The inhibitory effects of four inhibitors on the solution adsorption of CaCO3 on Fe3O4 and Fe2O3 surfaces

This study presents the inhibitory effects of four scale inhibitors, including polyacrylic acid (PAA), hydrolyzed polymaleic anhydride (HPMA), polyepoxysuccinic acid (PESA) and polyaspartic acid (PASP), on the adsorption of CaCO3 on the surfaces of Fe3O4 and Fe2O3. Samples were characterized using SEM and EDS and the average atomic number ratios of Ca/Fe were calculated. Inhibition effects followed the trend: PESA > PAA > PASP > HPMA and PESA > PASP > HPMA > PAA for Fe3O4 and Fe2O3, respectively. Molecular dynamics simulations based on the adsorption model of the scale inhibitor on the surface and calculations of the adsorption energy between the scale inhibitor molecule and the surface revealed that the relatively high scale inhibitory effect is due to low adsorption energy between the inhibitor molecule and the surface. Density Functional Theory (DFT) calculations of the model after adsorption revealed that the relatively low adsorption energy depends on the number of H-O bonds formed as well as those with higher Mulliken population values between the scale inhibitor and the surface.

ratios in different cases were obtained and compared with each other to evaluate the inhibition effects of the four inhibitors. We then established models of the scale inhibitor molecules with both the Fe 3 O 4 and Fe 2 O 3 surfaces using the Materials Studio.
The adsorption energies between the scale inhibitor and the surface were calculated and the results indicated that differences in the effects of the scale inhibitor in the scale inhibition process are attributed to the differences    Scaling. UP water was added to a beaker with an additional 30 mL UP water to compensate for evaporation loss (the evaporation loss amount was obtained experimentally). The water was heated to 51 °C on a stirring hotplate; CaCl 2 and NaHCO 3 were added to generate CaCO 3 .

Molecular Models and Simulation Details
Software and force field. In this study, the Amorphous Cell, Discover, Forcite, and Caste modules in Materials Studio 7.0 software were used. The Amorphous Cell module was used to create a mixed layer of water molecules and scale inhibitor molecules. The Discover module was used to minimize energy while the Forcite module was used to run molecular dynamics simulation programs using the COMPASS force field [13][14][15] 10.08 Å and 42.7 Å, respectively. All atoms on the surface were set in a fixed state. The surface model established is shown in Fig. 2.
The four scale inhibitor molecules were manually drawn (see Fig. 3). Since adsorptions are in solution, a mixed layer was established in the Amorphous Cell module using a scale inhibitor molecule and 20 water molecules. The a and b values of the mixed layer are identical to the surface model values. The surface model was combined with the mixed layer by using the layer program and both the scale inhibitor molecule and water molecules were set in a free state 24 . The initial adsorption models of all inhibitors on both surfaces are shown in Fig. 4.

Simulation.
After establishing the initial adsorption models, the energy was minimized using the discover module. Smart minimizer, which includes Steepest descent, Conjugate gradient and Newton, was selected as the energy minimization method in the module. The convergence of all methods was set at 10 −7 . The Forcite module   www.nature.com/scientificreports www.nature.com/scientificreports/ was used for molecular dynamics simulation. The NVT ensemble was used, the temperature was 324 K (i.e., 51 °C), the number of steps calculated was 20,000,000 and Berendsen was selected as Themostat. The adsorption models of the scale inhibitor molecule on the (111) surface of Fe 3 O 4 and the (104) surface of Fe 2 O 3 from molecular dynamics calculations are shown in Fig. 5. Finally, the Castep module was used for DFT calculations. In this module, GGA and PBE were selected as Functional, and Fine was selected as Quality.       Tables 1-4. Tables 1-4 show that the ratios of CaCO3 areas and the surface area of the suspended pieces in different solutions were obtained based on the average ratio of Ca and Fe atoms at each detection point (Table 5).
Since the areas of all detection points are identical, the area occupied by CaCO 3 increased and the scale inhibition effect degraded as the Ca/Fe ratio increased. As shown in Table 5, the Ca/Fe ratio in the absence of a scale inhibitor increased significantly relative to when an inhibitor was present.
In addition, the Ca/Fe ratios are different for different inhibitors. Indeed, the Ca/Fe ratios of the four inhibitors on the surface of Fe 3 O 4 increase in the following manner PESA < PAA < PASP < HPMA, indicating that inhibition of CaCO 3 scale on the Fe 3 O 4 surface follows the same sequence. The Ca/Fe ratios of the four scale inhibitors on the surface of Fe 2 O 3 follow the sequence of PESA < PASP < HPMA < PAA.

Calculation of adsorption energy. The inhibition of CaCO 3 surface adsorption by scale inhibitors is that
active sites on the surface prefer occupation by the inhibitor molecules relative to CaCO 3 . The adsorption energy between the inhibitor molecules and the surface is calculated by 25,26 : where + E surf inhi refers to the model energy in the presence of both surfaces and scale inhibitor molecules; E surf and E inhi refer to the model energy in the presence of surface or scale inhibitor molecules, respectively. The adsorption energies between the four inhibitor molecules and the surfaces are shown in Table 6.
All ΔE values in Table 6 are negative, indicating that adsorptions are spontaneous. As the adsorption energy decreased, the adsorption strength increased as did the adsorption stability. As shown in Table 6, ΔE follows the sequence of PESA < PAA < PASP < HPMA, indicating the adsorption strength of the inhibitors on the    Tables 5 and 6, the scale inhibition effect is related to the adsorption energy. The adsorption energies between Fe 3 O 4 and inhibitors PASP and PAA were similar, as were the Ca/Fe ratios and inhibition effects. For the Fe 2 O 3 surface, the PSAP and PESA adsorption energies were significantly lower than the adsorption energies of HPMA and PAA so the inhibitory effects and Ca/Fe ratios of PSAP and PESA were markedly lower for the Fe 2 O 3 surface.

DFT calculations.
As the bonds between the inhibitor molecule and the surface increased and the bonding Mulliken population value increased, the binding affinity of the scale inhibitor molecule and the surface increased so the adsorption energy decreased. Therefore, the difference in adsorption energy between the inhibitor and the surface can be attributed to the number of bonds between the inhibitor molecule and the surface as well as the bonding Mulliken population value. The bonding between each inhibitor and the surfaces is shown in Table 7.
As shown in Table 7 O 3 , and one of them had a Mulliken population value above 0.1. Therefore, the adsorption strength of PASP on Fe 2 O 3 was lower than PESA, but higher than HPMA. As only one H-O bond was generated between PAA and Fe 2 O 3 , the adsorption strength of PAA on Fe 2 O 3 was the lowest among all samples.

Conclusions
This study presents a study of the inhibitory effects of PAA, HPMA, PESA and PASP on the adsorption of CaCO 3 to the surfaces of Fe 3 O 4 and Fe 2 O 3 . According to average Ca/Fe ratios obtained by EDS, the scale inhibition effect follows the sequence of PESA > PAA > PASP > HPMA and PESA > PASP > HPMA > PAA for Fe 3 O 4 and Fe 2 O 3 surfaces, respectively. The adsorption energies between the inhibitor molecules and the surface were calculated by molecular dynamics simulations. The sequence of adsorption energies is PESA < PAA < PASP < HPMA and PESA < PASP < HPMA < PAA for Fe 3 O 4 and Fe 2 O 3 surfaces, respectively. A low adsorption energy means strong inhibitor adsorption on the surface and inhibition depends on adsorption strength. Thus, these results demonstrated that excellent inhibition is due to low adsorption energy between the scale inhibitor and the surface. The number of bonds generated and their Mulliken population values calculated by DFT indicated that low adsorption energy depends on the formation of considerable H-O bonds with high Mulliken population values between the scale inhibitor and the surface.