Atomistic simulations of pH-dependent self-assembly of micelle and bilayer from fatty acids

Abstract

Detailed knowledge of the self-assembly and phase behavior of pH-sensitive surfactants has implications in areas such as targeted drug delivery. Here we present a study of the formation of micelle and bilayer from lauric acids using a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with conformational sampling in explicit solvent and the pH-based replica-exchange protocol. We find that at high pH conditions a spherical micelle is formed, while at low pH conditions a bilayer is formed with a considerable degree of interdigitation. The mid-point of the phase transition is in good agreement with experiment. Preliminary investigation also reveals that the effect of counterions and salt screening shifts the transition mid-point and does not change the structure of the surfactant assembly. Based on these data we suggest that CpHMD simulations may be applied to computational design of surfactant-based nano devices in the future.

Figure 1

pH-dependent self-assembly of lauric acids. Representative snapshots at pH 4 (left), pH 7 (middle), and pH 9 (right). The tails of lauric acids are rendered in cyan while the protonated and deprotonated carboxyl headgroups are shown as blue and red spheres, respectively.

Figure 2

Proton titration of individual lauric acids in the aggregate. (a) The fraction of laurate ions vs. simulation time. (b) Simulated titration curve. Solid curve represents the fit to the Hill equation, which yields a pK_a value of 7.0 ± 0.2. The fractions of laurate ions were calculated using the data of the last 35 ns. The model pK_a value is 5.0.

Figure 3

Relative orientation of lauric acids at different pH conditions. (a) Probability distribution of the angles between lauric acid monomers (defined in the main text). The distribution obtained from the simulation of a pre-constructed micelle of 60 laurate anions is shown as the dashed curve. (b) P₂ order parameter (defined in the main text) as a function of pH. Error bars represent the standard deviation. (c) Probability distribution of the carbon-chain length (defined as the C1-C12 distance).

Figure 4

Average density (atoms/Ų) of C1 atoms in the xy-plane at pH 4 (top), 7 (middle), and 9 (bottom). Aggregate has been centered around the origin and rotated such that the average orientation vector $\vec{d}$ is aligned with the y-axis.

Figure 5

Number of hydrogen bonds between lauric acid headgroups, averaged over the final 35 ns of simulation. Error bars represent standard deviation.

Figure 6

Simulated titration curve with three different setups to model ionic screening. Red: No Debye-Hückel screening, no explicit ions. Filled black: Debye-Hückel term with ionic strength of 0.15 M, no explicit ions. Open black: Debye-Hückel term with ionic strength of 0.15 M, 20 sodium ions. Solid curves represent fits to the Hill equation.

Figure 7

Effect of including explicit ions. Probability distribution of the angles between lauric acids with two different setups to model ionic screening. (a) Debye-Hückel term with ionic strength of 0.15 M, no explicit ions. (b) Debye-Hückel term with ionic strength of 0.15 M, 20 sodium ions. The color scheme for pH conditions is the same as in Figure 3.