Polar liquid crystals in two spatial dimensions: The bridge from microscopic to macroscopic modeling

Wittkowski, Raphael; Löwen, Hartmut; Brand, Helmut R.

doi:10.1103/physreve.83.061706

Cited by 32 publications

(66 citation statements)

References 104 publications

(249 reference statements)

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“…The equations (1) and (2) are consistent with phenomenological symmetry arguments and involve the simplest nontrivial coupling between the two order parameter fields ψ 1 and P. As outlined in the supplemental material [31], they can also be derived from microscopic dynamical density functional theory within an appropriate gradient and Taylor expansion of the order parameter fields [19,32], see also [33].…”

Section: Arxiv:12093537v1 [Cond-matsoft] 17 Sep 2012mentioning

confidence: 93%

Traveling and Resting Crystals in Active Systems

2013

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A microscopic field theory for crystallization in active systems is proposed which unifies the phase-field-crystal model of freezing with the Toner-Tu theory for self-propelled particles. A wealth of different active crystalline states are predicted and characterized. In particular, for increasing strength of self-propulsion, a transition from a resting crystal to a traveling crystalline state is found where the particles migrate collectively while keeping their crystalline order. Our predictions, which are verifiable in experiments and in particle-resolved computer simulations, provide a starting point for the design of new active materials. PACS numbers: 64.70.dm,87.18.Gh,82.70.Dd Self-propelled particles [1] exhibit fascinating collective phenomena like swarming, swirling and laning which have been intensely explored by theory, simulation and experiment, for recent reviews see [2][3][4]. In marked contrast to passive particles, self-propelled "active" particles have an internal motor of propulsion, dissipate energy and are therefore intrinsically in nonequilibrium. Examples of active particles include living systems, like bacteria and microbes [5], as well as man-made microswimmers, catalytically driven colloids [6,7] and granular hoppers [8].If, at high densities, the particle interaction dominates the propulsion, crystallization in an active system is conceivable. It is expected that such "active crystals" have structural and dynamical properties largely different from equilibrium crystals due to the intrinsic drive. In fact, there is experimental evidence for active crystals, both from observations of hexagonal structures for catalytically-driven colloids [9] and honeycomb-like textures for flagellated marine bacteria [10,11]. Moreover, recent computer simulations have confirmed crystallization [12][13][14] and proved that melting of active crystals differs from its equilibrium counterpart. However, though field-theoretical modelling of active systems has been widely applied to orientational ordering phenomena [2,15], there is no such theory for translational ordering of active crystals nor has a systematic classification of active crystals been achieved.Here we present a microscopic field-theoretical approach to crystallization in active systems and we propose a minimal model which has the necessary ingredients for both, crystallization and activity. In doing so, we combine the phase-field crystal model of freezing [16] with the Toner-Tu model for active systems [17] using the concept of dynamical density functional theory [18,19]. On the one hand, the phase-field-crystal (PFC) model as originally introduced by Elder and coworkers [16,20] describes crystallization of passive particles on microscopic length and diffusive time scales. When brought into connection with dynamical density functional theory [21][22][23][24], the PFC model represents in principle a microscopic theory for crystallization, and it has been successfully applied to a plethora of solidification phenomena [16,20,[25][26][27][28][29]...

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Section: Arxiv:12093537v1 [Cond-matsoft] 17 Sep 2012mentioning

confidence: 93%

Traveling and Resting Crystals in Active Systems

2013

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“…Our dissipation functional is especially useful, if some of the relevant variables have to be parametrized and dynamical equations for the parameterizing quantities are needed. This is particularly the case in the derivation of PFC models [18][19][20][21] from EDDFT. Our theory can be applied by approximating the diffusion tensor in equation (47) and the transport matrices in equations (49) and (50) by the corresponding expressions in the hydrodynamic limit (see section 4.4.2).…”

Section: Discussionmentioning

confidence: 99%

“…In fact, these functions are assumed to be linear and homogeneous [31]. With this assumption, it is obvious that the dissipative currents J , t ), respectively, can be derived from a given dissipation functional R using equations (19). Analogously, the dissipative entropy current J σ D ( r, t ) can be derived:…”

Section: Nonequilibrium Dynamicsmentioning

confidence: 99%

Microscopic approach to entropy production

Wittkowski¹,

Löwen²,

Brand³

2013

J. Phys. A: Math. Theor.

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It is a great challenge of nonequilibrium statistical mechanics to calculate entropy production within a microscopic theory. In the framework of linear irreversible thermodynamics, we combine the Mori-Zwanzig-Forster projection operator technique with the first and second law of thermodynamics to obtain microscopic expressions for the entropy production as well as for the transport equations of the entropy density and its time correlation function. We further present a microscopic derivation of a dissipation functional from which the dissipative dynamics of an extended dynamical density functional theory can be obtained in a formally elegant way.

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“…The dynamic equations of ψ( r, t) and Q ij ( r, t) are deduced from classical dynamical density functional theory (DDFT), as written by [21,22],…”

Section: B Dynamic Equationsmentioning

confidence: 99%

“…Unlike growth into the isotropic phase, the growth kinetics is very anisotropic for small A 1 . That is, the growth of the crystal facet in [12]direction is faster than the growth of the [21]-facet. This leads to a smaller [12]-facet compared to the [21]-facet of the stationary crystal.…”

Section: Crystal Shape Of Ptc In Csa Phasementioning

confidence: 99%

Two-dimensional liquid crystalline growth within a phase-field-crystal model

et al. 2015

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By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from a isotropic phase is compared with that grown from a columnar/smectic A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of a classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process we analyse the topological structure of the nematic-order, which starts from nucleation of + disclinations. It is found that the orientational and the positional order do not evolve simultaneously, the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

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Polar liquid crystals in two spatial dimensions: The bridge from microscopic to macroscopic modeling

Cited by 32 publications

References 104 publications

Traveling and Resting Crystals in Active Systems

Traveling and Resting Crystals in Active Systems

Microscopic approach to entropy production

Two-dimensional liquid crystalline growth within a phase-field-crystal model

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