The inhibition effect mechanisms of four scale inhibitors on the formation and crystal growth of CaCO3 in solution

The experimentation, molecular dynamics simulation and DFT calculation were used to study the inhibition effects of four scale inhibitors, including polyacrylic acid (PAA), hydrolyzed polymaleic anhydride (HPMA), polyepoxysuccinic acid (PESA) and polyaspartic acid (PASP), on formation and crystal growth of CaCO3 in solutions. According to concentrations of Ca2+ in solutions, the sequence of inhibition effects of scale inhibitors on formation of CaCO3 in the solution was PESA > PASP > HPMA > PAA. Characterization of CaCO3 crystals by XRD and a laser particle size analyzer indicated that the sequence of inhibition effects of scale inhibitors on crystal growth of CaCO3 in solutions was PESA > HPMA > PASP > PAA. Interaction energies between the scale inhibitor molecule and Ca2+, and between the scale inhibitor molecule and the CaCO3 (104) surface indicated that the difference of the inhibition effects was derived from the difference in the interaction energy. The results of DFT calculation indicated that the difference between the interaction energies of these inhibitors and Ca2+ was derived from differences of number and the Mulliken population values of the chemical bonds which formed between the inhibitor molecule and Ca2+ and between the inhibitor molecule and the CaCO3 surface.

Produced water in gas fields is one of the by-products of natural gas production. Since the produced water contains a variety of ions, especially calcium, the formation of water-insoluble compounds is common via various chemical reactions. The most common compound is CaCO 3 , forming undesirable scale. Since the produced water is usually separated from the gas in the separator and then passed through the sewage pipe into other equipment, the sewage pipe is the most severely scaled area. The main target of scale inhibition in gas fields is also the sewage in sewage pipes.
For four common non-phosphorus scale inhibitors, including polyacrylic acid (PAA), hydrolyzed polymaleic anhydride (HPMA), polyepoxysuccinic acid (PESA) and polyaspartic acid (PASP), the scale inhibition effects on CaCO 3 in solution mainly include two aspects. One aspect is to inhibit the formation of CaCO 3 . When the scale inhibitor is present in the solution, the Ca 2+ concentration increases with the increase of the concentration of the scale inhibitor. Therefore, the amount of formed CaCO 3 decreases [1][2][3][4][5][6] . The other aspect is to inhibit the growth of CaCO 3 crystals. Calcite is the most stable crystal structure of CaCO 3 in general, and the most common solid in scale. PAA, HPMA, PESA and PASP can all be adsorbed to the main growth surface of the calcite crystal, therefore inhibiting the growth of crystals and resulting in the destruction of the regular shape of the calcite crystal [2][3][4][5][6][7][8][9][10] . This leads to the weakening of the crystal stability. The scale inhibition effect mechanisms among these scale inhibitors were also compared. HPMA has higher scale inhibition effect than PAA 3 , and PESA has better scale inhibition effect than PAA, HPMA and PASP 11,12 .
The previously reported research focused on describing the inhibitory effects from experimental results and lacked research on the mechanisms of inhibition. In this paper, we first evaluated the scale inhibition effect of four scale inhibitors based on the experimental results. We then established a molecular dynamics simulation model to calculate the interaction energies between the scale inhibitor molecules and Ca 2+ , as well as the scale inhibitor Experimental procedures. The scale inhibition effects of the scale inhibitor on CaCO 3 include the inhibition of formation and crystal growth of CaCO 3 . Therefore, the experiment was divided into two groups. The experimental temperature was set at 51 °C and the pH was 6.6-6.8. (The temperature and pH were the same operational conditions as the as at the sewage station). Experiment 1: inhibiting the formation of CaCO 3 . To begin, 1 L UP water (without scale inhibitor) and 0.99 L UP water with added scale inhibitor were added to each beaker. Additionally, 30 mL mixed solution (contains HCl, ammonia-ammonium chloride buffer solution and UP water) was added to each beaker during the experiment to control the pH of solution and compensate for the evaporation loss. The beakers were placed on a magnetic stirrer and heat to 51 °C. 0.959 g NaHCO 3 and 10 mL scale inhibitor were added to the solution. After stirring for 30 min, 0.933 g CaCl 2 was added into solution and start the experiment. The experiment duration was 24 h. After the experiment was completed, wait time of 6 h was needed to allow the CaCO 3 solid precipitate. The supernatant was poured into a Buchner funnel with double-layer filter paper for filtration. Each set of clear liquids was repeatedly filtered 3 times. The clear liquid after the third filtration was stored for examination. The experiment of inhibiting the formation of CaCO 3 was repeat three times. Experiment 2: inhibiting crystal growth of CaCO 3 . To begin, 1 L UP water (without scale inhibitor) and 0.99 L UP water with added scale inhibitor were added to each beaker. Additionally, 30 mL mixed solution (contains HCl, ammonia-ammonium chloride buffer solution and UP water) was added to each beaker during the experiment to control the pH of solution and compensate for the evaporation loss. The beakers were placed on a magnetic stirrer and brought to 51 °C. NaHCO 3 and CaCl 2 were added to the solution. After stirring for 30 min, the scale inhibitor was added to start the experiment. The experiment was left to react for 24 h. After the experiment completed, the turbid liquid was poured into a Buchner funnel with single-layer filter paper for filtration. After filtration, the filter paper containing the slurry of CaCO 3 was placed in an oven (105 °C) for 6 h. Then the dry CaCO 3 powder was stored for examination. The experiment of inhibiting crystal growth of CaCO 3 was repeat three times.

Molecular Models and Simulation Details
Software and force field. In this study, the amorphous cell, Discover, Forcite, and Castep 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] . The Castep module was used to calculate the bond number and the Mulliken population value between the scale inhibitor molecule and the surface. The functional used for these calculations is the GGA of Perdew, Burke, and Enzerhof (PBE) 16,17 . Molecular models. The four scale inhibitor molecules are drawn manually, as shown in Fig. 1. 3 . Since the scale inhibitors prevent the formation of CaCO 3 based on the Ca 2+ concentration, the interaction between the inhibitor molecules and Ca 2+ can be used to evaluate the scale inhibition effect 2,18-20 . The model used to examine the inhibition of the formation of CaCO 3 contained 1 scale inhibitor molecule, 1 Ca 2+ , and 20 water molecules and was built using the amorphous cell module in Materials Studio. The initial configuration of this model is shown in Fig. 2. In order to ensure the ionization of Ca in this model, its charge and force field were the same as those used for the Ca 2+ in the CaCO 3 molecule.

Model for inhibiting formation of CaCO
Model for inhibiting crystal growth of CaCO 3 . As shown in Fig. 3, the X-ray diffraction (XRD) spectrum of CaCO3 shows that the peak corresponding to the (104) surface was significantly higher than that of the other surfaces, in the absence of scale inhibitors. Hence, the (104) surface is used as the surface of the CaCO 3 crystal. The initial molecular models of the CaCO 3 crystals were imported from a software database. The designated surface was cut to obtain the required adsorption surface. The a, b and c values of the (104) surface model of the established CaCO 3 crystal were 8.09 Å, 9.98 Å and 37.91 Å, respectively. Since the rotation of CO 3 2− had a large influence on the adsorption process, the Ca and C atoms in the crystal surface were set to the fixed state, and the O atom was set to the free state 21 . A mixed layer, using one scale inhibitor molecule and 20 water molecules, was created in the amorphous cell module and the a and b values were chosen to be identical to the surface model values. The surface model was combined with the mixed layer by using thebuild layers program in Materials Studio software. The Finitial model for inhibiting the CaCO 3 crystal growth is shown in Fig. 4.  www.nature.com/scientificreports www.nature.com/scientificreports/ Simulation conditions. Once the models were created, the energy of each was minimized using the smart minimizer, which includes steepest descent, conjugate gradient and Newton methods. The convergence of all methods was set at 10 −7 . The Forcite module was used to perform molecular dynamics simulations. The  www.nature.com/scientificreports www.nature.com/scientificreports/ temperature was set to 324 K (i.e., 51 °C), and 20 million steps in the NVT ensemble were performed using a Berendsen thermostat. After the molecular dynamics simulations completed, the final state of the model is shown in Fig. 5. Finally, the Castep module of Materials Studio was used to perform DFT calculations. In this module, the PBE functional was chosen, and Fine was selected as Quality.

Results and Discussion
Scale inhibitor and Ca 2+ . The clear liquid was placed in an ion chromatograph (ICS-5000, Thermofisher Scientific CO., USA) for detection, and the obtained Ca 2+ concentration is shown in Table 1. www.nature.com/scientificreports www.nature.com/scientificreports/ As shown in Table 1, the concentration of Ca 2+ in the solution containing no scale inhibitor was significantly lower than that in the solution containing scale inhibitors, indicating that most of the Ca 2+ was formed as a precipitate of CaCO 3 in absence of scale inhibitors. Most Ca 2+ remained in a free state in presence of scale inhibitors. The sequence of Ca 2+ concentration in solutions containing different scale inhibitors was PESA > PASP > HPMA > PAA. Therefore, the sequence of effects of inhibiting the formation of CaCO 3 was PESA > PASP > HPMA > PAA.
Scale inhibitor inhibiting crystal growth of CaCO 3 . The experimentally obtained powders were examined by SEM (Quanta 250, FEI Co., USA), XRD (D8 ADVANCE, Bruker AXS CO., Germany) and laser particle analyzer (HYDRO2000 (APA2000), Malvern CO. UK), respectively. The CaCO 3 crystal morphology are shown in Figs 6-8. The XRD peak of the CaCO 3 (104) surface and the average volume of particle size of CaCO 3 crystal are shown in Figs 9 and 10 and Table 2, respectively.
As shown in Figs 6-8, in absence of scale inhibitors, the CaCO 3 crystal mainly exhibited long needle-like and hexahedral shapes. In presence of scale inhibitors, the particle size of the CaCO 3 crystal reduced significantly, and the CaCO 3 crystal exhibited short needle-like and irregular polyhedron shapes. As shown in Figs 9 and 10 and Table 2, the XRD peak of the (104) surface and the CaCO 3 crystal average volume particle size in presence of scale inhibitors were significantly smaller than those in absence of scale inhibitors.  www.nature.com/scientificreports www.nature.com/scientificreports/ Also as shown in Figs 6-10 and Table 2, in presence of scale inhibitors, the crystal growth of the (104) surface of CaCO 3 was suppressed, the overall growth rate of the crystal was decelerated, and the average volume particle size was reduced. The sequences of both XRD peak and the volume average particle size in solutions containing       Tables 3 and 4 are negative, indicating that the interactions between the inhibitors and Ca 2+ and CaCO 3 (104) are spontaneous. Comparing the values of ΔE 1 and ΔE 2 , the sequences of interaction energies between Ca 2+ and scale inhibitor molecules and the CaCO 3 (104) surface are PESA < PASP < HPMA < PAA and PESA < HPMA < PASP < PAA, respectively.
When the value of the interaction energy is more negative, the interaction modeled is more stable and the intensity of the action was higher. Therefore, the sequence of interaction strengths between Ca 2+ and the scale    www.nature.com/scientificreports www.nature.com/scientificreports/ inhibitor molecules is PESA > PASP > HPMA > PAA. The interaction between Ca 2+ and scale inhibitor molecules was the main reason for Ca 2+ to be in a free state. The inhibition of CaCO 3 formation by each scale inhibitor seen experimentally correlates with the sequence of interaction strengths between Ca 2+ and the scale inhibitor molecules.
The sequence of interaction strengths between the CaCO 3 (104) surface and the scale inhibitor molecules is PESA > HPMA > PASP > PAA. If the bonding strength between the scale inhibitor and CaCO 3 (104) surface was higher, the active growth point of the surface was occupied by the scale inhibitor molecule instead of the CaCO 3 molecule, which resulted in the surface growth rate decreasing and further resulted in the growth rate of CaCO 3 crystal decreasing. Therefore, the inhibition of CaCO 3 crystal growth by each scale inhibitor seems to follow the sequence of interaction strengths between the CaCO 3 (104) surface and the scale inhibitor molecules.
DFT calculations. The interaction between the two components was proportional to the number of chemical bonds formed between the two interacting components and the Mulliken population value of the bonds. The interaction energy was inversely proportional to the number of chemical bonds and the Mulliken population value of the bonds. The chemical bonds formed, bond lengths, and Mulliken populations for the interaction between the scale inhibitor molecule and the Ca 2+ and the CaCO 3 (104) surface are shown in Tables 5 and 6, respectively.
As shown in Table 5, the bonds formed between the Ca 2+ and the scale inhibitor molecules were formed by Ca 2+ and O atoms in the scale inhibitor molecules 24 . PESA and Ca 2+ formed four Ca-O bonds, the most bonds formed compared to the other three inhibitors. The interaction energy value between PESA and Ca 2+ was the lowest of any inhibitor, therefore, the interaction was the strongest. The other three scale inhibitors only formed one Ca-O bond with Ca 2+ . The sequences of the Mulliken population values of the bonds and interaction intensities for the other three inhibitors are both PASP > HPMA > PAA. The sequence of interaction energy values is PASP < HPMA < PAA. According to the number of bonds formed and the Mulliken population values of the bond(s), the sequence of interaction strengths between the scale inhibitors and Ca 2+ was PESA > PASP > HPMA > PAA, and the sequence of interaction energy values was PESA < PASP < HPMA < PAA.
As shown in Table 6, two types of chemical bonds are formed between the scale inhibitor molecules and the Therefore, the interaction strengths between PASP and PAA with the surface are weaker than those between PESA and HPMA with the surface. By comparing the Mulliken population values of the same type of chemical bonds, it can be concluded that the strength between PASP and the surface is higher than that between PAA and the surface. According to the number of bonds formed and the Mulliken population values of the bonds, the sequence of interaction strengths between the scale inhibitors and the CaCO 3 (104) surface is PESA > HPMA > PASP > PAA, while the sequence of interaction energy values is PESA < HPMA < PASP < PAA.

Conclusions
In this study, the mechanism of inhibition effects of PAA, HPMA, PESA and PASP on the formation and crystal growth of CaCO 3 in the solution were studied. According to the experimental results, the sequence of inhibition effects of scale inhibitor on formation of CaCO 3 is PESA > PASP > HPMA > PAA, while the sequence of inhibitory effects on crystal growth of CaCO 3 is PESA > HPMA > PASP > PAA. Calculating the interaction energies between the scale inhibitor molecules and Ca 2+ as well as the CaCO 3 (104) surface shows that the higher inhibition effect is derived from lower interaction energy values. DFT calculations indicate that lower interaction energy values are derived from the formation of a larger number of chemical bonds with higher Mulliken population values between the scale inhibitor and the Ca 2+ , as well as between scale inhibitor molecules and the CaCO 3 (104) surface. According to the mechanism of the four common inhibitors, the inhibition effects of other inhibitors could be evaluated by similar means in the future.