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chapter |
Conclusion |
In this thesis we have used the Trimer molecule to understand two of pre-eminent problems in molecular liquids; the fragility close to the glass transition temperature, and the slow crystal growth rates.
Our analysis of the dynamics of the trimer in @sec:Dynamics show that it is a suitable model of a fragile liquid, displaying the same liquid state dynamics as ortho-terphenyl. The combination of being able to visualise the entire simulation while also being able to explore larger and longer simulations allowed for a greater understanding of the behaviours of this molecule. The next step for continuing this analysis of dynamics is to apply these same analysis techniques to the Lewis--Wahnström model, giving an insight into whether these effects hold in 3D. A downside of using the 2D Trimer model is that there is only a single rotational degree of freedom in 2D, rather than the three degrees of freedom in 3D. The additional degrees of freedom available to rotations in 3D, could reduce the effect of the slow rotational motions. A further effect observed of the Trimer molecule, is the onset of dynamic heterogeneities above the melting point, suggesting dynamic heterogeneities are a property of the glass transition rather than the melting point.
With the Trimer being a suitable model to study the behaviour of supercooled liquids, in @sec:Glassy_Dynamics we introduced new dynamic quantities that describe the relaxation of each individual molecule. These new dynamic quantities are shown to be useful for the Trimer model, through are yet to be more widely tested. Further work applying these new tools to well characterised models, like Lewis--Wahnström, would greatly help develop their general applicability. These molecular relaxations provide a new method for investigating dynamic heterogeneities, finding the dynamic heterogeneities arise from the onset of jump dynamics (@sec:jump_dynamics). As the temperature decreases the size of translational and rotational motions increase and the dynamics can no longer be suitably described as Brownian causing a breakdown in the Stokes--Einstein--Debye dynamics. This breakdown is not only a result of the jump dynamics, where in @sec:sed we find coupling between rotational and translational motions, with structural relaxation requiring both motions to occur. The presence of jump dynamics and the coupling of rotational and translational motion results in the breakdown of the Stokes--Einstein--Debye relations and alternative models of dynamics are required for liquids close to the glass transition.
@Sec:Machine_Learning introduces a new machine learning methodology which is able to identify local structures which have a high incidence, like those within a crystal structure using clustering. We also introduce a supervised learning algorithm which is able to distinguish three crystal polymorphs of the Trimer from the liquid phase. The benefits of this machine learning approach is the potential to be applied to a range of crystal structures. Further work is to demonstrate this applicability to a range of different molecules and their crystal structures. The general nature of the approach has potential to describe a method that works for nearly any molecular crystal. The most difficult part of a general approach will be the transition from describing crystals in 2D space to describing crystals in 3D space, where the number of nearest neighbours increases from six to twelve, increasing the dimensionality of the feature space accordingly.
We use the machine learning algorithm in @sec:Crystal_Melting where the high accuracy allows us to measure melting rates which are 4 orders of magnitude slower than anything else in the literature. When fitting these melting rates to models of melting, we find that a Semi-Empirical Density functional model, which uses the fluctuations of a order parameter to best model the temperature dependence of the melting rate. This Semi-Empirical Density functional model explains the slow melting rates of the Trimer model through the rigidity of the liquid and crystal structures. A significant downside of the exceptionally slow melting rates, is that there was no observed crystal growth. A further study of the Trimer model could investigate methods for speeding up the crystal growth rates, with a potential method being modifications to the shape reducing the effective size of the outer particles. This reduced size would allow for more freedom of rotation and hence the fluctuations which the Semi-Empirical model is based on. Moving to studying a 3D system, like the Lewis--Wahnström model, would also increase the speed of growth, by providing more rotational degrees of freedom the liquid and crystal structures will be less constrained giving larger fluctuations of the order parameter used in the Semi-Empirical Density Fluctuation model.
While we are able to measure the melting rates of the Trimer,
we are unable to observe crystal growth
within the timescale of simulations.
@Sec:Melting_Behaviour investigates reasons for why
the growth rate is so phenomenally slow.
Here we find that the slow growth
is a result of the suppression of rotational motion
close to the surface of the crystal.
The lack of rotations within the crystal
is preventing the rotations within the liquid.
We can study the effect of this suppression
in the melting of the pg polymorph,
which shows suppression of rotations on the