Modelling W ater - University of California, Los...

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  • Modelling Water

  • Mercedes Benz-ene

    rij

    θiθj

    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

    κ × 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 α × 104

    ( C−1)

    IsothermalCompressibility

    T * T ( C)

    κ

    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

    + +

    + +

    _

    _

    +

    ElectrostaticPotentialψ (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 = Σ exp[−βPvj]∫∫∫dxBdyBdθ exp[−βuj]j=1

    3

    ∆ = (∆cell)N

    N !

  • Partition Function∆cell(T ,p ,N ) = 2πd2c (T )N {g1α1e−$HB/(kT ) + α2e−$D/(kT ) + g3α3}

    µ = −(kT/N ) ln∆ v (T ,P ) = −(∂µ/∂p )T

    g1 = kT/(πks) erf ( π2ks/(9kT ) )√√

    α1 = e [−p (3 3d2/4)]/(kT ) ]

    α2 = e [−p (2+ 3)d2/(4kT ) ]

    g3α3 = (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

    αP*

    κ�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)

    κ×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