Abstract: The beta-decay half-lives of 110 neutron-rich isotopes of the elements from 37 Rb to 50 Sn were measured at the Radioactive Isotope Beam Factory. The 40 new half-lives follow robust systematics and highlight the persistence of shell effects. The new data have direct implications for r-process calculations and reinforce the notion that the second (A approximate to 130) and the rare-earth-element (A approximate to 160) abundance peaks may result from the freeze-out of an (n, gamma) reversible arrow (gamma, n) equilibrium. In such an equilibrium, the new half-lives are important factors determining the abundance of rare-earth elements, and allow for a more reliable discussion of the r process universality. It is anticipated that universality may not extend to the elements Sn, Sb, I, and Cs, making the detection of these elements in metal-poor stars of the utmost importance to determine the exact conditions of individual r-process events.