Modelling hydrogels and fractal materials

Summary

There is growing interest in the importance class of materials known as hydrogels, which are formed by the aggregation of small building blocks until they gel (or percolate) across the sample. This imbues the sample with rigidity, but also leaves pores which can be useful for e.g. drug delivery, diffusion of metabolites/nutrient for tissue engineering applications, and so on. Biopolymer-based hydrogels, such as those built from proteins which are a subject of experimental research in the School of Physics, are particularly appealing for healthcare applications due to their high biocompatibility.

The mechanical properties of hydrogels are often crucial to their function. For instance, materials for wound healing must have a minimum strength, and substrates for tissue engineering can alter the cell types that derive from embedded stem cells. However, understanding and predicting the mechanical (and time-dependent mechanical, or viscoelastic) properties of hydrogels is challenging because of the way they form. Not only are they disordered, but they are typically fractal up to a characteristic size, both of which reduce the range of modelling tools that can be brought to this important class of material.

This PhD project will be about developing mathematical and/or computational models to predict the viscoelastic response of hydrogels and/or general fractal materials, using the non-invasive characterisation to understand trends and make predictions for future materials and applications. The style of project will depend on the applicant's abilities and interests, but may take the form of (a) Developing molecular dynamics code, or similar, to simulate the formation of fractal structure with hydrogels, and use the same code to predict the resulting gel's viscoelasticity, along with other important metrics such as porosity. This mainly computational project will likely include contact with the nearby protein hydrogel experimental group in Physics. Alternatively, (b) Develop a range of schematic fractal systems in an attempt to fully characterise and elucidate the relationship between fractality and viscoelasticity. Mathematical and/or computer tools will be used to predict the viscoelastic response and explain the observed trends. This more mathematical project will apply to hydrogels, but also fractal-cut materials such as kirigami.

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

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