Solubility of poorly soluble species in bulk and nanopores from grand-canonical Wang-Landau sampling
Abstract
Poorly soluble species can have mean populations below one in small systems such as nanopores. In this regime, the grand-potential minimum, which identifies the most probable particle number, differs from the ensemble-averaged solute loading. We use grand-canonical Wang-Landau sampling (GCWLS) to calculate the density of states Ω(NA, NB) for a binary Lennard-Jones mixture of solute B in solvent A, both in bulk and in slit pores. One set of GCWLS simulations gives ensemble averages over a range of chemical potentials, whereas conventional grand-canonical Monte Carlo (GCMC) simulation requires a separate simulation at each state point. Independent GCMC simulations confirm the GCWLS ensemble averages. The solvent number distribution is nearly Gaussian, whereas the dilute solute distribution is skewed and Poisson-like. The most probable solute number therefore lies below the ensemble-averaged loading ⟨ NB⟩ and is zero whenever ⟨ NB⟩<1. Reading the solute loading from the grand-potential minimum underestimates it and can falsely indicate that no solute is present. Defining the oversolubility as 𝒪B=xBconf/xBbulk, where xB is the solute mole fraction, we find 𝒪B≈12 in a pore of 3.5 particle diameters width when both wall interactions are repulsive. Adding wall-solute attraction moderately raises it to ≈13, whereas wall-solvent attraction lowers it to ≈3.4. This comparison shows that the wall-solvent interaction controls most of the enhancement. As the pore widens, 𝒪B decreases toward unity. In bulk and in nanopores alike, the solubility of poorly soluble species should be obtained from ensemble averages rather than from grand-potential minima.
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BibTeX
@misc{kajouri2026solubility,
title = {{Solubility of poorly soluble species in bulk and nanopores from grand-canonical Wang-Landau sampling}},
author = {Russell Kajouri and Adyant Agrawal and Philipp Stärk and Alexander Schlaich and Christian Holm},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16599},
eprint = {2610.16599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16599},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Solubility of poorly soluble species in bulk and nanopores from grand-canonical Wang-Landau sampling
AU - Russell Kajouri
AU - Adyant Agrawal
AU - Philipp Stärk
AU - Alexander Schlaich
AU - Christian Holm
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.16599
UR - https://arxiv.org/abs/2610.16599
AB - Poorly soluble species can have mean populations below one in small systems such as nanopores. In this regime, the grand-potential minimum, which identifies the most probable particle number, differs from the ensemble-averaged solute loading. We use grand-canonical Wang-Landau sampling (GCWLS) to calculate the density of states Ω(N_A, N_B) for a binary Lennard-Jones mixture of solute B in solvent A, both in bulk and in slit pores. One set of GCWLS simulations gives ensemble averages over a range of chemical potentials, whereas conventional grand-canonical Monte Carlo (GCMC) simulation requires a separate simulation at each state point. Independent GCMC simulations confirm the GCWLS ensemble averages. The solvent number distribution is nearly Gaussian, whereas the dilute solute distribution is skewed and Poisson-like. The most probable solute number therefore lies below the ensemble-averaged loading ⟨ N_B⟩ and is zero whenever ⟨ N_B⟩<1. Reading the solute loading from the grand-potential minimum underestimates it and can falsely indicate that no solute is present. Defining the oversolubility as 𝒪_B=x_B^conf/x_B^bulk, where x_B is the solute mole fraction, we find 𝒪_B≈12 in a pore of 3.5 particle diameters width when both wall interactions are repulsive. Adding wall-solute attraction moderately raises it to ≈13, whereas wall-solvent attraction lowers it to ≈3.4. This comparison shows that the wall-solvent interaction controls most of the enhancement. As the pore widens, 𝒪_B decreases toward unity. In bulk and in nanopores alike, the solubility of poorly soluble species should be obtained from ensemble averages rather than from grand-potential minima.
ER -