Association of Lennard-Jones particles in nanoconfined aqueous solution: Theory and molecular dynamics simulations

We develop a new Gibbs free energy-based association model and perform series of molecular dynamics (MD) simulations to study the association behavior of Lennard-Jones (LJ) particles in nanoconfined aqueous solution. In the association model, the total Gibbs free energy is the sum of free energy cost in the nucleation of a densely packed cluster with an isotropic shape and a radius dependent interfacial tension coefficient, and the translation entropy of dispersed particles outside the cluster. Two key theoretical expressions – total Gibbs free energy formula and the thermodynamic equilibrium equation – are obtained to estimate the cluster aggregation number for a given LJ particle number and the corresponding total Gibbs free energy. Using MD simulations, we observe that the association state transforms from the stable dispersion state, through the reversible state, finally to the stable aggregation state as the LJ particle number increases. In the reversible state, the system reversibly switch in between the dispersion and aggregation states. The existence of three types of association states is also found for LJ particles with the varied well depth. According to our model, the Gibbs free energy curve shows from a single minimum, through two minima, finally to a single minimum, leading to the transformation of association states. The occurrence of reversible state transition is attributed to the free energy barrier of the order of thermal fluctuation in water between the dispersion and aggregation states. These findings deepen the understanding of nucleation/aggregation of hydrophobic gas molecules or particles in solution under nanoconfinement.