Methane hydrate: interfacial nucleation
Crystal
Melted under vacuum (300 K), then pressurised under methane
(30 atm)
Time Evolution
Potential Energy (rolling average over 10 ps)
(n.b. should divide by 1654 to quote per mole of water
Density profile across interfaces
I = 0–0.3 ns
II = 9–10 ns
Hydrate Formation: Analysis
upper half of water film (0 – 20 Å)
lower half of water film(-20 – 0 Å)
Methane-Methane radial distribution functions, g(r)
Order parameters: 3-body
• Fluctuations from tetrahedral network
• Average over all triplets, based on central oxygen and “bonding” radius
Order parameters: “4-body”
• Locate a three H-bond chain
• Calculate torsion angle and triple product from “bond” vectors
• Mimic by two-molecules
• Average over coordination shell
Local Phase of Water Molecules• Define local order parameters that distinguish between
bulk phases
• Determine standard deviations, , within stable bulk phases (hydrate/ice)
• Assign individual molecule as hydrate/ice if all its order parameters agree with bulk values to within 2
Environment Liquid Hydrate IceF3 0.10 0.01 0.01F4 0.00 0.70 -0.40F4t 0.26 0.47 0.29
H-bond network angles
H-bond network torsions
Order parameters & melting
• Analysis of melting crystal shows order parameters are consistent
• Analysis of covariance matrix (bulk) shows they are independent
Characterising Molecular Order
• Define vector of three order parameters (f)
• Calculate covariance matrix for each molecule (C–1) for stable phases
• Eigenvalue analysis to de-correlate (y)
1
2
1
2
( )P e
e
f C f
y Λ y
-1
f
Λ U CU
y Uf
Local Phase Assignment
2 2i i i i iy
y Uf
• Calculate f for each molecule in arbitrary system
• Project onto eigenvectors (components of y)
• Compare with : assign “local phase” if all three components within 2(?) standard deviation of for that phase
Water in Hydrate Environment
Fraction of Hydrate-Water
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 10 20 30 40
time / ns
Control1
Control2
Control3
Distribution of order parameters
1 ns
Difference:22 ns - 1 ns
Animated Nucleation
Simulated Nucleation [ hydrate-waters )
3.3ns2.4ns 4.2ns 5.1ns
6.9ns6.0ns
1.5ns
7.8ns 20ns 40ns
0.6ns
10.5ns
Which hydrate structure?
type II
• Best signature is arrangement of dodecahedra
type I
Which hydrate structure?
• Early appearance of face-sharing dodecahedra
type II
• Oswald’s step rule: form the unstable polymorph first
• Experimental verification: time resolved X-ray powder study (Kuhs, 2002)
