372342 Different Ways of Looking at the Force Between Nano Particles
Nano particles, consisting of hundreds of atoms, are the building blocks of new materials with applications in various fields of modern engineering. Much about them, especially about their interaction with other nano particles, is known from experiments and molecular simulations. Due to their complex structure and interaction behavior, a good theoretical foundation is often missing.
Here we investigate capped gold nano particles and their effective interaction potentials obtained from atomistic molecular dynamics (MD) simulations. Pair- and 3-body potentials sufficiently describe their self-assembly. To apply the methodology of classical density functional theory we determine the density of the relevant interaction centers (SH, CH2, CH3 groups) from the simulation data. Following a naive, straightforward sampling procedure with a fixed lattice in space, the resulting density leads to an entropic contribution that is too large (up to 20%) in order to consistently explain the simulation data for different temperatures.
Naive sampling does not account for the momenta and the energy that are exchanged when coupled to a thermostat. Therefore we propose a method that corrects for the mechanical constraints imposed on the nano particles during the simulation. Applying this correction to the density, which employs principle component analysis, we obtain an entropic contribution that is significantly smaller than the one obtained from naive sampling and may, especially when the simulation time is short, explain the temperature dependence correctly.
To confirm the validity of our approach, we calculate the potential of mean force (PMF) using the corrected density in Wertheim's theory of hard sphere chains. Moreover, we compute the PMF via the interaction term in first order perturbation theory. All three approaches return similar PMF curves, although they differ considerably with respect to the number of input parameters and the computational effort. All three approaches predict the existence of a depletion force at small distances of the nano particles.
As MD simulations usually involve a thermostat and require mechanical constraints, at least on parts of the molecular structure, our correction method is applicable to many problems where a density can be obtained from MD data.