MC Results - Growth Rate

y/kT = 0.7 kJ mol-1 y/kT = 1.0 kJ mol-1

0.0 0.1 0.2 0.3 0.40.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

0.0055

0.0060

0.0065

ndefx=2 : ndefy=2 : x/kT=5.0 :

y/kT=0.7 : sizey=2

0 defects sizex=10 sizex=15 sizex=20

Gro

wth

Rat

e

Dm/kT

0.0 0.1 0.2 0.3 0.40.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

0.0055

0.0060

0.0065 ndefx=2 : ndefy=2 : x/kT=5.0 :

y/kT=1.0 : sizey=2

0 defects sizex=10 sizex=15 sizex=20

Gro

wth

Rat

eDm/kT

MC Results for Dm/kT = 0.2

0 impurities Length=10 units

Length = 15 units

Length = 20 units

MC results - summary

• Sudden change in slope at Dm/kT = 0.2 signals transition from step growth to island nucleation

glass ceiling for low dosage (kinetic) inhibitors?

• For x/kT = 0.7

(Dm/kT)* = 0.1 for defects of length = 10 units

(Dm/kT)* = 0.2 for defects of length = 15 and 20 units

• decreasing defect width has little effect on growth rate

• increasing x has little effect on growth rate

• increasing y reduces growth rate significantly

Gas Hydrates (Clathrate Hydrates)

• Two components open tetrahedral water lattice hydrophobic “guest”

molecules

• Three main crystal structures; probably two important for

environment & industry

• Each built from two water polyhedradiameter 8–9 Å

type I

type II

Clathrate Hydrates: Guests

• hydrophobic (natural gas)

• Acid Gases (H2S, CO2)

• cyclic ethers (DMO, TMO, THF)

• NOT ionic or strongly polar

• Size matches/determines structure

Hydrates: Phase Diagram

• Favoured by low temperatures and high pressures

• Typical of sub-sea pipelines, continental shoulders, tundra

Crystal Nucleation

• Activated process:Favourable “bulk” energyUnfavourable interfacial energyCritical “cluster” size

• Classical Nucleation Theory

• Fundamentally StochasticLong and random induction times (~ days)

FavourableUnfavourable

-20

-10

0

10

0 5 10r

delta-G

3 244

3G r r m D D

Nucleation in Other Aqueous Systems

• Matsumoto, Saito & Ohmine, Nature 2002

• MD

• Mild subcooling (ca 10 K)

• Multiple ms trajectories

• Critical nucleus built around on long-lived (1-2 ns) hydrogen bonds

Nature of the nucleus

• Non-spherical & not compact for ice

(from Matsumo et al, Nature 2002)