Density functional theory of heterogeneous crystallization

Neuhaus, Tim; Härtel, Andreas; Maréchal, Matthieu; Schmiedeberg, Michael; Löwen, Hartmut

doi:10.1140/epjst/e2014-02097-x

Cited by 22 publications

(22 citation statements)

References 62 publications

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“…To do so, local structures are identified and measured both in the experiments and in a compatible atomistic simulation, and a discrete, coarsegrained model for the structural differentiation is provided. We reveal that the local crystallisation mechanism is dominated by quasi-equilibrium processes, consistently with previous work [29,30]: this result potentially justifies the employment of techniques based on the usage of modified diffusion equationsà la Smoluchowski, such as dynamical density functional theory or phase field models [28,31,32].…”

Section: Arxiv:160309174v1 [Cond-matsoft] 30 Mar 2016supporting

confidence: 86%

Crystallisation driven by sedimentation: a particle resolved study

Turci¹,

Royall²

2016

J. Stat. Mech.

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Abstract. We investigate the effects of the reversal of the gravitational field onto a sedimented and partially crystallised suspension of nearly-hard sphere colloids. We analyse the structural changes that take place during the melting of the crystalline regions and the reorganisation and assembly of the sedimenting particles. Through a comparison with numerical simulation, we access the single-particle kinetics and identify the key structural mechanism in the competition between five-fold symmetric and cubic crystalline structures. With the use of a coarse-grained, discrete model, we reproduce the kinetic network of reactions underpinning crystallisation and highlight the main microscopic transitions.

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Section: Arxiv:160309174v1 [Cond-matsoft] 30 Mar 2016supporting

confidence: 86%

Crystallisation driven by sedimentation: a particle resolved study

Turci¹,

Royall²

2016

J. Stat. Mech.

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“…The DDFT framework has been shown to successfully model a wide variety of phenomena, from hard rod and hard sphere systems [5], mixtures [31], to the calculation of the van Hove distribution function for Brownian hard spheres [32] and even crystallisation [33]. Nevertheless, DDFT itself has no inherent capability of describing processes governed by fluctuations since they are averaged out during the derivation from the LE.…”

Section: Introductionmentioning

confidence: 99%

General framework for fluctuating dynamic density functional theory

et al. 2017

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We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical densityfunctional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

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“…There have also been several efforts to test the derived DDFTs and their predictive capabilities. In fact there have been successful applications to a wide spectrum of physical settings, from hard rod and hard sphere systems 35 , mixtures 33 , thermodynamic phase transitions such as nucleation and spinodal decomposition 54,76 to the calculation of the van Hove distribution function for Brownian hard spheres 46 and crystallization 64 .…”

Section: Introductionmentioning

confidence: 99%

Dynamical Density Functional Theory for Orientable Colloids Including Inertia and Hydrodynamic Interactions

2016

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Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been generalised to take into account both inertia and hydrodynamic interactions, two effects which strongly influence non-equilibrium properties. The present work further generalises this framework to systems of anisotropic particles. Starting from the Liouville equation and utilising Zwanzig's projectionoperator techniques, we derive the kinetic equation for the Brownian particle distribution function, and by averaging over all but one particle, a DDFT equation is obtained. Whilst this equation has some similarities with DDFTs for spherically-symmetric colloids, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. We further show that, in the overdamped (high friction) limit, the DDFT is considerably simplified and is in agreement with a previous DDFT for colloids with arbitrary shape particles.

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Density functional theory of heterogeneous crystallization

Cited by 22 publications

References 62 publications

Crystallisation driven by sedimentation: a particle resolved study

Crystallisation driven by sedimentation: a particle resolved study

General framework for fluctuating dynamic density functional theory

Dynamical Density Functional Theory for Orientable Colloids Including Inertia and Hydrodynamic Interactions

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