The sulphur phase diagram is one of the most complex ones of all elemental systems, competing with that of carbon. The flexibility of the bonds allows for a variety of motifs: rings of 5 or more atoms in various conformations, short diradical chains and thousands-atoms long polymers to name a few; which give rise to a plethora of structures: molecular & polymeric crystals of many different symmetries, amorphous solids and molecular & polymeric liquids. Modelling transitions between such phases is a challenging task, out of the reach of any current force fields (which are too inaccurate) or quantum mechanical methods (which are too slow and expensive). However, following the footsteps of similar work done on silicon, phosphorus and carbon, surrogate machine learning models mimicking quantum methods at a fraction of the cost could achieve this feat. In this work we propose several such models, prompted by the continuous evolution of the field, and benchmark them on a series of static and dynamic tests.

We successfully describe the ambient condition solid phase, melting, polymerisation and depolymerisation of sulphur: an achievement out of reach of any previous method. We also dedicate considerable effort to investigating the liquid-liquid phase transition recently reported in the experimental literature [1]. This consists of a change between low and high density liquid forms heralded by a jump in density and alterations in radial distribution functions and Raman spectra. While a simple analytical model to explain the transformation was proposed in a recent publication [2], a quantum-mechanically accurate exposition of the microscopic phenomena is desirable. Our models surpass previous length and time constraints and allow the simulation of liquid sulphur for up to hundreds of nanoseconds for thousands of atoms, which enable the reaching of thermal equilibrium and the obtaining of meaningful and precise measurements of the structure factors, cluster sizes and coordination statistics. We are able to characterise the two phases: one consisting of an almost even fraction of polymers and small rings and the other comprising mostly of tightly-packed polymers.

Another important contribution of this thesis is the in-depth display of the process of building a general potential for such a complex system. We showcase several methods for creating a relevant dataset, through: manual selection, iterative training and automated selection; which could prove useful for the community.

Furthermore, we investigate the effect of magnetic dipole moments on small sulphur clusters and condensed liquid phases, and put forward the first general machine-learning potential trained on spin-polarised data.