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Updated: Feb 8, 2026

Controlling the Size, Shape and Stability of Supramolecular Polymers in Water
Published on: August 2, 2012
Size and shape dependence of finite-volume Kirkwood-Buff integrals
Peter Krüger1, Thijs J H Vlugt2
1Graduate School of Engineering and Molecular Chirality Research Center, Chiba University, 1-33 Yayoi-cho, Inage, Chiba 263-8522, Japan.
Abstract:
Analytic relations are derived for finite-volume integrals over the pair correlation function of a fluid, the so-called Kirkwood-Buff integrals. Closed-form expressions are obtained for cubes and cuboids, the system shapes commonly employed in molecular simulations. When finite-volume Kirkwood-Buff integrals are expanded over an inverse system size, the leading term depends on shape only through the surface area-to-volume ratio. This conjecture is proved for arbitrary shapes and a general expression for the leading term is derived. From this, an extrapolation to the infinite-volume limit is proposed, which converges much faster with system size than previous approximations and thus significantly simplifies the numerical computations.
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