![]() ![]() 19 Therefore in the LP-forming systems, the temperature is Gels that melt above 45 and 30 ☌, respectively. 12, 13, 22, 14− 21 However, these studies were mostly conducted with agarose and gelatin 10, 11 There are various studiesĭescribing some trends and emergence of new shapes, e.g., helical Gel concentrations and the degree of cross-linking in gels also affect ![]() Studies demonstrated the effect of the initial concentrations of the Studies displaying the effects of electric, 7 and magnetic fields on LPs. Measured from the gel/outer electrolyte interface, respectively, and p is the so-called spacing coefficient.) There have been Where X ( n+1) and X n are the positions of the two consecutive zones Is represented as follows: p = X ( n+1)/ X n, (Spacing law is one of the benchmark characterizations of LPs and Other are mathematically explained by the “spacing coefficient”. 6 The positions of the zones with respect to each Product appears as differently spaced consecutive zones. (1-D), in two (2-D), or three dimensions (3-D). 5 Typically, the patterns are formed in a hydrogel medium where theĭiffusion of one reactant is directed in the other, in one dimension 2, 3 An importantĬlass of pattern-forming systems known as Liesegang patterns (LPs),ĭiscovered more than a century ago by Raphael Eduard Liesegang, 4 are periodic precipitation patterns resultingįrom the reaction–diffusion processes. The pattern formation by mathematical models, synthetic nonequilibriumĬhemical systems have been employed. Reveal the mechanisms behind the pattern formation and to describe These differences result from the varying externalĪnd internal factors that affect the formation of the patterns. There are always some differences between theįorms we encounter. For example, in the periodic patterns of rocks,
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