Monte Carlo computer simulation of sedimentation of charged hard spherocylinders

A cutoff-based method with charge-distribution-data driven pair potentials for efficiently estimating electrostatic interactions in molecular systems

We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.

Pre-Smectic Ordering and the Unwinding Helix in Monte Carlo Simulations of Cholesteric Liquid-Crystals

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.

Reduced-variance orientational distribution functions from torque sampling

We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.

Effect of sample height and particle elongation in the sedimentation of colloidal rods

We study theoretically the effect of a gravitational field on the equilibrium behaviour of a colloidal suspension of rods with different length-to-width aspect ratios. The bulk phases of the system are described with analytical equations of state. The gravitational field is then incorporated via sedimentation path theory, which assumes a local equilibrium condition at each altitude of the sample. The bulk phenomenology is significantly enriched by the presence of the gravitational field. In a suspension of elongated rods with five stable phases in bulk, the gravitational field stabilizes up to fifteen different stacking sequences. The sample height has a non-trivial effect on the stable stacking sequence. New layers of distinct bulk phases appear either at the top, at the bottom, or simultaneously at the top and the bottom when increasing the sample height at constant colloidal concentration. We also study sedimentation in a mass-polydisperse suspension in which all rods have the same shape but different buoyant masses.

Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.

Assessment of the Wolf method using the Stillinger-Lovett sum rules: From strong electrolytes to weakly charged colloidal dispersions

The Ewald method has been the cornerstone in molecular simulations for modeling electrostatic interactions of charge-stabilized many-body systems. In the late 1990s, Wolf and collaborators developed an alternative route to describe the long-range nature of electrostatic interactions; from a computational perspective, this method provides a more efficient and straightforward way to implement long-range electrostatic interactions than the Ewald method. Despite these advantages, the validity of the Wolf potential to account for the electrostatic contribution in charged fluids remains controversial. To alleviate this situation, in this contribution, we implement the Wolf summation method to both electrolyte solutions and charged colloids with moderate size and charge asymmetries in order to assess the accuracy and validity of the method. To this end, we verify that the proper selection of parameters within the Wolf method leads to results that are in good agreement with those obtained through the standard Ewald method and the theory of integral equations of simple liquids within the so-called hypernetted chain approximation. Furthermore, we show that the results obtained with the original Wolf method do satisfy the moment conditions described by the Stillinger-Lovett sum rules, which are directly related to the local electroneutrality condition and the electrostatic screening in the Debye-Hückel regime. Hence, the fact that the solution provided by the Wolf method satisfies the first and second moments of Stillinger-Lovett proves, for the first time, the reliability of the method to correctly incorporate the electrostatic contribution in charge-stabilized fluids. This makes the Wolf method a powerful alternative compared to more demanding computational approaches.