Patterning Trends and Chaotic Behavior in Co ²⁺ /NH ₄ OH Liesegang Systems

Co(OH) 2 Liesegang patterns from Co 2+ and NH 4 OH in gelatin are studied in thin glass tubes. The experiments are performed in the limit of large initial concentration difference (Δ) between the interdiffusing electrolytes. Patterning trends are investigated as the initial concentration product σ = [Co 2+ ] 0 [NH 4 OH is varied (we keep [NH 4 OH] 0 constant and vary [Co 2+ ] 0 in the limit of large Δ). Time series of the total number of bands in the pattern show a random distribution apparently indicating the chaotic character of that variable. When the bands are counted in the bottom portion of the pattern (the last 4 cm measured from the last band), their number (denoted ν therein) decreases monotonically with time at all concentrations. The pattern thus regularizes itself in that region. The spacing between the bands is measured as a function of distance from the junction between the co-precipitate solutions, at different initial concentrations. The variation of spacing with distance is found to fit a quadratic equation. The variation of spacing with concentration at a given location is also studied and is found to involve an exponential term. Then a generalized equation expressing the spacing as a function of concentration and distance is determined. A three-dimensional plot is constructed to represent the obtained variations. Our results are then compared with previous experimental findings and theoretical formulations of Liesegang preciptation phenomena.