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In addition, simulations have been very useful to locate and characterize gas-liquid (colloid-rich/colloid poor) phase separation of the Asakura-Oosawa effective potential,[108] clarifying that this belongs, as expected, to the Ising universality class. Investigations on binary mixtures of colloids and polymers[109] where non-ideality effects of the polymer are taken into account have also been explored. Colloid synthesis has evolved to such a degree[[119]] that it is nowadays possible to make colloidal particles of a wide range of shapes.[[121], [123], [125]] This, and the fact that anisotropic shapes occur in nature, has triggered studies on mixtures of non-spherical colloids plus added nonadsorbing polymers. 113, 2886 (2000).10.1063/1.1305867 31 A. N. Semenov and A. A. Shvets, "Theory of colloid depletion stabilization by unattached and adsorbed polymers", Soft Matter 11, 8863-8878 (2015).10.1039/c5sm01365h 32 H. N. W. Lekkerkerker, W. C.-K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren, "Phase-behavior of colloid plus polymer mixtures", Europhys. 96, 36006 (2011).10.1209/0295-5075/96/36006 82 N. Park and J. C. Conrad, "Phase behavior of colloid-polymer depletion mixtures with unary or binary depletants", Soft Matter 13, 2781-2792 (2017).10.1039/c6sm02891h 83 E. Stiakakis, G. Petekidis, D. Vlassopoulos, C. N. Likos, H. Iatrou, N. Hadjichristidis, and J. Roovers, "Depletion and cluster formation in soft colloid-polymer mixtures", Europhys. [Extracted from the article]

Combining elastic incoherent neutron scattering and differential scanning calorimetry, we investigate the occurrence of the volume phase transition (VPT) in very concentrated poly-(N-isopropyl-acrylamide) (PNIPAM) microgel suspensions, from a polymer weight fraction of 30 wt. % up to dry conditions. Although samples are arrested at the macroscopic scale, atomic degrees of freedom are equilibrated and can be probed in a reproducible way. A clear signature of the VPT is present as a sharp drop in the mean square displacement of PNIPAM hydrogen atoms obtained by neutron scattering. As a function of concentration, the VPT gets smoother as dry conditions are approached, whereas the VPT temperature shows a minimum at about 43 wt. %. This behavior is qualitatively confirmed by calorimetry measurements. Molecular dynamics simulations are employed to complement experimental results and gain further insights into the nature of the VPT, confirming that it involves the formation of an attractive gel state between the microgels. Overall, these results provide evidence that the VPT in PNIPAM-based systems can be detected at different time- and length-scales as well as under overcrowded conditions. [ABSTRACT FROM AUTHOR]

In this article, we examine the collective particle dynamics, as expressed by the time correlation function of the longitudinal particle current density, of several different fluids in the vicinity of their freezing points/lines. We consider and compare results obtained by dynamic light scattering for a suspension of hard spheres and by molecular dynamics for fluids with hard sphere and Lennard-Jones interactions. The latter are performed along both an isotherm and an isochore. In all cases, we find a qualitative change in the collective dynamics, within the resolution of the data, when their respective freezing lines are crossed. We associate this change with the onset of caging. The new results for the Lennard-Jones fluid reported here confirm that the occurrence of caging, found previously for systems of hard spheres, is a more general feature that distinguishes a metastable fluid from one in thermodynamic equilibrium. [ABSTRACT FROM AUTHOR]

The microstructure and rheological properties of a model colloidal system was probed in the vicinity of the glass transition by small-angle and ultra small-angle x-ray scattering, dynamic light scattering (DLS) and bulk rheology. The volume fraction of the particles was deduced by modeling the structure factor and the absolute scattered intensity in a self-consistent way. The glass transition ([lowercase_phi_synonym]G) was identified from the frequency dependence of the shear moduli in the linear regime. The experimentally observed behavior was then compared with the viscoelastic properties derived from mode-coupling theory (MCT) using the experimental structure factor as input to the theory. The ensemble-averaged intermediate scattering functions from DLS measurements were also compared with those calculated from the MCT and reasonable agreement was obtained. [ABSTRACT FROM AUTHOR]

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior. [ABSTRACT FROM AUTHOR]

We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction [lowercase_phi_synonym] we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low [lowercase_phi_synonym] and T. The former is rather vertical ([lowercase_phi_synonym] controlled), while the latter is rather horizontal (T controlled) in the [lowercase_phi_synonym]-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on [lowercase_phi_synonym], while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in [lowercase_phi_synonym] along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics. [ABSTRACT FROM AUTHOR]

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing—within the same model—the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = -1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress-strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

The addition of co-solutes to colloidal suspensions is often employed to induce tunable depletion interactions. In this work, we investigate effective colloidal interactions arising from binary co-solute mixtures of hard spheres and patchy particles. By changing the relative concentration of the two species, we show that the resulting effective potential V eff continuously changes from the one obtained for a single-component hard sphere co-solute to that mediated by the single-component patchy particle co-solute. Interestingly, we find that, independent of the relative concentration of the two components, the resulting V eff is additive, i.e., it is well-described by the linear combination of the effective interactions mediated by respective pure co-solutes. However, a breakdown of the additivity occurs when the co-solute mixture is close to the onset of a demixing transition. These results represent a step forward in understanding and predicting colloidal behavior in complex and crowded environments and for exploiting this knowledge to design targeted colloidal superstructures.

We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [N. Gnan and E. Zaccarelli, Nat. Phys. 15, 683 (2019)] where an inner Hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced by opposite forces, and (iii) a semi-flexible model where an angular potential between adjacent monomers induces strong particle deformations. By analyzing the dynamics of the three models, we find that in all cases, there exists a direct link between the system fragility and particle asphericity. Among the three, only the first model displays anomalous dynamics in the form of a super-diffusive behavior of the mean-squared displacement and of a compressed exponential relaxation of the density auto-correlation function. We show that this is due to the combination of internal elasticity and the out-of-equilibrium force self-generated by each ring, both of which are necessary ingredients to induce such a peculiar behavior often observed in experiments of colloidal gels. These findings reinforce the role of particle deformation, connected to internal elasticity, in driving the dynamical response of dense soft particles.

The growing interest in the dynamical properties of colloidal suspensions, both in equilibrium and under an external drive such as shear or pressure flow, requires the development of accurate methods to correctly include hydrodynamic effects due to the suspension in a solvent. In the present work, we generalize Multiparticle Collision Dynamics (MPCD) to be able to deal with soft, polymeric colloids. Our methods build on the knowledge of the monomer density profile that can be obtained from monomer-resolved simulations without hydrodynamics or from theoretical arguments. We hereby propose two different approaches. The first one simply extends the MPCD method by including in the simulations effective monomers with a given density profile, thus neglecting monomer-monomer interactions. The second one considers the macromolecule as a single penetrable soft colloid (PSC), which is permeated by an inhomogeneous distribution of solvent particles. By defining an appropriate set of rules to control the collision events between the solvent and the soft colloid, both linear and angular momenta are exchanged. We apply these methods to the case of linear chains and star polymers for varying monomer lengths and arm number, respectively, and compare the results for the dynamical properties with those obtained within monomer-resolved simulations. We find that the effective monomer method works well for linear chains, while the PSC method provides very good results for stars. These methods pave the way to extend MPCD treatments to complex macromolecular objects such as microgels or dendrimers and to work with soft colloids at finite concentrations.

A transition from solid-like to liquid-like behavior occurs when colloidal gels are subjected to a prolonged exposure to a steady shear. This phenomenon, which is characterized by a yielding point, is found to be strongly dependent on the packing fraction. However, it is not yet known how the effective inter-particle potential affects this transition. To this aim, we present a numerical investigation of the rheology of equilibrium gels in which a short-range depletion is complemented by a long-range electrostatic interaction. We observe a single yielding event in the stress-strain curve, occurring at a fixed strain. The stress overshoot is found to follow a power-law dependence on the Péclet number, with an exponent larger than that found in depletion gels, suggesting that its value may depend systematically on the underlying colloid-colloid interactions. We also establish a mapping between equilibrium states and steady states under shear, which allows us to identify the structural modifications induced by the presence of the shear. Remarkably, we find that steady states corresponding to the same Péclet number, obtained by different combinations of shear rate and solvent viscosity, show identical structural and rheological properties. Our results highlight the importance of understanding the coupling between colloidal interactions, solvent effects, and flow to be able to describe the microscopic organization of colloidal particles under shear.

We describe a combined experimental, theoretical, and simulation study of the structural correlations between cross-linked highly monodisperse and swollen Poly(N-isopropylacrylamide) microgel dispersions in the fluid phase in order to obtain the effective pair-interaction potential between the microgels. The density-dependent experimental pair distribution functions g(r)'s are deduced from real space studies using fluorescent confocal microscopy and compared with integral equation theory and molecular dynamics computer simulations. We use a model of Hertzian spheres that is capable to well reproduce the experimental pair distribution functions throughout the fluid phase, having fixed the particle size and the repulsive strength. Theoretically, a monodisperse system is considered whose properties are calculated within the Rogers-Young closure relation, while in the simulations the role of polydispersity is taken into account. We also discuss the various effects arising from the finite resolution of the microscope and from the noise coming from the fast Brownian motion of the particles at low densities, and compare the information content from data taken in 2D and 3D through a comparison with the corresponding simulations. Finally different potential shapes, recently adopted in studies of microgels, are also taken into account to assess which ones could also be used to describe the structure of the microgel fluid.

We performed extensive molecular dynamics (MD) simulations, supplemented by Mode Coupling Theory (MCT) calculations, for the square shoulder model, a purely repulsive potential where the hardcore is complemented by a finite shoulder. For the one-component version of this model, MCT predicted [Sperl et al., Phys. Rev. Lett. 104, 145701 (2010)] the presence of diffusion anomalies both upon cooling and upon compression and the occurrence of glass-glass transitions. In the simulations, we focus on a non-crystallising binary mixture, which, at the investigated shoulder width, shows a non-monotonic behaviour of the diffusion upon cooling but not upon isothermal compression. In addition, we find the presence of a disconnected glass-glass line in the phase diagram, ending in two higher order singularities. These points generate a logarithmic dependence of the density correlators as well as a subdiffusive behaviour of the mean squared displacement, although with the interference of the nearby liquid-glass transition. We also perform novel MCT calculations using as input the partial structure factors obtained within MD, confirming the simulation results. The presence of two hard sphere glasses, differing only in their hardcore length, is revealed, showing that the simple competition between the two is sufficient for creating a rather complex dynamical behaviour.

We report a numerical investigation of two colloids immersed in a critical solvent, with the aim of quantifying the effective colloid-colloid interaction potential. By turning on an attraction between the colloid and the solvent particles we follow the evolution from the case in which the solvent density close to the colloids changes from values smaller than the bulk to values larger than the bulk. We thus effectively implement the so-called (+, +) and (-, -) boundary conditions defined in field theoretical approaches focused on the description of critical Casimir forces. We find that the effective potential at large distances decays exponentially, with a characteristic decay length compatible with the bulk critical correlation length, in full agreement with theoretical predictions. We also investigate the case of (+, -) boundary condition, where the effective potential becomes repulsive. Our study provides a guidance for a design of the interaction potential which can be exploited to control the stability of colloidal systems.

By means of computer simulations and solution of the equations of the mode coupling theory (MCT), we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question, provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This disagreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting only between particles of different sizes. The small particles provide the bonds between the large ones. With a proper choice of the interaction parameters, as well as of the relative concentration of the two species, it is possible to control the effective valence. Here we focus on a specific choice of the parameters which favors tetrahedral ordering and study the equilibrium static properties of the system in a large window of densities and temperatures. Upon lowering the temperature we observe a progressive increase in local order, accompanied by the formation of a four-coordinated network of bonds. Three different density regions are observed: At low density the system phase separates into a gas and a liquid phase; at intermediate densities a network of fully bonded particles develops; at high densities--due to the competition between excluded volume and attractive interactions--the system forms a defective network. The very same behavior has been previously observed in numerical studies of nonspherical models for molecular liquids, such as water, and in models of patchy colloidal particles. Different from these models, theoretical treatments devised for spherical potentials, e.g., integral equations and ideal mode coupling theory for the glass transition, can be applied in the present case, opening the way for a deeper understanding of the thermodynamic and dynamic behavior of low valence molecules and particles.

We report a numerical investigation of the viscoelastic behavior in models for steric repulsive and short-ranged attractive colloidal suspensions, along different paths in the attraction strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass, and in the reentrant region where viscosity shows a nonmonotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent of the microscopic dynamics by comparing Newtonian and Brownian simulations for the same model. Finally, we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.