considerably increases with decreasing pressure than that observed for deionized water; the second peak appears in the vicinity of 0. Thus, HCl accelerated the decrease in the first absorption peak and backward shift of the wave peak.

Conclusions
Herein, molecular dynamics simulation was used to study the phosphorus adsorption mechanism via the HCl desorption of activated red mud particles.The desorption process was simulated using 0.2 mol L −1 of HCl and deionized water, and the results were compared.The main conclusions are as follows: (1) HCl accelerated the desorption of phosphorus on the surface of activated red mud particles than deionized water.
(2) Desorption by HCl mainly involved ionic bonding of H 2 PO 4 − to the surface of activated red mud particles and hydrogen bond breaking and decrease in van der Waals forces.
(3) The interaction between HCl and phosphorus accelerated diffusion, thereby decreasing the adsorption capacity.The diffusion coefficient and capacity increased with increasing temperature, whereas the smaller the adsorption amount decreased.
(4) HCl mainly desorbed phosphorus adsorbed by Ca and Al in activated red mud particles, whereas deionized water could only desorb phosphorus on the surface layer.

Figure 4 .
Figure 4. Modelling of desorption in deionised water and HCl: deionized water before desorption model (a) and after-desorption model (b), HCl before-desorption model (c) and after-desorption model (d).

Figure 5 .
Figure 5. Distribution of phosphorus concentration before and after phosphorus desorption using desorbents.

Figure 7 .
Figure 7. Mean-square displacement of phosphorus desorbed by desorbents at different temperatures.

Figure 8 .
Figure 8. Adsorption isotherms of phosphorus after desorption from deionized water (a) and HCl (b) at different temperatures and pressures.

Figure 9 .
Figure 9. Adsorption sites after phosphorus desorption by deionized water.

Figure 11 .
Figure 11.Energy distribution at different pressures after phosphorus desorption by deionized water at 308 K (a), 298 K (b), and 288 K (c).

Figure 12 .
Figure 12.Energy distribution at different pressures after phosphorus desorption by HCl at 308 K (a), 298 K (b), and 288 K (c).

Table 1 .
Calculated lattice parameters for different correlation functions.
[19] (Al 7.2 Si 8.8 O 32 ):Al 0.536 Ca 3 Fe 1.656 Si 2.805 O 12 :Fe 2 O 3 : (Na 7.54 (CO 3 )) (Si 6 Al 6 O 24 )(H2 O) 1.5 :SiO 2 :CaMg (CO 3 ) 2 (W/%) = 46.53%:33.36%:14.33%:4.15%:1.51%:0.11% of the periodically repeating unit cell in the 52.1 Å 52.1 Å 52.1 Å periodic box.As the hybrid system contained a large number of component structures, including covalent and proximate molecules, polymers and crystals, the universal force field was chosen for optimization(figure2)[19].Geometrically optimised activated red mud protocells, Ball and stick for the ball and stick model indicates the radius of the sphere of atoms, CPK indicates that the atoms will be rendered as a sphere with radius correlated to the van der Waals (vdW) radius of the atoms, Polyhedron indicates that solid coordination polyhedra are drawn around the cations, with the number of corners corresponding to the number of coordination sites, as defined by the bond connectivity, the H 2 PO 4 Phosphoric acid is a ternary acid with four forms of existence in aqueous solution, and the pH of the waste solution was 4. At pH 2.12-7.20,phosphorus in the solution mainly exists as H 2 PO 4 -,HCl and H 2 O structure were showed in figure 3. To analyze the surface of red mud containing H 2 PO 4 − , a layered interfacial supramolecular adsorption system modeled was Showed in figure 4. − .A cell containing 180 H 2 PO 4 − molecules and 1000 water media is placed on the red mud surface, and a 4-nm-thick vacuum layer was established on the model to eliminate the effect of periodic

Table 2 .
Binding energies of the two mixed systems (kJ/mol).

Table 3 .
Diffusion coefficient of phosphorus in deionized water and HCl.

Table 4 .
Equivalent heat of adsorption on the desorbent surface after desorption.