Physical Property Scaling Relationships for Polyelectrolyte Complex Micelles

Polyelectrolyte complex micelles (PCMs) are self-assembled nanoparticles formed by associative phase separation of hydrophilic neutral-charged block copolymers and polyelectrolytes and are effective in the delivery of hydrophilic payloads. Their attractive features include an ability to tune physical attributes such as core and corona size, particle shape, and stability, all of which are strongly dependent on the size and chemical structure of each polymer block. Previous studies have provided qualitative examples of these dependencies, but no quantitative structure-property relations have been developed to allow rational design of PCMs. Developing such design rules is crucial for applications and provides a greater understanding of the physics of polyelectrolyte assembly. In this work, we use small-angle X-ray scattering, electron microscopy, and light scattering to determine the scaling behavior of physical micelle parameters for commonly used, biologically relevant polyelectrolytes. As an example, for PCMs constructed from hydrophilic neutral-polyelectrolyte block copolymers and oppositely charged homopolymers, we find that the size of the PCM core increases strongly with the chain length of the polyelectrolyte block (proportional to N-0.73) but decreases weakly or is independent of the length of the other chains. We then compare our results to accumulated published data and theory to show strong agreement, suggesting that these laws are very general for PCMs.