Kinetics of Chain Exchange between Diblock Copolymer Micelles

Abstract

Chain-exchange kinetics strongly depends on polymer concentration, its compatibility with the solvent, temperature, etc. [6][7][8] An early theory for micelles of amphiphilic molecules [9] states that their relaxation involves: (1) a fast process associated with the quick exchange of single polymer chains between the micelles and the surrounding bulk phase, and (2) a slow process for the micelle fission/ fusion process. Halperin and Alexander [10] showed that the unimer expulsion/insertion has the lowest activation energy, while micelle fusion and fission are not favored either energetically or entropically. [10,11] They deduced a scaling law for the fast relaxation process using Kramer's rate theory, and described the relaxation kinetics by a single exponential decay function. It should be noted that these theoretical studies are based on the assumption of very long core or corona forming blocks, and do not take into account the dependence of the micelle size distribution and aggregation number on the corona-forming block length.A number of experimental studies found that the chain-exchange kinetics can be fitted by a doubleexponential function [6][7][8]12,13] and the phenomenon were attributed to micellar fusion/fission along with unimer expulsion/insertion though there was no conclusive evidence. These studies of system dynamics used Dissipative particle dynamics simulation is employed to study the chain exchange kinetics between micelles of diblock copolymer in aqueous solution via in silico hybridization method. One focus is placed on the effect of chain flexibility on the dynamic behavior by varying the spring constant in the bead-spring model. The length ratio of hydrophilic to hydrophobic block is also varied. It is found that chain expulsion/insertion is the dominant mechanism in the chain exchange process. The most interesting finding is the multimodal relaxation behavior for the chain exchange and expulsion when the spring constant is small or the length ratio of hydrophilic to hydrophobic block is large. This phenomenon is due to an increase in size polydispersity of micelles with rising population of small aggregates/micelles, for which the exchange kinetics is faster. Micelles with larger aggregation numbers (>10) are found to follow single exponential relaxation kinetics.

Langevin Dynamics Simulations of the Exchange of Complex Coacervate Core Micelles: The Role of Nonelectrostatic Attraction and Polyelectrolyte Length

“…In simulations of amphiphlic diblock copolymer micelles the expulsion rate slightly decreased when the corona block:core block length ratio was increased. 12,16 The change in micelle exchange rates was ascribed to the change in micelle aggregation number that occurred by increasing the corona:core block length ratio. Here we tried to minimize the effect of the corona block by keeping the corona:core block length ratio fixed.…”

“…This type of simulations has already shown its value in the studies on amphiphilic diblock copolymer micelle exchange. 12,14−16 In addition, coarse-grained dynamics simulations have also been used to study complex coacervation, 25,26 the formation of a single C3M, 27 and the static properties of multiple C3Ms. 28−30 We use the coarse-grained simulations to follow the initial micellization kinetics of multiple C3Ms.…”

“…A change of one of the system parameters can thus change which of the two mechanisms dominates or whether they both occur. As a result, micelle exchange rates can have a complex dependence on system parameters like core block length, 12−16 corona block length, 12,16,17 polymer concentration, 12,14 chain flexibility, 16 and interfacial tension between core and solvent. 12,14,18 Although the theory developed for amphiphilic diblock copolymer micelle exchange provides a good starting point to describe C3M exchange, it cannot describe the C3M exchange completely.…”

“…For amphiphilic diblock copolymer micelles the importance of exchange dynamics is widely recognized, and their exchange dynamics has been thoroughly studied. − These micelles consist of a single macromolecular species featuring an soluble and an insoluble block. Often, two different mechanisms are distinguished to describe the exchange of these micelles, based on the theoretical framework developed by Dormidontova .…”

“…A change of one of the system parameters can thus change which of the two mechanisms dominates or whether they both occur. As a result, micelle exchange rates can have a complex dependence on system parameters like core block length, − corona block length, ,, polymer concentration, , chain flexibility, and interfacial tension between core and solvent. ,, …”