Periodic Interfacial Precipitation in Polymer Films

Mueller, Karl F.

doi:10.1126/science.225.4666.1021

Cited by 42 publications

(12 citation statements)

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“…Cross sections of the film prepared at 125 °C show a number of layers of PbS aggregates parallel to the film surface of variable thickness near 1 gm, with variable spacings of tens of micrometers, which is undoubtedly the Liesegang ring phenomenon,19 but with the usual centimeter spacing and millimeter thickness in aqueous media reduced to micrometer size because of the much higher viscosity of the E-MAA copolymer. 20 We found the activation energy of aggregation of 0.25 M PbS (<2.5 nm PbS -4.5 nm PbS) in E-MAA to be 76 kcal. This coincides with an estimate for the energy of flow of the E-MAA copolymer.…”

Section: Sirmentioning

confidence: 81%

Polymer-trapped semiconductor particles

Mahler¹

1988

Inorg. Chem.

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Section: Sirmentioning

confidence: 81%

Polymer-trapped semiconductor particles

Mahler¹

1988

Inorg. Chem.

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“…This is regarded as a spatial periodic precipitation controlled process, which usually means a series of concentric rings or bands that are parallel to the diffusion front and formed by crystallization. [27][28][29] These phenomena can be seen as various processes in nature such as the formation of gallstones, mother of pearl, rings of trees, and zebra rocks. [30][31][32][33] Therefore, a multistep build-up process controlled by a spatially periodic precipitation mechanism is proposed here to explain the formation of multilayers (Fig.…”

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confidence: 99%

Hierarchical Assembly of Multilayered Hollow Microspheres from an Amphiphilic Pharmaceutical Molecule of Azithromycin

et al. 2008

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“…C, the initial separation of reactants leads to the formation of a dynamic reaction front. The presence of such a reaction interface is characteristic of many processes in nature [17][18][19][20][21][22]. Interesting properties of the front are the global reaction rate R͑t͒, the location of the center of the reaction front x f ͑t͒, the width of the front w͑t͒, and the local reaction rate at the center of the front R͑x f , t͒.…”

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confidence: 99%

Competing Reactions with Initially Separated Components

et al. 1996

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The first theoretical and experimental study of a competitive reaction with initially separated components is presented. Rich spatiotemporal reaction front patterns are produced by a simple theoretical reaction-diffusion model. Such patterns are observed experimentally for the reaction Cr 31 1 xylenol orange ͑XO͒ ! products. The conditions for these front patterns are significant differences in the microscopic reaction constants and in the initial densities of the competing species.[S0031-9007(96)00897-6] 05.40.+j In a series of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], it has been shown that elementary reaction-diffusion systems with initially separated components have very unusual dynamical properties. For the elementary reaction A 1 B ! C, the initial separation of reactants leads to the formation of a dynamic reaction front. The presence of such a reaction interface is characteristic of many processes in nature [17][18][19][20][21][22]. Interesting properties of the front are the global reaction rate R͑t͒, the location of the center of the reaction front x f ͑t͒, the width of the front w͑t͒, and the local reaction rate at the center of the front R͑x f , t͒. These reaction rate and front properties have been shown to follow a nonclassical behavior, with anomalous time exponents [1,5,6].The first level of complexity in chemical reaction kinetics is competing elementary reactions, which occur in many chemical systems [23]. These reactions also provide the simplest case for the formation of a complex reaction front pattern. In this Letter we show how such a pattern can be simply accounted for by two competing elementary reactions; two similar species, A 1 and A 2 , on one side of the initially separated system, compete to react with the species on the other side of the system, B, according to the schemeThese two processes are taking place simultaneously, each with a different microscopic reaction constant, k 1 and k 2 . In the simplest model of the A 1 B ! C initially separated system, the following set of mean-field reactiondiffusion equations for the local concentrations r a , r b has been assumed to describe the system [1]:≠r a ≠t D a = 2 r a 2 kr a r b ,where D a , D b are the diffusion constants, and k is the microscopic reaction constant. These equations are subject to the initial separation condition along the x axis, r a ͑x, 0͒ a 0 ͓1 2 H͑x͔͒,where a 0 , b 0 are the initial densities and H͑x͒ is the Heaviside step function, so that the A's are initially uniformly distributed on the left side ͑x , 0͒, and the B's on the right side ͑x . 0͒ of the initial boundary.In the mean-field description, which is valid [7] above d 2, the local production rate of C, is defined by the term R͑x, t͒ kr a ͑x, t͒r b ͑x, t͒, which is the basis for defining all other quantities of interest [1]. In our model (1), which allows for the existence of more than a single species on one side of the initially separated system, the products C 1 and C 2 are assumed to be either identical or experimentall...

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Periodic Interfacial Precipitation in Polymer Films

Cited by 42 publications

References 14 publications

Polymer-trapped semiconductor particles

Polymer-trapped semiconductor particles

Hierarchical Assembly of Multilayered Hollow Microspheres from an Amphiphilic Pharmaceutical Molecule of Azithromycin

Competing Reactions with Initially Separated Components

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