Swelling of Random Copolymer Networks in Pure and Mixed Solvents: Multi-Component Flory–Rehner Theory

Abstract

A generalized extension of Flory-Rehner (FR) theory is derived to describe equilibrium swelling of polymer networks, including copolymers with two or more chemically distinct repeat units, in either pure or mixed solvents. The model is derived by equating the chemical potential of each solvent in the liquid and gel phases at equilibrium, while assuming the deformation of the network chains is affine. Simplifications of the model are derived for specific cases involving homopolymer networks, copolymer networks, pure solvents, and binary solvent mixtures. With reasonable assumptions, the number of polymer-solvent interaction parameters that must be determined by experiments can be reduced to two effective parameters (θ and θ), which describe the net interactions between water/copolymer (θ) and ethanol/copolymer (θ), respectively. Experimental measurements of the swelling of random copolymer networks of n-butyl acrylate and 2-hydroxyethyl acrylate in water, ethanol, and a 100 g/L ethanol/water mixture are utilized to validate the model. For a random copolymer network, θ and θ can be obtained by fitting the three-component FR model to equilibrium swelling data obtained in the pure solvents. Predicted solvent volume fractions for swelling in water-ethanol mixtures obtained by inserting fitted values of θ and θ into the four-component FR model are in reasonable agreement with experimental measurements.

Modified Flory–Rehner Theory Describes Thermotropic Swelling Transition of Smart Copolymer Microgels

“…For the description of the swelling behavior of copolymer microgels, the classical Flory–Rehner theory for homopolymer microgels must be extended, since the different interactions of the individual comonomers must be taken into account. Such an extension of the Flory–Rehner theory was proposed by Godbole et al [ 40 ]. For a copolymer microgel with two comonomers a and b , the elastic contribution to the osmotic pressure is given by: where is the Boltzmann constant, T is the temperature and and are the volume fraction of comonomer a and b , respectively.…”

“… is the volume of the microgel in the collapsed state and is the number of polymer chains. The mixing contribution to the osmotic pressure for a copolymer microgel with two comonomers a and b is given by [ 40 , 41 ]: where is the volume fraction of the solvent s , and are the respective interaction parameters for characterizing the interaction between solvent and comonomer a and b , respectively and the interaction parameter which describes the interactions between comonomers a and b . As in the standard Flory–Rehner theory, the contributions to the free energy change are assumed to be a sum of the mixing contribution and the elastic contribution .…”

“…As in the standard Flory–Rehner theory, the contributions to the free energy change are assumed to be a sum of the mixing contribution and the elastic contribution . If (Equation ( 1 )) and (Equation ( 2 )) are equal in swelling equilibrium, Equation ( 3 ) is obtained for the thermodynamic description of the swelling behavior of a binary copolymer microgel [ 40 ]. with the relationships for the number of segments between two crosslinkers (where is the Avogadro constant and is the molar volume of the solvent) and the total polymer volume fraction , the Flory–Rehner Eq.…”

“…Despite of the large number of syntheses of statistical copolymer microgels, theoretical descriptions of the VPT of these systems are sparse [ 29 ]. A general extension of the Flory–Rehner theory was proposed by Godbole et al [ 40 ] which can be applied to describe the swelling behavior of copolymer microgels. In this paper the swelling properties of synthesized homopolymer microgels based on poly(NNPAM) (PNNPAM), poly(NIPAM) (PNIPAM), and poly(NIPMAM) (PNIPMAM) and nominally statistic copolymer microgels based on poly(NNPAM-co-NIPMAM), poly(NNPAM-co-NIPAM) and poly(NIPAM-co-NIPMAM) are investigated at a mesoscale level by photon correlation spectroscopy (PCS) and at a molecular level by Fourier transformation infrared spectroscopy (FTIR) in a temperature dependend manner.…”

“…To quantify the amount of the different monomers present in the copolymer microgels 1 H-NMR spectra were recorded. We use a general extension of the Flory–Rehner theory proposed by Godbole et al [ 40 ] combined with our recently introduced Hill-like model for the interaction parameter to quantify the -swelling curves of copolymer microgels obtained by PCS (please note that we use t as symbol for the temperature in Celsius to distinguish from absolute temperatures in Kelvin). The thermodynamic analysis uses such parameters as the volume phase transition temperature , the polymer volume fraction in the reference state and the number of segments (monomers) between two crosslinkers at different mole fractions of comonomers x in the microgels.…”