Intrinsic structure and dynamics of the water/nitrobenzene interface

TL;DR: In this article, a detailed and systematic molecular dynamics study of the water/nitrobenzene interface was performed, and the authors were able to obtain true intrinsic profiles for several properties (density, hydrogen bonds, molecular orientation, etc.) in the direction perpendicular to the interfacial plane.

Abstract: In this paper we present results of a detailed and systematic molecular dynamics study of the water/nitrobenzene interface. Using a simple procedure to eliminate fluctuations of the interface position, we are able to obtain true intrinsic profiles for several properties (density, hydrogen bonds, molecular orientation, etc.) in the direction perpendicular to the interfacial plane. Our results show that both water and organic interfacial molecules form a tightly packed layer oriented parallel to the interface, with reduced mobility in the perpendicular direction. Beyond this layer, water quickly restores its bulk structure, while nitrobenzene exhibits structural anisotropies that extend further into the bulk region. Water molecules that protrude farthest into the organic phase point one hydrogen atom in the direction perpendicular to the interface, forming a hydrogen bond with a nitrobenzene oxygen. By fitting both the global and the intrinsic density profiles, we obtain estimates for the total and intrinsi...

Summary

1. Introduction

• Finally, the authors mention another property that has originated some controversy over the years -the interfacial diffusion coefficient.
• D z was persistently lower than D xy for both liquids throughout the whole system.
• One conclusion is clear from all these studies -the interface strongly affects the diffusion coefficient.
• The authors make use of some recent advances in the theoretical description of interfaces [8] [9] [10] [11] [12] [13] [14] and perform a detailed and systematic MD study of the water/nitrobenzene interface.
• In the next section, the authors provide some computational details about their simulations.

2. Potentials and Methods

• The procedure to construct the initial two-phase configuration was as follows.
• First, two individual boxes with the same x and y dimensions, containing each of the pure liquids, were constructed and equilibrated.
• These boxes were then fitted together in the z direction, leaving a small gap between both phases so as to avoid atom overlap (this gap was approxiately 0.5 nm wide).
• Next, the whole system was translated in the z direction, using periodic boundary conditions, so that the center of mass of the organic phase corresponded to the geometric center of the simulation box.
• After the two-phase system was equilibrated, properties were sampled during 5 ns, divided in blocks of 200 ps for averaging purposes.

3.1 Interfacial Structure and Density Profiles

• In each slab, the authors calculated the instantaneous density of each species and averaged over all configurations.
• The authors have tested different slab widths and concluded that the value of 0.04 nm provides an adequate balance between accuracy of the resulting profiles and low statistical noise.
• The resulting "global" density profiles are shown in Figure 2 for both nitrobenzene models with a box size of L=3.5 nm.
• It is clear that the system consists of four distinct regions: bulk water, bulk organic and two interfaces.
• The interfacial regions are characterized by a smooth transition in the density of both species from bulk values to zero.

Figure 2

• In principle, there are two limiting cases that can produce a gradual decrease in density perpendicular to the interface: the interface is flat and the two phases intermix within a finite layer; or the interface is molecularly sharp but is broadened by thermal fluctuations.
• In each sub-box, the authors locate the limits of each phase (l), for both interfaces.
• This is defined as the z coordinate of the site of component i that protrudes furthest into the opposite phase but is still linked to the bulk of phase i (thus excluding overhangs and dissolved molecules from the definition of the interface).
• The authors have carefully verified that this criterion is robust and yields results that are reproducible.

Figure 3

• Once the phase limits have been found, the interface positions (h) and widths (w) can be calculated according to: 2 OL WL L l l h + = (2) EQUATION EQUATION where the subscripts L, R, W and O are for the left interface, the right interface, the water phase and the organic phase, respectively.
• In previous works where this method was employed, the maximum value of N was such that L/N was larger than the bulk correlation length.
• Indeed, capillary wave theory requires a lower cutoff for the thermal fluctuation wavelength, on the argument that a "capillary wave" is no longer meaningful beyond molecular dimensions (defined by ξ).
• Here, however, the authors go beyond this limit in an attempt to obtain further insight into the intrinsic structure of the interface.
• As such, the average width decreases with N while the position distributions become broader.

Figure 4

• The original form of CWT assumed a step function intrinsic density profile.
• The mean-field approach, on the other hand, assumes that the intrinsic profile is smooth, but neglects interfacial broadening by capillary waves 49 .
• Almost a decade ago, their group proposed using the method of dividing the xy plane into a mesh, described above, to calculate this profile 8 .
• In other words, one must use a lower wavelength cutoff for the fluctuations that is close to the value of the Lennard-Jones site diameter of the liquid 10 .
• The profile calculated in this way is free from thermal fluctuations of the interface position and shows the true intrinsic density variation at the interface.

Figure 5

• At N=1, the profiles are relatively smooth since they are broadened by thermal fluctuations, as already discussed.
• For a given N, the water density profile is calculated relative to the limits of the organic phase (and vice-versa for the organic profile).
• Figure 6 shows the water and nitrobenzene intrinsic profiles for both models and for different values of L (for L = 3.5 nm, the water intrinsic profile is obtained at N=10 and the organic intrinsic profile at N=11).
• Tarazona and co-workers 9 used a much more complex method for calculating the intrinsic profiles than the one proposed in this paper, based on using a set of pivot atoms to define the interface as a sum of Fourier components.
• Their method is still much more laborious than their procedure.

3.2 Interfacial Tension and Width

• The angle brackets denote an ensemble average, taking into account that in their simulations the box length in the direction normal to the interface is allowed to vary.
• Table 1 shows the calculated values of the interfacial tension from the virial route for their simulations.
• Compared to the experimental value for the water/nitrobenzene interface 51 , 25.5 mN/m, both the OPLS and the MB models overestimate the interfacial tension, with the latter yielding better agreement.
• The tension should depend strongly on the water/organic interactions, and in principle it should be possible to fine tune the values of the unlike pair interaction parameters to yield good agreement with experiment.
• Such an exercise is beyond the scope of this paper.

Table 1

• Another commonly used method to calculate the interfacial tension from simulations is by applying capillary wave theory.
• The next step is to calculate the total and intrinsic widths from the variance of the global and intrinsic density profiles, respectively.
• The values shown are an average over both components and both interfaces.
• In possession of both the total and the intrinsic widths, one can now calculate the capillary wave contribution to the width of the interface from equation ( 7) and apply equation ( 8) to extract the value of the interfacial tension.
• Comparing the size of the carbon tetrachloride molecule with that of nitrobenzene, it is expected that the bulk correlation length of the latter be somewhat larger.

Table 2

• Using the above procedure, the authors obtain interfacial tensions that are not very sensitive to the particular function used to fit the density profiles, provided that the slope of the initial density increase is well described.
• Indeed, the results obtained using equation ( 9) are very close to those obtained when equation ( 10) is employed (see Table 2 ).
• Another possibility, used in several previous studies 16, 17, 22, [24] [25] [26] , is to estimate the total interfacial width from the standard deviation of the distribution of interface positions .
• Following the reasoning described above, the correct value for the interfacial width should be calculated from the fluctuations in the location of the intrinsic interface (i.e., the distribution calculated by dividing the box length in segments of size L/N ≈ σ).
• The results for γ cw are not as close to γ V as those obtained from fitting the density profiles, but the agreement is still very good.

3.3 Radial Distribution Functions and Hydrogen Bonds

• As the authors move closer to the interface, there is a gradual depletion of the second peak, and the limiting value of the RDF also decreases.
• The position of the peaks and the intensity of the first peak (characteristic of hydrogen bonds) remain intact.
• This suggests that water keeps its highly H-bonded structure even in close vicinity to the organic phase.
• The authors observe the same trend as in the local profile, except that the density depletion is much more pronounced .
• Even the water molecules that are protruding furthest into the nitrobenzene phase maintain the two-peak structure that is characteristic of the bulk phase (the peak intensity is much lower and the statistics are poorer due to the small number of water molecules in that slice).

Figure 7

• The O W -H W RDFs of Figure 7 show that water retains its H-bonded structure even beyond the interface location.
• Two water molecules were considered to be hydrogen bonded if the distance between the hydrogen atom of one molecule and the oxygen atom of the other was below 0.24 nm.
• As a result of these two effects, the percentage of H-bonded water molecules actually increases from 73% in bulk to about 85% well beyond the global limit of the nitrobenzene phase.
• Once more, the same trend is observed, with a decreasing number of hydrogen bonds but with an increasing percentage of H-bonded molecules.

Figure 8

• Figure 9 shows the RDFs between the carbon atoms of nitrobenzene that are connected to the nitro group (C N ), as these are located practically at the centre of mass of the molecule.
• The curves furthest from the interface are identical to those of the pure component 46 .
• This peak is characteristic of nitrobenzene molecules that are packed close together with a tendency for antiparallel alignment 52 .
• In other words, the presence of the interface induces closer packing and antiparallel alignment of the nitrobenzene molecules, and this effect extends significantly towards the bulk organic region.
• The authors will examine this packing effect in more detail when they study the molecular orientations in section 3.4.

Figure 9

• It is also worth examining the cross-species RDFs, i.e. those referring to interactions between water and organic sites.
• Figure 10 shows two such RDFs, namely that between water hydrogens and nitrobenzene oxygens (O N ) and that between water oxygens and nitrobenzene hydrogens (H A ).
• In fact, both interfacial RDFs are similar to their bulk counterparts, but with lower peak intensities and lower limiting values, due to the density depletion at the interface.
• In fact, water molecules protruding well into the organic phase establish a significant proportion of bonds with nitrobenzene molecules.
• As the authors will see below, these hydrogen bonds will have a pronounced effect on the orientation of the interfacial molecules.

3.4 Molecular Orientation

• Finally, the water molecules that are protruding into the organic phase have one hydrogen pointing into the nitrobenzene phase and their molecular plane is perpendicular to the interfacial plane (θ = 30º; φ = 90º).
• These results are very similar to those obtained by Jedlovszky et al.
• 34 , which once again confirms that the orientation of the water phase depends little on the nature of the organic phase.

Figure 11

• The authors can now look at the same bivariate distributions, but based on a local definition of the interface (i.e. for N=10), which are plotted in Figure 12 .
• Both the isotropic orientation, for bulk water, and the parallel orientation (θ = 90º; φ = 0º), for interfacial water, are present in the intrinsic distributions.
• This means that one cannot speak in terms of a "layer" of water molecules possessing this arrangement.
• Rather, it is only the molecules that belong to water "fingers" protruding well into the organic phase (which are almost completely surrounded by nitrobenzene molecules) that are oriented perpendicularly to the interface.
• These authors have observed that only water molecules at the interface align parallel to the interfacial plane, but that this orientation is correlated with the local curvature of the interface, such that molecules belonging to extrusions of the surface (with positive curvature) align perpendicularly to the interface, with one hydrogen pointing towards the vapor.

Figure 12

• Previous simulations have shown that the nitro group is preferentially aligned with the aromatic plane and that the nitrobenzene molecule is quite rigid 46 .
• The nitrobenzene molecules that are in contact with the water phase are oriented with their plane parallel to the interface (θ = 90º; φ = 0º).
• Beyond this layer, the distributions recover the isotropic orientation typical of the bulk liquid.
• Results obtained in the water/OPLS system (not shown) are qualitatively very similar to those for the water/MB system.

Figure 13

• For the most part, both interfacial water and nitrobenzene molecules are oriented with their molecular plane parallel to the interface .
• These interfacial layers consist of closely packed molecules and are responsible for the first density peaks shown in the intrinsic density profiles .
• Thermal fluctuations induce the appearance of corrugations, leading some molecules to appreciably penetrate the opposite phase.
• This type of bond causes some of the nitrobenzene molecules to be oriented with one oxygen atom pointing into the water phase .
• As the authors move from the interfacial water layer into bulk water, the isotropic orientation and equilibrium density are recovered fairly quickly, due to the small molecular size of water and the high resilience of its hydrogen-bonded network.

3.5 Self-diffusion

• This value (open symbols) tends toward the diffusion coefficient calculated in pure SPC/E water 53 , shown as the dashed line.
• As the authors move in the direction of the organic phase, the lateral diffusion coefficient shows a slight decrease.
• First of all, even well within the bulk phase, D z does not reach the pure-component value, which probably means that their box is still not long enough in the z direction to eliminate all effects of the interface.
• Static properties, such as density profiles, hydrogen bonds and orientation distributions, are less sensitive to the presence of the interface and reach bulk values much earlier than dynamic properties like the diffusion coefficient.
• This property goes through a minimum, and molecules that protrude significantly into the organic phase are moving almost as fast as bulk molecules in the direction perpendicular to the interface.

Figure 16

• The corresponding results for the nitrobenzene diffusion coefficient are shown in Figure 17 .
• The trend observed for the lateral diffusion coefficient is the inverse of the water case, i.e.
• D xy increases slightly from the bulk value as the authors move toward the water phase.
• As for the perpendicular diffusion coefficient, the authors observe once more that it goes through a minimum as they move from bulk organic to water.

Figure 17

• The general trends observed in Figures 16 and 17 can be understood if the authors think of two limiting cases for diffusion: i) bulk molecules, i.e., molecules completely surrounded by other molecules of the same species; ii) dissolved molecules, i.e., molecules completely surrounded by molecules of the opposite species.
• Thus, both components of the water diffusion coefficient in Figure 16 should tend toward this value as the authors move into the bulk organic phase.
• These considerations are also able to explain some of the observed trends in previous studies 6, 17, 22, 24 , although the statistical accuracy of the latter are generally poorer.
• The limiting cases considered above explain the general trends, but are not sufficient to explain the minimum observed in D z .
• The authors results from the previous sections point to the existence of two interfacial layers, one on the water side and one on the organic side, with tightly packed molecules oriented parallel to the interfacial plane .

Figures

Figure 13. Bivariate orientation distribution of nitrobenzene molecules for the system water/MB at L=3.5 nm calculated in slices perpendicular to the interface using a global definition (N=1). Red corresponds to high normalized probability and blue to low probability. Slices, from top to bottom, correspond to positions relative to the limit of the organic phase of: -0.9, -0.7, -0.5, -0.3, - 0.1, 0.1, 0.3, 0.5 and 0.7.

Figure 8. Hydrogen bond profile as a function of position relative to the limit of the organic phase for the system water/MB at L=3.5 nm using a global (a) and a local (b) definition of the interface. The thick dashed line is the number of molecules in the first coordination shell, the thin dashed line is the number of water-water hydrogen bonds per molecule, the full line is the percentage of bonded water molecules and the dotted line is the number of water-nitrobenzene hydrogen bonds per water molecule. The water density profiles (thick lines) are superimposed for ease of visualization.

Figure 7. OW–HW radial distribution functions for the system water/MB at L=3.5 nm in slices perpendicular to the interface, defined globally (a) and locally (b). The curves, from top to bottom, correspond to positions relative to the limit of the organic phase of: 0.9, 0.7, 0.5, 0.3, 0.1, -0.1, -0.3, -0.5, -0.7 and -0.9 (negative values are within the organic phase).

Figure 9. CN–CN RDFs for the system water/MB at L=3.5 nm in slices perpendicular to the interface, defined globally (a) and locally (b). The curves correspond to the same positions relative to the limit of the water phase as in Figure 7, but the last five curves of part b are not statistically meaningful. The RDFs showing the onset of a peak at short distances are highlighted with thick lines.

Figure 2. Global density profiles for the water/OPLS (thin line) and water/MB (thick line). The organic phase is in the center and the water phase on both sides (see Figure 1).

Figure 14. Bivariate orientation distribution of nitrobenzene molecules for the system water/MB at L=3.5 nm calculated in slices perpendicular to the interface using a local definition (N=11). Red corresponds to high normalized probability and blue to low probability. Slices, from top to bottom, correspond to positions relative to the limit of the organic phase of: -0.1, 0.1, 0.3, 0.5, 0.7 and 0.9 (slices closer to the water phase are not statistically meaningful).

Figure 17. Nitrobenzene diffusion coefficient for the system water/MB at L=3.5 nm calculated in slices perpendicular to the interface, defined globally (a) and locally (b). Open symbols are for diffusion in the plane of the interface, closed symbols are for diffusion perpendicular to the interface and the dashed line is the pure-component diffusion coefficient. The density profiles (thick lines) are superimposed for ease of visualization.

Figure 10. HW–ON (a) and OW–HA (b) RDFs for the system water/MB at L=3.5 nm in the interface and in bulk.

Figure 6. Intrinsic density profiles for water (a) and nitrobenzene (b) relative to the limit of the opposite phase. The values of N for each profile are as follows: water at L=2.5 nm – N=7; water at L=3.5 nm – N=10; nitrobenzene at L=2.5 nm – N=8; nitrobenzene at L=3.5 nm – N=11. The thick lines are fits to the OPLS profiles using equation (9) and the dashed-dotted line is drawn with data read from Ref. 21.

Figure 15. Schematic representation of the structure of the water/nitrobenzene interface. The diagram shows a hypothetical cross section through the yz plane (i.e., perpendicular to the interfacial plane). Color coding is the same as in Figure 1. The thick line represents the interface and the thin dashed lines represent hydrogen bonds.

Figure 1. Snapshot of a simulation of the water/nitrobenzene interface showing the shape of the simulation box and the coordinate axes. Oxygen atoms are shown in blue, carbon atoms in purple, nitrogen atoms in green and hydrogen atoms in white.

Table 1 – Interfacial tensions and widths.

Table 2 – Interfacial tensions (in mN/m) and bulk correlation lengths (in nm) calculated by different methods.

Figure 11. Bivariate orientation distribution of water molecules for the system water/MB at L=3.5 nm calculated in slices perpendicular to the interface using a global definition (N=1). Red corresponds to high normalized probability and blue to low probability. Slices, from top to bottom, correspond to positions relative to the limit of the organic phase of: -0.9, -0.7, -0.5, -0.3, - 0.1, 0.1, 0.3, 0.5 and 0.7.

Figure 5. Density profiles for the system water/MB at L=2.5 nm at several sizes of mesh dividing the xy plane. The profiles are averaged over both interfaces and, for clarity, are shifted in the z direction so that their inflection point is at the origin.

Figure 16. Water diffusion coefficient for the system water/MB at L=3.5 nm calculated in slices perpendicular to the interface, defined globally (a) and locally (b). Open symbols are for diffusion in the plane of the interface, closed symbols are for diffusion perpendicular to the interface and the dashed line is the pure-component diffusion coefficient. The density profiles (thick lines) are superimposed for ease of visualization.

Figure 12. Bivariate orientation distribution of water molecules for the system water/MB at L=3.5 nm calculated in slices perpendicular to the interface using a local definition (N=10). Red corresponds to high normalized probability and blue to low probability. Slices, from top to bottom, correspond to positions relative to the limit of the organic phase of: -0.3, -0.1, 0.1, 0.3, 0.5 and 0.7 (slices closer to the organic phase are not statistically meaningful).

Figure 4. Probability distributions of the interface position (a) and width (b) for the system water/MB at L=2.5 nm at different mesh sizes dividing the xy plane. The distributions are averaged over both interfaces.

Figure 3. Diagram illustrating, in two dimensions, our method for determining the limits of each phase at N=1 (left box) and N=4 (right box). The thick line represents the interface and the vertical lines represent the limits of the water (dotted) and organic (dashed) phases. The thin horizontal lines in the box on the right-hand side show the division of the interface in 4 subsections.

Full text

1
Intrinsic Structure and Dynamics of the
Water/Nitrobenzene Interface
Miguel Jorge*, M. Natália D. S. Cordeiro*
REQUIMTE, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-
007 Porto, Portugal
Email addresses: miguel.jorge@fc.up.pt; ncordeir@fc.up.pt
Title Running Head: Intrinsic properties of the water/NB interface
Abstract
In this paper we present results of a detailed and systematic molecular dynamics study of
the water/nitrobenzene interface. Using a simple procedure to eliminate fluctuations of the
interface position, we are able to obtain true intrinsic profiles for several properties (density,
hydrogen bonds, molecular orientation, etc.) in the direction perpendicular to the interfacial
plane. Our results show that both water and organic interfacial molecules form a tightly packed
layer oriented parallel to the interface, with reduced mobility in the perpendicular direction.
Beyond this layer, water quickly restores its bulk structure, while nitrobenzene exhibits structural
anisotropies that extend further into the bulk region. Water molecules that protrude farthest into
the organic phase point one hydrogen atom in the direction perpendicular to the interface,
forming a hydrogen bond with a nitrobenzene oxygen. By fitting both the global and intrinsic

2
density profiles, we obtain estimates for the total and intrinsic interface widths, respectively.
These are combined with capillary wave theory to produce a self-consistent method for the
calculation of the interfacial tension. Values calculated using this method are in very good
agreement with direct calculations from the components of the pressure tensor.
Key words: liquid/liquid interface; surface tension; density profiles; molecular orientation;
diffusion coefficient; ion transfer.
1. Introduction
Interfaces between water and immiscible organic liquids are ubiquitous in nature, and are
important in a wide variety of chemical, physical and biological processes, such as phase transfer
catalysis, liquid-liquid extraction and drug delivery
1
. Understanding of these processes relies on
fundamental knowledge at the molecular level of the structural and dynamic characteristics of the
interface itself. Nitrobenzene was chosen as the organic liquid because it is widely employed in
electrochemical studies at interfaces
2-5
, but has received relatively little attention from the
theoretical point of view. In 1998, Michael and Benjamin
6
have presented an MD study of the
water/nitrobenzene interface, where they analyzed the structure of the interface and the effect of
molecular polarizability on interfacial properties. In a recent letter
7
, these simulations have been
extended to help explain X-ray reflectivity measurements. Since the original paper by Michael
and Benjamin
6
, our theoretical understanding of interfacial systems has evolved and new
methodologies have appeared
8-14
that are able to provide a more detailed picture of this interface.
In this paper, we make use of such recent developments to present a detailed and systematic
characterization of the local structure and dynamics of the water/nitrobenzene interface using
molecular dynamics (MD) simulations. In the future, we intend to study the transfer of
biologically important molecules (such as drugs and aminoacids) across this liquid/liquid
interface.

3
Despite recent advances
15
experimental techniques are still limited when it comes to
providing a detailed description of a liquid/liquid interface. This is mainly due to the fluidity of
the interface and to its buried nature, which precludes local experimental probing. Molecular
simulation techniques, on the other hand, are particularly suited for shedding light on atomic-
level phenomena, and have been widely applied to liquid/liquid interfaces (see review by
Benjamin
1
and references therein). Despite the large number of papers published on this topic
since Linse’s pioneering work on the water/benzene interface
16
, progress in our fundamental
understanding of interfacial properties has been relatively slow, perhaps due to the difficulty in
defining the interface itself. This was already recognized by Linse
16
, who employed a method
based on dividing the plane parallel to the interface in square meshes of variable degrees of
refinement (determined by parameter N, the number of squares in each direction). In each section,
he determined the limits of each phase and calculated a value for the interfacial thickness. The
average thickness was seen to decrease with mesh refinement, suggesting that the interface was
molecularly sharp and broadened by thermal fluctuations. Benjamin
17
later extended this method
to measure the average and fluctuations in both interface width and position. In his detailed study
of the water/1,2-dichloroethane system, he reached the same conclusions as Linse regarding the
structure of this interface. Indeed, a picture of an interface that is relatively sharp on a molecular
level, but exhibits corrugations caused by thermal fluctuations (or capillary waves) has emerged
from every simulation study of liquid/liquid interfaces using realistic potential models. To our
knowledge, the only exception has been a study by Carpenter and Hehre
18
of the water/hexane
interface, but this was later attributed to an incorrect choice of alkane potential parameters
19
.
The nature of the liquid/liquid interface described above has led to efforts aiming to
describe it using capillary wave theory (CWT)
20,21
. Most of these efforts rely on a relationship
established by CWT between the width of the interface due to capillary wave fluctuations (w
cw
)
and the macroscopic interfacial tension (
γ
)
21
:

4
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
ξπγ
L
Tk
w ln
2
cw
B
2
cw
(1)
where k
B
is the Boltzmann constant, T is the temperature, L is the length of the simulation box in
the directions parallel to the interfacial plane and
ξ
is the bulk correlation length. The latter
parameter is commonly defined, somewhat ambiguously, as being of the order of the molecular
diameter. Equation (1) is obtained by neglecting the effects of gravity, which is a reasonable
assumption at the small length scales employed in molecular simulations
1
. This equation was
used by several authors
6,17,22-26
to calculate the interfacial tension, using different methods for
estimating w
cw
and assuming values for
ξ
that ranged between 0.4 and 0.9 nm. Reasonable
agreement with experiment was sometimes found, but in most cases where the interfacial tension
of the simulated system (
γ
V
), calculated by the virial route, was also reported,
γ
cw
was
significantly below those values
6,17
. Thus, even though CWT in its original form can qualitatively
describe the nature of the interface, it is not always successful at predicting quantitative values of
the interfacial tension.
Another important property of interfacial systems that has been widely debated is the
density profile. Early simulations of liquid/liquid interfaces produced density profiles, calculated
by dividing the system in thin slices parallel to the interface, that exhibited large oscillations
extending into the bulk regions
6,16-19,22-24,27,28
. Such oscillations were tentatively attributed to
sampling insufficiencies. Indeed, increasing the system size and the sampling time led to a
smoothing of the fluctuations in the bulk regions, but oscillations near the interface remained
29
,
which suggests that they are intrinsic to the system. In an attempt to clarify this, Fernandes et al.
8
calculated density profiles of the water/2-heptanone system relative to a local definition of the
interface. This was achieved by applying the method used by Linse
16
and Benjamin
17
to
determine the limits of each phase, and then calculating the density profile relative to these limits.
Using this method, one is able to decouple fluctuations occurring in the interfacial plane from

5
those perpendicular to it. The resulting local density profiles showed relatively smooth bulk
regions and pronounced oscillations near the interface, more pronounced on the organic side
8
.
This method was later applied to other interfaces
25,26
, and oscillatory density profiles were also
obtained. Although these results point unequivocally to the existence of an intrinsic density
profile that is broadened by thermal fluctuations, it has not yet been shown that the method as it
stands does indeed yield this intrinsic profile. A recent paper by Chowdhary and Ladanyi
30
sheds
further light on this issue. They have adapted a procedure developed by Tarazona and co-
workers
9-11
and calculated the true intrinsic profile for several water/hydrocarbon interfaces. The
resulting profiles are qualitatively similar to those of Fernandes et al.
8
, but a critical comparison
of both methods was not attempted.
The presence of an interface strongly affects the molecular organization of both phases,
which becomes evident when one computes different properties as a function of the distance to
the interface. In previous molecular simulation studies of liquid/liquid interfaces, this effect has
been observed, for example, in density profiles (as discussed above), molecular packing and
orientation, hydrogen-bond formation, and so on. The effect of the interface on the hydrogen-
bonding structure of water is more or less consensual. In his early study, Linse
16
observed a
decrease in the number of H-bonds per molecule from the bulk region to the interface. However,
the total number of nearest neighbors in the first water coordination shell also decreased. The
combination of these two effects results in an increase of the percentage of hydrogen-bonded
water molecules near the interface. This suggests that interfacial water molecules arrange
themselves so as to maximize the possibility of forming hydrogen bonds. This conclusion was
corroborated in nearly all subsequent simulation studies
6,17,18,22-27,31
, and supported by
observations that radial distribution functions (RDFs) of interfacial water exhibited a similar
shape as those of bulk water
17,23-25,27
. A recent paper by Benjamin
32
provides some interesting
new insights on the dynamics of these hydrogen bonds.

Frequently asked questions

Q1. Why does the angle fall in the range of 0o?

Due to the equivalence between twopossible molecular normal vectors pointing in opposite directions, angle φ falls in the range 0º ≤ φ ≤ 90º. 

Q2. How long did the simulation take to obtain good statistics?

In this work, the authors use slices that are 0.25 nm thick, much thinner than slices used in previous studies6,17,22-24,33, but the authors are able to obtain good statistics due to the long simulation times employed. 

Q3. What is the first conclusion to draw?

The first conclusion to draw is that the intrinsic profiles are independent of system size, which means that their method of calculation gives reproducible results. 

Q4. What is the effect of the interface on the nitrobenzene molecules?

In other words, the presence of the interface induces closer packing and antiparallel alignment of the nitrobenzene molecules, and this effect extends significantly towards the bulk organic region. 

Q5. How did da Rocha and Benjamin6 estimate the capillary wave width?

In their study of the water/CO2 interface, da Rocha et al. 25 used the mean square deviation of the interface location calculated at L/N = 0.7 nm to estimate the capillary wave width and, assuming ξ=0.9 nm, obtained interfacial tensions in good agreementwith γV. 

Q6. What was the rescaled z coordinates of each atom?

For each configuration in the sampling stage, the authors rescaled the z coordinates of each atom by a fixed amount so that the center of mass of the organic phase is located at the origin. 

Q7. What is the effect of an interface on the molecular organization of water and hydrogen?

The presence of an interface strongly affects the molecular organization of both phases,which becomes evident when one computes different properties as a function of the distance to the interface. 

Q8. Why are the interfacial RDFs similar to their bulk counterparts?

In fact, both interfacial RDFs are similar to their bulk counterparts, but with lower peak intensities and lower limiting values, due to the density depletion at the interface. 

Q9. What is the trend of the diffusion coefficients of water and nitrobenzene?

as the authors move towards the bulk regions, the diffusion coefficients of both water and nitrobenzene tend toward case i), even though the perpendicular component does not reach the precise bulk value. 

Q10. What is the difference between the orientation of water molecules at the interface?

These authors have observed that only water molecules at the interface align parallel to the interfacial plane, but that this orientation is correlated with the local curvature of the interface, such that molecules belonging to extrusions of the surface (with positive curvature) align perpendicularly to the interface, with one hydrogen pointing towards the vapor. 

Q11. What is the important macroscopic property defining an interfacial system?

Figure 63.2 Interfacial Tension and WidthPerhaps the most important macroscopic property defining an interfacial system is theinterfacial tension. 

Q12. What is the result of fitting equation (10) to the intrinsic profiles?

The square root of the variance of a profile described by equation (10) is no longer equal to we, but is given instead by:( ) eo wAw += 1 (11)Figure 6 shows the result of fitting equation (10) to the intrinsic profiles.