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

Abstract

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.

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Introduction

Flocculation is an effective method in many water treatment engineering fields. Adding coagulant is the most important step in the flocculation 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 significantly 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 influence of electrostatic field 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 Fe³⁺ through ionization. But the Fe³⁺ is not stable in the water, which is quickly combined with the water molecules to form Fe(H₂O)₆³⁺. Then the Fe(H₂O)₆³⁺ will show a strong tendency to hydrolyse in water and form various hydroxyl iron ions.^10,11 When external electrostatic field is present, the process of Fe³⁺ combining with the water molecules will be influenced.

Therefore, in the present article the ferric chloride solution was taken as the study object, and the influence on the ferric chloride solution system caused by external electrostatic field during the time slot before the chemical reaction of Fe³⁺ and water molecules was studied. Since molecular dynamics (MD) simulation can cover up a time span of micro-seconds or nano-seconds, we used MD simulation to study the water shell radius of the hydrated Fe³⁺, the coordination number of water molecules, the average residence time of water molecules in water shell of Fe³⁺, the self-diffusion coefficient of Fe³⁺ and water molecules, the hydrogen bond structural parameters and the changes of solution viscosity under electrostatic fields with different intensity. The potential effects of these changes on the hydrolysis of Fe³⁺ and the condensation process of Fe³⁺ complexes were also analyzed.

The detailed description of the simulation

The changes of ferric chloride aqueous solution under electrostatic field 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 Fe³⁺ 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,^13–15 the SPC/E model was adopted for water molecules in our work. The ferric chloride solution with a concentration of 1.03 mol kg⁻¹ 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 Fe³⁺ ions, 2 Fe²⁺ ions and 214 Cl⁻ ions (a total of 4051 particles), which were placed in the box of 5 nm × 5 nm × 5 nm. The periodic boundary condition was used. In this paper, the GROMOS force field 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 field intensity was 20 ns. The Lennard-Jones potential parameters of each particle are listed in Table 1, and the potential parameters of Fe³⁺ and Fe²⁺ are referred in ref. 17. The electrostatic field intensity employed in the simulation process was set as 10⁵ V m⁻¹, 10⁶ V m⁻¹, 10⁷ V m⁻¹, 10⁸ V m⁻¹, respectively, and the direction of electrostatic field was along the direction of the Y axis. The finished 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 fluctuation 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 final 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 figures.

Table 1 Lennard-Jones potential parameters used in the MD simulations

	ε (kJ mol^−1)	σ (nm)
Fe^3+	2.166	0.191
Fe^2+	2.106	0.191
Cl^−	1.2889	0.3470
O	0.6502	0.3166

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Fig. 1 Figure of setup for simulations.

In order to verify the correctness of the simulation method, the self-diffusion coefficient of two kinds of iron ions, the self-diffusion coefficient of water molecules, the first peak position of the radial distribution function of the iron ion–water molecules and the water molecule coordination number of hydrated Fe³⁺ ion were calculated without external electrostatic field. The solution temperature was set as 300 K and the solution concentration was set as 0.11 mol kg⁻¹. The results were compared with the simulation and experimental results in other literatures. The results are shown in Table 2.

Table 2 The simulation results from our work comparing with other simulation method and experiment^a

	M1	M2	M3
a M1 is from our work, M2 is the result by other simulate method, M3 is from experiments.b From ref. 18 using MD simulation.c From ref. 17 using MD simulation.d From ref. 19 using diaphragm cell method.e From ref. 20 using diaphragm cell method.f From ref. 21 using X-ray.
DFe(III) (cm^2 s^−1 × 10^−5)	0.52	0.53^b, 0.50^c	0.56^d
DFe(II) (cm^2 s^−1 × 10^−5)	0.61	0.56^b, 0.69^c	0.7^e
nFe(III)–H2O	6.21	6^b, 6.46^c	6^f
nFe(II)–H2O	5.96	6^b, 6.23^b	6^f
Location of first peak of the gFe(III)–H2O(r) (nm)	0.202	0.196^b, 0.195^c	0.198^f
Location of first peak of the gFe(II)–H2O(r) (nm)	0.208	0.209^b, 0.212^c	0.210^f

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As can be seen from Table 2, the calculation results of D_Fe(III), D_Fe(II), n_{Fe(III)–H2O}, n_Fe(II)–H2O, location of the first peak of the g_{Fe(III)–H2O}(r) and g_Fe(II)H2O(r) are close to the results of other literatures, which proves that the MD simulation method in this paper is more reasonable and can be used to study the change of solution properties of ferric chloride solution under external electrostatic field.

Results and discussion

Radial distribution function

In this section, the values of P_{Fe(III)–H2O} (first peak value), P_Fe(III)–Cl, R_{Fe(III)–H2O}, n_{Fe(III)–H2O}, R_Fe(III)–Cl, n_Fe(III)–Cl were calculated under the external electrostatic field with intensity of 10⁵ V m⁻¹, 10⁶ V m⁻¹, 10⁷ V m⁻¹ and 10⁸ V m⁻¹, respectively, and the results were compared with that under no external electrostatic field. The radial distribution function was calculated according eqn (1):²²where N_A is the quantity of particle A, and N_B is the quantity of particle B; 〈ρ_B(r)〉 is the particle density of particle B at a distance r from particle A, and 〈ρ_B(r)〉_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 Fe³⁺ is calculated according to eqn (2):²³

where r_s1 is the location of the first local minimum of g_Fe–H2O(r).

The chloride ions coordination number of Fe³⁺ is calculated according to eqn (3):

where r_s2 is the location of the first local minimum of g_Fe–Cl(r).

The calculation results of radial first peak position of Fe³⁺–H₂O and P_{Fe(III)–H2O} are shown in Table 3 and Fig. 2. The results of R_{Fe(III)–H2O} and n_{Fe(III)–H2O} are shown in Fig. 3 and 4. The R_{Fe(III)–H2O} was obtained from the location of the first local minimum of g_Fe–H2O(r).

Table 3 Values of radial first peak position of Fe³⁺–H₂O and P_{Fe(III)–H2O} under electrostatic field with different intensity

Electrostatic field strength	0 V m^−1	10^5 V m^−1	10^6 V m^−1	10^7 V m^−1	10^8 V m^−1
Radial first peak position of Fe^3+–H2O (nm)	0.206	0.206	0.206	0.206	0.206
PFe(III)–H2O	21.952	21.768	21.667	21.663	21.517

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Fig. 2 Radial distribution function of Fe³⁺–H₂O under electrostatic field with different intensity.

Fig. 3 The radius of hydrated Fe³⁺–H₂O under electrostatic field with different intensity.

Fig. 4 The number of coordination water around Fe³⁺ under electrostatic field with different intensity.

According to Table 3 and Fig. 2 it can be seen that under electrostatic field with different intensity the position of first peak of g_Fe–H2O(r) are all 0.206 nm, which is consistent with the that under no electrostatic field. This indicates that electrostatic field has no influence on the position of first peak of g_Fe–H2O(r). But the external electrostatic field decreases the value of P_{Fe(III)–H2O}, and this value decreases with the increase of electrostatic field intensity. When the electrostatic field intensity are 0 V m⁻¹, 10⁵ V m⁻¹, 10⁶ V m⁻¹, 10⁷ V m⁻¹ and 10⁸ V m⁻¹, the P_{Fe(III)–H2O} values are 21.952, 21.768, 21.667, 21.663, 21.517 respectively. From Fig. 3, it is known that the value of R_{Fe(III)–H2O} decreases notably under electrostatic field. It can be seen that except for the value of R_{Fe(III)–H2O} is 0.264 nm when electrostatic field intensity is 10⁸ V m⁻¹, under other electrostatic fields the R_{Fe(III)–H2O} values are all 0.268 nm, which is only less 0.002 nm than that under no electrostatic field. Therefore, the external electrostatic field has little influence on the radius of hydrated Fe³⁺ ion. As shown in Fig. 4, compared with no external electrostatic field the value of n_{Fe(III)–H2O} under electrostatic field increases, and as electrostatic field intensity increases the value of n_{Fe(III)–H2O} is obviously increased.

When external electrostatic field is present the value of P_{Fe(III)–H2O} decreases, which indicates that the number of water molecule in the position of the first peak (0.206 nm) is reduced. But the ionic radius of the hydrated Fe³⁺ ion is not affected by electrostatic field, and the number of coordination water molecule of the hydrated Fe³⁺ ion is increased. The changes above indicate that the external electrostatic field makes more water molecules become the coordination water of Fe³⁺ ions, which means the external electrostatic field can enhance the interaction between Fe³⁺ ions and the nearby water molecules. This enhanced interaction is beneficial to the hydrolysis of Fe³⁺ ions in water. Hedstrom¹⁰ confirmed the existence of FeOH²⁺, Fe(OH)₂⁺ and Fe₂(OH)₂⁴⁺ during the hydrolysis process of Fe(III) salt, and measured their hydrolysis equilibrium constants. Biederman¹¹ found that except the above hydrolytic ions, Fe₃(OH)₄⁵⁺ (a kind of trimer) also existed. The equations of possible hydrolytic reaction of Fe³⁺ 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 Fe₂(OH)₂⁴⁺, because dipolymer Fe₂(OH)₂⁴⁺ has significant stability.^10,11,24,25 No matter what forms of hydrolysates produced by hydrolysis of Fe³⁺, water molecules are the main reactants. The electrostatic field enhances the interaction and the reaction probability of the Fe³⁺ and surrounding water molecules, which facilitates the polymerization of the complex form of the ferric monomer. This is beneficial to the enhancement of the coagulation effect of the ferric chloride coagulant.

The interaction between the Fe³⁺ and the surrounding water molecules is enhanced by the external electrostatic field, and it can be indirectly reflected from the distribution of the anion around the Fe³⁺. Fig. 5 and 7 show the value of P_Fe(III)–Cl, R_Fe(III)–Cl, n_Fe(III)–Cl under electrostatic field with different intensity.

Fig. 5 Radial distribution function of Fe³⁺–Cl under electrostatic field with different intensity.

From Fig. 5, it can be seen that the first peak position of the radial distribution function of Fe³⁺–Cl⁻ is 0.232 nm no matter whether there is external electrostatic field or not. But the electrostatic field reduces the value of P_Fe(III)–Cl, and as the intensity of the electrostatic field increases, the value of P_Fe(III)–Cl is getting smaller. When the electrostatic field intensity is 0 V m⁻¹, 10⁵ V m⁻¹, 10⁶ V m⁻¹, 10⁷ V m⁻¹ and 10⁸ V m⁻¹, the P_Fe(III)–Cl values are 19.332, 18.554, 16.837, 16.545, 15.395 respectively. From Fig. 6 and 7, the electrostatic field has little influence on the value of R_Fe(III)–Cl. No matter whether there is electrostatic field or not, the value is about 0.254 nm. But electrostatic field significantly reduces the coordination number of Cl⁻ around the Fe³⁺, and the coordination number decreases with the increase of the electrostatic field intensity.

Fig. 6 The radius of hydrated Fe³⁺–Cl⁻ under electrostatic field with different intensity.

Fig. 7 The number of coordination Cl⁻ around Fe³⁺ under electrostatic field with different intensity.

According to Debye–Huckel Theory proposed by Debye and Huckel in 1923, on the one hand, the Coulomb force between the Fe³⁺ and the Cl⁻ 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 Fe³⁺ (central ion), the Cl⁻ ions are more likely to appear than other Fe³⁺ ions. Therefore, it can be considered that the Cl⁻ ions with negative charges are relatively concentrated around the Fe³⁺ central ions. Comparing with Fig. 2 the reduction in value of P_Fe(III)–Cl is much more than P_{Fe(III)–H2O} with increase in the strength of the electrostatic field. This may because that the interaction between Fe³⁺ and H₂O is electrostatic interaction, but the interaction between Fe³⁺ and Cl⁻ is composed of electrostatic interaction and ionic polarization interaction. Electrostatic interaction and ionic polarization interaction are all caused by the electric field of electron cloud. Therefore the interaction between Fe³⁺ and Cl⁻ is easier to be influenced by external electric field than the interaction between Fe³⁺ and H₂O. In addition, the P_{Fe(III)–H2O} is higher as compared to the one given in ref. 26. Also in present study, the P_{Fe(III)–H2O} 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⁻¹, but the concentration in the reference is 4.1 mol kg⁻¹. We also run another simulation with the FeCl₃ concentration of 4.1 M for verification. The result showed that the intensity was higher for P_Fe(III)–Cl as compared to P_{Fe(III)–H2O}, 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 field, which indicates that the electrostatic field weakens the Coulomb force between the central Fe³⁺ and the surrounding Cl⁻ ions and reduces the number of Cl⁻ ions around the Fe³⁺. In the meantime, since there are only Cl⁻ and water molecules around Fe³⁺ ions, the vacancies produced by reduced Cl⁻ ions are replaced by water molecules. This also indirectly confirmed the increase of number of coordination water around Fe³⁺.

Diffusivity

In this section, the values of the self-diffusion coefficient of Fe³⁺ D_Fe(III) and water molecules D_H2O are calculated when the external electrostatic field intensity is 10⁵ V m⁻¹, 10⁶ V m⁻¹, 10⁷ V m⁻¹ and 10⁸ V m⁻¹ respectively, and these values are compared with that under no external electrostatic field. The self-diffusion coefficient is calculated according to eqn (5) ‘Einstein relation’:²⁷where 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_H2O under different electrostatic field are shown in Fig. 8 and 9.

Fig. 8 Self-diffusion coefficient of Fe³⁺ under electrostatic field with different intensity.

Fig. 9 Self-diffusion coefficient of H₂O under electrostatic field with different intensity.

As shown in Fig. 8, compared with the value of D_Fe(III) (0.0895 × 10⁻⁵ cm² s⁻²) under no electrostatic field, the D_Fe(III) increases under external electrostatic field. As the intensity of the electrostatic field 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_H2O becomes smaller with the intensity of the electrostatic field, which means the value of D_H2O is inversely proportional to the electrostatic field intensity.

The diffusion coefficient is an important parameter to study the thermodynamic properties of ferric chloride solution, and its change reflects 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 field enhances the activity of Fe³⁺ ions in the solution, which contributes to increase the collision probability of the Fe³⁺ with the water molecules, thus increases the probability of the Fe³⁺ to capture the coordination water and promotes the initial hydrolysis of the Fe³⁺. In addition, while the Fe³⁺ is hydrolyzing, the polymerization between different Fe³⁺ 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 Fe³⁺ also increases the collision probability between different Fe³⁺ and complex monomers, thus promotes the formation of polymers. The positive charge of the polymer is generally higher such as Fe₂(OH)₂⁴⁺ (dipolymer) with 4 positive charges and Fe₃(OH)₄⁵⁺ (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 field reduces the self-diffusion coefficient of water molecules, mainly because the interaction between Fe³⁺ and water molecules is enhanced by the electrostatic field, which means that the binding effect of Fe³⁺ on water molecules is enhanced.

Residence time of water molecules in the first water shell of Fe³⁺

The dynamical residence time of water molecules is an important parameter describing the effect of solute on water solvent. It can reflect 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 first water shell of solute ions.³⁰ In this paper, the residence time of water molecules was calculated by eqn (6):³¹where N_h is the number of coordination water of Fe³⁺. The residence time γ_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 first water shell, n_i is the number of water molecules entering and leaving the first water shell of Fe³⁺ ion in time t_i.

The calculation results of the residence time of water molecules under electrostatic field with different intensity are shown in Fig. 10.

Fig. 10 Average residence time of H₂O molecules around Fe³⁺ under electrostatic field with different intensity.

As shown in Fig. 10, the residence time γ_res of the water molecules under different electrostatic field is larger than that without electrostatic field. And with the increase of electrostatic field intensity, γ_res shows an upward trend. The external electrostatic field prolongs the residence time of water molecule, which is also related to the enhanced interaction between Fe³⁺ and water molecules. The results obtained above show that the electrostatic field can effectively enhance the electrostatic interaction between Fe³⁺ and water molecules, which makes Fe³⁺ 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 first water shell of Fe³⁺. According to eqn (7) it is known that the reduction of the frequency of entering and leaving the first 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 (τ_HB), which is due to the positive relationship between these two parameters and the strength of the hydrogen bond network.³⁴

In the Gromacs software, hydrogen bonding is defined from two aspects: the distance between donor (D) and receptor (A), and the angle of hydrogen-donor–acceptor. The specific definition 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-donor–acceptor 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 τ_HB can be calculated by eqn (8).³⁶

where C(τ) is a hydrogen bond correlation function. C(τ) is defined as:

C(τ) = 〈h_i(t)h_i(t + τ)〉 (9)

where h_i(t) = {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 = 0, 1, 2, 3. The lifetime and the number of hydrogen bonds in solutions under different intensities of electrostatic field are shown in Tables 4 and 5.

Table 4 Hydrogen bond life in solution under electrostatic field with different intensity

	Electrostatic field intensity
	0 V m^−1	10^5 V m^−1	10^6 V m^−1	10^7 V m^−1	10^8 V m^−1
Hydrogen bond life (ps)	7.53	7.53	7.53	7.52	7.50

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Table 5 The percentage of water molecules with n hydrogen bonds (f_n) under electrostatic field with different intensity. (n = 0, 1, 2, 3)

	Electrostatic field intensity
	0 V m^−1	10^5 V m^−1	10^6 V m^−1	10^7 V m^−1	10^8 V m^−1
f0 (%)	47.40	47.43	47.49	47.52	47.53
f1 (%)	35.54	35.56	35.56	35.59	35.62
f2 (%)	14.20	14.16	14.16	14.14	14.11
f3 (%)	2.81	2.81	2.81	2.80	2.78
nHB	2722.38	2721.14	2718.70	2716.35	2713.53

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It can be seen from Table 4 that the average lifetime of hydrogen bond in the solution decreases under the effect of electrostatic field, but the decrease is not obvious. Only when the intensity of the electrostatic field is large (10⁸ V m⁻¹), the average lifetime of hydrogen bond decreases from 7.53 ps to 7.50 ps. Therefore, the external electrostatic field 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 field intensity. The total number of water molecules involved in the bond formation decreases from 2722.38 to 2713.53. As the electrostatic field intensity rises from 0 V m⁻¹ to 10⁸ V m⁻¹, 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 field has little influence on the hydrogen bond average life, but has a significant influence on the number of hydrogen bonds. The electrostatic field 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 field, and this effect tends to be more significant with the increase of electrostatic field intensity. The increase in the number of monomer water molecules and dipolymers water molecules is beneficial to increase the diffusivity and permeability of water molecules. However, the result of the previous study shows that the self-diffusion coefficient of water molecules in the solution decreases under electrostatic field, which is mainly ascribed to the enhanced binding to water molecules caused by Fe³⁺. Therefore, the change of hydrogen bond structure in the solution also proves the enhancement of the binding effect of Fe³⁺ ions on water molecules under the electrostatic field.

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 confirmed that electrostatic field can influence the dynamic viscosity of solution.³⁷ The dynamic viscosity of the solution can be obtained by eqn (10):where ρ and V are the density and speed of solution, A is constant, and the two relations below must be satisfied:

a_x = A cos(k_z), k = 2π/l_z (11)

where l_z is the height of the box. The transient velocity V can be defined 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 field with different intensity is shown in Fig. 11.

Fig. 11 Viscosity of solution under different intensities of electrostatic field.

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 field, and it is positive correlation between viscosity of the solution and electrostatic field intensity. As the electrostatic field intensity rises from 0 V m⁻¹ to 10⁸ V m⁻¹, 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 fluid layers in the solution system. The viscosity is a macroscopic property to reflect 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 reflects the change of internal structure and kinetic parameters of the water solvent. The Bakker's study result³⁸ shows that the change of the viscosity of the ionic solution is directly related to the residence time of water molecules in the first 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 field can significantly 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 field 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 field and impurity Mg²⁺ ions on CaCl₂ solution. The results in the previous paper shows that under electrostatic field 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 field (magnetic field) can reduce surface tension of pure water, which means the electric field 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 field) can increase the activity and the other (from metal cations) can impair the activity. The D_H2O in the previous paper increased under electrostatic field, but decreases in the present article. This may because Fe³⁺ has a much bigger attraction to water molecule than Ca²⁺, and electrostatic field enhances this attraction of Fe³⁺, which means the inhibition effect gains the upper hand. Therefore, the lower D_H2O under electrostatic field in the present study leads to a longer average residence time of H₂O molecules around Fe³⁺, and the enhanced attraction from Fe³⁺ 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 fields with different intensity was studied by equilibrium molecular dynamics simulations for investigating the mechanism of enhanced electrocoagulation technique. The results show that external electrostatic field can change the distribution characteristics of water molecules around Fe³⁺. When electrostatic field is present, the first peak position of Fe³⁺–H₂O radial distribution function almost has no change, but the first peak value decreases, and the number of coordinated water molecules increases. The electrostatic field can change the diffusion characteristics of Fe³⁺ and water molecules in solution. Under the effect of electrostatic field, the self-diffusion coefficient of Fe³⁺ increases, but the self-diffusion coefficient of water molecules decreases, and the average residence time of water molecules in the first water shell of Fe³⁺ increases. The electrostatic field can change the structure of hydrogen bond network in solution. Under the effect of electrostatic field, 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 field intensity. The changes of these parameters show that the electrostatic field can enhance the interaction between Fe³⁺ and water molecules, and promote the hydrolysis of Fe³⁺ and the polymerization of ferric ion complex, which is beneficial to the enhancement of the effect of ferric chloride coagulant. In addition, the external electrostatic field 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 conflicts to declare.

Greek symbols and nomenclature

gA–B	Radial distribution function, nm
nA–B	Particle B coordination number around particle A
D	Diffusion coefficient, cm^2 s^−1
P	First peak intensity of gAB
γ	Residence time of water molecules, ps
τHB	Hydrogen bond lifetime, ps
C(τ)	Hydrogen bond correlation function
hi(t)	Heaviside unit step function
ρ	Density of solution
ν	Velocity of solution
η	Viscosity value of solution, mP s^−1

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 51408525).

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