  Gravitational waves from neutron star-black hole (NSBH) mergers that undergo
tidal disruption provide a potential avenue to study the equation of state of
neutron stars and hence the behaviour of matter at its most extreme densities.
We present a phenomenological model for the gravitational-wave signature of
tidal disruption, which allows us to measure the disruption time. We carry out
a study with mock data, assuming an optimistically nearby NSBH event with
parameters optimised for measuring the tidal disruption. We show that a
two-detector network of 40 km Cosmic Explorer instruments can measure the time
of disruption with a precision of 0.5 ms, which corresponds to a constraint on
the neutron star radius of 0.7 km (90\% credibility). This radius constraint is
wider than the constraint obtained by measuring the tidal deformability of the
neutron star of the same system during the inspiral. Moreover, the neutron star
radius is likely to be more tightly constrained using binary neutron star
mergers. While NSBH mergers are important for the information they provide
about stellar and binary astrophysics, they are unlikely to provide insights
into nuclear physics beyond what we will already know from binary neutron star
mergers.
