Gel dynamics in the mixture of low and high viscosity solvents: Re-entrant volume change induced by dynamical asymmetry

Abstract

When a gel swollen with a certain solvent is placed in the bath of another solvent, the gel swells or de-swells depending on the thermodynamic affinity to the gel. Toyotama et al. [Langmuir 22, 1952 (2006)] reported an unusual volume change of chemical gels that cannot be explained by the affinity difference: when a chemical gel saturated with water is immersed in ethylene glycol (EG), although those solvents have almost the same affinity to the polymer, the gel first shrinks and then re-swells and finally takes the same equilibrium volume as the initial. The re-entrant swelling was attributed to different diffusion rates between water and EG (dynamical asymmetry), but the detailed mechanism was not clarified. In this paper, we experimentally show that the characteristic times for the temporal shrinking and subsequent volume relaxation are proportional to the squared system size. This indicates that the phenomenon is governed by diffusive dynamics. According to this observation, we propose a coupled diffusion model explaining the physical mechanism of the re-entrant volume change.

Competition between Osmotic Squeezing versus Friction-Driven Swelling of Gels

“…Cylindrical (1 mm in diameter and 30 mm in length) and disk-shaped (80 mm in diameter and 20 mm in thickness) acrylamide gels were used for the solvent exchange experiment and for indentation test, respectively. The synthesis procedure of the gel (including the composition of the pre-gel solution) was identical to that in previous investigations [ 4 , 6 ]; see Section 4 for experimental details. The indentation test was done in order to measure the bulk mechanical property of the specimen gel and to check the consistency with the osmotic property; the used indenter is a stainless steel ball with a radius of .…”

“…In what follows, we discuss the experimental results based on the theoretical model developed in our previous investigation [ 4 ]. We introduce a simple modification to the theoretical setting, that is, the PEG in the outer solution exerts a constant (i.e., independent of time and position) osmotic pressure on the gel surface.…”

“…The Onsager principle gives a set of time-evolutional equations of the gel dynamics in the binary solvent [ 4 ] with the aid of the conservation laws: where and are the volume fraction and velocity of the i -th component, respectively (subscripts of “w”, “e” and “p” represent water, EG and polymer (of the gel network), respectively). Note that , where is the displacement of the gel network from the initial and equilibrium position (hereafter, we often use the dot notation for time derivatives).…”

“…Recent experimental and theoretical investigations, however, have revealed that for gels swollen in binary solvents, the molecular diffusion of the solvents couples strongly with the cooperative diffusion (i.e., the volume change) of the gel network even when the equilibrium swelling volume hardly depends on the mixing ratio of the binary solvent [ 3 , 4 ]. When an acrylamide gel saturated with ethylene glycol (EG), say “EG-swollen gel”, is immersed into a large amount of water, its volume once increases and then decreases toward the equilibrium value even though the gel has almost the same equilibrium swelling volume in EG and in water; and the time scale of the initial temporary swelling is much faster than that expected from the cooperative diffusion constant and the gel size.…”

“…The point to understand the above-mentioned non-monotonous volume change is the asymmetry in the friction coefficients of the solvents to the polymer [ 4 ]. After the immersing of an EG-swollen gel into water, the mutual diffusion (i.e., the mixing) of inner EG and outer water occurs.…”