  The self-consistent field theory is a popular and highly successful
theoretical framework for studying equilibrium (co)polymer systems at the
mesoscopic level. Dynamic density functionals allow one to use this framework
for studying dynamical processes in the diffusive, non-inertial regime. The
central quantity in these approaches is the mobility function, which describes
the effect of chain connectivity on the nonlocal response of monomers to
thermodynamic driving fields. In a recent study [Mantha et al, Macromolecules
53, 3409 (2020)], we have developed a method to systematically construct
mobility functions from reference fine-grained simulations. Here we focus on
melts of linear chains in the Rouse regime and show how the mobility functions
can be calculated semi-analytically for multiblock copolymers with arbitrary
sequences without resorting to simulations. In this context, an accurate
approximate expression for the single-chain dynamic structure factor is
derived. Several limiting regimes are discussed. Then we apply the resulting
density functional theory to study ordering processes in a two-length scale
block copolymer system after instantaneous quenches into the ordered phase.
Different dynamical regimes in the ordering process are identified: At early
times, the ordering on short scales dominates; at late times, the ordering on
larger scales takes over. For large quench depths, the system does not
necessarily relax into the true equilibrium state. Our density functional
approach could be used for the computer-assisted design of quenching protocols
in order to create novel nonequilibrium materials.
