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.
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