Connections between the Anomalous Volumetric Properties of

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Connections between the Anomalous Volumetric Properties of Alcohols in Aqueous Solution and the Volume of Hydrophobic Association Henry S Ashbaugh, J. Wesley Barnett, Alexander Saltzman, Mae Langrehr, and Hayden Houser J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08728 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 10, 2017

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The Journal of Physical Chemistry

Connections between the Anomalous Volumetric Properties of Alcohols in Aqueous Solution and the Volume of Hydrophobic Association Henry S. Ashbaugh1,* J. Wesley Barnett1, Alexander Saltzman1, Mae Langrehr2, and Hayden Houser1 1

2

Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA 70118

Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE 19716

Abstract The partial molar volumes of alcohols in water exhibit a non-monotonic dependence on concentration at room temperature, initially decreasing with increasing concentration before passing through a minimum and rising to the pure liquid plateau. This anomalous behavior is associated with hydrophobic interactions. We report molecular simulations of short chain alcohols and alkanes in water to examine the volumetric properties of these mixtures at infinite dilution over a range of temperatures. Our simulations find this anomaly disappears at a crossover temperature, above which the solute volume only varies monotonically with concentration. A Voronoi volume analysis of solution configurations finds that solutes in clusters take up less space than individual solutes at low temperature, and more space at elevated temperatures. These changes in cluster volumes are subsequently shown to correlate with the derivative of the solute partial molar volume with respect to solute concentration. The changes in solute volume upon nonpolar solute association impact the response of molecular-scale hydrophobic interactions for assembly with increasing pressure.

*

corresponding author: [email protected] 1

ACS Paragon Plus Environment


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Introduction The traditional undergraduate chemistry demonstration that the volume of ethanol and water solutions are less than the sum of its pure component volumes provides a simple, counterintuitive example to motivate students to question the differences between like and unlike molecular interactions in mixtures. A deeper thermodynamic consideration of the contributions to the total volume from ethanol and water reveals a more nuanced interplay between the components. While the hydrated partial molar volume of ethanol is generally lower than that of its pure liquid, consistent with contraction of the mixture, it also exhibits a significantly nonmonotonic dependence on concentration at room temperature (Figure 1). Starting from infinite dilution, the partial molar volume of ethanol initially falls with increasing concentration and passes through a minimum before climbing to a maximum for the pure alcohol. The GibbsDuhem relationship stipulates that the partial molar volume of water climbs to a maximum coincident with ethanol’s minimum. The magnitude of the rise in water’s volume is considerably less than the corresponding drop in ethanol’s volume, however, as the volume extrema lie at water rich compositions. This anomalous, non-monotonic dependence of the partial molar volume on concentration is more general, occurring for a number of alcohols

1-4

and polar

organic species, like THF,5 dioxane,6 DMSO,7 and butoxyethanol,8 in aqueous solution. Studies of alcohol/water mixtures have uncovered a number of anomalous composition dependent properties beyond the volume anomaly, including: asystematic variations in the mixing enthalpy with alkyl tail size;9-10 elevation of the temperature of maximum density;11-12 maxima in the sound speed;13-14 and cononsolvency of non-polar species.15-17 Considering the distinctive changes in the mixing enthalpy of alcohols of increasing hydrophobicity, Franks and Ives10 concluded alcohols may induce a sudden “cooperative failure” resulting from the inability

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of water to maintain a sample spanning hydrogen-bond network with increasing alcohol concentration. Dixit et al.,18 on the other hand, concluded from neutron scattering on methanol/water mixtures that while macroscopically these mixtures appear homogeneous, on the meso-scale the alcohol and water segregate into clusters that attempt to preserve remnants of water’s three-dimensional network. These structural features are subsequently postulated to underlie the anomalous thermodynamics of alcohol/water mixtures.19 In the dilute limit, combined femto-second resolved infrared and Raman multivariate curve resolution (RamanMCR) measurements find contacts between alcohols in water are effectively random,20 suggesting that anomalies initiated from the infinite alcohol dilution limit are not tied to strong specific interactions. Raman-MCR experiments probing hydration shells in the dilute regime, however, find non-polar alcohol tails induce strongly temperature dependent structures that are distinct from bulk water.21 The curious behavior of alcohol/water mixtures has spurred simulation studies to gain molecular insights into their origin. Many of those studies have focused on examining the dependence of energetic, structural, hydrogen-bonding, and dynamical properties on mixture composition.22-28 Simulations have been shown to capture the volume anomaly in methanol/water mixtures, although that study only considered the macroscopic thermodynamic phenomenon. Ichiye and coworkers,29-30 on the other hand, carried out a more detailed simulation study examining the connections between the volume anomaly in ethanol/water mixtures and molecular structure. They demonstrated that the magnitude of the volume anomaly is extremely sensitive to the water model selected, with greater accuracy obtained for models that more faithfully capture the properties of pure water and its hydrogen-bonding properties near nonpolar groups. They attributed the drop in the partial molar volume of ethanol with increasing

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concentration to inter-molecular hydrophobic contacts made between non-polar moieties. The concentration at which the partial molar volume occurs was found to correlate with the concentration at which the ethanol hydration shells touch. Motivated by the known sensitivity of hydrophobic effects on temperature and the observation of volumetric anomalies for a number of water-soluble organic species, we have carried out an expanded molecular simulation study of a number of hydrated short alcohols and alkane gases to determine their volumetric properties over a range of temperatures. These simulations focus on the low concentration regime in an effort to determine the fidelity of the models used in capturing the anomalous drop in solute volume starting from infinite dilution. A combined Voronoi volume and solute cluster analysis of configurations of ethane in water is performed to examine the role of intra-solute hydrophobic interactions on the drop and/or rise of the solute volume with increasing concentration. Based on these results, thermodynamic expressions are proposed to connect volumes of hydrophobic association, determined either from Voronoi analysis or the pressure dependence of the second osmotic virial coefficient, to the derivative of the solute partial molar volume with respect to the solute concentration at infinite dilution. The potential impact of increasing pressure on molecular-scale hydrophobic interactions for aqueous phase assembly is discussed in light of the present results.

Simulation Methodology Molecular dynamics simulations of mixtures of water with alcohols and alkanes were performed in the isothermal-isobaric ensemble31 using the GROMACS 5.0 simulation package.32 The temperature and pressure were controlled using the Nosé-Hoover thermostat33-34 and Parrinello-Rahman barostat,35 respectively. For the majority of simulations performed, water was

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modeled using the TIP4P/2005 potential,36 while the alcohols and alkanes were modeled using the TraPPE-United Atom potential.37 The TIP4P/2005 model was chosen since it provides one of the best classical representations of the liquid state properties of water over a broad range of conditions, while the TraPPE model similarly provides one of the best representations of organic liquid state properties. Previous simulations have established that mixtures of TraPPE organics in TIP4P/2005 water yields results in excellent agreement with the thermodynamics of hydrophobic hydration.38-39 To examine the impact of the water model used, one set of simulations were performed of methane in TIP3P water.40 The alcohols and alkanes simulated were methanol, ethanol, 1-propanol, methane, and ethane. Cross interactions between unlike Lennard-Jones sites were determined using Lorentz-Berthelot combining rules.31 Short-range van der Waals interactions were truncated beyond 9 Å with a mean field correction added for long-range contributions to the energy and pressure. Electrostatic interactions were evaluated using particlemesh Ewald summation.41 Water’s internal constraints were held fixed using the SETTLE algorithm,42 while the LINCS algorithm43 was used to constrain solute bonds. A time step of 2 fs was used to integrate the equations of motion. Two sets of simulations were performed: Simulations of ethanol/water mixtures over the full concentration range at 25°C and 1bar; and simulations of alcohols and alkanes at low concentrations in water over a range of temperatures. In the first set of simulations, we simulated ethanol/water mixtures at ethanol mole fractions of 0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.12, 0.14, 0.16, 0.18, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1 at temperatures of 0 °C, 12.5 °C, 25 °C, 37.5 °C, and 50 °C and 1 bar pressure to characterize the mixture molar volumes over the full concentration range. The total number of molecules was fixed at 4000. Production simulations at each concentration

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were conducted for 100 ns following at least 1 ns for equilibration. The partial molar volumes of ethanol (component 2) in water (component 1) was determined from the expression = +

,

,

(1)

where is the molar volume of the mixture and is the mole fraction of component i. The derivative in eq. (1) was evaluated by finite differences, enabling the determination of the partial molar volumes at the midpoints between consecutive simulated concentrations. Ethanol’s partial molar volume at infinite dilution was determined by extrapolation of the low concentration results to = 0. In the second set of simulations, we simulated the low concentration alcohols and alkanes in water over a range of temperatures at 1 bar. These simulations were conducted from 5 °C to 75 °C in 10 °C increments at 1 bar. In these simulations the total number of waters was fixed to 2000. For the alcohol simulations, the number of solutes was 5, 10, 15, 20, 25, 30, 35, or 40. For the alkane simulations the number of solutes was 5, 10, 15, 20, or 25. Simulations of pure water were performed at each temperature as well. Production simulations at each concentration were conducted for 100 ns following at least 1 ns for equilibration. The solute volumetric properties were determined by fitting the simulation molar volumes to the second order polynomial = + + .

(2)

Based on this expression the solute partial molar volume and its derivative with respect to the solute concentration at infinite dilution are = + ,

(3a)

and

,

6

= 2,


(3b)

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respectively. Voronoi volumes of water and solute clusters were evaluated by Monte Carlo integration. For every configuration analyzed, 106 points were randomly inserted into the simulation box and the closest heavy atom site (carbon or oxygen) were determined. The Voronoi volume of a given heavy atom site was determined as the total simulation box volume multiplied by the fraction of inserted points closest to that site.

Results and Discussion The partial molar volume of ethanol at 25°C as a function of concentration in aqueous solution determined from simulation is compared against experiment in Figure 1. The overall agreement between experiment and simulation is excellent, with simulations quantitatively capturing ethanol’s volume at high alcohol concentrations and semi-quantitatively capturing ethanol’s volumetric behavior in the low concentration limit. Significantly, the simulations capture the anomalous minimum in ethanol’s volume at low alcohol concentrations. While the experimental and simulation value for ethanol’s minimum volume of 53 cm3/mol is in good agreement, simulations predict the minimum occurs at a slightly lower concentration of x2 ≈ 0.036 than experiment at x2 ≈ 0.065. From the minimum to infinite dilution (x2 = 0), the experimental partial molar volume increases by 2 cm3/mol, while the simulation volume increases only by half that amount. Despite these differences, our results demonstrate simulations capture and may thereby provide molecular insights into the anomalous volumetric properties of alcohols in aqueous solution. In the absence of the volumetric anomaly, we would expect the partial molar volume of ethanol to vary monotonically from infinite dilution to the pure alcohol limit, implying the derivative of the partial molar volume with respect to x2 would be positive

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over the entire concentration range since the partial molar volume of ethanol at infinite dilution in water is generally lower than that of the pure alcohol. We may then take negative values of the

infinite dilution derivative, i.e.,

,

< 0, as a signature of the volumetric anomaly. Plotting

the mixture concentrations where the volume derivative is zero versus temperature (Figure 2) determines an envelope for the volume anomaly. The envelope for simulation is smaller than that of experiment, although the maximum temperatures below which the anomaly is observed nearly coincide. The curves traced out in Figure 2 correspond to so called Koga lines,8, 44-45 where third derivatives of the thermodynamic potential for aqueous solutions go to zero and define a boundary of thermodynamic anomalies distinct for hydrophobic and hydrophilic solutes. Koga has postulated this boundary indicates a hydrogen-bond percolation threshold. We compare the partial molar volumes of methanol, ethanol, and 1-propanol at 25°C from simulation against experiment in Table 1. We find good agreement between simulation and experiment. We do note that the difference between the simulations and experiments become more negative with increasing length of the hydrophobic tail, similar to previously reported differences between the volumes of methane through propane determined from simulations of the mixture models used here.39 Nevertheless, this difference is relatively small, amounting to ~3% of the total, giving us further confidence that our simulations provide a meaningful representation of the volumetric properties of alcohols in water.

We plot

,

determined from simulation as a function of temperature for methanol,

ethanol, and 1-propanol in Figure 3a. At low temperatures the volume derivative for these alcohols is negative, indicating our simulations anticipate a minimum volume anomaly for all of these alcohols. These derivatives increase with increasing temperature, however, and change sign

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at elevated temperatures. The temperature at which the derivative is zero indicates the point at which the minimum in the partial molar volume has shifted from finite alcohol concentrations to infinite dilution. The volume anomaly disappears above this temperature, corresponding to the

maximum temperature in Figure 2. Assuming

,

is a linear function of temperature, the

crossover temperature between the anomalous and non-anomalous behavior can be estimated (Table 2). While the simulation crossover temperatures for methanol and ethanol are indistinguishable within the error bars, the crossover temperature for 1-propanol is lower than that of ethanol by ~20°C. Experimentally the volume derivatives for methanol, ethanol, and 1propanol are negative at low temperatures, and increase with increasing temperature, in qualitative agreement with simulation (Figure 3a). The magnitude of the volume derivatives from simulation is less than that determined from experiment, consistent with the observation that simulations under predict the depth of the minimum of the partial molar volume relative to infinite dilution (Figure 1). While we were only able to find experimental results over a limited temperature range for these alcohols, it appears that the experimental results may exhibit an anomaly crossover at elevated temperatures. We report the linearly extrapolated experimental crossover temperatures from two different data sets in Table 2.1-2 The best agreement between experiment and simulation for the crossover temperature is obtained for ethanol. A wider range of experimental crossover temperatures is obtained for methanol and 1-propanol, however. It is perhaps not surprising that estimates for the crossover temperature is most uncertain for methanol, given the comparatively small magnitude of its volume derivative. The spread in experimental crossover temperatures for 1-propanol, however, makes it impossible to determine here whether the experimental crossover for 1-propanol is greater than or less than that of ethanol.

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At lower temperatures the magnitude of

,

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grows with the number of carbons in

the alcohol, suggesting the volume anomaly is connected to the hydration of the non-polar moities. To explore this connection, we simulated methane and ethane in water to isolate the hydrophobic portion of the solutes from polar hydroxyl group contributions. While these solutes do not form stable liquids under the simulated conditions, we can examine their behavior at

infinite dilution. In Figure 3b we plot

,

for methane and ethane from simulation as a

function of temperature. Similar to the alcohols, the volume derivative for these hydrocarbon gases is negative at lower temperature and becomes positive at elevated temperatures. The crossover temperature for methane and ethane is comparable to that for the alcohols (Table 1). Moreover, the crossover for ethane occurs ~10°C lower than that for methane, qualitatively similar to the simulation difference between ethanol and 1-propanol. Comparing the values of

,

at the low and high temperature extremes for methane and ethane to the alcohols, we

find the magnitude of the derivative for the alkanes is significantly greater than that of the alcohols. We conclude that the hydroxyl group suppresses the volumetric anomaly. Indeed, thinking of water itself as the shortest potential alcohol, with a hydrocarbon chain length of zero,

we expect the volume anomaly to disappear with

,

= 0 at all temperatures. The volume

anomaly then is a manifestation of hydrophobic effects. As an aside, the water model used can play a significant role on the observation of this water anomaly. Ichiye et al.,29-30 for example, found that the volume anomaly for ethanol/water

mixtures depends sensitively on the water model used. Here, we find

,

is positive for

methane in TIP3P water over the entire temperature examined (Figure 3b). Linearly

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extrapolating these results, we expect the volume anomaly to emerge below -2°C in TIP3P. Previous studies of the equation-of-state properties of TIP3P water have found this water’s characteristic anomalies are shifted to temperatures 10’s of degree lower than experiment and other models,38 consistent with the present results. We therefore restrict the remainder of our study to TIP4P/2005 water, which provides one of the best classical simulation representations of the equation-of-state properties of water36 and its mixtures with hydrophobic species.38-39, 46 Kirkwood-Buff theory connects the partial molar volume of a solute at infinite dilution to solvent packing about the solute.47 The Gibbs-Duhem equation, on the other hand, stipulates that the derivative of the pure solvent’s partial molar volume with respect to the solute concentration

is zero, i.e,

,

= 0. Subsequently, changes in the solute’s partial molar volume with

increasing concentration arise from inter-solute correlations, with the volume of associated solutes differing from dispersed solutes. To break the solute’s volume into contributions from monomeric, dimeric, and larger clusters, we perform a Voronoi analysis (Figure 4) over configurations of ethane in water.48-49 Results for ethane are reported here chosen since it exhibits the largest effect of all the solutes examined. Similar conclusions can be drawn from analysis of alcohol configurations. The Voronoi volume of a given heavy atom site (ethane carbon or water oxygen) is determined by the region of simulation box closest to that atom alone. We then divide the waters in the simulation box into bulk waters versus solute associated waters. Waters are deemed to be associated with a solute if the oxygen falls within 5.45 Å of either of an ethane’s carbons, corresponding to the distance to the first minimum of the oxygen-carbon correlation function. Two solutes are assumed to be associated if any water in the hydration shell of a solute is shared by that of the other. Larger clusters may subsequently be formed from associated pairs of solutes. Monomeric solutes do not share members of their hydration shell

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with any other solutes. Waters outside the hydration shell of all the solutes are assumed to represent the bulk. Based on this framework, we define the hydrated volume of a solute in a cluster of solutes as ∗ =

∗ !"∗ #

,

(4)

where ∗ is the total average Voronoi volume (solutes and shell waters) of the cluster, $∗ is the average Voronoi volume of a individual bulk water molecule, and % is the average number of waters associated with any of the solutes in the cluster. The partial molar volume of a solute at infinite dilution can be approximated as the hydrated volume of an unassociated solute, i.e., ≈ ∗ 1. The Voronoi analysis was conducted on simulations with 25 ethanes ( = 0.0123) to obtain good statistics on solute volumes in distinct clusters. The volumetric properties of ethane clusters are illustrated in Figure 5. While the Voronoi estimate under predicts the partial molar volume of ethane at infinite dilution over the entire temperature range simulated (Figure 5a), the root mean square error is 0.9 cm3/mol, less than ~2% of the total volume. This comparison supports the proposition that a solute’s volumetric properties are largely determined by the packing of waters in the first hydration shell. Moreover, the Voronoi estimate accurately captures ethane’s thermal expansivity in water. While the Voronoi estimate can be improved by incorporating waters beyond the first shell, systematically approaching the Kirkwood-Buff limit for an infinite shell, the present analysis permits a direct attribution of the solute volume to local packing effects and inter-solute association. The mean volumes of individual ethanes in clusters of size n at 5°C is reported in Figure 5b. Starting from dimer formation, ethane’s volume drops from its monomer value, consistent with the negative volumes of hydrophobic association at low temperatures inferred from the partial molar volume derivatives. Ethane’s volume drops even further for larger clusters, appearing to plateau for

12


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ethane hexamers and larger clusters. This plateau holds even for larger clusters beyond the range shown in Figure 5b. The continuing volume drop for trimers, tetramers, pentamers, and hexamers suggests that potentially increasing numbers of waters are affected with the increasing degree of association. The ethane hydration number (defined as the average number of waters in a cluster normalized by the number of solutes in the cluster, ()* = % /) as a function of the cluster size at 5°C is plotted in Figure 5c. Similar to the Voronoi volume, the hydration number is a decreasing function of the cluster size that drops from 24.5 waters per ethane for the monomer to plateau at 19.5 waters for hexamers and larger clusters. The correlation between the Voronoi volume of an ethane in a cluster versus its hydration number is approximately linear (Figure 5d) with a slope of 0.14 cm3/mol per water molecule; that is each ethane’s volume shrinks by 0.14 cm3/mol for each water expelled from the hydration shell into the bulk solvent upon association into clusters. Larger clusters are more efficient at expelling water, thereby reducing their volume It interesting that we find clusters significantly larger than dimers in this analysis at = 0.0123, despite the fact that infinite dilution implies only dimers contribute to the volume derivative. Part of the reason we observe multimer contributions arises from the definition of pair association used. Defining association by the overlap of the hydration shells of two solute hydrations shells implies that ethanes with two carbons up to 10.9 Å (= 2 × 5.45 Å, twice the hydration shell cut-off) away may be grouped together. The simulation volume fraction covered by the ethane hydration shells if they are all dispersed as monomers is ~30% (determined as the product of the solute concentration with the shell volume of a lone ethane). This volume fraction is closer to that of a liquid than a gas, so it is not surprising we observe significant association.

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The cluster volumes are robust to the consideration of less concentrated solutions, though their statistical uncertainty grows. Following the volume derivatives reported in Figure 3, we expect that as the temperature increases the cluster Vornoi volumes should similarly flip from decreasing to increasing with increasing cluster size. This expectation is borne out when we plot the changes in the relative volumes of ethane in clusters (i.e., Δ∗ = ∗ − ∗ 1) for temperatures from 5°C to 75°C (Figure 6a). The functional form of the cluster volume at each temperature is qualitatively the same, reaching a plateau with increasing n for hexameric and larger clusters. For low solute concentrations, the derivative of the solute’s partial molar volume at infinite dilution can be estimated from the relative cluster volumes from the approximate expression (derived in the Supporting Information)

,

≈2

/

∑ 1Δ∗

(5)

where 1 is the probability that ethane is in a cluster of n solutes, and are the total number of waters and solutes in the molecular simulation at which the cluster probabilities and volumes is evaluated (x2 = 0.0123). In difference to the fittings performed above to evaluate the volume derivative, eq. (5) requires only a single simulation be performed. In Figure 6b we report 1 at the low and high temperatures simulated needed to evaluate eq. (5). The temperature dependence of the cluster probability is weak, although we observe growth of larger clusters with increasing temperature consistent with the inverse dependence of hydrophobic aggregation with temperature.50-54 Comparing 1 against Δ∗ , the temperature dependence of the hydrophobic volume anomaly certainly arises predominantly from changes in the cluster volumes rather than reweighting of the distinct cluster contributions the solute volume.

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In Figure 7 we compare the temperature dependence of

,

for ethane estimated

from the Voronoi volume analysis (eq. (5)) against that determined from the concentration dependence of the molar volume of the mixture (eq. (3b)). The Voronoi analysis predicts a temperature dependence for

,

comparable to that determined from the simulation molar

volumes. More importantly, the Voronoi analysis correctly predicts ethane’s volume derivative changes sign from negative to positive values with increasing temperature, demonstrating the anomalous volumetric behavior can be traced to hydrophobic association. The Voronoi analysis, however, is shifted to more positive values of the volume derivative. The Voronoi analysis subsequently predicts a crossover from anomalous to normal behavior at 33°C, 16°C lower than determined from the simulation molar volumes (Table 2). We attribute the errors in the Voronoi estimate for the volume derivative to its focus on the first hydration shell, neglecting contributions from more distant waters. Nevertheless, this comparison demonstrates that first shell waters predominate the volumetric behavior of these solutes in water. Even at small, but finite, solute concentrations on the order of 1%, our Voronoi analysis finds that association between 10 or more solutes contribute to the derivative of the partial molar volume, indicating even smaller concentrations are necessary to isolate the impact of solute dimers. Recognizing that the association volume between two solutes is determined from the pressure derivative of their potential-of-mean force, the derivative of the partial molar volume at infinite dilution with respect to the solute mole fraction at infinite dilution can be reasoned to be related to the pressure derivative of the second osmotic virial coefficient as (derived in the Supporting Information)

,

5

= 2234 ,

15


(6)


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where 23 is the product of Boltzmann constant and the temperature, 4 is the number density of water, and 6 is the second osmotic virial coefficient. In a previous study of methane pair correlations in water using the same simulation models as used here, we fitted an analytical function to 6 to a thermodynamic expansion over a very wide range of temperatures and pressures.50 Following that expansion, the partial molar volume derivative at 1 bar pressure can be expressed as

,

= 7 8 + 8 3

(7)

where 8 = -378.2 cm6/(mol g) and 8 =1.131 cm6/(mol g K) for methane in water, the solvent mass density 7 has units of g/cm3, and 3 has units of K. Since the water density only varies by 3% over the simulated temperatures, eq. (7) predicts the volume derivative is effectively a linear function of temperature, in good agreement with the temperature dependence observed in

Figures 3 and 7. In Figure 3b we compare the virial prediction of

,

for methane against

that determined from simulation. Eq. (7) predicts the crossover from anomalous to normal behavior occurring at 3 = −8 /8 = 61.2°C, in excellent agreement with simulation (Table 2). The values of the derivative determined from eq. (7), however, are approximately half that determined from simulation. The Voronoi analysis above indicates that the association volumes of dimers are lower than that of larger clusters and that it is difficult to isolate dimer contributions to the molar volume at the finite concentrations simulated. It may be argued in this case that the difference between the virial and simulation values of the volume derivative can be attributed to contributions from multimeric association in the simulations. This suggests the curvature of changes from infinite dilution to the minimum. While not definitive, this curvature change is suggested by some experimental results for alcohols in water.2, 10 We do note

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that the relative Voronoi volumes of solutes in the dimeric and larger cluster appear to approximately go to zero at the same temperature (Figure 6a). We might then expect the crossover temperature from the virial and simulation calculations to coincide despite multimeric contributions in the simulation results.

Conclusions The present molecular simulation study on the anomalous decrease in the partial molar volume of alcohols in water starting from infinite dilution to increasing concentrations illuminates the role of hydrophobic interactions. Specifically, at low temperatures we found that the magnitude of this effect increases with increasing hydrophobicity of the alcohol, in agreement with experiment, and is magnified for purely hydrophobic gases in solution. As suggested by experiments, this anomaly disappears at a crossover temperature above which the partial molar volume increases with increasing concentration. We note that the observation of this hydrophobic volume anomaly at normal liquid conditions is dependent on quality of the water model used. For models like TIP3P, which provides a poorer representation of the equation-of-state properties of water, these volumetric anomalies appear to be shifted to much lower temperatures. A Voronoi analysis of simulation configurations traced the volume derivative anomaly to solute association into clusters with increasing concentration. The variation of the solute volume with association is strongly correlated with the shedding of hydration shell waters. The solute volume anomaly was shown to be tied to the pressure dependence of the second osmotic virial coefficient in solution, providing a route for inferring information on molecular-scale pairwise hydrophobic interactions.

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This work highlights the potential role of pressure on hydrophobic assembly processes in aqueous solution. Specifically, the decrease in the volume of small clusters of hydrophobic solutes at low temperatures indicates increasing pressure favors hydrophobic contacts that drive assembly. Indeed this effect may be even greater experimentally, as suggested by the larger derivatives observed for alcohols of increasing hydrophobicity (Figure 3a). With increasing temperature, the association volume becomes positive and pressure drives hydrophobic assemblies apart above the crossover temperature. Our observations and their qualitative agreement with experiment suggest hydrophobic interactions between individual nonpolar moieties do not drive pressure-induced increases in the critical micelle concentration of surfactants55 or protein denaturation.56 Subsequently, pressure effects on meso-scale assembly should account for the volumetric properties for the full hydrophobic assembly.57-58

Supporting Information Detailed derivations of eqs. (5) and (6).

Acknowledgements We are grateful to Ben Widom’s for his many insightful contributions that have profoundly shaped our understanding of the liquid state theory and simulation. This work has benefitted from insightful conversations with Dor Ben-Amotz and Gren Patey. We also would like to acknowledge financial support from the NSF-DMR (No. 1460637), NSF-CBET (No. 1403167), NSF-OIA (No. 1430280), and Louisiana Board of Regents Graduate Research Fellowship program (J.W.B.). Computational support was provided by the Louisiana Optical Network Initiative.

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Table 1. Infinite dilution partial molar volumes of alcohols in water at 25°C and 1 bar. The volumes are report in cm3/mol. The present simulation results are reported in the first column and experimental results are reported in the second two columns. simulation ref. 1 ref. 2 ---------------------------------------------------------------------------------------------------methanol 37.9±0.1 38.2 37.6 ethanol 53.9±0.1 55.2 55.2 1-propanol 68.7±0.1 70.8 71.4 ----------------------------------------------------------------------------------------------------

Table 2. Crossover temperature where

,

= 0 for the alcohols and alkanes in aqueous

solution. The temperatures are reported in °C. The present simulation results are reported in the first column and experimental results are reported in the second two columns. simulation ref. 1 ref. 2 ---------------------------------------------------------------------------------------------------methanol 60±8 62 30 ethanol 68±3 66 74 1-propanol 48±1 74 51 methane 59±2 --ethane 49±1 ------------------------------------------------------------------------------------------------------

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Figure 1. Partial molar volume of ethanol as a function of concentration in mixtures with water at 25°C and 1 bar pressure. The main figure shows details from experiment and simulations on the water rich side (x2 < 0.1) of the curve, while the inset figure shows the ethanol volume over the entire concentration range. The figure symbols are defined in the legend. The simulation error bars indicate one standard deviation. Experimental results are taken from ref. 1.

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Figure 2. Plot of the concentration at which the concentration derivative of ethanol’s partial molar volume in aqueous solution goes to zero at different temperatures. The temperautre for x2 = 0 are linearly interpolated/extrapolated from the results reported in Figure 3 and reported in Table 2. The lines indicate a parabolic fit to the points. Below the curve the partial molar volume derivative is negative and anomalous. The figure symbols are defined in the legend. Experimental results are taken from ref. 1.

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Figure 3. Derivative of the solute partial molar volume with respect to the solute mole fraction at infinite dilution as a function of temperature. Results for the alcohols and alkanes are reported in a and b, respectively. The figure symbols are defined in the legend. The simulation error bars indicate one standard deviation. Experimental results are taken from ref. 1.

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Figure 4. Schematic illustration of the Voronoi tessellation over solute monomers and clusters in aqueous solution. The black points correspond to water and solute heavy atom sites. The solute heavy atom cells are teal, while the water in the solute hydration shells are red. Bulk water cells are white. We show here a monomeric and dimeric solutes. Dimers and larger clusters are identified by grouping solutes that share hydration shell waters.

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Figure 5. Volume of hydrated ethane in aggregate clusters in water determined via the Voronoi tessellation carried out at = 0.0123. a) Comparison between the partial molar volume ( ) of ethane at infinite dilution in water against the volume of a monomeric ethane (cluster size of 1) evaluated via the Voronoi analysis (∗ 1) as a function of temperature. b) Voronoi volume of an individual ethane (∗ ) in a cluster of size n at 5°C. c) Hydration number (()* = % / ) of individual ethanes in a cluster of size n at 5°C. d) Correlation between the ethane Voronoi volumes against the hydration number at 5°C. The simulation error bars indicate one standard deviation. In cases where error bars are not visible, they are smaller than the figure symbols.

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Figure 6. Ethane cluster volumetric properties as a function of cluster size over a range of temperatures. a) Relative ethane Voronoi volumes (Δ∗ = ∗ − ∗ 1) in clusters of size n. Results for all simulations from 5°C to 75°C are reported, with increasing temperature indicated by the arrow. b) Probability (1) of finding an ethane in a cluster of size n at 5°C and 75°C. The simulation error bars indicate one standard deviation. In cases where error bars are not visible, they are smaller than the figure symbols.

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Figure 7. Comparison between ethane’s partial molar volume derivative with respect to the solute mole fraction at infinite dilution evaluated from the simulation molar volumes (eq. (3b)) and from the Voronoi cluster volumes (eq. (5)) as a function of temperature. The figure symbols are defined in the legend. The simulation error bars indicate one standard deviation. In cases where error bars are not visible, they are smaller than the figure symbols.

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TOC Graphic.

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Connections between the Anomalous Volumetric Properties of

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