Percolation in binary mixtures of linkers and particles: Chaining vs branching.

Equilibrium gels of colloidal particles can be realized through the introduction of a second species, a linker that mediates the bonds between 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 fC patches of type C and the linkers are patchy particles with 2 patches of type A and fB 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 takes place through AC bonds only. In model B, the linkers aggregate to particles through bonds BC only, making chaining and branching independent. The percolation behavior 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 favorable 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.

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.

Smoluchowski equations for linker-mediated irreversible aggregation.

We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.

Remnants of the disappearing critical point(s) in patchy fluids with distinct interaction patches.

We investigate the disappearance of the critical points of a model consisting of particles decorated with two patches of type A and a variable number (n) of patches of type B (2AnB patchy particles), in which only AA and AB bonds can form. This has been shown to exhibit a very rich phase behavior including one, two, or no liquid-vapor critical points, depending on two parameters: the ratio of the volumes available to each type of bond and the ratio of the bond strengths. We apply Wertheim's theory in the limit of strong AA bonds to a lattice version of the model [Almarza et al., J. Chem. Phys. 137, 244902 (2012)] and show that the critical point does not always vanish at zero density and temperature, in contrast with results for particles decorated with only one type of patch. We uncover two remnants of the critical points-the lines of maximum and ideal compressibility-that survive even when no critical points are present.

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. We show that the slow dynamics is universal, being also observed outside the coexistence region at low temperatures in the single phase region.

Effects of high-impact exercise on the physical properties of bones of ovariectomized rats fed to a high-protein diet.

The aim of this study was to evaluate the effects of high-impact physical exercise as a prophylactic and therapeutic means in osteopenic bones of rats submitted to ovariectomy and protein diet intake. A total of 64 Wistar rats were divided into eight groups (n = 8 each), being: OVX, ovx, standard diet and sedentary; OVXE, ovx, standard diet and jump; OVXP, ovx, high-protein diet and sedentary; and OVXEP, ovx, high-protein diet and jump; SH, sham, standard diet and sedentary; SHE, sham, standard diet and jump; SHP, sham, high-protein diet and sedentary; and SHEP, sham, high-protein diet and jump. OVX surgery consists of ovariectomy, and sham was the control surgery. The jumping protocol consisted of 20 jumps/day, 5 days/week. The bone structure was evaluated by densitometry, mechanical tests, histomorphometric, and immunohistochemical analyses. A high-protein diet resulted in increased bone mineral density (P = .049), but decreased maximal load (P = .026) and bone volume fraction (P = .023). The benefits of physical exercise were demonstrated by higher values of the maximal load in the trained groups compared to the sedentary groups (P < .001). The sham groups had decreased immunostaining of osteocalcin (P = .004) and osteopontin (P = .010) compared to ovx groups. However, the high-protein diet (P = .005) and jump exercise (P = .017) resulted in lower immunostaining of osteopontin compared to the standard diet and sedentary groups, respectively. In this experimental model, it was concluded that ovariectomy and a high-fat diet can negatively affect bone tissue and the high-impact exercise was not enough to suppress the deleterious effects caused by the protein diet and ovariectomy.

Generalization of Wertheim's theory for the assembly of various types of rings.

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by εAA and by εAB ≡ rεAA, respectively. The angle θ between the 2 A-patches on each particle is fixed at 60°, 90° or 120°. For values of r below 1/2 and above a threshold rth(θ) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when θ decreases. We show that the mechanism that prevents phase separation for models with decreasing values of θ is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings (loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of θ, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

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 ≡ εAB/εAA of the interaction between patches A and B, εAB, and between A patches, εAA (εBB 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°, 90°, or 120°) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant 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° but deteriorates as θ decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.

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.

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 exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur 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 are 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.

Reentrant phase diagram of network fluids.

We introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched" phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328 (2000)]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.

Communication: 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.

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(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(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 multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime.

Re-entrant phase behaviour of network fluids: a patchy particle model with temperature-dependent valence.

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost ε(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for ε(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles.

New computational solution to quantify synthetic material porosity from optical microscopic images.

This paper presents a new computational solution to quantify the porosity of synthetic materials from optical microscopic images. The solution is based on an artificial neuronal network of the multilayer perceptron type and a backpropagation algorithm is used for training. To evaluate this new solution, 40 sample images of a synthetic material were analysed and the quality of the results was confirmed by human visual analysis. In addition, these results were compared with ones obtained with a commonly used commercial system confirming their superior quality and the shorter time needed. The effect of images with noise was also studied and the new solution showed itself to be more reliable. The training phase of the new solution was analysed confirming that it can be performed in a very easy and straightforward manner. Thus, the new solution demonstrated that it is a valid and adequate option for researchers, engineers, specialists and other professionals to quantify the porosity of materials from microscopic images in an automatic, fast, efficient and reliable manner.

Equilibrium self-assembly of colloids with distinct interaction sites: thermodynamics, percolation, and cluster distribution functions.

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a--state-dependent--functionality f and unique bonding probability p. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Using statistical deformable models to reconstruct vocal tract shape from magnetic resonance images.

The mechanisms involved in speech production are complex and have thus been subject to growing attention by the scientific community. It has been demonstrated that magnetic resonance imaging (MRI) is a powerful means in the understanding of the morphology of the vocal tract. Over the last few years, statistical deformable models have been successfully used to identify and characterize bones and organs in medical images and point distribution models (PDMs) have gained particular relevance. In this work, the suitability of these models has been studied to characterize and further reconstruct the shape of the vocal tract in the articulation of Portuguese European (EP) speech sounds, one of the most spoken languages worldwide, with the aid of MR images. Therefore, a PDM has been built from a set of MR images acquired during the artificially sustained articulation of 25 EP speech sounds. Following this, the capacity of this statistical model to characterize the shape deformation of the vocal tract during the production of sounds was analysed. Next, the model was used to reconstruct five EP oral vowels and the EP fricative consonants. As far as a study on speech production is concerned, this study is considered to be the first approach to characterize and reconstruct the vocal tract shape from MR images by using PDMs. In addition, the findings achieved permit one to conclude that this modelling technique compels an enhanced understanding of the dynamic speech events involved in sustained articulations based on MRI, which are of particular interest for speech rehabilitation and simulation.

Structure and phase diagram of self-assembled rigid rods: equilibrium polydispersity and nematic ordering in two dimensions.

We investigate the influence of directional or bonding interactions on the structure and phase diagram of complex fluids. Using a generalization of the theory of associating fluids we study the interplay between the self-assembly process, driven by the bonding interactions, and the isotropic-nematic transition, driven by the anisotropic shape of the equilibrium clusters, for a model consisting of particles with two bonding sites and discrete orientational degrees of freedom. The theory is applied over a wide range of temperature and density in two dimensions and the results are compared with Monte Carlo simulations on the square lattice. The specific heat is shown to exhibit pronounced structure at the onset of self-assembly and at the nematic-isotropic transition that occur over a narrow range of temperature, at fixed density. The results reveal that bonding is enhanced by the nematic ordering, although a bonding temperature still occurs in the isotropic phase at low densities. The average rod length is described quantitatively in both phases, while the location of the ordering transition, which was found to be continuous, is predicted semiquantitatively by the theory.

Criticality of colloids with distinct interaction patches: the limits of linear chains, hyperbranched polymers, and dimers.

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA) not equal to 0, epsilon(AB)=epsilon(BB)=0) , hyperbranched polymers (epsilon(AB) not equal to 0, epsilon(AA)=epsilon(B)=0) , and dimers (epsilon(BB) not equal to 0, epsilon(AA)=epsilon(AB)=0) . These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when in(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

Coherence thresholds in models of language change and evolution: the effects of noise, dynamics, and network of interactions.

A simple model of language evolution proposed by Komarova, Niyogi, and Nowak is characterized by a payoff in communicative function and by an error in learning that measure the accuracy in language acquisition. The time scale for language change is generational, and the model's equations in the mean-field approximation are a particular case of the replicator-mutator equations of evolutionary dynamics. In well-mixed populations, this model exhibits a critical coherence threshold; i.e., a minimal accuracy in the learning process is required to maintain linguistic coherence. In this work, we analyze in detail the effects of different fitness-based dynamics driving linguistic coherence and of the network of interactions on the nature of the coherence threshold by performing numerical simulations and theoretical analyses of three different models of language change in finite populations with two types of structure: fully connected networks and regular random graphs. We find that although the threshold of the original replicator-mutator evolutionary model is robust with respect to the structure of the network of contacts, the coherence threshold of related fitness-driven models may be strongly affected by this feature.