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![Page 1: 1 Hydrophobic hydration at the level of primitive models Milan Predota, Ivo Nezbeda, and Peter T. Cummings Department of Chemical Engineering, University.](https://reader035.fdocuments.in/reader035/viewer/2022070407/56649e235503460f94b115a2/html5/thumbnails/1.jpg)
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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
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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
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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