Diffusion-induced spontaneous pattern formation on gela- tion surfaces

– Although the pattern formation on polymer gels has been considered as a result of the mechanical instability due to the volume phase transition, we found a macroscopic surface pattern formation not caused by the mechanical instability. It develops on gelation surfaces, and we consider the reaction-diffusion dynamics mainly induces a surface instability during polymerization. Random and straight stripe patterns were observed, depending on gelation conditions. We found the scaling relation between the characteristic wavelength and the gelation time. This scaling is consistent with the reaction-diffusion dynamics and would be a first step to reveal the gelation pattern formation dynamics. The macroscopic dissipative pattern formation has attracted considerable interest in several recent decades [1, 2]. Many kinds of soft matters have shown fascinating patterns. In particular, polymer gels create various surface patterns, which are typical non-equilibrium phenomena, under the volume phase transition [3]. Because the coupling of phase transition and pattern formation is interesting, the dynamics of this pattern formation has been extensively studied both in terms of experiments and theories [4, 5]. The mechanical instability due to swelling or shrinking of polymer gels plays a crucial role in such pattern formations. Obviously, this phenomenon does not result from diffusion dynamics. On the other hand, reaction-diffusion systems can also create dissipative patterns called Turing patterns [6]. For example, Quyang and Swinney presented some Turing patterns using the CIMA (Chlorite, Iodide, and Malonic Acid) reaction [7]. They used gels as a reaction base. It should be noticed that gels did not deform in their experiment. As mentioned above, gels and reaction-diffusion systems can create dissipative patterns independently. To our best knowledge, however, there is no report on the macroscopic pattern formation concerning both of them simultaneously, i.e., the pattern formation of gels themselves by the reaction-diffusion dynamics has not been discovered. In this paper we show such a pattern formation that we found on gelation surfaces. The behaviors of the pattern wavelength and the diffusion length are discussed through this investigation. It will be an evidence for the reaction-diffusion dynamics. We used the scaling analysis methods to reveal the characteristics of the pattern formation. In general, the scaling analysis methods are very useful to understand the polymer dynamics [8]. Moreover,