Structural and Dynamic Heterogeneity of Capillary Wave Fronts at

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Structural and Dynamic Heterogeneity of Capillary Wave Fronts at Aqueous Interfaces Tiecheng Zhou, Alex McCue, Yasaman Ghadar, Imre Bako, and Aurora Evelyn Clark J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07406 • Publication Date (Web): 05 Sep 2017 Downloaded from http://pubs.acs.org on September 9, 2017

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The Journal of Physical Chemistry

Structural and Dynamic Heterogeneity of Capillary Wave Fronts at Aqueous Interfaces

Tiecheng Zhoua, *, Alex McCuea, Yasaman Ghadara, Imre Bakób, and Aurora Clarka, * a

Department of Chemistry and the Materials Science and Engineering Program, Washington State University, Pullman, WA, USA b Institute of Organic Chemistry Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar Tudosó köú2, P.O. Box 286, Budapest, Hungary

corresponding authors: [email protected], [email protected] Abstract Using a unique combination of slab-layering analyses and identification of truly interfacial molecules, this work examines water:vapor and water:n-hexane interfaces, specifically the structural and dynamic perturbations of the interfacial water molecules at different locations within the surface capillary waves. From both the structural and dynamic properties analyzed, it is found that these interfacial water molecules dominate the perturbations within the interfacial region, which can extend deep into the water phase relative to the Gibbs dividing surface. Of more importance, is the demonstration of structural and dynamic heterogeneity of the interfacial water molecules at the capillary wave front, as indicated by the dipole orientation and the structural and dynamic behavior of hydrogen bonds and their networks.

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I. Introduction The change in physicochemical properties of solvents at liquid:vapor and liquid:liquid phase boundaries is of longstanding interest within a variety of scientific communities, from separations1-5 to colloidal science6-8. At its heart, a significant challenge is the study of the “interfacial region”, a volume of space where the properties vary to such an extent from the bulk liquid that it influences the chemical processes that may take place therein. Several surface sensitive experimental techniques have been developed to investigate the interfacial region, such as vibrational sum frequency generation (SFG) spectroscopy,9-14 second harmonic generation (SHG) spectroscopy,10, 15-16 X-ray reflectivity scattering17-23, and neutron scattering24. These experiments have been complemented by computational analyses in terms of the dipole orientations,25-30 hydrogen bonding28, 30-34 and other structural and dynamic properties35-38. In this context, the concept of the Gibbs dividing surface plays an important role as a reference point for investigating the changes in the water properties as a function of distance to the interface. The Gibbs dividing surface is generally defined as the position where the density of the solvent is half of its bulk. Once the Gibbs dividing surface is determined, the structural organization and dynamic features of a solvent may be analyzed in consecutive slab-layers parallel to the Gibbs dividing surface.30-31, 34, 39-40 The interfacial region can then be defined as the region where the properties of solvent have been perturbed relative to the bulk. However, these slab-averaging approaches have been criticized29, 41-45 as ignoring the thermal corrugated surface roughness of the interface, known as capillary waves. Capillary wave theory provides a mathematical formalism that separates the total interfacial width in terms of intrinsic and capillary wave components.17-

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18, 27, 46-48

The former is attributed to the intrinsic molecular structures with respect to the

to the instantaneous local surface while the latter is attributed to the width broadening due to the thermally corrugated capillary waves. In molecular simulations, different methods29,

41-45, 49

have been developed to

identify the molecules at the capillary wave fronts of the interface so as to remove the effect from capillary waves and obtain the corresponding intrinsic profile, which is the profile of molecular density or other properties as a function of distance from the instantaneous surface. For instance, the concept of the local interface position49-50 has been introduced to study the intrinsic profile of homopolymer interfaces49 and water:hydrocarbon interfaces28 by partitioning the system into several columns and determining the local Gibbs dividing surface therein. The intrinsic sampling method (ISM) has been applied to study the intrinsic structure of water:vapor and water:alkane interfaces.43-45 The Identification of the Truly Interfacial Molecules (ITIM) algorithm29, 51 has been developed to select the molecules at the capillary wave fronts of the interface. This algorithm has been used to investigate the molecular orientations of water at the vapor and organic interfaces,29, 52 the width of the water interface with apolar phases,52 the dynamics of water molecules at the vapor interface,42 and the surface tension of liquid:vapor interfaces38. ITIM also enables analysis of the subsequent molecular layers beneath the capillary wave front,41 where it has been demonstrated that the effect of the interface disturbs almost exclusively the surface layer and quickly vanishes beyond the second layer.41, 52 Yet, most of these works have averaged the properties of the molecules over the entire interfacial layer without considering their local positions at the capillary wave fronts. It has been shown from both the intrinsic sampling method43 and the ITIM method29,

3

52

that the preferential orientation of the



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interfacial water molecules depends on the local curvature at the interfaces, which hints at structural heterogeneity in the interfacial layer. To the best of our knowledge, the homogenous or heterogeneous characteristics of the interfacial surface at the capillary wave fronts have not been previously examined. One of the most interesting aspects of potential heterogeneity lies in the study of the hydrogen bond structures and dynamics. Toward that end, the ITIM method and slab-layering analyses have been combined to study the hydrogen bond structures and dynamics of the interfacial water molecules at the water:vapor and water:n-hexane interfaces. Specifically, ITIM is used to select the truly interfacial water molecules at the capillary wave fronts and the slab-layering analyses are used to bin different regions of the capillary wave fronts to assess the heterogeneity of the interfacial water molecules. Our results demonstrate that the interfacial molecules at the capillary wave fronts are the source of perturbations induced by the interface and these interfacial molecules are structurally and dynamically heterogeneous. This heterogeneity bears important relevance to interfacial phenomena and may influence kinetic processes at the interfacial region, for example solute transfer or molecular reactions that rely upon solvent organization and dynamics (e.g. dissociative metal-ligand complexation).

II. Computational Methods II.A Simulation Protocol and System Setup. Two systems have been studied: the first is the water:vapor interface and the second is the water:n-hexane interface. The simulation data has been previously published in the literature34, 40 using the LAMMPS53 package, with an abbreviated description provided herein. In the water:n-hexane system, the n-hexane was described by the AMBER-9954 force field, while water was described by a modified rigid TIP3P/Ew55 (Tables S1 in Supporting Information). The water:n-hexane simulation 4


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box (Lx = Ly = 40 Å, Lz = 140 Å) was constructed by a water region with 3205 molecules sandwiched between two n-hexane regions with a total of 586 molecules. The system was equilibrated successively in NVT and NPT ensembles for at least 1 ns with targeted temperature of 300K and pressure of 1 atmosphere. After equilibration, the production run was performed in NVE for 0.5 ns with trajectories saved every 25 fs, yielding a total of 20,000 snapshots for analysis. In the water:vapor system, two different water models were used so as to understand the effect of the force fields upon the water structure and dynamics near the interfacial region. In one case, 1204 water molecules described by the modified rigid TIP3P/Ew55 water model was simulated in a box of Lx = Ly = 33 Å, Lz = 100 Å. The detailed equilibration and production information described in a previous work34. In the other case, a simulation box of Lx = Ly = 25 Å, Lz = 75 Å was built with 512 water molecules in the center using the polarizable AMOEBA56 force field in TINKER57 that accounts for atomic multipoles and polarizability with the same equilibration and production protocols. During the NVE production runs, the system temperature had little fluctuation. For example, the temperature of the water:vapor system with AMOEBA force field was 304.6 ± 4.4 K. II.B Study of the interfacial region. Herein several different approaches have been employed to study the structural and dynamic properties of water at the interfacial region. 1.

Density Profiles and the Gibbs Dividing Surface. The density profile,

ρ(z), is obtained by dividing the simulation box into 1 Å slabs along the surface normal direction, z, and averaging the molecular density within each slab over the whole trajectory. The translation of the whole water phase, i.e. the movement of its center of mass (C.O.M), is negligible during our simulation (the standard deviation in C.O.M. is 0.1Å, see in Figure

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S11). The Gibbs dividing surface of water is then determined as the position where the total water density ρ(z) is half of its bulk value (1.01 g/cm3). Similarly, the Gibbs dividing surface of n-hexane is determined as the position where its density is half of its bulk value (0.64 g/cm3). For the water:n-hexane interface, there is a ~0.92 Å mismatch in the Gibbs dividing surface of water and that of n-hexane, which can be defined as the intrinsic width for this liquid:liquid interface (see Eqn(5)). 2.

Capillary Wave Theory. The total interfacial width consists of two

components: the intrinsic width and that due to capillary waves.17-18, 46-48 From molecular dynamics simulations, it is approximated that the two contributions can be decoupled so that the total density profile is a convolution of the intrinsic profile ψ(z) and the effect due to capillary waves.34, 47, 58 The corresponding width parameters can then be obtained by fitting the total density profile to an error function.34, 47-48, 58 The functional formalisms are slightly different for the liquid:vapor and liquid:liquid interfaces (details provided in Supporting Information). For the liquid:vapor interface, the total density profile of that liquid is fitted to an error function:48 =

+ − − + √ 1 2 2

where z0 is the position of Gibbs dividing surface, ρl is the density in the bulk phase and ρv that in the vapor phase. The total interfacial width (∆) is expressed in terms of the intrinsic width (∆0) and the width due to capillary waves:48 ∆ = ∆ +

! 2 2 "

∆ = 3 2

6


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where L is the length of the cross section of the simulation box L = Lx = Ly, and γ is the surface tension and B0 is the correlation length. For the liquid:liquid interface, on the other hand, the density of either liquid is generally fitted to the error function:59 &' = 0.5' − 0.5'

− ,'

√2, − ,- 4 % - = 0.5- − 0.5- $ √2, where ρw and ρh are the bulk density of water phase and n-hexane phase, z0,w and z0,h are the Gibbs dividing surfaces for the two liquids and wc is the capillary wave width parameter. In this way, the total interfacial width (w), the intrinsic interfacial width (w0), and the width due to capillary waves (wc) are determined as:59-60 & = + , / = 0 − 0 ,' , 5 ! % /, = 2 1 $

where L is the length of the cross section of the simulation box L = Lx = Ly, γe is the surface tension, and lb is the correlation length. One thing to note is that the interfacial width obtained from the capillary wave theory is dependent on the size of the system (see Eqn(2) and Eqn(5)). In this work, the cross section of the water:n-hexane interface is L = Lx = Ly = 40 Å and that of the water:vapor interface is L = Lx = Ly = 33 Å for TIP3P/Ew water model and L = Lx = Ly = 25 Å for the AMOEBA water model. 3. Truly Interfacial Molecules at the Capillary Wave Fronts. The ITIM29,

38, 41-42

algorithm was used to identify the truly interfacial molecules located at the capillary wave fronts that are exposed to the opposite phase. A probing ball of radius 1.25 Å was used along testing lines mesh-gridded in the interface plane (the xy plane) with 0.5 Å separation to select these interfacial molecules.42 The atoms that first encounter the probing ball are 7



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identified as the interfacial atoms and the corresponding molecules are identified as the interfacial molecules (see Figure S1 in the Supporting Information for the representative structure of these interfacial water molecules). The distribution of the density of the truly interfacial molecules can then be obtained and the full width at the half maximum of that Gaussian-like distribution can be defined as a descriptor of the interfacial width.29, 42 In addition to this metric, our focus is to examine the properties of the truly interfacial waters and to decompose their contribution to the overall averaged quantities typically studied within the interfacial region. 4. Dipole Orientation of the Water Molecules. The dipole orientation of water can be defined by the cosine of the angle θi between the unit vector along the dipole moment (μi) and the unit vector normal to the interface (nz) pointing towards the water phase (along the +z direction in all figures),

234 56 = 76 ∙

9 6

where a positive value of cos(θi) indicates that the dipole moment is pointing towards the water phase and vice versa. The direction of the dipole moment of a water molecule is chosen as the bisector of the H-O-H angle pointing from the oxygen end to the hydrogen end. The averaged cosine of angle θ, was calculated in a series of slab-layers along the z direction with a layer spacing of 0.1 Å as the dipole orientation profile for both the water:vapor interface and the water:n-hexane interfaces. Many previous studies25-26, 30, 36, 39 have reported the dipole orientation profile as a function of distance to the Gibbs dividing surface without differentiating the interfacial water molecules and those of the bulk. Using the ITIM method coupled with slab-layering analyses, we decomposed the two contributions and also study the dipole orientation of water molecules at different regions

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along the capillary wave fronts. Similar analyses have been performed to study the dipole orientation profile in three regions of the interfacial water layer at the vapor interface.29, 52 In this work, we present a more refined slab-layering analyses (layer spacing of 2 Å) for the dipole orientation distribution (the probability distribution of cos(θ)) of the interfacial water molecules and compare it to the other non-interfacial molecules . 5. Analysis of the Hydrogen Bond Structures. Prior works have investigated the perturbations of the water hydrogen bond (HB) network due to the presence of a liquid or vapor interface.28-32,

36, 42, 61

However, these studies have provided only the average

perturbations either: 1) within a slab region without differentiating the interfacial molecules or 2) among all the interfacial water molecules regardless of their locations within the capillary wave fronts. The HB characteristics of truly interfacial water molecules at different positions within the capillary wave fronts has not been discussed. Herein, the HB networks at the interfacial region were studied by combining the ITIM method and slablayering analyses (layer spacing of 2 Å). The essential properties of the hydrogen bond network have been analyzed using a graph theoretical approach implemented in the ChemNetworks62 package. Each snapshot is converted into a graph wherein the vertices represent water molecules and the edges between vertices represent intermolecular hydrogen bonds. A geometric HB definition has been used based on a distance threshold between the intermolecular O- and H-atoms of rO..H < 2.5 Å and an H-bond angle threshold of

∠ 6 7 ?,@ 6 6 − 1 ,@

6 where ni is the number of hydrogen bonded neighbors (degree of vertex i) and ?,@ is the

smallest sized of closest path that passes through the interested water molecule i and its two neighbor sites l and m, and the summation goes over all the possible neighbors. The cyclic coefficient can then be averaged for water molecules in certain layers with 2-Å spacing along the surface normal (z direction in our systems): B = 〈 6 〉 8

This coefficient has a value between zero and 1/3. If all the neighbor pairs of the vertices have a direct links to each other, then the overall cyclic coefficient approaches its maximum value of 1/3. Another descriptor associated with it is the cyclic number, defined as the number of cyclic entities that the molecule has involved in. These descriptors are related to the compactness of the extended HB structure and they cannot be easily decomposed to

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contribution from interfacial water molecules and the other bulk molecules. Thus, we only present the results averaged over all the water molecules within each slab-layers. 6. Analysis of the Hydrogen Bond Dynamics. Due to the use of a rigid cutoff to separate Hbonded pairs and non-bonded pairs, it has been noted previously that the time-dependent network will contain transient artifacts that can dramatically alter the analysis of the HB trajectories.65-66 These have been corrected using our recently reported procedure66 that takes into consideration the dynamic history of each HB, using a Persistence value of 150 fs and a Tolerance value of 100 fs. After correcting the HB networks, the persistence of each individual hydrogen bond (τi), which is the continuous time duration of the HB, is collected for all the possible HBs in the simulation system and the overall HB lifetime (τHB) is calculated as the average of the HB persistence weighted by the observed number N(τi) from the simulation: FG =

∑6 F6 IF6 9 ∑6 IF6

Similarly, the non-hydrogen-bonded (NHB) duration or the HB breakage interval, τi, is determined and the corresponding NHB lifetime τNHB can be calculated as the weighted average of the NHB persistence: FKG =

∑6 L6 IL6 10 ∑6 IL6

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Figure 1. Two HB breakage and reformation mechanisms: the first is HB fluctuation with the same partner, the second is HB reorientation via exchanging the HB partners. The reorienting O-H bond is denoted by H*.

Two HB breakage and reformation mechanisms are investigated (see Figure 1) to study the HB dynamics. HB fluctuation corresponds to the case where the reorienting H* reforms its hydrogen bond with the original acceptor water molecule after the breakage, while HB reorientation corresponds to the case where H* switches to another water molecule to form a new hydrogen bond. Each hydrogen bonded duration and hydrogen breakage interval can be assigned to either HB fluctuation or HB reorientation such that the overall HB lifetime and NHB lifetime can be decomposed into the two HB breakage and reformation mechanisms. These two mechanisms have been studied for water around hydrophobic solutes.67 III. Results and Discussion The water:vapor interface is usually regarded as a simple representation of the water hydrophobic interface and has been extensively studied.9, 13, 18, 26, 29-31, 34, 37, 42-43, 47-48, 68-69

Here we investigate the properties of water:vapor interface in comparison to that of

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water:n-hexane, specifically as it pertains to a combined ITIM and slab-layering analyses that enables a detailed understanding of the interfacial region where the water HB structure and dynamics are perturbed. The structural organization and the dynamic behavior of the HB network for water have been analyzed in consecutive slabs parallel to the Gibbs dividing surface in both the water:vapor and water:n-hexane systems. The analyzed structural properties include the dipole orientation, the average number of hydrogen bonds per water, and the interconnectedness of the hydrogen bond network (the cyclic coefficient and the cyclic number). At the same time, several dynamic properties of the hydrogen bond network have been evaluated, including the average hydrogen bond lifetime and the average non-hydrogen–bonded lifetime (or average hydrogen bond breakage duration) with consideration of the two HB breakage and reformation mechanisms. All the results have been decomposed into contributions from the interfacial and the non-interfacial water molecules. The Supporting Information provides hydrogen bond analyses of water in subsequent molecular layers (up to the third layer) at the water:vapor interface. In agreement with previous studies,

41, 52

the molecules in the first

molecular layer experience the most perturbations. As such, only the water molecules in the first molecular layer are regarded as the interfacial molecules in the main text and all the other molecules beneath the first layer are regarded as the non-interfacial molecules. Further, the positions of the interfacial water molecules are distinguished so as to learn about the structural and dynamic heterogeneity within the capillary wave fronts at the interfaces. For the sake of simplicity, the Gibbs dividing surface of the water phase, which is the position where the total density of water is half of its bulk value, is set to z = 0 Å as the reference point in all figures.

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III.A. System Validation: Comparisons of Average Interfacial Properties. Table S2 in the Supporting Information summarizes the interfacial width parameters that are commonly used in literature, including the density distribution of all the water molecules and that of the interfacial molecules, the fitting parameters of the density profile, and the parameters obtained from capillary wave theory. Although most values are not new, the results in Table S2 provide a full comparison of all these metrics for the water:vapor interface and water:n-hexane interface, and validate our calculations. The water density profile is presented in Figure 2 for water:vapor and water:nhexane interfaces with the decomposed density of interfacial water molecules. In Figure 2(A), it is observed that the total density profile of water:vapor interface is almost identical for TIP3P/Ew and AMOEBA water models. This indicates that the density profile is insensitive to the water force field, which agrees with the recent literature42 where similar density profiles are obtained for SPC/E, TIP4P, and TIP5P-E water models. The interfacial water molecules at the water:vapor interface have a Gaussian-like density distribution, with a maximum at z = ~ +2 Å from the Gibbs dividing surface. The distribution encompasses a broad interfacial region ~ 10 Å from z = −3 Å to z = +7 Å, indicating that the capillary waves of the water:vapor penetrate deep into the water phase relative to the position of the Gibbs dividing surface. Similar density distribution curves are observed for the water:n-hexane interface in Figure 2(B). In total, the truly interfacial water molecules at the capillary wave fronts, have a density maxima at +2 Å relative to the Gibbs dividing surface for both water:vapor and water:n-hexane interfaces. This illustrates that the Gibbs dividing surface, which is determined based on the total water density rather than the interfacial water

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density, may not be a good reference point for describing the actual position of the interface.

Figure 2. The density profile for (A) water:vapor interface and (B) water:n-hexane interface. The position of the Gibbs dividing surface of the water phase is shifted to z = 0 Å, i.e. the total density of water is half of its bulk at z = 0 Å. The short black lines indicate the analyzed 2 Å slabs with center position from −2 Å to +12 Å for the results below.

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Figure 3. The distribution of the cosine of the water dipole angle at consecutive 2-Å slablayers relative to the Gibbs dividing surface (z = 0 Å) for water:n-hexane interface. The water dipole angle is the angle between its dipole moment and the normal vector of the interface (pointing towards the water phase). The distribution of (A) all the water molecules, (B) the interfacial water molecules, (C) the non-interfacial water molecules are presented. The curves are labeled with the center position of the corresponding 2-Å layer (see Figure 2).

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III.B. Comparisons of Water Orientation in the Interfacial Region and Among Truly Interfacial Water Molecules. As previous work has revealed, the dipole of the water molecule at the vapor interface is preferentially oriented parallel to the interface,25-26, 30, 36 with one O-H bond pointing out of the water phase.9, 25 Further, the water molecules at the vapor side of the interface (the low water density region) have their dipole oriented slightly outside of the water phase.26, 30 Figure S2 shows the average water dipole orientation, , as a function of distance relative to the Gibbs dividing surface. Both water:vapor and water:n-hexane systems exhibit the previously described bimodal feature,26, 30 wherein the water dipole preferentially points outside of the water phase near the vapor side or hexane side of the interface (z < 0 Å) and preferentially points within the interface plane at the water side (z = 0 ~ 5 Å). A detailed dipole orientation distribution is illustrated in Figure 3 in terms of the distribution of cos(θ) at several 2-Å slab-layers (the slabs are marked with short black lines in Figure 2) relative to the Gibbs dividing surface for the water:n-hexane interface. When considering all the water molecules (Figure 3(A)), a uniform distribution is observed beyond +6 Å away from the Gibbs dividing surface into the water phase, indicative of the random dipole orientation of the bulk. Within the water:n-hexane interfacial region, the distribution has a broad peak around cos(θ) ~ 0, which reveals the preferential dipole orientation parallel to interface. On the hexane side of the interface (z = −2 Å and 0 Å), the broad peak shifts slightly towards negative cos(θ) value, while on the water side (z = +2 Å and +4 Å ) it shifts slightly towards positive cos(θ) value. This leads to the negative for z < 0 Å and the small positive for z > 0 Å in Figure S2(C). New insight is gleaned when the dipole orientation distribution is separated for the interfacial water molecules

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(Figure 3(B)) and that for the non-interfacial water molecules (Figure 3(C)). Specifically, a uniform distribution is observed for the non-interfacial water molecules in Figure 3(C) at all the slabs as close as +2 Å to the Gibbs dividing surface. Thus the non-interfacial water molecules, which are the molecules beneath the interfacial layer, already adopt a statistically random orientation. On the other hand, interfacial water molecules show clear preferential orientation across the whole interfacial region (from z = −2 Å to z = +6 Å) in Figure 3(B). Thus, the preferential orientation solely originates from the interfacial water molecules at the capillary wave fronts of the interface. More important to the current work, there is a clear shift in the peak of the distribution for interfacial water molecules from negative cos(θ) value at the hexane side (z = −2 Å) to positive cos(θ) value at the water side (z = +6 Å). Therefore, the preferential dipole orientation is dependent on the position of the interfacial water molecule within the capillary wave fronts, which can be measured by the distance to the Gibbs dividing surface. Those interfacial water molecules on the part of the capillary wave front that extends deep into the water phase exhibit preferential dipole orientation pointing toward the water phase, while those on the part of the capillary wave front that extends deep into the hexane phase exhibit preferential dipole orientation pointing out of the water phase. The distance dependence of the dipole orientation clearly demonstrates the heterogeneity of the interfacial water molecules. The same features are obtained in the dipole orientation distribution for the water:vapor interface in Figure S3 and S4 of Supporting Information. This complements prior literatures using the ITIM method for the water:vapor and water:organic liquid interfaces,29, 52 where the whole interfacial layer was divided into three sub-layers. This work provides the distribution of dipole orientation at more refined

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distance regions for the interfacial water molecules (which effectively divides the whole interfacial layer into 6 sub-layers) and contrasts it to the random orientation distribution from the non-interfacial water molecules. This allows us to demonstrate that not only does the preferential dipole orientation of water at the water:vapor and water:n-hexane interface derive predominantly from the interfacial water molecules but also that the preferential orientation depends on the location within the capillary wave fronts. III.C. Comparisons of the Structures of Hydrogen Bonding in the Interfacial Region and Among Truly Interfacial Water Molecules. The structural and dynamic properties of the HB network for waters in consecutive layers from z = −2 Å to z = +12 Å have been examined in the water:vapor and water:nhexane interfaces. The results have been further decomposed into the contribution from the interfacial water molecules and the other non-interfacial water molecules, so as to understand the properties of interfacial water molecules at the capillary wave fronts considering their local positions where the capillary wave front is extending into the water phase or the vapor/hexane phase. Figure 4 presents the average number of HBs per water, , at different distances to the Gibbs dividing surface of water:vapor and water:n-hexane interfaces. The of all the water molecules (circle-marked purple line) has a value of ~3.4 at z = +12 Å for both systems, representing the bulk-water limit. It decreases gradually as the interface is approached so that it is 2.26 at z = −2 Å for the water:vapor interface in Figure 4(A) with the TIP3P/Ew water model. The same trend is observed in Figure S5 in the Supporting Information with AMOEBA water model. Indeed, the hydrogen bond distribution of the interfacial molecules reveals large decreases in the concentration of water molecules that

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have 3 or 4 hydrogen bonds at the interface, as well as significant increases in concentration of water molecules with 1 or 2 hydrogen bonds (see Figure S6 − S8 in Supporting Information). However, the position at which the all-water (in purple) begins to drop is different in the water:vapor versus the water:n-hexane interfaces, i.e. it is at z = +2 ~ +4 Å in the former while it is at z = +4 ~ +6 Å in the latter. The relative concentrations of the interfacial and non-interfacial water molecules are illustrated in Figure S9. It can be seen that deep in the water region (z > +8 Å), all the water molecules are non-interfacial; as the interface is approached, the concentration of interfacial water molecules gradually increases until they are the dominate species at the interface. There is a clear switch in the major concentration at z = +2 ~ +4 Å for the water:vapor interface and at z = +4 ~ +6 Å for the water:n-hexane interface, which is coincident with the position where the overall starts to drop. Thus, the capillary wave fronts of water:hexane interface extend deeper into the water phase than that of water:vapor interface. This is consistent with the smaller surface tension, and the larger interfacial width parameters of the water:hexane interface as shown in Table S2. Further decomposition of this data (Figure 4) reveals that the of interfacial water molecules (diamond-marked blue line) decreases at the interfacial region while that of the non-interfacial ones (triangle-marked red line) is nearly constant for both systems. This demonstrates that the structural change of water at the interface derives solely from the truly interfacial molecules. Importantly, a significant change in of the interfacial water molecules at different distances from the Gibbs dividing surface is also observed. For example in the water:n-hexane interface the of the interfacial water molecules (diamond-marked blue line) is 3.24 at z = +4 Å while it changes to 2.26 at z = −2 Å in Figure 4(B). Again this demonstrates that the

20


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interfacial water molecules are structurally heterogeneous in the interfacial region and their HB structure depends on their location within the capillary wave fronts.

Figure 4. The average number of HBs per water as a function of distance to the Gibbs dividing surface (z = 0 Å) for (A) water:vapor interface and (B) water:n-hexane interface at 298K. The results are averaged within consecutive 2-Å slabs for all the water molecules (labeled as “All-waters”), the truly interfacial water molecules (labeled as “Interfacial”) and the other non-interfacial water molecules (labeled as “Non-interfacial”).

In addition to the local hydrogen bond structure, the concepts of interconnectivity within the network63 provides alternative descriptors for quantifying the hydrogen bond structures. The extent to which water molecules participate in unbroken hydrogen bonded pathways (primitive rings of hydrogen bonds), have been shown to elucidate important heterogeneities within binary solutions of water with formamide and methanol.63 Here, two descriptors, namely the local cyclic coefficient (R in Eqn(8)) and the cyclic number (the number of cyclic entities per water), have been analyzed for all the water molecules as a function of distance from the Gibbs dividing surface in Figure 5. We can see that the cyclic

21



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coefficient and the cyclic number decrease gradually at the interface for both water:vapor and water:n-hexane systems. For example in Figure 5(B), the cyclic coefficient decreases from 0.126 at z = +12 Å to 0.113 at z = −2 Å at the water:n-hexane interface; and the corresponding cyclic number decreases from 9.35 to 4.27. This illustrates that the water HB interconnectivity is significantly decreased near the interfacial region. Further, we can see that these descriptors start to drop at the similar distance (z = +4 ~ +6 Å) for the two systems, which indicates that the two interfaces have a similar effect in disturbing the extended interconnectivity of the water HB network.

Figure 5. The cyclic coefficient and cyclic number (See Eqns(7)-(8)) as a function of distance to the Gibbs dividing surface (z = 0 Å) for (A) water:vapor interface and (B) water:n-hexane interface with TIP3P/Ew water model. These results are calculated from all the water molecules of the systems.

In combination, these structural data reveal that the significant structural changes at the interfaces derive predominantly from the truly interfacial water molecules at the capillary wave fronts. These interfacial water molecules are structurally heterogeneous and their properties are highly dependent on the locations within the capillary wave fronts. The

22


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interfacial water molecules on the vapor or hexane side of the capillary wave undergoes significant structural changes while those on the water side behave more similar to the noninterfacial waters. Further, these structural changes take place in a broad interfacial region from the vapor or hexane side (z < 0 Å) to deep in the water side (z = + 6 Å). III.D. Comparisons of the Dynamics of Hydrogen Bonding in the Interfacial Region and Among Truly Interfacial Water Molecules. Complementary to the structural features discussed above, the dynamic features of water HB networks have been examined for the water:vapor and water:n-hexane interfaces. Each hydrogen bond has been assigned a position tag based on the coordinate of the oxygen atom from the donor water at the beginning of the hydrogen bonded duration. In this way, the average HB lifetime at different distance to the Gibbs dividing surface was obtained. Another dynamic feature of the HB network is the non-hydrogen-bonded lifetime (τ NHB), which characterizes the duration of hydrogen bond breakage. The detailed HB dynamics are resolved with respect to two HB breakage and reformation mechanisms (Figure 1), i.e. HB fluctuation corresponds to hydrogen bond reformation with the same partner while HB reorientation corresponds to a hydrogen bond reformation with a different partner. In Figure 6(A) it is observed that the HB lifetime for all water molecules (the black dashed line) is nearly constant ~ 1.10 ps across the whole interfacial region for the water:vapor interface with TIP3P/Ew water model. This suggests that the HB lifetime is only weakly disturbed by the water:vapor interface. On the other hand, the NHB lifetime of all water molecules increases significantly. Decomposition of the two HB breakage and reformation mechanisms reveals that this increase in NHB derives mostly from HB reorientation rather than fluctuation. For example, the NHB lifetime τ NHB associated with

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HB fluctuation for all the water molecules (triangle-marked purple solid line) increases from 0.19 ps at z = +12 Å in the bulk-limit region to 0.33 ps at z = −2 Å on the vapor side of the interface (1.74x increase relative to bulk). While the τNHB associated with HB reorientation motion (diamond-marked brown dotted line) increases substantially more, from 0.24 ps at z = +12 Å to 1.02 ps at z = −2 Å (4.25x increase relative to bulk). Further, by identification of the interfacial water molecules at the capillary wave fronts, we can see that the increase in NHB lifetime derives predominantly from the interfacial water molecules. For instance, the NHB lifetime of the HB reorientation motion for the interfacial water molecules (cross-marked blue dotted line) increases significantly from 0.28 ps at +8 Å to 1.02 ps while that for the non-interfacial water molecules (circlemarked orange dotted line) is nearly constant from +8 Å to +2 Å in Figure 6(A). This demonstrates that the water:vapor interface only disturbs the HB dynamics of the interfacial water molecules at the capillary wave fronts while almost no disturbance is on the non-interfacial molecules. Moreover, the large difference in NHB lifetime of the interfacial water molecules as a function of distance to the Gibbs dividing surface reveals dynamical heterogeneity in the interfacial water molecules at the capillary wave fronts. The same features are observed in Figure 6(B) and Figure 6(C) for water:vapor system with AMOEBA water model and the water:n-hexane system. Therefore, for both water:vapor and water:n-hexane interfaces, the changes in the HB dynamics at the interfacial region derive primarily from the interfacial water molecules at the capillary wave fronts. Further, the interfacial

water

molecules

show

significant

dynamical

heterogeneity

complementary to the structural heterogeneity reported in Section III.C.

24


that

is

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Figure 6. The average HB lifetime (τHB) and the average NHB lifetime (τNHB) for the interfacial water molecules, non-interfacial water molecules, and all the water molecules as a function of distance to the Gibbs dividing surface. (A) water:vapor interface with TIP3P/Ew water model, (B) water:vapor interface with AMOEBA water model, (C) water:nhexane interface with TIP3P/Ew water model. Contribution from the two dynamic mechanisms (see Figure 1) are investigated.

25



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Conclusions The structural and dynamical properties of waters at the capillary wave fronts of the water:vapor and the water:n-hexane interface has been studied using molecular dynamics simulations. The results have been analyzed using a unique combination of the ITIM method the slab-layering analyses. The analyzed structural descriptors include the dipole orientation distribution, the average number of hydrogen bonds per water, and the interconnectedness of the hydrogen bond network (cyclic coefficient and cyclic number). The dynamical descriptors include the average hydrogen bond lifetime, the average nonhydrogen–bonded lifetime (or average hydrogen bond breakage duration), considering the HB breakage and reformation mechanisms. These data show that both the structural and dynamic properties of water are disturbed by the interface up to 4 Å (6 Å) deep into the water phase from the Gibbs dividing surface for the water:vapor (water:n-hexane) interface. The perturbation derives predominantly from the interfacial water molecules, which are the molecules located right at the capillary wave fronts of the interfaces, while the non-interfacial molecules are nearly unperturbed. Though to some extent these observations have been discussed in prior literature, this study further demonstrates that the interfacial water molecules are heterogeneous across the interfacial region and their structural and dynamical properties depend on their locations within the capillary wave. The heterogeneity is manifested in terms of not only the dipole orientation but also the HB structures and HB dynamics. Heterogeneity within the capillary wave may be highly relevant to kinetically driven processes at the interfaces, for example transport or chemical

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reactions that depend upon solvent organizations and dynamics (e.g. dissociative metalligand complexation reactions).

Associated Content Supporting Information Details of the force field parameters, the capillary wave theory, surface tension and interfacial width, HB analysis within consecutive surface layers, and the additional HB properties for the water:vapor and water:n-hexane interfaces.

Acknowledgements This work is supported by a grant from Department of Energy, Basic Energy Sciences Heavy Element program (DE-SC0001815). This research used resources of the Oak Ridge Leadership Computing Facility located in the Oak Ridge National Laboratory, which is supported by the Office of Science within the Department of Energy under Contract No. DEAC05-00OR22725. Imre Bakó acknowledges the partial financial support of the Hungarian Scientific Research Fund (grant OTKA K108721).

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(66) Ozkanlar, A.; Zhou, T. C.; Clark, A. E. Towards a Unified Description of the Hydrogen Bond Network of Liquid Water: A Dynamics Based Approach. J. Chem. Phys. 2014, 141. (67) Galamba, N. Water Tetrahedrons, Hydrogen-Bond Dynamics, and the Orientational Mobility of Water around Hydrophobic Solutes. J. Phys. Chem. B 2014, 118, 4169-4176. (68) Dang, L. X.; Chang, T. M. Molecular Dynamics Study of Water Clusters, Liquid, and Liquid-Vapor Interface of Water with Many-Body Potentials. J. Chem. Phys. 1997, 106, 81498159. (69) Verde, A. V.; Bolhuis, P. G.; Campen, R. K. Statics and Dynamics of Free and HydrogenBonded Oh Groups at the Air/Water Interface. J. Phys. Chem. B 2012, 116, 9467-9481.

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Structural and Dynamic Heterogeneity of Capillary Wave Fronts at

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