Morphological thermodynamics for hard bodies from a controlled expansion

ABSTRACT

The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.

KEYWORDS:

• Soft matter
• geometry
• morphology
• colloids
• surface tension
• statistical mechanics
• statistical physics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In fact, rods are the only convex shape possible in 1d (as line segments) so they are really the one-dimensional analogue of any convex object.

2 This is true up to a normalisation constant, as $a_2$ conjugates with the intrinsic volume $V_2$ rather than the area $A=2V_2$. The usual planar surface tension is thus obtained as ${\gamma }_{\mathrm{\infty }}=a_2/2$.

Additional information

Funding

JFR and CPR acknowledge the European Research Council under the FP7 / ERC Grant Agreement No. 617266 “NANOPRS”. CPR would like to acknowledge the Royal Society for financial support.