Reactions at Polymer Interfaces: Transitions from Chemical to Diffusion-Control and Mixed Order Kinetics

TL;DR

This paper investigates the kinetics of reactions at polymer interfaces, revealing transitions from chemical to diffusion-controlled regimes and identifying mixed order kinetics based on reactivity and chain entanglement.

Contribution

It provides a detailed analysis of reaction kinetics at polymer interfaces, highlighting the transition points and regimes for different reactivities and chain entanglements.

Findings

Reactions follow second-order chemically controlled kinetics at low reactivity.

High reactivity induces a transition to diffusion-controlled kinetics with specific time dependencies.

Long-term kinetics are governed by diffusion of the dilute species, showing distinct power-law behaviors.

Abstract

We study reactions between end-functionalized chains at a polymer-polymer interface. For small chemical reactivities (the typical case) the number of diblocks formed, $R_t$, obeys 2nd order chemically controlled kinetics, $R_t \sim t$, until interfacial saturation. For high reactivities (e.g. radicals) a transition occurs at short times to 2nd order diffusion-controlled kinetics, with $R_t \sim t/\ln t$ for unentangled chains while $t/\ln t$ and $t^{1/2}$ regimes occur for entangled chains. Long time kinetics are 1st order and controlled by diffusion of the more dilute species to the interface: $R_t \sim t^{1/4}$ for unentangled cases, while $R_t \sim t^{1/4}$ and $t^{1/8}$ regimes arise for entangled systems. The final 1st order regime is governed by center of gravity diffusion, $R_t \sim t^{1/2}$.