Liquid water in confined media
nanofluidics
materials science
protein folding
cell membranes
Understanding how the physical properties of bulk water (e.g. hydrogen bond
network, diffusion, freezing point) are modified under confinement is relevant to a
variety of outstanding scientific problems, including:
» Studies of stability and enzymatic activity of proteins
» Oil recovery
» Nano-fluidics
» Heterogeneous catalysis (role of water-substrate interaction)
» Corrosion inhibition
Does a `confined water` phase exist, which
is independent of confining surfaces?
•
How do water structure and dynamics change at the nanoscale and are
there “fingerprints” of confined water?
•
What is the influence of the confining medium: confinement effects versus
interfacial properties?
•
How do electronic properties change?
•
Is flow affected in confined structures?
Confining Length
Graphite
Confining Dimension
Nanotubes
Confining Surface
Silicon Carbide
Outline
•Current description of structure and diffusion properties of
water, based on ab-initio simulations within Density Functional
Theory:
•Brief reminder about ab-initio simulations
•Simulations of interfaces with “hot” water
Beppu, Japan
•Water on a representative graphite and inside Carbon Nano
Tubes (CNT)
•Interface versus confinement effects
•IR spectroscopy
Ab-initio MD:
What do we do, in practice?
t
solid
F
from Density Functional Theory
(DFT) in a local density approximation.
Numerical solution of equations representing the
laws of quantum mechanics in an approximate, non
empirical manner
Improve upon solutions obtained within DFT, e.g.
using Quantum Monte Carlo or GW techniques
Ab-initio MD:
What do we do, in practice?
Solve set of N coupled, non linear partial differential
equations [Kohn-Sham equation] self-consistently,
using iterative algorithms, subject to orthonormality
constraints. N = # of electrons
    i  V (  , r ) i   i i i  1  N el


 ( r )
d r   V XC (  ( r ),   ( r ))
V (  , r )  V ion ( r )  
r  r


N el
Plane-wave basis sets and
2

pseudopotentials
 (r )    i (r )

i 1



The cost of solving the Kohn-Sham

  i ( r )  j ( r ) d r   ij
equations is eventually dominated by
orthogonalization (O(N3))
What are the obstacles on the road to
5000 atom ab-initio MD simulations ?
Ab-initio MD:
What do we do, in practice?
t
solid
F
from Density Functional Theory
(DFT) in a local density approximation.
Numerical solution of equations representing the
laws of quantum mechanics in an approximate, non
empirical manner
Improve upon solutions obtained within DFT, e.g.
using Quantum Monte Carlo or GW techniques
In the case of liquid water, we have compared
two ab-initio simulations approaches
Energy
In Born-Oppenheimer (BO)
dynamics, at each point on
the trajectory:
F = min[EKS]
..
MIRI = -IF
Time
In Car-Parrinello dynamics:
Energy
..
∂EKS[,R]
µi= -  ij j
∂i
..
∂EKS[,R]
MIRI = ∂RI
Time
For appropriate µ, electrons
“stay close” to BO surface
In the case of liquid water, we have compared
two ab-initio simulations approaches
Energy
In Born-Oppenheimer (BO)
dynamics, at each point on
the trajectory:
F = min[EKS]
..
MIRI = -IF
Time
In Car-Parrinello dynamics:
Energy
..
∂EKS[,R]
µi= -  ij j
∂i
..
∂EKS[,R]
MIRI = ∂RI
Time
For large µ, electrons can
“drift away” from BO surface
In the case of liquid water, we have compared
two ab-initio simulations approaches
Energy
In Born-Oppenheimer (BO)
dynamics, at each point on
the trajectory:
F = min[EKS]
..
MIRI = -IF
Time
Energy
In Car-Parrinello dynamics:
..
∂EKS[,R]
µi= -  ij j
∂i
..
∂EKS[,R]
MIRI = ∂RI
What are the simulation conditions (choice of µ, integration time step)
Time
which insure adiabatic dynamics (i.e. accurate calculation of electronic
structure at each MD step)?
Ab-initio structure and diffusion of bulk
water are only partially understood
•Poorly converged numerical results
have led to theoretical
misinterpretations.
•At experimental equilibrium density,
agreement with structure factors, g(r)
and diff. constants measured at 300 K is
obtained at ~ 350/400 K, using PBE.
•Role of energy functionals with exact
exchange, of proton quantum effects
and dispersion forces yet to be fully
sorted out; equilibrium theoretical
density yet uncertain.
Rigid water
Converged DFT results
Unconverged DFT results
Grossman et al, JCP 2004; Schwegler et al., JCP 2004; Sit and Marzari, JCP
2005; Pratt et al. PRE 2004; Fernandez-Serra and Artacho, JCP 2004.
Proton quantum effects may play an
important role in determining the
properties of the liquid, and
inaccuracies of DFT/PBE/BLYP may
be smaller than ~ 0.005 eV (in T)
Schwegler et al., JCP 2004; Allesch et al. JCP 2004
Proton quantum effects
Classical and Quantum [Path Integral Molecular Dynamics]
simulations of liquid water using ab-initio derived force fields (*):
F.Paesani, F.Iuchi and G.A.Voth, J.Chem.Phys.2007 (in press)
Conclusions differ from those of B.Chen, M.Klein and M.Parrinello, PRL 2005
(*)
Ab-initio structure and diffusion of bulk
water are only partially understood
Ab-initio derived force fields(*): qualitative agreement with
experiment
(*) Robert Bukowski, Krzysztof Szalewicz, Gerrit C. Groenenboom, Ad van der Avoird, Science 315, 1249 (2007)
Ab-initio simulations of water at interfaces are
carried out at 350/400 K instead of 300 K
Basic physical picture as provided by standard, quasi-tetrahedral model, is
reproduced by DFT/GGA
Hydrogen Bonds
Tetrahedral network
~ 3.6 bonds
/molecule,
consistent
with several
expt.
Simulations of confined water were carried out
at “high” temperature : T ~ 400 K
The first
coordination
shell
contains~ 4.2
molecules
Motivation: Conflicting statements
Confined water: controversial results from
experiment
Experiments on hydration water layers:
-
Kim H. I. et al Langmuir 19, 9271 (2003):
“Water structure can be perturbed tens of nm away from solid surface”;
-
L. Cheng et al PRL 87, 156103 (2001):
“The hydration structure has an oscillatory density profile extending ~10 Å from the
surface”;
Experiments on confined water:
-
Raviv et al Science 413, 51(2001):
“The viscosity of water remains comparable to its bulk value even within films down to
one or two monolayers thick.”
-
Naguib et al Nano Letters 4, 2237 (2004):
“When ultra-thin channels such as carbon NT contain water, fluid mobility is greatly
retarded compared to that on the macro scale”
-
J. K. Holt et al Science 2006
“Fast Mass Transport through Sub-2nm Carbon Nanotubes”
Motivation: Conflicting statements
Confined water: controversial results from
simulations
Simulations on confined water:
-
Mashl R. J. et al Nano Letters 3, 589 (2003):
“Water confined in carbon nanotubes of a critical size under ambient conditions (1 bar,
300 K) can undergo a transition into a state having ice-like mobility.”
-
Karla A. et al PNAS 100, 10175 (2003) and Hummer et al Nature 414, 188 (2001):
“The flow, through packed carbon NT membranes, appears frictionless and is limited
primarily by the barriers at the entry or exit of the NT pore.”
Ab-initio simulations:codes
• First principles molecular dynamics using
both Car-Parrinello and Born-Oppenheimer
algorithms. (GP and Qbox codes by F.
Gygi,UCD)
•Electronic structure and x-ray spectra
calculations with fine k-point grids (PWSCF
code: www.pwscf.org) and implementation of
XCH.
•IR spectra calculations using Maximally
Localized Wannier Functions
•Preparation of initial configurations for abinitio MD using classical potentials
(Gromacs: www.gromacs.org)
•Density Functional
Theory using GGA-PBE
functional
• Electron-ion interaction
using non-local
pseudopotentials
•Wave Functions expanded
in Plane Waves basis set :
85 Ry cutoff
•  point used for the BZ
integration in MD
simulations
Computational Strategy: confinement effects
Computational
Strategy
Confinement as a function of length scale
•Simulation time :
20-25 ps, except
for graphene with
d=2.50 nm (10 ps).
•We used D
instead of H for
computational
convenience.
d = 1.01 nm
d = 1.44 nm
d = 2.50 nm
Confinement in more than one dimension
# Water Molec.
# e-
None
64
512
SiC
57
1288
Graphite
32
496
Graphite
54 (49)
672
Graphite
108
1104
(14,0) CNT
34
1616
(19,0) CNT
54
1648
Surface
(14x0);d = 1.11 nm
(19x0); d = 1.50 nm
G.Cicero, J.Grossman, E.Schwegler, F.Gygi and G.G. submitted (2007)
Structural analysis for graphene sheets
•Interface: excluded volume plus a liquid layer with increased density (wrt bulk)
•Thin (~ 0.5 nm) interfacial liquid layer: macroscopic density depends on separation but
thickness and microscopic properties do not depend on separation
•Decrease of electronic density at the interface
•Enhancement of HB near the surface; changes in HB localized near the interfacial layer
Increased density in interfacial layer is found also for an
hydrogen terminated diamond surface (hydrophobic
layer)
Determination of interfacial structure
and of density of interfacial layer is
very sensitive to resolution
Electronic density profiles extracted from
measured X-ray reflectivity (R), i.e. ratio of
reflected to incident XR flux as a function
of incident angle: R proportional to
Interface
Water
Our results for e(r) are consistent
with experiment, but not with
interpretation in terms of rarefaction
of water at the interface.
A.Poynor et al. PRL 2006
Hydrophobic surface
Structural analysis for nanotubes
•Results similar to the graphene case, however layering effects are enhanced
Spatial distribution functions:
Interface structural analysis
SDF of Oxygen and
Hydrogen atoms of molecules
within 5 Å from the surface
shows influence of atomic
surface structure on water
orientation.
d = 1.44 nm
Interesting similarities with the benzene case:
M.Allesch E.Schwegler, G.Galli JPC-B 2007
Spatial distribution functions:
Interface structural analysis
SDF
of Oxygen
and
OH bonds
nearly
parallel to
Hydrogen
of molecules
the surfaceatoms
are preferred
in
within
from the surface
order 5toÅpreserve
in-plane
shows
H-bondinfluence
network.of atomic
surface structure on water
orientation.

z
Surface
Distribution of –OH
tilt angles show water
molecules closer to
the surface point one
hydrogen towards it 
sticky water
11
z (Å)
9
7
5
3
20
d = 1.44 nm
Interesting similarities with the benzene case:
M.Allesch E.Schwegler, G.Galli JPC-B 2007
40 60 80 100 120 140 160

Structure and orientation of interfacial water do
not depend on confinement distance
d = 1.44 nm
d = 1.01 nm
11
7
7
z (Å)
z (Å)
9
5
3
5
3
20
40 60 80 100 120 140 160

20
40 60 80 100 120 140 160

Perturbation induced by confining medium
appears to be extremely local in liquid water
Results of structural analysis robust wrt to density variation (10%)
Dipole moment of water molecules in confined
media
We have used maximally localized Wannier
functions to define molecular dipole moment
from optimized electronic wavefunctions
System
D(Debye)
Isolated H2O
1.8
Bulk H20
3.1
Gra (14.41 Å)
3.09
Gra (10.09 Å)
2.97
NT-(19x0)
2.92
NT-(14x0)
2.87
SiC-OH
3.09
• Magnitude of dipole moments
depend strongly on distance from
hydrophobic surface
• Consequences on lateral diffusion
and rotational dynamics
Dynamical properties: enhanced lateral diffusion and
faster re-orientational motion of confined water
Ab initio sim.
Classical sim.
• Our results on diffusion coefficients and re-orientational dynamics are consistent
with the findings of recent experimental measurements of fast mass transport in
CNT (Holt et al. Science 2006)—however they cannot explain the magnitude of the
effect observed experimentally
• Classical simulations with the SPC/E potential find the opposite trend as a
function of confinement (results sensitive to carbon-water interaction
potential)
Vibrational properties: power spectra of
water as a function of confinement
• Free OH bonds lead
to a strong high
frequency peak in the
power spectra of
confined liquid
0-3.5 Å
3.5-5 Å
5-9 Å
Bulk
• Low frequency band due to librational modes
decrease systematically with confinement
length scale
Interfacial effects can be measured!
IR spectrum of confined water
32 H2O + Graphite
 tanh(
 ( ) n ( ) 
V
 
2
)



dte
 i t
  (t)   
i
i
j
(0)
j

4
  6 R O  R D  R D  2  R W
1
2
s 1

M.Sharma, E..Schwegler, D.Donadio and G.G. (2007)
s
IR spectrum of H2O only confined in Graphite
How can the OH stretch of water be IR inactive?
Symmetric Stretch
Asymmetric Stretch
• It can’t …unless the surface has something to do with it.
• The dipole moment change due to the OH stretch is (almost)
compensated by the charge `transfer` between the p-orbitals on the
graphite surface and the water molecules!
• At finite T: important electro-dynamical coupling to the water-graphite
bonding, that cannot only be explained using simple dipolar forces.
What we have learned so far about confined water
• Perturbation induced by confinement is local
• No ice-like layer at the interface: liquid density
increases
• Rarefaction and decrease of density away from
the interface
• Dipole moment of water molecule at the
interface decreases(*)  lateral diffusion is
enhanced and re-orientational dynamics is
faster: Consistent with rapid flow in nanotubes
detected in recent experiments
• We predict that effects of OH bonds not engaged
in hydrogen bonding and changes in librational
modes are visible (although weak) in IR spectra.
Sticky yet fast
water molecules
at the interface
Complex electronic
interactions occurs
at the interface
(*) Consistent with results obtained for Benzene and HFB in water: M.Allesch, E.Schwegler and G.G. JPC-B 2007.
Water at hydroxylated Si-SiC(001) surface
Confinement between two fully hydroxylated
SiC surfaces at ~ 1.4 nm
Computational strategy
1
1)
2)
3)
2
3
Surface exposed to rigid water molecules
[M.Allesch et al. JCP 2004] to achieve equilibration
without allowing reactivity
Rigidity constraints released to allow for bondbreaking
Flexible water on the fully hydroxylated
surface
Interface structural analysis
Beyond ~ 3 Å from the surface,
water recovers bulk structural and
electronic properties.
Consistent with experiments on Mica
87, 156103 (2001)]
G.Cicero, J.Grossman, A.Catellani and G.Galli, JACS
127, 6830 (2005)
[PRL
Inhomogeneous, thin layers of dense water on
hydrophilic Si-SiC(001)
Thin (~ 3 A) interfacial layer
Inhomogeneous wetting dictated
by surface reconstruction (liquid
layer is not ice-like)
G.Cicero, J.Grossman, A.Catellani and G.G. JACS 2005
Changes in
electronic
structure
localized at
the interface
Many thanks to my collaborators
Giancarlo Cicero (University of Turin, Italy)
Manu Sharma (UCD)
Jeff Grossman (UCB)
Francois Gygi (UCD)
Eric Schwegler (LLNL)
Thank you!
Markus Allesch (University of Gratz, Austria)
Support from DOE/BES, DOE/SciDAC and LLNL/LDRD
Computer time: LLNL, INCITE AWARD (ANL and IBM@Watson), NERSC