  The Cahn--Hilliard equation is one of the most common models to describe
phase separation processes of a mixture of two materials. For a better
description of short-range interactions between the material and the boundary,
various dynamic boundary conditions for the Cahn--Hilliard equation have been
proposed and investigated in recent times. Of particular interests are the
model by Goldstein, Miranville and Schimperna (Physica D, 2011) and the model
by Liu and Wu (Arch.~Ration.~Mech.~Anal., 2019). Both of these models satisfy
similar physical properties but differ greatly in their mass conservation
behaviour. In this paper we introduce a new model which interpolates between
these previous models, and investigate analytical properties such as the
existence of unique solutions and convergence to the previous models mentioned
above in both the weak and the strong sense. For the strong convergences we
also establish rates in terms of the interpolation parameter, which are
supported by numerical simulations obtained from a fully discrete,
unconditionally stable and convergent finite element scheme for the new
interpolation model.
