Crystal Polymorphism in Hydrophobically Nanoconfined Water

Crystal Polymorphism in Hydrophobically Nanoconfined Water

Crystal Polymorphism in Hydrophobically
Nanoconfined Water
O. Vilanova, G. Franzese
Universitat de Barcelona
Water’s phase diagram
Phase diagram of bulk water presents up to 15 different phases
Typical H2O Molecular Models used in simulations
These models have a L-J interaction and an electrostatic term
of point charges qi , qj .
Eab =
ona X
onb
X
kC qi qj
i
j
rij
+
A
B
− 6
12
rOO rOO
a) 3-site model like in SPC, SPC/E, TIP3P; b) 4-site PPC; c) 4-site
TIP4P; d) 5-site TIP5P
(1)
Molecular Dynamics in a Water Monolayer
Molecular Dynamics simulations show different structures of
confined water depending on the confining plates separation h.
(Zangi & Mark, 2003) MD simulations using TIP5P
a) Monolayer liquid water h = 0.47 nm
b) Monolayer ice water h = 0.53 nm
c) Bilayer liquid water h = 0.58 nm
Coarse Grained model for Water
Consider a cell model in a square lattice with one molecule per
cell. Molecules can form hydrogen bonds when their facing arms
are in same state (shown as colors in the figure).
j
k
i
rmax
Coarse Grained model for Water II
We associate an increase of the total volume due to the formation
of HB. Add a contribution P vHB NHB to the enthalpy.
Low density
High density
(Soper,2008). Spacial distribution function g(r, θ, φ) for low (top) and
high (bottom) density water. In f), the second shell of nearest neighbors
collapses and is almost coincident with the inner shell.
Original Model
Lennard-Jones potential as the oxigen-oxigen interaction of
different molecules:
#
"
X r0 12 r0 6
−
HVW ≡
ε
rij
rij
i<j
ULJ
0
-ε/4
r0
rij
Original Model
Directional HB term, as the energy gain due to the formation of a
HB between facing arms of neighbor molecules:
X
HHB ≡ −J
βij = −JNHB
hi,ji
with βij = δσij ,σji Θ(rij − rmax ) and σij ∈ {1, 2, ...6}.
σji
σij
j
rmax
i σik σki
k
Example:
Molecules i and j can form a HB:
δσij ,σji = 1 and
Θ(rij − rmax ) = 1 → βij = 1
Molecules i and k can not: δσik ,σki = 1
but Θ(rij − rmax ) = 0 → βij = 0
Original Model
Cooperative HB term, energy gain (at low temperature) due to the
orientational ordering of the Hydrogen Bonds network:
XX
Hcoop ≡ −Jσ
δσik ,σil
i
a)
σa4
b)
σb4
(k,l)i
σa3
σa2
σa1
σb3
σb2
σb1
Example:
Molecule a has energy:
ECoop,a = −Jσ (δσa1 ,σa2 + δσa1 ,σa3 + · · · ) = 0
Molecule b has energy:
ECoop,b = −Jσ (δσb1 ,σb2 + δσb1 ,σb3 + · · · ) = −3Jσ
Extension to the Model
Three body O-O-O angular interaction between triplets of nearest
neighbor moleculs, due to the positional ordering induced by the
Hydrogen Bonds network:
X X
i
Hθ ≡ Jθ
βik βil cos(4θkl
− π)
i
j
θijk
i
k
hhk,liii
Computer Simulation Details
We perform efficient Monte Carlo simulations using hybrid
Wolff-Metropolis algorithm
N ∼ 1000 − 10000 molecules at constant P and T
Variables: 4N bond indices σij + N coordinate vectors ~ri + total
volume V
1 MC step = 5N + 1 Metropolis updates + 5 cluster updates
σij,old → σij,new = Rand[1, 6]
~ri,old → ~ri,new , where rxi,new = rxi,old + Rand[−δr, δr]
Vold → Vnew , where Vnew = Vold + Rand[−δV, δV ]
Accept an attemp change if ∆G < 0 or e−β∆G < Rand[0, 1]
∆G = ∆H − T ∆S = ∆U + P ∆V − T log(Vnew /Vold )
Phase Diagram I
Parameter set: = 1, J = 0.5, Jσ = 0.1, Jθ = 0.3
Phase Diagram II
Parameter set: = 1, J = 0.75, Jσ = 0.1, Jθ = 0.2
P T Phase Diagram
Pressure P[ / 3]
1.8
1.6
1.4
Triangular
crystal
1.2
1
|φ4| > 0.8
|φ6| > 0.8
min[g(r)] = 0
TMD
max[CP]
max[CPJ]
max[CPθ]
Liquid
0.8
0.6
0.4
0.2
0
Square
crystal
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Temperature T[ /kB]
Triple point
Liquid-liquid
Critical point
Liquid-gas
Critical point
Radial Distribution Function
g(r) ≡
1 X
δ(r − rij )
ρ2 V
i6=j
P(r < rij < r+dr) ∝ g(r)2πrdr
Figure: RDF of three different phases.
Radial Distribu on Func on
Structure at Low Pressure
4. 5
T=0.30
T=0.15
T=0.09
4
3. 5
3
2. 5
2
1. 5
1
0. 5
0
0
1
2
3
4
5
Distance
T=0.09
T=0.15
T=0.30
Orienta onal +
Transla onal
Square order
Orienta onal
Square order
No order
Radial Distribu on Func on
Structure at High Pressure
5
T=0.40
T=0.35
T=0.20
4. 5
4
3. 5
3
2. 5
2
1. 5
1
0. 5
0
0
1
2
3
4
5
Distance
T=0.20
T=0.35
T=0.40
Orienta onal +
Transla onal
Triangular order
Orienta onal
Triangular order
No order
Conclusions
We perform efficient Monte Carlo simulations of a coarse-grain
model of water and find two forms of ice.
The low density crystal phase has square symmetry as in MD
simulations.
At high pressure, the high density solid phase is hexatic and
separates a triangular crystalline phase from the liquid.
By tuning the parameters, we can induce crystallization at higher
or lower temperatures or pressures, or move the LLCP inside or
outside the liquid region. So we can predict different scenarios in
the phase diagram.