  Histogram-reweighting grand canonical Monte Carlo simulations are used to
obtain the critical properties of lattice chains composed of solvophilic and
solvophobic monomers. The model is a modification of one proposed by Larson
\emph{et al.} [J. Chem. Phys. 83, 2411 (1985)], lowering the ``contrast''
between beads of different type to prevent aggregation into finite-size
micelles that would mask true phase separation between bulk high- and
low-density phases. Oligomeric chains of length between 5 and 24 beads are
studied. Mixed-field finite-size scaling methods are used to obtain the
critical properties with typical relative accuracies of better than $10^{-4}$
for the critical temperature and $10^{-3}$ for the critical volume fraction.
Diblock chains are found to have lower critical temperatures and volume
fractions relative to the corresponding homopolymers. Addition of solvophilic
blocks of increasing length to a fixed-length solvophobic segment results in a
decrease of both critical temperature and critical volume fraction, with an
eventual slow asymptotic approach to the long-chain limiting behavior. Moving a
single solvophobic or solvophilic bead along a chain leads to a minimum or
maximum in the critical temperature, with no change in critical volume
fraction. Chains of identical length and composition have a significant spread
in their critical properties, depending on their precise sequence. The present
study has implications on understanding biomolecular phase separation and for
developing design rules for synthetic polymers with specific phase separation
properties. It also provides data potentially useful for the further
development of theoretical models for polymer and surfactant phase behavior.
