Monte Carlo simulation of micelle formation in mixed surfactants and palm-kernel oil esters-based nanoemulsion

For several years, the experimental laboratory and Molecular Dynamics (MD) simulation works was used to determine the behaviour and structural properties of nanoemulsions. In order to solve the problems related to transdermal drug nano-delivery system, the palm-kernel oil esters (PKOEs) nanoemulsion can act as chemical penetration enhancers with the help of non-ionic surfactants properties. Here, the stochastic numerical methods or Monte Carlo (MC) was suggested to develop new configurations of a system of interest. The physical properties of the mixed surfactants and nanoemulsions formulation were studied using the Metropolis Monte Carlo (MMC) algorithm while grand canonical Monte Carlo (GCMC) simulation was applied to investigate the displacements of critical micelle concentration (CMC) for both systems. Seven set of mixed surfactants (Brij 92, Brij 96 and water) models and five simulation sets of PKOEs nanoemulsion (PKOEs, Brij 92, Brij 96, isopropanol as co-surfactant and water) which were adapted from the experimental phase diagram was simulated using MMC algorithm up to 10 and 20 million MC steps, respectively in order to determine the most suitable composition of mixed surfactants and PKOEs nanoemulsion with water molecules.The chemical potential for both model systems were calculated using Reference Interaction Site Model (RISM) module. The most suitable composition from MMC simulations was then grouped to five systems of mixed surfactants and six systems for PKOEs nanoemulsion with a series of different values of temperature and chemical potential resulted from the histogram-reweighting. The latest model systems were used to simulate in grand canonical ensemble for 10 million MC steps with 50% of insertion and removal of molecules and 50% of reptation moves. From the results, the acceptance ratio for single atom moves of the mixed surfactants was increased as the percentage of surfactants was increased from 0.429 to 0.591 meanwhile the acceptance ratio for single atom moves for PKOEs nanoemulsion was decreased as the number of molecules increased from 0.600 to 0.587 due to the different composition of the surfactants and PKOEs nanoemulsion with water molecules where both systems formed spherical shape. The physical properties of models such as radius of gyration, solvent accessible surface area, radial distribution function and total energy were also determined. The chemical potential for the mixed surfactants was produced at the range of 0.77 - 2.06 J/mol while for the PKOEs nanoemulsion the value was ranged from 3.17 - 5.00 J/mol. The displacement of CMC was increased while the insertion and deletion ratio movement were decreased as the temperature and chemical potential increased due to the drop of density in the cubic box during the simulation. Therefore these observations indicated that the physical properties of mixed surfactant and PKOEs nanoemulsion systems were adequately described by the simulation. The acceptance ratio for displacement movement critical micelle concentration (CMC) for the mixed surfactants and PKOEs nanoemulsion systems was also considered accepted with reasonable values produced.

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