Modeling Surfactant Adsorption on Hydrophobic Surfaces

Surfactant adsorption on hydrophobic surfaces is of current interest in attempts to solubilize single-wall carbon nanotubes and to render quantum dots biocompatible. A coarse grained method is presented for incorporating a hydrophobic surface into existing liquid force fields by appealing to statistical mechanics and probability theory. The dimensionality problem which arises is overcome with an approximate treatment and the entire procedure is applied to aqueous $n$-alkyl poly(ethylene oxide) adsorbing onto a graphite surface. The simulations are in excellent agreement with atomic force microscopy data. The mechanism of micelle adsorption onto a partially coated surface is reported for the first time and has implications for the construction of nanotemplates.

Figure 1

(a) The probability distribution for the center of mass of two bonded particles interacting with the surface [see Eq. (5)]. The distribution is normalized to reach unity in the limit of infinite separation. The single particle—graphite parameters [see Eq. (1)] are $\rho =0.113{\AA }^{-3}$ (the graphite site is an ${\mathrm{sp}}^2$ hybridized carbon atom) and $ϵ=31.51\mathrm{K}$, $\sigma =3.566\AA$, which is the CTL2 carbon atom from CHARMM [22]. The CTL2-CTL2 bond is harmonic with $k=223934\mathrm{K}{\AA }^{-2}$ and $r_{\mathrm{eq}}=1.53\AA$. (b) The probability distribution for a fixed center of mass value $z=3.38\AA$, which corresponds to the circle in panel (a), of two bonded particles interacting with the surface from Eq. (5). Shown is the integrand in the numerator broken down into its three constituent terms, where the interaction term is normalized to have unit height for clarity since the denominator in Eq. (5) corrects for this arbitrary choice. The bond constrains the two particles to reside close to the center of mass and enhances the well depth over the noninteracting case. (c) Comparison of the potential experienced by one particle, and the potential experienced by the center of mass of two noninteracting particles, and two bonded particles. Parameters as in panel (a). (d) The effective potential experienced by the center of mass of an $\mathrm{\text{−}}\mathrm{O}\mathrm{\text{−}}{\mathrm{CH}}_2\mathrm{\text{−}}$ piece of poly(ethylene oxide) due to a graphite surface at $z=0$, and three approximations based on integrals of reduced dimensionality (see the text for details).

Figure 2

Snapshots of C12E5 surfactant adsorption onto a graphite surface as observed in simulations, at times of 0, 0.64, 3.30, 3.75, 4.30, and 6.00 ns, respectively. There are solid-liquid interfaces at the top and bottom of the simulation cell which are separated by 12 nm through the water and by 10 nm through vacuum (not shown); three dimensional periodic boundary conditions are employed.