Interactions between Per- and Polyfluoroalkyl Substances (PFAS) at the Water–Air Interface

Abstract

Per- and polyfluoroalkyl substances (PFAS)so-called “forever chemicals”contaminate the drinking water of about 100 million people in the U.S. alone and are inefficiently removed by standard treatment techniques. A key property of these compounds that underlies their fate and transport and the efficacy of several promising remediation approaches is that they accumulate at the water–air interface. This phenomenon remains incompletely understood, particularly under conditions relevant to natural and treatment systems where water–air interfaces often carry significant loads of other organic contaminants or natural organic matter. To understand the impact of organic loading on PFAS adsorption, we carried out molecular dynamics simulations of PFAS at varying interfacial densities. We find that adsorbed PFAS form strong mutual interactions (attraction between perfluoroalkyl chains and electrostatic interactions among charged head groups) that give rise to ordered interfacial coatings. These interactions often involve near-cancellation of hydrophobic attraction and Coulomb repulsion. Our findings explain an apparent paradox whereby PFAS adsorption isotherms often suggest minimal mutual interactions while simultaneously displaying a high sensitivity to the composition and density of interfacial coatings. Consideration of the compounds present with PFAS at the interface has the potential to allow for more accurate predictions of fate and transport and the design of more efficient remediation approaches.

Introduction

Per- and polyfluoroalkyl substances (PFAS) have emerged as an urgent threat to human health due to their widespread use, environmental persistence, adverse health impacts at trace concentrations, and inefficient removal by conventional water treatment approaches. A key property of these compounds is that they are highly surface active, such that adsorption to the water–air interface strongly impacts their retention in porous media, − their transport in the atmosphere (e.g., through sea spray and other aerosols), , and the efficacy of remediation techniques such as foam fractionation − and nanobubble-enhanced adsorption and degradation. −

In the past few years, experimental and theoretical studies have shed light on the affinity of PFAS for pristine water–air interfaces. − However, water–air interfaces in natural environments or treatment systems are rarely pristine: they often carry a significant load of organic compounds, including other contaminants or natural organic matter. − The affinity of PFAS for organic-loaded interfaces is consequently of practical importance in environmental chemistry. For example, it is critical to the design of remediation techniques that rely on high interfacial density, such as the addition of cofoaming agents in foam fractionation. Furthermore, PFAS are often present at contaminated sites in mixtures of multiple PFAS or other organic compounds, yet adsorption studies have generally examined individual PFAS in isolation. In particular, highly contaminated sites often contain a complex mixture of compounds including high levels of PFAS precursors (compounds that biotransform to terminal PFAS on time scales of months to years). These precursors remain sparsely studied and appear to be even more surface active than the terminal PFAS, with important implication for the persistence of contaminated groundwater plumes. , In short, there exists a strong need to understand the behavior of PFAS in mixtures and at high interfacial loadings that are representative of many environmental conditions.

An important fundamental measure of adsorption at high loadings is the adsorption isotherm, i.e., the relationship between the concentration of the compound at the interface (Γ, mol m^–2) and that in solution (C, mol m^–3). In the case of PFAS, experimental isotherms are often interpreted using the well-known Langmuir model, Γ = Γ_max C/(C + b), where Γ_max and b are compound-specific coefficients. However, the utility of this model represents a source of ongoing debate because of conflicting experimental results. ,,− Furthermore, the apparent applicability of the Langmuir modelat least under certain conditionsis unexpected because it implies that adsorbed compounds exhibit no net mutual interactions beyond the inevitable volume exclusion. This assumption appears inconsistent with observations that the adsorption of charged PFAS can be highly sensitive to salinity, attributed to the ability of electrolyte ions to screen Coulomb interactions between charged head groups. It also appears to conflict with experimental work on PFAS mixtures where competitive adsorptionin which the most surface-active agents in the mixture adsorb preferentiallyhas been observed between different PFAS compounds and, also, between PFAS and organic matter. − The inconsistencies outlined above highlight a need for a fundamental understanding of the interactions between PFAS and other organic molecules (including other PFAS and natural organic matter) at the water–air interface. The present work focuses on the simplest of these cases (adsorption of a single PFAS compound as a function of surface loading) and a somewhat more complex case (adsorption of equimolar mixtures of two PFAS compounds).

Molecular dynamics (MD) simulations are well-suited to investigate organic compounds and mixtures at the water–air interface as they provide a molecular-level view of the relevant compound interaction structures and energetics. , Recently, we demonstrated that these methods yield accurate predictions of the affinity of individual PFAS molecules for the interface at infinitely low loadings. Here, we use MD simulations to examine the interactions between adsorbed PFAS molecules as a function of surface loading and in mixtures. Our surface loadings correspond to aqueous concentrations exceeding those of individual PFAS in typical field conditions; they are intended to represent the high PFAS interfacial densities examined in studies of PFAS adsorption isotherms and, also, the high total interfacial densities comprising precursors, other synthetic contaminants, cofoaming agents, and natural organic matter of environmental and treatment systems. − To partly span the diversity of PFAS structures, we examine five anionic terminal PFAS with different carbon chain lengths and head groups, one zwitterionic terminal PFAS, and one cationic PFAS precursor (Figure ).

1.

Compounds investigated and illustration of the simulated configurations. (A) Classification, structures, and abbreviated titles of the compounds used in this work (PFOS: perfluorooctanesulfonate, PFHxS: perfluorohexanesulfonate, PFBS: perfluorobutanesulfonate, PFOA: perfluorooctanoate, PFBA: perfluorobutanoate, PFHxSaAm: perfluorohexane sulfonamido amine, 5:3 FtB: 5:3 fluorotelomer betaine). (B) Visualization of the systems containing PFOS at several loadings n (number of PFAS molecules per 3.2 × 3.2 nm² water–air interface). Red, white, cyan, pink, yellow, and navy spheres represent the atoms O, H, C, F, S, and Na, respectively.

Results

Validation Against Experimental Results

A key phenomenon that underlies measurements of PFAS adsorption at the water–air interface is the decrease in the surface tension with adsorption. In short, experimental results on the relation between water–air interfacial tension γ (mN m^–1) and PFAS concentration in water C (mol m^–3) are used to determine Γ through the Gibbs adsorption equation, where R is the universal gas constant (J mol^–1 K^–1) and T is absolute temperature (K):

$$\mathrm{\Gamma }=-\frac{C}{\chi \mathit{RT}}\left(\frac{\mathrm{d}\gamma }{\mathrm{d}C}\right)$$ 1

The formulation presented in eq follows the common assumption in PFAS adsorption studies that the solute activity coefficient can be approximated as unity. While there is debate regarding the appropriate form of the Gibbs adsorption equation to ionic surfactants, − methodologies applying eq to experimental surface tension data often employ a χ factor dependent on surfactant charge and solution salinity, with χ = 1 for nonionic surfactants and ionic surfactants in solutions with excess electrolyte and χ = 2 for ionic surfactants without excess electrolyte. , Experimental results on the relationship between γ and C for a specific surfactant and solution are often fitted using the semiempirical Szyszkowski equation:

$$\gamma ={\gamma }_0[1-a\ln (\frac{C}{b}+1)]$$ 2

where a (unitless) and b (mol m^–3) are fitting parameters and γ₀ (mN m^–1) is the interfacial tension of the solution without surfactant. Equation is strictly valid in conditions where adsorption follows a Langmuir isotherm, as shown by taking its derivative with respect to C and substituting into eq , which yields the Langmuir/Szyszkowski equation:

$$\mathrm{\Gamma }=\left(\frac{a{\gamma }_0}{\chi \mathit{RT}}\right)\frac{C}{C+b}$$ 3

Equation is identical to the Langmuir equation, with the coefficient (aγ₀/χRT) being equal to the maximum surface excess Γ_max.

In a recent study, we showed that MD simulations carried out with well-established interatomic potential models for water, organics, and inorganic ions , accurately predict the adsorption of PFAS and many other organic contaminants at infinitely low loadings. To verify the accuracy of our simulations at higher loadings, we compare predictions and measurements of the change in surface tension (Δγ = γ – γ₀) as a function of Γ for three of the compounds examined here (Figure ).

2.

Change in the surface tension of water (Δγ) with increasing surface excess (Γ) of perfluorobutanesulfonate (PFBS), perfluorohexanesulfonate (PFHxS), and perfluorooctanoate (PFOA). Blue and orange squares show MD simulation predictions obtained in this study for sodium PFAS salts at zero salinity (blue squares) or at 1 M NaCl (orange squares). Horizontal error bands on the data points represent uncertainty in the fraction of PFAS adsorbed at the interface versus that in solution (see Materials and Methods section). Solid lines show experimental behaviors calculated from the a and b parameters of the Langmuir/Szyszkowski equation evaluated by ref based on measurements of Δγ vs C. The dashed line in the panel (A) inset (χ = MD) shows a prediction of the 1 M NaCl MD simulation results, based on experimental data, accounting for the high surface-to-volume ratio of the water phase in the simulated system, as discussed in the SI. Shaded areas represent confidence bands associated with the conversion from the measured relation between Δγ and C to the inferred relation between Δγ and Γ. Note that surface excess is expressed here with the same units as n, i.e., as molecules per 10.24 nm² of interface.

Our calculations reveal a good agreement between predicted and measured surface tension values over a wide range of organic loadings. In the absence of excess salt (i.e., at 0 M NaCl), PFBS and PFHxS followed the experimental curve calculated using χ = 2. Results obtained for PFOA closely followed the χ = 1 curve, revealing unexpected sensitivity of χ to the identity of the anionic headgroup (carboxylate in PFOA and sulfonate in PFBS and PFHxS). In the absence of excess salt, a value of χ = 1 is expected only for nonionic surfactants, which suggests that PFOA and its counterion may form a strong uncharged complex. This hypothesis is consistent with the stronger localization of anionic charge on the two carboxylate O atoms vs the three sulfonate O atoms, which should result in stronger ion pairing of the carboxylic acids in solution. Analysis of our simulation trajectories from the perspective of the average atomic density profiles of Na⁺ ions and PFAS head groups in the direction normal to the surface reveals only minor differences in PFAS ion pairing with Na⁺ counterions between carboxylic and sulfonic compounds (Figure S1). However, observations of the configuration of Na⁺ ions and PFAS head groups within the plane of the interface reveal a stronger tendency toward clustering in the case of carboxylic compounds (Figure S2).

In an effort to resolve the unexpected variability in χ identified above, additional simulations of PFBS were conducted in a high salinity (1 M NaCl) solution (Figure A). At low loadings of n = 1 and 6 molecules per interface, the magnitude of the change in surface tension of the 1 M solution (Δγ) was significantly smaller than that in the 0 M solution (as shown in the Figure A inset) and more closely followed the χ = 1 than χ = 2 curve, as expected from theory. At higher loadings, results obtained at 1 M NaCl approached the χ = 2 curve. This transition from χ = 1 to 2 in our simulations at 1 M NaCl is expected: because of the high surface-to-volume ratio of the water phase in our simulated systems, the number of Na⁺ counterions contributed by the PFAS salt rapidly becomes larger than the number contributed by the NaCl electrolyte with increasing PFAS loading. A theoretical prediction of this effect is described in the SI and is shown by the dashed line in the Figure A inset.

Results for all compounds and mixtures examined in this study are presented in Figure S3. The trends observed among anionic compounds were consistent with those reported in experimental studies, i.e., greater surface activity was predicted for compounds with longer perfluorinated alkyl chain lengths, and surface tensions of mixtures were intermediate between those of their constituent components (Figure S3A,B). In contrast, the cation–anion mixture (PFHxS:PFHxSaAm) exhibited surface tensions that were not intermediate between those of the constituent compounds, indicating that adsorption is highly sensitive to Coulomb interactions between adsorbed PFAS molecules (Figure S3C). We note that the strong attraction between PFHxS and PFHxSaAm (discussed later in this work) would be expected to cause Δγ for the mixture to be lower than that for the individual constituents, whereas we observe the opposite. This observation may warrant further study of the energetics of mixtures of cationic and anionic PFAS.

The cationic PFAS precursor (PFHxSaAm) and fluorotelomer zwitterion (5:3 FtB) had the longest chain lengths of all compounds examined here (12 and 11 C atoms, respectively) and exhibited the two highest surface activities (Figure S3D). While precursor concentrations at contaminated sites are often unreported due to a lack of analytical standards for their detection, , our results indicate the potential for competitive adsorption between precursors and terminal compounds. In other words, water–air interfaces in the vadose zone at contaminated sites may act as a long-term reservoir of undetected PFAS precursors.

PFAS Orientation and Distribution in the Direction Normal to the Interface

Detailed examinations of PFAS orientation and distribution at the water–air interface reveal significant differences with surface loading, alkyl chain length, headgroup chemistry, and the presence of mixtures of several PFAS (Figures S4–S6). The long-chain compounds remained at the interface throughout the course of the simulation in all systems with n ≤ 20, while the short-chain compounds exhibited significant solubility in water, in agreement with experimental observations regarding the greater mobility of short-chain PFAS. The headgroup of each compound was anchored deeper in the water phase at low interfacial loadings than at high loadings (Figure S5), indicating that headgroup solvation decreased with interfacial crowding. At the highest loading (n = 40), all compounds distorted the water surface (Figure ) and several compounds exhibited density profiles suggestive of the formation of micelles or incipient bilayers (PFHxSaAm, PFHxS, 5:3 FtB, PFBA; Figures S5 and S6), in agreement with the low surface tensions observed for systems where PFAS are present at or above the critical micelle concentration.

Clear evidence of the strong interaction between PFAS molecules at the interface is that in 1:1 mixtures of oppositely charged compounds, the surfactant molecules adjusted their distribution in the direction normal to the interface to enhance interactions between the two species. Specifically, for PFHxS and its cationic precursor PFHxSaAm, the compounds were located at different distances relative to the interface in their respective single-species systems, but these locations converged in the mixture. The shifts in location served to better align the six-carbon fluorinated tails of PFHxS and PFHxSaAm, likely maximizing their favorable van der Waals interactions (vdW) (Figure A). To a lesser extent, the shift also enhanced the alignment of the anionic sulfonate headgroup of PFHxS with the sulfonamide linkage of PFHxSaAm, whose sulfur atom had the greatest individual positive charge in the molecule, possibly enhancing favorable electrostatic interactions (Figure B). In 1:1 mixtures of like-charged PFAS (PFOA:PFOS, PFBA:PFBS, and PFBS:PFOS), there was minimal shift in head or tail positions in the mixture as the initial locations in the single-species systems were similar between the two components of each mixture (Figures S7 and S8).

3.

Density distribution of selected atoms in PFHxS (green), PFHxSaAm (purple), and water (blue) in the direction normal to the water–air interface. Coordinate is relative to the location of the Gibbs dividing surface of water. For the PFAS, (A) shows the density distribution of atoms in the C₆F₁₃ tail at three different loading (n = 6, 10, and 20 from left to right), while (B) shows atoms in the sulfonate (SO₃) or sulfonamide linkage (SO₂) groups. Solid and dashed lines show results from simulations with a single PFAS species or a 1:1 mixture, respectively. Interfacial loading at each n value represents the total number of molecules per interface (e.g., n = 6 for single-species PFHxS represents 6 molecules of PFHxS per interface; n = 6 for the mixture represents 3 PFHxS and 3 PFHxSaAm molecules per interface.).

PFAS Clustering at the Interface

Additional evidence of PFAS–PFAS interactions at the water–air interface is provided by the radial distribution functions (RDFs) of PFAS head groups within the plane of the interface (Figure ). More precisely, we present RDFs that reflect the likelihood of finding two sulfonate S atoms or two carboxylate C atoms in identical PFAS molecules at any given interatomic distance, normalized to the expected number of neighbors at that distance if the PFAS were uniformly distributed at the interface. In other words, an RDF value of one would indicate no spatial correlation between PFAS head groups in the plane of the interface. Instead, results show significant spatial correlation between PFAS head groups, including the absence of neighbors at interparticle distances below ≈4 Å, associated with volume exclusion, and enhanced abundance of neighbors at distances of 6–7 Å, indicating clustering. For the sulfonates, the major RDF peak maintained a distance of 6.9 ± 0.1 Å at all loadings. Carboxylic compounds, in contrast, displayed a peak at a distance of 6.1 ± 0.4 Å at low loadings (n ≤ 10) that grew substantially and shifted abruptly to a distance of 5.1 ± 0.1 Å at higher loadings, indicating an abrupt PFAS rearrangement to form a tighter and more clustered interfacial coating (Figure S2). This abrupt enhancement in the clustering of carboxylic head groups at high loadings is even more clearly apparent in the number of first-shell neighbors, defined here as the coordination number at a radial distance of r ≤ 8 Å (Figure H). The average numbers of neighbors of the carboxylic compounds were only slightly larger than for the sulfonic compounds at n ≤ 10, but they begin to diverge at n = 20 to eventually reach a difference by a factor of 2 to 3. For the sulfonic compounds, the lower degree of clustering at the interface is accommodated via the movement of compounds from the interface into the bulk water phase at the highest loadings (Figure S4). The abrupt shift in the location and height of the RDF peaks of the carboxylic PFAS is reminiscent of a voltage-driven rearrangement of the in-plane interfacial structure reported for a butylmethylimidazolium hexafluorophosphate (BMI-PF₆) ionic liquid on an electrode surface. In our simulated systems, this effect may reflect the clustering of carboxylate head groups and Na⁺ counterions in the plane of the interface observed for PFOA (but not for PFOS) at n = 20 in Figure S2. This clustering also may explain the unexpected observation that χ = 1 for PFOA in Figure C. It also suggests a possible transition from χ = 2 to 1 with increasing PFOA loading that may be discernible in Figure C.

4.

Clustering of PFAS molecules within the plane of the interface. Left panels: Top-down views of water surfaces coated with n = 6 (A), n = 10 (D), and n = 20 (G) PFOS molecules. Upper right panels: two-dimensional (2D) RDFs of the PFAS head groups in the plane of the water–air interface for simulations containing a single species at different interfacial loadings (solid lines). Vertical dashed gray lines show the average interatomic distance of the first peak between carboxylic (B, C) or sulfonic (E, F) compounds, at low (n ≤ 10) or high (n ≥ 20) loadings for the carboxylic compounds and at all loadings for the sulfonic compounds. Dashed lines show the RDFs of identical PFAS compounds in a mixture of PFOA:PFOS (B, E) or PFBA:PFBS (C, F). Lower right panel (H): number of same-species neighbors within a radius of r = 8 Å in simulations containing a single species. The dashed yellow circle in panel (A) illustrates the neighbor distance cutoff of r = 8 Å used in panel (H).

Energetics of PFAS Clustering at the Interface

As a final measure of the interactions between PFAS at the water–air interface, we determined the potential energy difference associated with PFAS clustering, ΔE _cluster. More precisely, we calculated the impact of clustering (i.e., going from n systems with one PFAS per interface to one system with n PFAS and n – 1 systems with no PFAS) on the potential energy E associated with van der Waals (vdW) or Coulomb pairwise interactions in the simulated systems:

$$\mathrm{\Delta }{E}_{\mathrm{cluster},i}(n)=\frac{1}{2}[E_i(n)+(n-1){·E}_i(0)-n·E_i(1)]$$ 4

In eq , i = vdW or Coulomb and the 1/2 factor accounts for the presence of two interfaces in each simulated system. Results on the total potential energy of clustering associated with the sum of vdW and Coulomb interactions, normalized by n (i.e., ΔE _cluster(n)/n, shown by the gold symbols in Figure ) reveal only a minimal energetic tendency toward clustering in most conditions, in agreement with observations of Langmuir-like PFAS adsorption isotherms. The largest magnitude calculated for ΔE _cluster (n)/n (excluding the result for PFBS at n = 40, where the system may exceed the maximum stable interfacial loading) is −11.3 ± 2.4 kJ mol^–1 (i.e., −0.12 ± 0.025 eV), observed at n = 20 for the mixture of cationic and anionic PFAS (PFHxSaAm:PFHxS). For comparison, the free energy of adsorption of an isolated PFHxS molecule from liquid water to the water–air interface is −87.0 ± 2.1 kJ mol^–1.

5.

Potential energy of PFAS clustering at the interface, normalized to interfacial loading (i.e., (ΔE _cluster)/n), as a function of interfacial loading. Values of ΔE _cluster are calculated from all pairwise interatomic interactions within the short-range cutoff distance of 1.2 nm. Red and blue symbols show the contribution of pairwise Coulomb and van der Waals (vdW) interactions (generally unfavorable and favorable, respectively); yellow symbols show the sum of both contributions.

Whereas the overall magnitude of ΔE _cluster was consistently small in relation to the affinity of isolated PFAS molecules for the interface, the Coulomb and vdW contributions to ΔE _cluster had much larger positive or negative values. The Coulomb contribution demonstrated a strong energetic penalty associated with the congregation of like charges at the water surface (Figure A,B). This repulsion was strongly attenuated in the case of the anion–cation mixture with a complete disappearance at n ≤ 20, likely because of favorable Coulomb interactions between cationic and anionic head groups (Figure C). No obvious attenuation of the Coulomb contribution was observed for the zwitterionic system (Figure D), possibly because the different locations of positive and negative charges along the alkyl chain imposed significant separation between planes of cationic and anionic charges at the zwitterion-loaded interface.

In contrast to the repulsive Coulomb contribution to clustering, the vdW contribution demonstrated a strong energetic favorability likely associated with hydrophobic attraction between fluorinated tails. A significant modulation of the vdW contribution was observed as a function of the length of the perfluorinated alkyl chain for the three sulfonic PFAS studied (Figure B), with PFOS having a significantly more favorable vdW energy of aggregation than either PFBS or PFHxS at each loading.

Associated calculations showed that the vdW energy of clustering is consistent with a Langmuir-like representation of the differential energy of clustering, in agreement with the short-ranged nature of vdW interactions (Figure S9). The Coulomb energy of clustering is consistent, at loadings of n ≤ 20, with the Gouy–Chapman (GC) solution of the Poisson–Boltzmann equation; at higher loadings, the GC model no longer provides a suitable fit, in agreement with the expected inaccuracy of its mean field treatment of the electrical double layer on highly charged surfaces (Figure S9).

Discussion

Our results examine the interactions between PFAS molecules at the water–air interface. Although this phenomenon should be minimal in most natural systems, where PFAS concentrations are low, it is critical for the interpretation of PFAS adsorption isotherms, which are used to infer PFAS adsorption at low loadings. Furthermore, although we focus for simplicity on PFAS–PFAS interactions, our results are more broadly relevant to PFAS-organic interactions at the water–air interface.

The results presented here explain how PFAS can exhibit Langmuir-type adsorption, at least in some conditions, while also exhibiting high sensitivity to salinity and to the identity and abundance of other surfactant species present at the interface. Specifically, the minimal potential energy associated with PFAS clustering at the interface results from a near-cancellation of large favorable (hydrophobic) and unfavorable (Coulomb) interactions such that changes in either of these interactions (e.g., due to changes in alkyl chain length, salinity, or charge distribution in surfactant mixtures) have disproportionately large impacts on the overall energetics of clustering. Contradictory findings of either enhanced or limited PFAS sorption in the presence of organic carbon, depending on PFAS identity and concentration, may be attributable to this effect.

Our results also help explain observations of important differences in the efficacy of cofoaming agents in foam fractionation. For example, cationic cofoaming agents are generally significantly more effective for PFAS removal than either anionic (worst performance) or zwitterionic (intermediate performance) agents. , The lower electrostatic repulsion in cation–anion mixture of PFAS and cosurfactants may render adsorption to the water–air interface more favorable, resulting in denser and more stable foams for PFAS removal.

More broadly, our results suggest that the stability of organic coatings at the water–air interface involves a delicate balance of hydrophobic and Coulomb interactions, in agreement with observations of organic ions on electrode surfaces, such as the existence of a voltage-controlled abrupt transition in the interfacial structure of ionic liquids or the feasibility of controlling surfactant adsorption on electrode surfaces by using voltage and osmolytes to modulate the balance of electrostatic and hydrophobic interactions.

Taken together, our results indicate that lateral interactions between adsorbed PFAS are important at the water–air interface, and likely also at other hydrophobic surfaces such as on granular activated carbon and soil minerals. , Characterizations of the fate of PFAS in the environment and in treatment systems should consider not only the concentrations of PFAS themselves, which are typically low, but also those of precursors, other contaminants, and natural organic matter that can crowd the interface and either enhance or inhibit PFAS adsorption. Consideration of the compounds present with PFAS at the interface has the potential to allow for more accurate predictions of fate and transport and the design of more efficient remediation approaches.

Materials and Methods

MD Simulations

Simulated systems consisted of 1900 H₂O molecules in a 5.4 nm thick water slab positioned between regions of void space (more precisely, water vapor) in a periodically replicated simulation cell with dimensions 3.2 nm × 3.2 nm × 12 nm (Figure ). These dimensions are consistent with the thickness and cross-sectional area of the water slab in previous MD studies of surfactant adsorption. ,, PFAS compounds were initially placed in the void space near each surface of the water slab, with a charge-balancing sodium or chloride counterion placed near each headgroup. No counterions were added to the zwitterionic (5:3 FtB) system. Water molecules were represented with the SPC model and kept rigid by using the SHAKE algorithm. Sodium and chloride counterions were represented with the Dang–Smith model. For the 1 M NaCl simulation of PFBS (Figure A), 34 NaCl ion pairs were initialized in the void space with the PFBS compounds in addition to the Na⁺ counterions for the PFBS. PFAS compounds were constructed in their ionized form that predominates at pH 7 and modeled using the all-atom optimized potentials for liquid simulations (OPLS-AA) force field, with minor dihedral and charge adjustments made for moieties that do not exist within OPLS-AA. This combination of interatomic potential models was recently demonstrated to yield accurate predictions of the adsorption of organic contaminants (including PFAS) from bulk liquid water to the water–air interface. Pairwise interatomic interactions were computed up to a cutoff distance of 1.2 nm. Long-range Coulomb interactions were computed using the particle–particle particle-mesh (PPPM) algorithm. Each system was equilibrated in the microcanonical (NVT) ensemble for 10.4 ns. Production runs were subsequently carried out in the NVT ensemble at 298 K for 40 ns with a 1 fs time step. Simulations were performed using LAMMPS software (version 4 Feb 2020) on the Tiger cluster of the Princeton Institute for Computational Science and Engineering (PICSciE).

Radial Distribution Functions

Radial distribution functions (RDFs) were initially calculated using standard three-dimensional (3D) spherical shell normalization. Results were then renormalized relative to a uniform PFAS distribution in the 2D interfacial plane. Briefly, the LAMMPS output at each radial distance was multiplied by 4πr ²ρ_3Ddr and divided by 2πrρ_2Ddr, where r is the radial distance (Å), ρ_3D is the average density of PFAS molecules per ų of simulated system, ρ_2D is the average density of PFAS molecules per Ų of water–air interface, and dr (Å) is the bin width of the computation (0.02 Å). For the RDF of each constituent in a mixture, ρ_3D and ρ_2D were computed using the loading of each constituent rather than the total loading of both constituents.

Surface Tension

Surface tension (γ) was computed using the Irving–Kirkwood formula (eq ) from the diagonal pressure tensor components of the simulation cell.

$$\gamma =\frac{L_y}{2}\{P_{\mathit{yy}}-\frac{P_{\mathit{xx}}+P_{\mathit{zz}}}{2}\}$$ 5

In eq , L _y is the length of the simulation cell in the direction normal to the interface (12 nm) and P _xx , P _yy , and P _zz are the x, y, and z components of the pressure tensor. P _xx , P _yy , and P _zz were computed every time step and averaged over four successive 10 ns intervals of the production run. The four resulting γ values, calculated from four 10 ns intervals for each system, were treated as independent estimates to evaluate the average value and its 95% confidence interval (i.e., ± 2σ/(√d), with σ the standard deviation of the γ values calculated for the d = 4 intervals). Simulation results on the change in surface tension associated with PFAS adsorption, Δγ, were calculated relative to the surface tension observed in the absence of PFAS (52.0 ± 0.5 and 53.5 ± 0.1 mN m^–1 for pure water and a 1 M NaCl solution, in agreement with previous studies that used the same interatomic potential models for pure water and with the experimental difference between the surface tension of pure water vs a 1 M NaCl solution).

To compare MD simulation predictions of γ (determined as a function of surface loading n) and experimental results (determined as a function of aqueous concentration C), the Szyszkowski (eq ) and Langmuir/Szyszkowski (eq ) equations were rewritten as a single equation with parameter a by solving eq for b, substituting into eq , and solving for Γ:

$$\mathrm{\Gamma }={\mathrm{\Gamma }}_{\max }[1-e^{-(1-\frac{\gamma }{{\gamma }_0})/a}]$$ 6

Equation was used to compute the expected surface excess Γ corresponding to a range of interfacial surface tensions γ using a values reported based on experimental measurements for PFOA, PFBS, and PFHxS (Table S1) and γ₀ = 72 mN m^–1. The confidence bands on the experimental line represent ±2s _Γ, with s _Γ being the uncertainty computed via propagation of error of the given uncertainty in the Szyszkowski parameters from the literature (formula provided in SI).

For the simulation results at low loadings where the PFAS concentration in the bulk water film is essentially zero, the surface excess is obtained directly by dividing surface loading n by interfacial area. At higher loadings, for PFBS and PFHxS, a significant number of PFAS molecules were located in the bulk-liquid-like water phase, defined here as the midplane of the water slab, ≈3 nm from the interface. The shape of the PFHxS profiles suggests that a fraction of these compounds may be adsorbed at the interface from the bulk water side rather than being truly dissolved in water (Figure S4). For this reason, horizontal error bars on the simulation results in Figure reflect a range of possible values of the surface excess, depending on whether the compounds located within the water film are considered adsorbed or dissolved. Full details are provided in the SI.

Energetics

The intermolecular pairwise potential energy E _pair(n) was calculated by LAMMPS at each loading n as described in the main text (eq ). We note that even relatively soluble PFAS (such as PFBA) are strong surfactants and remain mostly located at the interface in our simulated configuration because of the high surface-area-to-volume ratio of the interface. Therefore, the impact of dissolved molecules on the average PFAS energetics is minimal in our simulations (and much smaller than other sources of uncertainty).

Point estimates were computed via eq using the average of d = 4 energy measurements from the four 10 ns intervals of the production run. Equation was then applied to each of the four 10 ns intervals of the production run of the organic-loaded and water–air only systems. Confidence intervals were calculated as ±2σ/√d, where σ is the standard deviation of the four intervals. Both ΔE _cluster(n) and the confidence intervals are normalized by n in Figure .

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.est.4c08285.

• Supporting methodological details, citation for repository with all MD input and output files, density profiles of counterions and head groups, visualizations of PFOA- and PFOS-loaded systems, surface tensions of all compounds and mixtures, density profiles of all compounds, head and tail atom density profiles of all mixtures, comparison of clustering energetics with theoretical models, and aqueous concentrations corresponding to system loadings (PDF)

A.C.L. and I.C.B. conceptualized the study; A.C.L. conducted the study; A.C.L. and I.C.B. analyzed the results and wrote the paper.

The authors declare no competing financial interest.