The model of Mu ¨ller and Polezhaev for periodic precipitation is applied to a salt system that can dissolve in excess diffusing electrolyte due to complex formation. A typical example is the Co(OH) 2 Liesegang pattern from Co 2+ and NH 4 OH, which propagates due to band formation ahead and band dissolution at the tail of the stratum (Co(OH) 2 dissolves in excess ammonium hydroxide forming Co(NH 3 ) 6 2+ ). Diffusion profiles are constructed by plotting the computed distance of the last band (d lb ) and that of the first band (d fb ) versus time. The propagation is investigated under two main conditions: at fixed concentration of the inner electrolyte (X 0 ) while varying that of the outer electrolyte (Y 0 ), and the reverse (i.e., at fixed Y 0 while varying X 0 ). While in the first case, the propagation is faster at higher Y 0 , the opposite trend is obtained when X 0 is varied, exactly reproducing the experimental observations in the literature on Co(OH) 2 . A correlation close to linear is found between the dissolution and precipitation events. The advancing banded patterns are also displayed in a special map representation combining the diffusion profiles with the band contours. A special criterion is developed, delineating the situations where either a single pulse or a stratum of bands propagates.

Periodic precipitation of sparingly soluble salts yields parallel Liesegang bands in 1D whose spacings obey either one of two known trends. The overwhelming trend is an increase in spacing as we move away from the junction, while some systems display a decrease in spacing as the bands get further away from the interface. The latter trend is much less common and is known as the revert spacing law. Whereas the direct (normal) spacing law is generally well-understood, the revert spacing trend has not been explicitly and distinctly elucidated. In this paper, we propose a mechanism of revert spacing governed by the adsorption of the diffusing CrO4(2−) ions on the formed PbCrO4 Liesegang bands and carry out a set of experiments that support the suggested scenario. It is shown that this adsorption increases as the band number (n) increases in revert spacing systems, while it decreases as n increases in direct spacing systems. It is concluded that this correlation in opposite directions decisively reveals the role of adsorption in the mechanism. The attraction between the CrO4(2−) and Pb(2+) in the gel causes the bands to form gradually closer and closer. Secondary structure (thinner bands formed within the main ones) obtained under some conditions is discussed in view of the light sensitivity of the chromate ion and the stability of the lead chromate sol.

We present here novel expermients on the formation of Liesegang rings in 2D. We consider the system of propagating Co(OH) 2 bands studied extensively in 1D, from the viewpoint of a large number of considerations. In this paper, we focus on morphological aspects and, in the first part, we seek to steer the appearance of the pattern to achieve a pre-determined morphology. We aim at attaining three main features: minimizing the re-dissolution of Co(OH) 2 at the back of the propagating pattern, clearing the fuzzy precipitate region lagging behind, and increasing the ring spacing. We vary three experimental parameters to achieve that threefold purpose: 1. decreasing the concentration of the diffusing (outer) electrolyte (NH 4 OH), 2. applying a constant electric field radially across the circular pattern, and, 3. increasing the gel concentration to a moderately high value. The best pattern was obtained under the conditions: 9% gelatin, [NH 4 OH] 0 ¼ 1.33 M, and applied potential V ¼ 4.0 V, for a 0.100 M CoCl 2 taken as constant throughout the whole set of experiments performed. The observations are discussed in relation to the effects that cause them, and the known properties of Liesegang patterns. In the second part of the study, we monitor distortions of the ring pattern from circular symmetry, by applying a constant linear electric field across the circular medium. Elliptical distortions are obtained, which become notably important as the applied potential increases through 1.75 V. The variation of the ring curvature with applied potential is quantified and discussed.

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This paper presents a study of some features and characteristics of the Co2+/NH4OH Liesegang system. The pattern of parallel Co(OH)2 bands displays peculiar properties that are unique among other Liesegang systems. First, the process of dissolution of bands at the top of the pattern coupled to the formation of new ones at the bottom results in a propagating pattern that moves down the tube. Second, the total number of bands N varies erratically with time, unlike other Liesegang systems in which N increases monotonically with time. These random oscillations in the variable N are related to the dissolution/precipitation scenario. New experiments are designed to obtain a rigorous measurement of the total number of bands. Image analysis software (SigmaScan) is used to accurately determine N and the distance of the first band from the junction between the two solutions, based on a cutoff zero absorbance criterion. A time series for N is obtained by monitoring the pattern for 40 consecutive days. This time series is then analyzed numerically using a “Chaos Data Analyzer” software. All the characterization tools (such as power spectra, phase portraits, Lyapunov exponents and fractal dimensions) suggest a chaotic behavior of deterministic nature. The distance of the first band from the interface is plotted versus time. The velocity of dissolution is determined by obtaining a functional fit from the time variation curve and then calculating a derivative curve of that fit. The derivative is particularly evaluated at t = 10 and 15 days (taken as reference days), thus yielding the velocity of the dissolution front. A similar method is used for the distance of the last band from the interface, to determine the velocity of the precipitation front. The measurements are performed for five different concentrations (C) of cobalt chloride and the dependence of the two front velocities on C is investigated. Both front velocities are found to decrease monotonically with increasing C with a linear correlation existing between them.