  Finite size effects come into play during the late stages of neutron star
binary inspiral, with the tidal deformability of the supranuclear density
matter leaving an imprint on the gravitational-wave signal. As demonstrated in
the case of GW170817, this leads to a constraint on the neutron star radius
(and hence the equation of state). A deeper understanding of the tidal response
requires an analysis of both the state and composition of matter. While these
aspects may not have dramatic impact, they could lead to systematic effects
that need to be kept in mind as the observational data become more precise. As
a step in this direction we explore the role of the composition of matter,
which is likely to remain "frozen" during the late stages of binary inspiral.
We provide the first in-depth analysis of the problem, including estimates of
how composition impacts on the effective tidal deformability. The results
provide improved insight into how aspects of physics that tend to be "ignored"
impact on binary neutron star gravitational-wave signals.
