  According to the universality hypothesis, the phase behavior of different
block copolymer melt models having fixed composition depends solely on two
parameters: the invariant chain length $\bar{N}$ and the effective interaction
parameter $\chi N$. If models behave universally, they can be compared to each
other and can predict experiment quantitatively. Here, we present a simple way
to achieve this universality for coarse-grained models. Our method relies on
the properties of the monomer interaction potential energy $z$ distribution. In
particular, models having near-symmetric $z$-distributions exhibit universal
phase behavior using the standard linear definition of the Flory-Huggins
parameter $\chi\propto\alpha$, where $\alpha =
\epsilon_{AB}-(\epsilon_{AA}+\epsilon_{BB})/2$, and $\epsilon_{xy}$ is the
interaction energy between monomers of type $x$ and $y$. Previously,
universality had been achieved using a nonlinear $\chi(\alpha)$ function which
is difficult to obtain and interpret physically. The main parameter controlling
the symmetry of the $z$-distribution is the monomer density $\rho$. Above
certain $\rho$, models have symmetric $z$-distributions, and their
order-disorder transition points follow the universal curve predicted by
Fredrickson-Helfand theory in the experimentally relevant $\bar{N} > 10^2$
range. On the other hand, low-$\rho$ models exhibit skewed $z$-distributions,
and the simple $\chi\propto\alpha$ formula is no longer universally applicable
to them. Our results can be used for correct block copolymer model building
leading to a simple and direct comparison of simulations to experiments, which
will facilitate the screening of new block copolymer morphologies and support
materials design.
