Multi-scale modelling of branched polymer melts

In the 20th century plastics became an indispensable part of modern life. Most plastic products are produced by melting polymer materials and moulding them into different shapes. The flow or rheological behaviour of molten polymers is highly sensitive to their molecular architectures and molecular weight distributions. Presence of a small amount of long chain branching structures in commercial polymers can alter their rheological and thus processing properties significantly. Therefore a thorough understanding of the relationship between polymer branching and rheology is of crucial importance to the multi-billion pounds plastics industry. The dominant contributions in defining this relationship come from two respects: entanglement effects among long polymer chains or branches and complexity in branching architectures.

The entanglement effects originate from the fact that long polymer chains can not pass through each other. As a consequence, the lateral motion of the chains are suppressed, leading to the extremely long relaxation time and characteristic viscoelastic behaviour of entangled polymers, which are qualitatively different from the viscous behaviour of fast relaxing simple liquids. Theoretical works on entanglement dynamics have been for 40 years primarily based on the tube theory. This model assumes that the motion of a linear polymer chain is restricted to a tube-like region along its contour formed by surrounding chains, similar to a snake slithering through an array of obstacles. Recent tube theories can provide appropriate description of the linear rheology of monodisperse linear polymers, but is facing serious difficulties in describing the branched polymers.

Synthesized branched polymers can have various architectures, such as star, H-shaped, comb and Cayley-tree polymers. The commercial polymers, such as metallocene polyethylene resins, can even have branches on branches, i.e., hyperbranching, structures. The branching structures prevent these polymers from sliding in the melt as do the linear chains. Instead a star polymer diffuses by retracting its arms all the way to the branch point, allowing this point to move a short distance, and then stretching out the arms again. This is analogous to an octopus entangled in an array of topological constraints (e.g., a fishing net). The relaxation time of stars thus grows exponentially with the length of the arms, in radical contrast to the power law chain-length dependence of the linear polymers. Polymers with more complicated architectures are assumed to relax in a hierarchical way. The relaxation starts from the retraction of the outermost branch arms and proceeds to inner segments layer by layer till the core of the molecule. Theoretical modelling of the branched polymers needs to address several essential questions including the dynamics of the branch arm retraction, the branch point diffusion and the hierarchical relaxation, as well as the reduced entanglement effects caused by the relaxation of surrounding polymers. The fast grow in computer power and simulation techniques enables us to examine these problems in great details. In this project, we propose to perform molecular dynamics simulations to investigate the relaxation dynamics of model branched polymers at the microscopic level. Special attention will be paid to examine and, if needed, re-formulate the assumptions and analytical expressions used in the current tube theories for describing the above-mentioned dynamic processes. Based on these microscopic understanding, more coarse-grained theoretical models will be developed, which will ultimately allow prediction of dynamics and rheology of general mixtures of branched polymers with arbitrary architectures over many decades of time and length scales.

The aim of this project is to establish a solid microscopic foundation for understanding the dynamics of entangled branched polymer melts, and subsequently develop coarse-grained theoretical models to quantitatively predict their dynamic and rheological properties. Both the results and methodologies produced in this project are beneficial to the wide polymer science, polymer industry and soft matter communities, and ultimately to the UK society as a whole.

1) Polymer physics and rheology. The tube theory has been dominantly used in modelling dynamics of entangled polymers for the past forty years. Though being qualitatively successful, its quantitative prediction power is still very limited, essentially due to the lack of a solid microscopic foundation. In this project we seek to tackle this long-standing problem using the microscopic molecular dynamics simulations. The simulation results and the subsequently developed theoretical models will be highly appreciated by the large number of polymer physicists and rheologists working in this field.

2) Polymer Industry. The understanding of the relationship between polymer branching architecture and rheology can benefit the polymer industry in two ways: 1) to predict the rheology of polymer samples with known architectures and 2) to deduce the architecture of a polymer sample from its rheological data. These knowledge will also help the polymer synthesis and processing engineers in designing novel polymer materials with desired processing properties and optimizing the current process for reducing economic and environmental costs. Considering the high weight of the polymer industry in the UK economy (2.1%) and the importance of plastics in modern life, the project should benefit the whole society in the long run.

3) Soft Matter Community. The dynamic properties of many other soft matter systems are also strongly affected by the entanglement effects and the hierarchical relaxation of branched molecules. Scientists working on these systems will be interested in using our research results to explain their experimental observations, and adopting our simulation and data analysis methodologies in their own molecular modelling. The broad impact of this project will then be reflected by the enormous applications of the soft matter materials in the chemical, biological, medical, energy and engineering sectors.

4) Educational Impact. As a fundamental research project, its long-term impact also lies in the educational sector. This project will support the professional career development of the appointed PDRA, making him/her a valuable asset to the UK economy and academia. Master and 4th year MMaths students will also get good opportunities to study polymer dynamics by doing dissertation projects in our group. In addition we will disseminate polymer science knowledge to a broad range of audiences by giving lectures, seminars and workshops. All these impacts will reward the UK economy and society in the long run.