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ow the
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d order
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200
Crystallisation kinetics
0
0
0.5
1
D. Quigley (Theory Group)
Figure 3. Total number of solid water molecules, and number
The rates at which crystals nucleate and grow from either a supercooled melt, or a within the largest cluster as a function of time minus the
induction
time
(t
)
to
the
first
nucleation
event
in
a
metadynamics
i
supersaturated solution, are essential inputs for solidification models in a variety of contexts. simulation of 2496 TIP4P water molecules freezing at 180 K.
These materials synthesis and processing, development of antifreeze strategies for Each
value isinclude plotted minus
the average equilibrium
(unbiased)
background value up to the formation of a critical cluster. The
cryopreservation, and understanding the formation of harmful biological crystals such as kidney total
number of molecules in the
simulation
is 2496.
stones. In principle, these rates can be obtained from atomistic computer modelling. Unfortunately the timescales involved are generally inaccessible to “brute force” simulation. t–ti (ns)
Several approaches exist to circumvent the timescale problem in this context. By creating crystalline seeds in the growth medium, one can use classical nucleation theory (CNT) to fit results to a kinetic model in which the nucleus size is a diffusive coordinate (random walk) on a 1D free energy landscape. Alternatively, this free energy can be calculated independently of CNT using biased simulation techniques (umbrella sampling, metadynamics and others), or the rate can be computed without reference to free energies via path sampling approaches (transition interface sampling, milestoning and more). 0.12
a critical
fluid at
Figure 4. Growth of a critical nucleus in a metadynamics
simulation
of 2496 ice TIP4P
water molecules
freezing
at 180
A crystalline nucleus forming within a K.
Hydrogen
bonds
molecules
identified
solid are
simulation of connecting
supercooled water. From as
[2]. highlighted. Solid molecules are identified by the same method
used in [7]. Times correspond to the x-axis in figure 3.
All of these techniques rely (to varying extent) on the assumption that complex dynamics involving thousands of atoms can be reduced to a one-­‐
dimensional diffusive variable. Errors in this assumption are often masked by inaccuracies of atomistic models resulting in incorrect thermodynamic parameters [1]. Recent work within the group has used simple lattice-­‐based crystallisation models (where the thermodynamics are well defined) to explicitly test this approximation, and found it lacking in many cases. In this project, we will extend this study to off-­‐lattice models of crystal nucleation and growth, and seek improved kinetic models for nucleation under realistic conditions. We will initially apply path-­‐sampling techniques to create benchmark data on nucleation rates. Such approaches can be biased by how one distinguishes atoms that are part of a crystal from those in the surrounding medium. However, recent algorithmic developments by collaborators in chemistry (Habershon group) raise the possibility of path sampling in which the bias is easily calculated and corrected for [2]. Equipped with accurate data on rates, we will develop models (beyond CNT) for the dynamics of nucleus size. Possibilities include the use of correlated random walks, consideration of depletion effects and the use of higher-­‐dimensional representations of the free energy surface. The project will be largely computational, but will require the student to develop an advanced understanding of statistical mechanics, thermodynamics and kinetic theory. Work will involve use of high performance computing facilities, parallel programming and also interfacing sampling algorithms and data analysis tools to simulation engines via scripting languages. [1] Zimmermann, DQ et al J. A. C.S., 2015, 137, 13352-13361
[2] DQ and Rodger, Mol. Simul., 2009, 35, 613-623
[3] S. Habershon, J. Chem. Phys. , 2015, 143, 094106