A cluster size distribution theory to study the thermodynamics and phase behavior of multi-bonding single site solutes in patchy colloidal mixtures

Noise, Fake News, and Tenacious Bayesians

A modeling framework, based on the theory of signal processing, for characterizing the dynamics of systems driven by the unraveling of information is outlined, and is applied to describe the process of decision making. The model input of this approach is the specification of the flow of information. This enables the representation of (i) reliable information, (ii) noise, and (iii) disinformation, in a unified framework. Because the approach is designed to characterize the dynamics of the behavior of people, it is possible to quantify the impact of information control, including those resulting from the dissemination of disinformation. It is shown that if a decision maker assigns an exceptionally high weight on one of the alternative realities, then under the Bayesian logic their perception hardly changes in time even if evidences presented indicate that this alternative corresponds to a false reality. Thus, confirmation bias need not be incompatible with Bayesian updating. By observing the role played by noise in other areas of natural sciences, where noise is used to excite the system away from false attractors, a new approach to tackle the dark forces of fake news is proposed.

Phase behavior and percolation in mixed patchy colloids

Patchy colloids can be modeled as hard spheres with directional conical association sites. A variety of physical phenomena have been discovered in the patchy colloid system due to its short range and directional interactions. In this work, we combined a cluster distribution theory with generalized Flory and Stockmayer percolation theory to investigate the interplay between phase behavior and percolation for a binary patchy colloid system. The binary patchy colloid system consists of solute molecules with spherically symmetric bonding sites and solvents with two singly bondable sites. Wertheim's first order thermodynamic perturbation theory (TPT1) has been widely applied to the patchy colloids system and it has been combined with percolation theory to study the percolation threshold. However, due to assumptions behind TPT1, it will lose accuracy for a system in which particles have multiple association sites or multiply bondable sites. A recently proposed cluster distribution theory accurately models association at sites that can form multiple bonds. In this work, we investigate the comparison among cluster distribution theory, TPT1, and Monte Carlo simulation for the bonding states of this binary system in which cluster distribution theory shows excellent agreement with Monte Carlo simulation, while TPT1 has a large deviation with the simulation. Cluster distribution theory was further combined with the Flory and Stockmayer percolation theory to investigate the interplay between phase behavior and percolation threshold. We found that the reduced density and the relative bonding strength of solvent-solvent association and solute-solvent association are key factors for the phase behavior and percolation. Percolation can form at low density and low temperature in the vapor phase of this binary system, where the star-like molecules with 12 long branches formed.

Integral equation theory for mixtures of spherical and patchy colloids. 2. Numerical results

Thermodynamic properties and structure of binary mixtures of patchy and spherical colloids are studied using a recently developed theory [Y. V. Kalyuzhnyi, et al., Soft Matter, 2020, 16, 3456]. The theory is based on a solution of the multidensity Ornstein-Zernike equation and provides completely analytical expressions for the structure factors of these systems and for all their major thermodynamical quantities. The considered mixtures are made up of particles of different size and with a different number of patches. A set of molecular simulation data has been generated to enable a systematic comparison and to access thus accuracy of the theoretical predictions. In general, the predictions of the theory appear to be in good agreement with computer simulation data. For the models with a lower number of patches (n_p = 1, 2) the theoretical results show very good accuracy. Less accurate are the predictions for the four-patch versions of the model. While theoretical results for the radial distribution functions are, generally, relatively accurate for all the models, results for thermodynamics deteriorate with increasing concentration of the spherical colloids. Possible ways to improve the theory are briefly outlined.

Self-assembly and phase behavior of mixed patchy colloids with any bonding site geometry: theory and simulation

Patchy colloids and associating fluids have attracted continued interest due to the interesting phase behavior and self-assembly in solution. The ability to fabricate patchy colloids with multiple attractive surface patches of different number, size, shape, and relative location makes patchy colloids a good candidate as building blocks to form complex advanced materials. However, a theory that clearly relates the self-assembled structures that form based on the anisotropic interactions has been missing. Although Wertheim's theory in the form of the SAFT model is widely used to predict self-assembly and phase behavior in solution, SAFT does not include multibody correlations necessary to model any shape of association site or sites that can form multiple bonds. We have recently developed a new theory for associating colloids that naturally incorporates multibody correlations based on a cluster distribution approach due to Bansal, Asthagiri, Marshall, and Chapman (BAMC). In this paper, we extended the cluster distribution theory to predict the thermodynamic properties and phase behavior of binary systems consisting of anisotropic particles with any geometry of bonding site. In particular, we consider self-assembly of Janus particles, Saturn particles, and ternary particles mixed with solvent colloids that have two directional patchy sites. Good agreement between theoretical predictions and molecular simulation is shown for self-assembly, thermodynamic properties in this system. Re-entrant phase behavior has been investigated and low density gels is predicted.

Integral equation theory for a mixture of spherical and patchy colloids: analytical description

An analytic theory for the structure and thermodynamics of two-component mixtures of patchy and spherical colloids is developed. The theory is based on an analytical solution of the multidensity Ornstein-Zernike equation supplemented by the associative Percus-Yevick closure relations. We derive closed-form analytic expressions for the partial structure factors and thermodynamic properties using the energy route for the model with arbitrary number of patches and any hard-sphere size ratio of the particles. To assess the accuracy of the theoretical predictions we compare them against existing and newly generated set of computer simulation data. In our numerical calculations we consider the model with equal hard-sphere sizes and one patch. Very good agreement between results of the theory and simulation for the pair correlation functions, excess internal energy and pressure is observed for almost all values of the system density, temperature and composition studied. Only in the region of low concentrations of spherical colloids the theoretical results become less accurate.