Kinetics of ordering in fluctuation-driven first-order transitions: Simulation and theory

Gross, N. A.; Ignatiev, Michael O.; Chakraborty, Bulbul

doi:10.1103/physreve.62.6116

Cited by 13 publications

(8 citation statements)

References 26 publications

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“…They obtained the free energy barriers to nucleation and the shape and size of critical droplets in the weak coupling limit. Gross et al [10] compared the predictions of the self consistent Hartree approximation with direct simulations of the Langevin dynamics, confirming the validity of the approximation.…”

Section: Introductionmentioning

confidence: 81%

Langevin dynamics of fluctuation-induced first-order phase transitions: Self-consistent Hartree approximation

Mulet¹,

Stariolo²

2007

Phys. Rev. B

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The Langevin dynamics of a system with a scalar-order parameter exhibiting a fluctuation-induced firstorder phase transition is solved within the self-consistent Hartree approximation. Competition between interactions on short and long length scales gives rise to spatial modulations in the order parameter, such as stripes in 2d and lamellae in 3d. We show that when the time scale of observation is small compared with the time needed for the formation of modulated structures, the dynamics is dominated by a standard ferromagnetic contribution plus a correction term. However, once these structures are formed, the long-time dynamics is no longer purely ferromagnetic. After a quench from a disordered state to low temperatures, the system develops growing domains of stripes ͑lamellae͒. Due to the character of the transition, the paramagnetic phase is metastable at all finite temperatures, and the correlation length diverges only at T = 0. Consequently, the temperature is a relevant variable: for T Ͼ 0 the system ends up forming domains of stripes with a finite correlation length while for T = 0 a scaling behavior in space and time, characteristic of smectic order, is obtained.

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Section: Introductionmentioning

confidence: 81%

Langevin dynamics of fluctuation-induced first-order phase transitions: Self-consistent Hartree approximation

Mulet¹,

Stariolo²

2007

Phys. Rev. B

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“…Here, a straightforward choice for the cut-off length is the interparticle/interatomic distance, which then removes the unphysical, small wavelength fluctuations [27,28,42,164]. A more elegant handling of the problem is via renormalizing the model parameters so that with noise one recovers the "bare" physical properties (as outlined for the Swift-Hohenberg model in reference [197]). Further systematic investigations are yet needed to settle this issue.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, the addition of noise to the EOM changes the free energy, the phase diagram, and the interfacial properties. While, in principle, correction of these is possible via parameter renormalisation [196,197], further study is needed in the case of PFC models. On the other hand, the original free-energy functional used in (i) seems to miss the effect of longer wavelength fluctuations, which could move the system out of a metastable state.…”

Section: Phase-field-crystal Models Applied To Nucleation and Patternmentioning

confidence: 99%

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Emmerich

Löwen

Wittkowski

et al. 2012

Advances in Physics

350

417

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Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic-and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Keywords: phase-field-crystal (PFC) models, static and dynamical density functional theory (DFT and DDFT), condensed matter dynamics of liquid crystals and polymers, nucleation and pattern formation, simulations in materials science, colloidal crystal growth and growth anisotropy * Corresponding authors. Emails: heike.emmerich@uni-bayreuth. de, hlowen@thphy.uni-duesseldorf.de, and grana@szfki.hu

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“…A variety of transitions in morphology and orientation occur as shear rate and temperature are changed. Stable configurations of lamellae lying along the flow with the normals differently oriented have been observed [9,10] and analyzed evaluating the effects of the flow on the fluctuation spectra [11,12,13,14].Non-stationary properties are far less considered [15,16,17,18]. In this Letter we study the effects of a simple planar shear flow on the ordering of the lamellar phase in a system quenched from an initially high temperature disordered state.…”

mentioning

confidence: 99%

“…Non-stationary properties are far less considered [15,16,17,18]. In this Letter we study the effects of a simple planar shear flow on the ordering of the lamellar phase in a system quenched from an initially high temperature disordered state.…”

mentioning

confidence: 99%

Ordering of the lamellar phase under a shear flow

2002

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The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion equation. Lamellae order preferentially with the normal along the vorticity direction. Typical lengths grow as γt 5/4 (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D = 3. [6]. A theoretical model for the general description of the lamellar-disordered phase transition was proposed by Brazovskii [7] who showed the first-order character of the transition induced by fluctuations.Lamellar phases under an applied shear flow show a very rich behavior which is relevant for many applications [8]. A variety of transitions in morphology and orientation occur as shear rate and temperature are changed. Stable configurations of lamellae lying along the flow with the normals differently oriented have been observed [9,10] and analyzed evaluating the effects of the flow on the fluctuation spectra [11,12,13,14].Non-stationary properties are far less considered [15,16,17,18]. In this Letter we study the effects of a simple planar shear flow on the ordering of the lamellar phase in a system quenched from an initially high temperature disordered state. We present the first analytical results on the kinetics of this system by solving the Brazovskii model in the limit of an infinite number of components of the order parameter. This is one of the few methods allowing an explicit solution for phase ordering systems [19]. A similar approach for fluids under shear flow has been used in [20,21,22,23,24,25,26,27].The behavior of quenched binary mixtures without imposed flows is characterized by dynamical scaling: The structure factor obeys C( k, t) = R(t) D f [kR(t)] where R(t) ∼ t α is the typical domain size and D is the space dimensionality [28,19]. In the case of a fluid with lamellar order, if the order parameter is not conserved as in the Swift-Hohenberg model for Raleigh-Bénard convection [29], regimes exhibiting dynamical scaling have been found [30]. In models with conserved order parameter, when diffusion is the only segregating physical mechanism, simulations show the entanglement of the fluid into frozen intertwined structures [31,32]. In this case the effects of hydrodynamical modes are crucial for reaching order on large scales [33].When shear is applied, our results show that lamellae grow preferentially with the perpendicular orientation [12], namely along the plane formed by the flow and the shear (velocity gradient) directions. Their typical size, obtained from the second momentum of the structure factor, grows as γt 5/4 √ ln t in the flow direction and as √ ln t in the shear direction. Surprisingly we find that dynamical scaling is obeyed in two dimensions but not in D = 3. Our results concern the cases of conserved and not conserved order parameter, and apply ...

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Kinetics of ordering in fluctuation-driven first-order transitions: Simulation and theory

Cited by 13 publications

References 26 publications

Langevin dynamics of fluctuation-induced first-order phase transitions: Self-consistent Hartree approximation

Langevin dynamics of fluctuation-induced first-order phase transitions: Self-consistent Hartree approximation

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Ordering of the lamellar phase under a shear flow

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