Atomistic Potentials for Trisiloxane, Alkyl Ethoxylate, and

Article pubs.acs.org/JPCB

Atomistic Potentials for Trisiloxane, Alkyl Ethoxylate, and Perfluoroalkane-Based Surfactants with TIP4P/2005 and Application to Simulations at the Air−Water Interface Rolf E. Isele-Holder* and Ahmed E. Ismail* Aachener Verfahrenstechnik: Molecular Simulations and Transformations and AICES Graduate School, RWTH Aachen University, Schinkelstraße 2, 52062 Aachen, Germany S Supporting Information *

ABSTRACT: The mechanism of superspreading, the greatly enhanced spreading of water droplets facilitated by trisiloxane surfactants, is still under debate, largely because the role and behavior of the surfactants cannot be sufficiently resolved by experiments or continuum simulations. Previous molecular dynamics studies have been performed with simple model molecules or inaccurate models, strongly limiting their explanatory power. Here we present a force field dedicated to superspreading, extending existing quantumchemistry-based models for the surfactant and the TIP4P/2005 water model (Abascal et al. J. Chem. Phys., 2005, 123, 234505). We apply the model to superspreading trisiloxane surfactants and nonsuperspreading alkyl ethoxylate and perfluoroalkane surfactants at various concentrations at the air−water interface. We show that the developed model accurately predicts surface tensions, which are typically assumed important for superspreading. Significant differences between superspreading and traditional surfactants are presented and their possible relation to superspreading discussed. Although the force field has been developed for superspreading problems, it should also perform well for other simulations involving polymers or copolymers with water.

1. INTRODUCTION Trisiloxane surfactants have the ability to greatly enhance the spreading of aqueous solutions on hydrophobic substrates. Because of the high spreading velocities, the unusually large spreading exponents, and the final contact angle, which is usually not measurable because it is so small, this phenomenon is also known as superspreading. Because of its relevance in both fundamental physics and industrial applications, this effect has been intensely studied and debated for more than two decades. However, a generally accepted theory explaining this phenomenon still does not exist.1−5 A central problem in understanding the mechanism for superspreading is that the molecular behavior of trisiloxane surfactants during the rapid spreading remains unknown. As a result, different competing ideas about the superspreading mechanisms based on different assumptions about the trisiloxane surfactant have been proposed. Stoebe et al.6 suggest that the rapid spreading is facilitated by unzipping at the contact line, in which parts of the vesicles formed by trisiloxane surfactants directly adsorb at the water−air interface, while other parts directly adsorb at the water−substrate interface. Kabalnov7 presents a theory in which the rapid spreading is attributed to a large spreading coefficient caused by the presence of vesicles in solution. Churaev et al.8 suggest that the rapid spreading results from formation of a thick precursor film stabilized by mutual repulsion of vesicles. Radulovic et al.9 posit that the spreading velocities are limited by diffusion of surfactants to the interfaces near the contact line, which is controlled by concentration © 2014 American Chemical Society

gradients. However, their analysis appears to have been based on experimental results for nonsuperspreading scenarios. In ref 4, it is argued that superspreading is driven by Marangoni stresses due to surface tension gradients, but they also argue that it is unclear how this process might work. Karapetsas et al.10 performed a computational fluid dynamics study in which the superspreading effect was captured if surfactants can adsorb (i) at the interfaces, and (ii) directly from the water−air interface to the water−substrate interface. It is again not clear, however, how this adsorption mechanism would proceed. It is suggested that this adsorption works via the formation of a bilayer that advances the droplet at the leading edge, an idea also supported by Ruckenstein in ref 11. In ref 12, it is argued that the rapid spreading of trisiloxane surfactants is related to the formation of surfactant aggregates at the interfaces. Thus, while there are various competing hypotheses on superspreading, there are still two main open questions: what is the mechanism for superspreading, and which properties of trisiloxane surfactants facilitate this phenomenon? A promising way to get deeper insight into the molecular-scale phenomena is to use molecular dynamics (MD) simulations. Indeed, there have already been several MD simulations related to surfactant-enhanced spreading and superspreading in particular. As part of a larger study, Nikolov et al.13 presented Received: March 25, 2014 Revised: July 6, 2014 Published: July 8, 2014 9284

dx.doi.org/10.1021/jp502975p | J. Phys. Chem. B 2014, 118, 9284−9297

The Journal of Physical Chemistry B

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examined the influence of temperature and surfactant concentration for DCCP layers. The remainder of this paper is divided into two main parts. Section 2 covers the force field development. In section 2.1 we motivate our choice of models and the starting point for the force field development. The required force field modifications are also discussed. The functional form of the force field is briefly presented in section 2.2, with a focus on the nonbonded interactions. The fitting procedure is described in section 2.3, followed by a brief validation of the developed force field in section 2.4, a discussion of the fitting strategy in section 2.5, and a brief assessment of the developed model in section 2.6. Section 3 describes the surfactant simulations performed with the revised force fields. After describing our methodology in section 3.1, we present our results in section 3.2. In section 3.3 we discuss how the findings might relate to superspreading. Conclusions are offered in section 4.

simulations with a trisiloxane surfactant at the air−water interface. They find that the headgroup of the trisiloxane has a very compact shape and related this to superspreading. As already pointed out in ref 14, however, visualization of their results suggests that the hydrophilic tail of their surfactant was stretched, whereas it is known from experiment that the tail has a helical configuration in water,15 indicating that the employed model is inaccurate. McNamara et al.16 performed simulations with simple model molecules, finding that linear surfactants can enhance wetting, especially when there are strong interactions between the substrate and the hydrophobic part of the surfactant. This finding is also confirmed in a study by Kim et al.17 In a simulation study by Shen et al. with stronger connection to superspreading,18 the influence of the shape of the surfactant, such as linear or T-shaped (as in trisiloxanes), has been compared using model Lennard-Jones (LJ) surfactants. It was found that Tshaped surfactants lead to faster spreading rates and smaller final contact angles. Moreover, it was found that under certain conditions T-shaped surfactants can promote bilayer formation. Finally, Halverson et al.19 have performed MD simulations of spreading droplets with more complex, realistic models. While simulations with alkyl ethoxylate surfactants showed behavior in agreement with experiment, the trisiloxane-laden droplet did not spread. It later turned out that realistic behavior of the simulations was hindered by the trisiloxane model, which failed to reproduce adequately the strong reduction in the surface tension of water caused by trisiloxane surfactants.14 To obtain improved understanding about superspreading from MD simulations, more realistic and reliable surfactant force fields are required. Here we present an atomistic model suitable for studying superspreading. This model contains parameters to describe alkane, perfluoroalkane, dimethylsiloxane, and poly(ethylene oxide) chains and their interactions with water, which can be used to model surfactants as well as polymers and copolymers. The model parameters are modifications of existing quantum-chemistry-based models of the aforementioned polymers.20−23 These models have been optimized for use with the TIP4P/2005 water model,24 which is especially suitable for use in interfacial systems because of its accurate representation of interfacial properties, such as surface tension.25 Although the model has been developed for application to superspreading, it is also suitable for other simulations involving the materials described above. Moreover, the force field can be extended using the original quantum chemistry methods and the fitting strategy used here. We apply the developed model to simulations of surfactants at the air−water interface. Related simulations with other surfactants have already been performed in various molecular simulation studies at the atomistic level. Bandyopadhyay et al.26,27 have performed simulations with monolayers of alkyl ethoxylate surfactants at high surface coverages with the SPC/E water model.28 This system has also been studied by Chanda et al.29 The anionic sodium bis(2-ethyl-1-hexyl) sulfosuccinate has been studied by the same authors30 with the TIP3P31 model. Atomistic simulation of gemini surfactants were performed by Khurana et al.32 with TIP3P at different surfactant concentrations. Simulations with alkyl ethoxylate and anionic sodium dodecyl sulfate surfactants at different concentrations are presented in ref 33. Tzvetanov et al.34 have studied the influence of the size of the simulation box in simulations with DPPC and dicaprin surfactants. The only simulation study with surfactants at interfaces involving the TIP4P/2005 model, to the best of our knowledge, was presented by Mohammad-Aghaie et al.,35 who

2. FORCE FIELD DEVELOPMENT 2.1. Initial Potentials and Required Modifications. Based on the considerations presented in section 1 of the Supporting Information, a nonpolarizable atomistic model appears to be the proper modeling depth and resolution. Before proceeding to the surfactant model, we first address the choice of water model. For spreading, an important criterion is a model’s ability to reproduce the high surface tension of water. Unfortunately, most popular nonpolarizable water models such as TIP3P, TIP4P,31 and SPC/E28 consistently underestimate the surface tension. For example, deviations from experiment are more than 10% for SPC/E and almost 30% for TIP3P at 300 K.25 We use the TIP4P/2005 model,24 which is the only currently available generic model whose surface tension agrees well with experiment.25 To build the trisiloxane surfactant molecule, we follow the typical approach of assembling it from molecular building blocks. The most popular generic models from which such building blocks can be obtained have been designed for biomolecular simulations, such as OPLS,36 GROMOS,37 CHARMM,38 and AMBER,39 or phase equilibria, such as TraPPE.40 While the former are typically optimized for use with a given water model, the latter typically do not contain water. Since the dedicated water model cannot easily be replaced by TIP4P/2005, such force fields cannot be used for our simulations without intensive testing. Another problem related to these force fields is that they typically do not contain parameters to describe dimethylsiloxanes, which is a necessity for superspreading. In principle, one could combine a generic models with a specialized dimethylsiloxane model, such as those of Sun et al.41 or Frischknecht et al.,42 but this is the approach already tried by Halverson et al.19 Moreover, these specialized models also might not work well with the TIP4P/2005 model. The models that meet our requirements best are quantumchemistry-based models for polyalkenes,20 poly(ethylene oxide) (PEO),22 poly(tetrafluoroethylene) (PTFE),21 and poly(dimethylsiloxane) (PDMS).23 Although these force fields are seemingly independent, the interactions of these force fields have been determined using similar quantum chemistry methods and have not been determined from empirical fits, indicating that they should be transferable. Furthermore, the alkane force field of ref 20 was used to generate the force fields in refs 21−23. Finally, the potentials and parameters are consistent throughout these force fields: for instance, the parameters for the van der Waals 9285



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Table 1. Experimental and Simulated Densities, Surface Tensions, and Heats of Vaporization for Model Compounds ρliq (g/L) exptla

material

originalb 60

hexane perfluorohexane DME OMTS

654.96 1679.863 861.366 815.568

644.43 (94) 1611.28 (384) 855.47 (100) 815.33 (48)

γ (mN/m) exptla

optimized

originalb

61

650.56 (26) 1648.61 (430) 859.59 (68) −

17.91 12.2364 23.9366 16.669

17.89 (50) 12.91 (70) 27.43 (60) 19.28 (100)

ΔvapH (kcal/mol) optimized

exptla

originalb

optimized

18.72 (50) 13.57 (70) 27.52 (60) −

62

7.27 (6) 7.91 (3) 8.51 (3) 10.38 (2)

7.56 (10) 8.28 (8) 8.61 (2) −

6.90 7.5165 8.6567 9.4570

a References for experimental values indicated in superscripts. bSimulated values using original force fields. cSimulated values using optimized force fields (OMTS force field was not modified). dValues in parentheses are twice the standard deviation of the mean obtained from the statistical uncertainty quantification.

partial charges, bond, angle, and dihedral potentials. The complete model is given in the Supporting Information. 2.3. Fitting Procedure. The parametrization of vdW interactions between the water and surfactant molecules is described in this section. The procedure for determining the remaining parameters, namely the modifications of the dispersion coefficients of the surfactant molecules and the determination of the few missing partial charges and parameters for bonded interactions, is given in the Supporting Information. The usual approach in force field development is to start with the simplest type of interactions, constrain the optimized parameters, and then move to more complex systems. This would suggest to start the polymer−water parametrization with alkane−water mixtures. Here, however, we follow a different approach and fit the PEO−water interactions first. The other compounds considered here mix poorly with water, so there is little experimental data available. Moreover, the proper description of PEO−water interactions can be quite challenging53−57 and should therefore be addressed first. Suitable parameters for the PEO−water interactions were determined from computations with dimethoxyethane (DME) and water. To fit the interactions, we follow three approaches. In the first approach, labeled as I, we fit the DME−TIP4P/2005 potential to a quantum chemistry-based potential for the DME− TIP4P model.54 In that work, the DME−TIP4P interactions were fit to energies obtained from quantum chemistry computations of different configurations of the DME−water dimer. Instead of redoing the quantum chemistry computations, we fit the DME−TIP4P/2005 interactions to the original DME− TIP4P force field for a similar set of configurations of the DME− water dimer, so that the DME−water interactions are indirectly fit to quantum chemistry computations. We dropped the requirement of geometric mixing for the dispersion coefficients because the quantum chemistry data could not be reproduced otherwise. In the second approach, labeled as II, we fitted LJ potentials to the Buckingham potential of the original force field, and defined the interaction parameters with water by applying standard Lorentz−Berthelot mixing rules to the fitted potential, as suggested by Ismail et al.58 In the third approach, labeled as III, we have simulated a series of DME−water mixtures with mole fraction xDME ≈ 0.18. The parameters were fit to reproduce experimental values for the liquid density and viscosity. During the iterative fitting, the radial distribution function was monitored to avoid demixing. In this approach, we applied geometric mixing for the dispersion coefficients. The LJ parameters for the interactions between the TIP4P/2005 hydrogens and the polymer compounds were set to zero in all three approaches. In the next step, the LJ parameters describing the interaction between water and the polymeric compounds for the C, O, and

(vdW) interactions for C, H, and O atoms are the same across all the force fields. To fully satisfy our needs, we made three modifications to these models. First, our developed force field is intended for interfacial simulations. For these systems, inclusion of long-range dispersion forces is critical to obtain accurate results.43−48 A prerequisite for the efficient application of long-range dispersion solvers49−51 is for dispersion coefficients to follow a geometric mixing rule, as discussed in ref 52. While these solvers can be used for other mixing rules, the most efficient simulationseven faster than simulations using truncationare facilitated by geometric mixing rules.52 Thus, we have reparametrized coefficients in the original force field which do not satisfy geometric mixing rules to provide optimal compatibility with long-range dispersion solvers. Theoretical arguments justifying our modifications are presented in section 2 of the Supporting Information. Next, the model was extended to work well with the TIP4P/2005 water model. Finally, for surfactants and copolymers composed of different parts of these polymers, a few bonded interactions and partial charges close to the linking points not available in the literature were parametrized. 2.2. Functional Form. The functional form of the force field is only briefly presented here. In particular, we describe the treatment of vdW interactions, because these were the parameters requiring the most modifications. The original force field for the polymers20−23 that we are modifying describes vdW interactions with a Buckingham potential UBuck = A exp( −Br ) −

C6 r6

(1)

where r is the distance between two particles and A, B, and C6 are coefficients to describe the interactions. The TIP4P/2005 model uses the LJ potential

ULJ =

C12 r

12

−

C6 r6

(2)

where the coefficient C12 describes the repulsive interactions. In the developed model, the interactions between water and nonwater molecules have been modeled using LJ potentials. To ensure optimal compatibility with long-range dispersion solvers,52 the C6 coefficients were obtained from the geometric mixing rule C6, ij =

C6, iiC6, jj

(3)

where the indices i and j refer to particles of different types. As discussed below, there was a scenario in which we discarded the use of this mixing rule. However, the final optimized force field presented here obeys geometric mixing for all dispersion coefficients. Aside from vdW interactions, the model uses fixed 9286



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requires selection of special mixing rules or modifications of the potentials.71,72 Enthalpies of mixing and excess volumes of the mixtures are shown in Figure 1. The agreement between experiment and

H atoms were constrained. The remaining Si−water and F− water interactions were parametrized to match experimental values for the octamethyltrisiloxane (OMTS)−water and perfluorohexane−water interfacial tensions. 2.4. Force Field Validation. Here we discuss some findings from our fitting procedure, as well as results obtained from the optimized force field. The details of the simulations reported here as well as the methods used to analyze the results are presented in the Supporting Information, where we also present the set of optimized parameters. For convenience, all parameters taken from the literature, including the bonded parameters, are also provided with references to the original sources. All simulations were performed with the LAMMPS MD package59 with in-house modifications summarized in the Supporting Information. 2.4.1. Nonbonded Surfactant Interactions. Results for the modified nonbonded surfactant interactions are presented here. The model was altered only by enforcing geometric mixing in the dispersion coefficients and scaling them by 2−3%. Moreover, mixing rules were introduced for the repulsive parameters not explicitly defined. Because the modifications are rather small, we restrict our attention to only a few results. Simulation results for the pure model compounds are summarized in Table 1. Overall, the agreement between experimental and simulated values is good. For hexane, DME, and OMTS, the deviation in the liquid densities is less than 2% for the original and less than 1% for the modified model. For perfluorohexane the deviations are larger: 4% for the original model and 2% for the modified model. Deviations in the surface tension are below 15% for all compounds for both models. For the heats of vaporizations, the maximum deviation of the original model from experiment (10%) occurs for OMTS. For the modified model, deviations of similar size are also obtained for hexane and perfluorohexane. For these compounds, the deviation is only around 5% in the original model. Compared to the original literature model, liquid densities are better reproduced for all compounds. The surface tensions and heats of vaporizations are also in good agreement, although they are slightly worse than those predicted by the original force field. The performance of both models to describe the properties in Table 1 is comparable; neither model strongly outperforms the other for any of the observed quantities. An advantage of the modified version of the model, however, is that dispersion coefficients follow geometric mixing rules, and thus long-range dispersion solvers can be applied more efficiently.52 The computational performance of the modified model will thus be better in simulations in which the application of these solvers is desirable, such as simulations of interfacial or strongly inhomogeneous systems. Because further increasing the dispersion coefficients would increase all of the quantities reported here, the resulting parameters are a trade-off between accuracy in the structural and energetic properties. Further optimization would have been possible either by modifying the repulsive parameters or by individually adjusting the dispersion coefficients. However, this would complicate extending the model, because the deviation from the original development would be greater. Moreover, as the agreement between experiment and simulation is sufficient for our purpose, we have refrained from further optimization. Simulations of mixtures of hexane and perfluorohexane like those described in ref 71 were used to validate the mixing rules introduced for the missing repulsive interaction coefficients, as properly describing these mixtures is challenging and typically

Figure 1. Excess quantities for mixtures of perfluorohexane and hexane: (top) excess molar volume, (bottom) enthalpy of mixing. Blue lines: experimental fits taken from ref 74 for excess volume and from ref 73 for heat of mixing. Red squares: simulated values for OPLS from ref 71. Green circles: simulated values using model presented here.

simulation is not perfect, but still significantly better than that obtained with the OPLS force field in ref 71. We compare our results to those obtained with OPLS because the simulation results for this model could be taken from the reference. We note that in ref 71 the deviations were not attributed to the OPLS model, but to the challenge of modeling alkane−perfluoroalkane mixing. The good agreement between experiment and simulation with the quantum-chemistry-based force field is mainly a result of the methodology used for the original force field, and only to a small extent a result of our modifications. 2.4.2. Surfactant−Water Interactions. In this section we briefly present results from the determination of interactions between the TIP4P/2005 model and our surfactant models. We start by giving results for the DME−water interactions before presenting results obtained for the other systems. Experimental liquid densities and values obtained from simulations with potentials I, II, and III (cf. section 2.3) are given in Figure 2. For the potential from approaches I and II, the agreement between experiment and simulation is insufficient. For intermediate concentrations, the deviation between I and experiment is more than 2.5%, and for II the deviation is almost 6%. In approach III, where we fit the DME−water potential to experimental data, the liquid density is reproduced well for all concentrations, with deviations between simulation and experiment less than 0.5%. The underprediction of the densities by potentials I and II is related to partial or full demixing. As can be seen from the radial distribution functions (RDFs) depicted in Figure 3, the first peak in the RDFs is distinctly below 1.0 for potential I and less than 0.25 for potential II, indicating demixing. Similar demixing in DME/water mixtures has already been detected by Fischer et al.53 with other force fields for water and DME. For potential III, 9287



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Figure 2. Experimental and simulated densities of DME−water mixtures at 318 K with model approaches I, II, and III. Experimental values were taken from ref 75.

Figure 4. Experimental and simulated values for the viscosity (top) and water diffusivities (bottom) of DME−water mixtures. Experimental viscosities were taken from ref 75. Original diffusivities were taken from ref 56, scaled diffusivities from ref 53.

Table 2. Experimental and Simulated Values for the Interfacial Tension between Model Compounds and Water

Figure 3. Radial distribution functions between the DME O and water O atoms for xDME ≈ 0.18. The low value of the first peak for potentials I and II indicates demixing.

γ (mN/m)

however, the compounds mix properly. The correct phase behavior is also confirmed by the free energy of solvating a DME molecule in water, which we have computed using thermodynamic integration.76 The simulated value is ΔsolGsim = −5.4 ± 0.3 kcal/mol, and the experimental value is ΔsolGexp = −4.8 kcal/ mol.77 Because of demixing and inaccurate reproduction of the density for potentials I and II, dynamic quantities were only determined for potential III and are depicted in Figure 4. For viscosities of the pure compounds, the deviation between simulation and experiment is around 7% for pure water and around 5% for pure DME. In the region of maximum deviation at xDME ≈ 0.2, the simulated value is around 14% higher than the experimental value, indicating that the dynamics are somewhat too slow in this region. For the diffusion coefficients, aside from the original experimental data from ref 56, this figure includes scaled values of the experimental data, as suggested in ref 53. For the experimental data, it is unclear whether the original or scaled data better represent the true value. The simulated diffusion coefficient is often below the experimental data, although the general trend that the diffusion coefficient passes through a minimum is reflected in the simulation results. Combining the results for the viscosities and the diffusion coefficients, it seems that the dynamics of the developed model is somewhat “slow” compared to reality. However, the agreement is sufficient for our purposes. The results of the simulations of the interfacial tension of systems of water with the model compounds hexane, perfluorohexane, and OMTS are given in Table 2. The agreement between simulated and experimental data is good for all three compounds. We note that no additional fit was required for the hexane−water interactions.

material

experimental

simulation

hexane perfluorohexane OMTS

50.38 (4)78 57.20 (13)79 40.5 (5)

52.03 (120) 57.94 (140) 40.3 (18)

2.5. Discussion of Fitting Strategies. In this section we discuss the three fitting strategies I, II, and III (cf. section 2.3) and provide explanations for the performance of the models obtained with the different approaches. In approach I we fit the DME−TIP4P/2005 potential to a previously developed quantum-chemistry-based DME−TIP4P model.54 Since the model obtained with this strategy is an indirect fit to quantum chemistry data, one might expect it to provide best results. While the original potential was successful in describing the mixture,54 the resulting model in this work provided a poor description of the system and resulted in demixing. Since we did not fit directly to quantum chemistry data, and since the potential upon which it was built was created with methods that were state of the art in 2002, one might argue that directly fitting to quantum chemistry data with more elaborate methods will improve the results. While we cannot guarantee that such an approach will not provide any benefits, we doubt that this approach will result in a model that will perform better than the model obtained with approach III. Aside from the potentially insufficient quantum chemistry data approach I was built upon, the reason for wrong mixing behavior lies within the TIP4P/2005 model itself. The TIP4P/2005 model is known to provide good results for many observables, such as liquid densities, surface tensions, and diffusivities;25 its ability to reproduce microscopic phenomena, however, is limited. Kiss and Baranyai showed that the TIP4P/2005 systematically underestimates the energy of the formation of small water clusters.80 Thus, the attraction between the TIP4P/ 9288



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experimental quantities, which limits transferability compared to the nonwater interactions. The difficulty of combining models developed with different strategiesthe quantum-chemistrybased nonwater models and the highly empirical TIP4P/2005 water modelis a general problem in force field development. It should be noted though that this problem is more or less pronounced for different models. For example, a quantumchemistry-based force field to describe the interactions of DME with the original TIP4P model was successful in describing properties of the mixture.54 Apparently, the capacity of TIP4P/ 2005 to reproduce a variety of quantities of pure water25 is achieved at the expense of difficulties when combined with other models. Yet, because of its accurate representation of surface properties and computational simplicity, it is still our model of choice.

2005 water molecules is too strong compared to real water or accurate quantum chemistry computations. To ensure mixing of DME with water, we must ensure that the DME−water interactions are sufficiently favorable to separate water molecules. Thus, these interactions will also have to be stronger than DME−water interactions in reality to compensate for the strong interactions of the TIP4P/2005 model. This cannot be achieved with a fit to quantum chemistry data. Approach II, in which the potential of the mixture was determined from fitting LJ potentials to the Buckingham potentials used for the polymer models, yielded phase behavior that was even worse than that found using approach I. Aside from the problem of too strong interactions between TIP4P/2005 molecules, there was an additional problem related to the functional forms of the Buckingham and LJ potentials. We used a simple least-squares fit with the additional constraint that the C6 coefficients in the final model will obey geometric mixing rules. As a result, the depth of the minima in the LJ potentials was less than the depth in the Buckingham potentials. Specifically, the depths in the LJ potentials were εO,LJ = 0.176 kcal/mol, εC,LJ = 0.041 kcal/mol, and εH,LJ = 0.003 kcal/mol, whereas the potential depths of the Buckingham potentials were εO,LJ = 0.206 kcal/mol, εC,LJ = 0.098 kcal/mol, and εH,LJ = 0.010 kcal/mol, i.e., significantly larger. When applying mixing rules to these reduced potential depths, the resulting ε’s describing the DME−water interactions were too small and caused the strong demixing. An alternative strategy to match the Buckingham and LJ potentials, for example by dropping the constraint of geometric mixing or constraining the depth of the potentials, might have improved the results, but the problem of the strong interactions among TIP4P/2005 water molecules remains. In approach III, we fit the DME−TIP4P/2005 interactions such that macroscopic observables are reproduced well. This strategy automatically compensates for the strong interactions of the TIP4P/2005 model and in this way provides correct densities of the mixture and a good estimate for the free energies of solvation ΔsolG. The dynamics obtained with this approach, however, were too slow compared to what is observed in experiment. For an effective model such as the one generated with approach III, it is difficult to make precise statements why it has certain featuresfor instance, why the dynamics are not reproduced better. An explanation could be that the resulting DME−water interactions of this fit are too strong compared to the DME−DME interactions and that the connections between DME and water molecules are therefore too stable. 2.6. Assessment of the Final Model. An advantage of the proposed force field is that it reproduces with reasonable accuracy quantities important for interfacial simulations, such as surface tensions, free energies, and structural properties.81 Dynamic quantities are also reproduced reasonably well, but not as accurately as the properties mentioned above. Moreover, a strong feature is that the parameters for the nonwater molecules are based on quantum chemistry computations. It was shown that this ensures transferability even for the difficult problem of mixtures of alkanes and perfluoroalkanes. The force field can therefore be extended to further compounds using the methods employed in the original development. Moreover, the detailed quantum-chemistry-based force field has the advantage of capturing features specific to the studied molecules, such as the flexible Si−O−Si angle for OMTS.23 A disadvantage of the model is that reasonable agreement between simulated and experimental quantities for mixtures with water could only be achieved by fitting parameters to reproduce

3. SIMULATIONS OF SURFACTANTS AT WATER SURFACES 3.1. Simulations Setup. We have performed a series of surfactant simulations with the alkyl ethoxylate, trisiloxane, and perfluoroalkane surfactants depicted in Figure 5. The chain

Figure 5. Alkyl ethoxylate (left), trisiloxane (center), and perfluoroalkane (right) surfactants. The hydrophilic part is the same for all surfactants. The atoms labeled with the red ovals were selected as “central” atoms of the surfactant for purposes of measuring the surface coverage and diffusion of the surfactants.

length of the hydrophilic part was n = 6 for all surfactants, which corresponds to experimental observations of superspreading with the trisiloxane surfactant. Simulations with the alkyl ethoxylate surfactant were performed with m = 10 for the hydrophobic part. Simulations with the perfluoroalkane-based surfactant were performed with m = 8. The box dimensions were 60 Å × 60 Å × 200 Å. The number of water molecules was 10 000 in all simulations. The number of surfactants at each interface was nS ∈ {18, 36, 54, 60, 72, 78, 84} corresponding to interfacial areas of Amol ∈ {200, 100, 66.67, 60, 50, 46.15, 42.85} Å2/molecule. For the trisiloxane surfactant, simulations were not performed with nS = 78 or nS = 84 because the surface was already overcrowded for nS = 72. Starting configurations were generated with Packmol.82 A slab of water molecules was generated in the center of the simulation box with interface parallel to the xy plane. The surfactant molecules were placed so that their hydrophobic parts were at the water surface when the simulations began. A Nosé−Hoover thermostat83 was used to keep the temperature at 298 K. The damping constant for the Nosé−Hoover thermostats was set to τT = 100 fs. The simulations were equilibrated for 1 ns. Afterward, data was taken from production runs over 7 ns. The SHAKE algorithm84 was used to constrain the shape of the water molecules. Long-range 9289



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trajectories, bending of the interface could be observed at the highest surfactant load, indicating that additional interfacial area is required to hold the surfactants, largely because of the bulkiness of the trisiloxane headgroup. This bending was not observed in any other simulation. Although this simulation was in an unphysical state, simulation results are reported for completeness. In addition to the analysis of overcrowding, we examined how much of the surface area is covered with surfactants using a twostep approach. First, we use the ITIM algorithm89 to identify atoms located at the interface. In this algorithm, spheres are moved along lines perpendicular to the interface. When the moving sphere touches an atom, the process is stopped and the touched atom is labeled as an interfacial atom. In our analysis, the lines were arranged on a regular grid with 1 Å spacing; atoms were treated as point particles. Because the probe radius influences the results, we tried different values ranging from rS = 2.0 Å to rS = 4.0 Å with a spacing of 0.1 Å. The influence of the probe radius rS is discussed in the Supporting Information. In the second step, the interfacial atoms are projected onto a plane and Voro++90,91 is used to construct an unweighted Voronoi tessellation. In Voronoi tessellation, each spatial point in a configuration is assigned to the nearest atom. The areas of the resulting Voronoi cells for each atom are then summed to determine the fraction occupied by water and the hydrophilic and hydrophobic parts of the surfactant (cf. labels in Figure 5). The areas obtained with this approach are projected areas and, since the interfaces are not strongly curved, are a reasonable approximation for the covered area. The process of defining occupied surface areas is illustrated in Figure 7.

electrostatic and dispersion interactions were computed with the PPPM with analytic differentiation,50,52,85 with parameters set according to our previous recommendations.52 Per-atom stresses were computed to enable more detailed analysis.86 Equations of motions were integrated with the rRESPA algorithm,87,88 with settings chosen as described in ref 52. All simulations were performed with the LAMMPS59 MD package with in-house modifications described in the Supporting Information. 3.2. Results and Discussion. To facilitate the analysis, we have defined a central atom, chosen to be close to the position where the surfactant changes from hydrophilic to hydrophobic, for computing RDFs and mean square displacements (MSDs). The central atoms of the surfactants are labeled in Figure 5. 3.2.1. Surface Load and Coverage. It is possible to start simulations in an unphysical state in which the surface is overloaded with surfactants. Because of the finite length of the simulations, there is the danger that the system cannot escape from this starting configuration. Therefore we first examine the surfactant load at the interface. As an indirect measure for whether the surface was overcrowded we have examined the positions of the central surfactant atoms in our simulations. Histograms of their positions are shown in Figure 6 for selected values of nS from

Figure 6. Histograms of the z position of the central atom (cf. Figure 5). For the trisiloxane surfactant with nS = 72, the curve shows secondary peaks, indicating overcrowding.

which the differences between the simulations become apparent. For the alkyl ethoxylate and the perfluoroalkane surfactant, the only visible effect in the range of examined surfactant loads is that the distribution broadens and the height of the peak is reduced. Moreover, the peaks at the left and right interfaces are not identical. The peaks have slightly different heights at high surfactant concentration, indicating that further sampling may be required to obtain more accurate values. For the trisilxoane surfactant, however, the situation is different. For low and intermediate concentrations, the behavior is the same as for the alkyl ethoxylates and perfluoroalkanes. At the highest concentration, however, the profile is much noisier, and the histogram shows secondary peaks, indicating that the system was in an unphysical, overcrowded state. Moreover, when visualizing the

Figure 7. Steps to approximate the covered surface area. Blue, water atoms; black, hydrophobic part of the surfactant; red, hydrophilic part of the surfactant. Upper left: snapshot of the simulation box with all atoms. Upper right: atoms defined as surface atoms by the ITIM algorithm. Lower left: top view of those atoms. Lower right: Voronoi tessellation. Images created with VMD.92

The results for the different surfactants at various concentrations are depicted in Figure 8 for rS = 2.0 Å. With increasing surfactant concentration, the area occupied by the hydrophobic part of the surfactant increases, while the areas covered by the hydrophilic part and water decrease. For very low concentrations, the area occupied by the hydrophilic and hydrophobic parts is approximately equal. The area occupied by the water molecules is 9290



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fixed surfactant load, the absolute position of the z value is of course reasonable quantity. The interface widens with increasing surfactant concentration for all three examined surfactants. While the thickness of the interface is only approximately 5 Å for pure water, the total width of the interface including the hydrophobic part of the surfactant becomes as large as 35 Å for the surfaces covered with alkyl ethoxylate and perfluoroalkane surfactants and 30 Å for trisiloxane surfactants at maximum coverage. Even for the smallest examined surfactant concentration nS = 18, the width of the interface increases to between 15 and 20 Å. The number densities of the water O atoms are shown on the left of Figure 9 for the different surfactants. In each case, the distribution broadens with increasing surfactant concentration. It is noteworthy, though, that the change of the curves is especially strong for low surfactant concentrations. For higher concentrations (nS ≥ 54) the profile does not broaden significantly. The distribution of the hydrophilic O atoms depicted in the middle row of Figure 9 becomes broader and higher with increasing surfactant concentration. For low concentrations, the distribution is rather narrow compared to higher concentrations for all three surfactants. This indicates that, at low concentrations, the hydrophilic part of the surfactant resides close to the interface. With increasing surfactant concentration, the interface becomes too narrow and the hydrophilic tail stretches out into the water phase. The extent of surfactant hydration is apparent from a comparison of the distribution of the water molecules and the hydrophilic O atoms. For low surfactant concentrations (nS ≤ 54), the distributions decay to zero at approximately the same value of z, which means that the hydrophilic parts are fully hydrated. For higher surfactant concentrations (nS = 84), however, the distribution of water molecules decays to zero more quickly, meaning that some of the hydrophilic O atoms stick out of the water surface. At high concentrations, the hydrophilic parts of the surfactants are only partly hydrated.

Figure 8. Surface area covered by water (blue), the hydrophilic (red), and the hydrophobic (black) part of the surfactant computed with rS = 2 Å. The hydrophobic part of the trisiloxane surfactant covers the surface more completely than the hydrophobic part of the other surfactants.

greater than the areas covered by the different parts of the surfactant for the lowest concentrations examined. The area occupied by the hydrophobic part of the trisiloxane surfactant grows more rapidly than the areas occupied by the hydrophobic parts of the other surfactants. At some point, however, the increase in area levels off for the trisiloxane, whereas it continues to grow for the other surfactants. Simultaneously, the hydrophilic area of the surfactant shrinks more rapidly for the trisiloxane surfactant, as does the water area. For nS ≥ 54, the area of the surface that is covered by water is approximately zero for all three surfactant types. 3.2.2. Density Profiles. Number density profiles ρnum of water and the different surfactant parts are depicted in Figure 9. The absolute value of the z dimensions between simulations with a different number of surfactants contains very limited information. The number of water molecules is identical in all simulations; thus, with increasing number of surfactants, the system grows and the entire interfacial region moves. Thus, the z positions of the density peaks move not only because the interface broadens but also because the interface itself moves. For

Figure 9. Number densities as a function of z. Rows from top to bottom: alkyl ethoxylate, trisiloxane, and perfluoroalkane surfactant. Columns from left to right: water O, hydrophilic O, and hydrophobic atoms. 9291



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models, A∞ mol is much smaller for the alkyl ethoxylate surfactant compared to macroscopic models and experiment. The deviations might be either a result of the experiments and modeling not being sufficiently accurate or that the state of maximum packing should already be attributed to lower values of the number of surfactants at the interfaces in our simulations. In the latter case, this would mean that our model does not reproduce well the reduction of the surface tension for the alkyl ethoxylate surfactant. There is no indication from our simulations, however, that suggests that simulations with either the alkyl ethoxylate or perfluoroalkane surfactant with nS = 84 were overcrowded. Given that small differences of end caps of large molecules can have strong effects,93−98 the deviations in Table 3 might also result from that the maximum packing for the reference data has been determined from surfactants with a hydroxyl end group, whereas the surfactants in our simulations have a methyl end group. For nS ≤ 36 surfactants at each interface, the surface tension decreases only slightly for all surfactant types. Beyond this concentration, however, the surface tension of the trisiloxane system drops rapidly. For the alkyl ethoxylate and perfluoroalkane surfactants, the surface tensions drops in this region, too, but not as steeply as for the trisiloxane surfactant. In addition to the overall surface tension, we determined the contributions from Coulomb γC, dispersion γD, repulsive γR, and bonded γB interactions, as shown in Figure 11. The bonded interactions include contributions from the SHAKE algorithm. The kinetic energy contribution is included in the total but not shown separately. For contributions from Coulomb interactions, the dropoff is steeper for the trisiloxane, and for full coverage drops to almost zero. The stronger decay compared to the other surfactant types may be related to the strong quadrupole of the trisiloxane headgroup, which shields the Coulomb interactions of the dipolar water molecules. In simulations with the alkyl ethoxylate and the perfluoroalkane surfactants, whose hydrophilic tail partial charges are all zero in our model, Coulomb interactions on water molecules close to the interface are exerted mainly from water molecules and surfactant tails closer to the bulk. These interactions “pull” the water molecules at the interface toward the bulk, hence the positive contribution of the Coulomb interaction to the surface tension. In simulations with the trisiloxane surfactant, however, the quadrupolar trisiloxane headgroup attracts water molecules close to the interface with a force in opposite direction and in this way further reduce the contribution of Coulomb interactions to the surface tension. For the alkyl ethoxylate and perfluoroalkane surfactants, the Coulomb contribution drops more slowly with increasing surfactant concentration. Moreover, γC levels off for high surfactant concentrations. The plateau region with nS ≥ 54 coincides with a cessation in the broadening of the density profile of the water molecules. For the pure water interface, the contributions from the bonded γB and dispersion γD interactions are positive, while the repulsive γR interactions are negative. For the alkyl ethoxylate and perfluoroalkane surfactants, the contributions first increase in magnitude, before changing sign with increasing surfactant concentration. For the highest concentrations, the influence of these contributions is strongly reversed. For the trisiloxane surfactant, the behavior is similar, but not as extreme as for the other surfactants, and does not pass through a turning point. The change in sign shows that, for low surfactant coverages, the surface tension is a result of negative (attractive) stresses

The distributions of the hydrophobic atoms are depicted in the right column of Figure 9. Like the hydrophilic part, the distribution is narrow for low surfactant loads, but broadens with increasing concentration. For the alkyl ethoxylate and perfluoroalkane surfactants, this is the result of the hydrophilic chains starting to lift away from the interface and stretching into the vapor phase. Despite the bulkiness of its headgroup, the distribution also broadens for the trisiloxane surfactant. This is a result of the flexible Si−O backbone of the hydrophobic head, which permits strong bending. The flexibility is demonstrated from angles and orientations of the Si atoms in the headgroup in the Supporting Information. 3.2.3. Surface Tensions and Stress Profiles. Surface tensions and stress profiles were determined using the same approach that was used in section 2.4. Simulated values for the surface tension at different surfactant concentrations and experimental values for the free and fully covered surfaces are depicted in Figure 10. For

Figure 10. Simulated and experimental surface tensions. Red diamond: experimental value for pure water.99 Other scatter points: simulated values. Dashed lines: experimental values for fully covered surfaces.100,101 Experimental data for the alkyl ethoxylate surfactant were measured for a slightly different surfactant with m = 11 (cf. Figure 5) and hydroxyl end cap. Shaded area: range of experimental values at fully covered surfaces for slightly different perfluoroalkane surfactants with m = 3−5 and n = 3−5 (cf. Figure 5).93,102,103

the highest surfactant concentrations in simulations that are not overcrowded (nS = 84 for the alkyl ethoxylate and perfluoroalkane surfactants, and nS = 60 for the trisiloxane surfactant), the simulated surface tensions are in agreement with experimental values at fully crowded surfaces of similar surfactants. For the area per molecule at maximum packing A∞ mol, however, there are deviations between modeling and experiment, as shown in Table 3. While for the trisiloxane surfactant the result from the simulation is in between the values obtained from macroscopic Table 3. Surface Area Per Surfactant Molecule at the Interfaces at Maximum Packing surfactant

A∞ mol,Neut (Å2)a

A∞ mol,Lang (Å2)b

A∞ mol,Frum (Å2)c

A∞ mol,Sim (Å2)d

trisiloxanee alkyl ethoxylatef perfluoroalkaneg

− 55 ± 3h −

70.6i 68j −

54.3i 56j −

60 43 43

a Obtained from neutron reflectivity measurement. bObtained from a Langmuir model. cObtained from a Frumkin model. dEstimated from our simulations. eTrisiloxane surfactant in experiment had a hydroxyl end group. fAlkyl ethoxylate surfactant in experiment had a hydroxyl end group and the hydrophobic chain contained one additional CH2 group. gNo reference data available. hTaken from ref 104. iTaken from ref 105. jTaken from ref 101.

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Figure 12. Surface tension profiles in z direction of all interactions. Thickness of the lines correspond to statistical uncertainties. From top to bottom: alkyl ethoxylate, trisiloxane, and perfluoroalkane surfactant. Because the data of the Coulomb interactions are noisier, the data are subject to stronger uncertainties.

simulations, as shown below. Other difficulties with applying these algorithms is that either the number of clusters has to be specified in advance or the algorithm must be trained to provide the correct number of clusters, both of which are not a viable option here because we have neither a training data set nor a priori information about the number of clusters. Instead, we use two-dimensional RDFs in the xy plane of the center atoms of the surfactants defined in Figure 5 to study the interfacial surfactant structure. While this method does not provide direct information on formed clusters, it is simple and robust and reveals much useful information about the structure of the simulated system. Before discussing the RDFs of the different compounds, we note that the RDF can be nonzero at rxy = 0, as the distance in the z dimension is neglected. Surfactants whose central atoms are aligned normal to the interface contribute to the RDF at rxy = 0. It is interesting to note that the effect of overlapping surfactants is strongest for the alkyl ethoxylate surfactant. For the perfluoroalkane surfactant, which is structurally similar to the alkyl ethoxylate, overlaps did not occur. Evidence for cluster formation can be found by analyzing the surfactant RDFs in Figure 13 at the lowest concentration. Aside from having prominent peaks for short distances, indicating increased surfactant clustering, the RDFs are distinctly below unity at rxy = 30, half the cell size in the x and y directions. This means that the size of the clusters observed in our simulations is similar to the interfacial area of the simulation, which means that the size and structure of the clusters are strongly influenced by finite-size effects and have to be viewed with great caution. Cluster formation at low surfactant concentrations is also evident from observing the surfactant positions, as shown in Figure 14. For each surfactant type, the surfactants are connected to form a single, large entity. At higher surfactant concentrations, the RDFs are approximately unity at the cutoff, but show pronounced peaks for short distances in the xy plane. Compared to lower surfactant concentrations, these RDFs no longer demonstrate cluster

Figure 11. Simulated surface tension divided into several contributions. From top to bottom: Coulomb, bonded/SHAKE, and dispersion, repulsion interactions. The Coulomb contribution decays stronger for the trisiloxane surfactant; the other contributions are strongly reversed with increasing surfactant concentration.

tangential to the interface, whereas positive (repulsive) stresses perpendicular to the interface contribute to the surface tension for high surfactant coverages. The change of the stress profiles in z dimension of γB,z, γD,z, and γR,z is depicted in the Supporting Information for the alkyl ethoxylate surfactant at different concentrations. The local distribution of the total surface tension across the interface is shown in Figure 12. Because of strong fluctuations in the Coulomb contributions, the data is relatively noisy, but some interpretations are possible. Despite the very different behaviors of the contributions to the surface tension (cf. Figure 11 and Figure S7 in the Supporting Information), the overall local contributions for the surfactant-laden systems have a simple behavior. In the void and in the bulk the contribution is zero, and in between there is a single peak in the region of stress. The only exception to this is the trisiloxane surfactant for nS ≥ 54, in which a repulsive (negative) peak is found ahead of the attractive layer. 3.2.4. Surfactant Structure at the Interfaces. It is well-known that, away from the interface, surfactants tend to form aggregates depending on the surfactant type and concentration.106 The formation of clusters or aggregates at the interfaces has received attention only in a few studies for trisiloxane surfactants.107 Here we examine aggregate formation at the interface. Shao et al. discuss cluster formation algorithms that could be used to identify aggregates.108 Aside from different clustering methods providing very different results for the same data set, a difficulty of these algorithms is that they are mainly beneficial for systems in which multiple distinct clusters are formed, which is not the case for the spatial distribution of surfactants in our 9293



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Figure 15. Diffusion coefficient in the xy plane as a function of surfactant concentration.

surfactant loads shows that mutual hindrance of the hydrophobic groups starts to influence the dynamics. Yet, the difference in diffusion coefficients of different surfactants is relatively small compared to the overall change for increasing surfactant load. 3.3. Relevance for Superspreading. We now briefly discuss how our findings are connected to superspreading. The most prominent difference between the trisiloxane surfactant and the other surfactants is the steeper gradient of the surface tension as a function of surfactant concentration, which could potentially influence generation of surface tension gradients in spreading surfactant-laden droplets and thus contribute to faster spreading. Another feature related to surface tension is the well-known fact that the trisiloxane surfactant lowers the surface tension more strongly than many other surfactants. Finally, for the trisiloxane surfactant, we detected repulsive forces at the outermost part of the surfactant layer, which can act as an additional driving force. We found that clusters are formed at the interfaces for all three surfactants, which argues against the relation between formation of surfactant aggregates and superspreading suggested in ref 12. It should be noted, though, that we only detected formation of surfactant aggregates. The present simulations are not sufficient to analyze possible differences among the aggregates; thus, it is possible that aggregate formation plays an important role in superspreading. Since superspreading is a dynamical process, one might expect to see major differences in the dynamic behavior compared to nonsuperspreading surfactants. However, the diffusion dynamics of the surfactants at the interface were not significantly different from one another. Given the reasonable applicability of the developed model to dynamic quantities, we conclude that the superspreading effect cannot be attributed to diffusion kinetics lateral to the interface. We would like to note, though, that we are not aware of a theory on surfactant-enhanced wetting that is based on peculiarities of these kinetics. It is the transport from

Figure 13. 2D RDFs of the center atoms. From top to bottom: alkyl ethoxylate, trisiloxane, and perfluoroalkane surfactant. For low surfactant concentrations the formation of clusters becomes obvious from the value below unity at the cutoff distance of 30 Å.

formation, as the RDF is unity for distances much less than half the box size. As the surface is already almost fully covered, as shown in Figure 8, this does not prove that stable aggregates are not formed at the interface. 3.2.5. Surfactant Dynamics. To classify the interfacial dynamics of the surfactants, we computed the two-dimensional MSDs and diffusion coefficients of the central surfactant atoms (cf. Figure 5) in the xy plane using the same approach as in section 2.4. More details on the computations of the diffusion coefficients and results for the MSDs are discussed in the Supporting Information. From the diffusion coefficients in Figure 15, it is clear that the dynamics of the system slow down with increasing surfactant concentration. Especially at low surfactant concentrations, the different head groups do not seem to influence the results. The different surfactants have similar diffusion coefficients at low concentrations, suggesting that the diffusion coefficient is mainly influenced by the velocity of the hydrophilic tail dissolved in the water phase and that the mutual hindrance of the hydrophobic parts is a secondary factor. For high surfactant concentrations, the decay in the diffusivity levels off. Moreover, that the diffusion coefficients for the different surfactants are different at higher

Figure 14. Top view of interfaces in simulations with 18 surfactants. From left to right: alkyl ethoxylate, trisiloxane, and perfluoroalkane surfactants. The hydrophilic part of the surfactant is colored red, the hydrophobic black; water is omitted for clarity. Box boundaries are depicted as gray lines. Formation of clusters is evident from the large connected void areas. The size of the clusters is similar to the interfacial area, suggesting that the results are influenced by finite-size effects. Images created with VMD.92 9294



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ACKNOWLEDGMENTS We thank Markus Schmidt from AVT-TVT at RWTH Aachen University for experimental support and Jonathan Halverson from Brookhaven National Laboratory for helpful discussions. Financial support for R.E.I. from the Deutsche Forschungsgemeinschaft (German Research Foundation) through Grant GSC 111 is gratefully acknowledged.

the bulk to the interfaces, which is inaccessible from the simulations reported here, that is relevant for the spreading velocities.5,9

4. CONCLUSIONS We have extended quantum-chemistry-based force fields for several polymers to work optimally together with the TIP4P/ 2005 water model and long-range dispersion solvers. We examined different strategies to achieve agreement between simulation results and experimental data. A quantum-chemistrybased approach failed to provide accurate results. The reason for the failure is possibly related to the too strong attraction between TIP4P/2005 water molecules compared to real water. The final model, which was obtained from an empirical fit, accurately represents structural and energetic quantities as well as dynamical properties. Furthermore, the model is computationally simple enough to enable large-scale simulations. The model has been developed with application to surfactants and superspreading in mind, but should also perform well for problems involving longer surfactants, such as polymers or copolymers and water. In particular, the model should provide accurate results in interfacial simulations. The model is currently applicable to systems involving oligomers of alkanes, poly(ethylene oxide)s, perfluoroalkanes, and dimethylsiloxanes, but can be extended to further compounds by applying the methods presented in the original force fields and those used here. The model has been applied to alkyl ethoxylate, trisiloxane, and perfluoroalkane surfactants at the water interface. The model accurately represents characteristic surfactant properties, and especially their effect on the surface tension of water. We examined differences between the surfactant molecules, the most important of which is their effect on surface tension. The steeper gradient of the surface tension with surfactant concentration for the trisiloxane surfactants might affect formation of Marangoni stresses. The success of the developed model makes it a promising candidate for future simulation studies in which it could be used in droplet spreading simulations or as a starting point for coarse graining.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Discussion on the required modeling depth and resolution. Procedures for optimizing the dispersion coefficients of the polymer models and the parametrization of missing partial charges and bonded interactions. Simulation setup and analysis methods to support section 2.4. Results for the flexibility and orientation of the trisiloxane headgroup. Discussion on the influence of the probe sphere radius. Example plots for local, separated stress profiles for the alkyl ethoxylate surfactant. Discussion on the 2D MSDs of the surfactants. Optimized force field parameters. Description and source code files of modifications of the LAMMPS MD package. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest. 9295



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