Dynamic Landau Theory for Supramolecular Self-Assembly

TL;DR

This paper develops a simplified dynamical Landau theory to model supramolecular self-assembly kinetics, capturing complex behaviors like hysteresis and lag time with fewer parameters than traditional pathway-specific models.

Contribution

It introduces a phenomenological Landau theory that reduces parameter complexity while accurately describing generic self-assembly behaviors.

Findings

Describes hysteresis, overshooting, and lag time in polymerization.

Identifies pathway controller as a key kinetic parameter.

Provides conditions for observing different kinetic phenomena.

Abstract

Although pathway-specific kinetic theories are fundamentally important to describe and under- stand reversible polymerisation kinetics, they come in principle at a cost of having a large number of system-specific parameters. Here, we construct a dynamical Landau theory to describe the kinetics of activated linear supramolecular self-assembly, which drastically reduces the number of parameters and still describes most of the interesting and generic behavior of the system in hand. This phenomenological approach hinges on the fact that if nucleated, the polymerisation transition resembles a phase transition. We are able to describe hysteresis, overshooting, undershooting and the existence of a lag time before polymerisation takes o?, and pinpoint the conditions required for observing these types of phenomenon in the assembly and disassembly kinetics. We argue that the phenomenological kinetic parameter in our theory is a pathway controller, i.e., it controls the relative weights of the molecular pathways through which self-assembly takes place.