Why Is Gyroid More Difficult to Nucleate from Disordered Liquids than Lamellar and Hexagonal Mesophases?

Abstract

Block copolymers, surfactants, and biomolecules form lamellar, hexagonal, and gyroid mesophases. Across these systems, the nucleation of lamellar from the disordered liquid is the easiest and the nucleation of gyroid the most challenging. This poses the question of what are the factors that determine the rates of nucleation of the mesophases and whether they are controlled by the complexity of the structures or the thermodynamics of nucleation. Here, we use molecular simulations to investigate the nucleation and thermodynamics of lamellar, hexagonal, and gyroid in a binary mixture of particles that produces the same mesophases as those of surfactants and block copolymers. We demonstrate that a combination of averaged bond-order parameters q̅ and q̅ identifies and distinguishes the three mesophases. We use these parameters to track the microscopic process of nucleation of each mesophase and investigate the existence of heterogeneous nucleation (cross-nucleation) between mesophases. We estimate the surface tensions of the liquid/mesophase interfaces from nucleation rates using classical nucleation theory and find that they are comparable for the three mesophases with values that are about a third of those expected for liquid-crystal interfaces. The driving forces for nucleation, on the other hand, are quite different and increase in the order gyroid < hexagonal < lamellar at any temperature. We find that the nucleation rates of the mesophases follow the order of their driving forces. We conclude that the difficulty to nucleate the gyroid originates in its lower temperature of melting and extremely low entropy of melting compared to those of the hexagonal and lamellar mesophases.

Mirror Symmetry Breaking and Network Formation in Achiral Polycatenars with Thioether Tail

“…For all homologues, there is a 6–12 K supercooling of the Iso–Cub transition compared to the Cub–Iso transition temperature on heating which is a typical feature of cubic LC phases with 3D periodicity (Table 1 ). [63] A series of sharp SAXS peaks appear at the Iso‐Cub bi transition, replacing the single diffuse scattering observed in the isotropic liquid state. Based on the positions of the scattering maxima two types of Cub bi phases can be distinguished.…”

Developing Local Order Parameters for Order–Disorder Transitions From Particles to Block Copolymers: Methodological Framework

“…Because the phase boundaries are only approximate, we cannot estimate the degree of supersaturation (DSS) quantitatively; however, we know qualitatively how far we are from the phase boundary in each case which suffices for the scope of this work. The lamellar phase is reported to have almost no nucleation barrier up to 8% below its melting temperature or in this case the ε AB value at the phase boundary. The cylinder phase also exhibits a similar trend.…”

“…Recently, Kumar and Molinero demonstrated the use of bond orientational order parameters to investigate the nucleation of lamellar, cylinder, and gyroid phases in a binary mixture of nanoparticles (henceforth termed the KM model) that produce BCP-like phases . While their OPs represent a significant advance and a systematic approach to identify and track the growth of the phases studied, alternative OPs could offer certain qualitative or quantitative advantages.…”

Unsupervised learning of atomic environments from simple features

“…Binary systems in general pose a serious challenge due to their combined translational and compositional order [7]. Because particles remain locally amorphous and primarily adopt compositional ordering over multiple coordination shells, order parameters are often ported imprecisely to new problems to provide simple descriptions of order-disorder transitions [30], or designed ad hoc for a particular study. [31] As in Ref.…”