Temperature and Pressure Dependence of the Interfacial Free Energy against a Hard. Surface in Contact with Water and Decane. J.

Transcription

1 Temperature and Pressure Dependence of the Interfacial Free Energy against a Hard Surface in Contact with Water and Decane Henry S. Ashbaugh *, Natalia da Silva Moura, Hayden Houser, Yang Wang, Amy Goodson, and J. Wesley Barnett Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA, * corresponding author: hanka@tulane.edu

2 Abstract. Theoretical descriptions of molecular-scale solvation frequently invoke contributions proportional to the solvent exposed area, under the tacit expectation that those contributions are tied to a surface tension for macroscopic surfaces. Here we examine the application of revised scaled-particle theory (RSPT) to extrapolate molecular simulation results for the wetting of molecular-to-meso-scale repulsive solutes in liquid water and decane to determine the interfacial free energies of hard, flat surfaces. We show that the RSPT yields interfacial free energies at ambient pressures that are consistently greater than that obtained from the liquid-vapor surface tensions of water and decane by ~4%. Nevertheless, the hard surface and liquid-vapor interfacial free energies are parallel over a broad temperature range at 1 bar indicating similar entropic contributions. With increasing pressure, the hard, flat interfacial free energies exhibit a maximum in the vicinity of ~1000 bar. This non-monotonic behavior in both water and decane reflects solvent dewetting at low pressures, followed by wetting at higher pressures as the solvents are pushed onto the solute. By comparing the results of RSPT against classic scaledparticle theory (CSPT), we show CSPT systematically predicts greater entropic penalties for interface formation, and makes inconsistent predictions between the pressure dependence of the interfacial free energy and solvent contact density with the solute surface. 2

3 Introduction. The instinctive connections between molecular-scale solvation and macroscopic interface formation have motivated the development of phenomenological area-based correlations for describing solubility and biomolecular conformational stability [1-6]. When the thermodynamic response of non-polar species solubilization in water to temperature perturbations are compared against the macroscopic water-vapor surface tension, however, these presumed connections are questionable [7]. For instance, at room temperature the hydration free energies of non-polar gases increase with increasing temperature, indicating that molecular-scale hydration is entropically unfavorable, while the water-vapor surface tension decreases with increasing temperature, revealing macro-scale interface formation is entropically favorable. These distinctions point to fundamental solvation thermodynamic changes over the length scales of interest for understanding self-assembly phenomena, where molecular species come together in water to form meso-scale and larger structures [8, 9]. It has subsequently been shown that the crossover between microscopic and macroscopic behavior is buried in temperature dependent curvature corrections for the surface tension [10, 11]. When the pressure dependence of hydration thermodynamics is examined, to understand phenomena like the pressure denaturation of proteins [12, 13], the connection to macroscopic interface formation is further confounded since high pressure state points can lie far from liquid-vapor coexistence. Headway towards linking molecular-scale solubilization and macro-scale interface formation can be made by considering idealized hard sphere, cavity-like solutes, whose predominant solvent interaction is through their excluded volume. Hard sphere solutes are considered excellent reference states for perturbation theories upon which to build solvation theories. The quality of theoretical descriptions of solvation of a broad range of more realistic 3

4 solutes, in turn, demands the underlying reference state is well characterized. Scaled-particle theory (SPT) bridges limiting microscopic and macroscopic theoretical expressions to build a unified thermodynamic framework for describing hard sphere solvation over all length scales. In its original development classical SPT (CSPT) was applied to describe hard sphere solvents, which allow the introduction of microscopic/macroscopic self-consistency constraints to ensure a well-behaved theoretical description [14, 15]. When CSPT is applied to solvents with more realistic interactions, however, these self-consistency checks do not hold, requiring the introduction of experimental quantities, like the solvent density and pressure, as well as an effective hard sphere diameter for the solvent [16]. CSPT has found some success at correlating the solubility of molecular-scale solutes in realistic solvents [17-19], although its application to describe macroscopic interfacial thermodynamics is questionable [20, 21]. Stillinger recognized that simple macroscopic equation-of-state properties were not sufficient in order to realize a unified picture of molecular solute and flat interface hydration [21]. In response to the deficiencies of CSPT at describing realistic fluids, Stillinger reformulated SPT to incorporate the experimental pair-correlation function of water and liquid-vapor surface tension in addition to the solvent density and pressure. Ashbaugh and Pratt [22, 23] subsequently extended Stillinger s ideas to incorporate multibody-correlations obtained from molecular simulations over a wider range of solute sizes in their formulation of the SPT solvation free energy. This revised SPT (RSPT) was subsequently used to examine phenomena including the differences between non-polar solvation in water and organic solvents, hydrophobic entropy convergence, and the thermodynamic crossover from microscopic-to-macroscopic hydration [11, 22, 23]. The initial applications of RSPT utilized the experimental liquid-vapor surface tension as an input [21-24], limiting its description to state points close to liquid-vapor coexistence 4

5 where this approximation is thought to be accurate. This requirement can be relaxed by incorporating additional simulation information on the solvation of meso-scale solutes to constrain the fitting of the hard, flat interfacial free energy [25-27]. The extension of RSPT to incorporate meso-cavity information has been successfully applied to study solvation in the Lennard-Jones [28] and water-like Jagla liquids [29]. The interfacial free energies determined along the saturation curves of these liquids are in reasonable agreement with their liquid-vapor surface tensions, albeit systematically shifted up by 5 to 10%. This shift has been attributed to suppressed capillary fluctuations at a rigid boundary and/or finite simulation size effects. The pressure dependence of the hard, flat interfacial free energy of the Lennard-Jones liquid has also been studied [30], demonstrating that the interfacial free energy exhibits a maximum as a function of pressure as a result of the dewetting of hard surfaces at low pressure [31]. While RSPT has been applied to describe the solvation of hard spheres in water and hexane [23], in those cases the interfacial free energy was assumed to conform to the liquidvapor surface tension at coexistence. Although this approximation has been shown to be reasonably accurate for the Lennard-Jones fluid along the binodal curve [28], this has not been demonstrated for more realistic solvents and certainly breaks down for compressed liquids off coexistence [30]. Here we revisit the application of RSPT to hard sphere solvation in water and decane to extract the interfacial thermodynamic properties of solvating a hard, flat interface from simulations of meso-scale repulsive solutes in solution. This interfacial free energy is evaluated as functions both of temperature and pressure. The resultant thermodynamic dependencies are compared against the liquid-vapor surface tension in the case of the temperature dependence, and the excess solvent adsorption in the case of the pressure dependence. 5

6 Revised Scaled-Particle Theory. The development of RSPT and its application to understanding the temperature and pressure dependence of hard sphere solvation has been presented over a series of previously published papers [22, 23, 28, 30]. Here we summarize the most pertinent features of the theory for the work presented here. The chemical potential of a solute can be divided into ideal and excess contributions, reflecting the properties of an individual solute possessing only intramolecular interactions and the work of turning on intermolecular interactions coupling that solute with the solute medium, respectively. Solute partitioning between two phases is ultimately determined by differences in its excess chemical potential between the two media. The excess chemical potential itself can be further divided between the work associated with opening up a solute shaped cavity in solution and subsequently turning on attractive interactions between the solute and the solvent. SPT [14, 15] considers the process of growing an empty spherical cavity of solventexcluding radius R into solution, equivalent to the solvation of a hard sphere (HS) solute. The excess hard sphere solute solvation free energy,, can subsequently be evaluated from the work of inflating the hard sphere cavity from nothing to R via the integral 4, (1) where kt is the product of Boltzmann s constant and the temperature, is the average pure solvent site number density, and, referred to as the contact correlation function, reports the contact values of the radial distribution function between a cavity of radius and the solvent at contact. Note here that is the density of solute excluding solvent sites. Water is modeled as having only one excluding site centered on its oxygen, while decane has ten excluding sites placed on each of its carbon unit centers. The grouping of terms corresponds to the 6

7 force per unit area acting on the cavity surface as a function of its radius, while 4 is the differential volume change to inflate the sphere from to so that eq. (1) can be thought of as the pressure/volume work required to grow the solute into solution. SPT subsequently shifts the point of view from direct evaluation of from molecular simulations over a broad range of solute sizes using techniques like Widom s test particle insertion [32] to evaluation of the contact correlation function. The classic development of SPT (CSPT) derives an analytical function for the contact correlation by smoothly joining known microscopic and macroscopic functional forms at the point at which pair-correlations between solvent molecules begin to contribute to the contact correlation function [14-16]. Stillinger [21] subsequently demonstrated that accounting for the experimental solvent pair correlation and macroscopic liquid-vapor surface tension yields an improved description of hard sphere solvation in water, remedying a number of the erroneous predictions of CSPT for the hydration of macroscopic surfaces. Extending Stillinger s framework to account for even higher order solvent correlations, Ashbaugh and Pratt [22, 23] proposed a revised approach to model the excess chemical potential by combining simulation results for hard sphere solutes determined from molecular simulations with a phenomenological thermodynamic expression for the solvation of a curved macroscopic surface. The excess chemical potential determined from their RSPT approach applicable over all length scales is , (2) where is the probability that a cavity of radius randomly inserted within the solvent is devoid of solvent centers, is the known bulk pressure, is the interfacial free energy for creating a hard, flat interface in solution, represents the first order curvature correction for the 7

8 interfacial free energy, while,, and correspond to higher order terms in the macroscopic free energy expansion. The function is a switching function that shifts the excess chemical potential between the microscopic simulation results to the macroscopic phenomenological expression. We use a cubic function to switch from the simulation and macroscopic extremes between and 13 1,, 2,, 0,. (3) The RSPT expression for the contact correlation function is determined by differentiating eq. (2) with respect to, yielding (4) The contact correlation function over all length scales is obtained by fitting eq. (4) to molecular simulation results at a fixed temperature and pressure. Specifically, molecular simulations are performed over a range of temperatures and pressures to determine the solvent density and s in the pure solvent, while the contact correlation at a number of distinct solute sizes is determined by simulating explicit solutes in solution and measuring the contact value of the solute-solvent radial distribution function at contact. The parameters,,,, and are left as fitting parameters at each state point to minimize the mean square difference between eq. (4) and the simulation results. We note that has been assumed to be equal to the liquid-vapor surface tension in our initial application of RSPT, while here it is included a fitting parameter. 8

9 The wetting of the hard, flat interface can be inferred from the pressure dependence of. From RSPT the pressure derivative of the interfacial free energy of a flat interface is determined by extrapolating simulation results for molecular and meso-scale solutes to the flat interface limit. This is achieved by parsing eq. (2) into contributions from the volume and area of the cavity as 4, (5) which defines the curvature dependent interfacial free energy,, through the difference between the excess chemical potential and pressure times the solvent excluded volume, 4 / 3. In the limit of a macroscopic surface asymptotically approaches. The pressure derivative of can subsequently be shown to be determined as. (6) Here is the radial distribution function between a hard sphere solute of radius and the solvent as a function of the separation. The radial distribution function integral corresponds to the solute s partial molar volume less its solvent excluded volume (4 /3) and a small kinetic contribution proportional to the solvent compressibility [33]. Following eq. (6) we can see that the interfacial free energy is a decreasing function of pressure when the solvent wets the solute interface ( > 0, solvent wetting), and is an increasing function of pressure when the solvent dewets the solute interface ( < 0, solvent dewetting). In practice the net solvent excess can be determined from molecular simulations as, (7) where is the isothermal compressibility of the pure solvent, is the average simulation volume of solvent molecules and 1 solute, and is the average simulation volume of 9

10 solvent molecules with no added solute. We note that the difference corresponds to the solute s partial molar volume. In practice the volume of pure solvent molecules is determined from the volume of a single pure solvent simulation appropriately scaled to the required number of solvent molecules. Substituting eq. (2) into eq. (5) and taking the pressure derivative, the RSPT expression for the excess solvent adsorption is 1. (8) As for the contact correlation function, the pressure derivatives of the parameters,,,, and are fitted to simulation results obtained at fixed volume of the solute radius obtained via eq. (7). On the other hand, the microscopic simulation results for the excess solvent adsorption are obtained from hard sphere insertion calculations into the pure solvent as / /, (9) where the angle brackets indicate averages evaluated from pure solvent simulations with molecules, and indicates the total interaction between a randomly inserted hard sphere of radius with the solvent. Simulation Methods. Molecular dynamics simulations of individual repulsive, spherical solutes in solution with water or decane were performed in the isothermal-isobarric ensemble using the GROMACS 5.0 simulation package [34]. The temperature and pressure were controlled using the Nosé-Hoover thermostat [35, 36] and Parrinello-Rahman barostat [37], respectively. In a first set of isobaric simulations 10 temperatures from K to K in 10 K increments was simulated at 1 bar, while in a second set of isothermal simulations the pressure was set to 1, 500, 1000, 1500, 10

11 2000, 2500, and 3000 bar at K. Water was modeled using the TIP4P/2005 potential [38] while decane was modeled using the Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) potential [39]. Soft, repulsive solute interactions were modeled using a shifted Weeks-Chandler-Andersen (WCA) potential [40], 4,,, 2 /, 0, 2 / 2 /, (10) where and in this expression are the Lennard-Jones diameter and well-depth, respectively, while corresponds to a vertical shift of the excluded volume divergence used here to tune the effective solute size. In our study we used values of = Å and = kj/mole for the interaction between the solute and water s oxygen or with any methyl/methylene carbon unit of decane. These parameters correspond to the cross interactions between water and TraPPE-UA methane [39] obtained using Lorentz-Berthelot combining rules [41]. The parameter was varied between 0 Å and 7 Å in 0.5 Å increments for a total of 15 different sized solutes. Simulations were conducted of one solute in a bath of anywhere between 648 to 2307 water molecules or 73 to 222 decane molecules depending on the solute size. Additional simulations with 1000 water molecules or 68 decane molecules and no added solute were performed to characterize pure solvent properties. Short-range van der Waals interactions were truncated beyond 12 Å. No long-range correction was applied since the inhomogeneity introduced by the larger spherical solutes complicates evaluation of an analytical mean field correction. Electrostatic interactions were evaluated using particle-mesh Ewald summation [42]. Water s internal constraints were held fixed using the SETTLE algorithm [43]. Simulations were conducted at each state point for 100 ns following at least 1 ns for equilibration using a time step of 2 fs. Partial molar volumes for the repulsive solutes were determined as the difference in the 11

12 average simulation volume for the system with and without the solute added, i.e., [44, 45]. While the simulation integration techniques used to propagate the equations of motion are applicable only to continuous interaction parameters, SPT presumes the solute/solvent interaction is a hard, discontinuous potential. Subsequently, we use WCA perturbation theory to approximate the radial distribution function between a hard solute and the solvent using the correlations evaluated from our continuous interaction simulations [40]. Inverting WCA theory to perturb from the continuous interaction reference system to the discontinuous interaction, the hard sphere/solvent radial distribution function is approximated as /Θ, (11) where is the radial distribution function between the soft, repulsive solute and solvent explicitly determined from our simulations, Θ is the heaviside step function, and is the hard sphere solute/solvent interaction radius. The hard sphere radius in eq. (11) is determined by satisfying the constraint equation [46] /Θ14 0. (12) This constraint amounts to requiring that the partial molar volume of the repulsive solute and its hard sphere counterpart are equal [33], which we assume is true here (i.e., ). We illustrate the relation between the repulsive and hard solute radial distribution functions in water and decane for 0 at 25 C and 1 bar in Figure 1 as determined using eq. (11) using the optimized radius. An alternate approach to calculating would be to perform non- Boltzmann weighted sampling of our simulation configurations to transform the repulsive interaction ensemble into the hard interaction ensemble [46]. Even though this approach yields results in excellent agreement for those determined via WCA theory and reported in Figure 1, 12

13 non-boltzmann weighted sampling fails for larger solutes and at high pressures. The reason the non-boltzmann sampling fails here is because for a simulation configuration to count towards the reweighted sample no waters should be found at separations less than the radius R. When waters are found within R the configuration is automatically rejected since the change in the interaction energy is infinite to perturb between the WCA and hard sphere states. At high pressure waters are pushed more firmly into the solute s excluded volume, resulting in significant fractions of the simulation configurations not contributing to the final non-boltzmann reweighted average. Given the excellent quantitative agreement between the configurations determined by the thermodynamically exact non-boltzmann weighted sampling procedure and those determined following WCA theory at low pressures for smaller solutes, we assume below that WCA theory provides accurate results over the full range of simulation conditions considered above. As shown in the results and discussion section below, the pressure dependence of the surface free energies determined from RSPT fitting to the WCA results is consistent with that inferred from the excess solvent adsorptions evaluated via eq. (7) giving us confidence that these results are thermodynamically consistent. To determine the surface tensions of water and decane along the saturation curve using the same solvent models and dispersion interaction cut-off procedure as used above, we simulated a liquid slab in equilibrium with its vapor at 10 temperatures from K to K in 10 K increments in the canonical ensemble. In these simulations we had 1000 waters in a rectangular simulation box of dimensions 31.1 Å 31.1 Å 62.1 Å and 62 decanes in a rectangular simulation box with dimensions Å. These canonical ensemble simulations were carried for 100 ns at each state point following at least 1 ns for equilibration. 13

14 The liquid-vapor surface tension,, was evaluated from the difference between the diagonal components of the pressure tensor [47], (13) where is the box length along the axis normal to the interface (equal to the longest axis box length above), and is the component of the pressure tensor directed along the -axis ( =,, or ). Results and Discussion. Temperature dependence of the surface free energy. Contact correlation functions for hard sphere solutes in water and decane determined by fitting eq. (4) to our simulations are plotted in Figure 2 for temperatures ranging from K to K at 1 bar. Overall the agreement between the RSPT fit and the simulation values of the contact correlation functions is excellent. These results agree with the previously reported temperature dependences, showing that the magnitude of the contact correlation for cavities with radii greater than ~3 Å is a decreasing function of temperature [22]. Moreover, the shapes of these contact correlation functions agree with those previously observed in water and organic solvents [22, 23, 48]. Specifically, the contact correlation in water starts at 1 for cavities of zero radius, grows to a peak near ~3 Å, followed by an asymptotic decay to the density dictated by the wall contact theorem, / (the compressibility factor), which is significantly less than 1 for liquids at ambient pressure. That is, as the solute becomes larger water progressively pulls away from and dewets the surface. The contact correlation in decane, on the other hand, is not as large in magnitude as in water and exhibits a cusp near ~0.77 Å. This cusp arises from intramolecular correlations between bonded carbons on the same chain, occurring at half the carbon-carbon 14

15 bond length (1.54 Å) [23, 49]. The bonding cusp is followed by a peak near ~3 Å, after which the function asymptotically decays to the compressibility factor as decane dewets the solute analogously to water. The interfacial free energies for the hard, flat solute/solvent interface,, determined by fitting eq. (4) to the simulation contact correlation function, are plotted in Figure 3 as a function of temperature at 1 bar. The interfacial free energies for both solvents are decreasing functions of temperature, indicating that creation of a macroscopic hard interface in solution is entropically favorable (i.e., / 0). Comparing against previously reported liquid-vapor surface tensions,, for TIP4P/2005 water [50] and TraPPE-UA decane [51] we find that the RSPT fits under-predict these results. Nevertheless, and appear parallel to one another in both solvents, vertically shifted by a constant. This suggests that the surface entropies of the hard and liquid-vapor interfaces are nearly the same, and that the difference between them is largely due to the surface enthalpy. We note that although the previously reported s for water and decane were corrected for truncation of dispersion interactions beyond their simulation cut-off, we did not include such corrections in our solvation simulations since the spherical solute inhomogeneity complicates calculation of mean-field corrections for the missing interactions (see Simulation Methods). To assess the effect of the cut-off on the liquid-vapor surface tension, we evaluated from simulations of a liquid slab in contact with its vapor using the same cut-off scheme as was used in our solvation simulations. The liquid-vapor tensions of water and decane determined from the cut-off simulations are lower than those with cut-off corrections (Figure 3). Moreover, the cut-off s fall ~4% below determined by our RSPT fits. Similar positive differences between and were observed for the Lennard-Jones [26, 28] and Jagla [29] liquids along their saturation curve. 15

16 While originally developed to describe fluids interacting predominantly through hard interactions, CSPT has been used to describe the properties of real fluids by substituting experimental densities and pressures into the associated equations. In this case, CSPT predicts the hard, flat interfacial free energy is [21], (14) where is the solvent s effective hard sphere diameter, is the molecular number density of the solvent (as opposed to site density used in RSPT above), and 6 is the solvent packing fraction. Predictions for as a function of temperature are compared against RSPT and liquid-vapor interfacial results in Figure 3, assuming values of 2.8 Å and 6.94 Å for water and decane, respectively. The water diameter conforms to its typically assumed value, while the decane diameter was obtained by matching the solvents van der Waals volume to that of a single sphere (i.e., /6 ). While CSPT does predict that the interfacial free energy of water is greater than that of decane with values comparable in magnitude to those determined from RSPT, the predicted temperature dependencies differ significantly. For water, CSPT predicts that is an increasing function of temperature and therefore entropically unfavorable, in difference to the observations above for liquid-vapor and hard interface formation. CSPT does predict that in decane is a decreasing function of temperature. The slope predicted by CSPT, however, is lower in magnitude than that observed by RSPT, indicating that CSPT predicts a lower entropic benefit for creating an interface in decane. These observations suggest CSPT provides an incomplete account of interface formation, ascribing a higher entropic cost in both water and decane. Pressure dependence of the surface free energy The dependence of the hard sphere contact correlation function in decane for pressures from 1 to 3000 bar at 25 C is illustrated in 16

17 Figure 4. Generally speaking, the simulation values of the contact correlation at a fixed radius are an increasing function of pressure. Indeed, the macroscopic plateau value of the contact correlation function rises above one for pressures greater than ~1000 bar, as pressure suppresses hard wall dewetting (i.e., The compressibility factor / is greater than one for > ~1000 bar). Similar to the 1 bar isobar results shown in Figure 2, RSPT provides an excellent quantitative description of the contact correlation function of hard spheres in decane. While not shown, the pressure dependence of the contact correlation function in water is qualitatively similar to that in decane for radii beyond the carbon-carbon bonding cusp, with a comparably excellent description provided by RSPT. The pressure dependence of in water and decane as determined from the fit of eq. (4) (e.g., Figure 4) are plotted in Figure 5. We note that while the hard interface is propped up by the solute at high pressure, the liquid-vapor interface is not stable, negating comparison between these two cases. In both solvents displays a non-monotonic dependence on pressure, exhibiting a maximum near ~1000 bar. The pressure dependence for is asymmetric with respect to pressure in both solvents, with a rapid initial rise at low pressures followed by a more gradual drop following the maximum. A similar asymmetric dependence of was observed for hard surfaces immersed in the Lennard-Jones solvent from conditions along the saturation curve into the compressed liquid [30]. In that work, the non-monotonic dependence of with pressure was shown to be described by the excess solvent adsorption, which we subsequently evaluate here for water and decane. The ratio of the excess solvent adsorption to the solvent density (i.e. /) for hard spheres in water as a function of the inverse solute radius (1/) are plotted for various pressures at K in Figure 6. This ratio was evaluated from our simulation volumes using eq. (7). 17

18 Over the solute sizes simulated, the excess water adsorption is positive. At 1 bar, however, the excess solvent adsorption extrapolated down to a flat interface (1/ = 0) clearly tends towards negative values, indicating dewetting [52]. This mirrors the behavior of the contact correlation function reported in Figure 2, where the contact density in water is greater than the bulk density for solutes smaller than ~10 Å and lower than the bulk density for larger solutes. As the pressure increases, however, the extrapolated flat interface excess solvent adsorption appears to change sign from negative to positive, indicating that water is pushed back on to the solute surface. Similar behavior is observed in decane, and is in line with behavior previously observed in the Lennard-Jones liquid [30]. The net solvent adsorption at the flat interface, and subsequently the pressure derivative of, can be determined by fitting eq. (8) to the simulation results for finite sized solutes and extrapolating to 1/ = 0. The RSPT fit quantitatively describes the simulation results over all size scales (Figure 6) and captures the compressibility of water s adsorption next to the solute interface. In particular, the extrapolated flat interface desorption is largest at 1 bar and becomes progressively more positive with increasing pressure, changing from net desorption to adsorption near ~1000 bar in reasonable agreement with the location of the maximum in the interfacial free energy of water with increasing pressure. Qualitatively similar results are observed for decane s surface adsorption. The thermodynamic consequences of the excess solvent flat surface adsorption can be realized by comparing it against the pressure derivative of the interfacial free energy (Figure 7). Specifically, we compare / obtained from the fits of eq. (8) against the pressure derivative of the interfacial free energies reported in Figure 5. The pressure derivative of was determined by fitting the interfacial free energies to a fourth order polynomial in the solvent density (Figure 5) and using the chain rule to evaluate the derivative as / 18

19 / /. The pressure dependence of the solvent density was determined by fitting the simulation results at a fixed temperature to the Tait equation (1/ 1, where,, and are fitting parameters) [53], which provides an excellent quantitative description of isothermally compressed liquids (The fit parameters for and the Tait equation are provided in the Supplemental Materials). In both solvents the pressure derivatives of the interfacial free energy agree quantitatively with the results obtained from extrapolating the excess solvent adsorption to 1/ 0 (Figure 7), confirming their thermodynamic connection. Moreover, the solvent adsorption results provide a physical rationalization of the asymmetry of the interfacial free energy dependence on the pressure. At low pressure where the solvent strongly desorbs from the interface to form a vapor layer enveloping the solute, we obtain a large, positive interfacial free energy derivative and resulting initial fast rise in. This vapor layer is quite compressible, however, such that the solvent desorption drops steeply with increasing pressure. Around 1000 bar (slightly lower in decane), where the contact density as dictated by the compressibility factor approaches that of the bulk solvent, the excess solvent adsorption changes sign to net adsorption (i.e., / becomes negative) and the rate of change of the interfacial free energy derivative with increasing pressure drops as a result of the progressively liquid-like contacting solvent layer becoming less compressible. For the sake of completeness, we compare the predictions of CSPT for the interfacial free energy to assess its description of excess solvent adsorption/desorption. For both water and decane is observed to only be a decreasing function of pressure (Figure 5) when we employ the same solvent diameters used in Figure 3. As can be inferred from eq. (6), CSPT predicts the solvent is positively adsorbed to the hard, flat interface; that is to say the theory predicts the surface is wetted even at 1 bar. Like RSPT, CSPT ascribes a contact value for the 19

20 contact correlation function of / for the flat interface, which is on the order of to 0.01 in water and decane at 1 bar. CSPT thereby paradoxically predicts that the solvent pulls away from the flat surface as indicated by the contact correlation, but that the surface is fully wetted as indicated by the negative slope of with respect to pressure. This slope is even greater in magnitude than that observed for at even the largest pressures simulated (Figure 5), indicating CSPT predicts even stronger wetting at 1 bar than observed for the simulated surfaces at 3000 bar. If we examine the dependence of the excess water adsorption on the compressibility factor, the RSPT fits show the excess adsorption changes sign from desorption to adsorption near a value of the compressibility factor of / 1 (Figure 8). This suggests that water desorption/adsorption is observed when the contact density is less/greater than the bulk solvent density. We are not guaranteed that the sign change occurs when / 1 since the solvent adsorption is determined by an integral over the solvent correlations into the bulk (eq. (6)). Nevertheless, it is physically reasonable to expect a positive correlation between the flat wall contact density and excess solvent adsorption as shown in Figure 8. Surprisingly, CSPT predicts that the excess solvent adsorption is practically independent of pressure (Figure 8). As suggested in Figure 5, CSPT predicts positive water adsorption for 2.8 Å. Allowing the effective hard diameter of water to be variable, we find that CSPT does predict solvent desorption for sizes greater than ~3.05 Å. The insensitivity of the excess solvent adsorption to pressure, however, implies that CSPT predicts solvent desorption when the compressibility factor is unreasonably greater than 1. As in the case of the temperature dependence of the interfacial free energy, we find the CSPT description of interfacial solvation and wetting is incomplete. 20

21 Conclusions. Here we have presented a detailed SPT analysis of the formation of a hard, flat interface in liquid water and decane as the limiting behavior of an infinitely large hard sphere solute in solution. The hard interfacial free energy in water and decane as a function of temperature near liquid-vapor coexistence closely follows the true liquid-vapor surface tension for the same solvent models using the same dispersion cut-off, shifted upwards only by ~4%. For a thick vapor-like boundary between the bulk solvent and solute s excluded volume we expect the interfacial free energy to be equal to the sum of the liquid-vapor surface tension with a negligible vapor-wall tension. Nevertheless, the nearly parallel hard and liquid-vapor interfacial free energies indicate that entropies of hard interface formation in either solvent are favorable and effectively the same as that of the liquid-vapor interface. While the liquid-vapor interface is unstable in the compressed liquid, the hard interfacial free energies in water and decane, buttressed by the explicit solute, display a non-monotonic dependence on pressure with a maximum in the neighborhood of ~1000 bar. This somewhat surprising dependence on pressure was shown to be directly related to the excess solvent adsorption against the solute surface. At low pressures dewetting of the solute surface (negative adsorption) inflates the solute s partial molar volume larger than its solvent excluded volume, resulting in the interfacial free energy increasing with increasing pressure. As solvent is pushed back onto the solute surface with increasing pressure, shrinking the solute volume below the solvent excluded volume, the interfacial free energy becomes a decreasing function of pressure in concert with the solvent rewetting the surface and the surface excess becoming positive. The relatively lower compressibility of the contacting liquid layer at high pressure compared to the 21

22 low pressure dewetted vapor layer gives rise to an asymmetric dependence of the interfacial free energy with pressure. Comparing the interfacial thermodynamic predictions of CSPT against RSPT, which is fitted to quantitatively reproduce a wide range of molecular simulation results for water and decane, we find CSPT provides an unsatisfactory description of flat interface formation. For instance, CSPT predicts liquid interface formation is less entropically favorable than observed from our results against hard solutes or for the liquid-vapor interface. Indeed, the predicted interfacial entropy of water is negative, counter to the expectation (and observation) that liquid interfaces next to vapors or zero density voids is more disordered. Using standard values for the effective solvent diameter, CSPT predicts the interfacial free energy is a strongly decreasing function of pressure beginning from the coexistence curve, indicative of net solvent adsorption. This prediction is incongruous with the simultaneous CSPT prediction that the solvent contact density against the flat interface is significantly less than the bulk. Moreover, CSPT predicts the excess solvent adsorption is practically independent of pressure, no matter if the adsorption corresponds to surface wetting or dewetting. These erroneous predictions point to deeper thermodynamic inconsistencies for CSPT applied to realistic solvents, so that care should be taken when drawing conclusions from this theory on the temperature and pressure dependencies of meso-scale and larger solute solvation. Supplementary Material See the supplementary material for fits of the simulation density as a function of pressure to the Tait Equation, polynomial fits of the surface free energy at elevated pressure as a function of 22

23 density, and fits of the simulation surface tension as a function of temperature to a scaling expression. Acknowledgements. We gratefully acknowledge financial support from the NSF (OIA ), a Louisiana Board of Regents Graduate Research Fellowship (JWB), and Tulane s Center for Engaged Learning and Teaching. 23

24 Figure Captions. Figure 1. Radial distribution function between a monotonic solute in water and decane at 25 C and 1 bar. The black and red dashed lines correspond to the simulation results for the unshifted WCA solute ( = 0) in water and decane, respectively. The results in water are shifted up by 0.5 for clarity. The black and red solid lines correspond to the hard solute results in water and decane, respectively, calculated following the WCA perturbation expression (eq. (11)). The solute s hard solvent excluded radii in water and decane optimized following eq. (12) and 3.37 Å and 3.38 Å, respectively. The open points correspond to the values of the radial distribution function at contact with the hard solutes, used as the simulation value of the contact correlation function at the optimized hard sphere radius. Figure 2. Contact correlation function for hard spheres in water and decane at various temperatures at 1 bar pressure. The black filled and red open circles correspond to the contact values of the hard sphere solute/solvent radial distribution functions obtained from explicit solute simulations in water and decane (e.g., Figure 1), respectively. The lines correspond to RSPT fits (eq. (4)) to the simulation results. For these fits = Å and = Å. The temperatures K, K, K, K and K are plotted from the top to bottom (following the blue arrow) for each set of contact correlations in each solvent. The simulation error bars are smaller than the plotted symbols. Figure 3. Comparison of the interfacial free energies as a function of temperature determined from SPT and liquid-vapor surface tensions extracted from molecular simulation. Figures a) and b) report results for water and decane, respectively. The filled red circles correspond to 24

25 obtained from RSPT fits (eq. (4)) to the simulation contact correlation functions (e.g., Figure 2). The thick black solid line corresponds to previously reported results for TIP4P/2005 water [50] and TraPPE-UA decane [51] corrected for long-range potential truncation. These previously reported results were fitted to a temperature dependent functional form to obtain a smooth function (see Supplemental Materials). The open blue circles correspond to molecular simulations of a liquid slab in contact with its vapor using the same interaction potential cut-off as in the solvation simulations. The dashed green line corresponds to CSPT predictions (eq. 14) for the using diameters of water and decane of 2.8 Å and 6.94 Å, respectively. Our simulation error bars are comparable to the plotted symbols. Figure 4. Contact correlation function for hard spheres in decane at K at various pressures. The open red circles correspond to contact values of the hard sphere solute/solvent carbon unit radial distribution function obtained from explicit solute simulation results. The lines correspond to fits of eq. (4) to the simulation results. For these fits = Å and = Å. The pressures plotted correspond to 1 bar, 1000 bar, 2000 bar, and 3000 bar from the bottom to the top (following the blue arrow). The simulation error bars are smaller than the plotted symbols. Figure 5. Pressure dependence of the hard flat interfacial free energy in water and decane at K. Figures a) and b) report results for water and decane, respectively. The filled red circles correspond to obtained from RSPT fits (eq. (4)) to the simulation contact correlation functions (e.g., Figure 4). The dashed red line corresponds to the fits of to a fourth order polynomial in the solvent density (see Supplemental Materials). The thick black line 25

26 corresponds to CSPT predictions (eq. (14)) for the using diameters of water and decane of 2.8 Å and 6.94 Å, respectively. The simulation error bars are smaller than the plotted symbols. Figure 6. The excess solvent adsorption as a function of the inverse radius for hard spheres solutes in water at K at various pressures. The filled black circles correspond to simulation measurements of the excess solvent adsorption from simulations of individual solutes in solution (evaluated via eq. (7)). The black lines correspond to RSPT fits (eq. (8)) to the simulation results. For these fits = Å and = Å. The open circles at 1/ 0 correspond to the extrapolated values of the excess solvent adsorption at a flat interface ( ). The pressures plotted correspond to 1 bar, 1000 bar, 2000 bar, and 3000 bar from the bottom to the top (following the blue arrow). The simulation error bars are comparable to the plotted symbol sizes. Figure 7. Pressure derivative of the hard flat interfacial free energy as a function of pressure at K. Figures a and b correspond to results in water and decane, respectively. The filled red points correspond to the results obtained from extrapolating RSPT fit for the excess solvent adsorption to the flat interface (1/ 0) (e.g., Figure 6). The dashed red lines indicate results obtained from the derivative of the functional fits of to the solvent density (Figure 5) and the solvent density to the Tait equation (see Supplemental Materials). The reported error bars correspond to one standard deviation. 26

27 Figure 8. Correlation between water s excess adsorption against a hardflat interface versus the solvent compressibility factor (/) at K. The filled red points correspond to the results obtained from extrapolating RSPT fit for the excess solvent adsorption to the flat interface (1/ 0) (e.g., Figure 6). The dashed black lines correspond to CSPT predictions obtained from the pressure derivative of eq. (14) using effective water hard diameters from 2.8 Å to 3.2 Å (values indicated in the figure). The reported error bars correspond to one standard deviation. 27

28 References. [1] H. H. Uhlig, J. Phys. Chem. 41, 1215 (1937). [2] D. D. Eley, Trans. Faraday Soc. 35, 1421 (1939). [3] R. B. Hermann, J. Phys. Chem. 76, 2754 (1972). [4] J. A. Reynolds, D. B. Gilbert, and C. Tanford, Proc. Natl. Acad. Sci. USA 71, 2925 (1974). [5] C. Chothia, Nature 248, 338 (1974). [6] K. A. Sharp, A. Nicholls, R. F. Fine, and B. Honig, Science 252, 106 (1991). [7] D. Chandler, Nature 437, 640 (2005). [8] K. Lum, D. Chandler, and J. D. Weeks, J. Phys. Chem. B 103, 4570 (1999). [9] D. M. Huang, P. L. Geissler, and D. Chandler, J. Phys. Chem. B 105, 6704 (2001). [10] D. M. Huang, and D. Chandler, Proc. Natl. Acad. Sci. USA 97, 8324 (2000). [11] H. S. Ashbaugh, Chem. Phys. Lett. 477, 109 (2009). [12] J. F. Brandts, R. J. Oliveira, and C. Westort, Biochem. 9, 1038 (1970). [13] W. Kauzmann, Nature 325, 763 (1987). [14] H. Reiss, Adv. Chem. Phys. 9, 1 (1965). [15] H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959). [16] H. Reiss, H. L. Frisch, E. Hefland, and J. L. Lebowitz, J. Chem. Phys. 32, 119 (1960). [17] R. A. Pierotti, J. Phys. Chem. 67, 1840 (1963). [18] R. A. Pierotti, J. Phys. Chem. 69, 281 (1964). [19] R. A. Pierotti, Chem. Rev. 76, 717 (1976). [20] G. Graziano, J. Phys. Chem. B 110, (2006). [21] F. H. Stillinger, J. Soln. Chem. 2, 141 (1973). [22] H. S. Ashbaugh, and L. R. Pratt, Rev. Mod. Phys. 78, 159 (2006). [23] H. S. Ashbaugh, and L. R. Pratt, J. Phys. Chem. B 111, 9330 (2007). [24] H. S. Ashbaugh, D. Asthagiri, L. R. Pratt, and S. B. Rempe, Biophys. Chem. 105, 323 (2003). [25] F. M. Floris, J. Phys. Chem. B 109, (2005). [26] M. P. Moody, and P. Attard, J. Chem. Phys. 115, 8967 (2001). [27] F. Sedlmeier, and R. R. Netz, J. Chem. Phys. 137, (2012). [28] H. S. Ashbaugh, J. Chem. Phys. 130, 8 (2009). [29] J. R. Dowdle, S. V. Buldyrev, H. E. Stanley, P. G. Debenedetti, and P. J. Rossky, J. Chem. Phys. 138, 12 (2013). [30] H. S. Ashbaugh, and T. M. Truskett, J. Chem. Phys. 134, 10 (2011). [31] F. Van Swol, and J. R. Henderson, Phys. Rev. A 43, 2932 (1991). [32] B. Widom, J. Phys. Chem. 86, 869 (1982). [33] J. G. Kirkwood, and F. P. Buff, J. Chem. Phys. 19, 774 (1951). [34] B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, J. Chem. Theory Comp. 4, 435 (2008). [35] S. Nose, J. Chem. Phys. 81, 511 (1984). [36] W. G. Hoover, Phys. Rev. A 31, 1695 (1985). [37] M. Parrinello, and A. Rahman, J. App. Phys. 52, 7182 (1981). [38] J. L. F. Abascal, and C. Vega, J. Chem. Phys. 123, (2005). [39] M. G. Martin, and J. I. Siepmann, J. Phys. Chem. B 102, 2569 (1998). [40] J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971). 28

29 [41] M. P. Allen, and D. J. Tildesley, Computer simulation of liquids (Oxford University Press, Oxford, UK, 1987). [42] T. Darden, D. York, and L. Pedersen, J. Chem. Phys. 98, (1993). [43] J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977). [44] H. S. Ashbaugh, J. W. Barnett, N. da Silva Moura, and H. E. Houser, Biophys. Chem. 213, 1 (2016). [45] L. N. Surampudi, and H. S. Ashbaugh, J. Chem. Eng. Data 59, 3130 (2014). [46] D. Chandler, Introduction to modern statistical mechanics (Oxford University Press, New York, 1987). [47] J. S. Rowlinson, and B. Widom, Molecular theory of capilarity (Dover Publications, Inc., Mineola, NY, 1982). [48] L. R. Pratt, and A. Pohorille, Proc. Natl. Acad. Sci. USA 89, 2995 (1992). [49] A. Jain, and H. S. Ashbaugh, J. Chem. Phys. 129, (2008). [50] C. Vega, and E. de Miguel, J. Chem. Phys. 126, (2007). [51] D. A. Hernandez, and H. Dominguez, J. Chem. Phys. 138, (2013). [52] F. M. Floris, J. Phys. Chem. B 108, (2004). [53] J. H. Dymond, and R. Malhotra, Int. J. Thermophys. 9, 941 (1988). 29

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