  Dynamic density functionals (DDFs) are popular tools for studying the
dynamical evolution of inhomogeneous polymer systems. Here, we present a
systematic evaluation of a set of diffusive DDF theories by comparing their
predictions with data from particle-based Brownian dynamics (BD) simulations
for two selected problems: Interface broadening in compressible A/B homopolymer
blends after a sudden change of the incompatibility parameter, and microphase
separation in compressible A:B diblock copolymer melts. Specifically, we
examine (i) a local dynamics model, where monomers are taken to move
independently from each other, (ii) a nonlocal "chain dynamics" model, where
monomers move jointly with correlation matrix given by the local chain
correlator, and (iii,iv) two popular approximations to (ii), namely (iii) the
Debye dynamics model, where the chain correlator is approximated by its value
in a homogeneous system, and (iv) the computationally efficient "external
potential dynamics" (EPD) model. With the exception of EPD, the value of the
compressibility parameter has little influence on the results. In the interface
broadening problem, the chain dynamics model reproduces the BD data best.
However, the closely related EPD model produces large spurious artefacts. These
artefacts disappear when the blend system becomes incompressible. In the
microphase separation problem, the predictions of the nonlocal models (ii-iv)
agree with each other and significantly overestimate the ordering time, whereas
the local model (i) underestimates it. We attribute this to the multiscale
character of the ordering process, which involves both local and global chain
rearrangements. To account for this, we propose a mixed local/nonlocal DDF
scheme which quantitatively reproduces all BD simulation data considered here.
