The Mullins-Sekerka flow describes the motion of the interface between two material phases, where the normal velocity at each point of the interface is a nonlocal quantity of the mean curvature. It appears as the sharp interface limit of the Cahn-Hilliard equation which models the phase transition phenomena, and inherits a gradient flow structure. In this talk, I am going to describe the asymptotic behavior of the Mullins-Sekerka flow around the equilibrium in the 2d full space setting. By exploring the gradient flow structure and the intrinsic convexity properties of the energy, we obtain a refined convergence rate of the energy and energy dissipation. This is based on joint work with Maria Westdickenberg and Michael Westdickenberg.