Langmuir 2001, 17, 1773-1783
1773
Molecular Simulation of a Dichain Surfactant/Water/
Carbon Dioxide System. 1. Structural Properties of
Aggregates
S. Salaniwal,†,‡ S. T. Cui,†,‡ H. D. Cochran,†,‡ and P. T. Cummings*,‡,§
Department of Chemical Engineering, University of Tennessee,
Knoxville, Tennessee 37996-2200, Departments of Chemical Engineering, Chemistry, and
Computer Science, University of Tennessee, Knoxville, Tennessee 37996-2200, and Chemical
Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6224
Received April 12, 2000. In Final Form: October 11, 2000
Molecular dynamics simulation of a dichain surfactant + water + carbon dioxide (solvent) system is
performed to study the structural properties of reversed micelle-like surfactant aggregates formed in the
system. The simulations use a detailed and realistic molecular model for the surfactant molecule and
explicit representation of the water and solvent molecules to enable quantitative comparisons with a prior
experimental (small-angle neutron scattering) study. The results of the simulation are found to be in
reasonable agreement with experimental values. The simulations show that the size and shape of the
surfactant aggregates depends on their water-to-surfactant ratio. A higher water-to-surfactant ratio results
in larger and more spherical aggregates. The two distinct tails of the surfactant molecule exhibit different
conformations in carbon dioxide indicating contrasting CO2-philic behavior. The perfluoroalkane tails
assume more extended conformation than the alkane tails. The microstructure of the aqueous core reveals
that the water molecules in the interfacial region are strongly oriented in response to the electric fields
of the anionic headgroups and sodium counterions, while water near the center of the core approaches
bulklike properties with the presence of a hydrogen-bonded network.
Introduction
Over the past few years, molecular simulation techniques have been increasingly applied to investigate the
morphology, dynamics, and rheology of surfactant aggregates (micelles) formed in aqueous system.1-14 The
* To whom correspondence may be addressed.
† Department of Chemical Engineering, University of Tennessee.
‡ Chemical Technology Division, Oak Ridge National Laboratory.
§ Departments of Chemical Engineering, Chemistry, and Computer Science, University of Tennessee.
(1) Karaborni, S.; et al. Simulating the Self-Assembly of Gemini
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advantage of these techniques lies in their ability to use
simple molecular models for surfactant molecules (e.g.,
bead-spring model used by Smit et al.)7-9 and other
simplifications, such as constrained aggregate3-5 or latticebased simulations,13,14 to obtain a description of the size,
shape, surface roughness, and the internal structure of
micelles. In fact, in some instances,1,9 these studies have
even helped clarify interpretations of prior experimental
results. In certain conditions where experiments are
impractical or impossible (e.g., high temperatures and
pressures), molecular simulation techniques can be successfully applied to obtain the much-needed information
about the various properties of surfactant aggregates.
Surprisingly, very few simulation studies15-17 have addressed the phenomenon of surfactant aggregation in
nonpolar solvents. The phenomenon of surfactant aggregation in nonpolar solvents (e.g., benzene, toulene,
cyclohexane, carbon tetrachloride, etc.) results in the
formation of aggregates known as reversed (or inverted)
micelles (RMs). Structurally, these aggregates are characterized by the presence of a hydrophilic (often aqueous)
core that is surrounded by a hydrophobic corona made up
of surfactant tail groups. In essence, the structure of RMs
is simply reversed from their aqueous counterparts
because of the reversal in the roles of the hydrophilic and
hydrophobic moieties of the surfactant molecules. These
aggregates find numerous applications in fields such as,
(14) Floriano, M. Antonio; Caponetti, E.; Panagiotopoulos, A. Micellization in Model Surfactant Systems. Langmuir 1999, 15, 31433151.
(15) Linse, P. Molecular dynamics study of the aqueous core of a
reversed ionic micelle. J. Chem. Phys. 1989, 90 (9), 4992-5004.
(16) Tobias, D. J.; Klein, M. L. Molecular Dynamics Simulations of
a Calcium Carbonate/Calcium Sulfonate Reverse Micelle. J. Phys. Chem.
1996, 100, 6637-6648.
(17) Brown, D.; Clarke, J. H. R. Molecular Dynamics Simulation of
a Model Reverse Micelle. J. Phys. Chem. 1991, 92, 2881-2888.
10.1021/la000554f CCC: $20.00 © 2001 American Chemical Society
Published on Web 02/10/2001
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Langmuir, Vol. 17, No. 5, 2001
lubrication, emulsion polymerization reactions, drug
delivery, and enhanced oil recovery, to name a few.
Recently, some experimental studies18-24 have investigated the feasibility of using carbon dioxide (CO2) as a
nonpolar solvent medium for the formation of RMs. Carbon
dioxide is a nonpolar compound that is a chemically inert
(nontoxic, nonflammable) and an environmentally benign
alternative to potentially hazardous industrial solvents
currently in use. Also, its easy availability and low cost
make it a cheap raw material. Thus, formation of
surfactant aggregates in CO2 offers the possibility of
carrying out a wide range of industrial operations in a
medium with minimum environmental impact. Unfortunately, as shown by Consani and Smith,25 most of the
industrially available surfactant molecules are incapable
of forming stable RMs in CO2 because of their negligible
solubility. This is attributed to the fact that most of these
surfactants are suited for aqueous solvents while CO2 is
relatively nonpolar (CO2 has a weak quadrupole) because
of its low polarizibility and dielectric constant. This has
motivated a number of experimental efforts26-34 focused
on discovering suitable surfactant molecules. These surfactants are termed “CO2-philic” surfactants because they
should exhibit favorable interactions with CO2 to enable
dispersion of the aggregates. Although these studies have
been partially successful in identifying a few CO2-philic
surfactant molecules, little is known about the factors
determining CO2-philicity. Knowledge of these underlying
principles can be quite helpful in guiding future efforts in
discovering or designing new and improved CO2-philic
surfactants that are suitable for industrial applications.
(18) Hoefling, T. A.; Enick, R. M.; Beckman, E. J. Microemulsions in
Near-Critical and Supercritical CO2. J. Phys. Chem. 1991, 95, 71277129.
(19) Hoefling, T. A.; et al. The Incorporation of a Fluorianted Ether
Functionality into a Polymer or Surfactant to Enhance CO2-Solubility.
J. Supercrit. Fluids 1992, 5, 237-241.
(20) Newman, D. A.; et al. Phase Behavior of Fluoroether-Functional
Amphiphiles in Supercritical Carbon Dioxide. J. Supercrit. Fluids 1993,
6, 205-210.
(21) Hoefling, T. A.; et al. Design and Synthesis of Highly CO2-soluble
Surfactants and Chelating Agents. Fluid Phase Equilib. 1993, 83, 203212.
(22) Jimenez, M. M.; Luque de Castro, M. D. Reverse-micelle
formation: a strategy for enhancing CO2-supercritical fluid extraction
of polar analytes. Anal. Chim. Acta 1998, 358, 1-4.
(23) Iezzi, A.; et al. Gel formation in carbon dioxide-semifluorinated
alkane mixtures and phase equilibria of a carbon dioxide-perfluorinated
alkane mixture. Fluid Phase Equilib. 1989, 52, 307-317.
(24) Wikramanayake, R.; Enick, R.; Turberg, M. The phase behavior
and gel formation of binary mixtures of carbon dioxide and semifluorinated alkanes. Fluid Phase Equilib. 1991, 70, 107-118.
(25) Consani, K. A.; Smith, R. D. Observations on the Solubility of
Surfactants and Related Molecules in Carbon Dioxide at 50 °C. J.
Supercrit. Fluids 1990, 3, 51-65.
(26) DeSimone, J. M.; Guan, Z.; Elsbernd, C. S. Synthesis of
Fluoropolymers in Supercritical Carbon Dioxide. Science 1992, 257,
945-947.
(27) DeSimone, J. M.; et al. Dispersion Polymerizations in Supercritical Carbon Dioxide. Science 1994, 265, 356.
(28) Johnston, K. P.; et al. Water-in-Carbon Dioxide Microemulsions: An Environment for Hydrophiles Including Proteins. Science
1996, 271, 624-626.
(29) Harrison, K. L.; et al. Water-in-Carbon Dioxide Microemulsions
with a Fluorocarbon-Hydrocarbon Hybrid Surfactant. Langmuir 1994,
10, 3536-3541.
(30) Heitz, M. P.; et al. Water Core within Perfluoropolyether-Based
Microemulsions Formed in Supercritical Carbon Dioxide. J. Phys. Chem.
1997, 101, 6707-6714.
(31) McClain, J. B.; et al. Design of Nonionic Surfactants for
Supercritical Carbon Dioxide. Science 1996, 274, 2049-2052.
(32) McFann, G. J.; Johnston, K. P.; Howdle, S. M. Solubilization in
Nonionic Reverse Micelles in Carbon Dioxide. AIChE J. 1994, 40, 543555.
(33) Fulton, J. L.; et al. Aggregation of Amphiphilic Molecules in
Supercritical Carbon Dioxide: A Small-Angle X-ray Scattering Study.
Langmuir 1995, 11, 4241-4249.
(34) Cooper, A. I.; et al. Liquid-Liquid Extractions Using DendrimerModified Carbon Dioxide. Nature 1997, 389, 368-371.
Salaniwal et al.
Molecular simulation techniques can play an important
role in developing this much-needed knowledge base.
As an initial step in this direction, we performed
molecular dynamics (MD) simulation of a dichain surfactant + water + carbon dioxide (solvent) system. The
dichain surfactant molecule [(C7F15)(C7H15)CHSO4-Na+]
(also known as a hybrid surfactant molecule) is one of the
few CO2-philic surfactant molecules that has been shown29
to form RMs with aqueous cores in CO2. Recently, Eastoe
et al.35 performed a small-angle neutron scattering (SANS)
study on the dichain surfactant system and obtained
information regarding the structural properties (size and
shape) of the RMs formed. In the simulations presented
here, this particular surfactant molecule was chosen for
two main reasons. First, in terms of the molecular
complexity this is a relatively small molecule compared
to other known CO2-philic surfactant molecules. Thus,
from a computational perspective, it is relatively easy to
model this surfactant to a sufficient degree of detail and
study the aggregation behavior for a relatively large
system size. Second, the structural properties of the
surfactant aggregates estimated from simulations can be
quantitatively compared to the experimental results of
Eastoe et al.35 In our previous paper,36 we presented
preliminary results showing the spontaneous aggregation
of the dichain surfactant and water molecules into RMlike aggregates in this ternary system. The results
presented there were for a small (exploratory) system that
was used to test the feasibility of these simulations. In
this paper, we present additional simulations on a much
larger system intended to reproduce the experimental
system.35 We also describe the detailed molecular models
for the dichain surfactant molecule, water, and carbon
dioxide adopted for this study and the simulation methodology used to simulate this complex physical system.
Quantitative comparisons of the simulation results with
the experimental results of Eastoe et al.35 are presented.
Also, microscopic structural details of the aqueous core
are presented.
POTENTIAL MODELS
Since one of the objectives of the present work is to
make quantitative comparisons with the experimental
work of Eastoe et al.,35 a high degree of realism is desirable
to accurately represent all the intermolecular interactions
present in the system. Thus, the simulations presented
in this work involve detailed and realistic molecular
models for all the three chemical species (dichain surfactant, water, and carbon dioxide) present in the system.
Although this makes the system computationally complex
and demanding, it minimizes any artificiality that might
be included in the system and affect the dynamics of
surfactant aggregation and/or the morphology of the
aggregates formed. With these factors in consideration,
the potential model for the hybrid surfactant molecule
used in this simulation study was constructed by assembling existing models for each of the four functionally
distinct parts of the molecule, i.e., the alkane tail,
perfluoroalkane tail, sulfate headgroup, and the sodium
counterion. This allows the surfactant model to capture
most of the essential characteristics of the real dichain
surfactant molecule.
(35) Eastoe, J.; et al. Droplet Structure in a Water-in-CO2 Microemulsion. Langmuir 1996, 12, 1423-1424.
(36) Salaniwal, S.; et al. Self-Assembly of Reverse Micelles in Water/
Surfactant/Carbon Dioxide Systems by Molecular Simulation. Langmuir
1999, 15 (16), 5188-5192.
Dichain Ternary System
Langmuir, Vol. 17, No. 5, 2001 1775
For interactions between unlike sites (on the same or
different molecules) we have used the conventional
Lorentz-Berthelot combining rules without any fitted
binary parameter.
Alkane Tail. The potential model for the alkane tail
of the surfactant molecule is the united atom model for
alkanes proposed by Siepmann and co-workers37 (SKS
model). This model accurately predicts the experimentally
measured phase envelopes of n-alkanes. More importantly,
as shown by Cui et al.,38 the SKS model predicts the
solubility of n-alkanes in CO2 that is also consistent with
experimentally determined values. In this potential model,
each of the methylene (CH2) and methyl (CH3) functional
groups is represented by a single spherical interaction
site (united atom) with its interaction center located at
the center of the carbon atom. The interaction sites are
connected via rigid bonds of length 1.54 Å. Interaction
sites on different surfactant molecules and those on the
same molecule separated by more than three bonds
interact via the well-known 12-6 Lennard-Jones (LJ)
potential given by
[( ) ( ) ]
ULJ(rij) ) 4ij
σij
rij
12
-
σij
rij
6
(1)
where ij is the well depth and σij is the zero point of the
potential between site i and site j. The LJ size parameters
for the methyl and methylene functional groups are same
(σCH3 ) σCH2 ) 3.93 Å) while the well-depth energy
parameters are CH3/k ) 114 K and σCH2/k ) 47 K,
respectively. The intramolecular interactions include the
bond-angle bending potential to account for the bond
vibrational motion, and torsional angle potential to
account for the spatial orientation of the tails. The bond
angle bending potential is described by a harmonic
function of the form
Ubending(θi) )
1
k (θ - θeq)2
2 θ i
(2)
where θeq is the equilibrium angle between successive
bonds and kθ is the force constant and is a measure of the
rigidity of the bond angle. The torsional angle potential
for the alkane tail is given by39
3
Utorsion(φ) )
ai cos(iφ)
∑
i)0
(3)
where φ is the torsional angle that is defined as the angle
between the normal to the two planes, each of which is
formed by three successive interaction sites. Table 1 lists
the potential parameters for the alkane model.
Perfluoroalkane Tail. The potential model for the
perfluoroalkane tail used in this study is that proposed
by Cui et al.40 and is quite similar to that of the alkane
tail described above. This model was chosen because it is
fitted to the phase envelope of n-perfluroralkanes and
also does good de novo prediction of pefluoroalkane/CO2
phase equilibrium.38 United atoms with effective LJ well(37) Siepmann, J. I.; Karaborni, S.; Smit, B. Simulating the critical
behavior of complex fluids. Nature 1993, 365, 330-332.
(38) Cui, S. T.; Cochran, H. D.; Cummings, P. T. Vapor-liquid phase
coexistence of alkane carbon dioxide and perfluoralkane carbon dioxide
mixtures. J. Phys. Chem. 1999, 103, 4485-4491.
(39) Ploeg, P. van der; Berendsen, H. J. C. Molecular dynamics
simulation of a Bilayer membrane. J. Chem. Phys. 1982, 76, 32713276.
(40) Cui, S. T.; et al. Intermolecular potentials and vapor-liquidphase equilibria of perfluorinated alkanes. Fluid Phase Equilib. 1998,
146, 51-61.
Table 1. Potential Parameters for theIntramolecular and
Intermolecular Degrees of Freedom for the Alkane Tail
and the Perfluoroalkane Tail
type of interaction
alkane tail
perfluoroalkane tail
σCH3 ) σCH2 ) 3.93 Å
CH3/k ) 114 K
CH2/k ) 47 K
bond-angle bending kb ) 62500 K/rad2
θeq ) 114.0°
torsional
a0 ) 1078.16 K
a1 ) 355.03 K
a2 ) -68.19 K
a3 ) 791.32 K
Lennard-Jones
interactions
σCF3 ) σCF2 ) 4.60 Å
CF3/k ) 79 K
CF2/k ) 30 K
kb ) 62500 K/rad2
θeq ) 114.6°
a0 ) 959.4 K
a1 ) -282.7 K
a2 ) 1355.2 K
a3 ) 6800.0 K
a4 ) -7875.3 K
a5 ) -14168.0 K
a6 ) 9213.7 K
a7 ) 4123.7 K
depth and size parameters are used to represent the CF2
and CF3 functional groups of the tail (σCF3 ) σCF2 ) 4.6 Å,
CF3/k ) 79 K, σCF2/k ) 30 K). The bond length between the
united atoms is assumed fixed at 1.54 Å. The nonbonded
interactions are described via a 12-6 LJ potential (eq 1)
while the bond-angle bending and torsional angle potential
account for the intramolecular interactions. The bond
angle potential is similar to that of the alkane tail (eq 2)
with the only difference being the slightly larger (114.6°)
equilibrium bond angle. The torsional angle potential for
the perfluoroalkane tail is given by
7
Utorsion(φ) ) a0 +
ai (cos φ)i
∑
i)1
(4)
where φ is the dihedral angle. The important features of
the torsional potential for perfluoroalkane are that it has
a twisted trans minimum at a dihedral angle of φ ∼ 17°,
a gauche minimum at φ ∼ 125°, and a second gauche
minimum at around φ ∼ 83°. Table 1 also lists the potential
parameters for the perfluoroalkane model.
Sulfate Headgroup and Sodium Counterion. The
potential model for the sulfate headgroup of the surfactant
molecule is a fully atomistic (each interaction site represents an individual atom) model proposed by Cannon
and co-workers.41 The molecule has a rigid tetrahedral
structure (O-S-O bond angle of 109.4°) with the sulfur
atom at the axis and the oxygen atoms at the four apexes.
The bond between the sulfur and oxygen atoms is fixed
at 1.489 Å. To account for electrostatic interactions, the
sulfur atom carries a charge of +2e while three oxygen
atoms each carry a charge of -1e. The fourth oxygen atom
does not carry any negative charge as it is attached to the
CH group, which in turn is attached to the two tails. A
sum of Coulombic (for electrostatic interactions) and LJ
terms describes the intermolecular interactions
U(rij) )
qiqj
∑i ∑j r
ij
[( ) ( ) ]
+ 4ij
σij
rij
12
-
σij
rij
6
(5)
where qi represents the Coulombic charge on the atom i.
A single LJ sphere with a unit positive charge represents
each sodium ion. Table 2 lists the potential parameters
for sulfur and oxygen atoms and sodium ion used in this
study. According to this molecular model, each surfactant
molecule consists of 21 interaction sites including one for
the Na+ ion.
(41) Cannon, W. R.; Pettitt, B. M.; McCammon, J. A. Sulfate Anion
in Water: Model Structural, Thermodynamic, and Dynamic Properties.
J. Phys. Chem. 1994, 98, 6225-6230.
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Salaniwal et al.
Table 2. Potential Parameters for the Sulfur and Oxygen
Atoms of the Headgroup and the Sodium Counterion
atom type
σ (Å)
/k (K)
q (e)
sulfur
oxygen
sodium
3.55
3.15
2.667
126
126
37.65
+2
-1
+1
Table 3. Potential Parameters for the Carbon Dioxide
Potential Model
atom type
σ (Å)
/k (K)
q (e)
carbon
oxygen
2.757
3.033
28.129
80.507
+0.6512
-0.3256
Table 4. Potential Parameters for the SPC/E Potential
Model for Water
atom type
σ (Å)
/k (K)
q (e)
hydrogen
oxygen
0.0
3.166
0.0
78.2
+0.4238
-0.8476
Carbon Dioxide. The carbon dioxide (solvent) molecules are represented by a simple site-based potential
model proposed by Harris and Yung,42 which has been
shown to accurately reproduce the experimental vaporliquid coexistence curve and critical point. The model
consists of three LJ interaction sites with a Coulombic
charge centered on each atom. The molecule has a rigid
linear (O-C-O bond angle ) 180°) geometry with the
C-O bond length of 1.149 Å. The carbon atom carries a
charge of +0.6512e while the two oxygen atoms carry a
charge of -0.3256e each to make the molecule electrically
neutral. Table 3 lists the parameters of the potential model.
Water. For water molecules, the extended simple point
charge (SPC/E) potential model of Berendsen et al.43 is
used in this study. The model has a single LJ site for the
oxygen atom that also carries a charge of -0.8476e. The
two hydrogen atoms are simply represented by point
charges, each carrying a charge of +0.4238e. Rigid
molecular geometry is assumed with the O-H bond length
of unity and H-O-H bond angle equal to the tetrahedral
angle (109.4°). Table 4 lists the potential parameters for
this model.
Simulation Methodology
Molecular dynamics simulations of two different system
sizes were performed. The first system (referred to as the
small system) consists of 30 dichain surfactant, 132 water,
and 2452 CO2 molecules. This system (with approximately
8300 interaction sites) was chosen for exploratory calculations (with computational economy in mind) and to
provide qualitative insight into the dynamics of aggregation and the morphology of the aggregates. Some preliminary results on this system were reported previously.36
The state conditions used with this system were, T ) 310
K and Fsolvent ) 0.482 g/cm3. These conditions were chosen
to ensure that CO2 was in the supercritical state. The
critical point of CO2 is Tc ) 304.3 K, Pc ) 73.8 bar, and
Fc ) 0.468 g/cm3. The second system (referred to as the
large system) has 33 surfactant, 1175 water, and 12 800
CO2 molecules at T ) 298 K and Fsolvent ) 0.848 g/cm3. This
system mimics the surfactant and water concentrations,
temperature, and density used by Eastoe et al.35 in their
SANS study of this ternary system. The system size
corresponds to one “average-sized” aggregate observed by
(42) Harris, J. G.; Yung, K. H. Carbon Dioxide’s Liquid-Vapor
Coexistence Curve and Critical Properties as Predicted by a Simple
Molecular Model. J. Phys. Chem. 1995, 99, 12021-12024.
(43) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing
Term in Effective Pair Potentails. J. Chem. Phys. 1987, 91, 6269-6271.
Figure 1. Snapshots of the starting configurations for the small
system used in this study: (a) aggregated configuration and (b)
scattered configuration. The color scheme of the various species
is as follows: light blue for perfluoroalkane tail, dark blue for
alkane tail, yellow for sulfur, red for oxygen, white for hydrogen,
and gray for sodium.
Eastoe et al.35 In this system, the CO2 is in the hightemperature liquid state at 500 bar. The equations of
motion for each interaction site were solved using the
Rattle algorithm44 to constrain the rigid bond lengths in
molecules. The time step used to solve the equations of
motion was 1.483 fs.
As discussed in the following paper of this series,
aggregation of reverse micelles with aqueous cores in
carbon dioxide from this system, with the scattered
starting configuration, is rapid, on the order of 0.2 µs,
compared with the 1-10 µs for a typical oil-in-water
micelle, because of the strong Coulombic forces present
in the system studied here in comparison with the much
weaker hydrophobic forces in the oil-in-water system.
The simulations were performed with two independent
initial conditions, viz., (a) an aggregated starting configuration and (b) a scattered starting configuration, shown
in Figures 1 and 2 for the small system and the large
system, respectively. In the aggregated starting config(44) Andersen, H. C. Rattle: a velocity verlet version of the shake
algorithm for molecular dynamics calculations. J. Comput. Phys. 1983,
52, 24-34.
Dichain Ternary System
Langmuir, Vol. 17, No. 5, 2001 1777
Figure 2. Snapshots of the starting configurations for the large
system used in this study: (a) aggregated configuration and (b)
scattered configuration. The color scheme of the various species
is as follows: light blue for perfluoroalkane tail, dark blue for
alkane tail, yellow for sulfur, red for oxygen, white for hydrogen,
and gray for sodium.
uration, all the water molecules were placed within a
spherical core at the center of a cubic simulation box. The
surfactant molecules with fully extended tails were placed
on the surface of the core with their headgroups pointing
toward the center. Structurally, this configuration resembles a reversed micellar aggregate and hence the term
aggregated starting configuration. In contrast, the scattered starting configuration has all the water molecules
scattered within the simulation box. These initial conditions are two of the infinite configurations that can be
used as starting conditions and were chosen solely for the
sake of convenience.
Results and Discussion
Figure 3 shows the snapshots of the small system (from
aggregated starting configuration), large system (from
aggregated starting configuration), and large system (from
scattered starting configuration) at 1.036, 1.0, and 2.0 ns,
respectively. In all these snapshots, the CO2 molecules
are intentionally hidden so that the surfactant aggregates
can be seen clearly. All the figures show the presence of
surfactant aggregates in the system that have the ap-
Figure 3. Snapshots of the small system (aggregated starting
configuration), large system (aggregated starting configuration),
and large system (scattered starting configuration) at (a) 1.036,
(b) 1.0, and (c) 2.0 ns. The color scheme of the various species
is as follows: light blue for perfluoroalkane tail, dark blue for
alkane tail, yellow for sulfur, red for oxygen, white for hydrogen,
and gray for sodium.
pearance of RMs, i.e., aggregates consisting of aqueous
cores surrounded by surfactant molecules with their
headgroups immersed in the core and the tails form a
corona. Figure 3a shows the system consists of three
roughly similar-sized aggregates with their aqueous cores
well shielded from the surrounding solvent. The surfactant
aggregates formed in the small system with scattered
starting configuration (not shown) were also similar to
those shown in Figure 3a. Parts b and c of Figure 3 show
that the aggregates formed in the large systems have their
aqueous cores considerably exposed to the surrounding
solvent. This difference between the small and the large
system could be attributed to the higher water-tosurfactant molar ratio, Wo, in the large system (Wo ∼ 35
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Langmuir, Vol. 17, No. 5, 2001
Salaniwal et al.
for the large system; cf. Wo ∼ 4 for the small system).
Figure 3b shows that during the time interval of 1.0 ns,
the aggregated starting configuration of the large system
evolves into a configuration with a large aggregate
consisting of most of the surfactant and water molecules
(the few remaining surfactant and water molecules were
distributed between three smaller aggregates). On the
other hand, the scattered starting configuration of the
large system evolves into a configuration consisting of
five small-sized surfactant aggregates. Since the overall
composition of the large system corresponds to one
average-sized aggregate observed by Eastoe et al.,35 the
expected final state in the large system is a single
surfactant aggregate consisting of all the surfactant and
water molecules. Thus, it can be argued that Figure 3b
is much closer to the expected final state compared to
Figure 3c. On the basis of the times corresponding to these
configurations, it can also be stated that the aggregated
starting configuration of the large system approaches the
expected final state in a shorter time compared to the
scattered starting configuration. In our next paper,45 we
demonstrate that the scattered starting configuration of
the large system follows a realistic trajectory and should
also reach the expected final state in ∼200 ns. In essence,
using the aggregated starting configuration as the initial
condition for the large system simply reduces the time
needed to approach the expected final state thereby
allowing the study of the structural properties of surfactant
aggregates in a reasonable amount of computer time. Thus,
the structural properties of the largest aggregate in Figure
3b can be quantitatively compared to the experimental
results of Eastoe et al.35
Aggregate Size and Shape. The general structural
properties of the RM-like aggregates formed in the
simulations presented above can be characterized by the
shape and size of their aqueous cores. A good measure of
the size is the radius of gyration (Rg), which is a measure
of the distribution of the mass of atomic groups or
molecules that constitute the aqueous core relative to its
center of mass. Since the core is essentially made up of
water molecules, sodium ions, and anionic headgroups,
the mass of only these groups (tail groups are not
considered) is considered in the estimation of Rg. The Rg
of the aqueous core (to be compared with the core radius
fitted to the SANS data) can be calculated by the equation
Rg2 )
∑i mi(ri - ro)2/∑i mi
(6)
where mi is the mass of atom i located at a radial distance
ri from the center of mass of the aggregate core (ro). The
shape of the aqueous core can be quantified using two
different parameters, namely, the ratio of the largest to
the smallest principal moments of inertia (Imax/Imin) and
the eccentricity (η). The eccentricity is calculated by the
equation
η)1-
Imin
Iavg
(7)
where Iavg is the average of all the three components of the
principal moment of inertia. Both these parameters
provide a measure of the deviation from a perfectly
spherical object (Imax/Imin ) 1, η ) 0). The uncertainty in
(45) Salaniwal, S.; Cui, S. T.; Cochran, H. D.; Cummings, P. T. Selfassembly in a dichain surfactant/water/carbon dioxide system via
molecular simulation. 2. Aggregation dynamics. Langmuir 2001, 17,
1784.
Table 5. Structural Properties of the Largest Aggregate
Formed in the Large Simulation System (Aggregated
Starting Configuration)
water
surfactant
Wo
Rg (Å)
Imax/Imin
η
As (Å2)
this work
SANS experiments
916 ( 10
26
35.2
15.4 ( 0.2
1.3 ( 0.1
0.12 ( 0.05
115 ( 3
35
20.5 ( 1.0
140
the values of these parameters reflects the effect of the
spatial or temporal fluctuations in the shape of the aqueous
core. Together these two parameters can reveal details of
the actual shape (spherical, cylindrical, or disklike) of the
aggregates.
Table 5 provides the structural properties of the largest
aggregate in Figure 3b along with the experimental values
measured by Eastoe et al.35 via SANS experiments. The
radius of gyration (Rg) of the aggregate formed in this
simulation study is 15.4 ( 0.3 Å. This is in reasonable
agreement with the experimentally reported value of 20.5
( 1.0 Å, given that the time for which the simulation has
been carried may be considerably shorter than that
required to achieve a final equilibrium state. The shape
parameters for the aggregate are Imax/Imin ) 1.2 ( 0.1 and
η ) 0.1 ( 0.05 (no experimental data available), which
indicates that the aggregate is nearly spherical with small
fluctuations. This is expected because of the high Wo in
this aggregate. The high value of Wo provides the aggregate
with an aqueous core of considerable volume (and surface
area) thereby facilitating a low packing density of surfactant molecules around the aqueous core. To characterize
the shape of the aggregates formed in the experimental
investigation, Eastoe et al.35 determined the surface area
of the aqueous core per surfactant molecules (As), given
by the equation
As ) 4πRg2/Ns
(8)
where Ns is the aggregation number (number of surfactant
molecules in the aggregate). In essence, this quantity is
a measure of the packing density of the surfactant
molecules in the aggregate and, thus, can be related to
the shape of its aqueous core. The value of As for the
aggregate estimated from the simulation is 115 Å2, which
is in approximate agreement with the experimentally
reported value of 140 Å2.35
The structural characteristics of the large aggregate in
Figure 3b merit some additional discussion. First, the
question must be addressed, “Is this aggregate structurally
similar to the reverse micelles observed in the SANS
experiments?” The only way to answer this is as follows:
(a) The models used have been tested and have yielded
results in reasonable agreement with the relevant experimental data in the literature, and (b) as shown in
Table 5, the simulation results are in reasonable agreement with all of the experimentally measured structural
properties of reverse micelles. A second issue then arises,
the large aggregate in Figure 3b does not look like the
common picture of a reverse micelle; a large portion of the
aqueous core is directly exposed to the CO2, and the
surfactant molecules are not uniformly distributed on the
interface. In fact, the experimental result (As ) 140 Å2)
indicates that even more of the aqueous core should be
exposed, and even though on average the surfactant
distribution on the interface should be uniform, this does
not imply that the instantaneous distribution should be
Dichain Ternary System
Langmuir, Vol. 17, No. 5, 2001 1779
Table 6. Structural Properties of Surfactant Aggregates
Formed in the Small System (Aggregated Starting
Configuration)
water
surfactant
Wo
Rg (Å)
Imax/Imin
η
aggregate no. 1
aggregate no. 2
aggregate no. 3
26
10
2.6
6.2 ( 0.1
1.8 ( 0.1
0.28 ( 0.02
57
9
6.3
7.2 ( 0.2
1.7 ( 0.3
0.27 ( 0.08
49
11
4.4
6.9 ( 0.1
1.5 ( 0.1
0.13 ( 0.03
uniform. Perhaps the common picture of a reverse micelle
should be reconsidered.
For surfactant aggregates formed in the small system
(Figure 3a), the structural properties are influenced by
the low water-to-surfactant ratio (Wo ∼ 4) in this system.
Table 6 lists the Rg, Imax/Imin, and η values for the three
aggregates shown in Figure 3a. The Rg values for all the
three aggregates lie within the range of 6.2-7.2 Å
indicating nearly equal-sized aggregates. The Imax/Imin
values for all the three aggregates are significantly greater
than unity and the η values are significantly greater than
zero. Thus, the aggregates formed are highly nonspherical
compared to those formed in the large system. Clearly,
the low Wo in this system results in aggregates with much
smaller aqueous cores (smaller Rg), thereby resulting in
significantly higher packing density of surfactant molecules. Another factor that may also contribute to the high
nonsphericity in these aggregates is the ineffective
dielectric screening of ionic headgroups. The simulations
showed that most of the water molecules (∼94%) in the
small system lie within the hydration shell of anionic
headgroups and Na+ ions (in contrast to ∼62% for the
large system) and thus very few water molecules were
available to provide the dielectric screening of ionic
charges. As a result the interactions between ionic charges
lead to the distortion of the interface. Similar results
regarding the nonsphericity of aggregates with low waterto-surfactant ratio (Wo ) 2) were obtained by Brown and
Clarke17 for a model reversed micelle. Interestingly, the
standard deviations in the values of Imax/Imin and η for the
aggregates of Figure 3a, as shown in Table 6, are quite
low. As mentioned earlier, these deviations are a measure
of the fluctuations in the shape of the aggregates. The low
value of these deviations suggests that the temporal
fluctuations in the shape of these aggregates are quite
low. The fluctuations observed in the time evolution of
Imax/Imin and η are more prominent in aggregate no. 2
than in the other aggregates. This can be attributed to a
slightly higher water-to-surfactant ratio in this particular
aggregate (Wo ∼ 6) compared to the other two aggregates.
Aggregate Microstructure. Having established that
the structure of the largest aggregate formed in the large
system (Figure 3a) with aggregated starting configuration
is in reasonable agreement with the experimental findings,
it is logical to explore the microstructure of this aggregate.
Molecular simulations provide an effective tool to obtain
this information. A primary measure of the microscopic
structure is the singlet distribution function (singlet radial
density) profiles of the various atomic groups or molecules
constituting the aggregate. As the name suggests, the
singlet distribution function is a time-averaged measure
of the distribution of an atom or molecule from a reference
point. It is calculated by the equation
F(r) ) 〈N(r)〉/4πr2∆r
(9)
where 〈N(r)〉 is the time average of the number of an atom
or molecule that is found in a shell of thickness ∆r at a
Figure 4. Structural properties of the aggregate formed in
the large system with aggregated starting configuration: (a)
water and carbon dioxide; (b) microstructure of surfactant
molecule.
radial distance r from a reference point. The center of
mass of the aqueous core represents a suitable reference
point.
Figure 4 shows the microscopic details of the largest
aggregate formed in the large system with aggregated
starting configuration (Figure 3b). Figure 4a shows the
density profile of water and CO2 (solvent) molecules. The
density of water in the aqueous core is ∼1.0 g/cm3
indicating the presence of bulklike water. A broad (∼1015 Å) interfacial region is observed, where the water
density decreases while the CO2 density increases as the
distance from the center of mass of the increases. The
solvent density approaches its bulk density of ∼0.85 g/cm3
outside the interfacial region. Negligible penetration of
the solvent molecule into the aqueous core of the aggregate
is observed. This is consistent with the high ionic strength,
I ∼ 1.5, due to the ionic headgroups and the counterions
in the small aqueous core. Figure 4b plots F(r) as a function
of the radial distance (r) for the various groups of the
surfactant molecules. The distribution of the headgroups
shows a peak at ∼17.2 Å indicating the presence of
headgroups at the surface of the aqueous core. The
distribution for the Na+ ions is quite similar to that for
the headgroups implying that the Na+ ions also reside at
the surface of the aqueous core and may be ion-paired to
the anionic headgroups. The density distribution of the
two tails suggests that the tails form the corona of the
aggregate. The distribution of the perfluoroalkane tail is
shifted slightly away from the center of mass and is an
indication of its CO2-philic behavior.
Figure 5 shows the microscopic details of the aggregates
formed in the small system (Figure 3a). The figures show
that the core of the aggregates is essentially made up of
1780
Langmuir, Vol. 17, No. 5, 2001
Salaniwal et al.
Figure 6. Time evolution of the % trans bonds (extent of fully
extended tails) for the perfluoroalkane tail and the alkane tail
of the C7-tailed hybrid surfactant.
Figure 5. Structural properties of the aggregate formed in
the small system with aggregated starting configuration: (a)
water and carbon dioxide; (b) microstructure of surfactant
molecule.
water molecules and the sodium ions. The headgroups lie
at the surface of the aqueous cores while the tails form
the corona surrounding the cores. The nonzero radial
density of the headgroups within the core (r < 6.2 Å) is
not due to the penetration of the headgroups but simply
an artifact of the highly nonspherical shape of these
aggregates (Table 6). Also, the presence of numerous peaks
and troughs in the radial density distribution of the sodium
ions and anionic headgroups is a manifestation of the rigid
structure of the aqueous core. The rigid structure of the
aqueous core also manifests itself in the considerably high
water density observed in Figure 5a. The radial density
distributions of the two tails are quite similar except for
a slight shift away from the center of mass observed for
the perfluoroalkane tail. As mentioned earlier, this is due
to the CO2-philic nature of this tail.
Tail Conformation. A good measure of the CO2-philic
behavior of the two different tail groups is the degree to
which these tails are fully extended. Figure 6 plots the
fraction of torsional angles in each tail that are in trans
conformation (fully stretched) as a function of time for the
small system with aggregated starting configuration.
Similar results were obtained for the large systems as
well. The perfluoroalkane tails have an average of 90 (
2% trans conformation compared to 74 ( 5% for the alkane
tails. This implies that the perfluoroalkane tails are
approximately 16% more extended than the alkane tails.
Interestingly, the behavior of the two tails is quite opposite
in vacuo. The perfluoroalkane tail has a trans conformation
of 80% in vacuo compared to 89% for the alkane tail. Thus,
in the presence of carbon dioxide as a solvent medium,
the perfluoroalkane tails assume more extended conformations in vacuo, and the alkane tails assume more
Figure 7. Radial distribution of the functional groups of the
perfluoroalkane tail and the alkane tail for the C7-tailed hybrid
surfactant.
collapsed conformations in vacuo. This is an indication of
the fact that the perfluoroalkane tails are more CO2-philic
than the alkane tails.
More detailed information on the spatial conformation
of the two tails can be obtained by calculating the
distribution of the radial position of each segment
(functional group) of the tails from the CH group, as shown
in Figure 7. The common feature of the two tails evident
from the figure is the progressive broadening of the
distribution for groups farther away from the headgroup.
The broadening is relatively larger for the alkane tail
compared to that for the perfluoroalkane tail because of
the relative stiffness of the perfluoroalkane tail. Also, the
distributions of the first two segments are the same for
the two tails. The broadening is attributed to the fact that
the farther away the segment is from the headgroup the
more freedom it has to move. This mobility is due to the
ability of torsional angles associated with these segments
to switch back and forth between trans and gauche
conformations. For the alkane tail the distribution of
farther segments exhibits two distinct peaks reflecting a
1 to 3 ratio of gauche-to-trans conformation of the torsional
angles associated with these segments. Thus, the perfluoroalkane tails are more extended and less mobile than
the alkane tails.
Structure of the Aqueous Core. As shown earlier,
the surfactant aggregates formed in this simulation study
are characterized by the presence of aqueous cores. These
aqueous cores can provide a medium for solubilizing polar
Dichain Ternary System
Figure 8. Radial distribution function (rdf) for (a) Na-Na
pair and (b) Na-headgroup pair.
Figure 9. Radial distribution function (rdf) for the (a) Nawater pair and (b) headgroup-water pair.
and/or polymeric substances in CO2. Thus, understanding
the detailed structure of water in these aqueous cores is
of fundamental importance in understanding the solubilization characteristics and behavior of solutes.
To get an insight into the detailed structural characteristics of the aqueous cores, Figure 8 plots the radial
distribution function (rdf) for Na-Na and Na-X pairs (X
denotes the anionic headgroups) in the largest aggregate
shown in Figure 3b. As discussed earlier, the structural
properties of this surfactant aggregate are closest to the
RMs observed by Eastoe et al.35 via SANS experiments.
Since the reference ion is located at the interface (Figure
4b), its environment is anisotropic, even at small distances.
As a result, the rdf decays to zero with increasing radial
distance instead of approaching unity as observed for
isotropic systems. Figure 8 shows that Na-X rdf has a
prominent first peak at 2.45 Å and a minimum at 3.2 Å.
The secondary peaks in the rdf at 3.9 and 4.5 Å are due
to the remaining two negatively charged oxygens on the
headgroup. There are about ∼0.75 Na+ ions within 3.2 Å
of each headgroup, implying that most of the Na+ ions are
ion paired to the surfactant headgroup. The Na-Na rdf
shows a peak at 3.7 Å, a broad minimum at 5.0 Å, and a
second peak at 6.3 Å, indicating a weaker ion-ion
correlation, as expected. The location of the first peak at
3.7 Å is a manifestation of the fact that the Na+ ions are
primarily located at the interfacial region. Figure 9 shows
the rdf for the Na-W (W denotes water molecules) and
X-W pairs. The rdf for the Na-W shows a distinct
hydration shell with a maximum at 2.5 Å. A second
Langmuir, Vol. 17, No. 5, 2001 1781
Figure 10. Interparticle-dipole vector angle angular distribution function (adf) for water molecules lying within the
primary hydration shell of the ions.
hydration peak exists at 4.4 Å. Thus, there exist two
distinct hydration shells for the Na+ ion implying a strong
structuring of water molecules around the reference ion.
The average number of water molecules in the first
(primary) hydration ions is ∼4. The rdf for the X-W shows
a less prominent first peak at 4.1 Å and weak second peak
at 6.0 Å. The presence of a less prominent and broad first
peak in the X-W rdf may be attributed to the “correlation
hole effect”46 and is related to the tetrahedral geometry
of the surfactant headgroups. Since each headgroup has
three negatively charged oxygen atoms at a fixed distance
from each, a number of possibilities exist in which a
particular water molecule can exist around the reference
ion. As a result, the pair correlation function involves
averaging over distances that involve the van der Waal
diameter (σ) as well as the length scale corresponding to
fixed interatomic distances. Thus, the peak in the X-W
rdf is broader and lower. The average number of water
molecules in the first hydration shell of the ionic headgroup
is ∼9, implying a higher degree of hydration of the
headgroup compared to the Na+ ion because it is larger
than the Na+ ion and has more charges.
An important characteristic of the water molecules in
the aqueous core is the extent of their hydrogen bonding.
In this study, a hydrogen bond is defined to exist if any
one of the O-H bonds of a particular water molecule is
collinear with an oxygen atom of a neighboring water
molecule. To analyze the orientation of the water molecules, angular distribution functions (adf) are used.
Figure 10 shows the adf’s of the interparticle-dipole vector
for water molecules belonging to the primary hydration
shell of the Na+ ion and sulfate headgroup. The adf for the
Na+ ion shows a monotonic decrease along the angular
range indicating the alignment of water in such a way
that the dipole of water molecules is collinear with the
Na+ ions. This is due to the strong electrostatic interaction
between Na+ ion and the negatively charged oxygen atom
of water molecules. The adf for the headgroup shows a
peak at cos φ ∼ 0.6 (φ ∼ 53°) which is due to the fact that
the anionic headgroup interacts with positively charged
hydrogen atoms of the water molecules thereby aligning
the water dipole at the angle of ∼53°. This clearly shows
that the strong electric fields from the Na+ ion and the
anionic headgroup tend to orient the water dipole vectors
in their primary hydration shells. As expected, the
orientation effects are relatively stronger for the Na+ ions
(46) Chandler, D. Introduction to Modern Statistical Mechanics;
Oxford University Press: New York, 1987.
1782
Langmuir, Vol. 17, No. 5, 2001
Salaniwal et al.
distance of 3.3-6.0 Å from the reference ion (secondary
hydration shell) show very little orientation compared to
those in the primary hydration shell. The water molecules
lying at distances larger than 6.0 Å show negligible
orientation effects. Similar results were found for the water
molecules around the sulfate headgroups. Thus, on the
basis of this analysis the water molecules in the aqueous
core can be divided into two distinct populations, the
interfacial water which lies in the primary hydration shell
and bulklike water which lies outside the primary
hydration shell. Figure 11 shows the orientation of water
molecules present in the bulklike region of the aqueous
core. Figure 11a shows the adf for the dipole-dipole vector
angle for the water molecules. The figure shows most of
the water pairs have a dipole-dipole vector angle alignment greater than φ ∼ 0°. Thus, water molecules exhibit
a tendency to form hydrogen bonds (a hydrogen bond is
defined if one of the OH bond of a water molecule is
collinear with the oxygen atom of a neighboring water
molecule) in the bulklike region, as expected. Figure 11b
shows the adf for the interparticle-dipole vector angle.
The adf shows a distinct peak at cos φ ∼ 0.6 (φ ∼ 53°).
Figure 11c shows the adf for the interparticle-bond vector
angle and shows two peaks, one at cos φ ∼ -0.3 (φ ∼ 107°)
and the other at cos φ ∼ 1 (φ ∼ 0°). The two peaks
correspond to the two bond vectors in a water molecule.
The positions of the two peaks clearly indicate the
collinearity of OH bond on the water molecules with the
oxygen atom of the reference molecule.
Conclusions
Figure 11. Angular distribution functions (adf’s) for (a) dipoledipole vector angle, (b) interparticle-dipole vector angle, and
(c) interparticle-bond vector angle for water molecules within
the bulklike region of the aqueous core.
than the headgroups due to the delocalization of negative
charges on the anionic headgroup. The adf’s for the
interparticle-bond vector angle for water molecules (not
shown for brevity) residing in the primary hydration shell
also exhibit strong orientation effects of the two ionic
species. The adf for the Na+ ion shows a peak at cos φ ∼
-0.5 (φ ∼ 120°), while the adf for the anionic headgroup
shows a peak at cos φ ∼ 1 (φ ∼ 0°). This is another indication
that the water molecules directly associated to the two
ionic species are oriented in response to the strong electric
fields of the ions.
For water molecules lying deeper within the core, beyond
the primary hydration shell, decreases in the orientation
effects are noted. The water molecules lying within the
Molecular dynamics simulations of two system sizes
(small system and large system) are presented. The small
system is used for exploratory calculations, while the
composition and the solvent condition of the large system
mimic the experimental system studied by Eastoe et al.,35
thus enabling quantitative comparison with experiments.
The simulations showed that the shape and size of the
aggregate formed in the large system (aggregated starting
configuration) are in reasonably good agreement with
experimental values. In contrast, the properties of the
aggregates formed in the small system are influenced by
the low water-to-surfactant ratio in this system. The
aggregates formed in the small system are quite small
and considerably nonspherical compared to those formed
in the large system.
In the present study, advantage was taken of the MD
simulation technique to explore the microstructure of the
aggregates formed. The radial density distribution of the
various molecules constituting the aggregate showed that
the aqueous core essentially consisted of water molecules
and Na+ ions. The sulfate headgroups are primarily
situated at the surface of the aqueous core. The radial
density distribution of the two tails indicated the presence
of a corona surrounding the aqueous core and thereby
effectively shielding it from the nonpolar solvent. Negligible penetration of the solvent molecules in the aqueous
core is observed. For the aggregate in the large system,
the density of water near the center of the core is ∼1.0
g/cm3, indicating the presence of bulklike water. A fairly
broad (10-15 Å) interfacial region is observed. The adf’s
of the water molecules in aqueous core revealed that the
water molecules in the interfacial region are strongly
oriented in response to the electric fields of the anionic
headgroups and Na+ ions, while those near the center of
the core exhibit a hydrogen-bonded network. The tail
conformations indicate that the perfluoroalkane tails are
more extended than the alkane tails, which is opposite to
Dichain Ternary System
that observed in vacuo. Thus, the perfluoroalkane tails
exhibit more CO2-philic behavior than the alkane tails.
Acknowledgment. We are pleased to acknowledge
support of this work by the Chemical and Thermal Systems
Division of the National Science Foundation under Grant
Number CTS-9613555 at the University of Tennessee and
by the Chemical Sciences Division of the Department of
Energy at Oak Ridge National Laboratory. Oak Ridge
Langmuir, Vol. 17, No. 5, 2001 1783
National Laboratory is managed by Lockheed Martin
Energy Research Corp. for the Department of Energy
under Contract Number DE-AC05-96OR2246. We are also
pleased to acknowledge the allocation of computational
time on the Cray T3E at the National Energy Research
Scientific Computing Center at Lawrence Berkeley National Laboratory.
LA000554F