The Landau free energy of hard ellipses obtained from microscopic simulations

Luo, Alan M.; Sagis, Leonard M.C.; Ilg, Patrick

doi:10.1063/1.4868988

Cited by 13 publications

(10 citation statements)

References 25 publications

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“…Metropolis MC using single-particle moves for hard ellipsoids without capillary interactions. [63] We then turn on capillary interactions for the VMMC run. Averages are taken over 20-50 independent runs, with each 10 5 MC sweeps taking roughly 1.5 − −2 hours on an Intel Xeon E5-2680v3 CPU, with the longer times relating to higher densities and aspect ratios.…”

Section: Simulation Detailsmentioning

confidence: 99%

“…This is to be contrasted with the results for k = 4 ellipsoids, where we find a smectic-like structure 4 , with both local and global 305 order. The initial configuration in this case is already ordered (since k = 4 hard ellipses at a density of η = 0.7 are in the nematic phase at equilibrium) [63] so the final structure is also ordered, with the capillary interaction imposing a smectic-like ordering on the nematic initial condition. On the other hand, the initial configuration of k = 2 hard ellipses at η = 0.7 is isotropic.…”

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confidence: 91%

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Self-assembly of ellipsoidal particles at fluid-fluid interfaces with an empirical pair potential

Luo

Vermant

Ilg

et al. 2019

Journal of Colloid and Interface Science

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Colloidal particles adsorbed at fluid-fluid interfaces interact via mechanisms that can be specific to the presence of interfaces, for instance, lateral capillary interactions induced by nonspherical particles. Capillary interactions are highly relevant for self-assembly and the formation of surface microstructures, however, these are very challenging to model due to the multibody nature of capillary interactions. This work pursues a direct comparison between our computational modelling approach and experimental results on surface microstructures formed by ellipsoidal particles. We begin by investigating the accuracy of using pairwise interactions to describe the multibody capillary interaction by contrasting exact two- and three-particle interaction energies and we find that the pairwise approximation appears reasonable for the experimentally relevant configurations studied. We then develop an empirical pair potential and use it in Monte-Carlo type simulations to efficiently model the structure formation process for relevant particle properties such as aspect ratio, contact angle and surface coverage, and succeed in reproducing our experimental observations where we spread sterically-stabilised ellipsoidal particles onto an oil-air interface at high surface coverage. At lower surface coverages, we find that the self-assembly process falls into the diffusion-limited colloid aggregation universality class.

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Section: Simulation Detailsmentioning

confidence: 99%

mentioning

confidence: 91%

Self-assembly of ellipsoidal particles at fluid-fluid interfaces with an empirical pair potential

Luo

Vermant

Ilg

et al. 2019

Journal of Colloid and Interface Science

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“…The Landau-de Gennes expansion coefficients a, T * , w and u can be determined from microscopic information by simulation [17,18] or by experimental information about the values of several quantities at the isotropic-nematic transition in the pure liquid crystal: the magnitude of the discontinuity of the nematization S, the temperature shift between the transition temperature, the limit of meta-stability T * , the phase-transition latent heat and the correlation length [19]. Elastic constants such as K can be calculated from microscopic information about the direct correlation function for the mesogens in a liquid crystal [20,21], or by analysis of long-wavelength director fluctuations using molecular simulations [22,23].…”

Section: Methodsmentioning

confidence: 99%

Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

et al. 2021

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We study nonlinear dynamical equations for coupled conserved and non-conserved fields describing nanoparticle concentration and liquid crystal order parameter, respectively, and solve them numerically over bidimensional domains. These equations model the rapid segregation of nanoparticles away from nematic domains, which has been observed experimentally in a suspension of gold nanoparticles in 5CB below the isotropic-nematic transition temperature. We contrast the different behaviors obtained when the LC order parameter is treated as a scalar or a tensor, as well as the different rates of evolution observed with each of these. We find, after an instantaneous quench lowering the temperature below the transition one, an initial linear regime where the ordering of the nematic phase proceeds exponentially with time. Only after a lag period the nanoparticle material couples effectively to the LC order parameter and segregates to regions that are less orientationally ordered (extended domain walls for a scalar order parameter, but point disclinations for a tensor one). The lag period is followed by the onset of nonlinear dynamics and saturation of the order parameter. The choice of a scalar or tensor LC order parameter does not change this sequence but results in a clear overshooting of the nonlinear saturation level for the tensor order parameter case. These results are found to be insensitive to weak anchoring due to coupling of gradients of the conserved and non-conserved variables, for the nanoparticle concentrations and anchoring parameters studied. Our modeling approach can be extended in a straightforward manner to cases where the cooling rate is finite and to other systems where a locally conserved concentration is coupled to a orientation field, such as active Langmuir monolayers, and possibly to other examples of nonlinear dynamics in ecological or excitable media problems.

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“…A system of hard ellipsoidal particles is among the simplest models of anisotropic particles. The phase behavior has been explored extensively by various theoretical approaches and simulations in both two-dimensional hard ellipses [14][15][16][17][18][19][20][21][22] and three-dimensional hard ellipsoids. [23][24][25][26][27][28][29][30] Recently, colloidal ellipsoids have been employed to experimentally explore a number of novel physical phenomena induced by particle shape.…”

Section: Introductionmentioning

confidence: 99%

“…The phase behavior has been explored extensively by various theoretical approaches and simulations in both two-dimensional hard ellipses [14][15][16][17][18][19][20][21][22] and three-dimensional hard ellipsoids.…”

Section: -13mentioning

confidence: 99%

Glass formation in a mixture of hard disks and hard ellipses

Duan

Sun

et al. 2015

The Journal of Chemical Physics

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We present an event-driven molecular dynamics study of glass formation in two-dimensional binary mixtures composed of hard disks and hard ellipses, where both types of particles have the same area. We demonstrate that characteristic glass-formation behavior appears upon compression under appropriate conditions in such systems. In particular, while a rotational glass transition occurs only for the ellipses, both types of particles undergo a kinetic arrest in the translational degrees of freedom at a single density. The translational dynamics for the ellipses is found to be faster than that for the disks within the same system, indicating that shape anisotropy promotes the translational motion of particles. We further examine the influence of mixture's composition and aspect ratio on the glass formation. For the mixtures with an ellipse aspect ratio of k = 2, both translational and rotational glass transition densities decrease with increasing the disk concentration at a similar rate and hence, the two glass transitions remain close to each other at all concentrations investigated. By elevating k, however, the rotational glass transition density diminishes at a faster rate than the translational one, leading to the formation of an orientational glass for the ellipses between the two transitions. Our simulations imply that mixtures of particles with different shapes emerge as a promising model for probing the role of particle shape in determining the properties of glass-forming liquids. Furthermore, our work illustrates the potential of using knowledge concerning the dependence of glass-formation properties on mixture's composition and particle shape to assist in the rational design of amorphous materials.

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The Landau free energy of hard ellipses obtained from microscopic simulations

Cited by 13 publications

References 25 publications

Self-assembly of ellipsoidal particles at fluid-fluid interfaces with an empirical pair potential

Self-assembly of ellipsoidal particles at fluid-fluid interfaces with an empirical pair potential

Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

Glass formation in a mixture of hard disks and hard ellipses

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