methane hydrate: interfacial nucleation crystal melted under vacuum (300 k), then pressurised under...
Post on 22-Dec-2015
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Methane hydrate: interfacial nucleation
Crystal
Melted under vacuum (300 K), then pressurised under methane
(30 atm)
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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
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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)
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Order parameters: 3-body
• Fluctuations from tetrahedral network
• Average over all triplets, based on central oxygen and “bonding” radius
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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
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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
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Order parameters & melting
• Analysis of melting crystal shows order parameters are consistent
• Analysis of covariance matrix (bulk) shows they are independent
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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
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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
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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
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Distribution of order parameters
1 ns
Difference:22 ns - 1 ns
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Animated Nucleation
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Simulated Nucleation [ hydrate-waters )
3.3ns2.4ns 4.2ns 5.1ns
6.9ns6.0ns
1.5ns
7.8ns 20ns 40ns
0.6ns
10.5ns
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Which hydrate structure?
type II
• Best signature is arrangement of dodecahedra
type I
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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)