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In this study, Brownian Dynamics simulations are implemented to investigate the motion of a bottom-heavy Janus particle near a wall under varying shear flow conditions and at small P\'eclet (Pe) numbers. The stochastic motion of the Janus particle impacted by surface forces is described using a set of coupled Langevin equations that takes into account the Janus particle orientation. Interactions arising from surface potentials are found to depend on the separation distance between the Janus particle and the wall, the properties of the surfaces involved, and the thickness of the Janus particle cap. When shear flow is introduced in the system, the dynamical behavior of the Janus particle is also governed by the strain rate. Furthermore, the effect of friction on the dynamical behavior of the Janus particle under shear flow is investigated and reveals that the rotational motion of the Janus particle slows down slightly when the particle is close to the surface. In summary, we demonstrate the ability to utilize Brownian Dynamics simulations to capture the rich dynamical behavior of a bottom-heavy Janus particle near a wall and under a range of shear flow conditions, cap thicknesses, and surface charges.

Nano- to micro-sized particles with differently charged surface areas exhibit complex interaction patterns, characterized by both opposite-charge attraction and like-charge repulsion. While several successful models have been proposed in the literature to describe directional attraction, models accounting for both directional attraction and directional repulsion are much less numerous and often tailored to specific microscopic systems. Here we present a simple and versatile patchy model, where the interaction energy of a pair of particles is a sum of interactions between sites of different types located within the particle volume. We implement different formulations of this model in both a self-developed Monte Carlo code and the widely used LAMMPS Molecular Dynamics simulation software, providing basic toolkits for both simulation methods and, in the latter case, for different algorithms. By comparing physical observables and code performances, we discuss the different models, methods, and algorithms, offering insights into optimization strategies and tricks of trade., Comment: main: 14 pages, 5 figures; supplemental: 17 pages, 10 figures

The behaviour and stability of soft and biological matter depend significantly on electrostatic interactions, as particles such as proteins and colloids acquire a charge when dispersed in an electrolytic solution. A typical simplification used to understand bulk phenomena involving electrostatic interactions is the isotropy of the charge on the particles. However, whether arising naturally or by synthesis, charge distributions are often inhomogeneous, leading to an intricate particle-particle interaction landscape and complex assembly phenomena. The fundamental complexity of these interactions gives rise to models based on distinct assumptions and varying degrees of simplifications which can blur the line between genuine physical behaviour and artefacts arising from the choice of a particular electrostatic model. Building upon the widely-used linearized Poisson-Boltzmann theory, we propose a theoretical framework that -- by bridging different models -- provides a robust DLVO-like description of electrostatic interactions between inhomogeneously charged particles. By matching solely the {\em single-particle} properties of two different mean-field models, we find a quantitative agreement between the {\em pair interaction energies} over a wide range of system parameters. Our work identifies a strategy to merge different models of inhomogeneously charged particles and paves the way to a reliable, accurate, and computationally affordable description of their interactions., Comment: 10 pages, 5 figures (main) plus 7 pages, 2 figures (supplemental)

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases, via the formation of so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other - referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e. V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate -- by means of both Molecular Dynamics and Monte Carlo simulations -- the described two-step process: we first optimize a target bent-core unit and we then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

Recently synthesized colloids and biological systems such as proteins, viruses and monoclonal antibodies are heterogeneously charged, i.e., different regions of their surfaces carry different amount of positive or negative charge. Because of charge anisotropy, the electrostatics interactions between these units through the surrounding medium are intristically anisotropic, meaning that they are characterized not only by the attraction between oppositely-charged regions but also by the repulsion between like-charged areas. Recent experiments have shown that the liquid-liquid phase separation of these systems can be driven by anisotropic electrostatics interactions, but it is not clear how the emerging aggregates are affected by charge imbalance and charge patchiness. The ability to experimentally control these two quantities calls for a theoretical understanding of their interplay, which we address here at the critical point. We consider a coarse grained model of anisotropically charged hard spheres whose interaction potential is grounded in a robust mean field theory and perform extensive numerical Monte Carlo simulations to understand the aggregation behavior of these units at the critical point. Stemming from the simplicity of the model, we address the interplay between charge imbalance and charge patchiness with the use of three parameters only and fully rationalize how these features impact the critical point of the model by means of thermodynamic-independent pair properties.

Nanometer-sized clusters are often targeted due to their potential applications as nanoreactors or storage/delivery devices. One route to assemble and stabilize finite structures consists in imparting directional bonding patterns between the nanoparticles. When only a portion of the particle surface is able to form an inter-particle bond, finite-size aggregates such as micelles and vesicles may form. Building on this approach, we combine particle shape anisotropy with the directionality of the bonding patterns and investigate the combined effect of particle elongation and surface patchiness on the low density assembly scenario. To this aim, we study the assembly of tip-functionalised Janus hard spherocylinder by means of Monte Carlo simulations. By exploring the effects of changing the interaction strength and range at different packing fractions, we highlight the role played by shape and bond anisotropy on the emerging aggregates (micelles, vesicles, elongated micelles and lamellae). We observe that shape anisotropy plays a crucial role in suppressing phases that are typical to spherical Janus nanoparticles and that a careful tuning of the interaction parameters allows to promote the formation of spherical micelles. These finite-size spherical clusters composed of elongated particles might offer more interstitials and larger surface areas than those offered by micelles of spherical or almost-spherical units, thus enhancing their storage and catalytic properties.

In recent years, experimental and theoretical investigations have shown that anisotropic colloids can self-organise into ordered porous monolayers, where the interplay of localised bonding sites, so called patches, with the particle's shape is responsible for driving the systems away from close-packing and towards porosity. Until now it has been assumed that patchy particles have to be fully bonded with their neighbouring particles for crystals to form, and that, if full bonding cannot be achieved due to the choice of patch placement, disordered assemblies will form instead. In contrast, we show that by deliberately displacing the patches such that full bonding is disfavored, a different route to porous crystalline monolayers emerges, where geometric frustration and partial bonding are pivotal in the structure formation process. The resulting dangling bonds lead to the emergence of effectively chiral units which then act as building blocks for energetically equivalent crystal polymorphs., Comment: 15 pages, 10 figures, Electronic Supporting Information included at the end

Globular proteins as well as recently synthesized colloids engineered with differently charged surface regions have in common a reduced bonding valence and a complex interaction pattern dominated by like-charge attraction and opposite-charge repulsion. While the impact of low functionality on the condensation of the liquid phase has been extensively studied, the combined effect of limited bonding valence and particle charge heterogeneity on the liquid-liquid phase separation has not been investigated yet. We numerically tackle this challenge in a systematic fashion by taking advantage of an efficient coarse-grained model grounded into a robust mean-field description. We consider a relatively simple surface pattern consisting of two charged polar caps and an oppositely charged equatorial belt and investigate how the interplay between geometry and electrostatics affect the critical point parameters. We find that electrostatics has a dramatic effect on the condensation of the liquid phase -- especially in the regime of large polar caps., Comment: 12 pages, 8 figures