Molecular dynamics simulation of the distribution of potassium perfluorooctanesulfonate in water

We used the molecular dynamics method to simulate the behavior of potassium perfluorohexanesulfonate (KPFOS) in water/gas system. The results indicate that PFOS− can spontaneously migrate to the water/gas interface and form a layered structure with hydrophobic tail chains facing the gas phase and hydrophilic sulfonic acid groups immersed in the water phase, while some PFOS− molecules within the solution formed spherical micelles. Both the number density and charge density distributions confirm that PFOS− and K+ are mainly distributed at the water/gas interface, and a small amount of PFOS− and K+ are distributed in the bulk solution. Based on the results of radial distribution function, the probability of K+ appearing near oxygen atoms in PFOS− is very high due to electrostatic attraction. Based on the IGMH analysis, the oxygen atoms in PFOS− can form multiple hydrogen bonds with adjacent water molecules, while there is only weak van der Waals interaction between K+ and water molecules.


Introduction
Surfactants are widely used in everyday products such as soap and shampoo (Presley et al. 2021;Subhodip et al. 2022;Tripathy et al. 2018).Surfactants are also used in mineral flotation, textile printing and dyeing, paper manufacturing, and other industrial applications (Huang et al. 2020;Ambreen et al. 2021;Mohammad et al. 2019).Likewise, in the oil and gas development industry, surfactants have also made a splash.In many cases, oil and gas wells productive are not always satisfactory due to differences in formation pressure.Effective measures must be taken to increase production in wells with low pressure and/or permeability (Xinhua and Jun 2018).Hydraulic fracturing is widely regarded as the most effective method of increasing oil and gas well production at the moment (Fujian et al. 2019;Li et al. 2019).During hydraulic fracturing, a high volume of fluid is used to transport a proppant (such as ceramsite and/ or quartz sand) into the reservoir, where it is used to create numerous, microscopic cracks in the dense rock.The liquid then flows back, leaving the proppant in the fractures while maintaining the crack patency, which increases oil and gas well production (Zhifeng et al. 2019;Mingjun et al. 2022;Yong-Cun et al. 2021).Surfactants are typically added to fracturing fluid to reduce water/gas surface tension and thus reduce liquid flowback resistance (Nur and Sheng 2020;Tianbo et al. 2017;SalahEldin et al. 2019).
There have been extensive studies on fluorocarbon surfactants as they are the most widely used type of surfactant in the oil and gas industry (Lipei et al. 2020;Yongfei et al. 2018).Zhang et al. synthesized some novel oil-soluble fluorinated surfactants (Ding et al. 2019).These surfactants showed good effect on reducing the surface tension of organic solutions.The surface tension of nitromethane reduced by about 40% when the concentration of 1e was 0.1 mol/L.The surface tension of toluene was reduced by about 20% when the concentration of 1a was 0.1 mol/L.For real-world use, researchers have focused on perfluorocarbon surfactants that are soluble in water.Chen et al. synthesized fluorinated anionic surfactant sodium p-perfluorononenyloxy benzene sulfonate (SPBS) (Lijun et al. 2011).This surfactant has excellent surface activity and combined properties; when the concentration of SPBS is 1 g/L, the minimum surface tension can reach 18 mN/m.Lee et al. synthesized several novel anionic fluorinated surfactants with two short fluorocarbon chains per molecule (Kang et al. 2018).The CMC of the final products was found to be low (0.31-1.15 mmol/L), and their surface tension in 1% aqueous solution was within the range of 15.7-22.8mN/m.
In the past few decades, both hydrocarbon and fluorocarbon surfactants have been widely reported, with researchers increasingly turning to molecular dynamics (MD) simulation to delve deeply into the mechanism of action of fluorocarbon surfactants at the molecular/atomic level (Van Gunsteren Wilfred and Berendsen 1990;Hollingsworth and Dror 2018).Yuan et al. studied several counterions with dodecyl sulfate (DS − ) at the air/water interface using molecular dynamics (MD) simulations (Guokui et al. 2016).The results show that weak C-H-O hydrogen bonds are formed between the polar head and alkane chains of counterions; the hydrogen bonds play an important role in the formation of mixed adsorption layer.Zhang employed MD simulations to investigate the microscopic properties of nonionic fluorocarbon surfactants at the air/water interface (Li et al. 2014).It was observed that the structure of fluorocarbon surfactants at the air/water interface was more ordered than that of hydrocarbons, which is dominated by the van der Waals interaction between surfactants and water molecules.Dong et al. used a joint experimental and simulation approach to investigate the structure of perfluorooctanoate ammonium (PFOA) micelles in aqueous solutions (Dengpan et al. 2021), focusing on the understanding of ethanol addition on PFOA micelle formation and structure.Both experiments and simulations have demonstrated a transition from co-surfactant to co-solvent behavior as ethanol concentration increases, with the latter also providing insight into how to achieve co-solvent conditions with other additives.
In this paper, the MD simulation method was used to simulate the dispersion of a fluorocarbon surfactant in water in order to understand the mechanism of surfactant action from a microscopic perspective.Herein, potassium perflurohexanesulfonate (CAS No: 3871-99-6, abbreviated as KPFOS) was selected as the research object (Evans et al. 2012); its CMC is about 0.8-1 mmol/L in pure water (Boudreau et al. 2003;Xuanqi et al. 2011).The research method used herein is not limited to KPFOS, and the method can be applied to molecular simulation research on more complex fluorocarbon surfactants.

Computational
Firstly, the structure of PFOS − was optimized by using the ORCA software version 5.0.4 (Neese et al. 2020;Frank 2012)  constant time was 0.2 ps.The Coulomb interaction calculation method was PME algorithm (Tom et al. 1993), the cutoff was 1 nm, and the van der Waals interaction algorithm was cut off with the cutoff distance of 1 nm.VMD 1.9.3 software (William et al. 1996) was used for visual observation.
Independent gradient model based on Hirshfeld partition (IGMH) analysis steps: select all atoms/molecules within 3.5 nm of an atom/molecule in VMD and then use ORCA to obtain the wavefunction information; the single-point energy calculation level is B3LPY D3 ma-def2-TZVP.After obtaining the wave function information, use Multiwfn for IGMH analysis (Tian and Qinxue 2022).

Snapshots before and after simulation
As soon as the simulation begins, we can see the random distributed PFOS − spontaneously migrate to the water/gas interface, and form micelles inside the bulk solution, as shown in the supporting information video.The snapshots before and after the simulation are shown in Fig. 1A, B.
Before MD simulation starts, PFOS − and K + are both randomly distributed in the aqueous solution, as shown in Fig. 1A, and there are few distribution rules.After MD, PFOS − is mainly distributed at the water/gas interface, which is consistent with the theory of surfactants reducing surface tension.At the same time, the spherical aggregate of PFOS − appears in the bulk aqueous solution.That is, at this concentration (40 mmol/L, higher than cmc), PFOS − can not only distribute on the surface of water, but also form spherical micelles in the water.This is also consistent with the theory of forming micelles in water.K + is randomly distributed in bulk aqueous solution without aggregations.
There are no water molecules or KPFOS in the vacuum layer and all KPFOS are distributed in the solution.As a result, the density of KPFOS (including number density and charge density) within a unit volume in the water phase is of interest.

Number density distribution
Since PFOS − is mainly distributed at the water/gas interface, and there are also PFOS − micelles in the bulk solution, K + are distributed inside the solution; as a result, it is worth studying how many PFOS − or K + are distributed in per unit volume in the simulation box.
With the center of the boxes as the origin, the number density distribution of PFOS − and K + in Y direction is shown in Fig. 2. Before MD, as depicted in Fig. 2A, the number density of PFOS − and K + molecules on both sides is 0 and the number density in the bulk solution is irregular, which is consistent with the snapshot of the KFPOS solution shown in Fig. 1A.Interestingly, as the simulation is completed, the number density distribution of PFOS − and K + in the solution is very regular, and the number density graphics are also quite interesting.In Fig. 2B, at a distance of about 4 nm from the center of the box, the number density of PFOS − is the highest, approximately 0.4 per nm −3 ; in the center of the box, due to the presence of PFOS − micelles, the highest number density is approximately 0.1 per nm −3 ; in the remaining space of the solution, the number density of PFOS − is almost zero.It is evident that compared to PFOS − , K + is always distributed inside the aqueous solution and does not appear at the water/gas interface.Within the bulk solution where the PFOS − number density is the highest, the K + number density is also as high as up to about 0.26 per nm −3 ; this means that the probability of K + appearing near PFOS − is high.Within the solution, the number density of Fig. 2 Number density of PFOS − and K + distribution before and after MD simulation K + is approximately 0.07 per nm −3 , much lower than that near the water/gas interface.
From Fig. 2B, it can be concluded that the PFOS − layer thickness is about 1.58 nm at the air/water interface.Combining the snapshots in Figs.1B, 2B, it can be concluded that at the water/air surface, PFOS − is not a straight molecule but exhibiting a certain degree of curvature, and PFOS − is not uniformly and neatly arranged on the surface of the solution but exhibits multiple layers "lying on the side" on the water surface.

Charge density distribution
Similarly, charge density distribution is also worth studying.Similar to Fig. 2, taking the center of the boxes as the origin, the charge density distribution of PFOS − and K + in Y direction is shown in Fig. 3.
In Fig. 3A, the charge density of PFOS − is negative, the charge density of K + is positive, and charge density distributions are irregular.As shown in Fig. 3B, after the simulation, the distribution of charge density is significantly different from Fig. 3A.Since the negatively charged PFOS − gathers at the water/gas interface, the maximum PFOS − charge density is about 0.02 per nm −3 at about 3.8 nm from the box center.In addition, the charge density of PFOS − is also negative with very low value in the center of the box, indicating the existence of very small amounts of PFOS − molecules, which is attributed to the spherical micelles in the solution.Comparatively, K + is distributed within the solution and is mainly located near the location where PFOS − is distributed-due to the attraction with opposite electrical properties, K + exhibits a layered distribution from 3.5 nm of the center.However, there are still some K + within the solution, which are free and do not always appear near PFOS − .

Radial distribution function
The radial distribution function (RDF) can describe the configuration of PFOS-and K + .It indicates the position of a given particle , the distance of particle from particle (the probability of distribution around ), that can represent the order degree of the two components.
where g (r) is the average probability of particle appear- ing within the distance of r and r + Δr away from the i th particle .N and N are the number of and particles, respectively.V s is the volume of the simulation box; r is the distance between two kinds of particles; n i (r) is the number of particles within the distance of r and r + Δr away from the i th particle .
From Fig. 4, it is evident that the RDF between the oxygen atom in PFOS − and K + has the first peak at 0.27 nm, indicating the probability of K + appearing at a distance of 0.27 nm from the oxygen atom on the sulfonic acid radical is the highest; this is the first coordination layer.A secondary weak peak appears at about 0.47 nm; this is attributed to the second coordination layer.This proves that PFOS − and K + with opposite electrical properties have a high probability of appearing in pairs, but not every anion can pair with cations.

Analysis of weak intermolecular interactions
In 2022, Lu et al. proposed an independent gradient model (IGM) (Corentin et al. 2017(Corentin et al. , 2018) method based on Hirshfeld partition of molecular density (called IGMH) (Tian and Qinxue 2022).IGMH has a rigorous physical basis, it is defined on the actual molecular density rather than the 4 r 2 Δr ⟩ Fig. 3 Charge density of PFOS − and K + distribution before (A) and after (B) MD simulation promolecular density, and the latter one completely ignores the electron transfer and polarization during formation of the current system from isolated atoms.As mentioned above, PFOS − is mainly distributed at the water/gas interface and the hydrophilic sulfonic acid mainly faces the water; the weak interaction between water and PFOS − is worth studying.Similarly, the weak interaction between K + in water and water is also worth studying.
As shown in Fig. 5, there are mainly two kinds of weak interactions in the IGMH analysis graphs.The first one is 5 H-bonds formed by the three oxygen atoms in PFOS − and adjacent water molecules, as shown in the blue isosurface in Fig. 5A.In addition, due to the negative charge of fluorine atoms, and coincidentally, so long as the distance and angle between the fluorine atom and adjacent water molecules conform to the characteristics of H-bond, as shown in the red circle in Fig. 5A, we believe that fluorine atoms can also form H-bonds with water molecules, depending on the distribution of water molecules.This is the difference between our research results and those of Zhang et al. (2014).
In the second weak interaction, there are several water molecules distributed around the K + , and negative charged oxygen atoms in water molecules are directed toward K + ; the weak interaction between water molecules and K + is van der Waals interaction (green isosurface in Fig. 5B), indicating that the interaction between water molecules and potassium ions is extremely weak.As K + is a single atom; the direction of van der Waals interactions depends on the distribution of water molecules.Quantum chemical calculations KPFOS is not a new substance, its properties and practical applications have been extensively studied.However, as far as we know, there is no report of KPFOS at the level of quantum chemistry.Since KPFOS is a salt that easily ionizes in water, PFOS − needs to be studied only at the quantum chemistry level.
It is well known that the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) determine the capacity of the molecule to accept electrons and provide electrons (Saeva et al. 1989;Sharmili et al. 2020), respectively.From Fig. 6, it is evident that the oxygen atoms in PFOS − mainly determine the capacity of the PFOS − molecule to accept electrons and fluorocarbon chains mainly determine the capacity to provide electrons.
Furthermore, the distribution of electrostatic potential (Zhang and Tian 2021) was analyzed by Multiwfn.The overall surface of PFOS − is 294.4Å 2 ; this is also the total surface area of the negative surface area.The molecular polarity index (MPI) of PFOS − is 0.011 a.u., much higher than the MPI of water (0.003 a.u.); this also proves that PFOS has strong hydrophobicity.The nonpolar surface area of PFOS − is 0 Å 2 and the polar surface area is 294.42Å 2 , which proves that PFOS − is a total polar molecule and has strong ability to combine with other substances through electrostatic or H-bond interactions.It can be seen from Fig. 7 that the surface electrostatic potential of negatively charged PFOS − is negative, and the electrostatic potential on the fluorocarbon chain is significantly lower than that on the sulfonic acid group (compared in absolute values); that is to say, the net charge is mainly distributed on the sulfonic acid group.

Conclusions
In this paper, we used molecular dynamics method to study the dispersion of a simple surfactant potassium perflurohexanesulfonate (KPFOS) in water.At a concentration higher than the CMC, not only is PFOS − distributed on the surface of water/ gas, thereby reducing surface tension, but also forms micelles in aqueous solutions.At the water/gas interface, the hydrophobic fluorocarbon chain of the PFOS − faces toward the gas phase, and the hydrophilic sulfonic acid group is immersed in water.K + is mainly distributed near the plane layer of sulfonic acid groups, and a small proportion is distributed in the bulk solution.Both number density and charge density distribution confirm this point view.The oxygen atom in the sulfonic acid group can inevitably form multiple hydrogen bonds with water, which has a strong attraction effect; fluorine atoms can also form hydrogen bonds with water, resulting in weak attraction, but that's not always the case either as it depends on the distribution distance and angle of water molecules distribution.K + only has van der Waals interactions with surrounding water molecules, and the oxygen atoms in the water molecules face K + ; this is attributed to the mutual attraction of opposite atomic charges.
Fig. 1 Snapshots of KFPOS solution before (A) and after (B) MD simulation

Fig. 4
Fig. 4 RDF of K + between oxygen atom in PFOS −

Fig. 6 Fig. 7
Fig. 6 Contour plots and energies of HOMO and LUMO of PFOS − (Green and blue correspond to the parts with positive and negative isosurfaces, respectively)