60th Annual Report on Research 2015

Surfactants can aggregate into micelles due to their amphiphillic nature. This aggregation is dependent on surfactant concentration, solvent environment as well as temperature and pressure. More computationally challenging is to look at the formation of micelles at extremes of temperature and pressure. To achieve the correct timescale necessary to observe micelle formation, we have formulated a new coarse-grained model of surfactants molecules with explicit solvation that can be used in a wide range of thermodynamic conditions. As mentioned in last year report, we have developed a water-explicit coarse-grained model of nonionic surfactants. The model surfactant we are using for our study is of the form C_nE_n, where E is an ether group.

Our CG surfactant model represents each heavy atom in the surfactant with one CG bead. For our simulations we are using the surfactant C₁₂E₅. As seen in Figure 1, this model uses 4 bead types.

 Figure 1: C₁₂E₅ represented by 4 CG beads.

The carbons that belong to the alkyl tail (Ch) have different properties than the ones in the polar regions (Cp), therefore we have used different bead types that has a different LJ interaction with the solvent. Also the beads that model the ester oxygens (O) do not exhibit hydrogen-bonding capabilities between themselves, whereas the bead that encompasses the hydroxy group (OH) does. Bonds and angles are represented by harmonic potentials between atoms. For groups that can form hydrogen bonds, the three-body Stillinger-Weber potential is used, as with the water model. A Lennard-Jones 9-6 potential is used for pair interactions with groups that do not form hydrogen bonds. As discussed in our update last year, to obtain the correct balance of hydrophobic/hydrophilic driving forces, we have initially parameterized a heteropolymer model with only two different coarse-grained bead types, polar (P) or hydrophobic (H), to exhibit cold and pressure denaturation. Once we observed the right hydrophobic/hydrophilic trends with changes in temperature and pressure we have moved towards the modeling of -alkyl polyoxyethelyne ether (C₁₂E₅). As we did for the heteropolymer model, by using a three body anisotropic potential we have mimicked in an effective way the hydrogen bonding between the O and OH and the water solvent, and between the OH groups. As mentioned in last year report, we did a further parametrization from the heteropolymer model by comparing simulations of two surfactants in water with our CG model to all-atom simulations of the same system.

In the past year, we have used this model to examine the temperature and pressure stability of micelle formation. Simulations were performed using 160 surfactants in water at a concentration of 16mM. All CG simulations were performed in LAMMPS, using the model described above. Simulation length varied depending on the temperature, with a minimum simulation length of 150ns used to determine whether micelles could form. The maximum simulation length used was 650ns, needed to observe micelles reaching their maximum size. Eleven different temperatures were used for simulations (275, 300, 325, 330, 335, 340, 350, 400, 500, 600K), with two simulations performed at each temperature. Looking at micelle formation across this range of temperature (see Figure 2), we found a temperature stability window to exist between 335K and 500K.

Figure 2: Snapshots of the largest micelle over time in a simulation at a temperature of 350K. The alkyl domain is in blue and the ether domain is in red.

As seen in Figure 2, outside of this window micelles are not able to form. Simulations were considered to be able to form a micelle if they could form a stable aggregate of 8 surfactants or larger. Figure 3 shows snapshots of the growth of a micelle over time. Micelles were able to form a clear hydrophobic core with as few as 8-10 surfactants. This core remained defined as the micelles grew to their eventual maximum size. The largest micelles observed were at 350K. These micelles reached ~70 surfactants in size at ~400ns. In most of our simulations, the largest micelle was the only micelle, which formed, the only exceptions were at 400K, where two micelles of approximately equal size formed, and at 350K, when a large micelle split into two smaller micelles.

Figure 3: Snapshots of the largest micelle over time in a simulation at a temperature of 350K. The alkyl domain is in blue and the ether domain is in red.

To determine why micelles were not able to form at low temperature, we examined properties of smaller clusters of surfactants. These small clusters of surfactants form and break quickly, and are present across all temperature conditions. Looking at the radius of gyration of two closely interacting (dimerized) surfactants across temperatures (Figure 4), we can see that there is a large increase below 350K. This indicates that surfactants are no longer clustering or interacting strongly, which may explain the lack of micelles at low temperature. This figure also shows that there is a minimum in the hydrophobic radius of gyration at 350K. This indicates that the hydrophobic core is most stable around this temperature.

Figure 4: Radius of gyration vs temperature for clusters of two surfactants.

Simulations have also been performed at varying pressure using the same model. Since 350K appears to be the most stable temperature for micelle formation, this is the temperature we used for our pressure simulations. These simulations used the same model and surfactant as our temperature simulations, with 9 pressures simulated so far (1atm, 250atm, 300atm, 350atm, 400atm, 500atm, 1000atm, 2500atm, 5000atm). While our simulations at varying pressure are still ongoing, we have been able to observe a pressure stability limit for micelle formation. Figure 5 shows micelle formation at some of the lower pressures, and shows that micelle formation is no longer present when you reach 500atm. Further work will examine the why the micelles are no longer forming, and see if the interactions are similar to those at low temperature.

Figure 5:  Size of largest cluster vs time for simulations at a temperature of 350K and varying pressure.