Mathematical analysis of nanostructured electrochemical systems for lithium batteries and solar cells

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute


As the pressures of climate change becomes larger there is great interest in making highly efficient methods for generating and storing electrical energy. There is enormous interest in making batteries that exploit various lithium-based materials. These devices contain a solid anode and a solid cathode immersed in either a polymer, or solvent based electrolyte. Efficient batteries require that the thickness of both the cathode and anode materials are small in order both to reduce electrical resistance and to allow lithium to rapidly insert and de-insert itself from the solid electrode materials (by a process called intercalating). Furthermore they require that the surface area of the interface between the electrolyte and the anode (and cathode) should be made as large as possible in order to give sufficient lithium intercalation to allow practical levels of charging and discharging. As a result of these requirements batteries are currently designed with a nanostructured anode (and cathode) made either in a organised manner or by pressing grains together. Understanding how such nanostructures should be optimised in order to maximise energy efficiency is a major challenge. This is further complicated by the fact that the solid materials expand significantly (up to three times) when lithium is intercalated during charge and discharge of the battery creating both mechanical deformations and changes in the electrochemical behaviour of the surfaces. In order for such designs to be understood, and to be optimised, requires mathematical models to be developed and analysed that account for the critical properties of the nanostructure, the intercalation processes and the electrical properties of the materials. To replace existing high-efficiency high-cost silicon based solar cells there is significant interest in developing inexpensive polymer-based, and dye-sensitised, solar cells.Design of solar cells may seem unconnected from batteries but there is considerable similarity in the physical processes, mathematical models and geometry of the nanostructure of both these devices which provide the opportunity for a concerted theoretical program of research with significant technology transfer. Both types of solar cell that we consider here consist of two materials with different electrochemical properties separated by an interface (in the case of a dye-sensitised solar cell this interface is coated with a photo-absorbing dye monolayer). Efficient solar absorbtion requires that the interface between the two main materials is as large as possible while maintaining good electrical conduction. Nanostrucutred materials are being explored in order to meet these requirements. In order to optimise solar cell design models are required that account for solar absorbtion, the complex geometry of the nanostructure and charge transportation in the materials and across the interface.The purpose of this proposal is to develop novel mathematical techniques and models motivated by and closely aligned to practical developments in the complex nanostructure of these electrochemical systems. By analysing such models the most important mechanisms and features of the devices in determining their efficiency will be explored and identified.

Planned Impact

(SOCIETY) Novel electrical energy generation and storage devices provides the UK and world communities with technologies for reducing dependency on non-sustainable methods of energy production. Increasing the efficiency of such devices extends the possible range of applications in which they can be practically exploited. Hence the outcomes form this proposal will indirectly impact on the methods available for policy makers to reduce the UK's energy dependency. (ECONOMIC) In the medium term the ideas generated and disseminated through this proposal should help industry to develop practical efficient designs for batteries and solar cells that will facilitate their commercialisation. The involvement of two companies (Nexeon Ltd. and TIAX LLC) directly in this research will ensure that the research ideas transfer as rapidly as possible to industry. These connections ensure that the ideas will both foster global economic performance and that of the UK. (KNOWLEDGE) This research will generate new methods, new models and new problems for applied mathematicians to use and study. The understanding developed through the proposal will benefit chemists, engineers, material scientist and physicists working on the fundamental science and device development of lithium-ion batteries and dye-sensitised and polymer solar cells. This benefit is not solely restricted to researchers in the UK but will reach the international community both directly, by the involvement of Australian researchers, through dissemination at international conferences and in quality journals articles covering a range of disciplines. (PEOPLE) The proposed program of research will train two PDRAs in research methods across a wide range of disciplines. As such their skills are highly marketable and furthermore, since they will be training in the area of renewable energy, we expect them to contribute significantly, in the future, to the rapidly growing renewables industry.


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Description The grant concerned solar cells and lithium ion batteries. On the solar cell side we have developed a model describing the production of thin films of perovskite, an exciting new material for use in solar cells. The model predicts the quality of the coating as a function of the experimental parameters, and can therefore be used to tune the manufacturing process. On the lithium ion battery side we have developed models describing the swelling of micro-structured battery electrodes as lithium ions are inserted (i.e. as the battery is charged or discharged). We have used these models to predict failure criteria for constrained electrodes. We have averaged these microscale models to develop a whole-battery model capable of predicting the stress and deformation of a battery as well as its electrical properties. Such a model will be useful for predicting (and improving) battery life.
Exploitation Route The whole-battery models might be used to improve battery design, to either increase the power/energy density or to maximise battery life. The microscopic models might be relevant to the design of electrodes using new materials such as silicon, which deform much more under lithiation than traditional electrode materials.
Sectors Energy

Description The model for the manufacture of perovskite films has been an aid to Prof Snaith's group in their manufacture of perovskite solar cells. Through Prof Snaith's work the quality of these cells has increased dramatically, and they are causing much excitement in the solar cell world. They are still in the research and development stage, but in the future there is likely to be a considerable economic impact to the UK. The battery work is also likely to lead to improved battery design, and therefore economic impact, though it is at an earlier stage. It has led directly to three ongoing company sponsored student projects which are part of the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling (EP/L015803/1). It also led to further funding through a Faraday Institution Fast Start Project, which will accelerate the industrial impact of the work.
Sector Energy
Impact Types Economic

Description Faraday Institition Fast Start Programme
Amount £8,999,323 (GBP)
Funding ID FIRG003 
Organisation Department for Business, Energy & Industrial Strategy 
Sector Public
Country United Kingdom
Start 03/2018 
End 02/2021