Kinetic Phase Diagram and Scaling Relations for Stationary Diffusional Growth

Brener, Efim A.; Müller‐Krumbhaar, H.; Temkin, D. E.

doi:10.1209/0295-5075/17/6/010

Cited by 124 publications

(79 citation statements)

References 18 publications

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“…It is observed that the top surface of the lamellar crystal is also undulated a few nm in height as indicated by the radial stripes. In films thinner than 15nm, the crystal morphology changes to that observed in the diffusion-controlled growth [6], as shown in Fig.1 b to f. In 14 nm thick films, the crystal shows the splitting of growth face to have many irregular branches typical in the dense branching morphology (DBM) or compact seaweed (CS) [11,12] . The envelope of this branching structure is nearly circular; we call hereafter this envelope "average front" in contrast to the local growth interface of its branch [13].…”

Section: Resultsmentioning

confidence: 86%

Crystal Growth of Isotactic Polystyrene in Ultrathin Films: Film Thickness Dependence

Taguchi

Miyaji

Izumi

et al. 2002

Journal of Macromolecular Science, Part B

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The film thickness dependence of crystal growth is investigated for isotactic polystyrene (it-PS) in thin films, the thickness of which is from 20nm down to 4nm. The single crystals of it-PS grown at 180 in the ultrathin films show the morphology typical in the diffusion-controlled growth: dense branching morphology (DBM), fractal seeweed (FS). The characteristic length of the morphology, i.e. the width of the branch, increases with decreasing film thickness. The thickness dependence of the growth rate of crystals shows a crossover around the lamellar thickness of the crystal, 8 nm. The thickness dependences of the growth rate and morphology are discussed in terms of the diffusion of chain molecules in thin films.

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Section: Resultsmentioning

confidence: 86%

Crystal Growth of Isotactic Polystyrene in Ultrathin Films: Film Thickness Dependence

Taguchi

Miyaji

Izumi

et al. 2002

Journal of Macromolecular Science, Part B

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“…It is important to note that eq 3, with the boundary conditions at the interface given by eqs 1 and 4, is similar to the equation used by Müller-Krumbhaar and collaborators [10][11][12][13][14][15] 20 That is, if eq 1 would be written as…”

Section: Resultsmentioning

confidence: 98%

Pattern Formation and Morphology Evolution in Langmuir Monolayers

et al. 2006

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We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. During domain growth, we found a morphology transition from tip splitting to side branching; doublons were also found. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: dioctadecylamine, ethyl palmitate, and ethyl stearate. In addition, we observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. For the case of dendritic morphologies, we measured the radius of the dendrite tip as a function of the dendrite length as well as the spacing of the side branches along a dendrite. Finally, a possible explanation of why Langmuir monolayers present this kind of nonequilibrium growth patterns is presented. In the steady state, the growth behavior is determined by Laplace's equation in the particle density with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted.

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“…Apparently, we have lost the general picture given by the diffusional model proposing the existence of a diffusion zone, which with eq 7 and the boundary conditions given by eqs 1 and 2, successfully explains the pattern formation and the morphology evolution in LMs. 27,28 In the same way, apparently, we have also lost the connection with the morphology diagram with regions of different morphological structures, [6][7][8][9][10][11] determined by the control parameters ∆ and ε, as explained above. Here, we will assess in what conditions the 2D hydrodynamic eq 4 can recover that picture related to pattern formation and to the morphology diagram.…”

Section: Morphology Evolution In Langmuirmentioning

confidence: 99%

Domain Growth, Pattern Formation, and Morphology Transitions in Langmuir Monolayers. A New Growth Instability

2010

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The aims of this study are the following two: (1) To show that in Langmuir monolayers (LM) at low supersaturation, domains grow forming fractal structures without an apparent orientational order trough tip splitting dynamics, where doublons are the building blocks producing domains with a seaweed shape. When supersaturation is larger, there is a morphology transition from tip splitting to side branching. Here, structures grow with a pronounced orientational order forming dendrites, which are also fractal. We observed this behavior in different Langmuir monolayers formed by nervonic acid, dioctadecylamine, ethyl stearate, and ethyl palmitate, using Brewster angle microscopy. (2) To present experimental evidence showing an important Marangoni flow during domain growth, where the hydrodynamic transport of amphipiles overwhelms diffusion. We were able to show that the equation that governs the pattern formation in LM is a Laplacian equation in the chemical potential with the appropriate boundary conditions. However, the underlying physics involved in Langmuir monolayers is different from the underlying physics in the Mullins-Sekerka instability; diffusional processes are not involved. We found a new kind of instability that leads to pattern formation, where Marangoni flow is the key factor. We also found that the equations governing pattern formation in LM can be reduced to those used in the theory of morphology diagrams for two-dimensional diffusional growth. Our experiments agree with this diagram.

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Kinetic Phase Diagram and Scaling Relations for Stationary Diffusional Growth

Cited by 124 publications

References 18 publications

Crystal Growth of Isotactic Polystyrene in Ultrathin Films: Film Thickness Dependence

Crystal Growth of Isotactic Polystyrene in Ultrathin Films: Film Thickness Dependence

Pattern Formation and Morphology Evolution in Langmuir Monolayers

Domain Growth, Pattern Formation, and Morphology Transitions in Langmuir Monolayers. A New Growth Instability

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