LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Molecular simulation of dispersed fluid phases and H bonding fluids Martin Horsch, Steffen Reiser, Stephan Werth, and Hans Hasse Manchester, 3 rd July 2013 Microporous and Soft Matter Group Seminar
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Dispersed fluid phases in equilibrium • Droplet + metastable vapour liquid 2 γ = Δ p vapour R γ 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 2
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Dispersed fluid phases in equilibrium • Droplet + metastable vapour 2 γ = Δ p R γ Spinodal limit: For the external phase, metastability breaks down. 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 3
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Equilibrium vapour pressure of a droplet Canonical MD simulation of LJTS droplets Down to 100 mole- cules: agreement with CNT ( γ = γ 0 ). 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 4
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Equilibrium vapour pressure of a droplet Canonical MD simulation of LJTS droplets Down to 100 mole- cules: agreement with CNT ( γ = γ 0 ). At the spinodal, the results suggest that R γ = 2 γ / Δp → 0. This implies = lim → γ 0 , R 0 γ as conjectured by Tolman (1949) … 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 5
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Surface tension from molecular simulation Integral over the pressure tensor Test area method: Small deformations of the volume (Source: Sampayo et al. , 2010) virial route test area surface tension / εσ -2 surface tension / εσ -2 LJSTS fluid ( T = 0.8 ε ) equimolar radius / σ Mutually contradicting N liq simulation results! 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 6
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Analysis of radial density profiles The thermodynamic approach of Tolman (1949) relies on effective radii: • Equimolar radius R ρ (obtained from the density profile) with [ ] [ ] ∞ R ∫ ∫ ′ ′ ′ = − + − = ρ 2 2 Γ dR R ρ ( R ) ρ dR R ρ ( R ) ρ 0 0 R ρ • Laplace radius R γ = 2 γ / Δp (defined in terms of the surface tension γ ) Since γ and R γ are under dispute, this set of variables is inconvenient here. 1 -3 density / σ equimolar radius R ρ 0.1 LJTS fluid T = 0.75 ε / k T = 0.75 ε 0.01 0 5 10 15 20 distance from the centre of mass / σ 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 7
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Analysis of radial density profiles Various formal droplet radii can be considered within Tolman’s approach: • Equimolar radius R ρ (obtained from the density profile) • Capillarity radius R κ = 2 γ ∞ / Δp (defined by the planar surface tension γ ∞ ) • Laplace radius R γ = 2 γ / Δp (defined by the curved surface tension γ ) The capillarity radius can be obtained reliably from molecular simulation. 1 -3 capillarity radius density / σ equimolar radius R ρ R κ = 2 γ 0 / ∆ p 0.1 LJTS fluid T = 0.75 ε / k T = 0.75 ε 0.01 0 5 10 15 20 distance from the centre of mass / σ Approach: Use γ / R γ = Δ p /2 instead of 1/ R γ , use R κ = 2 γ 0 / Δp instead of R γ . 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 8
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Extrapolation to the planar limit Radial parity plot • The magnitude of the excess equimolar radius is consistently found to be smaller than σ / 2. • This suggests that the curvature dependence of γ is weak, i.e. that the deviation from γ ∞ is smaller than 10 % for radii larger than 5 σ . • This contradicts the results from the virial route and confirms the grand canonical and test area simulations. 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 9
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Gas bubbles in equilibrium • Droplet + metastable vapour • Bubble + metastable liquid liquid 2 γ = Δ p R γ vapour Spinodal limit: For the external phase, metastability breaks down. Planar limit: The curvature changes its sign and the radius R γ diverges. 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 10
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Interpolation to the planar limit Nijmeijer diagram • Convention: Negative curvature (bubbles), positive curvature (droplets). • Properties of the planar interface, such (Δ p / 2 R ρ ) / εσ -2 as its Tolman length, can be obtained by interpolation to zero curvature. • A positive slope of Δ p /2 R ρ over 1/ R ρ in the Nijmeijer diagram corresponds to a negative δ, on the order of -0.1 σ here, conforming that δ is small . • However, R → 0 for droplets in the spinodal limit for the surrounding vapour (Napari et al.) implies γ → 0. 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 11
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Finite size effects for planar liquid slabs By simulating small liquid slabs, 0.8 curvature-independent size effects local density / σ -3 can be considered. 0.6 0.4 T = 0.7 ε 0.2 0 y / σ ρ = ( y 0) -6 0 6 = 1 – a ( T ) d -3 ′ ρ ( ) T As expected, the density in the centre of nanoscopic liquid slabs deviates significantly from that of the bulk liquid at saturation. liquid slab thickness d / σ 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 12
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Curvature-independent size effect on γ Surface tension for thin slabs: Relation with γ ( R ) for droplets? reduced tension γ ( d )/ γ 0 liquid slab thickness d / σ γ ( , ) d T b T ( ) = − 1 Correlation: γ 3 ( ) T d 0 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 13
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Curvature-independent size effect on γ Surface tension for thin slabs: Relation with γ ( R ) for droplets? δ 0 is small and probably negative reduced tension γ ( d )/ γ 0 reduced tension γ ( R )/ γ 0 Malijevský & Jackson (2012): δ 0 = -0.07 “an additional curvature dependence of the 1/ R 3 form is required …” liquid slab thickness d / σ γ ( , ) d T b T ( ) R / σ = − 1 Correlation: γ 3 ( ) T d 0 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 14
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse The nature of the hydrogen bond Pauling (1960, “The Nature of the Chemical Bond”) on the hydrogen bond: It “was for some time thought to result from the formation of two covalent bonds,” but it “is now understood that the hydrogen bond is largely ionic” Hope: H bonds can be described by simple electrostatics (point charges). New IUPAC definition (2011): “The hydrogen bond is an attractive interaction … from a molecule … X —H in which X is more electronegative than H, and … in which there is evidence for bond formation.” 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 15
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse The nature of the hydrogen bond Pauling (1960, “The Nature of the Chemical Bond”) on the hydrogen bond: It “was for some time thought to result from the formation of two covalent bonds,” but it “is now understood that the hydrogen bond is largely ionic” Hope: H bonds can be described by simple electrostatics (point charges). New IUPAC definition (2011): “The hydrogen bond is an attractive interaction … from a molecule … X —H in which X is more electronegative than H, and … in which there is evidence for bond formation.” “The forces involved … include ● those of an electrostatic origin, ● those arising from … partial covalent bond formation …, ● and those originating from dispersion.” 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 16
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Molecular modelling approaches for H∙∙∙O short-range square well simple approach O — H O O - LJ H polarizable models H + + rest O — H O O - LJ internal degrees of rest freedom O H Oxygen: LJ concentric with negative charge Hydrogen: Positive partial charge (no LJ) O 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 17
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Molecular modelling approaches for H∙∙∙O short-range square well simple “beak” approach O — H O O H polarizable models H rest O — H O O internal degrees of rest freedom O H Oxygen: LJ concentric with negative charge Hydrogen: Positive partial charge (no LJ) O 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 18
LTD Lehrstuhl für Thermodynamik Prof. Dr.-Ing. H. Hasse Simple beak-shaped hydroxyl group model Ethanol: ● three LJ interaction sites ● three point charges Simple electrostatic sites account for polarity as well as H bonding . - + + Beak-like OH group (Schnabel) This approach is also valid for methanol and mixtures of H bonding fluids. 3rd July 13 M. Horsch, S. Reiser, S. Werth, H. Hasse 19
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