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The free energy changes ΔG associated with turning on oil-water attractive interactions (obtained using Eq. (2)) are compared with the average energies 〈Ψ〉(0) and 〈Ψ〉(1), and plotted as a function of the oil drop's solvent accessible surface area, A. The inset shows the fractional contribution of the fluctuation entropy TS Ψ to ΔG extrapolated to large A (as described in the text).
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(a) The average oil-water interaction energy β⟨Ψ⟩(ξ) is plotted as a function of the coupling parameter ξ for oil drops with radii R = 0.2, 0.4, 0.6, 0.8, and 1.0 nm, from top to bottom. (b) Probability distributions P (ξ)(Ψ) for the size R = 0.2 nm drop β 〈Ψ〉(ξ) points at ξ = 0 and ξ = 1. The distribution width σΨ = is related to the slope of the curves in (a) as indicated by Eq. (8). (c) Same as in panel (b), but for a size R = 1.0 nm drop, and the distributions are shown for all simulated ξ-values.
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Interfacial fluctuations in the cohesive (van der Waals) interactionenergy of spherical oil-drops with water provide evidence of a length scale dependent transition from linear to non-linear response behavior. For sub-nanometer oil-drop sizes, energy fluctuations are found to be independent of the van der Waals coupling strength, while nanometer (and larger) size oil drops experience highly non-linear energy fluctuations. The latter behavior is linked to enhanced hydrophobic density fluctuations and the emergence of entropic contributions to oil-water cohesive interactionfree energies.
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