A Monte Carlo Simulation of the Formation of Micelles in a Ternary System of Water, Oil and Amphiphilic Polymers

Abstract

We performed a Monte Carlo simulation for the formation of micelles in a ternary system composed of water solvent, oil solute (1%) and amphiphilic diblock copolymers (around 1%) on a simple cubic (3-D) lattice (51×51×51), using Metropolis algorithm. The diblock copolymers (50 chains) were expressed by the bond fluctuation model where each chain is composed of one hydrophobic end cube and four hydrophilic cubes connected by virtual fluctuating bonds.
We assumed that the configurational energy depends only on the attractive interaction energy (E_po) between a hydrophobic part of a copolymer and a neighboring oil cell, and the attractive interaction energy (E_oo) between neighboring oil cells. In this simulation, we drew a phase diagram and estimated the magnitudes of E_po and E_oo realizing the stable formation of micelles, which are composed of oil aggregates, hydrophobic part of copolymers, and hydrophilic part of copolymers, from inner to outer sides.
As a result, it was found that E_po≥1.9 k_BT and E_oo≥2.3 k_BT are needed to form micelles. Here E_oo should be the lowest value 2.3 k_BT on the lower boundary (E_po=1.9 k_BT), and E_po should be less than 2.6 k_BT on the lower boundary (E_oo=2.3 k_BT).