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The Complex Fluids and Theoretical Polymer Physics research group focuses on the structure and dynamics of complex fluids, with polymeric fluids being the overarching theme.

Our research ideology is to work on theoretical models of complex fluids and use extensive computer simulations to inform and verify these models. The theoretical models we are working with range from stochastic differential equations to partial differential equations to constitutive equations (tensor ODEs). The simulation techniques include Molecular Dynamics, Monte-Carlo and Brownian Dynamics, as well as field-theoretic simulations.

The Complex Fluids and Theoretical Polymer Physics group became part of Department of Mathematics and Statistics in 2007.

We collaborate with a wide range of theoretical and experimental groups around the world, including the universities of Kyoto, Michigan, ETH Zurich, Julich and others. Our research is mainly funded by the Engineering and Physical Sciences Council (EPSRC).

In the Department of Mathematics and Statistics, we have growing links with the groups of Data Assimilation and Inverse Problems and Statistical Mechanics, Probability and Stochastic Analysis. Over the last six years the group has built significant computational resources, with 500 processor cores available currently.

Research projects

Molecular dynamics and entanglements (Dr Zuowei Wang)

Most of the problems of polymer dynamics arise from the lack of clear definition of polymer entanglement. We perform large scale molecular dynamics simulations of dense polymeric systems of various topology (linear, stars, rings) and propose microscopic definition of polymer entanglements. Much of the work is then directed to investigating entanglement properties in different systems and thus informing simpler and coarser models.

Slip-spring model of entangled polymers (Dr Zuowei Wang)

A single chain stochastic model (Likhtman, 2005) represents a crucial step in hierarchical modelling, bridging the gap between multi-chain molecular dynamics simulation and the tube theory. We are working on improving the model and its relationship to the tube model.

Branched polymer rheology (Dr Zuowei Wang)

Branched polymers, such as stars, H-shaped polymers and combs, is a relatively new direction of the group. The challenge here is extremely slow dynamics due to the fact that usual reptation motion is suppressed by the branch points. We are working on new computational methods such as forward flux sampling and others to speed up MD and slip-springs simulations.

Computational and theoretical modelling of supramolecular polymer networks (Dr Zuowei Wang)

Supramolecular polymer networks are formed by the reversible cross-linking of macromolecules via transient physical interactions, such as hydrogen bonding, p-p stacking and ionic interactions. These nanostructured materials, sometimes known as self-healing materials, have a wide range of potential applications due to their unique ability to self-repair.

We are interested in the dynamic and rheological properties of these fascinating systems in relation to their topological structure formation. Our studies are performed using hybrid molecular dynamics/Monte Carlo simulations and theoretical modelling. These works are done in close collaborations with experimental groups.

Wetting processes and dynamic contact angle (Dr Alex Lukyanov)

Wetting processes and dynamic contact angle (Lukyanov, Likhtman) phenomena associated with dynamic contact angle at a moving contact line are central to various microfluidic applications, coating and ink-jet printing technologies. Many aspects of the dynamic wetting problem have been haunting researchers over the last 40 years due to various paradoxes which appear in macroscopic modelling of this problem.

Our recent studies of the moving contact-line problem via molecular dynamics simulations have shown that the dynamic contact angle effect (Lukyanov, Likhtman 2013) is essentially conditioned by the microscopic processes in a small region, several atoms wide, around the contact line, basically at nanoscale. We are interested in microscopic modelling of the processes taking place at moving contact lines to understand the origin of the dynamic wetting effects in situations involving simple and complex interfaces, e.g. interfaces laden with polymers, particles and surfactants.

Capillary effects and interfaces in simple and complex liquids (Dr Alex Lukyanov)

The modern drive towards miniaturisation and nanotechnology raises the importance of interfacial science to a new level. Due to widespread of microfluidic applications, the flows during their operation become more and more dominated by the effects of capillarity.

This presents an opportunity to control and fine-tune various micro-flows by manipulating interfacial properties via the creation of complex interfaces. On the other hand, this calls for detailed theoretical analysis of structure and dynamics of such interfaces in strongly non-equilibrium conditions. We study such dynamic interfacial processes in our group from the first microscopic principles, using large-scale molecular dynamics simulations.

Magnetoviscosity of dipolar colloidal fluids (Dr Patrick Ilg)

The viscosity of dipolar colloidal fluids (ferrofluids) can be manipulated by varying an external magnetic field. Current constitutive models suffer from the lack of knowledge about the relevant microstructure. Our simulations provide information on the field- and flow-induced structural changes and will allow us to formulate improved constitutive equations for dipolar colloidal fluids.

Field-dependent mechanical properties of ferrogels (Dr Patrick Ilg)

When magnetic particles are brought into polymer gels, their soft solid-like behaviour responds strongly to external fields. From a theoretical point of view, the coupling of the translational and rotational dynamics of the magnetic particles to the polymer matrix is largely unknown. From detailed microscopic simulations we want to extract information on how to modify the classical Brownian Dynamics of the particles when they move not through a simple liquid but through a viscoelastic environment.

Rheology of supercooled liquids (Dr Patrick Ilg)

The viscosity of liquids increases enormously when cooled down towards the glass transition without apparent change of their microstructure. By analysing the underlying potential energy landscape of a binary Lennard-Jones system, we identify cooperative rearranging regions that grow in size upon cooling.

Our simulation results help to improve and provide a microscopic basis of current theories of the dynamics and rheology of glassy systems.

Polymer brushes under shear (Dr Patrick Ilg)

Polymer brushes are very effective in lubricating surfaces. We use nonequilibrium molecular dynamics simulations in order to investigate the effect of semi-flexibility as well as different polymer architectures on the resulting coefficient of friction of the polymer-coated surface.

Complex fluid-fluid interfaces (Dr Patrick Ilg)

Fluid-fluid interfaces can be stabilised by adsorbed multi-block copolymers that self-assemble into complex microstructures. We study the influence of the microstructure on the stability and surface rheology with a multi-scale approach, combining molecular simulations and non-equilibrium thermodynamics modelling.

Conformational transition and self-assembly of charged polymers (Dr Zuowei Wang)

Charged polymers are abundant both in nature, such as DNA and proteins, and in synthesised materials. The study of charged polymers is not only inspired by the rich physical properties and so numerous applications resulted from the long-range Coulombic interactions among charged groups, but also the understanding of the functioning of biological systems.

Our researches in this direction are focused on theoretical and computational modelling of the conformational transition of diblock polyampholyte chains and the self-assembly behaviour of charged block copolymers and mixtures of oppositely charged polyelectrolytes. These studies are related to the DNA and protein association.

Colloidal dipolar fluids (Dr Zuowei Wang, Dr Patrick Ilg)

Colloidal dipolar fluids, such as ferrofluids, electrorheological (ER) and magnetorheological (MR) fluids, are composed of magnetic particles of nano- to micrometer sizes suspended in carrier liquids. Their magnetic, structural and rheological properties are reversibly tunable by the application of magnetic fields.

We study the field-induced physical properties of these fluids using computer simulations and theoretical modelling. Special attentions are paid to effectively handling the long-range dipole-dipole interactions among magnetic particles.

Atomistic simulation of nanostructured polymeric and surfactant materials (Dr Zuowei Wang)

Molecular dynamics simulations at the atomistic level can provide microscopic understanding of physical properties of soft matter materials that are generally hard to achieve in experiments. This type of simulation also constructs the basis for developing more coarse-grained computational models.

The systems we are working on include polymer melts, surfactant micelles, polymer-drug conjugates, etc. The simulation results are directly compared with experimental measurements and contribute to the development of coarse-grained models in the group.

Field-theoretic simulations for block copolymers

Monte Carlo field-theoretic simulation is a novel and very promising technique for studying the fluctuation effects in block copolymers. In opposite to the chain-based simulation methods, the field-theoretic approach allows to consider very large polymerisation indexes.

Mathematically, the technique is related to the well-known self-consisted field theory, but instead of using the mean-field approximation, it exactly describes the composition fluctuations, which are particularly important in the proximity of the order-disorder transition and in the disordered phase.

We focus on the fluctuation corrections to the mean-field predictions for the disordered-state structure factor and the order-disorder transition in a symmetric diblock-copolymer melt.


PhD Students

  • Dipesh Amin
  • Jack Kirk
  • Changqiong Wang
  • Jian Zhu
  • Chris Davies
  • Jing Cao

Former group members


We run a regular seminar series, with a mixture of internal and external speakers.

Our aim is to provide the chance to engage with the different research projects going on and to stimulate discussions and new ideas. Therefore, we want this seminar to be informal and lively, with the emphasis on explaining ideas, plans and problems.

Summer Term 2024

28 May

10:00 to 11:00 Maths 212

Speaker: Prof Yuichi Masubuchi, Nagoya University, Japan

Title: Relationship between fracture of networks and the cycle rank

Abstract: The influence of node functionality (f) on the fracture of polymer networks remains unclear. While many studies have focused on multifunctional nodes with f > 4, recent research suggests that networks with f = 3 exhibit superior fracture properties compared to those with f = 4. To clarify this discrepancy, we conducted phantom chain simulations for star-polymer networks varying f between 3 and 8. Our simulations utilized equimolar binary mixtures of star branch prepolymers with a uniform arm length. We employed a Brownian dynamics scheme to equilibrate the sols and induce gelation through end-linking reactions. We prevented the formation of odd-order loops algorithmically, owing to the binary reaction and second-order loops. We stored network structures at various conversion ratios (φc) and minimized energy to reduce computation costs induced by structural relaxation. We subjected the networks to stretching until fracture to determine stress and strain at break and work for fractures, εb, σb, and Wb. These fracture characteristics are highly dependent on φc for networks with a small f but relatively insensitive for those with a large f. Thus, the networks with small f exhibit greater fracture properties than those with large f at high φc, whereas the opposite relationship occurs at low φc. We analyzed εb, σb, and Wb concerning cycle rank ξ and broken strand fraction φbb. We found that εb, σb/φbb, and Wb/φbb monotonically decrease with increasing ξ, and the data for various f and φc superpose with each other to draw master curves. These results imply that the mechanical superiority of the networks with small f comes from their smaller ξ that gives higher εb, σb/φbb, and Wb/φbb than the networks with large f.


25 April

14:00 to 15:00 Maths 108

Speaker: Nuofei Jiang (Université Catholique de Louvain, Belgium)

Title: Potential Universal Extensional Rheology in Concentrated Polymeric Liquids

Abstract: Polymer dynamics is universal in the linear viscoelastic regime, while the recent experiments show that the nonlinear extensional rheology of polymer melts is highly sensitive to the chemical composition and thus has the non-universal feature. To understand this transition, in this work, the variation of inter-chain interaction in the coarse-grained (CG) molecular dynamics (MD) simulation systems of polymer melts is investigated in terms of the frictional coefficient, which is thought to be the critical factor in explaining the observed non-universality. The frictional coefficients in the simulation systems are quantified from the expressions we proposed very recently (Jiang, N.; van Ruymbeke, E., Macromolecules 2023, 56 (8), 2911-2929.), which are based on the analytical relationships between the frictional coefficient and the observable quantities. After the validation of the CG MD simulation with experimental data and our expressions, it is shown that those frictional coefficients can be universally related to the projection areas of the polymer coils. Moreover, this projection-friction relationship indicates a Kuhn-scale criterion of extensional viscosity, which suggests a universal extensional rheological response will be observed when the samples have the same number of Kuhn segments N_k and the same reduced density n_k defined as the ratio of the Kuhn length to the packing length. This criterion is tested on a series of new simulation systems designed to show universal nonlinear extensional rheology, as well as the existing experimental data in the literature. The results in this work provide a helpful guideline in searching for the potential universal nonlinear flow behaviors in the experimental samples.


Spring Term 2018

9 January 
Alberto Montefusco (ETH Zurich)
Coarse-graining via large-deviation theory 

22 January


Andreas Menzel (University of Düsseldorf)
Mesoscopic modelling of magnetic gels and elastomers

Autumn Term 2016

13 October 

Hisham Al-Obaidi, Pharmacy, University Reading   
Analysis of molecular interactions in polymeric solid dispersions

20 October 


Alex Lukyanov
Hydrodynamics of moving contact lines: macroscopic versus microscopic 

Summer Term 2016

22 June 

Adrian Baule, Queen Mary College, London
Mean-field approach for random close packings of
non-spherical particles

19 July 

Hongzia Guo, Institute of Chemistry, Chinese Academy of Sciences,
Beijing, China

Constructing the systematic coarse-grained model for polymers with
good transferability and representability

Spring Term 2016

2 February 

Jing Cao
Simulating Startup Shear of Entangled Polymer Melts

10 February 

Dipesh Amin

11 February 


Richard Graham, University of Nottingham
Modelling entangled polymers under flow: recent observations and analytic results

17 February 


Jack Kirk
Surface dynamics of flexible polymer melts

26 February  


Michael Rubinstein, University of North Carolina
Complexation of oppositely charged polyelectrolytes and diblock polyampholytes

2 March 


Anoop Varghese
Mesoscopic hydrodynamic simulations of simple fluids and colloids under shear flow

16 March 


Jing Cao
Microscopic picture of constraint release effect in entangled star polymer melts

23 March 


Jing Cao
Microscopic picture of constraint release effect in entangled star polymer melts - continued

13 April 


Alex Lukyanov
The mechanism of dynamic contact angle at nano-scale

21 April

Alex Lukyanov
The mechanism of dynamic contact angle at nano-scale

27 April 


Apostolos Evangelopoulos
Wetting of polymer nanodroplets