The statistical theory of transport in polymer networks and gels, which are examples of mesoscale porous structures holds many challenges, including connections between structures across length scales, their associated mechanics, and role of thermal fluctuations.
An important “real life” problem where all these concepts come together is metal corrosion and transport of small molecules through polymer barrier films applied to coatings. Despite a significant body of experimental research there is currently no reliable theoretical/computational model that can predict the performance of coatings in inhibiting corrosion.
The challenge in this PhD project is to develop appropriate realistic models that efficiently connect phenomena at different length-scales synergistically with experiments to quantitatively predict the overall coating performance.
Mesoscopic modelling using polymer theory (UoS – PhD) – The main objectives of your PhD will be to: (i) Develop microscopic models of random networks and develop effective coarse-graining procedures to arrive at effective free energy functionals for such systems. (ii) Use the free energy functional and statistical mechanical techniques rooted in mean field theory and self-consistent field theory (SCFT)  to understand molecular transport through mesoscopic porous structures. (iii) Develop coarse-grained molecular dynamics simulations to understand the role of network structure, mechanical properties, and thermal fluctuations on transport of small molecules. (iv) Use the results to inform a mesoscale model of effective transport through porous media and match the predictions against experiments. (v) Since the models developed are general we will extend them to understand properties of random networks maintained far from equilibrium that has a bearing on biological systems.
The project will involve working as part of a multidisciplinary team, interacting with both experimentalists and theory experts, in the Physics Department, our colleagues and collaborators in Chemistry and Mechanical Engineering in Sheffield; and also the School of Materials at the University of Manchester and our industrial sponsor Akzo-Nobel.
Students with a First class or high 2:1 in Physics, Mathematics (with a focus on courses in Applied Mathematics) are encouraged to apply. A familiarity with computer programming is an added plus.
 Krawczyk, J et al, "Elasticity Dominated Surface Segregation of Small Molecules in Polymer Mixtures", PRL (2016) 116 art no 208301; Souche M, Long D, "Case-II diffusion and solvent-polymer films drying: A meso-scale model", EPL 77 art no 48002, 2007.