A new methodology for parameterising coarse-grained forcefields to model polymers in molecular dynamics simulations is presented, using the recently developed SAFT-γ Mie equation of state [1]. This parameterization approach follows previous strategies in modelling smaller molecules using the aforementioned equation of state. [2] [3] [3]

The input parameters in the equation of state are the constituent parameters of the Mie force equation [1], which can be directly used in molecular simulations. The group contribution property of the equation of state allows for producing transferable Mie type forcefields for polymers, given that thermodynamic properties of small molecules containing the monomers are known. By parameterising the Mie forcefield for the monomer, the properties of a polymer of any size can be predicted by modelling a chain of monomers corresponding to the size of the polymer.

First for a range of common polymers (namely polyethylene, polypropylene, polyisobutylene, polybutadiene, polyisoprene and polystyrene), the methodology of the parameterisation is demonstrated. PVT properties of systems containing polymers as calculated by both molecular dynamics simulations and the equation of state are compared to experimental data. For a wide range of pressures and temperatures, it is shown that the error in calculating densities for each polymer is less than 1%.

Subsequently, MD simulations and the equation of state are used to independently calculate thermodynamic properties of polymers in solution and polymer blends. For high-density polyethylene and polyisobutylene, LCSTs are predictive without any adjustments to the cross interaction parameters for a range of solvents. For other systems an adjustment of less than 5% to the cross interaction parameter is required.

Finally, for cases of polystyrene-b-polyisoprene and polystyrene-b-polybutadiene block copolymers, simulations are carried out to demonstrate the applicability of this methodology in modelling self-assembly of diblock copolymers and in predicting the order-disorder transition temperatures of such systems. A phase map of the systems studied is compared to experimental measurements.

It is therefore concluded that SAFT-γ Mie forcefields are representative, transferable and robust in calculating thermodynamic and structural properties of polymers. Repeating monomer units can be used to model polymers of any size. Properties can be calculated from either simulations or the equation of state, giving the same results. Coarse-graining allows for larger systems to be simulated than atomistic models, and therefore phenomena such as microphase separation and self-assembly of diblock copolymers can be observed at the length and time scales provided by this methodology.

[1] Müller, A. E., & Jackson, G. (2014). *Annual review of chemical and biomolecular engineering* *, 5*, 405-427.

[2] Avendano, C., Lafitte, T., Galindo, A., Adjiman, C. S., Jackson, G., & Müller, E. A. (2011). *The Journal of Physical Chemistry B , 115*(38), 11154-11169.

[3] Avendaño, C. , Lafitte, T., Adjiman, C. S., Galindo, A., Müller, E. A., & Jackson, G. (2013). *The Journal of Physical Chemistry B , 117* (9), 2717-2733.

[4] Ervik, Å., Jiménez Serratos, G., & Müller, E. A. (2017). *Computer Physics Communications* *, 212*, 161-179.

Engineered self-assembly , Challenges and advances in fluid phase equilibria