Structure of a methanol±water microdroplet: a molecular simulation study
Elena N. Brodskaya*
a
and Simon W. de Leeuw
b
a
Department of Chemistry, St. Petersburg State University, 198904 St. Petersburg, Russian Federation. Fax: +7 812 428 6939;
e-mail: elena@coll.chem.lgu.spb.su
b
Department of Applied Physics, Delft University of Technology, 2628 CF Delft, The Netherlands.
Molecular dynamics simulations provide evidence of strong reorientational effects of methanol molecules in the surface layer of aMolecular dynamics simulations provide evidence of strong reorientational effects of methanol molecules in the surface layer of a
microdroplet, composed of an equimolar mixture of methanol and water, so that the orientational bias of methanol molecules inmicrodroplet, composed of an equimolar mixture of methanol and water, so that the orientational bias of methanol molecules in
the mixture appears to be stronger than in droplets of pure methanol.the mixture appears to be stronger than in droplets of pure methanol.
The behaviour of amphiphiles in the interface between polar
and nonpolar phases is one of the more interesting problems of
the investigation of the water±amphiphile solutions. The
simplest amphiphilic substances are alcohols, of which
methanol is a prime example. Molecular simulations of
alcohols and their mixtures by Monte Carlo (MC) and
molecular dynamics (MD) methods were carried out in a
number of studies. These simulations allow one to calculate in
a straightforward manner the static and kinetic properties of
the system under investigation. The surface properties of these
systems were subject of a number of studies where the liquid±
vapour interface of methanol and its aqueous solutions was
considered.
1±6
One of the principal quantities of interest in the
investigation of the interface of liquid±vapour polar fluid is
the surface potential w which can be determined as the
difference of the electric potentials of liquid j
l
(l) and gas j
g
(g)
phases, that is w = j
l
7 j
g
. The value of w in the case of
methanol and water±methanol mixtures was calculated in
studies by Matsumoto et al.,
1,3
Baraclough et al.
2
and more
recently by Zakharov and Brodskaya.
6
Unfortunately the
results of these studies do not agree with each other and with
experimental values.
7
The discrepancy between the results can
partly be ascribed to different definitions of the surface
potentials. Thus Matsumoto et al.
1,3
and Baraclough et al.
2
employ a definition, in which only dipolar contributions to the
surface potential are included. Wilson et al.
8
have pointed out,
that in addition to the dipolar contribution one should also
include a purely quadrupolar term. Zakharov and Brodskaya
6
obtained the value of w directly from a calculation of the local
electric potential j(r) for small clusters of methanol, as
described in earlier studies of water clusters.
9,10
Their results
confirmed the importance of the quadrupolar contributions to
the surface potential.
In this work we present preliminary results of MD
simulations of a cluster, consisting of 128 molecules of
equimolecular methanol±water mixture. For comparison
clusters of pure water and methanol with the same number
of molecules were considered as well. The average diameter of
such micro-objects is about 20±30 A, which corresponds to
about ten molecular diameters. Though the local density in the
central region of the system approaches the value of the bulk
liquid, the other local properties, such as energy and pressure,
do not reach their bulk values. For this reason these
microdroplets are usually referred to as clusters in order to
stress their strong nonuniformity. One should be careful
however to avoid possible confusion of such clusters, which
are stable isolated objects, with the clusters arising inside a
hydrogen bonded liquid by fluctuations, as presumed by a
number of theories and observed in simulations of associating
liquids.
11
The success of the molecular simulations depends to a large
degree on the quality of the molecular model together with the
intermolecular potential. Reasonably efficient models are the
empirical models proposed by Jorgensen both for water
12
and
methanol.
13
Although not perfect these models describe the
properties of liquid water and methanol at ambient pressures
quite reasonably over a wide range of temperature.
13,14
The
molecular dynamics simulations were carried out using
constraint dynamics,
15
which take into account the rigidity
of molecules. The temperature was about 300 K. The time step
was equal to 1 fs, the equilibration time exceeds 200 ps, and
duration of the production run was more than 900 ps. The
coordinate origin is placed in the centre of mass of the system.
On the average the systems were spherically symmetrical, so
that all one-body local properties are functions of the distance
from the centre of the cluster. These functions are called the
radial profiles. The systems of N = 128 molecules was placed
in a loose spherical shell with a short-ranged, smooth repulsive
field. The value of the radius R
sh
of this shell was nearly three
times more than the radius of the equimolecular dividing
surface R
e
which can be taken as a characteristic radius of the
cluster size. This allows to avoid the influence of the shell on
the properties of the cluster. This dividing surface is defined by
the condition of zero excess density, i.e. zero adsorption:
3N 4pr
l
R
3
e
À r
g
R
3
sh
À R
3
e
(1)
where r
l
and r
g
are the densities of the bulk liquid and vapour
phases.
The first characteristic of the local structure is the local
density, shown in Figure 1 which diplays the radial profiles of
the partial density of water r
w
(r), the methanol oxygen density
r
O
(r), the density of the methyl group r
CH
3
(r) and the total
density r(r). All densities are in atoms (molecules)/A
3
. The
radius of the equimolecular surface is about 10.7Æ0.5 A. It
seems that methanol prevails in the surface layer, but in the
central part of the cluster at r<6 A the fraction of methanol is
about 0.44.
It is interesting that the inner part of the surface layer inside
the equimolecular sphere at 5 A< r<10 A is enriched by water
and the partial local density of water has a maximum at
r = 7.5 A. The tendency of such a behaviour for the local
density of water in the surface of water±methanol solution was
noticed recently by Benjamin
5
and Matsumoto et al.
3
In the
case of the cluster this fact results in the higher value of the
total local density r(r). This feature is specific for the local
density in the mixture and should be contrasted to the
behaviour of the local density in clusters of pure water and
methanol. In Figure 2 the local densities of all clusters are
compared. It seems likely that the peculiarity of the local
density in the mixture will disappear when the cluster size
increases. But this assumption needs to be checked by
considering larger clusters.
In comparison with the pure liquids the orientational
structure of the surface layer of solution changes strongly.
This can be seen clearly from the partial densities of the
oxygen and methyl groups shown in Figures 1 and 2 for the
clusters of the mixture and pure methanol (curves 3a and 3b).
Although in both systems the methyl groups are directed
towards to the vapour phase, this effect is much greater in the
surface layer of solution. Such behaviour is characteristic of
amphiphilic substances. At the same time a substantial change
in the dipole orientations is observed. It is well known,
6,9
that
in the surface layer of pure liquid the dipole moments are
– 18 –
Mendeleev Commun., 1997, 7(1), 18–20