Computation of Surface Forces


Principal Investigator

Siewert-Jan Marrink

Department of Applied Mathematics,

Research School of Physical Sciences and Engineering

Over the past 15 years, the Department of Applied Mathematics in RSPhysSE has pioneered the
measurement and calculation of forces between colloidal particles in aqueous solutions. The forces are predominantly controlled by the electrostatic interaction between charged surfaces and the associated ions in the solution.

Recently we have developed methods which evaluate surface forces using average potentials between ions in aqueous solution. In this project we calculate average potentials between an ion and the interface which will be used in accurate evaluation of forces between surfaces.

In an application of the method we investigate the interaction of hexagonally packed DNA molecules. This interaction was measured experimentally some time ago,




Stjepan Marcelja

Department of Applied Mathematics,

Research School of Physical Sciences and Engineering




w10 - PC



What are the results to date and the future of the work?

During the last year we developed the necessary software to compute ion-surface potentials of mean force, and obtained first high quality data for the monovalent ion-surface potential in the case of a free surface.

Now we would like to extend these calculations towards divalent ions and towards specific mineral surfaces. Once the potentials of the mean force are known, we can use the anisotropic HNC program to calculate ion density profiles near a surface and surface-surface interaction for planar surfaces. In more complicated geometries we can use the potentials of mean force in Brownian Dynamics or Monte Carlo type of calculations.

In a separate simulation, we calculate the osmotic pressure between aligned DNA molecules, which provides a classical example of an electrical double layer interaction between strongly charged macromolecules. We used published Na+-Na+ potentials of mean forces in aqueous solutions obtained in a simulation of a single ion pair. The preliminary results indicate that the observed hydration effect of unknown origin is in fact caused by the short-range oscillatory interaction between counterions near the DNA surface. With this work we intend to show that the concepts of the Stern layer in planar systems and the Manning counterion condensation in polyelectrolytes are one and the same physical phenomenon caused by the hitherto neglected short-range part of the ion-ion interaction in the aqueous environment.

- Appendix A

What computational techniques are used?

The MD technique numerically solves Newton's equations of motion for a system of interacting particles. Most of the computer time is required to accurately calculate the long-range forces in the system, which are however very important in the type of system we are studying.

We use GROMACS (H. J. C. Berendsen, D. van der Spoel & R. van Drunen, Comp. Phys. Comm. 91, 1995, 43-56) source code which is highly optimised for this type of computations, with locally written subroutines. An MD run of approximately 1 ns per position is needed in order to get converging results. With the desired system size, the GROMACS program is able to perform an MD simulation on the PC at a speed of 10 ps per CPU hour.

Appendix A -