(775f) Development of a Coarse-Grained Force Field for Aqueous Non-Ionic Surfactant Systems Using a Molecular Based Equation of State

Development
of a Coarse-Grained Force Field for aqueous non-ionic surfactant systems using
a molecular based equation of state

Olga Lobanova, Carmelo Herdes, George Jackson, Erich A. Müller

Department of
Chemical Engineering, Imperial College London, U.K.

Keywords: force field,
coarse-graining, equation of state, non-ionic surfactants

The understanding of phase behavior and thermodynamic
properties of amphiphilic systems is an essential
component in the design of complex fluid mixtures commonplace, such as health
care products, pharmaceutical industry, and environmental protection. However,
the sheer complexity and diversity of these systems, the large number of
possible components and process conditions makes the experimental study an
overwhelming task. While modern simulation techniques allow an insight into
phase behavior of complex fluid systems, the appropriate choice of the modeling
technique is crucial, as some properties are not accessible due to limited resolution
and reproducibility. The use of coarse-grained molecular simulation, as opposed
to a fully detailed atomistic approach, overcomes some of the limitations of
spanning the time and length scales required to study the kinetics and
self-assembly of complex systems. The problem of parameterization of the force
field is a key factor since the accuracy and robustness of the force field
determines the reliability of the molecular simulation results.

Monoalkyl ethers of poly(ethylene) glycols, (CiEj),
are particularly interesting for their wide range of applications, particularly
due to their rich mesophase phase behavior.
Therefore, those systems have been widely studied both experimentally [1] and
by molecular simulation [2]. These surfactants exhibit self-assembly in aqueous
solution, as do their more complex biological analogues, with the added simplicity
of being non-ionic. Most coarse-grained (CG) simulations are based on
intermolecular potentials, which are effectively integrated version of more
fine-resolution atomistic-level models [3,4].

In opposition to this, in this work we develop a CG model
where the force field parameters are obtained from a top-down approach, by
effectively averaging a large number of macroscopic thermodynamic states with
the aid of a fluid equation of state. We use the Statistical Associating Fluid

Theory (SAFT-γ Mie EoS) to obtain the potential parameters for coarse-grained
moieties [5,6,7]. The potential parameters for these CG
"super-atoms" are estimated from thermophysical
properties (density, vapour pressure, surface
tension, etc.) of simple organic molecules, e.g., alkanes and ethers that share
chemical commonalities with the segments of the amphiphile.
The cross-interaction parameters are obtained from the properties of the
corresponding mixtures.

Molecular Dynamics simulations in an explicit solvent are
carried out at different surfactant concentrations to investigate the thermodynamic,
interfacial and structural properties of the systems. For a low surfactant
concentration, we observe self-assembly into micellar
aggregates (Fig. 1), as well as the interchange of the single surfactant with
the micelle, the fusion and the separation of two micelles and other
equilibrium and dynamic signatures of micellar
systems. Using a cluster analysis algorithm, we are able to identify individual
micelles and calculate relevant structural properties, such as aggregation
number, aggregate size distribution and shape, radius of gyration and density
profiles. For higher surfactant concentrations, the formation of hexagonal and
lamellar phases is observed. Further validation of the CG model has been
undertaken in respect to water-air tension, surface excess properties, nematic order parameter, critical
micelle concentration and aggregate properties of amphiphiles
of different chain length.

It is very gratifying to find that the proposed force field
is transferable for prediction of various properties of these mixtures and also
for mixtures of the components of related homologues. In this manner, the SAFT-
γ Mie Eos establishes a direct robust link to macroscopic properties and
enables the estimation of the CG force field parameters in a very fast and
efficient way. The force field parameters obtained from the equation of state,
can be used as a direct input in molecular simulation to explore different
properties of the mixture that are usually not accessible via an equation of
state, such as structural and interfacial properties.

Fig. 1: Experimental
phase diagram for C10E4 surfactant in water (taken from Fournial et al. [8]) and snapshots
corresponding to the simulation results at 298 K at 5 wt%,
50 wt% and 70 wt%
surfactant in water. The blue line denotes the nematic
order parameter calculated for the surfactant concentration range between 50
and 90 wt%.

References

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[2] Jusufi, A.; Sanders S.; Klein
M.L.; Panagiotopoulos A.Z.; J. Phys. Chem. B, 115, 990 (2011)

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[4] Voth G. A.; Izvekov.S.; J. Phys. Chem. B, 109, 2469 (2005).

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[6] Lafitte, T.; Avendano, C.; Papagioannou, V.; Galindo, A.; Adjiman,
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[7] Avendano, C.; Lafitte, T.; Adjiman, C. S.; Galindo, A.; Muller, E. A.; Jackson, G.; J. Phys. Chem. B, 117, 2717 (2013)

[8] Fournial,
A.-G.; Zhu,Y.; Molinier, V.; Vermeersch, G.; Aubry, J.-M.; Azaroual, N; Langmuir, 23, 11443 (2007)