  This article focuses on phase and aggregation behavior for linear chains
composed of blocks of hydrophilic and hydrophobic segments. Phase and
conformational transitions of patterned chains are relevant for understanding
liquid-liquid separation of biomolecular condensates, which play a prominent
role in cellular biophysics, but also for surfactant and polymer applications.
Previous studies of simple models for multiblock chains have shown that,
depending on the sequence pattern and chain length, such systems can fall into
one of two categories: displaying either phase separation or aggregation into
finite-size clusters. The key new result of the present study is that both
formation of finite-size aggregates and phase separation can be observed for
certain chain architectures at appropriate conditions of temperature and
concentration. For such systems, a bulk dense liquid condenses from a dilute
phase that already contains multi-chain finite-size aggregates. The
computational approach involves several distinct steps using
histogram-reweighting grand canonical Monte Carlo simulations, which are
described here in some level of detail.
