Interacting nanoparticle systems numerical techniques

Because of the long-range and reduced symmetry of the dipole-dipole interaction, analytical methods such as the thermodynamic perturbation theory presented in Section II.B.l. will be applicable only for weak interaction. Numerical simulation techniques are therefore indispensable for the study of interacting nanoparticle systems, beyond the weak coupling regime. 

Numerical methods with different time- and length scales are employed and developed to investigate material properties and behaviors. Among them, molecular modeling can predict the molecular behaviors and correlate macroscopic properties of a material with various variables. The most popular techniques include molecular mechanics (MM), MD, and Monte Carlo (MC) simulation. These techniques are now routinely used to investigate the structure, dynamics, and thermodynamics of inorganic, biological, and polymer systems. They have recently been used to predict the thermodynamic and kinetic properties of nanoparticle-matrix mixtures, interfacial molecular structure and interactions, molecular dynamic properties, and mechanical properties. 

As the DPD method has been detailed extensively elsewhere [55], here we provide only a brief description of the technique. Similar to MD simulations, DPD captures the time evolution of a many-body system through the numerical integration of Newton s equation of motion, dvi/dt = 5, where the mass m of a bead of any species is set to 1. (We use the term bead to refer to a single point particle in the numerical simulation, and the term particle to refer to a nanoparticle, the interaction of which with a membrane is studied here.) Unlike MD simulations,... 

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