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Influence on ferric chloride aqueous solution caused by external electrostatic field: a molecular dynamics simulation study

A detailed analysis of structural properties and dynamic properties of ferric chloride aqueous solution under external electrostatic fields with different intensities was performed by molecular dynamics (MD) simulations. The effects on the ferric chloride aqueous solution caused by using an electrostatic field were examined in terms of the radial distribution function of the Fe3+ ion and water molecule/Cl−, coordination number of water/Cl− around the Fe3+ ion, characteristics of hydrogen bonds, solution viscosity, and how these effects influence the hydrolysis process of the Fe3+ ion. The goal behind the study is to attain additional insights into the mechanism of electrocoagulation when ferric chloride is used as coagulant, and provide a fundamental basis for the practical use of this technology.


Introduction
Flocculation is an effective method in many water treatment engineering elds. Adding coagulant is the most important step in the occulation process. The most widely used coagulants are aluminium salt and ferric salt. Aluminium salt has a certain biological toxicity to human beings, which has a correlation with the occurrence of Alzheimer's disease. 1,2 Therefore the use of aluminium salt coagulant may cause the secondary pollution of raw water. Compared with the aluminium salt coagulant, the ferric salt coagulant has the advantages of no biological toxicity, higher coagulation and settlement rate, better dewatering of sludge and shorter water treatment time. 3 However, in the practical application of ferric salt coagulant, there are still many disadvantages such as the high dosage required, high cost and secondary environmental pollution. Therefore, an enhanced electrocoagulation technique has been developed. The enhanced electrocoagulation technique can effectively improve coagulation efficiency and signicantly reduce coagulant dosage. At present, the enhanced electrocoagulation technique has been widely used in the treatment of many kinds of wastewater, such as dye and non-ferrous waste water, oily wastewater and municipal wastewater, which has achieved good results. Many researchers have done a lot of research on the mechanism and optimization method of the enhanced electrocoagulation technique, 4-9 but most of the research only stays in the stage of observing and analysing experimental phenomena and does not obtain the reliable intrinsic micro mechanism. This is mainly due to the rapid hydrolysis reaction when the coagulant is dissolving in the water, 3 and this process is difficult to observe and measure through experimental methods. Therefore, studying the inuence of electrostatic eld on the hydrolysis process of ferric salt is important to explore the mechanism of electrocoagulation.
Ferric chloride is the most widely used ferric salt coagulant. It is a kind of Fe(III) salt. When the Fe(III) salt enters the water, it will generate Fe 3+ through ionization. But the Fe 3+ is not stable in the water, which is quickly combined with the water molecules to form Fe(H 2 O) 6 3+ . Then the Fe(H 2 O) 6 3+ will show a strong tendency to hydrolyse in water and form various hydroxyl iron ions. 10,11 When external electrostatic eld is present, the process of Fe 3+ combining with the water molecules will be inuenced. Therefore, in the present article the ferric chloride solution was taken as the study object, and the inuence on the ferric chloride solution system caused by external electrostatic eld during the time slot before the chemical reaction of Fe 3+ and water molecules was studied. Since molecular dynamics (MD) simulation can cover up a time span of micro-seconds or nanoseconds, we used MD simulation to study the water shell radius of the hydrated Fe 3+ , the coordination number of water molecules, the average residence time of water molecules in water shell of Fe 3+ , the self-diffusion coefficient of Fe 3+ and water molecules, the hydrogen bond structural parameters and the changes of solution viscosity under electrostatic elds with different intensity. The potential effects of these changes on the hydrolysis of Fe 3+ and the condensation process of Fe 3+ complexes were also analyzed.

The detailed description of the simulation
The changes of ferric chloride aqueous solution under electrostatic eld were investigated by equilibrium molecular dynamics. The simulations were performed in the NPT ensemble (at constant particle number, pressure and temperature) using the GROMACS package. 12 All the simulated temperatures were set at 300 K by using Berendsen temperature coupling method. The pressures were set at 1 atm. Since the chemical reaction of Fe 3+ and water molecules doesn't begin at that initial time slot, the water molecules will not be broken. In addition, SPC/E model is one of the most popular water models for the remarkable accuracies of various properties over wide temperatures and pressures. In particular, this model reproduces the dielectrostatic constant quite well as compared with other models, which is very important for the salt-water mixtures. Therefore, according to the simulation method of salt-water system, [13][14][15] the SPC/E model was adopted for water molecules in our work. The ferric chloride solution with a concentration of 1.03 mol kg À1 was selected as the research object. According to the requirement of the composition ratio of ferrous chloride in ferric chloride coagulant in the Chinese national standard GB-4482-2006 "water treatment agent ferric chloride", 2 ferrous chloride molecules were added into the system. According to the concentration of the solution, the whole simulation system consisted of 3765 water molecules, 70 Fe 3+ ions, 2 Fe 2+ ions and 214 Cl À ions (a total of 4051 particles), which were placed in the box of 5 nm Â 5 nm Â 5 nm. The periodic boundary condition was used. In this paper, the GROMOS force eld was used to calculate the interaction between iron ions and water molecules. 15 When calculating the Lennard-Jones interaction, the cut-off was set as 1 nm. Fast Particle-Mesh ESD electrostatic method (PME) 16 was used to calculate the electrostatic interaction with a real space cut-off of 0.7 nm. The value of Fourier spacing was 0.12 nm. The time step length used for all simulations was 2 fs, 15 and the simulation time of each electrostatic eld intensity was 20 ns. The Lennard-Jones potential parameters of each particle are listed in Table 1, and the potential parameters of Fe 3+ and Fe 2+ are referred in ref. 17. The electrostatic eld intensity employed in the simulation process was set as 10 5 V m À1 , 10 6 V m À1 , 10 7 V m À1 , 10 8 V m À1 , respectively, and the direction of electrostatic eld was along the direction of the Y axis. The nished system model is shown in Fig. 1. Since the parameters will change easily during the whole simulation time, it is necessary to evaluate the degree of numerical uctuation in this process. The results of the parameters were obtained from the last 10 ns of every simulation. The 10 ns was divided into ten segments, and we obtained 10 parameter values from each segment. The nal result of parameter was obtained from the average of the 10 parameter values. In addition, the volatility of the data was measured by standard deviation marked as error bar in the gures.
In order to verify the correctness of the simulation method, the self-diffusion coefficient of two kinds of iron ions, the selfdiffusion coefficient of water molecules, the rst peak position of the radial distribution function of the iron ion-water molecules and the water molecule coordination number of hydrated Fe 3+ ion were calculated without external electrostatic eld. The solution temperature was set as 300 K and the solution concentration was set as 0.11 mol kg À1 . The results were compared with the simulation and experimental results in other literatures. The results are shown in Table 2.
As can be seen from Table 2

Radial distribution function
In this section, the values of P Fe(III)-H 2 O (rst peak value), P Fe(III)-Cl , R Fe(III)-H 2 O , n Fe(III)-H 2 O , R Fe(III)-Cl , n Fe(III)-Cl were calculated under the external electrostatic eld with intensity of 10 5 V m À1 , 10 6 V m À1 , 10 7 V m À1 and 10 8 V m À1 , respectively, and the results were compared with that under no external electrostatic eld. The radial distribution function was calculated according eqn (1): 22 where N A is the quantity of particle A, and N B is the quantity of particle B; hr B (r)i is the particle density of particle B at a distance r from particle A, and hr B (r)i local is the particle density of particle B averaged over all spheres around particle A with radius r max . Usually the value of r max is half of the minimum box length.
The water molecule coordination number of Fe 3+ is calculated according to eqn (2): 23 where r s1 is the location of the rst local minimum of g Fe-H 2 O (r). The chloride ions coordination number of Fe 3+ is calculated according to eqn (3): where r s2 is the location of the rst local minimum of g Fe-Cl (r). The calculation results of radial rst peak position of Fe 3+ -H 2 O and P Fe(III)-H 2 O are shown in Table 3 and     respectively. From Fig. 3, it is known that the value of R Fe(III)-H 2 O decreases notably under electrostatic eld. It can be seen that except for the value of R Fe(III)-H 2 O is 0.264 nm when electrostatic eld intensity is 10 8 V m À1 , under other electrostatic elds the R Fe(III)-H 2 O values are all 0.268 nm, which is only less 0.002 nm than that under no electrostatic eld. Therefore, the external electrostatic eld has little inuence on the radius of hydrated Fe 3+ ion. As shown in Fig. 4, compared with no external electrostatic eld the value of n Fe(III)-H 2 O under electrostatic eld increases, and as electrostatic eld intensity increases the value of n Fe(III)-H 2 O is obviously increased. When external electrostatic eld is present the value of P Fe(III)-H 2 O decreases, which indicates that the number of water molecule in the position of the rst peak (0.206 nm) is reduced. But the ionic radius of the hydrated Fe 3+ ion is not affected by electrostatic eld, and the number of coordination water molecule of the hydrated Fe 3+ ion is increased. The changes above indicate that the external electrostatic eld makes more water molecules become the coordination water of Fe 3+ ions, which means the external electrostatic eld can enhance the interaction between Fe 3+ ions and the nearby water molecules. This enhanced interaction is benecial to the hydrolysis of Fe 3+ ions in water. Hedstrom 10 conrmed the existence of FeOH 2+ , Fe(OH) 2 + and Fe 2 (OH) 2 4+ during the hydrolysis process of Fe(III) salt, and measured their hydrolysis equilibrium constants. Biederman 11 found that except the above hydrolytic ions, Fe 3 (OH) 4 5+ (a kind of trimer) also existed. The equations of possible hydrolytic reaction of Fe 3+ ions in water shows as below: Under normal conditions the complex form of the ferric monomer produced by hydrolysis intensively tends to be polymerized, and the most likely product is the dipolymer Fe 2 (OH) 2 4+ , because dipolymer Fe 2 (OH) 2 4+ has signicant stability. 10,11,24,25 No matter what forms of hydrolysates produced by hydrolysis of Fe 3+ , water molecules are the main reactants. The electrostatic eld enhances the interaction and the reaction probability of the Fe 3+ and surrounding water molecules, which facilitates the polymerization of the complex form of the ferric monomer. This is benecial to the enhancement of the coagulation effect of the ferric chloride coagulant. The interaction between the Fe 3+ and the surrounding water molecules is enhanced by the external electrostatic eld, and it can be indirectly reected from the distribution of the anion around the Fe 3+ . Fig. 5 and 7 show the value of P Fe(III)-Cl , R Fe(III)-Cl , n Fe(III)-Cl under electrostatic eld with different intensity.
From Fig. 5, it can be seen that the rst peak position of the radial distribution function of Fe 3+ -Cl À is 0.232 nm no matter whether there is external electrostatic eld or not. But the electrostatic eld reduces the value of P Fe(III)-Cl , and as the intensity of the electrostatic eld increases, the value of P Fe(III)-Cl is getting smaller. When the electrostatic eld intensity is 0 V m À1 , 10 5 V m À1 , 10 6 V m À1 , 10 7 V m À1 and 10 8 Fig. 6 and 7, the electrostatic eld has little inuence on the value of R Fe(III)-Cl . No matter whether there is electrostatic eld or not, the value is about 0.254 nm. But electrostatic eld signicantly reduces the coordination number of Cl À around   the Fe 3+ , and the coordination number decreases with the increase of the electrostatic eld intensity.
According to Debye-Huckel Theory proposed by Debye and Huckel in 1923, on the one hand, the Coulomb force between the Fe 3+ and the Cl À makes the ions tend to be orderly arranged as in the lattice. On the other hand, the Brownian motion will make the ions in a random distribution. Since Brownian motion is not strong enough to counteract the Coulomb force, the result of the interaction between these two forces is bound to form such a situation: around a Fe 3+ (central ion), the Cl À ions are more likely to appear than other Fe 3+ ions. Therefore, it can be considered that the Cl À ions with negative charges are relatively concentrated around the Fe 3+ central ions. Comparing with Fig. 2 the reduction in value of P Fe(III)-Cl is much more than P Fe(III)-H 2 O with increase in the strength of the electrostatic eld. This may because that the interaction between Fe 3+ and H 2 O is electrostatic interaction, but the interaction between Fe 3+ and Cl À is composed of electrostatic interaction and ionic polarization interaction. Electrostatic interaction and ionic polarization interaction are all caused by the electric eld of electron cloud. Therefore the interaction between Fe 3+ and Cl À is easier to be inuenced by external electric eld than the interaction between Fe 3+ and H 2 O. In addition, the P Fe(III)-H 2 O is higher as compared to the one given in ref. 26. Also in present study, the P Fe(III)-H 2 O is higher as compared to P Fe(III)-Cl whereas in ref. 26, the trend is opposite. We believe that this phenomenon may be caused by the difference of solution concentration. Our solution concentration is 1.03 mol kg À1 , but the concentration in the reference is 4.1 mol kg À1 . We also run another simulation with the FeCl 3 concentration of 4.1 M for verication. The result showed that the intensity was higher for P Fe(III)-Cl as compared to P Fe(III)-H 2 O , which met with the result in the reference.
From Fig. 5 and 7, it is found that P Fe(III)-Cl and n Fe(III)-Cl are reduced simultaneously under the electrostatic eld, which indicates that the electrostatic eld weakens the Coulomb force between the central Fe 3+ and the surrounding Cl À ions and reduces the number of Cl À ions around the Fe 3+ . In the meantime, since there are only Cl À and water molecules around Fe 3+ ions, the vacancies produced by reduced Cl À ions are replaced by water molecules. This also indirectly conrmed the increase of number of coordination water around Fe 3+ .

Diffusivity
In this section, the values of the self-diffusion coefficient of Fe 3+ D Fe(III) and water molecules D H 2 O are calculated when the external electrostatic eld intensity is 10 5 V m À1 , 10 6 V m À1 , 10 7 V m À1 and 10 8 V m À1 respectively, and these values are compared with that under no external electrostatic eld. The self-diffusion coefficient is calculated according to eqn (5) 'Einstein relation': 27 where r i (t) is the position of molecule i at t time, and r i (0) is the initial position of molecular i. The bracket represents the ensemble average. The calculated results of D Fe(III) and D H 2 O under different electrostatic eld are shown in Fig. 8 and 9. As shown in Fig. 8, compared with the value of D Fe(III) (0.0895 Â 10 À5 cm 2 s À2 ) under no electrostatic eld, the D Fe(III) increases under external electrostatic eld. As the intensity of the electrostatic eld increases, the value of D Fe(III) is bigger. However, it can be seen from Fig. 9 that, contrary to the change trend of D Fe(III) , the self-diffusion coefficient of water molecules D H 2 O becomes smaller with the intensity of the electrostatic eld, which means the value of D H 2 O is inversely proportional to the electrostatic eld intensity.
The diffusion coefficient is an important parameter to study the thermodynamic properties of ferric chloride solution, and its change reects the activity change of particles in solution, which will directly affect the equilibrium of the hydrolysis reaction. The results in Fig. 8 show that the electrostatic eld enhances the activity of Fe 3+ ions in the solution, which contributes to increase the collision probability of the Fe 3+ with the water molecules, thus increases the probability of the Fe 3+ to capture the coordination water and promotes the initial hydrolysis of the Fe 3+ . In addition, while the Fe 3+ is hydrolyzing, the polymerization between different Fe 3+ ions will also occur, which can produce the ferric complexes in the form of polymer. 10,11 The increase of the self-diffusion coefficient of Fe 3+ also increases the collision probability between different Fe 3+ and complex monomers, thus promotes the formation of polymers. The positive charge of the polymer is generally higher such as  (tripolymer) with 5 positive charges. The more charges can make stronger adsorption capacity. In addition, it is known from Fig. 9 that the effect of electrostatic eld reduces the selfdiffusion coefficient of water molecules, mainly because the interaction between Fe 3+ and water molecules is enhanced by the electrostatic eld, which means that the binding effect of Fe 3+ on water molecules is enhanced.
Residence time of water molecules in the rst water shell of Fe 3+ The dynamical residence time of water molecules is an important parameter describing the effect of solute on water solvent. It can reect the migration characteristics and stability of water molecules in the presence of solute. 28,29 Residence time of water molecules is the average time for water molecules to stay in the rst water shell of solute ions. 30 In this paper, the residence time of water molecules was calculated by eqn (6): 31 where N h is the number of coordination water of Fe 3+ . The residence time g i of each water molecule can be calculated by eqn (7): Where t i is the total existence time of the molecule i in the rst water shell, n i is the number of water molecules entering and leaving the rst water shell of Fe 3+ ion in time t i . The calculation results of the residence time of water molecules under electrostatic eld with different intensity are shown in Fig. 10.
As shown in Fig. 10, the residence time g res of the water molecules under different electrostatic eld is larger than that without electrostatic eld. And with the increase of electrostatic eld intensity, g res shows an upward trend. The external electrostatic eld prolongs the residence time of water molecule, which is also related to the enhanced interaction between Fe 3+ and water molecules. The results obtained above show that the electrostatic eld can effectively enhance the electrostatic interaction between Fe 3+ and water molecules, which makes Fe 3+ to attract more water as the coordination water molecules. Then more water molecules' mobility is limited, thus the diffusivity of water molecules is reduced. The diffusion of water molecules has direct relation with the residence time of water molecules, 32 the decrease of the diffusion of water molecules will reduce the frequency of water molecules entering and leaving the rst water shell of Fe 3+ . According to eqn (7) it is known that the reduction of the frequency of entering and leaving the rst water shell will prolong the residence time of each water molecule, which makes the mean residence time of water molecules prolonged.

Hydrogen bond
Hydrogen bond plays a important part during the process of hydrolysis, polymerization and adsorption. The hydrogen bond network structure in the solution directly affects the adsorption properties of polymeric ferric chloride. 33 Therefore, in this section the strength characteristics of hydrogen bond network are studied, including the number of hydrogen bonds (n HB ) and the average lifetime of hydrogen bonds (s HB ), which is due to the positive relationship between these two parameters and the strength of the hydrogen bond network. 34 In the Gromacs soware, hydrogen bonding is dened from two aspects: the distance between donor (D) and receptor (A), and the angle of hydrogen-donor-acceptor. The specic denition is as follows: (1) The distance between donor and acceptor is less than van der Waals distance (3.5 A).
(2) The angle of hydrogen-donor-acceptor is less than 30 .
In this simulation, the donor and acceptor are oxygen atoms in different water molecules. The angle of the hydrogen-donoracceptor is expressed by :HD-OD-OA.
Hydrogen bonds exist widely among water molecules in water. Due to the dynamic characteristics of water molecules, the hydrogen bonds between the water molecules are constantly forming and breaking at the same time. 35 Therefore, hydrogen bond lifetime represents the average time of hydrogen bond in this dynamic process. The hydrogen bond lifetime s HB can be calculated by eqn (8). 36 where C(s) is a hydrogen bond correlation function. C(s) is dened as: where h i (t) ¼ {0,1} is the Heaviside unit step function, which means that if two molecules formed hydrogen bonds at time 0 and t, the function value is 1, and otherwise 0. The number of hydrogen bonds (n HB ) and the percentage of water molecules with n hydrogen bonds (f n ) were investigated, where n ¼ 0, 1, 2, 3. The lifetime and the number of hydrogen bonds in solutions under different intensities of electrostatic eld are shown in Tables 4 and 5.
It can be seen from Table 4 that the average lifetime of hydrogen bond in the solution decreases under the effect of This journal is © The Royal Society of Chemistry 2018 electrostatic eld, but the decrease is not obvious. Only when the intensity of the electrostatic eld is large (10 8 V m À1 ), the average lifetime of hydrogen bond decreases from 7.53 ps to 7.50 ps. Therefore, the external electrostatic eld has little effect on the average life of hydrogen bonds. However, according to Table 5 the number of hydrogen bonds decreases with the increase of electrostatic eld intensity. The total number of water molecules involved in the bond formation decreases from 2722.38 to 2713.53. As the electrostatic eld intensity rises from 0 V m À1 to 10 8 V m À1 , the proportion of the water molecules which do not participate in forming hydrogen bond rises from 47.40% to 47.53%, the proportion of water molecules involved in forming 1 hydrogen bonds rises from 35.54% to 35.62%, the proportion of water molecules involved in forming of 2 hydrogen bonds decreased from 14.20% to 14.11%, and the proportion of water molecules involved in forming 3 hydrogen bonds declined from 2.81% to 2.78%.
The change of the hydrogen bond structure parameters indicates that the electrostatic eld has little inuence on the hydrogen bond average life, but has a signicant inuence on the number of hydrogen bonds. The electrostatic eld can effectively destroy the hydrogen bond inside the water cluster in the solution, and reduce the number of water molecules involved in the formation of multiple hydrogen bonds. In addition, the rise of the proportion of water molecules involved in forming 0 and 1 hydrogen bonds means that the number of monomer water molecules and dipolymers water molecules increased under electrostatic eld, and this effect tends to be more signicant with the increase of electrostatic eld intensity. The increase in the number of monomer water molecules and dipolymers water molecules is benecial to increase the diffusivity and permeability of water molecules. However, the result of the previous study shows that the self-diffusion coef-cient of water molecules in the solution decreases under electrostatic eld, which is mainly ascribed to the enhanced binding to water molecules caused by Fe 3+ . Therefore, the change of hydrogen bond structure in the solution also proves the enhancement of the binding effect of Fe 3+ ions on water molecules under the electrostatic eld.

Viscosity
The dynamic viscosity of the solution is an important parameter for the conformation change of the solution. The change of viscosity of ferric chloride solution will affect the Brown motion characteristics of the ferric complex formed by hydrolysis and the rate of particles collision probability, thus affect the polymerization. It has been conrmed that electrostatic eld can inuence the dynamic viscosity of solution. 37 The dynamic viscosity of the solution can be obtained by eqn (10): where r and V are the density and speed of solution, A is constant, and the two relations below must be satised: where l z is the height of the box. The transient velocity V can be dened by the Fourier coefficients: where v i,x is the component of velocity V in the X axis, r i,z is the coordinate of the atom in Z axis, and m i is the atomic mass. The viscosity value of solution under electrostatic eld with different intensity is shown in Fig. 11.
From the calculation results of the viscosity of Fig. 11, it is found that the viscosity of ferric chloride solution increases under the action of electrostatic eld, and it is positive correlation between viscosity of the solution and electrostatic eld intensity. As the electrostatic eld intensity rises from 0 V m À1 to 10 8 V m À1 , the viscosity of the solution rises from 1.8 mPa to 1.832 mPa s. The viscosity of the solution is a parameter to measure the friction between the uid layers in the solution system. The viscosity is a macroscopic property to reect the friction effect of all the particles in the solution, which is related to the number of hydrocarbon bonds in the solution and the molecular weight of the particles. Since there is no hydrocarbon bond in the solution system, the change of solution viscosity directly reects the change of internal structure and kinetic parameters of the water solvent. The Bakker's study result 38 shows that the change of the viscosity of the ionic solution is directly related to the residence time of water molecules in the rst water shell of the hydrated ion. If the residence time is prolonged, the viscosity of the solution will correspondingly increase.
According to the results in Fig. 10, the external electrostatic eld can signicantly prolong the residence time of water molecules, thus increasing the viscosity of the solution. In addition, the results of Fig. 11 are consistent with the calculation results of the diffusion coefficient of the water molecules under the electrostatic eld in Fig. 9. There is a negative correlation between the diffusion of water molecules and the viscosity of the solution, which means the decrease of the diffusion of water molecules can lead to the increase of solution viscosity. The increase of solution viscosity is not conducive to the destabilization and collision aggregation of colloid particles during the later reaction. Therefore, viscosity increase should be relieved during the application of the technique of electrocoagulation, such as using the method of adjusting the reaction temperature.
In our previous work, 32 we discussed the impact of an electrostatic eld and impurity Mg 2+ ions on CaCl 2 solution. The results in the previous paper shows that under electrostatic eld the D Ca increased, which meets with the D Fe in the present article. But the viscosity trend in the two studies is opposite. The experimental results from previous ref. 39 showed that the electric eld (magnetic eld) can reduce surface tension of pure water, which means the electric eld can reduce the viscosity of pure water. But the presence of metal cations will increase the viscosity of solution because of the bound effect to the water molecules. So there will be two opposite effects to the water molecules, one (from electric eld) can increase the activity and the other (from metal cations) can impair the activity. The D H 2 O in the previous paper increased under electrostatic eld, but decreases in the present article. This may because Fe 3+ has a much bigger attraction to water molecule than Ca 2+ , and electrostatic eld enhances this attraction of Fe 3+ , which means the inhibition effect gains the upper hand. Therefore, the lower D H 2 O under electrostatic eld in the present study leads to a longer average residence time of H 2 O molecules around Fe 3+ , and the enhanced attraction from Fe 3+ leads to a less number of hydrogen bonds between water molecules.

Conclusions
In the present article, the change of microscopic properties of ferric chloride solution under electrostatic elds with different intensity was studied by equilibrium molecular dynamics simulations for investigating the mechanism of enhanced electrocoagulation technique. The results show that external electrostatic eld can change the distribution characteristics of water molecules around Fe 3+ . When electrostatic eld is present, the rst peak position of Fe 3+ -H 2 O radial distribution function almost has no change, but the rst peak value decreases, and the number of coordinated water molecules increases. The electrostatic eld can change the diffusion characteristics of Fe 3+ and water molecules in solution. Under the effect of electrostatic eld, the self-diffusion coefficient of Fe 3+ increases, but the self-diffusion coefficient of water molecules decreases, and the average residence time of water molecules in the rst water shell of Fe 3+ increases. The electrostatic eld can change the structure of hydrogen bond network in solution. Under the effect of electrostatic eld, the average lifetime of hydrogen bond in the solution has no obvious change, but the number of hydrogen bonds decreases, and the proportion of water molecules that do not participate in bonding and to participate in the formation of 1 hydrogen bond has increased. The change amplitude of the parameters above is bigger with the increase of electrostatic eld intensity. The changes of these parameters show that the electrostatic eld can enhance the interaction between Fe 3+ and water molecules, and promote the hydrolysis of Fe 3+ and the polymerization of ferric ion complex, which is benecial to the enhancement of the effect of ferric chloride coagulant. In addition, the external electrostatic eld increases the viscosity of the solution. This change is not conducive to the interaction of colloid particles in the solution. Therefore, the viscosity of solution should be controlled during the practical application of the technique of electrocoagulation.

Conflicts of interest
There are no conicts to declare.
Greek symbols and nomenclature g A-B Radial distribution function, nm n A-B Particle B coordination number around particle A D Diffusion coefficient, cm 2 s À1 P First peak intensity of g AB g Residence time of water molecules, ps s HB Hydrogen bond lifetime, ps C(s) Hydrogen bond correlation function h i (t) Heaviside unit step function r Density of solution n Velocity of solution h Viscosity value of solution, mP s À1