  After initial proof-of-principle demonstrations, optically pumped
nitrogen-vacancy (NV) centres in diamond have been proposed as a non-invasive
platform to achieve hyperpolarisation of nuclear spins in molecular samples
over macroscopic volumes and enhance the sensitivity in nuclear magnetic
resonance (NMR) experiments. In this work, we model the process of polarisation
of external samples by NV centres and theoretically evaluate their performance
in a range of scenarios. We find that average nuclear spin polarisations
exceeding 10% can in principle be generated over macroscopic sample volumes
($\gtrsim\mu$L) with a careful engineering of the system's geometry to maximise
the diamond-sample contact area. The fabrication requirements and other
practical challenges are discussed. We then explore the possibility of
exploiting local polarisation enhancements in nano/micro-NMR experiments based
on NV centres. For micro-NMR, we find that modest signal enhancements over
thermal polarisation (by 1-2 orders of magnitude) can in essence be achieved
with existing technology, with larger enhancements achievable via
micro-structuring of the sample/substrate interface. However, there is
generally no benefit for nano-NMR where the detection of statistical
polarisation provides the largest signal-to-noise ratio. This work will guide
future experimental efforts to integrate NV-based hyperpolarisation to NMR
systems.
