Introduction

Often the best way to learn a new computational platform is to study working examples.  This website presents a collection of MD simulations using Gromacs, which our group uses extensively for research in soft matter.  Topics covered will include simple fluids, charged systems, colloidal particles, self-assembly, and polymers.  The examples are small enough to run in a few hours on a few cores, but realistic in how they exploit simulations to explore the origin of material properties.

The examples illustrate techniques in setting up simulations, perturbing systems with applied forces or deformations, and analyzing the results.  Each is presented as a lab exercise, including the physical background and instructions for execution, followed by a detailed solution with all files and commands needed to run the simulation and analyze the results.

Colloidal forces

The colloid particles in the water can interact with each others in means of many possible forces, including van der Waals force, Coulomb interaction, hydrogen bond interaction…etc. The surrounding solute also plays a role on influencing the interaction potential. To understand the potential dependence with solute and without solute, and attraction or repulsion relations between colloid particles, the potential of mean force (PMF) along with separated distance is the key factor we want to investigate. By holding particles with respect to different relative distance, we  can get the idea of potential tendency of depletion force of colloids.

One can use GROMACS to see the influence of different ions and of their concentrations on the depletion force of colloid particles.

Dielectric response

Ions in solution perturb the arrangements of nearby water molecules, both sterically and electrostatically.  Ions take up space, which in itself leads to a nonuniform average concentration of nearby water molecules, with an exclusion radius, a shell of near neighbors, and decaying oscillations as the local concentration relaxes to its average value.  And the ionic charge orients nearby water molecules, with positive ions like Na+ tending to attract the negatively charged oxygen atoms and repel positively charged hydrogen atoms on water.

We can use MD simulations to explore this screening behavior of water in the vicinity of ions,  by performing a simulation in which a single Na+ ion is fixed in the center of a box of water.  From the simulation trajectory, we would like to compute the average electric field, dipole orientation, charge density, and distribution of molecules near the fixed ion.

Double layers

When an ionic solution is placed between oppositely charged parallel plates or subjected to an electric field, the ions in the solution arrange themselves in a fashion, which results in the lowest possible energy for the system. This causes the positive charges to concentrate near the negative plate, forming a layer over the electrode and similarly the negative charges to populate in the vicinity of the positively charged plate. This results in the screening of the electric field in the bulk solution. The deposited ionic layer now attracts counter ions due to coulombic interactions and this results in the formation of a “double layer”.

MD simulations can be employed to investigate different ionic solutions and the properties of the resultant double layer. One can use various GROMACS utilities to visualize the spatial evolution of system properties like water dipole orientation, charge density, electric field, and so on, at the electrode-electrolyte interface. In this tutorial, we analyzed 3 different aqueous salt systems namely NaCl, NaNO₃ and NH₄Cl.

Entropic springs

Stretching a polymer chain results in the reduction of configurations the molecule can access, leading to a decrease in entropy. A restorative force (entropic force) results because of the systems tendency to increase in entropy. For small displacements the entropic force acts proportionally to displacement, coining the term entropic springs for long chain molecules.  

MD simulations can be used to study the entropic restoring force of a long chain, by performing a series of simulations in which a chain of 200 beads is stretched at fixed degrees.  From the simulation force output, we would like to compute the entropic spring constant, as well as compare the spring constants for different chain stiffness. 

Liquid-vapor tension

Forming an interface from a bulk slab of material always involves performing work on the system.  Maintaining that interface also requires work in the form of surface tension.  However, the energy required to form a liquid-vapor interface is different than the energy required to maintain it.  This difference is the result of surface entropy that is present when measuring surface tension but is absent when measuring the surface energy.  MD simulations can quantify this entropic contribution to the surface free energy.

Spherical micelles

Dodecyl sulfate (DS) is an amphiphile that forms spherical micelles in aqueous solution. A monomer of DS consists of 12 alkane-carbon (hydrophobic) attached to a sulfate (SO₄^2-) group (hydrophilic), making the whole molecule negative-one-charged. Counter-ions (Na⁺) are added to the aqueous solution, stabilizing the micelle formation.

This MD tutorial is aimed toward forming an equilibrated spherical DS micelle in an ionic solution using GROMACS 5.1.4. Also, several common MD analysis for DS micelle will be demonstrated.