Non-equilibrium nature of two-dimensional isotropic and nematic coexistence in amyloid fibrils at liquid interfaces.

Two-dimensional alignment of shape-anisotropic colloids is ubiquitous in nature, ranging from interfacial virus assembly to amyloid plaque formation. The principles governing two-dimensional self-assembly have therefore long been studied, both theoretically and experimentally, leading, however, to diverging fundamental interpretations on the nature of the two-dimensional isotropic-nematic phase transition. Here we employ single-molecule atomic force microscopy, cryogenic scanning electron microscopy and passive probe particle tracking to study the adsorption and liquid crystalline ordering of semiflexible β-lactoglobulin fibrils at liquid interfaces. Fibrillar rigidity changes on increasing interfacial density, with a maximum caused by alignment and a subsequent decrease stemming from crowding and domain bending. Coexistence of nematic and isotropic regions is resolved and quantified by a length scale-dependent order parameter S(2D)(d). The nematic surface fraction increases with interfacial fibril density, but depends, for a fixed interfacial density, on the initial bulk concentration, ascribing the observed two-dimensional isotropic-nematic coexistence to non-equilibrium phenomena.