Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels

Abstract

A full quantitative description of the swelling of smart microgels is still problematic in many cases. The original approach of Flory and Huggins for the monomer–solvent interaction parameter χ cannot be applied to some microgels. The reason for this obviously is that the cross-linking enhances the cooperativity of the volume phase transitions, since all meshes of the network are mechanically coupled. This was ignored in previous approaches, arguing with distinct transition temperatures for different meshes to describe the continuous character of the transition of microgels. Here, we adjust the swelling curves of a series of smart microgels using the Flory–Rehner description, where the polymer–solvent interaction parameter χ is modeled by a Hill-like equation for a cooperative thermotropic transition. This leads to a very good description of all measured microgel swelling curves and yields the physically meaningful Hill parameter ν. A linear decrease of ν is found with increasing concentration of the cross-linker N,N′-methylenebisacrylamide in the microgel particles p(NIPAM), p(NNPAM), and p(NIPMAM). The linearity suggests that the Hill parameter ν corresponds to the number of water molecules per network chain that cooperatively leave the chain at the volume phase transition. Driven by entropy, ν water molecules of the solvate become cooperatively “free” and leave the polymer network.

Comparison of different approaches to describe the thermotropic volume phase transition of smart microgels

“…To account for the cooperativity of the volume phase transition, Leite et al and Friesen et al [31,32] proposed a Hill-like model for the interaction parameter that yields physically meaningful parameters [Eq. ( 16)].…”

“…is the relative temperature. The relative temperature t rel (t) is used analogously to the polymer concentration [32]. The Hill-like equation describes the cooperativity of the binding of water by the polymer.…”

“…If N Gel is homogeneously distributed in the gel and the cross-linker is fully incorporated, N Gel can be calculated by Eq. ( 22) [32].…”

“…In the present paper, the parameter of the Flory-Rehner equation has been successfully modeled, either by a series expansion or by a more advanced Hill-like equation which describes the microgel collapse as a cooperative thermotropic transition [31,32]. It is physically clear that in the cross-linked networks of p(NIPAM) particles with the crosslinker N,N-methylenebisacrylamide (BIS) studied here, the polymeric chains are mechanically connected.…”

“…Due to this the Hill-like equation yields a very good description of all microgel swelling curves measured in the present work. It also provides a physically meaningful parameter , the so-called Hill parameter [32]. The experimentally observed linear decrease in with increasing concentration of the cross-linker BIS in the microgel particles suggests that the Hill parameter is related to the mean number of water molecules per network chain cooperatively leaving the chain at the volume phase transition.…”