Micellar solutions contain surfactant aggregates with different aggregation numbers [1] but it is quite difficult to observe the size distribution of the aggregates in laboratory experiments, e.g., using dynamic light scattering and nuclear magnetic resonance methods. In this respect, molecular dynamics modeling methods can be of great use, since they allow one to study transport and structural properties of a single aggregate with arbitrary aggregation number [2] and of a set of aggregates. This communication presents the results of complex all-atom molecular dynamics modeling of aqueous solutions of an ionic surfactant (sodium dodecyl sulfate, SDS) [3,4], also in the presence of decane molecules solubilized in SDS micelles [5], and of the solutions of a nonionic surfactant C12E4 in polar (water) and non-polar (heptane) solvents. In the case of SDS, both salt-free micellar solutions and solutions with the additions of sodium chloride and calcium chloride were considered. When constructing the models of the considered molecular systems, the all-atom force fields CHARMM36 and CGenFF v. 4.4 were used. Molecular dynamics simulations were carried out using the MDynaMix and Gromacs 2020.1 software packages.
During the simulations, spontaneous formation of one or several aggregates in the simulation box took place. By analyzing the molecular dynamics trajectories, we calculated the diffusion coefficients and the average radii of the formed aggregates which enabled us to estimate the viscosities of the simulated micellar solutions using the Stokes-Einstein formula [4,5]. At certain concentrations of CaCl2, the formation of “islands” consisting of negatively charged head groups of SDS and positively charged Ca2+ ions was observed in the crowns of the aggregates which in its turn led to the formation of stable dumbbell-shaped micelles [5].
We also studied the direct and inverse micelles of the nonionic surfactant C12E4 formed, respectively, in water at T=298 K and in heptane at T=223 K. For a system made of 100 C12E4 molecules and 4000 heptane molecules and simulated at a temperature T=283 K the 1 μs long molecular dynamics trajectory was obtained which made it possible to obtain a distribution of aggregates over the aggregation numbers. The distribution included not only the inverse micelles but also surfactant monomers, dimers, trimers, etc, as it should be in real micellar solutions [1]. Such distributions, in principle, can be used to estimate the work of aggregation of a micelle [6]. The local maximum of the obtained distribution was located at n=87 close to the distribution’s right end. This fact can be related to the effect of the small size of the simulation cell [7].
Acknowledgements This work has been supported by the grant from the Russian Foundation for Basic Research (RFBR 20-03-00641_A).
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