Eur. Phys. J. E (2015) 38: 105
https://doi.org/10.1140/epje/i2015-15105-5

Regular Article

Dynamic Landau theory for supramolecular self-assembly

¹ Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
² Institute for Theoretical Physics, Utrecht University, 3584 CE, Utrecht, The Netherlands

^* e-mail: n.tiwari@tue.nl

Received: 14 August 2015
Accepted: 28 August 2015
Published online: 29 September 2015

Abstract

Although pathway-specific kinetic theories are fundamentally important to describe and understand 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 off, 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.