### PHD Projects in Theoretical Soft Condensed Matter and Biophysics

I can suggest a variety of possible PhD projects in the general areas of theoretical soft condensed matter and biological physics spanning the research areas described below. If you are heading for a good degree in physics or mathematics and are interested in any of these (or have ideas about related) problems then drop me a line.

Note that most positions are funded for UK students, with some possibilities for European Union students. Students from elsewhere will have to apply for funding for overseas students, either from their own country or through other EU and UK schemes.

More details on funding possibilities and the application procedure can be found here.

### Soft Matter and Complex Fluids

The physics of soft materials involves, (but is not restricted to) the study of emulsions, gels, foams, colloids, synthetic and bio-polymer melts and solutions, liquid crystals and other such systems. They are characterised by geometric structures on a mesoscopic scale several orders of magnitude bigger than the molecular scale but well below the macroscopic (human) scale. Over the last few decades, we have come to realise that by understanding this structure (which can be described using simple geometrical models with a small number of physical parameters) it is possible to come up with a set of general principles, to understand many features of their macroscopic behaviour. It turns out that many microscopic details like detailed chemical structure can simply be used to determine the specific values of the physical parameters of the coarse-grained mesoscopic models. Of course this is not the whole story, a current active area of research is the study of soft systems to find out exactly those macroscopic properties cannot be separated from the microscopic details. The separation of this mesoscopic scale from the macroscopic allows one to use the powerful techniques of statistical mechanics. The study of complex fluids is an interdisciplinary field with many fruitful interactions between physicists, chemists, and engineers and mathematicians.

### Dynamics of lipid membranes

Lipid membranes are thin sheets made up of layers of phospholipid molecules. Phospholipids (e.g. 1-palmitoyl 2-oleoyl phosphatidyl choline) are amphiphilic with the hydrocarbon tail of the molecule being hydrophobic; its polar head hydrophilic. They form bilayers in aqueous solution and mono-layers at the air-water or oil-water interface. From a statistical mechanical point of view they represent an interesting class of fluctuating two-dimensional (fluid) manifolds (sort of a higher dimensional polymer) which can be characterised by a small number of geometric quantities. They has been much experimental and theoretical study of their structure, self assembly, phase behaviour, transport and elasticity, as well as their interactions with other macromolecules. Lipid membranes are also important model systems for biological membranes, composite objects built from a large variety of lipids and proteins. Bio-membranes are also not passive, actively controlling the structures and environments of the cell suggesting that understanding them requires a dynamic and not equilibrium description. Recently there has been much interest in rafts' and multicomponent lipid membranes and the role they may play in cell signalling and function. We are interested in dynamical models of inhomogeneous lipid membranes. In particular, we are interested in the dynamics of objects embedded in lipid membranes, the coupling to the dynamics of the membrane as well as the coupling of the dynamics of the membrane to the hydrodynamics of the fluid it is embedded in.

### Polymer Physics

Polymers are long chain molecules made up of repeating units called monomers linked together by (covalent) bonds. Typically a polymer is synthesised out of a small number of repeating chemical groups which are attached end-to-end. As well as linear polymers it is possible to make branched objects, or objects with non-trivial topology. It turns out that many (physical) properties of polymers and polymer solutions can be understood without any knowledge of the chemical structure of the polymers from which they are made. In fact this is what attracted a number of physicists to the study of polymeric materials in the first place. Rather it turns out that it is the geometry and topology of the polymer chains that determine many of these properties. Polymeric materials are characterised by the large role that Entropy (Thermal Fluctuations) play in their physical properties. Typically the elasticity of polymeric solids has the opposite temperature behaviour as that of simple crystalline solids because long polymers have a random-coil like structure at finite temperatures. The dynamics of polymeric fluids is complicated and often displaying what is called Non-Newtonian behaviour with complicated flow behaviour as a function of deformation. In comparison water (the archetypal Newtonian fluid) has a much simpler flow behaviour. We are interested in predicting the macroscopic properties of polymer solutions from simplified mesoscopic' models of the polymers which are defined using only geometrical and topological quantities. Recently there has been much interest in semiflexible polymers who in addition to the entropic contribution (leading to the random coil conformations of flexible polymers) have an enthalpic bending energy contribution to their free energy. As well as having very different static and dynamic behaviour from classical flexible polymers, they are important as good models for the behaviour of a number of biological polymers. We are interested in developing models of the dynamics of semiflexible polymer solutions to explain both scattering and rheological experiments.

### Charged Polymers: Polyelectrolytes

Polyelectrolytes are macromolecules with ionisable groups which dissociate into a charged polymer and oppositely charged counter-ions in polar solvents. Most bio-polymers are charged polymers ( DNA, RNA are negatively charged and proteins have both positive and negative charges). There are also many examples of synthetic charged polymers (e.g. Polystyrene-sulphonate) which have many industrial applications because they are water soluble. Charged polymer systems have a rich spectrum of physical behaviour with dramatically different properties from neutral polymers. This is due to the long range nature of the Coulomb interactions between monomers. In addition they are always associated with small charged mobile counter-ions which dissociate from their backbones and interact strongly with the polymer chains. The physics of the counter-ions plays a central role in determining the properties of polyelectrolyte solutions. Charged polymer systems cannot be understood without understanding their counter-ions. We study various aspects of charged polymer systems particularly the role of counter-ion fluctuations in the attractions between highly charged macromolecules.

### Microrheology

Soft materials are often viscoelastic meaning that their response to deformation has aspects that are like solids (elastic) and liquids (viscous). Conventional rheology measures this viscoelasticity by studying the response of the material to a macroscopic deformation requiring large (macroscopic) samples. If you have a limited amount of your soft material or wish to look at the short time behaviour, it is difficult to perform such experiments. The new experimental technique of microrheology looks at the (thermal) motion of small particles embedded in a material and tries to extract the bulk rheological properties. Only small amounts of material are need and high frequency (short time) behaviour can be easily probed. We try to understand the relation between the microscopic rheological behaviour and the bulk rheology.

### Biological Physics

The sub-cellular world has many components in common with soft condensed matter systems (polymers, amphiphilic molecules, colloids, and liquid crystals). But (and this is what makes it so fascinating) it has novel properties which are not present in traditional complex fluids. These new features include a number of specific interacting elements present that are crucial for biological function. The addition of these elements which can be both active and passive, lead to a highly non-equilibrium system with a rich spectrum of behaviours. A new generation of experiments using physical probes are giving us an unprecedented view of this non-equilibrium system at work. The search is on for an as yet undiscovered hierarchy of organisational principles which will enable us to understand these exceedingly complex systems!

### The Eukariotic Cell Cytoskeleton

The cytoskeleton provides both the supporting structure of the cell and the vehicle for internal transport processes. It is a network of long protein filaments, mainly microtubules, actin filaments and intermediate filaments, coupled by smaller proteins, such as molecular motors and cross-linkers. Motor proteins are molecular machines that convert chemical energy derived from the hydrolysis of ATP (Adenosine TriPhosphate) into mechanical work, generating forces and motion of the filaments relative to each other in this{\em active} complex fluid. We study the mechanics and organisation of the cell cytoskeleton viewing it as a solution of filaments interacting with active cross-links.

### Bio-polymers

Many biological molecules are polymers (long chain molecules made up of a variety of repeating units called monomers). Examples are DNA ( monomers are nucleotides, adenine and thymine, guanine and cytosine[A-T,C-G]), RNA ( monomers are nucleotides adenine, guanine, cytosine, and uracil [AGCU]), proteins ( whose monomers are amino-acids), filamentous protein aggregates (e.g. F-Actin) whose monomers are globular proteins (e.g. G-Actin). We study the response of single bio-polymers to mechanical force.

### Molecular Machines

Molecular motors are machines that convert chemical energy to mechanical work. Examples are the cytoplasmic motors that move along biological (protein) tracks in the cell by converting the energy released upon ATP hydrolysis into mechanical work. These complex machines act as the inspiration for the design of macromolecular devices with the ability to sort, sense and transport material in chip-sized laboratories. We are interested in models for the design of both biological and synthetic molecular machines driven by chemical reactions.

### Single Molecule Mechanics

New experimental developments have meant that it is now possible to manipulate man bio-polymers one molecule at a time. This can lead to important insights about how they function in-vivo. The conformational dynamics of single molecules can be studied experimentally using atomic force microscopy, fluorescence probes and a number of other techniques. We try to model the statistical mechanics and dynamics of single molecules of proteins and DNA using coarse-grained models.