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Modelling Water
Mercedes Benz-ene
rij
!i!j
K Silverstein, ADJ Haymet, K Dill, JACS 120: 3166-3175 (1998)A Ben Naim, J. Chem. Phys. 54: 3682 ( 1971)
u(r) = (a/r)12 - (b/r)6
H bond = Gaussian NPT Monte Carlo Nonpolar solute:
MB ‘Ice” MB ‘Liquid’
Pressure Melts MB IceSimple Material
SOLID LIQUID
GAS
SOLID LIQUID
GAS
T
P
T
!S!V ! !P!T < 0< 0
Water
Clapeyron Relation
Anomalous Properties of Water
0
2
4
6
Cp *Cp (cal mol!1 C!1)
16
17
18
19
0
1
2
3
0.12 0.16 0.20 0.24 0.2840
45
50
-25 0 25 50 75 100
! " 106
(bar!1)
1
1.1
1.2
1.3
1.4
V */n V(cm3 mol!1)
18
18.5
19
19.5
0
2
4
6
0
2
4
6
8
ThermalExpansion " " 104
( C!1)
IsothermalCompressibility
T * T ( C)
!
MB Model Experiments
The Hydrophobic Effect
Water Oil
Thermal Behavior of Nonpolar Transfers
Hydrophobicity:Temperature Dependence
MB Model Experiments
0.5
0.8
1.1
1.4
0.16 0.20 0.24 0.28
30
40
50
60
300 350 400 450 500 550
0
50
100
150
200
-20
-10
0
10
20
-2
2
6
10
-0.6
-0.4
-0.2
0
0.2
0.4
(cm3 mol 1)
(J mol 1 K 1)
* (K)
(kJ mol 1)
Hydrophobic Heat CapacityCold Water Hot Water
Solute Orders Water−TΔS >> 0
Solute Disorders WaterΔH >> 0
Orientational Preferences Decrease with Temperature
Solute-Water Water-Water
First-Shell Water OrientationsDepend on Solute Size
Hydrogen Bond Angle (Degrees)
0 1 2 3 4
0 60 0 600 600 60 0 60 0 60
Number of Hydrogen Bonds
0
0.6
0
0.06
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
Fraction
Fraction
Hydrophobic SolutesProperties Differ: Large vs. Small
-20
20
40
60
0 1 2 3 4
0
-2
2
4
6
0
!Htr and T!Str
("HB)!Cp,tr/dsolute
SmallSolutes
LargerSolutes !h0
!Cp
T!s0
Solute Diameter (#HB)
Free Energy of Transfer:Mechanism Changes with Solute Size
SmallSolutes
LargerSolutes
!Gtr
0 1 2 3 4 50
1
2
3
Solute Diameter ("HB)
Small Ions Order Water.Large Ions Disorder Water.
80
40
0
!40
!80
0.5 1 1.5 2 2.5
r/Å
!S/J mol!1 K!1
Li+
Cs+
Rb+
Na+
K+
F!
I!
Cl!
Br!
Chaotropes
Kosmotropes
MB + Dipole Water Modelfor Ion Solvation
!1
+1
Ion
Chaotropes & KosmotropesTheory Experiment
!0.5
0.5
1.5
0.5 1.5 2.5r/Å
T* =0.22
Li+
Cs+Rb+
Na+
K+
F!
I!
Cl!
Br!
!80
0
80
0.5 1.5 2.5r/Å
Li+
Cs+
Rb+
Na+
K+
F!
I!
Cl!
Br!
!!S
Small Ions Order Water
r
+ +
+ +
_
_
+
ElectrostaticPotential! (r)
Small Cations & Large Anions
++
_
_
_+
Water Around IonsElectrostatic Ordering Around Small Ions
F
Water Around Ions
Water Around IonsHydrophobic Ordering Around Large Ions
Water Around Ions
Li+
Electrostatic Ordering Around Small Ions
Water Around Ions
Na+
Water Around Ions
The Hofmeister Series of Ions!Log (Relative Solubility)
0.2
0
0.1
0.5 1.0
OH_
F_
Cl_
Br_
I_
0Salt Concentration (M)
Hofmeister Effect: Hydrophobes Excluded from Ion Shell
gih(r*) gih(r*) gih(r*)
r* r*0 1 2
r*30 1 2 30 1 2 3
F
3-State 3-Water (3S3W)Model
Cagelike Dense Open
BC
A
A
B
C
A
BC
Partition Function
!cell = ! exp[!"Pvj]"""dxBdyBd# exp[!"uj]j=1
3
! = (!cell)N
N !
Partition Function!cell(T ,p ,N ) = 2"d2c (T )N {g1#1e!$HB/(kT ) + #2e!$D/(kT ) + g3#3}
µ = !(kT/N ) ln! v (T ,P ) = !(%µ/%p )T
g1 = kT/("ks) erf ( "2ks/(9kT ) )" "
#1 = e [!p (3 3d2/4)]/(kT ) ]"
#2 = e [!p (2+ 3)d2/(4kT ) ]"
g3#3 = (kT/pd2)e {!1+ [p (2+ 3)d2]/(4kT ) }"
Anomalous Thermodynamics of Water
Theory Experiments
0.5
0.6
0.7
0.3
0.33
0.36
-0.5
0
-0.5
0
0.005
0.01
0.015
0
0.01
0.02
0.4 0.5
6
12
0.4 0.5
3
6
vr
!P*
"�T*
cP/kB
Tr
Phase Diagram of Water
0 0.25 0.5 0.75 1
-6
-4
-2
0
2
4
-2
0
2
4
Tr
LogP r
DS
OSTheory
Experiment
Liquid
LiquidSolid formsof water
Vapor
Vapor
L-Ltransition
Proposed L-Ltransition
A Phase Transition inSupercooled Water
PG DeBenedetti, Metastable Liquids, Concepts and Principles, 1996
80
70
60
50
20!40 !20 !20!40 2000 40
100
90
80
T ( C) T ( C)
!"106 bar!1 Cp (J K!1 mol!1)
Supercool Transition:Melting Cages to Dense Liquid
Silverstein et al, JACS 120: 3166 (1998) Southall & K Dill, J Phys Chem 104: 1326 (2000)
Hribar et al, JACS 124: 12302 (2002) Truskett and Dill, J Phys Chem B 106, 11829 (2002)
Dill et al, Ann Rev Bioph Biomol Struc, 34, 173 (2005)
Kevin Silverstein Tony HaymetTom Truskett Tomaz UrbicBarbara Hribar-Lee Vojko Vlachy
Thanks To:
www.dillgroup.ucsf.edu
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