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.
