Numerical methods

Modeling of atomic and continuum scale molecular systems using computer simulations has become very important in order to comply and accompany experiments. Numerical simulations is not only used as a tool to test theoretical predictions, but also to predict unknown behaviour at length and time scales impossible to probe with experimental techniques.

Here we present an example on how molecular dynamics, handy for numerical simulations at the atomic and molecular scale, can be used in order to compute forces between small nanoparticles suspended in a liquid.

Molecular dynamics

Confinement of Lennard-Jones particles

Assuming that atoms are point particles, and affected by a set of conservative potentials: \(U = U_{coul} + U_{vdw} + ...\) (also known as a force field) the force acting on one particle can be found by evaluating the derivative of the potential: \(\mathbf{F} = - \nabla U\). Since there are many atoms, each and every one affected by the potentials of the other atoms, the total force acting on one particle is found by summing over the interactions from all the other particles. From Newtons second law of motion: \(\mathbf{F} = m\mathbf{a}\), when we know the total force \(\mathbf{F}\), on a body, we may find the acceleration \(\mathbf{a}\), of each atom: and thereby its velocity and position at a given time.

With the current computational power, numerical calculations with millions of atoms over nano second time scales is accessible using super computers. An additional advantage of molecular dynamics (MD) is that we are in full control over the thermodynamic conditions of the simulated system.

A clear disadvantage of MD lies in the assumption that the atoms are point particles with little (or usually no) electronic structure, therefore it is difficult to describe chemical reactions. This has to be taken into account both when setting up the simulation and when developing the force field.

ESR's in the NanoHeal project, employ MD to simulate atomistic systems of calcium carbonates in aqueous solutions. However, in order to probe systems with larger sized particles and longer time scales, coarse-grained MD methods are implemented. Macro-molecules or grains consisting of many atoms are in this approach described as single particles. Since the formal degrees of freedom effectively is reduced, this imparts significant computational speedup.

Simulations of water confined between calcite crystal surfaces at nanoconfinement conditions

In the video, linked below, a molecular dynamics (MD) simulation of two calcite crystal surfaces in water is shown. In the simulation, the lower surface is kept fixed, whereas the upper surface is constrained from moving in the horizontal plane by a harmonic potential. A force equivalent of 500 MPa is constantly applied to the upper surface. Initially, the intersurface separation is 2 nm. The final intersurface separation is 0.8 nm. In the end, after 200 pico seconds,  there are four layers of water trapped in the nanoconfinement. In the above figure, a similar setup is shown containing a pure Lennard-Jones fluid, where the structuring of the liquid molecules is clearly visible in the confinement close to the solid surfaces.

Measuring the mechanical responses of magnesian calcites

In the video linked below, a MD simulation of the straining of a pure calcite crystal along the crystallographic c-axis is shown. At approximately 15% strain, the carbonate molecules starts to twin on the (10.4) plane, performing a 90 degree rotation from their original orientation.

Furthermore, in a different setup, a spherical high density cluster of 40mol% magnesium in the calcite, is strained along the c-axis of the crystal at constant strain rate. The crystal still undergoes twinning. However, the nanoparticle acts as a grain boundary, and the twinning does not extend to inside the nanoparticle.

By Gøran Brekke Svaland
Published Feb. 13, 2018 12:55 PM - Last modified Nov. 12, 2018 6:32 PM