Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

Abstract

We evaluate the grand potential of a cluster of two molecular species, equivalent to its free energy of formation from a binary vapour phase, using a non-equilibrium molecular dynamics technique where guide particles, each tethered to a molecule by a harmonic force, move apart to disassemble a cluster into its components. The mechanical work performed in an ensemble of trajectories is analysed using the Jarzynski equality to obtain a free energy of disassembly, a contribution to the cluster grand potential. We study clusters of sulphuric acid and water at 300 K, using a classical interaction scheme, and contrast two modes of guided disassembly. In one, the cluster is broken apart through simple pulling by the guide particles, but we find the trajectories tend to be mechanically irreversible. In the second approach, the guide motion and strength of tethering are modified in a way that prises the cluster apart, a procedure that seems more reversible. We construct a surface representing the cluster grand potential, and identify a critical cluster for droplet nucleation under given vapour conditions. We compare the equilibrium populations of clusters with calculations reported by Henschel et al. [J. Phys. Chem. A 2014;118:2599] based on optimised quantum chemical structures.

Keywords:

• Clusters
• aerosols
• sulphuric acid
• nonequilibrium molecular dynamics
• nucleation

Acknowledgements

We thank George Jackson, Erich Müller and Patricia Hunt for their support and we acknowledge the UCL Legion High Performance Computing Facility (Legion@UCL), and associated support services.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

GVL was supported through a studentship in the Centre for Doctoral Training on Theory and Simulation of Materials managed by the Department of Physics at Imperial College, funded by the Engineering and Physical Sciences Research Council (EPSRC) of the UK [grant number EP/G036888]; JYP was funded by an EPSRC Undergraduate Vacation Bursary.