  In view of recent intense experimental and theoretical interests in the
biophysics of liquid-liquid phase separation (LLPS) of intrinsically disordered
proteins (IDPs), heteropolymer models with chain molecules configured as
self-avoiding walks on the simple cubic lattice are constructed to study how
phase behaviors depend on the sequence of monomers along the chains. To address
pertinent general principles, we focus primarily on two fully charged
50-monomer sequences with significantly different charge patterns. Each monomer
in our models occupies a single lattice site and all monomers interact via a
screened pairwise Coulomb potential. Phase diagrams are obtained by extensive
Monte Carlo sampling performed at multiple temperatures on ensembles of 300
chains in boxes of sizes ranging from $52\times 52\times 52$ to $246\times
246\times 246$ to simulate a large number of different systems with the overall
polymer volume fraction $\phi$ in each system varying from $0.001$ to $0.1$.
Phase separation in the model systems is characterized by the emergence of a
large cluster connected by inter-monomer nearest-neighbor lattice contacts and
by large fluctuations in local polymer density. The simulated critical
temperatures, $T_{\rm cr}$, of phase separation for the two sequences differ
significantly, whereby the sequence with a more "blocky" charge pattern
exhibits a substantially higher propensity to phase separate. The trend is
consistent with our sequence-specific random-phase-approximation (RPA) polymer
theory, but the variation of the simulated $T_{\rm cr}$ with a previously
proposed "sequence charge decoration" pattern parameter is milder than that
predicted by RPA. Ramifications of our findings for the development of
analytical theory and simulation protocols of IDP LLPS are discussed.
