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Understanding Nonlinear Dynamics of Associative Polymers for Healthcare and Sustainable Applications: Computer Simulations and Mathematical Modelling

   Department of Mathematics and Statistics

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  Dr Z Wang, Dr A Lukyanov  Applications accepted all year round  Competition Funded PhD Project (UK Students Only)

About the Project


Associative polymers are macromolecules containing associative groups, also called stickers, that undergo reversible association to physically cross link the polymers into transient networks. The reversibility and flexibility of such supramolecular polymer networks find them numerous applications as smart materials, e.g., for self-healing and controllable drug release in healthcare, reprocessable and recyclable materials for sustainable environment, and stimuli-responsive matrices in sensing and actuation [1-3]. The study of associative polymers is thus of strong interdisciplinary nature, both fundamentally and practically, and has attracted extensive interests from many STEM, healthcare and environmental sectors.  

To develop novel associative polymer systems with fascinating functions on demand, it is essential to understand their dynamic and mechanical behaviours in connection with the transient network formation and evolution and consequently develop theoretical models to make quantitative predictions. This is a highly challenging task due to the large varieties in the parent polymer compositions and the types of noncovalent interactions of the stickers, as well as interplay between the parent polymer dynamics and the breaking/reforming kinetics of the physical cross-links. Extensive experimental and theoretical works have been dedicated to tackle this problem [1-6]. Current theoretical models are able to qualitatively and sometimes semi-quantitatively describe the linear dynamics of associative polymers with simple compositions, such as linear polymers with stickers located at the chain ends or along the backbones [3-5], but the nonlinear behaviours of these systems under shear or extensional flows are far from being well understood [6], not to mention the polymer systems with more complicated architectures and stickers with high association energies and functionalities. It is thus the aim of this PhD project to shed light on resolving some of the challenges in this exciting research field.  

Research Targets and Methods

In this project, the student will take a combined computer simulation and mathematical modelling approach to study the structural and dynamic properties of model associative polymers under shear and extensional flows. In our research group, an efficient GPU-based hybrid molecular dynamics/Monte Carlo simulation package has been developed for studying the equilibrium and non-equilibrium/nonlinear behaviours of linear polymers with stickers at the chain ends (i.e. telechelic chains) [5-6]. This package will be extended to study associative polymers with more complicated architectures and compositions and also containing different types of stickers. Depending on background and interest, the student can also incorporate machine learning and statistical sampling algorithms into the simulation package to allow the exploration of a broad parameter space that is not accessible to standard brute force simulations. Detailed analyses of the simulation data will be carried out to achieve a clear microscopic picture of the structural formation and evolution in different model associative polymer systems, which will be applied to examine existing theoretical models and if needed refine them or reconstruct new mathematical models. 

 The simulation jobs will be submitted to the Reading Academic Computing Cluster and one of the world-top computing facilities (Young supercomputer) dedicated to molecular simulation. The student will have opportunities to collaborate or interact with experts in machine learning and statistical sampling methods at the University of Reading and many leading experimental and theoretical groups in relevant research fields across the world. 

Work Plan - The project is structured along with the following successive tasks: 

Stage 1: Literature review and study background knowledge, including computer simulation techniques, polymer physics/fluid mechanics theories; Perform simulations of model non-associative and associative polymers to get familiar with the GPU-codes and produce publishable results.

Stage 2: Extend the existing simulation code for studying associative polymers with different compositions and stickers with different types of interactions and potential incorporate machine learning and statistical sampling algorithms; Perform extensive simulations and data analyses of model associative polymers under flows for providing clear microscopic pictures of their non-equilibrium/nonlinear structural and dynamic behaviours.

Stage 3: Continue with simulation and analysis works in Stage 2; Compare simulation results with experimental data for interpreting experimental observations; Examine existing theoretical models and if needed refine or modify them based on microscopic understanding obtained in simulations; Wrap up research outcomes for scientific publications.

Qualification: A BSc (2:1 or above) or MSc degree in any of the following subjects: Mathematics, Statistics, Physics or Chemical Physics, Computer Science or Engineering. Some experience in programming with C/C++, Matlab, or any other programming languages is preferred.

Start date: within Academic Year 2022/23 

Funding Notes

- EPSRC PhD studentship for 4 years, plus an annual tax-free stipend (currently £17,688)
- restricted to UK student only


[1] Cordier, P., F. Tournilhac, C. Soulié-Ziakovic and L. Leibler, Self-healing and Thermoreversible Rubber from Supramolecular Assembly, Nature 451 (2008) 977–980.
[2] Seiffert, S. and J. Sprakel, Physical Chemistry of Supramolecular Polymer Networks, Chem. Soc. Rev., 41 (2012) 909-930.
[3] Wu, S., and Q. Chen, Advances and New Opportunities in the Rheology of Physically and Chemically Reversible Polymers, Macromolecules, 55 (2022) 697-714.
[4] Rubinstein, M., and A. N. Semenov, Dynamics of entangled solutions of associating polymers, Macromolecules 34 (2001) 1058–1068.
[5] Chen, Q., G. J. Tudryn, and R. H. Colby, Ionomer dynamics and the sticky Rouse model, J. Rheol. 57 (2013) 1441–1462.
[6] Dipesh, A., A. E. Likhtman and Z. W. Wang, Dynamics in Supramolecular Polymer Networks Formed by associating Telechelic Chains, Macromolecules 49 (2016), 7510-7524.
[7] Dipesh, A. & Z. W. Wang, Nonlinear Rheology and Dynamics of Supramolecular Polymer Networks Formed by Associative Telechelic Chains under Shear and Extensional Flows, J. Rheol. 64 (2020) 581-60.

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