**Structure of a Hydrophobic Polyelectrolyte Chain with a Random Sequence**

MK Chae and NK Lee and Y Jung and JF Joanny and A Johner, MACROMOLECULES, 55, 6275-6285 (2022).

DOI: 10.1021/acs.macromol.2c00779

Most theoretical efforts address regular polyelectrolytes (PEs) with the charges equally spaced or smeared out along the polymer backbone, encouraged by the long-range character of the electrostatic interaction. Hydrophobic PEs undergo a transition from a uniglobular state to a multiglobular pearl-necklace state when the charge of the PE increases. The pearl necklace is a compromise between the Rayleigh instability of a charged droplet and chain connectivity. The standard pearl-necklace model for a hydrophobic PE describes regular sequences and can be considered as a mean field model for a random PE. The structure of random PEs results from the interplay between the disorder along the sequence and thermal fluctuations. We show that random PEs are not energetically driven toward configurations with equal pearls except for rare fluctuations with a number of pearls much smaller than typical under the given conditions. A streamlined energetic description of the space of states is provided. We demonstrate by molecular dynamics (MD) simulations that, indeed, weakly charged, random PEs typically do not split evenly and show how they populate the space of states. The compact set of most populated configurations defines an order in the pearl size distribution. We further consider PE with Markovian sequences, which exhibit short-range correlations, encompassing alternating sequences (regular, half-charged PE), random sequences (half-charged on average PE), and positively correlated sequences (blocky PE).

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