Dielectric constant of solvents at nano to bulk regimes: linear response theory and statistical mechanics-based approaches

Statistical mechanics and generalised linear response theory based approaches are employed to derive the analytical expressions for size-dependent dielectric constant and normalised orientation polarisation of solvents. As an illustrative example, water is considered and the dielectric constants for the same are calculated over the entire range of water clusters. Our results reveal that the dielectric constant and normalised orientation polarisation are monotonically increasing with the increase in the number of solvent molecules and converge to the respective bulk values in the thermodynamic limit. More importantly, the dielectric constant of water is found to be independent of the nature, geometry and microscopic charges of the non-spherical ions. This finding offers a new platform for calculating the hydration energy and orientation polarisation based on linear response theory for different kinds of ions in the solvent medium.