Liesegang phenomena, a function of diffusion and reaction conditions, form attractive and unique periodic stripe patterns. Such pattern formation frequently inspires microstructural design in materials science. Moreover, mor- phological pattern transitions between periodic precipitation and tree-like crystal aggregates are scientifically interesting [1] [2] . Liesegang phenomena usually manifest themselves when a concentrated salt solution diffuses through a gel that contains another electrolyte at a lower concentration. Diffusion and chemical reactions cause little precipiation of otherwise soluble salts in a periodic manner. The precipitation and redissolution reactions for a generic metal ion M²⁺ are as follows:

When NH₄OH diffusion causes metal ions to precipitate in the form of M(OH)₂, redissolution at the top of the pattern induces a Liesegang band.

Recent research indicates that spontaneous diffusion-related self-organization dynamics and irreversible re- actions or precipitation systems based on Ostwald supersaturation theory explain Liesegang pattern formation [3] . However, nonlinearily hinders elaboration of the exact mechanism.

Microwave radiation may be helpful in this context. Microwave radiation has recently been a very active area of research due to the many advantages of nonthermal effects such as reaction promotion, nucleation induction, and diffusion facilitated by the molecular vibration of polar molecules [4] [5] . We hypothesized that the reaction and diffusion characteristics of a Liesegang system could be modulated or explained via various microwave properties. In addition, Liesegang phenomena may suggest a new application of microwave radiation and suitable operating conditions for highly functional inorganic nanomaterials. Salt and gel concentration [6] , inner electrolyte species, and so on are essential for solving the diffusion challenge of Liesegang phenomena. In this study, we varied salt species and microwave output to understand the microwave effect. We used a microwave reactor equipped with an in situ observation system to analyze the dynamic growth behavior of the periodic pattern.

To form a Liesegang pattern, we used a gel because it can prevent precipitate sedimentation and hydrodynamic turbulence. A salt was added to a prepared gelatin-based gel [7] [8] . In this study, gelatin and salt concentration were constant, and we used three salt species containing the same metal ion: Co(NO₃)₂, CoCl₂, and CoSO₄ (Table 1). These salts were selected because counterion species is a major controlling factor in pattern formation. The counterion modulates the solubility, diffusion coefficient, and dielectric constant of each salt, which is a function of microwave adsorption. We first heated a solution (i.e., gel and salt) to 90˚C. We then poured the solution into a glass test tube (φ: 13 mm; height: 100 mm; volume: 5 mL) and gradually cooled it to room temperature to impart a homogeneous gelatin network structure. Temperature is the most important factor for pattern formation; we used two different methods, microwave irradiation (MW) and conventional heating (oil bath, OB) for maintaining solution temperature. After we poured 2 mL of a 28% ammonium solution at the gel surface, we covered it with a silicon rubber lid. Ammonium salt precipitates via ammonium ion diffusion into the gel, and Liesegang stripe-pattern formation starts from the top surface to the bottom of the tube. We measured the stripe number and length for the two heating methods.

Figures 2-7 show photographs of the stripe pattern near the gel surface for each salt under MW or OB conditions after 30 min. The experiment involves precipitation after the salt concentration in the gel exceeds the critical values (i.e., the solubility due to ammonium ion diffusion). We observed a stripe pattern in the case of Co(NO₃)₂

and CoCl₂. However, the pattern induced by CoSO₄ was not clear; 30 min may be insufficient for stable precipitation because of its higher solubility. We did not observe an expected pattern transition (e.g., a tree-like pattern [1] ) in this experiment, and the parallel stripe pattern remained even under microwave irradiation.

To aid in understanding the mechanism of stripe-pattern formation, Figures 8 and 9 plot the stripe number and length, respectively, in relation to reaction time. Filled and open symbols indicate MW and OB conditions,

respectively. Although precipitation starts just after contact with the ammonium solution, either the stripes do not immediately form or the camera resolution limit precludes sufficiently fast and precise image acquisition; accordingly, we assigned the initial number of stripes as 0. We counted the number of stripes after approximately 25 min. The stripe length linearly increased with reaction time (Figure 9). After 30 min of reaction time, nonthermal effects induced by microwave irradiation caused the stripe number and length to increase more rapidly for MW relative to OB. This is attributable to enhanced molecular diffusion and facilitated supersaturation. Molecular vibration induced by microwave irradiation accelerates ionic diffusion. Moreover, such vibration readily induces supersaturation of the precipitate. Consequently, cyclic periods of supersaturation, nucleation, and depletion become faster. However, temperature must be carefully controlled to modulate such cycling.

Figure 10 and Figure 11 show an almost linear relation of stripe number and length, after 30 min of irradiation, with respect to microwave power for Co(NO₃)₂ and CoCl₂. MW imparted a greater effect than OB. Consequently, microwave irradiation more effectively induced precipitation via supersaturation. Strip pattern formation did not proceed readily for CoSO₄, even at a higher microwave irradiation power.

To understand the mechanisms of precipitation and diffusion in Liesegang patterns, experiments varying the salt species and microwave power were conducted in an oil bath and microwave reactor equipped with in situ observation system. Stripe length and number increased more quickly with respect to time under microwave irradiation than oil bath heating, and also increased with respect to microwave irradiation power. We explained these findings in the context of nonthermal effects (i.e., higher molecular diffusion and facilitated supersaturation) that are accelerated by radiation-induced molecular vibration. Microwave irradiation can modulate the diffusion and

manifestation of Leisegang patterns, and may be a useful tool in other fine-scale, nonequilibrium self-organiza- tion processes that involve precipitation and nonlinearity.