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

Abstract

The description of gel swelling by Flory and Rehner using the original Flory–Huggins interaction parameter for the polymer–solvent interaction cannot be applied to most smart microgels. Here, we compare descriptions of the swelling curves of such microgels using series expansions of the Flory–Huggins parameter $$\chi$$ χ with the results of Hill-like equation for $$\chi$$ χ . We study N-isopropyl-acrylamide particles at different concentrations of the cross-linker N,N-methylenebisacrylamide. The hydrodynamic radius $$R_{\mathrm {H}}$$ R H of the microgel particles is determined using photon correlation spectroscopy. The fits with the series expansion of $$\chi$$ χ nicely follow the experimental data. However, already with the first-order series expansion, the computed $$\Theta$$ Θ temperatures are not physically reasonable. Moreover, the physical meaning of the parameters of the series expansion is not clear. The Hill-like equation, which we recently introduced, yields a good description of all measured microgel swelling curves and provides physically meaningful parameters. For instance, the Hill parameter $$\nu$$ ν corresponds to the number of water molecules per network chain cooperatively leaving the chain at the volume phase transition. Graphical abstract Different approaches to model the Flory-Huggins interaction parameter are explored and compared with respect to the quality of the fit of microgel swelling curves.

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

“…As expected, the values for are very close and have an average value of 48 ( Table 1 and Figure 4 ) which is also consistent with previous studies [ 35 , 36 , 38 , 49 , 50 ]. The differences between the values might be due to the different distributions of the cross-linker in the particular microgel particles.…”

“…In the future, the universal monomer specific parameters , , and the concentration dependent parameter can be used as reference parameters for fitting different homopolymer and copolymer systems. The generalized Flory–Rehner theory [ 40 ] using the Hill-like model [ 35 , 36 , 38 ] needs just three fitting parameters , , and to describe the swelling curves of various copolymer microgels for which the swelling behavior of the respective homopolymer is already known.…”

“…Using the Hill-like model, Leite et al [ 38 ] and Friesen et al [ 35 ] were able to describe the swelling behavior of various homopolymer microgels. We have shown in a previous work that the Hill-like model for the interaction parameter, yields physically meaningful parameters in contrast to the original approach of Flory and to series expansions of [ 36 ]. The Hill-like model is given by: where is the value of the parameter at , is the first temperature data point, and is the last (end) temperature point of the data set, a is the slope of the baseline, b is the dimensionless amplitude parameter of the Hill transition, K is the half-saturation constant, is the half-temperature, is the Hill parameter and is the relative temperature.…”

“…However, the coefficients of such series expansions are physically difficult to interpret. Furthermore, the series expansions do not take into consideration the cooperativity of the volume phase transition coming from the chemical coupling of polymer chains [ 34 , 35 , 36 , 37 ]. Tiktopul et al [ 34 ] investigated the cooperativity of the coil-globule transition of poly(NIPAM) by microcalorimetry and have shown that the polymer does not undergo a globule-coil transition according to the all-or-none mechanism.…”

“…The process is rather gradually cooperative. Leite et al [ 38 ] and Friesen et al [ 35 , 36 ] proposed a Hill-like model that accounts for cooperativity of the volume phase transition. However, it is an even greater challenge to describe the swelling behavior of copolymer microgels thermodynamically and at least for higher comonomer contents standard models for fail.…”