Critical cross-linking to mechanically couple polyelectrolytes and flexible molecules

Abstract

Molecules cooperate through a variety of mechanical interactions. A fundamental challenge in engineering de novo materials and systems is the identification of molecular structures that define fundamental building blocks – e.g., single structural units. Here, we report a systematic study of the effect and balance of molecular rigidity and variable cross-linking (such as electrostatic or H-bonding) on the resulting cooperative behavior of a molecular complex. Through a simple elastic model, we determine general conditions for mechanical coupling of flexible molecules of finite rigidity via discrete cross-links with finite stiffness. We demonstrate the atomistic mechanism of cooperative deformation (or mechanical coupling) by applying an ideal structural model, derived to solve the representative vibrational modes, and used to extract the effective bending rigidity as a physical metric for complexation. As a case study, we explore the complexation of weak polyelectrolytes used in layer-by-layer assembly, due to their known variation in molecular rigidity and electrostatic cross-linking (as a function of pH). The model is parameterized by previous full atomistic investigations of the constitutive polyelectrolytes: poly(acrylic acid), PAA, and poly(allylamine hydrochloride), PAH, which have persistence lengths on the order of a single nanometer, and are typically considered flexible molecules. We predict the optimal ionization level to induce mechanical coupling and cooperative deformation. Moreover, we indicate a critical regime of allowable cross-link densities which facilitates complexation, for molecules with finite rigidity in general, such as H-bonded polypeptide β-strands, DNA, and collagen. From these results, it is possible to predict when (or if) molecules act as a single mechanical unit.