Influence of Electrostatic Field on Mixed Aqueous Solution of Calcium and Ferrous Ions: Insights from Molecular Dynamics Simulations

Abstract

In order to investigate the anti-scaling and anti-corrosion characteristics of an electrostatic anti-fouling system in the application process, the influence of an electrostatic field (EF) on the structure and dynamics of hydrated Ca²⁺ and hydrated Fe²⁺ in a mixed aqueous system was studied through the calculation and analysis of the radial distribution function (RDF), self-diffusion coefficients, viscosity, and hydrogen bond structure by using molecular dynamics simulation. The study results show that the EF can decrease the radius of the first water shell of hydrated Ca²⁺ but increase that of Fe²⁺, which will reduce the possibility of forming calcite. The EF can make water molecules and Fe²⁺ more active, which can hinder iron release and thus decrease iron corrosion products. In addition, the EF can enhance the hydrogen structure of water molecules in the aqueous solution.

1. Introduction

Fouling and iron corrosion are common problems in the water industry. Fouling results in degradation in the performance of heat exchangers. Iron corrosion can destroy the pipe and pollute the drinking water due to the suspension of iron particles. An electrostatic anti-fouling (EAF) system is one of the most common and effective ways to solve these problems. Water scale is almost entirely composed of calcium carbonate (CaCO₃), which naturally occurs in six various forms: calcite, aragonite, vaterite, two hydrate phases, and amorphous calcium carbonate (ACC). ACC is perhaps the most vital to growth processes since it can create the precursor to the crystallization of those phases and plays a critical role in the biomineralization process for this substance [1]. Thus, the electric field’s impact on calcium carbonate has been the focus of the great majority of studies looking into the anti-fouling mechanism of EAF. It consists of two main aspects: how calcium carbonate crystals are formed and how the structure of scale crystals changes under electric fields. The impact of an electric field on calcium carbonate crystallization was studied by Qi et al. [2]. Their results show that the electric field applied to the CaCO₃ solution affects the lattice structure and crystal shape of CaCO₃ crystals. According to Li et al. [3], the scale sample produced by electrostatic water included more aragonite than before. Most equipment in industrial systems is made of carbon steel, and its main chemical composition is iron. Therefore, researchers who investigate the mechanism of metal corrosion tend to use iron as the study object. Lin et al. [4] found that the electric field accelerates steel corrosion, and the electric field favors the generation of plate-shaped γ-FeOOH and inhibits the formation of α-FeOOH. In addition, the scaling of calcium carbonate has a certain influence on iron corrosion. Sarin et al. [5] found that CaCO₃ plays a role in reducing iron release, which can alleviate water pollution problems, and Harris et al. found that the scaling tendency in water is the main factor determining the corrosion rate of iron [6]. The different contents of metal cations (including Fe²⁺) in aqueous solutions also have a certain influence on the precipitation process of CaCO₃ [7]. Less attention has been paid to the impact of an electrostatic field (EF) on the microcosmic particle structure in aqueous systems.

Due to the relatively poor solubility of calcium carbonate, there are nearly zero CO₃²⁻ ions in hard water, but HCO₃⁻ ions are plentiful. As hydrated ions, Ca²⁺ and Fe²⁺ can be found in aqueous solutions. Additionally, these hydrated ions form hydrogen bonds with additional water molecules [8,9,10]. The formation, growth, and crystal structure of calcium carbonate precipitates are mainly determined by the structural and dynamic properties of Ca²⁺. Fe²⁺ plays an important role in the metal corrosion process. The main reactions of iron corrosion are shown below.

The iron in the material loses two electrons and forms Fe²⁺.

$$\mathrm{Fe}\to {\mathrm{Fe}}^{2+}+2{\mathrm{e}}^{-}$$

(1)

Electron acceptors such as oxygen or hydrogen ions in aqueous solutions serve to complete the reaction.

$$\frac{1}{2}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}+2{\mathrm{e}}^{-}\leftrightarrow 2\mathrm{O}{\mathrm{H}}^{-}$$

(2)

$$2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2$$

(3)

Ferrous solids such as ferrous hydroxide can form.

$${\mathrm{Fe}}^{2+}+2\mathrm{O}{\mathrm{H}}^{-}\to \mathrm{Fe}{(\mathrm{OH})}_2$$

(4)

Fe(OH)₂ can be further oxidized to Fe(OH)₃ attached to the wall of the tube.

$$4\mathrm{Fe}{(\mathrm{OH})}_2+{\mathrm{O}}_2+2{\mathrm{H}}_2\mathrm{O}\to 4\mathrm{Fe}{(\mathrm{OH})}_3$$

(5)

Therefore, by examining the impact of an EF on the structure and molecular dynamics of hydrated calcium ions and hydrated divalent iron ions, the mechanism of scale inhibition and corrosion under EAF in aqueous solutions may be more readily ascertained. This paper’s study involves a blend of CaCl₂ and FeCl₂. The position of the first water shell of calcium ions and divalent iron ions, the framework of hydrated calcium ions and divalent iron ions, the self-diffusion coefficients of calcium ions, divalent iron ions, and water molecules, and hydrogen bonding in the liquid solution were all investigated using MD simulations to study the structural and kinetic properties of aqueous CaCl₂ solutions under an external EF. It should be noted that although the materials in this study and our previous work [11] are mixed aqueous solutions of two ions containing calcium ions, there are significant differences in the research details between the two. Our previous work mainly focused on the influence of magnesium ion impurities on the scaling process of calcium ions during the operation of the EAF system. However, in this study, we chose to pay attention to the influence of the EAF system on the corrosion process of iron water transmission pipes.

2. Model and Simulation Details

An equilibrium MD simulation was performed by using the Gromacs 5.0.2 software [12]. NPT ensembles were used for all simulations. The thermostat was adjusted to 300 K. The pressure was established at 1.01 × 10⁵ Pa. As stated in

Table 1. Composition of the CaCl₂ solution studied by Gromacs.

Sample	[H2O]	[Fe2+]	[Ca2+]	[Cl−]	[Total]
0F	1110	0	80	160	1350
10F	1110	10	80	180	1380
20F	1110	20	80	200	1410
30F	1110	30	80	220	1440

NOTE: “0F” indicates no Fe²⁺ ions were added, “10F” indicates 10 Fe²⁺ were added, “20F” indicates 20 Fe²⁺ were added, and “30F” indicates 30 Fe²⁺ were added.

, four sets of aqueous solution systems were constructed. The CaCl₂ aqueous solution had a concentration of 4 mol/kg, and there was only a 0.5 percent difference in concentration between models and tests [13]. In our study, the water molecule was represented by the SPCE model. In this simulation, ion–water interactions were simulated using the GROMOS force field [14,15,16]. A cutoff of 1.2 nm was used for Lennard-Jones interactions, and a real-space cutoff of 1.2 nm was used for electrostatic interactions when using the particle mesh Ewald (PME) [15] technique. Fourier spacing has a value of 0.12 nm. The Lennard-Jones potential parameters for the particles utilized in the GROMOS force field are shown in

Table 2. The MD simulations employed the Lennard-Jones potential parameters according to the combining rules of Lorentz and Berthelot, i.e., ε_ij = (ε_iiε_jj)^1/2, σ_ij = (σ_ii + σ_jj)/2.

	εii/(kj/mol)	σii/nm
Ca2+	0.5069	0.2813
Fe2+	2.135 × 10−6	1.9129
Cl−	1.2889	0.3470
O	1.7250	0.2626

. The Lennard-Jones parameters of Fe²⁺ were taken from Fernanda et al. [17]. All of the simulations employed a 2.0 fs time step, and a 2.5 × 10⁴ ps simulation time was used to confirm the stability of the system setup. Following a 1 × 10⁴ ps period of system equilibration, the structures and characteristics of the sample (apart from the self-diffusion coefficient data) were determined throughout a 1.5 × 10⁴ ps period (the final 1.5 × 10⁴ ps of each simulation). By computing the average result of 1.5 × 10⁴ ps, which was separated into ten segments, the average values of the parameters were acquired. The leapfrog method is a type of integration algorithm used for motion equations. The simulation box measures 4 nm, 4 nm, and 3 nm in length. The EF was 1 V/μm in intensity. The EF was used in a certain way (corresponding to the y-axis). The simulations were run as described in the step above. Previous research has confirmed the accuracy of our MD simulations and error analyses [18].

3. Results and Discussion

3.1. Structural Parameters

The hydration shell regulates the mobility of ion pairs in the solution and the interaction between ion pairs [19]. A change in the hydration shell can affect calcium carbonate precipitation [20], and the layers of hydration around these ions define the route(s) for crystal formation in aquatic settings [21]. In this segment, the average radii of the first water shells of Ca²⁺ (R_Ca-O), Fe²⁺ (R_Fe-O), Ca²⁺ (n_Ca-O), Fe²⁺ (n_Fe-O), Ca²⁺ (n_Ca-O), and Fe²⁺ (n_Fe-O) under an external EF and under no EF are provided.

It is possible to determine R_Ca-O and R_Fe-O from the RDF [g(r)]; [g(r)] [22] is calculated as shown in Equation (6):

$$g_{AB}(r)=\frac{\langle {\rho }_B(r)\rangle }{{\langle {\rho }_B\rangle }_{local}}=\frac{1}{{\langle {\rho }_B\rangle }_{local}}\frac{1}{N_A}{\displaystyle \sum _{i\in A}^{N_A}{\displaystyle \sum _{j\in B}^{N_B}\frac{\delta (r_{ij}-r)}{4\pi r^2}}}$$

(6)

where ‹ρ_B(r)› is the particle density of particle B on all spheres surrounding particle A with radius r_max, ‹ρ_B›_local is the particle density of particle B at distance r around particle A, N_A denotes the number of particles A, and N_B denotes the number of particles B. Typically, r_max has a value equal to half of the box’s minimum length.

The values of n_Ca-O and n_Fe-O are calculated using Equation (7) [14]:

$$n_{\mathrm{Ca}}^{\mathrm{O}}(r_s)=4\pi {\rho }_0{\displaystyle {\int }_0^{r_s}{g}_{\mathrm{CaO}}}(r)r^{2}dr$$

(7)

For n_Ca-O, r_s is the location of the first local minimum of g_CaO(r), which is also the location of R_Ca-O; for n_Fe-O, r_s is the location of the first local minimum of g_FeO(r), which is also the location of R_Fe-O.

Figure 1 shows RDFs and the corresponding running integration number of the CaCl₂ solution containing different numbers of Fe²⁺. The coordinates of the first peak in g_CaO(r), the coordinates of the first peak in g_FeO(r), R_Ca-O, R_Fe-O, n_Fe-O and n_Ca-O are presented.

According to Figure 1a,c,e, it can be seen that the height of the first peak in Fe²⁺-O g(r) is higher than its Ca²⁺-O g(r) counterpart. The first peak position of Fe²⁺-O g(r) is less than the first peak position of Ca²⁺-O g(r), which implies that Fe²⁺ has a smaller size than Ca²⁺, and the hydrated structure of Fe²⁺ is more stable than Ca²⁺ [23]. Furthermore, the higher the content of Fe²⁺ ions, the lower the heights of the first peak in Ca²⁺-O g(r). Fe²⁺ was added, but it had no discernible impact on R_Ca-O. With an increase in the amount of Fe²⁺ supplied, the n_Ca-O drops. The decrease in n_Ca-O could be due to the more stable hydrated structure of Fe²⁺ compared to Ca²⁺, which means that fewer water molecules remain in the water shell of Ca²⁺. In the CaCl₂ solution containing Fe²⁺ under an EF, Figure 1b,d,f demonstrate that the values of R_Ca-O decrease while the values of n_Ca-O increase, which is consistent with our earlier research on “pure” CaCl₂ aqueous solutions [24]. This is because the average binding ability of water molecules increases monotonically as the hydration shell becomes smaller [25,26]. In addition, the larger height and sharpness of the ferrous peak suggest a more stable structure under the EF, which means that the EF can make the Fe²⁺ radius smaller. The enthalpy of formation of ACC clusters decreases as the coordination number increases in the first hydration shell of Ca²⁺, and the stability of ACC correlates with water content. Experimentally, it has been proposed that “transient” ACC is largely anhydrous, while “stable” ACC contains some water [20]. Therefore, the EF increases the coordination number in the first hydration shell of Ca²⁺ and decreases the enthalpy of ACC, which can enhance the stability of ACC. To a certain extent, the EF reduces the possibility of ACC converting to calcite by changing the structure of the first hydration shell of Ca²⁺, which will play a role in scale inhibition (according to our previous study [27]). The creation of carbonate ions close to Ca²⁺ is made easier by the reduced radius of the initial water shell of Ca²⁺, which promotes the development of calcium carbonate crystals [24].

Figure 1 shows that the values of R_Fe-O range between 0.230 and 0.240 nm, and the values of n_Fe-O are distributed between 4.800 and 5.000, which is consistent with the results reported in Reference [28]. In CaCl₂ solution under an EF, the values of R_Fe-O are larger, and the values of n_Fe-O are lower. According to experimental findings [29], this suggests that the EF decreases hydration between Fe²⁺ and water molecules.

In addition, we also calculated the RDF of chloride ions around Ca²⁺ and Fe²⁺ under an EF (not shown here). The calculation results show that although the influence of the EF on the distribution of chloride ions around cations is small, it enhances the interaction between cations and anions (the number of anions around cations increases slightly). This is consistent with the conclusion of our previous paper. Therefore, the distribution of chloride ions is not analyzed in detail in this section.

3.2. Self-Diffusion Coefficients of Ca²⁺ and Fe²⁺ and Water Molecule

This section examines Ca²⁺, Fe²⁺, and water molecule self-diffusion coefficients in the presence of an exogenous EF in the CaCl₂ aqueous solution system. An important factor that may affect the course of chemical reactions in aqueous systems is the self-diffusion coefficient of ions. In addition, the self-diffusion coefficient may change significantly when the structure of the cation or anion is changed or another ion is involved [30]. It is worth noting that, in the simulation model in this paper, the solution seems to be strongly concentrated since there is 4 mol/kg CaCl₂, which means 4 mol of Ca²⁺ and 8 mol of Cl^- dissolved in 55.6 mol of water that solvates them (see Table 1). It may be considered that there are no free water molecules, because all water molecules seem to become ionic coordination water. This may make water molecules lack independent diffusivity. In fact, as the ions move in the water, the coordination water around the ions is not fixed, and they will be constantly replaced by the surrounding water molecules [13]. Therefore, the water molecules in this paper can be considered to have independent diffusivity, but this diffusivity will be affected by ions.

In this research, the “Einstein relation” [31] was used to calculate the self-diffusion coefficients of Ca²⁺(D_ca) and water molecules (D_o):

$$D=\underset{\mathrm{t}\to \infty }{\lim }\frac{1}{6t}\langle {\left[r_i\left(t\right)-r_i\left(0\right)\right]}^2\rangle$$

(8)

where r_i(0) is the starting position, the parentheses represent the set mean, and r_i(t) is the numerator position i at time t. Fitting the slope of the linear component of the mean square displacement (MSD) and dividing by six are the particular steps in computing the self-diffusion coefficient of a particle. The RANSAC algorithm determines the linear component of the MSD. RANSAC is a technique for robust model fitting in the presence of outliers in the data [32].

The impact of Fe²⁺ on the values of D_ca and D_o with and without an EF is shown in

Table 3. The 10⁵ self-diffusion coefficients of Ca²⁺ (D_ca) and water molecules (D_o) with no Fe²⁺ ions added (0F) and ten Fe²⁺ added (10F), twenty Fe²⁺ added (20F), and thirty Fe²⁺ added (30F) with and without EF.

Sample	Average 10−5 cm2·s−1	St.dev 10−5 cm2·s−1	Average 10−5 cm2·s−1	St.dev 10−5 cm2·s−1
	Without Electrostatic Field		Under Electrostatic Field
Dca
0F	0.0608	0.0003	0.0707	0.0001
10F	0.0185	0.0005	0.0239	0.0001
20F	0.0124	0.0003	0.0137	0.0007
30F	0.0108	0.0005	0.0128	0.0001
Do
0F	0.6626	0.0004	0.7276	0.0003
10F	0.1837	0.0004	0.1870	0.0006
20F	0.1573	0.0005	0.1596	0.0001
30F	0.1283	0.0005	0.1343	0.0003
DFe
10F	0.0188	0.0009	0.0195	0.0004
20F	0.0158	0.0004	0.0180	0.0002
30F	0.0142	0.0002	0.0172	0.0004

. With regard to the self-diffusion coefficient, the standard deviation of the simulation results presented in Table 3 is conservatively estimated to be in the region of 0.41%–5.11%. Table 3 shows that whether or not there is an EF, the values of D_ca and D_o both drop as the amount of Fe²⁺ increases. Moreover, the higher the Fe²⁺ ion content, the lower the values of D_ca and D_o. In addition, Table 3 shows that the external EF can increase the values of D_ca and D_o no matter how much Fe²⁺ exists in the CaCl₂ aqueous solution during all simulations.

The valence and structural order of cations in aquatic environments impact the rate at which water molecules diffuse [33]. According to Table 3, the values of D_o are 0.6626 × 10⁻⁵ cm²·s⁻¹ and 0.7276 × 10⁻⁵ cm²·s⁻¹ without and with an EF, respectively, when Fe²⁺ is not in the solutions, in contrast to the values of D_o in the range of 0.12 × 10⁻⁵ cm²·s⁻¹–0.18 × 10⁻⁵ cm²·s⁻¹ when different numbers of Fe²⁺ ions are present. It is worth noting that when iron ions exist, the existence of an electric field can only slightly increase the diffusion coefficient of water molecules (with an increase of about 5%), which may be due to the binding of iron ions to water molecules, weakening the influence of the electric field. Water molecules that are coupled to metal ions are successfully immobilized in relation to the bulk water by being contained in a hydration layer [21]. As a result, when Fe²⁺ is available in the CaCl₂ solution, its significant capacity to bind to water molecules restricts the activity of the water molecules. The D_o values decline. The presence of Fe²⁺ is responsible for the decrease in the self-diffusion coefficient of Ca²⁺. The CaCl₂ aqueous solution becomes more compact due to the electrostatic contact between Fe²⁺ and the water molecule. Ca²⁺ activity is constrained, and its self-diffusion coefficient is decreased.

The EF lowers the water molecule’s self-diffusion coefficient while increasing the hydrogen bond network’s binding capacity in pure water solutions [34]. However, the findings in Table 3 demonstrate that for the four example CaCl₂ aqueous solutions, the EF may increase the water molecule’s self-diffusion coefficient. Therefore, the rise in the diffusion coefficient of water molecules in aqueous CaCl₂ solutions can be attributed to the activity of metal ions in the solution. When Ca²⁺ and Fe²⁺ diffuse, they either displace their solvated shells along their trajectories or break the strong connections with the initial water shell [35]. Thus, the EF increases the activity of Ca²⁺ and Fe²⁺ and influences the relatively stable water molecule hydrogen bond network.

As can be seen in Table 3, the self-diffusion coefficients of water molecules and Fe²⁺ in aqueous CaCl₂ solutions grow in the presence of EF. The speed at which oxidants are transported to the scale’s surface may be increased by increasing the activity of water molecules, which can reduce iron release and the amounts of iron corrosion products that dissolve in water [36,37]. Water contamination issues may be resolved. Additionally, the rise in D_o and D_Fe may indicate that the EF has the ability to accelerate the oxidation of Fe²⁺.

3.3. Viscosity of the CaCl₂ Aqueous Solution

Generally, the formation of calcium carbonate precipitation involves three stages: nucleation, grain growth, and aggregation of CaCO₃ crystals [38]. The viscosity of the solution affects the precipitation of calcium carbonate and the corrosion behavior of iron in the solution [39,40,41,42,43]. According to experimental findings, the crystallinity of scale-forming ions mixed with water is inversely related to the viscosity of a liquid [44]. A liquid’s dynamic viscosity is another kinetic characteristic that affects how quickly solutes in the liquid alter their conformation. It is susceptible to an EF [44].

The following equation can be used to determine the viscosity (η):

$$\eta =\frac{A}{V}\frac{\rho }{k^2}$$

(9)

where ρ and V stand for density and velocity, respectively; A is a constant [44], and we can deduce the following from a cosine that meets both requirements:

$$a_x=A\cos (kz),k=2\pi /l_z$$

(10)

where l_z is the box’s height. In the simulation, the instantaneous V is defined as a Fourier coefficient:

$$V(t)=\frac{2{\displaystyle \sum _{i=1}^N{m}_i{v}_{i,x}(t)}\cos [k{r}_{i,z}(t)]}{{\displaystyle \sum _{i=1}^N{m}_i}}$$

(11)

where m_i is the mass of an atom, r_i,z is the z coordinate, and v_i,x is the x component of the velocity. The amplitude of the velocity profile can be completely formed before measuring the average for V.

Four sample CaCl₂ aqueous solutions’ viscosities under an EF are shown in Figure 2. For comparison, the values in the absence of the EF are shown. As shown in Figure 2, the presence of Fe²⁺ increases the viscosity values in the CaCl₂ system, and four typical aqueous CaCl₂ solutions become viscous in the presence of Fe²⁺. The EF also reduces the viscosity of aqueous CaCl₂ solutions.

The molecular weight of the particles inside the system is inversely proportional to the dynamic viscosity, which is a reflection of a sort of friction brought on by fluid motion in the solution system. Bakker [45] found that viscosity is a distinct feature that describes the typical behavior of a large number of water molecules in aqueous solutions and that specific ions have a significant effect on the viscosity of water because of the extended lifetime of their initial hydration shells. Viscosity is substantially influenced by the water molecules’ extended residence periods in ion hydration shells. The aqueous solution of CaCl₂ also has no carbon–hydrogen bonds, making it an inorganic salt. Therefore, changes in the viscosity of CaCl₂ solutions can be attributed to changes in the structural and kinetic properties of the water molecules.

Figure 2 demonstrates that without the EF, the viscosities of the four example CaCl₂ aqueous solutions are 9.49 × 10⁻³ Pa·s, 16.31 × 10⁻³ Pa·s, 17.24 × 10⁻³ Pa·s, and 17.81 × 10⁻³ Pa·s. This means that the addition of Fe²⁺ can cause a relatively high viscosity in CaCl₂ aqueous solutions. Dian et al. [46] studied Ca²⁺ solvation using polarizable atomic multipole potential, and their results show that the lifetime of water molecules in the first solvation shell of Ca²⁺ is 18 picoseconds (ps) when the temperature is 298 K. The experimental [47] values of the lifetime of water molecules in the first solvation shell of Fe²⁺ were determined in the range of 10⁵–10⁶ ps when the temperature is 298.15 K, in contrast to only a few picoseconds for Ca²⁺. Therefore, the addition of Fe²⁺ forms a water shell, which can lead to a longer residence time for water molecules in Fe²⁺ hydration shells compared to Ca²⁺. Therefore, the viscosity of the solution is greatly increased by Fe²⁺. Furthermore, the mobility of water molecules is related to the viscosity of the solution. According to Table 3, the activity of water molecules is more limited when the Fe²⁺ ion content increases, and this may result in a rise in the solution’s viscosity.

Figure 2 demonstrates that when Fe²⁺ ions are available in the solution, the EF can reduce the viscosity of CaCl₂ aqueous solutions. This is due to the fact that the EF reduces the mean dynamic residence time of water at Ca²⁺ and increases the activity of water molecules, both of which lead to a drop in dynamic viscosity. The viscosity of the salt solution can be reduced by the EF [48]. Electrostatic interaction between the water molecule and Fe²⁺ might raise the viscosity of the solution. This indicates that the dynamic viscosity of the CaCl₂ solution can be reduced by the presence of Fe²⁺ and an external EF. In conclusion, the aqueous CaCl₂ solution can become more viscous when Fe²⁺ ions are present, and the viscosity can be reduced when an EF is applied to an aqueous CaCl₂ solution that contains Fe²⁺. The decrease in viscosity of CaCl₂ aqueous solutions, on the one hand, means that the scale-forming ions in the solution are reduced [40] and the fluidity of the solution is enhanced [49]. On the other hand, the decrease in the viscosity of CaCl₂ aqueous solutions reduces the aggregation of calcium carbonate precipitates [41,42,43], which plays an effective role in anti-fouling. The decrease in solution viscosity reduces the adhesion of the electrode surface to ions and increases the rate of transport of oxidants, which can influence the capacitance values of the double layer and reflect changes in the surface state of the corrosion metal [36,37].

3.4. Effect of Fe²⁺ and Electric Field on Hydrogen Bonds

The hydrogen bond network that is generated by water molecules has a significant impact on the precipitation of calcium carbonate [20,21] and is strongly connected to the chemical and physical characteristics of aqueous solutions [50,51]. The dissolution of calcium carbonate and corrosion products is influenced by the nature of the hydrogen bond network. According to Gromacs software, a hydrogen bond occurs when a donor and acceptor are separated by a van der Waals (VDW) length less than 3.5Å(r) and when the hydrogen donor–acceptor angle is less than 30° [52]. The geometrical hydrogen bond requirement is displayed in Figure 3. The oxygen atoms in water molecules are the study’s donors and acceptors. This work estimated the hydrogen bond angle as ∠O_D-H_D- O_A(θ), which is a suitable angle that is frequently used in the literature and offers helpful insight into the flexibility of donor hydrogen bonds [53]. Calculating the number of hydrogen bonds allows one to assess the overall importance of a hydrogen bond. The number of hydrogen bonds and the strength of the hydrogen bonds are positively correlated [52].

The current study looked at both the number of hydrogen bonds (n_HB) and the percentage of water molecules with n or more hydrogen bonds (f_n). Without the addition of Fe²⁺ (0F) and with the addition of 10 Fe²⁺ (10F), 20 Fe²⁺ (20F), and 30 Fe²⁺ (30F), the values of f_n and n_HB in CaCl₂ aqueous solutions are shown in

Table 4. The proportion of water molecules that have n hydrogen bonds (f_n), the amount of Fe²⁺ that was added F(n*F), and the average number of hydrogen bonds per water molecule (n_HB).

	Without Electrostatic Field				Under Electrostatic Field
	0F	10F	20F	30F	0F	10F	20F	30F
f0(%)	58.09	61.54	62.20	65.02	57.99	60.93	61.10	64.08
f1(%)	31.17	29.75	29.16	28.39	31.08	29.88	29.80	29.36
f2(%)	8.23	7.37	7.30	6.59	8.34	7.80	7.70	7.04
f3(%)	1.56	1.29	1.28	1.18	1.63	1.34	1.36	1.27
nHB	580.67	536.78	528.55	512.19	584.43	549.33	546.80	524.60

. (30F). Additionally, the effect of the EF is demonstrated.

Table 4 demonstrates how the EF may alter the percentage of molecules without hydrogen bonds while increasing the percentage of molecules with one to three hydrogen bonds and the average number of hydrogen bonds in a water molecule, regardless of the presence or absence of Fe²⁺. The proportion of water molecules with n or more hydrogen bonds might be used to define the dimension of the water cluster. For instance, the size of the water cluster increases with the proportion of molecules with two or three hydrogen bonds. The decrease in f₀ and the rise in n_HB, f₁, f₂, and f₃ indicate that water molecule activity is constrained and that more water molecules are shifting from the free state to the hydrogen-bonded state. This indicates that the EF improves the hydrogen structure of the water molecules to some extent. The findings in Table 4 further demonstrate that, regardless of whether the EF is administered or not, Fe²⁺ can enhance f₀ and reduce n_HB, f₁, f₂, and f₃. Additionally, in the CaCl₂ systems, n_HB, f₁, f₂, and f₃ decrease as the amount of Fe²⁺ rises, whereas f₀ increases. This is the result of the Fe²⁺ ion’s ability to attract ion–dipole interactions, which retains water molecules in the ion hydration shell and reduces the number of water molecules bound by hydrogen bonds [54]. This results in fewer hydrogen bonds being created, an increase in the percentage of molecules without hydrogen bonds, a drop in the percentage of molecules with one to three hydrogen bonds, and a rise in the mean number of hydrogen bonds per water molecule.

4. Conclusions

A methodical long-time balanced molecular dynamics simulation was used to examine the structural and dynamic characteristics of mixed solutions of CaCl₂ and FeCl₂ under an EF. Some significant findings were made.

(1)

Compared to Ca²⁺, the hydrated structure of Fe²⁺ is more stable. The EF may raise the first water coordination number for Ca²⁺ and reduce the radius of hydrated Ca²⁺. The EF has the ability to reduce the first water coordination number for hydrated Fe²⁺ and expand its radius. The presence of Fe²⁺ has no discernible impact on the radius of hydrated Ca²⁺; however, it can lower the first water coordination number of Ca²⁺.

(2)

The viscosity of CaCl₂ in an aqueous solution can be efficiently raised by Fe²⁺. The presence of an EF can make the mixed aqueous solution less viscous.

(3)

The self-diffusion coefficient of Ca²⁺ can be lowered by Fe²⁺. Ca²⁺, Fe²⁺, and water molecules’ self-diffusion coefficients can all be increased by an EF.

(4)

An EF can enhance the hydrogen structure of the water molecules in the aqueous solution.

To sum up, the EF generated by an EAF system can change the structure of the solvent layer of Ca²⁺, resulting in a reduction in the possibility of Ca²⁺ forming high-density calcite scale. In addition, the existence of an EF can also increase the activity of water molecules and reduce the viscosity of the solution, which will effectively hinder the release of Fe²⁺ in water and the formation of iron corrosion products.