Nonequilibrium adsorption of 2AnB patchy colloids on substrates

We study the irreversible adsorption of spherical $2AnB$ patchy colloids (with two $A$-patches on the poles and $n$ $B$-patches along the equator) on a substrate. In particular, we consider dissimilar $AA$, $AB$, and $BB$ binding probabilities. We characterize the patch-colloid network and its dependence on $n$ and on the binding probabilities. Two growth regimes are identified with different density profiles and we calculate a growth mode diagram as a function of the colloid parameters. We also find that, close to the substrate, the density of the network, which depends on the colloid parameters, is characterized by a depletion zone

Nonequilibrium self-organization of colloidal particles on substrates: adsorption, relaxation, and annealing

Colloidal particles are considered ideal building blocks to produce materials with enhanced physical properties. The state-of-the-art techniques for synthesizing these particles provide control over shape, size, and directionality of the interactions. In spite of these advances, there is still a huge gap between the synthesis of individual components and the management of their spontaneous organization towards the desired structures. The main challenge is the control over the dynamics of self-organization. In their kinetic route towards thermodynamically stable structures, colloidal particles self-organize into intermediate (mesoscopic) structures that are much larger than the individual particles and become the relevant units for the dynamics. To follow the dynamics and identify kinetically trapped structures, one needs to develop new theoretical and numerical tools. Here we discuss the self-organization of functionalized colloids (also known as patchy colloids) on attractive substrates. We review our recent results on the adsorption and relaxation and explore the use of annealing cycles to overcome kinetic barriers and drive the relaxation towards the targeted structures

Adsorbed films of three-patch colloids: Continuous and discontinuous transitions between thick and thin films

We investigate numerically the role of spatial arrangement of the patches on the irreversible adsorption of patchy colloids on a substrate. We consider spherical three-patch colloids and study the dependence of the kinetics on the opening angle between patches. We show that growth is suppressed below and above minimum and maximum opening angles, revealing two absorbing phase transitions between thick and thin film regimes. While the transition at the minimum angle is continuous, in the Directed Percolation class, that at the maximum angle is clearly discontinuous. For intermediate values of the opening angle, a rough colloidal network in the Kardar-Parisi-Zhang universality class grows indefinitely. The nature of the transitions was analyzed in detail by considering bond flexibility, defined as the dispersion of the angle between the bond and the center of the patch. For the range of flexibilities considered we always observe two phase transitions. However, the range of opening angles where growth is sustained increases with flexibility. At a tricritical flexibility, the discontinuous transition becomes continuous. The practical implications of our findings and the relation to other nonequilibrium transitions are discussed

Kinetic interfaces of patchy particles

We study the irreversible adsorption of patchy particles on substrates in the limit of advective mass transport. Recent numerical results show that the interface roughening depends strongly on the particle attributes, such as, patch-patch correlations, bond flexibility, and strength of the interactions, uncovering new absorbing phase transitions. Here, we revisit these results and discuss in detail the transitions. In particular, we present new evidence that the tricritical point, observed in systems of particles with flexible patches, is in the tricritical directed percolation universality class. A scaling analysis of the time evolution of the correlation length for the aggregation of patchy particles with distinct bonding energies confirms that the critical regime is in the Kardar-Parisi-Zhang with quenched disorder universality class

Dynamics of patchy particles in and out of equilibrium

We combine particle-based simulations, mean-field rate equations, and Wertheim's theory to study the dynamics of patchy particles in and out of equilibrium, at different temperatures and densities. We consider an initial random distribution of non-overlapping three-patch particles, with no bonds, and analyze the time evolution of the breaking and bonding rates of a single bond. We find that the asymptotic (equilibrium) dynamics differs from the initial (out of equilibrium) one. These differences are expected to depend on the initial conditions, temperature, and density

Optimal number of linkers per monomer in linker-mediated aggregation

We study the dynamics of diffusion-limited irreversible aggregation of monomers, where bonds are mediated by linkers. We combine kinetic Monte Carlo simulations of a lattice model with a mean-field theory to study the dynamics when the diffusion of aggregates is negligible and only monomers diffuse. We find two values of the number of linkers per monomer which maximize the size of the largest aggregate. We explain the existence of the two maxima based on the distribution of linkers per monomer. This observation is well described by a simple mean-field model. We also show that a relevant parameter is the ratio of the diffusion coefficients of monomers and linkers. In particular, when this ratio is close to ten, the two maxima merge at a single maximum

Field-driven dynamical demixing of binary mixtures

We consider mixtures of two species of spherical colloidal particles that differ in their hydrodynamic radii, but are otherwise identical, in the presence of an external field. Since the particle-particle and particle-field interactions are the same for both species, they are completely mixed in the thermodynamic limit in the presence of any static field. Here, we combine Brownian Dynamics and Dynamic Density Functional theory of fluids to show that for sufficiently large differences in the hydrodynamic radius of the particles (and corresponding differences in their electrophoretic mobilities) dynamical demixing is observed. These demixed states are transient but, under certain conditions, packing effects compromise the relaxation towards the thermodynamic states and the lifetime of the demixed phases increases significantly

Crossover from three- to six-fold symmetry of colloidal aggregates in circular traps

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap

How the site degree influences quantum probability on inhomogeneous substrates

We investigate the effect of the node degree and energy $E$ on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependence of the quantum probability for each site on its degree. For bi-regular structures, we prove analytically that the probability $P_k(E)$ of finding the particle on any site with $k$ neighbors is independent of $E$. For more general structures, the dependency of $P_k(E)$ on $E$ is discussed by taking into account exact results on a one-dimensional semi-regular chain: $P_k(E)$ is large for small values of $E$ when $k$ is also small, and its maximum values shift towards large values of $|E|$ with increasing $k$. Numerical evaluations of $P_k(E)$ for two different types of percolation clusters and the Apollonian network suggest that this feature might be generally validComment: 19 pages, 6 figures, original articl

The magnetocaloric effect from the point of view of Tsallis non-extensive thermostatistics

In this work we have analyzed the magnetocaloric effect (MCE) from the Tsallis thermostatistics formalism (TTF) point of view. The problem discussed here is a two level system MCE. We have calculated, both analytically and numerically, the entropy of this system as a function of the Tsallis' parameter (the well known q-parameter) which value depends on the extensivity (q<1) or non-extensivity (q>1) of the system. Since we consider this MCE not depending on the initial conditions, which classify our system as a non-extensive one, we used several greater than one q-parameters to understand the effect of the nonextensive formalism in the entropy as well as the magnetocaloric potential, $\Delta S$. We have plotted several curves that shows precisely the behavior of this effect when dealt with non-extensive statistics.Comment: 11 pages. 10 figures. Preprint forma