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Hydrophobic hydration at the level of primitive models

Milan Predota, Ivo Nezbeda, and Peter T. Cummings

Department of Chemical Engineering, University of Tennessee

Chemical Sciences Division, Oak Ridge National Laboratory

Institute of Chemical Process Fundamentals, Academy of Science, Czech Republic

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Outline

Primitive models of water

Simulation of hydrophobic hydration

Structure of solvation shell• Orientational arrangement of water molecules around the solute

• Hydrogen bonding

• Dependence on the solute diameter

Chemical potential of the solute

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Play the same role for associative fluids as the hard sphere system for simple fuids• Capture the most important interactions, predict structure

Direct link between the observed properties and interaction potential• Unambiguous interpretation of simulation results

Short ranged, simple• Easy to simulate

Amenable to theoretical approach• Perturbation theories - TPT, SAFT

• Reference system for the parent realistic point-charge model

Very good structure, thermodynamics incomplete

Primitive models of water

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Repulsions - hard core and like sites• Hard sphere potential

Hydrogen bonding - attraction between unlike sites• Square well potential

(1) (2)

,

(1) (2)

,

1,2 ; | |;

| |;

PM HS OO O HS i j Ri j

SW i ji j

U U R U

U

r r

r r

1O HB

Interaction potential

5

4-site EPM4 model - geometry of TIP4P model

- tetrahedral angle HOH=109°

- |OH|=0.5, |OM|=0.15

- inverse temperature =6

- packing fraction = N/6V=0.35

5-site EPM5 model - geometry of ST2 and TIP5P model

- tetrahedral angles, |OH|= |OM|= 0.5

- symmetry of negative (M) and positive (H) sites

- =5, =0.3

Primitive models of water

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r/rmax

1 2

gOO

0

1

2

3

Comparison of EPM with experiment O-O pair correlation function

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Hydrophobic hydrationChanges that take place in bulk water when a single non-polar molecule is

brought into it

Hard sphere solute of diameters d = 0-1.6, 2, 3, 4, 5, and

= hard wall

Only solute - oxygen (hard core) repulsion hydrophobic hydration

Small solutes - virtual insertion, simulation of pure homogenous water, N=1024

Intermediate and large solutes - simulation of N water molecules + 1 solute

Hard wall - 2D periodic system confined between two parallel walls pure nonhomogeneous water

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Orientational ordering in the solvation shell

0 20 40 60 80 100 120 140 160 180

0.5

1.0

1.5

2.0

S

H

H

O

EPM4

0 20 40 60 80 100 120 140 160 180

0.5

1.0

1.5

2.0d=1 d=2d=3d=4d=5wall

S

H

HO

Solutes up to d=2 the same shape, more pronounced for larger solutes

Larger solutes reorientation

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Preferred configurations, EPM4

Innermost shellpoor bonding

Outer shell

=0°=55°

120°=70°, 180°

50°0°, 100°

Small and medium size solutes

Large solutes

solute solute

solute

=0°=55°

solute

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0 20 40 60 80 100 120 140 160 180

0.5

1.0

1.5

2.0

2.5

Angular distribution in the solvation shellat the hard wall, EPM4

Weak hydrogen bonding in the layer closest to the solute, sacrificing bond by pushing the hydrogen to the soluteStrong bonding in the subshell of the first solvation shell furthest from the solute

0 20 40 60 80 100 120 140 160 180

0.5

1.0

1.5

2.0

2.5

0.11 0.34 0.57

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Orientational ordering in the solvation shell

0 20 40 60 80 100 120 140 160 180

0.8

1.0

1.2EPM5

0 20 40 60 80 100 120 140 160 180

0.5

1.0

1.5

2.0

d=1d=2 d=3d=4d=5wall

Monotonous dependence of distribution of =SOH on diameter d

Symmetry of H- and M sites symmetric distribution of Flat distribution of , two preferred orientations

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Preferred configurations, EPM5

= 0°, 180°= 55°, 125°

= 90°= 55°, 125°

= 55°, 125°=70°, 180°

More favorable for large solutes

Two preferred orientations for all solute sizes

solute

solutesolute

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Solvation shell of EPM4 at a hard wall

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Solvation shell of EPM5 at a hard wall

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Number of hydrogen bonds per moleculeBonding in the vicinity of the solute reduced for large solutes up to

24 % for EPM4 and 8% for EPM5

Small enhancement of bonding around the second maximum of CF

EPM4

r-rc

0.0 0.5 1.0 1.5 2.0

Nb

2.4

2.6

2.8

3.0

3.2

d=1 d=2 d=3 d=4 d=5 wall

EPM5

r-rc

0.0 0.5 1.0 1.5 2.0

Nb

3.4

3.6

3.8

16Distribution of number of bondsin the first solvation shell

The most probable number of bonds of EPM4 is 3, as opposed to 4 for EPM5, significant number of 1-bonded EPM4 molecules

Much larger decrease of 4-bonded molecules in the vicinity of a wall for EPM4

EPM4

Number of bonds per molecule

0 1 2 3 4 50.0

0.2

0.4

EPM5

Number of bonds per molecule

0 1 2 3 40.0

0.2

0.4

0.6 pured=1d=2d=3d=4d=5wall

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Thermodynamic properties

EPM

4

EPM

5

d P Nb(1) Nb

(bulk) S

ex, (der) S

ex, ()

pure 3.65 — 3.11 — —1 3.71 3.10 3.11 5.9 5.52 3.64 2.85 3.12 27.6 25.73 3.57 2.86 3.12 77 724 3.62 2.83 3.12 164 1575 3.64 2.80 3.10 302 290 3.63 2.45 3.00 — —

pure 3.58 — 3.68 — —1 3.55 3.66 3.68 5.7 6.12 3.59 3.65 3.69 26.1 27.43 3.59 3.63 3.69 73 764 3.60 3.56 3.69 158 1635 3.59 3.57 3.68 292 300 3.59 3.46 3.68 — —

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Comparison with realistic modelsSmall solutes

• General agreement• Small decrease of hydrogen bonding in the solvation shell• Strengthened orientational alignment to preserve bonding• Water molecules straddle the solute

Large solutes and hydrophobic wall• Lack of data• Model dependent behavior - different potentials• Experimental support for behavior consistent with EPM4

• Surface vibrational spectroscopy• Du, Q., Freysz, E., and Shen, Y.R., 1994, Science 264, 826• 25% of nonbonded OH groups at interface

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Hydrophobic hydration of inert gases and methane

d [Å] D/dH2O Nc a Nc

EPM4 NcEPM5 -S/k a

SEPM4

SEPM5

Ne 3.035 1.10 15 13.8 14.9 5.7 7.5 6.5Ar 3.415 1.24 17 15.7 16.3 8.6 9.5 8.4Kr 3.675 1.34 19 16.3 16.8 10.6 11.1 10.0Xe 3.975 1.45 21 17.9 17.1 10.7 13.0 11.9

CH4 3.730 1.35 19 16.6 16.9 10.7 11.4 10.3

a Guillot, B., Guissani, Y., and Bratos, S., 1991, J. Chem. Phys. 95, 3643

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Excess chemical potential of solute

exS

0

3;

1d

d

d

ex

S 0 ln 1 ;

ex

*S 2W

'

'3 1

'd d

dd

d

exS 2

2d

dd P

d

ex 2 3S 0 1 2 3d a a d a d a d

ex ln exp U

Rigorous link between the derivative of chemical potential and contact density

Exact limiting behavior

Cubic polynomial for d- dependence of excess chemical potential

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Temperature dependence of the Henry’s law constant

Methane• Hard sphere of relative diameter

d = 1.35

Chemical potential• Cubic polynomial

Equation of state• Reference system for EPM

pseudo-hard body• Wertheim’s perturbation theory

No adjustable parameter

Nezbeda, I., 2000, Fluid Phase. Equil., 170, 13

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Conclusions

Studied hydrophobic hydration of extended primitive models of water over the whole range of solute diameters, including flat surface

Solute sizes up to d = 2-3• Behavior of both models is qualitatively the same and in agreement with realistic

models

Larger solutes• Entropic effects dominate the energy effects in the interfacial layer of EPM4

reorientation, lack of bonding

• Strong bonding of EPM5 preserved in the solvation shell for all solutes

Detailed study of hydrophobic hydration of realistic models needed• More support for behavior consistent with EPM4

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Acknowledgement

Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, DOE

Grant Agency of the Academy of Sciences of the Czech Republic