Investigation of the Liquid-Vapor Interface of Water-Formamide

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Investigation of the Liquid-Vapor Interface of Water-Formamide Mixtures by Computer Simulation and Intrinsic Surface Analysis Balint Kiss, Balázs Fábián, Abdenacer Idrissi, Milán Sz#ri, and Pal Jedlovszky J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05874 • Publication Date (Web): 01 Aug 2018 Downloaded from http://pubs.acs.org on August 7, 2018

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The Journal of Physical Chemistry

Investigation of the Liquid-Vapor Interface of WaterFormamide Mixtures by Computer Simulation and Intrinsic Surface Analysis Bálint Kiss,1,2 Balázs Fábián,3,4 Abdenacer Idrissi,2 Milán Szőri,1 and Pál Jedlovszky5* 1

Institute of Chemistry, University of Miskolc, Egyetemváros A/2, H-3515 Miskolc, Hungary

2

University of Lille, Faculty of Sciences and Technologies, LASIR (UMR CNRS 8516), 59655 Villeneuve d’Ascq, France

3

Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, Szt. Gellért tér 4, H-1111 Budapest, Hungary

4

Institut UTINAM (CNRS UMR 6213), Université Bourgogne Franche-Comté, 16 route de Gray, F-25030 Besançon, France

5

Department of Chemistry, Eszterházy Károly University, Leányka utca 6, H3300 Eger, Hungary

*

Electronic mail: [email protected]

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Abstract

Molecular dynamics simulations of the liquid-vapor interface of water-formamide mixtures of different compositions, spanning the entire composition range, have been performed on the canonical (N,V,T) ensemble at 300 K. The layer of the surface molecules has been identified and analyzed in detail in terms of the intrinsic Identification of the Truly Interfacial Molecules (ITIM) method. The obtained results reveal the strong lateral hydrogen bonding ability of the surface molecules in these systems. Thus, surface molecules form a percolating lateral hydrogen bonding network in every case, which makes the surface layer noticeably more compact than the subsequent subsurface molecular layers. Unlike molecules mix with each other even on the molecular scale. Neither strong adsorption, nor lateral selfassociation of any of the components in the surface layer has been observed, although formamide exhibits a slight ability of being accumulated in the surface layer. Further, in contrast with the aforementioned percolating lateral hydrogen bonding mixed network of the surface water and formamide molecules, no such network of the like molecules is observed, even in the case of their large excess at the surface of the mixed systems. The orientational preferences of the surface molecules are also governed by the requirement of maximizing their hydrogen bonds. The main preference of both molecules is found to be the parallel alignment with the macroscopic plane of the liquid surface. The dynamics of the surface molecules is also dominated by the hydrogen bonding of unlike pairs. Thus, water stabilizes the stay of the formamide molecules at the liquid surface, while formamide immobilizes water molecules within the surface layer, preventing them from considerable lateral diffusion during their entire stay at the liquid surface.

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1. INTRODUCTION

Liquid formamide (FA) and its aqueous mixtures are systems of great importance both from the scientific and industrial point of view. Thus, among others, these systems are extensively used as plasticizers,1 softener for papers, and solvent of alkaline and alkaline earth metals as well as heavy metal salts.2 From the theoretical point of view, the importance of formamide comes from the fact that it is the smallest molecule containing a peptide bond. Thus, aqueous formamide solutions are often used as biomimetic models to study the formation and breaking of both peptide3 and hydrogen bonds4,5 in hydrated proteins and polypeptides as well as the role of water in determining the kinetics and thermodynamics of the reactions of these macromolecules.6 Similarly to water, formamide molecules can both accept (by the O atom) and donate (by the N atom) two H atoms for hydrogen bonding. As a consequence, liquid formamide consists of an infinite, percolating network of hydrogen bonds,7,8 which results in an unusually high dielectric constant of 109 of this liquid.9 Since water is also known to be a hydrogen bond network forming liquid,10,11 water and formamide molecules can substitute each other in their hydrogen bonding network,12 and hence the mixing of these two liquids is often considered as being nearly ideal.13,14 Indeed, these two compounds are fully miscible with each other,15 and the thermodynamic properties, such as energy, entropy and free energy, depend almost linearly on the composition.16 Further, the change of these quantities upon mixing was found to be very close to the ideal value (i.e., zero for the energy, and –R Σxi lnxi for the entropy, R and xi being the gas constant and the mole fraction of the ith component, respectively).16-19 Due to the above reasons, several potential models have been proposed in the literature,20-25 and the properties of liquid formamide7,8,22-27 as well as of water-formamide mixtures5,12-14,19,28-31 have been thoroughly studied by computer simulation methods. Surprisingly, however, we are not aware of any such study concerning the liquid-vapor interface of these systems, although the above questions concerning the mixing of these molecules as well as the biomimetic modeling of polypeptides are also highly relevant at the surface of their liquid phase. Further, the potential key role formamide might have played in the formation of several building blocks of biomacromolecules, such as nucleotides and amino acids, during the prebiotic evolution32-34 as well as the role of formamide as atmospheric pollutant35 are all closely related to the behavior of formamide at the surface of its aqueous solutions.



When simulating a liquid-vapor interface, one has to take into account the fact that the liquid surface is not flat on the microscopic length scale; instead, it is corrugated by capillary waves. Although the importance of this fact was already recognized and taken into account in the very first simulations of liquid-vapor interfaces,36,37 in the vast majority of the early simulations of such systems the effect of the capillary waves was simply neglected, and the flat Gibbs dividing surface was used in the analyses instead of the real, wavy surface of the liquid phase. This treatment was later shown to introduce a systematic error of unknown magnitude into several calculated properties (e.g., structure, composition) of the interface,38,39 and this systematic error can even propagate to the thermodynamic properties of the system.40 Proper treatment of the capillary waves requires the determination of the real, capillary wave corrugated intrinsic liquid surface (and define distances from the interface relative to this surface rather than to the (fictitious) flat Gibbs dividing surface), and, correspondingly the determination of the full list of the truly interfacial molecules (i.e., the ones staying right at the boundary of the two phases). Since the pioneering work of Chacón and Tarazona,41 several such methods have been proposed in the literature,38,42-44 some of which does not even limited by the assumption that the interface is macroscopically flat.45-47 In the past decade, intrinsic surface analyzing methods have been widely and successfully applied to study the properties of the surface of several neat molecular38-40,48-51 and ionic liquids,52-56 their mixtures,57 as well as of binary molecular liquid mixtures58-63 and aqueous electrolyte solutions.64 In such studies, a number of interface related problems have been addressed, such as adsorption,58-63 alignment38-40,48-63 and dynamics65-67 of the interfacial molecules, association of molecules at the liquid surface,61,68 explanation of the surface tension anomaly of water,69,70 investigation of the properties of Newton black films,71 the immersion depth of various surfactants in the liquid phase,72 or the plausibility of the ‘HCN World’ hypothesis concerning the prebiotic synthesis of biomolecules,61 analysis of the contribution of the subsequent subsurface molecular layers to the surface tension,73 calculation of the profiles of various physical quantities, such as the energy,74 density,41,43,74-78 solvation free energy,79,80 lateral pressure73,74 and electrostatic potential64 relative to the intrinsic liquid surface, etc. Among the various intrinsic surface analyzing methods, the Identification of the Truly Interfacial Molecules (ITIM)38 turned out to be an excellent compromise between computational cost and accuracy.44 In the ITIM analysis, the interfacial molecules are scanned by throwing (virtual) spherical test particles of a given radius to the surface of the liquid phase to be analyzed from the bulk opposite phase along test lines perpendicular to the macroscopic plane of the surface.


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Each test particle is stopped once it hits the first molecule belonging to the phase of interest. The molecules that are touched by at least one of these test spheres are “visible” from the opposite phase, and hence they are regarded as being interfacial, while those molecules which are not touched by any of the test spheres are not seen from the opposite phase, and thus they are regarded as being beneath the liquid surface, in the bulk liquid phase.38 The method can easily treat systems of partial miscibility, i.e., when the concentration of certain molecules is not negligible even in the opposite phase.40,57 Clearly, the analysis requires the use of a freely chosen parameter, i.e., the radius of the probe sphere. However, the use of such a free parameter is inherent in any intrinsic analysis,44 and there are physically meaningful ways of setting its value.38,44,81 A great advantage of the ITIM method is that by removing the molecules identified as belonging to the surface layer, and repeating the entire analysis, the full set of molecules constituting the second (third, etc.) subsurface molecular layers can also easily be identified.38 In this paper, we investigate in detail the properties of the liquid-vapor interface of water-formamide mixtures of various compositions, ranging from neat water to neat formamide, by molecular dynamics (MD) computer simulation and ITIM surface analysis. Among others, the adsorption of formamide in the surface layer, the lateral self-association, orientation, and dynamics of the surface molecules, as well as their lifetime and at the liquid surface are discussed in detail. The remainder of the paper is organized as follows. In section 2, details of the calculations performed, including MD simulations and ITIM analyses are provided. In section 3, the obtained results are presented and discussed in detail, while the main conclusions of this study are summarized in section 4.

2. COMPUTATIONAL DETAILS

Molecular dynamics simulations of the liquid-vapor interface of water-formamide mixtures of different compositions, including the two neat systems, have been performed on the canonical (N,V,T) ensemble at the temperature of 300 K. The basic simulation box has contained 4000 molecules, among which 0, 400, 800, 1200, 1600, 2000, 2400, 2800, 3200, 3600, and 4000 have been formamide in the different systems. These systems are referred to here as the 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100% FA systems, respectively. The X, Y and Z edges of the basic box have both been 300 Å, 50 Å, and 50 Å long, respectively, X being the axis perpendicular to the macroscopic liquid surface.



Formamide molecules have been described by the CHARMM27 force field,23 while water was modeled by the rigid SPC/E potential.82 The choice of these potential models has been dictated by the fact that this model combination turned out to be the best in describing the mixing properties of water and formamide.16 All molecules have been treated as rigid bodies in the simulations; their geometries have been kept unchanged using the LINCS algorithm.83 The energy of the system has been pairwise additive, i.e., the total potential energy of the system has been calculated as the sum of the pair interaction energies of the molecules, and the interaction energy of a molecule pair has been obtained as the sum of the Lennard-Jones and charge-charge Coulomb contributions of all pairs of their respective atomic interaction sites. The interaction parameters of the two models used in the simulations are collected in Table 1. All interactions have been truncated to zero beyond the center-center cut-off distance of 15 Å; the long-range part of the electrostatic interaction has been taken into account by means of the smooth variant of the Particle Mesh Ewald method84 using a mesh spacing of 1.2 Å. The simulations have been performed with the GROMACS 5.1.4 program package.85 The temperature of the systems has been controlled with the Nosé-Hoover thermostat86,87 with a time constant of 0.2 ps. The equations of motion have been integrated in time steps of 1 fs. At the beginning of each simulation, the required number of water and formamide molecules have been placed in a basic simulation box the edges Y and Z of which have been 50 Å, while the length of the X edge has roughly corresponded to the density of the liquid phase. After proper energy minimization, these bulk liquid systems have been equilibrated for 2 ns. Then the X edge of the basic box has been increased to 300 Å, resulting in a system containing the liquid-vapor interface. The interfacial systems have been further equilibrated for 4 ns. Finally, during the 4 ns long production phase of the simulations, 4000 equilibrium sample configurations, separated by 1 ps long trajectories each, have been dumped for the subsequent analyses. All results have been averaged over the two liquid-vapor interfaces present in the basic box. The intrinsic surface of the liquid phase has been determined on the sample configurations by the ITIM method.38 In the ITIM analysis, a probe sphere of the radius of 1.25 Å has been moved along test lines parallel with the X edge of the basic box, arranged in a 125 × 125 grid. The entire analysis has been repeated three times per system; hence, the molecules constituting the first three molecular layers at the liquid surface have been separately identified. An equilibrium snapshot of the surface portion of the 50% FA system is shown in Figure 1 as taken out from the simulation, in which the molecules belonging to the


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first three layers at the liquid surface are separately indicated. Further, the surface tension of the systems simulated, calculated through the difference of the lateral and normal pressure components,88 are collected in Table 2. As is seen, both models underestimate the surface tension of the corresponding neat liquid (i.e., 72,8 mN/m for water, 58.2 mN/m for formamide) by about 15%, which is also reflected in the somewhat too low surface tension values of the liquid. However, apart from this slight downshift, the composition dependence of the surface tension follows the experimental trend.

3. RESULTS AND DISCUSSION

3.1. Density Profiles. The (non-intrinsic) number density profiles of the water and formamide molecules as well as the mass density profiles of the entire systems and their surface layer along the macroscopic surface normal axis, X, are shown in Figure 2, as obtained in selected systems. As is seen, not only the mass density profiles change smoothly between the liquid and vapor phase, but the number density profiles of both molecules also show rather little structure at the interface: apart from a tiny peak occurring at the liquid side of the interface on the formamide density profiles in the systems of low FA mole fraction, these profiles also change smoothly between the two phases. This result is in contrast with our previous findings concerning the liquid surface of aqueous solutions of methanol,58 acetonitrile,59 dimethyl sulfoxide,60 and HCN,61 and suggests that, in contrast with the above solutes, formamide does not show considerable adsorption at the surface of its aqueous solutions. To further investigate this point, we show the composition of the first three molecular layers at the liquid surface (in terms of the FA mole fraction) as a function of the composition of the bulk liquid phase in Figure 3. The FA mole fraction in the bulk liquid phase has simply been estimated from the average molecular number densities of water and formamide in the 10 Å wide liquid slab in the middle of the basic simulation box (i.e., at |X| < 5 Å). As is seen from Fig. 3, FA is only very weakly adsorbed at the liquid surface. Thus, in systems of low FA concentration, the mole fraction of FA in the surface layer is about twice as much as in the bulk liquid phase, while in systems of higher FA concentration the difference between the surface and bulk mole fraction values remains below 50%. This behavior is in a clear contrast with what was seen at the surface of the aqueous solution of, e.g., HCN, where an order of magnitude difference was observed between the surface and bulk mole fractions of the solute.61 Furthermore, again in a clear contrast with the behavior of the aqueous solutions of



HCN,61 acetonitrile,59 and acetone,63 this adsorption is strictly restricted to the first molecular layer at the liquid surface; the composition of the second and third layers always agrees with that of the bulk liquid phase. When comparing the mass density profiles of the entire systems with that of their surface layer (Fig. 2), it is seen that the surface layer extends well into the X range of constant mass density in every case. Conversely, the density profile of the second and even the third layer (not shown) strongly overlap with the X range of intermediate densities between the two phases in every system. This finding stresses the importance of employing an intrinsic method in analyzing the surface of these systems, clearly demonstrating that the identification of the interfacial region through the non-intrinsic density profile results in the misidentification of a large number of molecules both as interfacial and non-interfacial ones. As it is expected,89 the density profiles of the individual molecular layers beneath the liquid surface can be very well fitted by Gaussians. The width of these Gaussians, σ, can serve as an estimate of the width of the corresponding layer. The σ values obtained in the first, second, and third molecular layer beneath the surface in the various systems (denoted by

σL1, σL2, and σL3, respectively) are summarized in Table 2. It is seen that, upon approaching the interface, the σ values in the mixed systems become smaller, indicating that the corresponding molecular layers get progressively more compact. Thus, the second and third layers are 3-5% and 5-10% thicker than the first layer in every mixed system. This finding is again in contrast with what was seen at the surface of other aqueous liquid mixtures,61-63 and suggests the presence of a strong H-bonding network in the surface layer, which can partly compensate the energy loss of the surface molecules due to the vicinity of the vapor phase, and which makes the surface layer unusually compact. This point is further addressed in a subsequent section.

3.2. Lateral Distribution of the Surface Molecules. As it has been discussed above, the water and formamide molecules do not show considerable microscopic separation along the macroscopic surface normal axis, X, as the compositions of the subsequent molecular layers are rather similar to each other and to that of the bulk liquid phase. To further analyze the arrangement of the two kinds of molecules around each other, here we investigate the possibility of their lateral microscopic self-association within the surface layer. For this purpose, we have projected the centers-of-mass of the surface layer molecules to the macroscopic plane of the interface, YZ, and calculated the area distribution of the Voronoi


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cells of these projections. In a two-dimensional set of seeds (i.e., the projections of the molecular centers), the Voronoi cell of a given seed is the locus of the points in the plane that are closer to this seed than to any other one.90-92 If the seeds are evenly distributed in the plane, the area of their Voronoi cells, A, follows a gamma distribution,67,93,94 i.e., P ( A) = a Aν −1 exp(−νρA) .

(1)

In this equation, ν and ρ are free parameters, while the factor a normalizes this probability distribution to unity. On the other hand, if the seeds show considerable self-association, leaving large empty areas between them, the Voronoi cells of the seeds located at the boundary of these empty domains are considerably larger than those being inside the selfassociates. As a consequence, the corresponding P(A) distribution deviates considerably from eq. 1, exhibiting a long, exponentially decaying tail at large area values.95 To check the possible self-association of the like molecules in binary systems, the P(A) distribution should be calculated considering only one type of the molecules, and disregarding the other one. Thus, self-associates of the disregarded component are transformed to empty domains, and hence the P(A) distribution of the component considered exhibits the exponentially decaying tail. On the other hand, in the lack of such self-associates of the disregarded component, the P(A) distribution of the component considered still follows eq. 1.96 Figure 4 shows the P(A) distribution of the projections of the surface molecules to the YZ plane, considering both kinds of molecules as well as only formamides and only waters, as obtained in selected systems. As is seen, when one component is disregarded, the resulting distribution is broader than that obtained by considering both components, and gets progressively broader with increasing mole fraction of the disregarded component. More importantly, the P(A) distributions obtained by considering only one of the components can always be reasonable well fitted by eq. 1. To magnify the small deviations from the fit at large area values, the obtained data are shown on a logarithmic scale in Fig. 4. Yet, slight deviations of the simulated data from eq. 1 is only seen at large A values in the systems of low FA concentration, indicating that no strong self-association of the like molecules occurs even within the surface layer. In other words, water and FA molecules turn out to be miscible with each other on the molecular scale even at the surface of their mixtures. This behavior of FA is again in a clear contrast with that of HCN,61 acetonitrile,59 and acetone,63 and is in accordance with the claim that the mixing of FA with water is nearly ideal.13,14,16



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3.3. Hydrogen Bonding at the Liquid Surface. The observed molecular scale miscibility of the water and formamide molecules in the surface layer suggests that, similarly to the bulk liquid phase,12 they can substitute each other in the hydrogen bonding network, and together form an infinite, percolating two-dimensional network at the liquid surface. The formation of such a percolating mixed network of water and formamide molecules has already been observed in three dimensions, in the bulk liquid phase.12 Further, a two-dimensional percolating H-bonding network of the molecules is also known to exist at the surface of water at room temperature.69,70 To address this point, we have calculated the size distribution of the hydrogen bonding clusters in the surface layer of the systems simulated. The size of a cluster, n, is simply the number of molecules forming it (irrespectively of whether they are water or FA). In order to consider only the two-dimensional, surface clusters, all these molecules have to be part of the surface layer. Two molecules belong to the same cluster if they are connected by a chain of H-bonded molecule pairs. Two molecules are considered here as being H-bonded to each other if (i) the distance of the H-donor (i.e., water O or formamide N) and H-acceptor (i.e., water O or formamide O) atoms is less than 3.5 Å, and (ii) the distance of the donated H atom and its acceptor is less than 2.4 Å. These cut-off distances correspond to the first minimum position of the corresponding partial pair correlation functions. (It should be noted that although formamide is able to form also weak, C-H….O type hydrogen bonds, we use the term ‘hydrogen bond’ referring only to strong, O-H or N-H donated H-bonds throughout this paper.) The size distribution of the surface clusters, P(n), is shown in Figure 5 as obtained in the systems simulated. At the percolation threshold, the P(n) distribution of an infinitely large system follows a power law, i.e.,

P(n) ~ n −α .

(2)

with the universal exponent a = 2.05 in two-dimensional systems.97 The critical line corresponding to the P(n) distribution at the percolation threshold is also indicated in Fig. 5. As is seen, the calculated P(n) distribution exceeds the critical line at large cluster sizes in every case, indicating that the mixed H-bonding clusters of the water and FA molecules within the surface layer indeed span the entire liquid surface. By contrast, the P(n) distribution of both the clusters built up solely by water molecules at the surface of the 10%


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FA system, and those built up solely by formamide molecules at the surface of the 90% FA system drop below the critical line at small n values, and remain below it in the entire n range (see the inset of Fig. 5). This finding shows that, contrary to the mixed clusters, the surface clusters of only like molecules do not span the liquid surface even if this component is in a large excess in the surface layer.

3.4. Surface Orientation. The full description of a rigid molecule relative to an external direction (and, thus, also to an external plane) requires two independent orientational variables. Therefore, the full description of the orientational statistics of such molecules relative to an external direction or plane can only be done through the bivariate joint distribution of these two variables.98,99 Clearly, the two angular polar coordinates of the external vector in a local Cartesian frame fixed to the individual molecules represent a sufficient choice of such an independent orientational variable pair. However, considering also the fact that the polar angle ϑ is the angle between two general spatial vectors, but φ is formed by two vectors that are restricted to lay in a given plane (i.e., the xy plane of the local frame) by definition, uncorrelated orientation of the molecules with the external plane (liquid surface) corresponds to a uniform bivariate distribution only if cosϑ and φ are chosen to be the orientational variables.98,99 In order to analyze the orientational distribution relative to the macroscopic plane of the liquid surface, YZ, here we define the above local Cartesian frames in the following way. For water, its origin is located at the O atom, axis z points along the main symmetry axis of the molecule, oriented in such a way that the z coordinates of the H atoms are positive, axis y is parallel with the line connecting the two H atoms, while axis x is the molecular normal. For FA, the origin is at the N atom, axis z is the molecular normal, axis x points along the N-C bond from the N to the C atom, while axis y is perpendicular to both axes x and z, and is oriented in such a way that the y coordinate of the O atom is positive and that of the H atom is negative. The definition of these local frames as well as of the polar angles ϑ and φ, describing the alignment of the macroscopic surface normal vector, X, in these frames are illustrated in Figure 6. By our convention, the surface normal vector, X, is oriented in such a way that it points from the liquid to the vapor phase. It should also be noted that the symmetry of the molecules restricts the range of cosϑ and φ that corresponds to different orientations. Hence, the above frames have always been chosen in such a way that the relations φ ≤ 90o (for water) and 0 ≤ cosϑ (for FA) hold.



In order to investigate also the effect of the local curvature of the liquid surface on the preferred orientations, we have also calculated the P(cosϑ,φ) orientational distributions, besides the entire surface layer, also in its separate regions A, B, and C. These regions are defined through the mass density profile of the surface layer, as follows. Region B covers the X range in which the density of the surface layer exceeds half of its maximum value, while regions C and A cover the X ranges located closer to and farther from the bulk liquid phase, respectively, than that of region B. Thus, region C covers typically the negatively curved troughs, while region A the positively curved crests of the molecularly rough liquid surface. The definition of zones A, B, and C of the surface layer is illustrated in Fig. 6. The P(cosϑ,φ) orientational maps of the water and FA molecules are shown in Figures 7 and 8, respectively, as obtained in the entire surface layer as well as in its separate regions A, B, and C in selected systems. The preferred orientation of the water molecules in the entire surface layer as well as in its highest populated region, B, corresponds to cosϑ = 0 and φ = 0o, while that of the formamide molecules to cosϑ = 1. (It should be noted that, in the case of cosϑ = 1, the vector X is projected to a single point in the xy plane of the local frame (see Fig. 6), and hence all points of the P(cosϑ,φ) orientational map laying along the cosϑ = 1 line correspond to the same orientation.) These preferred orientations, denoted here as Iw (for water) and IFA (for formamide) and illustrated in Figure 9.a, correspond to the parallel alignment of the respective molecules with the macroscopic plane of the surface, YZ. The planar FA molecules can donate and accept hydrogen bonds within their molecular plane. Further, in cases of water-donated H atoms, the donor water molecule can still lay in this plane, while in cases of water-accepted H-bonds the water molecule has to only slightly twist out from this plane, as reflected in the small shift of the Iw peak of the water orientation map to somewhat larger cosϑ values with increasing FA concentration. Thus, the observed preferential alignment of both molecules with the macroscopic plane of the surface enables them to form a strong H-bonding network at the liquid surface. The possible hydrogen bonding alignments of a FA and a water molecule, both of which are aligned in their preferred surface orientation, are illustrated in Figure 9.b. Both molecules prefer somewhat different orientations at the tips of the crests (in region A) and in the bottom of the troughs (in region C), i.e., at the strongly positively and negatively curved portions, respectively, of the molecularly rough liquid surface. Thus, the peak of the water orientation map is shifted to negative cosϑ values in region A, and to C positive cosϑ values in region C. In the corresponding orientations, marked as I A w and I w ,


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respectively, and shown also in Fig. 9.a, the water molecule is tilted from the parallel alignment with the YZ plane, and points towards the bulk liquid phase (in orientation I A w ) and towards the vapor phase (in orientation I C w ) with its H atoms. Further, in region A, the peak of the preferred orientation of the FA molecules is shifted to smaller cosϑ values along the

φ = 0o (or φ = 360o, being equivalent with the former, see Fig. 6) line. In this orientation, marked here as IIFA, the plane of the formamide molecule is tilted somewhat from the YZ plane, pointing with the CHO group to the vapor, and with the NH2 group to the liquid phase. In region C, the preferred orientation of the FA molecules corresponds to cosϑ = 0 and

φ = 180o, and highly preferred alignments also extend to larger cosϑ values. The corresponding orientation, marked here as IIIFA, is perpendicular to the macroscopic plane of the surface, and the NH2 group points straight to the vapor phase. The extension of this peak to larger cosϑ values corresponds to the tilt of the molecule from the perpendicular alignment in such a way that, within the constraint set by the alignment of the molecular plane, the NH2 group still points as straight to the vapor phase as possible. Orientations IIFA and IIIFA are also illustrated in Fig. 9.a. The orientational preferences observed in regions A and C are all governed by the requirement of maximizing the number of possible hydrogen bonds a surface molecule can form. Thus, in orientation I A w the water molecule sacrifices one of its H-bonds, while three of its possible hydrogen bonding directions (i.e., two O-H bonds and a lone pair) point flatly toward the bulk liquid phase, straddling along the locally positively curved surface. Conversely, in orientation I C w one hydrogen bonding direction (i.e., a lone pair) points straight to the bulk liquid phase, while the other three ones straddle along the locally negatively curved surface, pointing flatly to the vapor phase. In this way, water molecules C oriented in alignments I A w and I w in regions A and C, respectively, can safely maintain three

and four H-bonds, respectively, with their neighbors. Similarly, in alignment IIFA the formamide molecule sacrifices one of the two possible H-accepting directions of its O atom, while the other one as well as the two N-H bonds point flatly toward the bulk liquid phase. In alignment IIIFA, preferred at locally negatively curved portions of the surface, the two N-H bonds point flatly toward the vapor phase, straddling along the curved surface. Thus, FA molecules in alignment IIFA in region A can maintain three, while those of alignment IIIFA in region C four hydrogen bonds with their neighbors. It



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is also clear that an FA molecule of alignment IIFA can easily form a H-bond with a water A molecule of I C w , while a formamide of orientation IIIFA can hydrogen bond to a water of I w .

Possible hydrogen bonding patterns of neighboring surface FA and water molecules, both aligned in one of their preferred orientations, and their relation with the local curvature of the molecularly rough surface are illustrated in Figure 9.c.

3.5. Dynamics of the Surface Molecules. To investigate the dynamics of the molecules within the surface layer, we have calculated their survival probability and mean residence time as well as their lateral diffusion coefficient, D||, within the surface layer. The survival probability, L(t), is defined as the probability that a molecule that belongs to the surface layer at t0 will stay in this layer up to t0+t. Since the departure of the molecules from the liquid surface is governed by first order kinetics, the L(t) survival probability is expected to follow an exponential decay, and hence can be fitted by the function exp(-t/τsurf), where τsurf is the mean residence time of the molecules in the surface layer. However, besides leaving the liquid surface permanently, the molecules may departure from the surface layer also temporarily, due to a fast oscillatory move. Therefore, the L(t) data can be well fitted by the sum of two decaying exponentials, i.e., by the function L(t ) = A1 exp(−t / τ osc ) + A2 exp(−t / τ surf ) .

(3)

The first of these two exponentials corresponds to the fast oscillatory move, τosc being its characteristic time, while the second one corresponds to the permanent departure of the molecules from the surface. The L(t) data obtained both for the water and FA molecules in selected systems are shown in Figure 10. To emphasize the exponential decay of the curves, the insets show the same data on a logarithmic scale. The sum of the two exponential functions fitted to these data is also indicated. As is seen, the obtained fit is almost perfect in every case. The characteristic time of the fast, oscillatory move, τosc, is always found to be 2.0 ± 0.5 ps, being smaller for the water than the FA molecules. Since this value is rather close to the trajectory length between two subsequent sample configurations of 1 ps, we cannot analyze this fast oscillatory motion of the surface molecules in more detail. The mean surface residence time values, τsurf, are collected in Table 2 for both molecules. As is seen, formamide molecules stay considerably, i.e., by 4-6 times longer at the liquid surface than waters. Interestingly, the mean surface residence time of the water molecules does not show any apparent composition dependence


Page 15 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(although it is slightly larger in neat water than in the mixed systems). Although the mean surface residence time depends, besides the strength of the lateral H-bonds, also on a number of other factors (e.g., the number and strength of the off-layer hydrogen bonds66,67), this finding correlates well with the fact that in the surface layer the average interaction energy of a hydrogen bonded water-water and water-FA pairs both turn out to be -20.7 kJ/mol. On the other hand, the τsurf value of FA clearly decreases with increasing formamide concentration, being about 30% smaller at the surface of neat formamide than in the 10% FA system. This finding indicates that the presence of water stabilizes the stay of the formamide molecules at the surface of the liquid phase of their mixtures. The lateral diffusion coefficient of the molecules, D||, can be obtained through the Einstein relation,100 i.e.,

D|| =

MSD , 4t

(4)

where MSD is the mean square displacement of the molecules within the macroscopic plane of the liquid surface, YZ, by fitting a straight line to the calculated MSD vs. t data. The time evolution of the MSD of the individual molecules has only been calculated during which they have remained in the surface layer. The linear fitting of the MSD(t) data has been done, however, only above 5 ps, in order to ensure that the molecules are no longer in the ballistic regime, and their mobility is already governed by diffusive motion. The MSD(t) data corresponding both to the water and the FA molecules, together with the straight lines fitted to them, are shown in Figure 11 as obtained in selected systems. Further, the D|| values obtained for both types of molecules from eq. 4 are summarized in Table 2. In analyzing the lateral diffusion of the molecules within the surface layer, first the relation of their mean surface residence time, τsurf, and the characteristic time of their diffusion, τD, has to be checked. Thus, in cases when τsurf is larger than τD, the molecules exhibit considerable diffusion within the surface layer during their stay there. On the other hand, if the relation τD > τsurf holds, surface diffusion cannot be discussed meaningfully, as the surface lifetime of the molecules is simply too short for considerable diffusion occurring within this time. In this case, the mobility of the molecules is inherently three-dimensional, not being limited to the liquid surface even for a short time. The characteristic time of the two-dimensional diffusion can be calculated as67,101



τD =

Page 16 of 43

Am , 4D||

(5)

2 LY LZ < N surf >

(6)

where

Am =

is the average area per molecule in the surface layer, LY, LZ, and being the lengths of the basic box in the Y and Z directions and the mean number of the surface molecules, respectively, and the factor 2 in eq. 6 accounts for the two interfaces present in the basic box. The τD values obtained for the water and FA molecules in the different systems simulated are also included in Table 2. As is seen, for water, τsurf is larger than τD only at the surface of the neat system; these two time scales are roughly equal in the 10% FA system (similarly to what was seen previously at the surface of a neat Lennard-Jones liquid65), while in the systems of higher formamide concentration the diffusion of the water molecules clearly occur on a larger time scale than their mean surface residence time, indicating that water molecules typically leave the surface of these systems before they could make considerable diffusion there. Since the mean surface residence time of the water molecules is insensitive to the composition of the system, the reason for this behavior is the increase of τD with increasing formamide concentration. In other words, our finding indicates that formamide molecules stabilize the water molecules at their position in the surface during the entire time scale of their stay at the surface of such mixtures. It is also seen that, for formamide, τsurf is always noticeably, i.e., by a factor of 2-5 larger than τD, indicating that formamide molecules do diffuse at the liquid surface of their aqueous mixtures. The surface diffusion coefficient of formamide is rather insensitive to the composition, as it only exhibits a slight (i.e., about 30%) decrease in the entire composition range with increasing FA mole fraction. It is also seen that the surface diffusion of the FA molecules is considerably slower in their aqueous mixtures than that of the water molecules at the surface of neat water, i.e., where they do exhibit a noticeable diffusion at the liquid surface.

4. SUMMARY AND CONCLUSIONS

In this paper, the intrinsic liquid surface of water-formamide mixtures of different compositions has been investigated in detail by means of molecular dynamics simulations and ITIM analysis. The general picture that emerges from the various results of this study is that 16 Environment ACS Paragon Plus

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the surface properties of these mixtures are governed by the strong and extensive hydrogen bonding between the surface molecules. Similarly to the bulk liquid phase,12 water and FA molecules turn out to be able to substitute each other even in the two-dimensional H-bonding network at the surface of their mixtures. Orientational preferences of the surface molecules are found to be governed by the requirement of maximizing the H-bonds they can form. Thus, both molecules prefer parallel alignment with the macroscopic plane of the liquid surface. Further, at the positively curved crests and negatively curved troughs of the molecularly rough surface preferences for such orientations are emerging that enable the molecules to maintain three and four stable H-bonds, respectively, at these strongly curved surface portions. The two-dimensional, lateral H-bonding network formed by both kinds of molecules is clearly percolating at the liquid surface in the entire composition range. This strong lateral hydrogen bonding makes the surface layer more compact than the subsequent molecular layers, a feature that is in a clear contrast with what was previously observed at the surface of other aqueous solutions.61-63 Furthermore, the water and FA molecules of the surface layer are found to be miscible with each other even on the molecular scale. Thus, no large selfassociates of the like molecules are found at the surface in any composition. As a consequence, in contrast with the percolating lateral mixed network of both molecules, no such network of only like molecules is observed at the surface of the mixed systems even if the given component is in a large excess. In accordance with their aforementioned lateral mixing on the molecular scale, no strong association of the like molecules is seen along the surface normal direction either, as no strong ability of the components for considerable surface adsorption is seen; the mole fraction of FA is only found to be slightly larger in the surface layer than in the subsequent molecular layers and in the bulk liquid phase. The observed dynamical behavior of the surface molecules is also consistent with this general picture. Thus, due to their extensive hydrogen bonding, water molecules stabilize the stay of the FA molecules at the liquid surface. Furthermore, FA molecules immobilize the water molecules in the surface layer, preventing them from exhibiting considerable diffusion at the liquid surface during their entire stay there. Summarizing, our results indicate that, similarly to the bulk liquid phase,13,14,16 the mixing of the water and FA molecules is close to be ideal even at the liquid surface, as unlike molecules can substitute each other in the extensive hydrogen bonding network, and hence mix with each other even on the molecular scale.



Acknowledgements. The authors acknowledge financial support from the NKFIH Foundation, Hungary (project number 119732) and by the Hungarian-French TéT (PHC Balaton) program under project Nos. 36402ND (France) and TÉT_15-1-2016-0029 (Hungary). This research was supported by the European Union and the Hungarian State, cofinanced by the European Regional Development Fund in the framework of the GINOP-2.3.415-2016-00004 project, aimed to promote the cooperation between the higher education and the industry. M. Sz. gratefully acknowledges the financial support from the János Bolyai Research Scholarship of the Hungarian Academy of Sciences (BO/00113/15/7), and from the New National Excellence Program of the Ministry of Human Capacities (ÚNKP-17-4-IIIME/26). B. F. gratefully acknowledges the financial support from the New National Excellence Program of the Ministry of Human Capacities (ÚNKP-17-3-I).

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Sega, M. The Role of a Small Scale Cutoff in Determining Molecular Layers at Fluid Interfaces. Phys. Chem. Chem. Phys. 2016, 18, 23354-23357.

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Hess, B. P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 116-122.

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Essman, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, 8577-8594.

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Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, 1695-1697.

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Page 26 of 43

Page 27 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Tables Table 1. Interaction Parameters of the Molecular Models Useda molecule

formamide

water a

atom

q/e

σ/Å

ε/kJ mol-1

C

0.42

3.564

0.293

O

-0.51

3.029

0.502

H(C)

0.08

2.352

0.090

N

-0.69

3.296

0.837

H

0.35

0.400

0.192

O

-0.8476

3.166

0.650

H

0.4238

-

-

q is the fractional charge, σ and ε are the Lennard-Jones distance and energy parameters,

respectively.


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 28 of 43

Table 2. Various Properties of the Systems Simulated.a system

-1

γ/mN m

σL1/Å

σL2/Å

σL3/Å

τsurf/ps

D||/Å2ps-1

τD/ps

water

FA

water

FA

water

FA

0% FA

60.2

3.69

3.67

3.70

12.5

-

8.0

-

0.547

-

10% FA

55.2

3.97

4.08

4.22

11.3

67.8

11.7

13.3

0.448

0.393

20% FA

53.4

4.08

4.27

4.46

11.1

59.8

13.6

15.8

0.422

0.366

30% FA

53.1

4.15

4.37

4.55

11.1

55.0

14.9

17.9

0.412

0.345

40% FA

53.0

4.20

4.42

4.59

11.3

53.1

17.8

19.1

0.360

0.336

50% FA

52.7

4.27

4.50

4.63

11.3

51.0

17.8

20.3

0.376

0.331

60% FA

52.5

4.28

4.50

4.61

11.0

49.9

19.8

21.6

0.353

0.323

70% FA

51.5

4.31

4.52

4.61

11.3

49.2

20.3

22.3

0.356

0.324

80% FA

50.8

4.32

4.54

4.60

11.6

48.9

19.7

24.0

0.380

0.312

90% FA

51.4

4.42

4.61

4.66

11.3

48.9

18.8

24.4

0.408

0.316

100% FA

49.0

4.34

4.39

4.44

-

48.9

-

26.0

-

0.307

a

Error bars of the surface tension data are in the order of ±1 mN/m, and affect the last shown decimal digit of all other data.

28

ACS Paragon Plus Environment

Page 29 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure legends Figure 1. Equilibrium snapshot of the 50% FA system, as taken out from the simulation. Molecules belonging to the first, second, and third molecular layer beneath the liquid surface are marked by blue, red, and green colors, respectively; molecules located beneath the third subsurface molecular layer are marked by grey color. Lighter and darker shades of the colors correspond to the water and formamide molecules, respectively. The snapshot only shows the X > 0 Å half of the basic box.

Figure 2. Number density profile of the water (top panel) and formamide (second panel) molecules as well as the mass density profile of the entire system (third panel) and of the surface layer of the liquid phase (bottom panel) along the interface normal axis, X, as obtained from the simulations of different systems. Black solid lines: 0% FA system, red dashed lines: 20% FA system, green dotted lines: 40% FA system, blue dash-dotted lines: 60% FA system, orange dash-dot-dotted lines: 80% FA system, magenta short dashed lines: 100% FA system. The inset shows the mass density profile of the first three layers (with black, red, and green colors, respectively) in the equimolar system. All profiles shown are averaged over the two interfaces present in the basic simulation box.

Figure 3. Composition (in terms of FA mole fraction) of the first (red), second (green), and third (blue) molecular layer as the function of the bulk liquid phase composition. The lines connecting the symbols are just guides to the eye. For reference, the straight line corresponding to the bulk phase composition itself is also shown (black solid line).

Figure 4. Area distribution of the Voronoi polygons corresponding to the projections of the surface molecules to the macroscopic plane of the surface, YZ, when considering all surface molecules (top panel), only the surface formamide molecules (middle panel), and only the surface water molecules (bottom panel) in the different systems simulated (symbols). The color coding of the various systems is the same as in Fig.2. Solid lines show the best fit to the simulation data according to eq. 1.

29 ACS Paragon Plus Environment


Figure 5. Size distribution of the hydrogen bonded clusters, formed by both molecules, within the surface layer of the systems simulated (full black circles), together with the critical line of eq. 1 corresponding to the percolation threshold (solid red lines), shown on a double logarithmic scale. The data corresponding to the 90% FA, 80% FA, 70% FA, 60% FA, 50% FA, 40% FA, 30% FA, 20% FA, 10% FA, and 0% FA systems are shifted upwards by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 orders of magnitude, respectively, for better visibility. The inset compares the size distribution of the H-bonded clusters of solely the water molecules in the surface layer of the 10% FA system (open circles), and that of solely the FA molecules in the surface layer of the 90% FA system (filled circles) with the critical line of eq. 1 corresponding to the percolation threshold (solid red line).

Figure 6. Top: definition of the local Cartesian frames fixed to the individual water (left) and formamide (right) molecules, and of the polar angles ϑ and φ in these frames. Bottom: definition of the regions A, B, and C of the surface layer.

Figure 7. Orientational maps of the water molecules in the entire surface layer (last column) as well as in its separate regions C (first column), B (second column), and A (right column). For the definition of these regions, see the text and Fig. 6. Lighter shades of grey correspond to higher probabilities. The notation of the orientations corresponding to the different peaks is also indicated.

Figure 8. Orientational maps of the formamide molecules in the entire surface layer (last column) as well as in its separate regions C (first column), B (second column), and A (right column). For the definition of these regions, see the text and Fig. 6. Lighter shades of grey correspond to higher probabilities. The notation of the orientations corresponding to the different peaks is also indicated.


Page 30 of 43

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Figure 9. (a) Illustration of the orientations preferred by the water and formamide molecules in the entire surface layer as well as in any of its separate regions A, B, and C, relative to the surface normal vector (pointing, by our convention, towards the vapor phase), X. (b) Illustration of the possible hydrogen bonds formed by a water and a formamide molecule, both aligned according to their main orientational preference, in the surface layer. (c) Illustration of possible hydrogen bonding alignments of water and formamide molecules, both oriented according to their preferences, in portions of different local curvatures of the surface layer. The solid curved is a schematic representation of the liquid surface.

Figure 10. Survival probability of the water (top panel) and formamide (bottom panel) molecules within the surface layer in the various systems simulated (symbols). The color coding of the various systems is the same as in Fig.2. Solid lines show the best fit to the simulation data by the sum of two exponentially decaying functions. The insets show the same data on a logarithmic scale, to emphasize the exponential decay of the survival probability.

Figure 11. Mean square displacement of the water (top panel) and formamide (bottom panel) molecules within the macroscopic plane of the surface, YZ, as a function of time (symbols). The color coding of the various systems is the same as in Fig.2. Solid lines show the straight lines fitted to the simulation data above 5 ps.



Page 32 of 43

Figure 1. Kiss et al.


Page 33 of 43


ρwater/Å

-3

0.04

water number density 0% FA system 20% FA system 40% FA system 60% FA system 80% FA system 100% FA system

0.03 0.02 0.01 0.00

FA number density

ρFA/Å

-3

0.015 0.010

-3 surf

total mass density 1 -3

0.000 1.2 1.0 0.8 0.6 0.4 0.2 0.0

ρ /g cm

ρ /g cm

-3

0.005

ρ /g cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50% FA system

0 20

30 X/Å 40

0.5 first layer mass density

0.4 0.3 0.2 0.1 0.0 0

10

20

30

40


50

X/Å

60



1.0

FA mole fraction in the surface layers

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 43

0.8

bulk liquid phase first layer second layer third layer

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

FA mole fraction in the bulk liquid phase


1.0

Page 35 of 43


P(A)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.1

all molecules

0.01

0% FA system 20% FA system 40% FA system 60% FA system 80% FA system 100% FA system

1E-3

1E-4

0.1

formamide molecules

0.01

1E-3

1E-4

water molecules

0.1

0.01

1E-3

1E-4 0

50

100


150

2 200

A/Å



11

P(n)

10

10

P(n)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 43

10

1 0.1

9

0.01

8

1E-3

10 10

water in 10% FA formamide in 90% FA threshold line

1

10

n

7

10

0% FA 6

10

10% FA 5

10

4

10

20% FA

3

10

30% FA

2

10

40% FA

1

10

50% FA

0

10

60% FA

-1

10

70% FA

-2

10

80% FA

simulation data threshold line

-3

10

90% FA 100% FA

-4

10

1

10

n


100

Page 37 of 43


X z

z

X

ϑ

ϑ y

H

H

H

H

φ

N

x

O

ρmax liquid phase

ρ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ρmax/2

vapor phase

ρmax/2

B

A

C X


y

φ

O C H

x



region B

φ/deg

90

60

90

φ/deg

90

φ/deg

90

entire surface

region A

60

φ/deg

region C

60

0% FA system

45

cosϑ

90

0

cosϑ

0

cosϑ

0 -1

1

Iw 0

cosϑ

1

cosϑ

1

90

0 -1

0

cosϑ

1

90

45

IC w 0

cosϑ

1

0 -1

A Iw 0

cosϑ

0 -1

0 -1

0

cosϑ

1

20% FA system

Iw 0

cosϑ

1

0 -1

50% FA system

Iw 0

cosϑ

1

90

70% FA system

45

A Iw 0

cosϑ

0 -1

1

Iw 0

cosϑ

1

90

45

Iw

0 -1

1

90

φ/deg

45

1

45

45

Iw

cosϑ

90

φ/deg

φ/deg

φ/deg

0

cosϑ

0 -1

1

90

45

IC w

0

45

90

45

A Iw

φ/deg

φ/deg

IC w

0

45

90

45

90

0 -1

cosϑ

0 -1

1

90

45

0 -1

0

φ/deg

90

0 -1

0 -1

1

45

Iw

Iw

90

φ/deg

0 -1

cosϑ

0 -1

1

90

45

IC w

0

φ/deg

φ/deg 45

0 -1

1

φ/deg

90

0

A Iw

φ/deg

0 -1

1

Iw

φ/deg

0

30

φ/deg

0 -1

30

IC w cosϑ

φ/deg

30

φ/deg

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 43

90% FA system

45

A Iw 0

cosϑ


1

0 -1

Iw 0

cosϑ

1

Iw

Page 39 of 43


region B

φ/deg 0 0.0

IIIFA

IFA

180

0.5

cosϑ

0 0.0

1.0

0.5

cosϑ

0 0.0

0 0.0

0.5

cosϑ

360

0.5

360

φ/deg

IIIFA

IFA

180

cosϑ

0 0.0

1.0

0.5

cosϑ

1.0

360

180

0 0.0

IIIFA 0.5

180

cosϑ

1.0

0 0.0

0 0.0

IFA 0.5

cosϑ

1.0

IIFA 0.5

0 0.0

1.0

cosϑ

0.5

IIFA cosϑ

0 0.0

1.0

IIFA cosϑ


80% FA system

0.5 cosϑ 1.0

360

IIFA

0.5

1.0

IFA

180

0.5

cosϑ

50% FA system

360

IIFA

180

0 0.0

cosϑ 1.0

IFA

180

180

360

φ/deg

360

0 0.0

0.5

30% FA system

360

180

1.0

φ/deg

φ/deg

360

180

IFA

180

1.0

0 0.0

cosϑ 1.0

IIFA

φ/deg

0 0.0

IIIFA

IIFA 0.5

cosϑ 1.0

IFA

180

360

φ/deg

180

0 0.0

0.5

10% FA system

360

IIFA

180

0.5 cosϑ 1.0

360

φ/deg

360

0 0.0

0.5 cosϑ 1.0

360

φ/deg

180

cosϑ 1.0

360

φ/deg

360

0.5

IIFA

φ/deg

cosϑ 1.0

0 0.0

IFA

180

φ/deg

0.5

0 0.0

180

φ/deg

IFA

180

faw10L1FA

φ/deg

0 0.0

IIIFA

360

Y Axis Title

φ/deg 180

IIFA

φ/deg

360

φ/deg

360

φ/deg

360

entire surface

region A

φ/deg

region C

φ/deg

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0

IFA

180

0 0.0

0.5

cosϑ

1.0

100% FA system


Page 40 of 43


X

(a)

IIFA

A Iw

IFA

Iw

IIIFA

IC w

Iw

IFA

(b) Iw

IIFA IFA A Iw

Iw

(c)

IC w

IIIFA


Page 41 of 43


1.0 0.8

L(t)

1

water

L(t)

0.1

0.6

0.01

0.4

1E-3

0

20

40

60

80

100

t/ps

0.2 0.0

1

L(t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8

formamide

0.6 0.1

0.4

0

20

40

60

0.0 0

20

100

t/ps

0% FA system 20% FA system 40% FA system 60% FA system 80% FA system 100% FA system

0.2

80

40

60


t/ps

80

100


Figure 11.

2

Kiss et al.

MSD / Å

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 43

60 water

40

20

0 60 formamide

40 0% FA system 20% FA system 40% FA system 60% FA system 80% FA system 100% FA system

20

0 0

5

10

15


20

t/ps

25

30

Page 43 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphics:

INTERFACIAL PROPERTIES Strong lateral H-bonding Slight surface accumulation of formamide Immobilized surface water No self-aggregation

water

MD simulation

formamide


Investigation of the Liquid-Vapor Interface of Water-Formamide

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