arXiv subjects

J. M. Tavares

Publications and source records attributed to J. M. Tavares.

18 recordsLinked to original sources

arXiv2025

Rigid m-percolation in limited-valence gels

Determining the onset of rigidity in gels is a fundamental challenge with significant practical implications across different applications. Limited-valence, or patchy-particle systems have proven to be a valuable model to study the relationship between microscopic interactions and macroscopic mechanical properties. It has been suggested that the emergence of rigidity coincides with the formation of an infinitely spanning cluster of particles with at least three bonds. This work explores this hypothesis, its implications, and its broader applicability across a range of system parameters, by associating the emergence of rigidity with m-percolation transition for m=3. The properties of m-percolation are developed using a mean-field theoretical approach validated with numerical simulations, and used to build phase and rigidity diagrams for different particle valences of both single-component systems and binary mixtures of patchy particles. The difference between connectivity and rigidity percolation thresholds is found to reduce with increasing valence, providing an explanation for the challenges encountered in experimental attempts to distinguish isotropic connectivity percolation from the onset of rigidity. For binary mixtures, we found a robust minimum average valence, below which the gel is never rigid.

cond-mat.soft↗

arXiv2022

Percolation in binary mixtures of linkers and particles: chaining {\it {vs}} branching

Equilibrium gels of colloidal particles can be realized through the introduction of a second species, a linker that mediates the bonds between the colloids. A gel forming binary mixture whose linkers can self-assemble into linear chains while still promoting the aggregation of particles is considered in this work. The particles are patchy particles with $f_C$ patches of type $C$ and the linkers are patchy particles with $2$ patches of type $A$ and $f_B$ patches of type B. The bonds between patches of type $A$ ($AA$ bonds) promote the formation of linear chains of linkers. Two different ways (model A and model B) of bonding the linkers to the particles - or inducing branching - are studied. In model A, there is a competition between chaining and branching, since the bonding between linkers and particles is done through $AC$ bonds only. In model B linkers aggregate to particles through bonds $BC$ only, making chaining and branching independent. The percolation behaviour of these two models is studied in detail, employing a generalized Flory-Stockmayer theory and Monte Carlo simulations. The self-assembly of linkers into chains reduces the fraction of particles needed for percolation to occur (models A and B) and induces percolation when the fraction of particles is high (model B). Percolation by heating and percolation loops in temperature composition diagrams are obtained when the formation of chains is energetically favourable, by increasing the entropic gain of branching (model A). Chaining and branching are found to follow a model dependent relation at percolation, which shows that, for the same composition, longer chains require less branching for percolation to occur.

cond-mat.soft↗

arXiv2021

Building up DNA, bit by bit: a simple description of chain assembly

We simulate the assembly of DNA copolymers from two types of short duplexes (short double strands with a single-stranded overhang at each end), as described by the oxDNA model. We find that the statistics of chain lengths can be well reproduced by a simple theory that treats the association of particles into ideal (i.e., non-interacting) clusters as a reversible chemical reaction. The reaction constants can be predicted either from Santalucia's theory or from Wertheim's thermodynamic perturbation theory of association for spherical patchy particles. Our results suggest that theories incorporating very limited molecular detail may be useful for predicting the broad equilibrium features of copolymerisation.

cond-mat.soft↗

arXiv2020

Smoluchowski equations for linker-mediated irreversible aggregation

In order to study linker-mediated aggregation of colloidal particles with limited valence, we combine kinetic Monte Carlo simulations and an approximate theory based on the Smoluchowski equations. We found that aggregation depends strongly on two parameters, the ratio of the number of linkers and particles and the ratio of their diffusion coefficients. These control parameters are absent in single-species aggregation and provide a much greater variety and control of the resulting structures. We show that aggregation is non-trivial when two time scales of aggregation are present. Our aggregation dynamics theory is in qualitative and quantitative agreement with kinetic Monte Carlo simulations. Our results show how the optimal aggregation may be tuned through the ratio of the linkers and particles and that of the diffusion coefficients.

cond-mat.soft↗

arXiv2018

Dynamics of a network fluid within the liquid-gas coexistence region

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class.

cond-mat.soft↗

arXiv2017

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.

cond-mat.soft↗

arXiv2014

Three-dimensional patchy lattice model: ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with $2$ patches of type $A$ and $10$ patches of type $B$. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self-assembly of chains, rings and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension of Wertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio $r\equivε_{AB}/ε_{AA}$ of the interaction between patches $A$ and $B$, $ε_{AB}$, and between $A$ patches, $ε_{AA}$ ($ε_{BB}$ is set to $0$) as well as the relative position of the $A$ patches, i.e., the angle $θ$ between the (lattice) directions of the $A$ patches. We found that both $r$ and $θ$ ($60^\circ,90^\circ,$ or $120^\circ$) have a profound effect on the phase diagram. In the empty fluid regime ($r < 1/2$) the phase diagram is re-entrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for $θ=120^\circ$ but deteriorates as $θ$ decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.

cond-mat.soft↗

arXiv2012

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibits reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occurs for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria is so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here.

cond-mat.soft↗

arXiv2012

The nature of the ordered phase of the confined self-assembled rigid rod model

We investigate the nature of the ordered phase and the orientational correlations between adjacent layers of the confined three-dimensional self-assembled rigid rod model, on the cubic lattice. We find that the ordered phase at finite temperatures becomes uniaxial in the thermodynamic limit, by contrast to the ground state (partial) order where the orientation of the uncorrelated layers is perpendicular to one of the three lattice directions. The increase of the orientational correlation between layers as the number of layers increases suggests that the unconfined model may also exhibit uniaxial ordering at finite temperatures.

cond-mat.stat-mech↗

arXiv2012

Reply to Comment on Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods

We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods, on the square lattice, which is reported by Lopez et al. to exhibit random percolation criticality in the canonical ensemble, in sharp contrast to (i) our results of Ising criticality for the same model in the grand canonical ensemble [Phys. Rev. E 82, 061117 (2010)] and (ii) the absence of exponent(s) renormalization for constrained systems with logarithmic specific heat anomalies predicted on very general grounds by Fisher [M.E. Fisher, Phys. Rev. 176, 257 (1968)].

cond-mat.stat-mech↗

arXiv2011

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, ε^\star_AB, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of ε^\star_AB, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multicritical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime.

cond-mat.soft↗

arXiv2011

The criticality of self-assembled rigid rods on triangular lattices

The criticality of self-assembled rigid rods on triangular lattices is investigated using Monte Carlo simulation. We find a continuous transition between an ordered phase, where the rods are oriented along one of the three (equivalent) lattice directions, and a disordered one. We conclude that equilibrium polydispersity of the rod lengths does not affect the critical behavior, as we found that the criticality is the same as that of monodisperse rods on the same lattice, in contrast with the results of recently published work on similar models.

cond-mat.soft↗

arXiv2010

The effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods

Extensive Monte Carlo simulations were carried out to investigate the nature of the ordering transition of a model of adsorbed self-assembled rigid rods on the bonds of a square lattice [Tavares et. al., Phys. Rev E 79, 021505 (2009)]. The polydisperse rods undergo a continuous ordering transition that is found to be in the two-dimensional Ising universality class, as in models where the rods are monodisperse. This finding is in sharp contrast with the recent claim that equilibrium polydispersity changes the nature of the phase transition in this class of models [L`opez et. al., Phys. Rev E 80, 040105(R)(2009)].

cond-mat.stat-mech↗

arXiv2005

Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e. it can be analyzed in terms of its $f(α)$ multifractal spectrum. For low dipolar strengths, the $f(α)$ spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing dipolar strength both the minimal local growth exponent $α_{min}$ and the information dimension $D_1$ decrease, while the fractal dimension remains the same.

cond-mat.stat-mech↗

arXiv2005

The nature of the phase transition in dipolar fluids

Monte Carlo computer simulations of a quasi two dimensional (2D) dipolar fluid at low and intermediate densities indicate that the structure of the fluid is well described by an ideal mixture of self-assembling clusters. A detailed analysis of the topology of the clusters, of their internal energy and of their size (or mass) distributions further suggests that the system undergoes a phase transition from a dilute phase characterized by a number of disconnected clusters to a condensed phase characterized by a network or spanning (macroscopic) cluster that includes most of the particles in the system.

cond-mat.soft↗

arXiv2004

Diffusion-limited deposition of dipolar particles

Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered deposits. In the dipolar regime, the order and geometry of the clusters depend on the strength of the interactions and the magnetic properties are tunable by controlling the growth conditions. At later stages, the growth is dominated by thermal effects and the diffusion-limited universal regime obtains, at finite temperatures. At low temperatures the crossover size increases exponentially as T decreases and at T=0 only the dipolar regime is observed.

cond-mat.stat-mech↗

arXiv2003

Deposition of magnetic particles: A computer simulation study

We report a Monte Carlo simulation of deposition of magnetic particles on a one-dimensional substrate. Incoming particles interact with those that are already part of the deposit via a dipole-dipole potential. The strength of the dipolar interaction is controlled by an effective temperature $T^*$, the case of pure diffusion-limited deposition being recovered in the limit $T^*\to\infty$. Preliminary results suggest that the fractal dimension of the deposits does not change with temperature but that there is a (temperature-dependent) cross-over from regimes of temperature-dependent to universal behaviour. Furthermore, it was found that dipoles tend to align with the local direction of growth.

cond-mat↗

arXiv2002

Orientational order in Deposits of Magnetic Particles

We present preliminary results for the orientational order in deposits of dipolar particles, on one dimensional substrates. The deposits are generated using a model where the incoming dipolar particle interacts with the other particles in the deposit via a dipole-dipole potential. The interdipolar vectors are restricted to lie on a square lattice although the dipole moments are free to rotate in three dimensions. The path of the incoming particle is generated through a Monte Carlo scheme controlled by an effective temperature T, the case of pure diffusion-limited deposition corresponding to T=infinity$. We calculate the ferromagnetic and nematic order parameters and the dipolar orientational probability density of the deposits, at various stages of growth and two effective temperatures. The dipolar angular correlations along the rows and columns of the lattice are also investigated. We find that the orientational order of the deposits depends strongly on the lattice structure, the stage of growth and the effective temperature.

cond-mat.stat-mech↗