Molecular simulation of dispersed fluid phases and H bonding fluids - - PowerPoint PPT Presentation

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Molecular simulation of dispersed fluid phases and H bonding fluids - - PowerPoint PPT Presentation

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LTD Lehrstuhl fr 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

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SLIDE 1

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, 3rd July 2013 Microporous and Soft Matter Group Seminar

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SLIDE 2

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

2 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Droplet + metastable vapour

γ

R γ p Δ 2 =

Dispersed fluid phases in equilibrium

liquid vapour

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SLIDE 3

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

3 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Droplet + metastable vapour

Spinodal limit: For the external phase, metastability breaks down.

γ

R γ p Δ 2 =

Dispersed fluid phases in equilibrium

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SLIDE 4

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

4 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Equilibrium vapour pressure of a droplet

Canonical MD simulation of LJTS droplets Down to 100 mole- cules: agreement with CNT (γ = γ0).

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SLIDE 5

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

5 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Equilibrium vapour pressure of a droplet

Canonical MD simulation of LJTS droplets Down to 100 mole- cules: agreement with CNT (γ = γ0). At the spinodal, the results suggest that Rγ = 2γ / Δp → 0. This implies as conjectured by Tolman (1949) … , lim =

→ γ

γ

R

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SLIDE 6

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

6 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Surface tension from molecular simulation

Integral over the pressure tensor

(Source: Sampayo et al., 2010)

equimolar radius / σ Test area method: Small deformations of the volume Mutually contradicting simulation results! virial route test area surface tension / εσ -2

LJSTS fluid (T = 0.8 ε)

Nliq surface tension / εσ -2

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SLIDE 7

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

7 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Analysis of radial density profiles

The thermodynamic approach of Tolman (1949) relies on effective radii:

  • Equimolar radius Rρ (obtained from the density profile) with
  • Laplace radius Rγ = 2γ/Δp (defined in terms of the surface tension γ)

Since γ and Rγ are under dispute, this set of variables is inconvenient here.

[ ] [ ]

) ( ) (

2 2

= ′ ′ − + ′ − =

∫ ∫

∞

ρ ρ

R R

ρ R ρ R dR ρ R ρ R dR Γ

distance from the centre of mass / σ 5 10 15 20 density / σ

  • 3

0.01 0.1 1 T = 0.75 ε/k equimolar radius Rρ LJTS fluid T = 0.75 ε

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SLIDE 8

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

8 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Analysis of radial density profiles

Various formal droplet radii can be considered within Tolman’s approach:

  • Equimolar radius Rρ (obtained from the density profile)
  • Capillarity radius Rκ = 2γ∞/Δp (defined by the planar surface tension γ∞)
  • Laplace radius Rγ = 2γ/Δp (defined by the curved surface tension γ)

The capillarity radius can be obtained reliably from molecular simulation. Approach: Use γ/Rγ = Δp/2 instead of 1/Rγ, use Rκ = 2γ0/Δp instead of Rγ. distance from the centre of mass / σ 5 10 15 20 density / σ

  • 3

0.01 0.1 1 T = 0.75 ε/k equimolar radius Rρ capillarity radius Rκ = 2γ0/∆p LJTS fluid T = 0.75 ε

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SLIDE 9

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

9 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, 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.

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SLIDE 10

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

10 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Droplet + metastable vapour
  • Bubble + metastable liquid

Spinodal limit: For the external phase, metastability breaks down. Planar limit: The curvature changes its sign and the radius Rγ diverges.

γ

R γ p Δ 2 = liquid vapour

Gas bubbles in equilibrium

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SLIDE 11

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

11 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Interpolation to the planar limit

Nijmeijer diagram

  • Convention: Negative curvature

(bubbles), positive curvature (droplets).

  • Properties of the planar interface, such

as its Tolman length, can be obtained by interpolation to zero curvature.

  • A positive slope of Δp/2Rρ over 1/Rρ 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. (Δp / 2Rρ) / εσ -2

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SLIDE 12

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

12 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Finite size effects for planar liquid slabs

By simulating small liquid slabs, curvature-independent size effects can be considered.

  • 6

6 liquid slab thickness d / σ local density / σ -3 0.2 0.4 0.6 0.8 y / σ ( 0) ( ) y T ρ ρ = ′ T = 0.7 ε = 1 – a(T)d -3 As expected, the density in the centre of nanoscopic liquid slabs deviates significantly from that of the bulk liquid at saturation.

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SLIDE 13

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

13 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Curvature-independent size effect on γ

Relation with γ(R) for droplets?

3

( , ) ( ) 1 ( ) d T b T T d γ γ = − liquid slab thickness d / σ reduced tension γ(d)/γ0 Correlation: Surface tension for thin slabs:

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SLIDE 14

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

14 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Curvature-independent size effect on γ

Relation with γ(R) for droplets? δ0 is small and probably negative Malijevský & Jackson (2012): δ0 = -0.07 “an additional curvature dependence of the 1/R3 form is required …” R / σ reduced tension γ(R)/γ0

3

( , ) ( ) 1 ( ) d T b T T d γ γ = − liquid slab thickness d / σ reduced tension γ(d)/γ0 Correlation: Surface tension for thin slabs:

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SLIDE 15

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

15 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

The nature of 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” Pauling (1960, “The Nature of the Chemical Bond”) on the hydrogen bond: 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.” Hope: H bonds can be described by simple electrostatics (point charges).

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SLIDE 16

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

16 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

The nature of 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” Pauling (1960, “The Nature of the Chemical Bond”) on the hydrogen bond: 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.”

Hope: H bonds can be described by simple electrostatics (point charges).

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SLIDE 17

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

17 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

O O H Molecular modelling approaches for H∙∙∙O

short-range square well simple approach

O O H H

rest rest

Oxygen: LJ concentric with negative charge Hydrogen: Positive partial charge (no LJ) polarizable models internal degrees of freedom

O — H O O — H O

+ +

  • LJ

LJ

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SLIDE 18

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

18 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

O O H

short-range square well simple “beak” approach

O O H H

rest rest

Oxygen: LJ concentric with negative charge Hydrogen: Positive partial charge (no LJ) polarizable models internal degrees of freedom

O — H O O — H O Molecular modelling approaches for H∙∙∙O

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SLIDE 19

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

19 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Simple beak-shaped hydroxyl group model

This approach is also valid for methanol and mixtures of H bonding fluids. Ethanol:

  • three LJ interaction sites
  • three point charges

Simple electrostatic sites account for polarity as well as H bonding.

  • +

+

Beak-like OH group (Schnabel)

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SLIDE 20

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

20 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Simple beak-shaped hydroxyl group model

This approach is also valid for methanol and mixtures of H bonding fluids. Ethanol:

  • three LJ interaction sites
  • three point charges
  • +

+

temperature / K

Source: Guevara Carrión et al. (2008)

self-diffusivity / nm2ns-1 experiment Schnabel et al. model

  • t

h e r m

  • d

e l s liquid ethanol (p = 100 kPa)

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SLIDE 21

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

21 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Hydrogen bonding in molecular simulation Hydrogen bonding in molecular simulation

equimolar mixture of methanol and carbon dioxide 350 K 100 kPa

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SLIDE 22

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

22 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Hydrogen bonding in molecular simulation Hydrogen bonding in molecular simulation

equimolar mixture of methanol and carbon dioxide 350 K 100 kPa

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SLIDE 23

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

23 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Zoom in: Point charge models of H bonding

beak fluid (asymmetric) symmetric charges The Stockmayer dipole is decomposed into two separate point charges: reflects OH group structure negative and positive sites are equal σ LJ σ LJ d d

+ +

  • dipole μ = dq
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SLIDE 24

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

24 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Potential energy surface

beak fluid Electrostatic contribution to the dimer bond energy:

π π

  • π
  • π

symmetric charges

π π

  • π
  • π

H — H repulsion electropositive site repulsion electronegative site repulsion angle ϑ1 angle ϑ2 angle ϑ

1

a n g l e ϑ2

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SLIDE 25

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

25 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Hydrogen bonds in the liquid phase

As expected, hydrogen bonding depends significantly on the distance between the partial charges (and on the dipole) for both model classes. beak fluid dipole elongation d / σ monomer fraction symmetric charges dipole elongation d / σ μ2 = 2.6 μ2 = 3.2 μ2 = 4 μ2 = 4.9 μ2 = 6 T = 0.7 Tc ρ = ρ' ( T )

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SLIDE 26

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

26 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

As desired, both the dipole strength μ2 (→ polarity) and the elongation d (→ intensity of H bonding) influence the VLE behaviour. d = 0.3 d = 0.5 d = 0.4 Beak fluid

VLE of the asymmetric beak fluid

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SLIDE 27

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

27 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

The symmetric model does not capture the thermodynamics of hydrogen bonding: Phase behaviour is controlled by polarity only. d = 0.3 d = 0.5 d = 0.4 Symmetric charges

VLE of the model with preserved symmetry

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SLIDE 28

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

28 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Classical molecular models of water

TIP4P/2005 SPC/E Water models following the simple beak approach (SPC, TIP3P, SPC/E) are quite popular. However, their overall reliability is relatively limited: “Olympic medalists” from benchmark

  • f Vega and Abascal (2011)

Vega and Abascal: “ Neglecting polarizability prevents an accurate description of ” pressure-related properties like B( T ), ps( T ), and pc.

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SLIDE 29

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

29 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Recent developments in modelling water

New TIP4P-like four-site model of Huang et al. (2012) T / K ρ / mol l-1 water ethylene glycol water T-1

/ K-1

ps / MPa model DIPPR Nearly perfect agreement for critical properties, including pc. (However, comparably poor for the liquid density at low temperatures …)

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SLIDE 30

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

30 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Literature models:

  • Scattering of model parameters

Reference property:

  • Density ρ

Ions 1 CLJ 1 point charge

  • Modelling aqueous electrolyte solutions

Molecular models: Water 1 CLJ 3 partial charges

+ +

  • Parameters fpr Na+:

1.9 < σNa+

/ Å < 4.1

0.06 < εNa+ / K < 1068.8 Large deviation from experimental data!

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SLIDE 31

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

31 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Adjustable parameters:

  • Ions: 1 CLJ with 1 point charge (±1e): 2 parameters

Parameter optimization for alkali halides

  • σion, εion

Target:

  • Reduced density for varying salinity at T = 293 K, p = 1 bar

Simulation conditions:

  • Monte Carlo simulations
  • SPC/E water model
  • Simulation code: extended version of ms2

ρ

‰= ρsolution

ρpure solvent =ρ

‰(σcat,σan,ϵcat ,ϵan, x)

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SLIDE 32

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

32 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Adjustment:

Reduced density over salt concentration

m

Reduced density of NaCl solutions (T = 298 K, p = 1 bar) Sensitivity study:

  • σion dominant
  • εion negligible

ρ

‰=ρ ‰(σcat,σan, x)

m=dρ

‰

dx =d ρ

‰

dx (σcat ,σan)

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SLIDE 33

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

33 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

σLi = 1.88 Å σNa = 1.89 Å σK = 2.77 Å σRb = 3.26 Å σCs = 3.58 Å

Anions

σF = 3.66 Å σCl = 4.41 Å σBr = 4.54 Å σI = 4.78 Å

Aqueous electrolyte solutions: Overview

Reduced density (T = 293 K, p = 1 bar)

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SLIDE 34

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

34 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Reasonable parameter

range: 200 K ≤ εBr- ≤ 400 K

Fine tuning of the molecular models Fine tuning of the molecular models

  • Similar dependence of

Di on εi for all alkali and halide ions Adjustment of the LJ energy parameters εion to the self-diffusion coefficient in solution (T = 298 K, p = 1 bar) (water model: SPC/E)

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SLIDE 35

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

35 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Reasonable match:

εBr- = 200 K Adjustment of the LJ energy parameters εion to the first peak in the radial distribution function (T = 293 K, p = 1 bar)

  • Final compromise:

εcat = εan = 200 K

Fine tuning of the molecular models Fine tuning of the molecular models

(water model: SPC/E)

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SLIDE 36

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

36 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Experimental

data (this work)

  • Simulation

Temperature dependence of the density

Predictions for aqueous solution (T = 333 K, p = 1 bar)

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SLIDE 37

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

37 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Experimental

data (this work)

  • Simulation

Temperature dependence of the density

Predictions for aqueous solution (T = 333 K, p = 1 bar)

slide-38
SLIDE 38

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

38 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Ions 1 CLJ 1 point charge

  • Non-aqueous electrolyte solutions (CH3OH)

Methanol 2 CLJ 3 partial charges Reference property:

  • Reduced density
  • +

+

Molecular models: Simulation:

  • MC simulations at T = 298 K, p = 1 bar

ρ

‰= ρsolution

ρpure solvent

slide-39
SLIDE 39

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

39 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse

Methanolic electrolyte solutions

Predictions (T = 298 K, p = 1 bar)

  • Experimental

data (this work)

  • Simulation
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SLIDE 40

LTD Lehrstuhl für Thermodynamik

  • Prof. Dr.-Ing. H. Hasse

Conclusion

40 3rd July 13

  • M. Horsch, S. Reiser, S. Werth, H. Hasse
  • Mechanical and thermodynamic routes lead to contradicting results for

the curvature dependence of the surface tension. Present results for the excess equimolar radius confirm the thermodynamic route.

  • The surface tension of the dispersed liquid phase is reduced due to a

curvature-independent effect which is present in planar slabs as well as spherical droplets.

  • By simulating the beak fluid, i.e. the OH group without a rest, it is shown

that point charge models can adequatetly cover polarity and hydrogen bonding as related, but distinct effects.

  • Molecular models were developed for alkali and halide ions, which

were fitted to aqueous electrolyte solution properties and correctly predict properties of non-aqueous solutions as well.