Biomacromolecules rely on the precise placement of monomers to encode information for structure, function, and physiology. Efforts to emulate this complexity via the synthetic control of chemical sequence in polymers are finding success; however, there is little understanding of how to translate monomer sequence to physical material properties. Here we establish design rules for implementing this sequence-control in materials known as complex coacervates. These materials are formed by the associative phase separation of oppositely charged polyelectrolytes into polyelectrolyte dense (coacervate) and polyelectrolyte dilute (supernatant) phases. We demonstrate that patterns of charges can profoundly affect the charge–charge associations that drive this process. Furthermore, we establish the physical origin of this pattern-dependent interaction: there is a nuanced combination of structural changes in the dense coacervate phase and a 1D confinement of counterions due to patterns along polymers in the supernatant phase.

Oppositely charged polyelectrolytes can undergo a macroscopic, associative phase separation in solution, via a process known as complex coacervation. Significant recent effort has gone into providing a clear, physical picture of coacervation; most work has focused on improving the field theory picture that emerged from the classical Voorn-Overbeek theory. These methods have persistent issues, however, resolving the molecular features that have been shown to play a major role in coacervate thermodynamics. In this paper, we outline a theoretical approach to coacervation based on a transfer matrix formalism that is an alternative to traditional field-based approaches. We develop theoretical arguments informed by experimental observation and simulation, which serve to establish an analytical expression for polymeric complex coacervation that is consistent with the molecular features of coacervate phases. The analytical expression provided by this theory is in a form that can be incorporated into more complicated theoretical or simulation formalisms, and thus provides a starting point for understanding coacervate-driven self-assembly or biophysics.

Charged polymers are ubiquitous in biological systems because electrostatic interactions can drive complicated structure formation and respond to environmental parameters such as ionic strength and pH. In these systems, function emerges from sophisticated molecular design; for example, intrinsically disordered proteins leverage specific sequences of monomeric charges to control the formation and function of intracellular compartments known as membraneless organelles. The role of a charged monomer sequence in dictating the strength of electrostatic interactions remains poorly understood despite extensive evidence that sequence is a powerful tool biology uses to tune soft materials. In this article, we use a combination of theory, experiment, and simulation to establish the physical principles governing sequence-driven control of electrostatic interactions. We predict how arbitrary sequences of charge give rise to drastic changes in electrostatic interactions and correspondingly phase behavior. We generalize a transfer matrix formalism that describes a phase separation phenomenon known as “complex coacervation” and provide a theoretical framework to predict the phase behavior of charge sequences. This work thus provides insights into both how charge sequence is used in biology and how it could be used to engineer properties of synthetic polymer systems.