Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

Abstract

We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment of the relevant orientational degrees of freedom. Of particular interest is the construction of the nonlinear and coupling terms. This allows for interesting insights into the microscopic justification of phenomenological constructions used in PFC models for active particles and mixtures, the approximations required for obtaining them, and possible generalizations. Second, the derived model is investigated using linear stability analysis and nonlinear methods. It is found that the model allows for a rich nonlinear behavior with states ranging from steady periodic and localized states to various time-periodic states. The latter include standing, traveling, and modulated waves corresponding to spatially periodic and localized traveling, wiggling, and alternating peak patterns and their combinations.

25 pages, 7 figures

References in corpus (31)

• Motility-Induced Phase Separation
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Pressure and Phase Equilibria in Interacting Active Brownian Spheres
• Activity-induced phase separation and self-assembly in mixtures of active and passive particles
• Classical dynamical density functional theory: from fundamentals to applications
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Derivation of the phase field crystal model for colloidal solidification
• Morphology changes in the evolution of liquid two-layer films
• Small activity differences drive phase separation in active-passive polymer mixtures
• Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps
• Gradient dynamics models for liquid films with soluble surfactant
• Solidification fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids
• Active Brownian particles at interfaces: An effective equilibrium approach
• Dynamical Crystallites of Active Chiral Particles
• Phase behaviour and dynamical features of a two-dimensional binary mixture of active/passive spherical particles
• Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers
• Collective dynamics of active Brownian particles in three spatial dimensions: a predictive field theory
• Localized states in coupled Cahn-Hilliard equations
• Controlling the microstructure and phase behavior of confined soft colloids by active interaction switching
• Two-dimensional localized states in an active phase-field-crystal model
• Confinement-induced accumulation and spontaneous de-mixing of microscopic active-passive mixtures
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions
• Perspective: New directions in dynamical density functional theory
• How many ways a cell can move: the modes of self-propulsion of an active drop
• Localized states in passive and active phase-field-crystal models
• Efficient calculation of phase coexistence and phase diagrams: application to a binary phase-field crystal model
• Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles
• Containing a pandemic: Nonpharmaceutical interventions and the "second wave"
• Is thermodynamics fundamental?
• Active Brownian particles in external force fields: field-theoretical models, generalized barometric law, and programmable density patterns

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