Multi-scale modelling of branched polymer melts

Lead Research Organisation: University of Reading
Department Name: Mathematics and Statistics


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.

Planned Impact

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.
Description In this project, multiscale computer simulation and theoretical modelling studies are carried out for establishing a microscopic understanding of the dynamics of entangled branched polymers and consequently developing coarse-grained theoretical models for describing their dynamic and rheological properties over many decades of time and length scales. The research outcomes have been published in high-profile scientific journals and presented in some of the most influential international/national conferences in the research field. Some of the key findings are listed below.

1) In the J. Chem. Phys. [143 (2015) 204105] paper, we investigated the first passage time problem of the Rouse chain model, which can be directly mapped to the arm retraction dynamics in entangled branched polymers. We demonstrated by direct and forward flux sampling simulations that this problem should be treated as a multi-dimensional, instead of the generally assumed one-dimensional, problem. A new theory was then developed to solve this problem analytically, which together with our simulation results indicated that some widely used theoretical models can overestimate the arm retraction time by a factor of 10 or more. This finding should make essential contribution for developing quantitative theories of dynamics and rheology of entangled branched polymers.

2) In the Macromolecules [49 (2016) 5677] paper, we combined molecular dynamics and slip-spring model simulations to study constraint release effects in entangled star polymer melts. Our analysis of persistent close contacts between neighbouring polymers provided clear evidence to support the binary picture of entanglements that had been subject to long-term debate. The simulation results revealed a new arm relaxation mechanism in which the broad constraint release spectrum, together with the excluded volume of entanglements and reflecting boundaries at branch points, lead to accelerated release of entanglements from the arm free ends. These findings call for examination of the microscopic foundation of conventional tube-based models and development of quantitative theories with consideration of more microscopic details.

3) In the ACS Macro Lett. [4 (2015) 1376] paper, molecular dynamics simulations were performed for investigating the origin of the stress overshoot of entangled linear polymer melts in startup shear. At low shear rates the stress overshoot was found to arise from chain segment orientation instead of chain stretching. The stress-optical law is thus validated consistently in both equilibrium and shear simulations, as noted experimentally. This study also uncovered flaws in some previously reported simulation works on the same topic.

4) Highly efficient simulation techniques and software packages are developed for studying the linear and non-linear dynamic and rheological behaviour of entangled polymer melts. These include: a) a combined slip-spring model and forward flux sampling method for studying the dynamics and rheology of highly entangled branched polymers which are generally inaccessible to direct simulation methods but highly desired for the development of quantitative theories on entangled branched polymers [J. Chem. Phys., 147 (2017) 044907]; b) a GPU based molecular dynamics simulation package that can study both the equilibrium and extensional flow behaviour of various polymer systems, including entangled polymers and associative polymers [Macromolecules, 49 (2016) 7510].

5) In the Polymers [11 (2019) 496] paper, we performed single-chain slip-spring model simulations of entangled star polymers in the absence of constrain release. The simulation results examined and verified several assumptions made in the tube-based theoretical models. The entanglement molecular weights extracted from static and dynamic properties of the star polymers show good agreement with each other. We were also able to determine the tube survival function of star arms through the mean first-passage time spectrum of the tube segments which demonstrates reasonably good agreement with experimental data. These findings provide very useful information for developing quantitative theories for describing and predicting the rheological and dynamic behavior of entangled branched polymers.
Exploitation Route Our research group at the University of Reading will continue the computer simulation and theoretical modelling studies of entangled branched polymers. Special attentions will be paid to the nonlinear dynamic and rheological behaviour of these polymer systems under both shear and extensional flows, which are much less understood in comparison with the equilibrium or linear behaviour of these systems. Researches in this direction are of both fundamental and practical importance, because they are closely related to the industrial processing of such polymeric materials. The studies will be significantly facilitated by the highly efficient GPU based molecular dynamics simulation package developed partly under the support of this EPSRC grant.

The research outcomes of this project are disseminated by publications in high profile scientific journals and presentations in international/national conferences and seminars. Researchers from both academic and industrial backgrounds can make use of our research findings and the proposed simulation and data analysis techniques to promote their own research works in the related fields, such as polymer dynamics, rheology and engineering.
Sectors Agriculture, Food and Drink,Chemicals,Education,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology

Description The research outputs of this project have been presented in the Reading Scholars Programme (2018) and also in a Six-Form Personal Development Day Event in a local high school (2019) for inspiring the interests of local students in Mathematical and Material Sciences.
First Year Of Impact 2018
Sector Agriculture, Food and Drink,Chemicals,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology
Impact Types Societal

Description EPSRC DTP Studentship Competition 2017 (University of Reading)
Amount £60,490 (GBP)
Funding ID GS17-010 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 09/2017 
End 08/2020
Title A combined slip-spring model and forward-flux sampling method for studying dynamics and rheology of entangled branched polymers 
Description The study of dynamics and rheology of well-entangled branched polymers remains a challenge for computer simulations due to the exponentially growing terminal relaxation times of these polymers with increasing molecular weights. The combined coarse-grained slip-spring model and forward flux sampling method is an efficient computer simulation algorithm developed for studying the dynamic and rheological properties of entangled star polymers. It is one of the very first applications of transition path sampling methods in the study of entangled polymers. This method can be applied to predict the entire relaxation spectrum of branch arms and the experimentally measurable relaxation correlation functions of highly entangled star polymers by reaching their terminal relaxation times which are far beyond the accessibility of standard fine- or coarse-grained simulation models. 
Type Of Material Computer model/algorithm 
Year Produced 2017 
Provided To Others? Yes  
Impact As reported in the 2017 Journal of Chemical Physics paper (147, 044907) by Zhu, Likhtman and Wang (members supported by this award), the combined slip-spring model and forward flux sampling method has been applied to study the terminal relaxation behavior of entangled star polymers with arm lengths up to 16 entanglements, which are not accessible to existing brute force simulations in the absence constraint release. It can also predict the entire relaxation spectrum of star arms as well as the experimentally measurable relaxation correlation functions, such as the dielectric or arm end-to-end vector relaxation functions and the stress relaxation functions. Such correlation functions are generally not discussed in other forward flux sampling studies. Therefore this simulation method provides an efficient tool for studying the dynamics of highly entangled branched polymers which are generally inaccessible to direct simulation methods but highly desired for the development of quantitative theories on entangled branched polymers. 
Description Dynamics in bidispersed entangled polymer melts 
Organisation Chinese Academy of Sciences
Department Institute of Chemistry
Country China 
Sector Academic/University 
PI Contribution My research team will be working on the coarse-grained computer simulations and theoretical modelling of dynamics of entangled polymer melts.
Collaborator Contribution The partner of this project provides the research funding to cover the computational costs and hosting my team members to carry out research work in their institute. My collaborations will also be working on atomistic simulations of entangled polymer melts.
Impact A joint research paper on computer simulation studies of the dynamics of bidisperse entangled linear polymer melts is under preparation. This is a multi-disciplinary research project, which involves polymer physics and chemistry, rheology and computational physics.
Start Year 2014
Description Reading Scholars Programme 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact A cohort of 30-40 A-level students, who are interested in University studies of mathematics and science subjects, visited the University of Reading as part of the Reading Scholars programme. Dr. Zuowei Wang gave a presentation to them on how mathematical knowledge can be used to solve real-world problems in related to polymer and soft matter materials, which surprised the students as a complete new point of view that they didn't hear or think about before and inspired their interests in the study and research works along these directions.
Year(s) Of Engagement Activity 2018