# Modeling Surfactant Adsorption on Hydrophobic Surfaces

## Contents

## General Information

**Authors:** S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein

**Publication:** Physical Review Letters

**Keywords:** Surfactant, micelle, adsorption

## Summary

As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulating single wall carbon nanotubes or solubilization of hydrophobic quantum dots. However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations. This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide)) adsorption on an hydrophobic surface (graphite). This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center of masses, then returning to the explicit model for the surface. The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.

## Theory

For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0. They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z. For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface. Probability distributions are used for the interactions rather than potential energies since they are more tractable for larger numbers of particles. For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:

<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math>

where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. So, the probability that the c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:

<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math>

and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then

<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-2z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math>

which are appropriately normalized and have features shown in Fig. 1.

## Simulation

Applying these probability distributions for large numbers of particles is more tricky. One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper). Another challenge is the large number of particles that must be incorporated in the simulation. To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position. The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide). One method is to coarse grain <math>CH_2</math> then combine it with O. Another method is to coarse grain CHO, then combine it with H. The third method is to coarse grain HH and CO separately, then combine the pairs. Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them. The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods. These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface. The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> groups at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant. Specific parameters used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and interfacial surface tension. The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.

## Results and discussion

As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy. C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface. The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2b). However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface. The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2c,d) The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2e). Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data (Fig. 2f). Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment. An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled. As explained in [1], this method is computationally more efficient and holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions, including examining how different surfactants solubilize carbon nanotubes and or how to deposit quantum dots on a substrate.

## References

[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.

Entry by: Xingyu Zhang, AP225, Fall 2012