Micellization and Partition Equilibria in Mixed Nonionic/Ionic Micellar Systems: Predictions with Molecular Models.

In practical applications, surfactant solutions are mostly used in mixtures of nonionic and ionic surfactants because they have improved characteristics compared to those of single surfactant solutions. By adjusting the composition of the micelles and the pH value, the solubilization of solutes can be enhanced. Nevertheless, the partitioning of solutes between nonionic/ionic mixed micelles and the aqueous phase is studied to a much lesser extent than for single surfactant solutions. Theoretical methods to predict partition equilibria in mixed micelles are of interest for screening studies. For those, the composition of the mixed micelle has to be known. Here we investigate mixtures of TX-114 (Triton X-114), Brij35 (C12E23), SDS (sodium dodecyl sulfate), and CTAB (cetyltrimethylammonium bromide). First, to investigate the surfactant compositions in the micelles, molecular dynamics (MD) self-assembly simulations were applied. Thereafter, the predictive COSMO-RS model, which applies the pseudophase approach, and its extension to anisotropic systems termed COSMOmic were compared for the prediction of partition equilibria in mixed micelles, where various molar ratios of the surfactants were considered. It could be demonstrated that both methods are applicable and lead to reasonable predictions for neutral molecules. However, taking into account the three-dimensional structure of the micelle is beneficial because the calculations with COSMOmic are in better agreement with experimental results. Because the partitioning behavior of ionizable molecules in mixed micelles is of particular interest, the partitioning of ionized isovanillin in mixed Brij35/CTAB micelles at different micelle compositions was calculated with COSMOmic. Using a thermodynamic cycle, the position-dependent pKa of isovanillin within the micelle is calculated on the basis of COSMOmic free energy profiles. As a result, the protolytic equilibrium of isovanillin within the micelles can be taken into account, which is crucial for the reliable prediction of partition coefficients.

Solute Partitioning in Micelles: Combining Molecular Dynamics Simulations, COSMOmic, and Experiments.

The partition equilibria of solutes between micelles and an aqueous phase is a key factor in many applications. Depending on the task, many micelle-solute combinations are possible. Therefore, theoretical methods to predict the partition behavior in micellar systems are needed. Here, two predictive methods are evaluated and compared. First, it is shown how molecular dynamics simulations (MD) with the umbrella sampling method can be used to calculate free energy profiles in micellar systems. The second applied method is an extension of the COSMO-RS theory to anisotropic systems termed COSMOmic. Both methods are compared by means of free energy profiles and experimental micelle/water partition coefficients. A particular focus is on the partitioning of ionized solutes. As experimental data for partitioning in micelles especially for charged solutes is rare, partition coefficients were also determined experimentally. To get a general understanding of micelles examples of all micelle classes (classified by headgroup charge) are studied: nonionic Triton X-114 (TX114), zwitterionic miltefosine (HePC), anionic sodium dodecyl sulfate (SDS), and cationic cetyltrimethylammonium bromid (CTAB). The free energy profiles of neutral solutes obtained from MD simulations and COSMOmic are in an overall good agreement, and partition coefficients from both methods are in good agreement with experimental data. Depending on the system, the results for charged solutes show some deviations between the methods and experimental data.

Molecular Modeling of Triton X Micelles: Force Field Parameters, Self-Assembly, and Partition Equilibria.

Nonionic surfactants of the Triton X-series find various applications in extraction processes and as solubilizing agents for the purification of membrane proteins. However, so far no optimized parameters are available to perform molecular simulations with a biomolecular force field. Therefore, we have determined the first optimized set of CHARMM parameters for the Triton X-series, enabling all-atom molecular dynamics (MD) simulations. In order to validate the new parameters, micellar sizes (aggregation numbers) of Triton X-114 and Triton X-100 have been investigated as a function of temperature and surfactant concentration. These results are comparable with experimental results. Furthermore, we have introduced a new algorithm to obtain micelle structures from self-assembly MD simulations for the COSMOmic method. This model allows efficient partition behavior predictions once a representative micelle structure is available. The predicted partition coefficients for the systems Triton X-114/water and Triton X-100/water are in excellent agreement with experimental results. Therefore, this method can be applied as a screening tool to find optimal solute-surfactant combinations or suitable surfactant systems for a specific application.

Predicting solute partitioning in lipid bilayers: Free energies and partition coefficients from molecular dynamics simulations and COSMOmic.

Quantitative predictions of biomembrane/water partition coefficients are important, as they are a key property in pharmaceutical applications and toxicological studies. Molecular dynamics (MD) simulations are used to calculate free energy profiles for different solutes in lipid bilayers. How to calculate partition coefficients from these profiles is discussed in detail and different definitions of partition coefficients are compared. Importantly, it is shown that the calculated coefficients are in quantitative agreement with experimental results. Furthermore, we compare free energy profiles from MD simulations to profiles obtained by the recent method COSMOmic, which is an extension of the conductor-like screening model for realistic solvation to micelles and biomembranes. The free energy profiles from these molecular methods are in good agreement. Additionally, solute orientations calculated with MD and COSMOmic are compared and again a good agreement is found. Four different solutes are investigated in detail: 4-ethylphenol, propanol, 5-phenylvaleric acid, and dibenz[a,h]anthracene, whereby the latter belongs to the class of polycyclic aromatic hydrocarbons. The convergence of the free energy profiles from biased MD simulations is discussed and the results are shown to be comparable to equilibrium MD simulations. For 5-phenylvaleric acid the influence of the carboxyl group dihedral angle on free energy profiles is analyzed with MD simulations.

Diffusion of chain molecules and mixtures in carbon nanotubes: the effect of host lattice flexibility and theory of diffusion in the Knudsen regime.

A novel algorithm for modeling the influence of the host lattice flexibility in molecular dynamics simulations is extended to chain-like molecules and mixtures. This technique, based on a Lowe-Andersen thermostat, maintains the advantages of both simplicity and efficiency. The same diffusivities and other properties of the flexible framework system are reproduced. Advantageously, the computationally demanding flexible host lattice simulations can be avoided. Using this methodology we study the influence of flexibility on diffusion of n-alkanes inside single-walled carbon nanotubes. Furthermore, results are shown for diffusion of two mixtures (methane-helium and ethane-butane). Using these results we investigate the accuracy of theories describing diffusion in the Knudsen regime. For the dynamics in carbon nanotubes the Knudsen diffusivities are much too low. The Smoluchowski model gives better results. Interestingly, the extended Smoluchowski model can reproduce our simulation results obtained with a rigid host lattice. We modify this model to also treat collisions with a flexible interface correctly. As the tangential momentum accommodation coefficient is needed for the theoretical models, we introduce a simple concept to calculate it.

Combining reactive and configurational-bias Monte Carlo: confinement influence on the propene metathesis reaction system in various zeolites.

In order to efficiently calculate chemical equilibria of large molecules in a confined environment the reactive Monte Carlo technique is combined with the configurational-bias Monte Carlo approach. To prove that detailed balance is fulfilled the acceptance rule for this combination of particular Monte Carlo techniques is derived in detail. Notably, by using this derivation all other acceptance rules of any Monte Carlo trial moves usually carried out in combination with the configurational-bias Monte Carlo approach can be deduced from it. As an application of the combination of reactive and configurational-bias Monte Carlo the influence of different zeolitic confinements (MFI, TON, LTL, and FER) on the reaction equilibrium and the selectivity of the propene metathesis reaction system was investigated. Compared to the bulk phase the conversion is increased significantly. The authors study this reaction system in the temperature range between 300 and 600 K, and the pressure range from 1 to 7 bars. In contrast to the bulk phase, pressure and temperature have a strong influence on the composition of the reaction mixture in confinement. At low pressures and temperatures both conversion and selectivity are highest. Furthermore, the equilibrium composition is strongly dependent on the type of zeolite. This demonstrates the important role of the host structure in catalytic systems.

Temperature and size effects on diffusion in carbon nanotubes.

We study the self-diffusion of simple gases inside single-walled carbon nanotubes at the zero-loading limit by molecular dynamics simulations. The host-framework flexibility influence is taken into account. In particular, we study the influences of nanotube size and temperature. For the carbon-nanotube radius-dependent self-diffusivities, a maximum is observed, which resembles the so-called levitation effect. This occurs for pores having a radius comparable to the position of the interaction-energy minimum. Surprisingly, the temperature influence is not uniform throughout different pore sizes. Diffusivities are expected to increase with temperature. This effect is observed for carbon nanotubes distinctly larger than the guest molecules. Remarkably, for smaller pores, the self-diffusivities decrease with increasing temperature or exhibit a maximum in the temperature dependence. This effect is caused by competing influences of collision frequency and temperature.

A novel algorithm to model the influence of host lattice flexibility in molecular dynamics simulations: loading dependence of self-diffusion in carbon nanotubes.

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.

Understanding the loading dependence of self-diffusion in carbon nanotubes.

The influence of flexible walls on the self-diffusion of CH4 in an isolated single walled carbon nanotube, as an example, is studied by molecular dynamics simulations. By simulating the carbon nanotube as a flexible framework we demonstrate that the flexibility has a crucial influence on self-diffusion at low loadings. We show how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. The reproduction of the results of a flexible carbon nanotube by a rigid nanotube simulation is excellent.