Early Stage of Spinodal Decomposition in 2D

Joly, Simon; Raquois, Agnes; Parı́s, F.; Hamdoun, B.; Auvray, Laurent; Ausserré, Dominique; Gallot, Yves

doi:10.1103/physrevlett.77.4394

Cited by 37 publications

(46 citation statements)

References 11 publications

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“…The Ostwald ripening of islands and holes may be easily followed and has provided significant insight into the motion of block copolymers into and out of these structures. Initially, islands and holes form randomly over the sample surface by a process analogous to spinodal decomposition [153,154]. Typically, the average size of the islands increases through coalescence of smaller domains and the growth of larger domains at the expense of smaller ones through an Ostwald ripening process [155][156][157][158][159][160][161][162].…”

Section: Thicker Films and Bulk Order Evolutionmentioning

confidence: 99%

Patterning with block copolymer thin films

Segalman

2005

Materials Science and Engineering: R: Reports

929

921

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The nanometer-scale architectures in thin films of self-assembling block copolymers have inspired a variety of new applications. For example, the uniformly sized and shaped nanodomains formed in the films have been used for nanolithography, nanoparticle synthesis, and high-density information storage media. Imperative to all of these applications, however, is a high degree of control over orientation of the nanodomains relative to the surface of the film as well as control over order in the plane of the film. Induced fields including electric, shear, and surface fields have been demonstrated to influence orientation. Both heteroepitaxy and graphoepitaxy can induce positional order on the nanodomains in the plane of the film. This article will briefly review a variety of mechanisms for gaining control over block copolymer order as well as many of the applications of these materials. Particular attention is paid to the potential of perfecting long-range two-dimensional order over a broader range of length scales and the extension of these concepts to functional materials and more complex architectures. #

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Section: Thicker Films and Bulk Order Evolutionmentioning

confidence: 99%

Patterning with block copolymer thin films

Segalman

2005

Materials Science and Engineering: R: Reports

929

921

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“…This last stage, as observed in two-dimensional demixion of copolymers [13] and as suggested initially by Langer [14], can be described as a process of synchronous fusion and evaporation of domains, spatially alternated. It corresponds to the evolution that breaks the least the symmetries of the pattern.…”

mentioning

confidence: 99%

1D Cahn–Hilliard dynamics: Ostwald ripening and application to modulated phase systems

Villain-Guillot¹

2008

Physics Letters A

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Using an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition, we compute the characteristic time for one step of period doubling in Langer's self similar scenario for Ostwald ripening. As an application, we compute the thermodynamically stable period of a 1D modulated phase pattern. * Electronic address: s.villain@cpmoh.u-bordeaux1.fr

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“…After an initial stage the wave amplitude grows, until it saturates, i.e. the maxima and minima reach the maximum and minimum of the free energy potential, and the symmetry with respect to the initial value of the field is lost [5]. Afterwards the clusters of the minority phase coalesce via diffusive annihilation of interfaces.…”

mentioning

confidence: 99%

Phase separation in systems with absorbing states

1998

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Abstract. -We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics, there are some basic properties differing from standard phase separation. We study analytically and numerically this class of systems; in particular we determine the phase diagram, the growth laws in one and two dimensions and the presence of scale invariance. Some applications are also discussed.The presence of conservation laws plays a key role in determining the phenomenology and critical behavior of phase transitions both in equilibrium and nonequilibrium systems. For instance, the dynamics of models for magnetism change dramatically depending on whether the order parameter is a conserved quantity or not [1]. In the conserving case, models may exhibit phenomena such as spinodal decomposition (SD hereafter) and droplet growth via condensation-evaporation [2, 3, 4], which are absent in models with non-conserving dynamics. The problem of SD that appears, for instance in binary alloys, polymers and spin systems with conserved magnetization, have attracted a lot of interest in the last decades [2,3,4], and despite the efforts devoted to understand their phenomenology, some of their aspects remain unclear. The key issue is that of understanding the dynamics of a system quenched from a state in the homogeneous phase into a broken-symmetry phase. Depending on the value of the conserved order parameter, M , different types of morphologies can show up. The archetypal field theory representing this class of systems is the model B (or Cahn-Hilliard equation), defined by the following Langevin equationTypeset using EURO-L A T E X

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Early Stage of Spinodal Decomposition in 2D

Cited by 37 publications

References 11 publications

Patterning with block copolymer thin films

Patterning with block copolymer thin films

1D Cahn–Hilliard dynamics: Ostwald ripening and application to modulated phase systems

Phase separation in systems with absorbing states

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