# Spin dynamics and optimisation of dynamic nuclear polarisation at cryogenic temperatures

Lead Research Organisation:
University of Nottingham

Department Name: Sch of Physics & Astronomy

### Abstract

Nuclear Magnetic Resonance (NMR) is a technique that is based on the measurement of a weak sample magnetisation that arises from the interaction of a strong external magnetic field with various types of nuclei in the sample which carry magnetic moments. The interaction force generated by the external magnetic field on the magnetic moments of the nuclei tends to align the nuclei in an orientation parallel to the external field direction. However, thermal motion counteracts this alignment and since the interaction force between external field and magnetic moments is only very weak there is only a small difference between the population of nuclei that have a parallel alignment and the population of spins that are aligned in the opposite (or anti-parallel) direction. This is the reason why NMR techniques are usually considered to be not highly sensitive.The thermal motion can be reduced by cooling the sample to very low temperatures using liquid helium. As a consequence the sample magnetisation increases. Unpaired electrons, which possess a magnetic moment and which interact about 3 orders of magnitude stronger than protons with the external magnetic field are at a temperature of 1K and a modest external magnetic field of 3.5T almost fully aligned with the direction of the external field. In NMR terminology this means that the electrons are 100% polarised. Unpaired electrons couple to magnetically active nuclear spins and it is possible to use this interaction to transfer the electronic polarisation onto the magnetically active nuclei. In principle, the electrons are used to align the nuclei in one direction. This process is called dynamic nuclear polarisation. The dynamics of the process can be derived using quantum mechanics. However, the mathematical formulation of quantum mechanics means that the problem becomes difficult to be solved in case a system of many coupled nuclei is assumed. This proposal investigates mathematical strategies to obtain the dynamical information for systems of many coupled spins. Furthermore, the system parameters are measured that are needed to make the model calculations meaningful. In a second step strategies are investigated in theory and afterwards in experimental implementations to optimise the transfer of polarisation between the electron system and the nuclear system.The key objective of this project is to gain insight into the dynamics of dynamics nuclear polarisation and then use this information to generate higher levels of nuclear polarisation on an even faster time scale. The outcome of the project will benefit numerous applications of nuclear magnetic resonance spectroscopy and magnetic resonance imaging which are limited by the low sensitivity. Using efficient DNP strategies is will be possible to generate high polarisation for studies of molecular dynamics or also for applications of medical diagnostics by imaging the distribution and metabolic conversion of pre-polarised molecules.

### Planned Impact

NMR (Nuclear Magnetic Resonance) spectroscopy, microscopy and imaging techniques play a major role in numerous fields of science ranging from physics, chemistry, material sciences, biology to medicine. Development of multidimensional techniques in NMR allows obtaining structural and dynamic information with atomic resolution. Though the method is non-invasive its intrinsic low sensitivity has limited NMR in a number of applications, for instance in nanoscience, in the detection of fast dynamics on the molecular level or in acquiring signal from molecules in low concentration both in vitro and in vivo or from molecules bound to surfaces. Dynamic nuclear polarisation has the potential to overcome the sensitivity issue and to help open up new applications of NMR spectroscopy and imaging. The research of this project focuses at the investigation of the spin dynamics during DNP. This is important since a detailed understanding is necessary for further optimisation of the DNP strategy and for the design of novel polarisation transfer protocols that lead to higher nuclear polarisation and faster build up rates. I envisage that the proposed research will have a three-fold impact. First, it will contribute directly to the generation of knowledge about the spin physics involved in DNP and will help in understanding the complex processes on the quantum mechanical level. As a result optimised experimental protocols will provide improved DNP. Second, the new experimental protocols developed in the project will be of direct relevance to many studies currently been carried out by other academic group worldwide. New ideas and techniques that can advance the research field of DNP NMR will assist in making this hyperpolarisation technique applicable to a wider set of experimental conditions and will contribute to establish robust protocols for its routine use. Third, there will be potential impact on the commercial sector since several companies are already involved in the production of DNP hardware (Bruker, Oxford Instrument, GE HealthCare, JEOL) or have expressed an interest in starting their own research and development program (Varian-Agilent). Subsequently there will be further impact in many areas of science as a consequence of more efficient DNP strategies. Some examples are provided in the more detailed 'pathways to impact' statement in the attachments.

### Publications

Karabanov A
(2011)

*On the accuracy of the state space restriction approximation for spin dynamics simulations.*in The Journal of chemical physics
Karabanov A
(2015)

*Dynamic Nuclear Polarization as Kinetically Constrained Diffusion.*in Physical review letters
Karabanov A
(2012)

*Quantum Mechanical Simulation of Cross Effect DNP Using Krylov-Bogolyubov Averaging*in Applied Magnetic Resonance
Karabanov A
(2012)

*Quantum mechanical simulation of solid effect dynamic nuclear polarisation using Krylov-Bogolyubov time averaging and a restricted state-space.*in Physical chemistry chemical physics : PCCP
Karabanov A
(2014)

*Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator*in Molecular Physics
Karabanov A
(2012)

*Erratum to: Quantum Mechanical Simulation of Cross Effect DNP Using Krylov-Bogolyubov Averaging*in Applied Magnetic Resonance
Kwiatkowski G
(2014)

*The Role of the Interaction Frame in the Theoretical Description of Solid Effect Dynamic Nuclear Polarization*in Israel Journal of ChemistryDescription | We have developed novel simulation techniques fro large coupled spin networks. This makes it possible to investigate the dynamics of polarisation buildup in solid state samples during DNP. Such kind of simulation are important since it will enable use to optimise thje DNP process. We have also build a double tuned cavity for ENDOR experiments and using optimal control in DNP. |

Exploitation Route | Not yet used by others. We will try to take this forward in another grant application. Update: we have successfullly applied for another project funded by EPSRC. For this project we have joined forces with two colleagues from theoretical physics. This new project builds on findings of the previous project for which this entry is generated. |

Sectors | Chemicals |

Description | Not yet. We have developed novel simulation techniques but they have not been used yet by other groups. |

First Year Of Impact | 2013 |