Crystal Polymorphism in Hydrophobically Nanoconfined Water. O. Vilanova, G. Franzese Universitat de Barcelona

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1 Crystal Polymorphism in Hydrophobically Nanoconfined Water O. Vilanova, G. Franzese Universitat de Barcelona

2 Water s phase diagram Phase diagram of bulk water presents up to 15 different phases

3 Typical H2O Molecular Models used in simulations These models have a L-J interaction and an electrostatic term of point charges q i, q j. ona onb E ab = i j k C q i q j + A r ij roo 12 B roo 6 (1) a) 3-site model like in SPC, SPC/E, TIP3P; b) 4-site PPC; c) 4-site TIP4P; d) 5-site TIP5P

Molecular Dynamics in a Water Monolayer Molecular Dynamics simulations show different structures of confined water depending on the confining plates separation

4 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

5 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). k j i r max

Coarse Grained model for Water II We associate an increase of the total volume due to the formation of HB. Add a contribution P v HB N HB to the enthalpy.

6 Coarse Grained model for Water II We associate an increase of the total volume due to the formation of HB. Add a contribution P v HB N HB 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.

7 Original Model Lennard-Jones potential as the oxigen-oxigen interaction of different molecules: H VW [ ( ) 12 ( ) ] 6 r0 r0 ε r i<j ij r ij U LJ 0 -ε/4 r 0 r ij

8 Original Model Directional HB term, as the energy gain due to the formation of a HB between facing arms of neighbor molecules: H HB J i,j β ij = JN HB with β ij = δ σij,σ ji Θ(r ij r max ) and σ ij {1, 2,...6}. σ ji σ ij i j σ ik σ ki r max k Example: Molecules i and j can form a HB: δ σij,σ ji = 1 and Θ(r ij r max ) = 1 β ij = 1 Molecules i and k can not: δ σik,σ ki = 1 but Θ(r ij r max ) = 0 β ij = 0

9 Original Model Cooperative HB term, energy gain (at low temperature) due to the orientational ordering of the Hydrogen Bonds network: H coop J σ i (k,l) i δ σik,σ il a) σ a4 b) σ b4 σ a3 σ a1 σ a2 σ b3 σ b1 σ b2 Example: Molecule a has energy: E Coop,a = J σ (δ σa1,σ a2 + δ σa1,σ a3 + ) = 0 Molecule b has energy: E Coop,b = J σ (δ σb1,σ b2 + δ σb1,σ b3 + ) = 3J σ

10 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: H θ J θ i k,l i β ik β il cos(4θ i kl π) j θ i jk i k

11 Computer Simulation Details We perform efficient Monte Carlo simulations using hybrid Wolff-Metropolis algorithm N molecules at constant P and T Variables: 4N bond indices σ ij + N coordinate vectors r i + total volume V 1 MC step = 5N + 1 Metropolis updates + 5 cluster updates σ ij,old σ ij,new = Rand[1, 6] r i,old r i,new, where r xi,new = r xi,old + Rand[ δr, δr] V old V new, where V new = V old + 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(v new /V old )

12 Phase Diagram I Parameter set: ɛ = 1, J = 0.5, J σ = 0.1, J θ = 0.3

13 Phase Diagram II Parameter set: ɛ = 1, J = 0.75, J σ = 0.1, J θ = 0.2 Pressure P[ / 3 ] P T Phase Diagram Triangular crystal Square crystal Liquid Temperature T[ /k B ] φ 4 > 0.8 φ 6 > 0.8 min[g(r)] = 0 TMD max[c P ] max[c PJ ] max[c Pθ ] Triple point Liquid-liquid Critical point Liquid-gas Critical point

14 Radial Distribution Function g(r) 1 ρ 2 V δ(r r ij ) i j P(r < r ij < r+dr) g(r)2πrdr Figure: RDF of three different phases.

Structure at Low Pressure Radial Distribu on Func on 4.

09 0 1 2 3 4 5 Distance T=0.09 T=0.15 T=0.

15 Structure at Low Pressure Radial Distribu on Func on T=0.30 T=0.15 T= Distance T=0.09 T=0.15 T=0.30 Orienta onal + Transla onal Square order Orienta onal Square order No order

16 Structure at High Pressure Radial Distribu on Func on T=0.40 T=0.35 T= Distance T=0.20 T=0.35 T=0.40 Orienta onal + Transla onal Triangular order Orienta onal Triangular order No order

17 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.

Monte Carlo simulation of confined water

Monte Carlo simulation of confined water Author: Guillermo Cámbara Ruiz Advisor: Giancarlo Franzese Facultat de Física, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain. Abstract: In living