Dynamical arrest transition of a bidisperse two-patchy colloidal dispersion: A dynamic Monte Carlo study.

During the last few years, patchy colloidal dispersions have emerged as ideal candidates of glass-formers of systems composed of particles that interact with non-isotropic potentials. However, from the computational point of view, the characterization of their dynamical properties close to the glass transition via any kind of molecular dynamics simulation technique can be very difficult due to the slowing down of both the rotational and translational dynamics. Although a plethora of dynamical techniques have been developed to account for the dynamics of patchy colloids, new and complementary simulation techniques are required to explore, much faster and more efficiently, the dynamical arrest transition of patchy colloidal dispersions when computer simulation consists of a large number of particles and, due to the slow particle dynamics at the glass transition, an extended time window is explicitly required. Then, in this contribution, by means of the so-called dynamic-Monte Carlo method, we report on the dynamical arrest transition, both rotational and translational, of a bidisperse patchy colloidal dispersion, following three different paths along the density-temperature plane, including high densities and low temperatures. Although this method has not been extensively tested at extreme thermodynamic conditions, we show that even at the dynamical arrest transition, it allows us to extract good dynamical data from a complex system. Therefore, it turns out to be a promising technique to explore the onset of vitrification of anisotropic colloidal particles.

Patchy colloidal gels under the influence of gravity.

In this contribution, gravitational effects in gel-forming patchy colloidal systems are studied. We focus on how the gel structure is modified by gravity. Through Monte Carlo computer simulations of gel-like states recently identified by the rigidity percolation criterion [J. A. S. Gallegos et al., Phys. Rev. E 104, 064606 (2021)], the influence of the gravitational field, characterized by the gravitational Péclet number, Pe, on patchy colloids is studied in terms of the patchy coverage, χ. Our findings point out that there exists a threshold Péclet number, Peg, that depends on χ above which the gravitational field enhances the particle bonding and, in consequence, promotes the aggregation or clustering of particles; the smaller the χ value, the higher the Peg. Interestingly, when χ ∼ 1 (near the isotropic limit), our results are consistent with an experimentally determined threshold Pe value where gravity affects the gel formation in short-range attractive colloids. In addition, our results show that the cluster size distribution and the density profile undergo variations that lead to changes in the percolating cluster, i.e., gravity is able to modify the structure of the gel-like states. These changes have an important impact on the structural rigidity of the patchy colloidal dispersion; the percolating cluster goes from a uniform spatially network to a heterogeneous percolated structure, where an interesting structural scenario emerges, namely, depending on the Pe value, the new heterogeneous gel-like states can coexist with both diluted and dense phases or they simply reach a crystalline-like state. In the isotropic case, the increase in the Pe number can shift the critical temperature to higher temperatures; however, when Pe > 0.01, the binodal disappears and the particles fully sediment at the bottom of the sample cell. Furthermore, gravity moves the rigidity percolation threshold to lower densities. Finally, we also note that within the values of the Péclet number here explored, the cluster morphology is barely altered.

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions.

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials.

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

Determining depletion interactions by contracting forces.

Depletion forces are fundamental for determining the phase behavior of a vast number of materials and colloidal dispersions and have been used for the manipulation of in- and out-of-equilibrium thermodynamic states. The entropic nature of depletion forces is well understood; however, most theoretical approaches, and also molecular simulations, work quantitatively at moderate size ratios in much diluted systems since large size asymmetries and high particle concentrations are difficult to deal with. The existing approaches for integrating out the degrees of freedom of the depletant species may fail under these extreme physical conditions. Thus, the main goal of this contribution is to introduce a general physical formulation for obtaining the depletion forces even in those cases where the concentration of all species is relevant. We show that the contraction of the bare forces uniquely determines depletion interactions. Our formulation is tested by studying depletion forces in binary and ternary colloidal mixtures. We report here results for dense systems with total packing fractions of 45% and 55%. Our results open up the possibility of finding an efficient route to determine effective interactions at a finite concentration, even under non-equilibrium thermodynamic conditions.

Concentration and size effects on the size-selective particle purification method using the critical Casimir force.

Critical Casimir force (CCF) is a solvent fluctuation introduced interaction between particles dispersed in a binary solvent. Recently, it has been demonstrated that the CCF induced attraction between particles can trigger particle size-sensitive aggregation, and has thus been used as an efficient way to purify nanoparticles by size. Here, combining small angle neutron scattering and dynamic light scattering, we investigate the effects of size and concentration on this particle size separation method. Increasing the particle concentration does not significantly affect the purification method, but the solvent composition needs to be adjusted for an optimized efficiency. This purification method is further demonstrated to work also very efficiently for systems with particle size ranging from 15 nm to about 50 nm with a very large size polydispersity. These results indicate that for both short-ranged and long-ranged attraction relative to the particle diameter, the CCF introduced particle aggregation is always size sensitive. This implies that particle aggregation is strongly affected by size polydispersity for many colloidal systems. We further propose a method to use light scattering to help identify the temperature range within which this particle purification method can work efficiently instead of using neutron scattering.

Potential-invariant network structures in Asakura-Oosawa mixtures with very short attraction range.

We systematically investigated the structure and aggregate morphology of gel networks formed by colloid-polymer mixtures with a moderate colloid volume fraction and different values of the polymer-colloid size ratio, always in the limit of short-range attraction. Using the coordinates obtained from confocal microscopy experiments, we determined the radial, angular, and nearest-neighbor distribution functions together with the cluster radius of gyration as a function of size ratio and polymer concentration. The analysis of the structural correlations reveals that the network structure becomes increasingly less sensitive to the potential strength with the decreasing polymer-colloid size ratio. For the larger size ratios, compact clusters are formed at the onset of network formation and become progressively more branched and elongated with increasing polymer concentration/attraction strength. For the smallest size ratios, we observe that the aggregate structures forming the gel network are characterized by similar morphological parameters for different values of the size ratio and the polymer concentration, indicating a limited evolution of the gel structure with variations of the parameters that determine the interaction potential between colloids.

Competing interactions in the depletion forces of ternary colloidal mixtures.

Depletion interactions between colloidal particles surrounded by smaller depletants are typically characterized by a strong attraction at contact and a moderately repulsive barrier in front of it that extends at distances similar to the size of the depletants; the appearance and height of the barrier basically depend on the concentration and, therefore, the correlation between depletants. From a thermodynamic point of view, the former can drive the system to phase separation or toward non-equilibrium states, such as gel-like states, but its effects on both local and global properties may be controlled by the latter, which acts as a kind of entropic gate. However, the latter has not been entirely analyzed and understood within the context of colloidal mixtures mainly driven by entropy. In this contribution, we present a systematic study of depletion forces in ternary mixtures of hard spherical particles with two species of depletants, in two and three dimensions. We focus the discussion on how the composition of the depletants becomes the main physical parameter that drives the competition between the attractive well and the repulsive barrier. Our results are obtained by means of the integral equation theory of depletion forces and techniques of contraction of the description adapted to molecular dynamics computer simulations.

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions.

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.

Arrested dynamics of the dipolar hard sphere model.

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (soft core) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: at low (η = 0.2) and intermediate (η = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations (η≥ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.

Assessment of the Wolf method using the Stillinger-Lovett sum rules: From strong electrolytes to weakly charged colloidal dispersions.

The Ewald method has been the cornerstone in molecular simulations for modeling electrostatic interactions of charge-stabilized many-body systems. In the late 1990s, Wolf and collaborators developed an alternative route to describe the long-range nature of electrostatic interactions; from a computational perspective, this method provides a more efficient and straightforward way to implement long-range electrostatic interactions than the Ewald method. Despite these advantages, the validity of the Wolf potential to account for the electrostatic contribution in charged fluids remains controversial. To alleviate this situation, in this contribution, we implement the Wolf summation method to both electrolyte solutions and charged colloids with moderate size and charge asymmetries in order to assess the accuracy and validity of the method. To this end, we verify that the proper selection of parameters within the Wolf method leads to results that are in good agreement with those obtained through the standard Ewald method and the theory of integral equations of simple liquids within the so-called hypernetted chain approximation. Furthermore, we show that the results obtained with the original Wolf method do satisfy the moment conditions described by the Stillinger-Lovett sum rules, which are directly related to the local electroneutrality condition and the electrostatic screening in the Debye-Hückel regime. Hence, the fact that the solution provided by the Wolf method satisfies the first and second moments of Stillinger-Lovett proves, for the first time, the reliability of the method to correctly incorporate the electrostatic contribution in charge-stabilized fluids. This makes the Wolf method a powerful alternative compared to more demanding computational approaches.

Spherical harmonic projections of the static structure factor of the dipolar hard sphere model: Theory vs simulations.

We investigate the static correlations of a dipolar fluid in terms of the irreducible coefficients of the spherical harmonic expansion of the static structure factor. To this end, we develop a theoretical framework based on a soft-core version of Wertheim's solution of the mean spherical approximation (MSA), which renders the analytical determination of such coefficients possible. The accuracy of this approximation is tested by a comparison against the results obtained with the assistance of extensive molecular dynamics simulations at different regimes of concentration and temperature. Crucial aspects for the comparison of the results provided by the two methods are carefully discussed, concerning the different reference frames used in theory and simulations to describe rotations and orientations, and leading to important differences in the behavior of correlation functions with the same combination of spherical harmonic indices. We find a remarkable agreement between the two approaches in the fluid regime, thus providing a first stringent comparison of the irreducible coefficients of the spherical harmonic expansion of the dipolar fluid's static structure factor, provided by the MSA theory and molecular dynamics simulations.

Reversible Aggregation and Colloidal Cluster Morphology: The Importance of the Extended Law of Corresponding States.

Cluster morphology of spherical particles interacting with a short-range attraction has been extensively studied due to its relevance to many applications, such as the large-scale structure in amorphous materials, phase separation, protein aggregation, and organelle formation in cells. Although it was widely accepted that the range of the attraction solely controls the fractal dimension of clusters, recent experimental results challenged this concept by also showing the importance of the strength of attraction. Using Monte Carlo simulations, we conclusively demonstrate that it is possible to reduce the dependence of the cluster morphology to a single variable, namely, the reduced second virial coefficient, B_{2}^{*}, linking the local properties of colloidal systems to the extended law of corresponding states. Furthermore, the cluster size distribution exhibits two well-defined regimes: one identified for small clusters, whose fractal dimension, d_{f}, does not depend on the details of the attraction, i.e., small clusters have the same d_{f}, and another related to large clusters, whose morphology depends exclusively on B_{2}^{*}, i.e., d_{f} of large aggregates follows a master curve, which is only a function of B_{2}^{*}. This physical scenario is confirmed with the reanalysis of experimental results on colloidal-polymer mixtures.

Friction and diffusion of a nano-colloidal disk in a two-dimensional solvent with a liquid-liquid transition.

We report on the friction and diffusion of a single mobile nano-colloidal disk, whose size and mass are one and two orders of magnitude, respectively, greater than the molecules of the host solvent; all particles are restricted to move in a two-dimensional space. Using molecular dynamics simulations, the variation of the transport coefficients as a function of the thermodynamic state of the supporting fluid, in particular, around those states in the neighbourhood of the liquid-liquid phase coexistence, is investigated. The diffusion coefficient is determined through the fit of the mean-square displacement at long times and with the Green-Kubo relationship for the velocity autocorrelation function, whereas the friction coefficient is computed from the correlation of the fluctuating force. From the determination of the transport properties, the applicability of the Stokes-Einstein relation in two dimensions around the second critical point is discussed.

Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential.

In the same sense as in the extended law of corresponding states [M. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)], we propose the use of the second virial coefficient to map the hard-sphere potential onto a continuous potential. We show that this criterion provides accurate results when the continuous potential is used, for example, in computer simulations to reproduce the physical properties of systems with hard-core interactions. We also demonstrate that this route is straightforwardly applicable to any spatial dimension, does not depend on the particle density and, from a numerical point of view, is easy to implement.

Single file dynamics in soft materials.

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.

Counterion accumulation effects on a suspension of DNA molecules: Equation of state and pressure-driven denaturation.

The study of the effects associated with the electrostatic properties of DNA is of fundamental importance to understand both its molecular properties at the single molecule level, like the rigidity of the chain, and its interaction with other charged bio-molecules, including other DNA molecules; such interactions are crucial to maintain the thermodynamic stability of the intra-cellular medium. In the present work, we combine the Poisson-Boltzmann mean-field theory with an irreversible thermodynamic approximation to analyze the effects of counterion accumulation inside DNA on both the denaturation profile of the chain and the equation of state of the suspension. To this end, we model the DNA molecule as a porous charged cylinder immersed in an aqueous solution. These thermo-electrostatic effects are explicitly studied in the particular case of some genes for which damage in their sequence is associated with diffuse large B-cell lymphoma.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics.

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

Structure of colloidal gels at intermediate concentrations: the role of competing interactions.

Colloidal gels formed by colloid-polymer mixtures with an intermediate volume fraction (ϕc ≈ 0.4) are investigated by confocal microscopy. In addition, we have performed Monte Carlo simulations based on a simple effective pair potential that includes a short-range attractive contribution representing depletion interactions, and a longer-range repulsive contribution describing the electrostatic interactions due to the presence of residual charges. Despite neglecting non-equilibrium effects, experiments and simulations yield similar gel structures, characterised by, e.g., the pair, angular and bond distribution functions. We find that the structure hardly depends on the strength of the attraction if the electrostatic contribution is fixed, but changes significantly if the electrostatic screening is changed. This delicate balance between attractions and repulsions, which we quantify by the second virial coefficient, also determines the location of the gelation boundary.

Characterisation of the thermodynamics, structure and dynamics of a water-like model in 2- and 3-dimensions.

The physical properties of colloidal particles suspended in an aqueous environment are well-understood when the latter is considered to be a continuum and a structureless medium. However, this approach fails to explain complex phenomena, for example, the critical Casimir forces among colloids and the colloidal self-assembly near critical solvents, and the inertial contribution of the solvent molecules on the diffusion of non-spherical Brownian particles. Therefore, the role played by the solvent on the physical properties of colloidal dispersions is of paramount relevance. Recently, there has been an interest in the (non-trivial) diffusion mechanisms of a nano-colloidal particle in a solvent that undergoes a vapour-liquid transition. Nonetheless, the models typically used to incorporate the solvent details do not capture quantitatively the thermodynamic properties of real substances. It is then important to study the Brownian motion of colloids in more realistic models. To reach such goal, one first has to characterise the thermodynamic states and the microscopic features of the solvent. Hence, in this contribution, we have investigated the coexistence densities of a core-softened potential in two- and three-dimensions, whose potential parameters are able to capture some anomalies of water. We show that in the two-dimensional case, the potential model exhibits, besides the normal vapour-liquid coexistence region, additional liquid-liquid coexistence densities. We particularly focus our attention to the structural properties and the dynamical behaviour of the solvent around the liquid-liquid critical point and assess the differences with the three-dimensional case.