arXiv subjects

Raphael Wittkowski

Publications and source records attributed to Raphael Wittkowski.

77 records · Page 5Linked to original sources

arXiv2011

Dynamical density functional theory for colloidal particles with arbitrary shape

Starting from the many-particle Smoluchowski equation, we derive dynamical density functional theory for Brownian particles with an arbitrary shape. Both passive and active (self-propelled) particles are considered. The resulting theory constitutes a microscopic framework to explore the collective dynamical behavior of biaxial particles in nonequilibrium. For spherical and uniaxial particles, earlier derived dynamical density functional theories are recovered as special cases. Our study is motivated by recent experimental progress in preparing colloidal particles with many different biaxial shapes.

cond-mat.soft↗

arXiv2011

Brownian dynamics of a self-propelled particle in shear flow

Brownian dynamics of a self-propelled particle in linear shear flow is studied analytically by solving the Langevin equation and in simulation. The particle has a constant propagation speed along a fluctuating orientation and is additionally subjected to a constant torque. In two spatial dimensions, the mean trajectory and the mean square displacement (MSD) are calculated as functions of time t analytically. In general, the mean trajectories are cycloids that are modified by finite temperature effects. With regard to the MSD different regimes are identified where the MSD scales with t^a with a = 0,1,2,3,4. In particular, an accelerated (a = 4) motion emerges if the particle is self-propelled along the gradient direction of the shear flow.

cond-mat.soft↗

arXiv2011

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

Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions. Starting from microscopic density functional theory, we derive a phase-field-crystal expression for the free-energy density which involves three local order-parameter fields, namely the translational density, the polarization, and the nematic order parameter. Various coupling terms between the order-parameter fields are obtained which are in line with macroscopic considerations. Since the coupling constants are brought into connection with the molecular correlations, we establish a bridge from microscopic to macroscopic modeling. Our theory provides a starting point for further numerical calculations of the stability of polar liquid-crystalline phases and is also relevant for modeling of microswimmers which are intrinsically polar.

cond-mat.soft↗

arXiv2011

Stability of liquid crystalline phases in the phase-field-crystal model

The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order parameter, and the mean local direction of the orientations. The equilibrium free-energy functional involves local powers of the order parameters up to fourth order, gradients of the order parameters up to fourth order, and different couplings between the order parameters. The stable phases of the equilibrium free-energy functional are calculated for various coupling parameters. Among the stable liquid-crystalline states are the isotropic, nematic, columnar, smectic A, and plastic crystalline phases. The plastic crystals can have triangular, square, and honeycomb lattices and exhibit orientational patterns with a complex topology involving a sublattice with topological defects. Phase diagrams were obtained by numerical minimization of the free-energy functional. Their main features are qualitatively in line with much simpler one-mode approximations for the order parameters.

cond-mat.soft↗

arXiv2010

Derivation of a three-dimensional phase-field-crystal model for liquid crystals from density functional theory

Using a generalized order parameter gradient expansion within density functional theory, we derive a phase-field-crystal model for liquid crystals composed by apolar particles in three spatial dimensions. Both the translational density and the orientational direction and ordering are included as order parameters. Different terms involving gradients in the order parameters in the resulting free energy functional are compared to the macroscopic Ginzburg-Landau approach as well as to the hydrodynamic description for liquid crystals. Our approach provides microscopic expressions for all prefactors in terms of the particle interactions. Our phase-field-crystal model generalizes the conventional phase-field-crystal model of spherical particles to orientational degrees of freedom and can be used as a starting point to explore phase transitions and interfaces for various liquid-crystalline phases.

cond-mat.soft↗