  With the recent advent of multi-messenger gravitational-wave astronomy and in
anticipation of more sensitive, next-generation gravitational-wave detectors,
we investigate the dynamics, gravitational-wave emission, and nucleosynthetic
yields of numerous eccentric binary neutron-star mergers having different
equations of state. For each equation of state we vary the orbital properties
around the threshold of immediate merger, as well as the binary mass ratio. In
addition to a study of the gravitational-wave emission including $f$-mode
oscillations before and after merger, we couple the dynamical ejecta output
from the simulations to the nuclear-reaction network code \texttt{SkyNet} to
compute nucleosynthetic yields and compare to the corresponding results in the
case of a quasi-circular merger. We find that the amount and velocity of
dynamically ejected material is always much larger than in the quasi-circular
case, reaching maximal values of $M_{\rm ej, max} \sim 0.1 \, M_{\odot}$ and
$v_{\rm max}/c \sim 0.75$. At the same time, the properties of this material
are rather insensitive to the details of the orbit, such as pericenter distance
or post-encounter apoastron distance. Furthermore, while the composition of the
ejected matter depends on the orbital parameters and on the equation of state,
the relative nucleosynthetic yields do not, thus indicating that kilonova
signatures could provide information on the orbital properties of dynamically
captured neutron-star binaries.
