Phase behavior of mixtures of hard colloids and soft coarse-grained macromolecules.

Effective "soft" interactions between macromolecules such as polymers, amphiphilic dendrimers, and suitably designed DNA based dendritic molecules have been shown to be purely repulsive and non-diverging. We report the structure and phase behavior of a mixture of hard colloids and soft coarse-grained macromolecules. Through the use of Reference Interaction Site Model theory and molecular dynamics simulations we find that hard colloids and soft macromolecules act as depletants toward each other, generating a medium-induced effective attraction. This effective attraction leads to the formation of non-dispersed phases at high densities. At low and high fractions of hard colloids the system macrophase separates into two disparate regions of hard colloids and soft macromolecules. However, this system microphase separates into a hard-rich and soft-rich self-assembled domains at intermediate compositions. The formation of microphase separated structure in this system of isotropic, disconnected, and purely repulsive colloids is surprising and quite novel. This behavior is likely due to a softening of the interface between hard-rich and soft-rich self-assembled domains. Molecular dynamics simulations have revealed that the microphase separated state has an overall disordered bicontinuous morphology. The hard-rich domain forms an ordered FCC structure and the soft-rich domain forms a disordered cluster-fluid, making the structure simultaneously ordered and disordered.

Polymer-mediated self-assembly, dispersion, and phase separation of Janus nanorods.

The challenge of stabilizing polymer nanocomposites lies in the fact that nanoparticles tend to phase separate from the polymer melt due to an entropic 'depletion attraction' between nanoparticles. Additionally, composites of polymer and nanorods show a decrease in miscibility with increasing nanorod aspect ratio [U. K. Sankar and M. Tripathy, Macromolecules, 2015, 48, 432-442; U. Erigi, U. Dhumal and M. Tripathy, J. Chem. Phys., 2021, 154, 124903]. In this work, we have studied the structure and phase behaviour of polymer-Janus nanorod mixtures using Polymer Reference Interaction Site Model (PRISM) theory and molecular dynamics simulations. The composite system of polymer and Janus nanorods of two different thicknesses, at various Janus nanorod densities, and for different interaction strengths between polymer and attractive sites of Janus nanorods (εpa), is investigated for their miscibility and self-assembly. At low Janus nanorod density, PRISM theory predicts transitions from the entropic depletion-driven contact aggregation of Janus nanorods to a well-dispersed phase to the bridging-driven phase separation of Janus nanorods, with increasing εpa. This behaviour is similar to earlier predictions for homogeneous nanorods. However, molecular dynamics simulations do not confirm the bridging-driven phase separation at high εpa predicted by PRISM theory. We find that both PRISM theory and molecular dynamics simulations are in agreement in the intermediate and high Janus nanorod density regimes. PRISM theory predicts, and simulations confirm, that at high Janus nanorod densities, the system undergoes a transition from depletion-driven macrophase separation to dispersion to chemical anisotropy-driven self-assembly with increasing εpa. The self-assembly at high εpa is mediated by the polymer. At intermediate Janus nanorod densities, the usual transition from an entropic depletion-driven macrophase separation to dispersion is predicted at low εpa. At high εpa, both PRISM theory and molecular dynamics simulations show transition to a state that is simultaneously macrophase separated and microphase separated (self-assembled).

Growth transitions and critical behavior in the non-equilibrium aggregation of short, patchy nanorods.

We have carried out Monte Carlo simulations to study the non-equilibrium aggregation of short patchy nanorods in two dimensions. Below a critical value of patch size ([Formula: see text]), the aggregates have finite sizes with small radii of gyration, [Formula: see text]. At [Formula: see text], the average radius of gyration shows a power law increase with time such that [Formula: see text], where [Formula: see text]. Above, [Formula: see text], the aggregates are fractal in nature and their fractal dimension depends on the value of patch size. These morphological differences are due to the fact that below the critical value of patch size ([Formula: see text]), the growth of the clusters is suppressed and the system reaches an 'absorbed state.' Above [Formula: see text], the system reaches an 'active state,' in which the cluster size keeps growing with a fixed rate at long times. Thus, the system encounters a non-equilibrium phase transition. Close to the transition, the growth rate scales as [Formula: see text], where [Formula: see text]. The long-time growth rate varies as [Formula: see text] where [Formula: see text]. These scaling exponents indicate that the transition belongs to the directed percolation universality class. The patchy nanorods also display a threshold patch size ([Formula: see text]), beyond which the long-time growth rate remains constant. We present geometric arguments for the existence of [Formula: see text]. The fractal dimension of the aggregates increases from 1.75, at [Formula: see text], to 1.81, at [Formula: see text]. It remains constant beyond [Formula: see text].

Phase behavior of polymer-nanorod composites: A comparative study using PRISM theory and molecular dynamics simulations.

Well-dispersed composites of polymer and nanorods have many emerging applications and, therefore, are an important area of research. Polymer reference interaction site model (PRISM) theory and molecular dynamics simulations have become powerful tools in the study of the structure and phase behavior of polymer nanocomposites. In this work, we employ both PRISM theory and molecular dynamics simulations to determine the structure and spinodal phase diagram of 1% volume fraction of nanorods in a polymer melt. We make quantitative comparisons between the phase diagrams, which are reported as a function of nanorod aspect ratio and polymer-nanorod interactions. We find that both PRISM theory and molecular dynamics simulations predict the formation of contact aggregates at low polymer-nanorod attraction strength (γ) and bridged aggregates at high polymer-nanorod attraction strength. They predict an entropic depletion-driven phase separation at low γ and a bridging-driven spinodal phase separation at high γ. The polymer and nanorods are found to form stable composites at intermediate values of the polymer-nanorod attraction strength. The fall of the bridging boundary and the gradual rise of the depletion boundary with the nanorod aspect ratio are predicted by both PRISM theory and molecular dynamics simulations. Hence, the miscible region narrows with increasing aspect ratio. The depletion boundaries predicted by theory and simulation are quite close. However, the respective bridging boundaries present a significant quantitative difference. Therefore, we find that theory and simulations qualitatively complement each other and display quantitative differences.

The effect of surface roughness on the phase behavior of colloidal particles.

Shape anisotropy of colloidal particles can give rise to complex intermolecular interactions that determine particle packing and phase behavior. The vapor-liquid coexistence curves of attractive rough particles display a shift when compared to attractive smooth spherical particles. We use Integral Equation Theory (IET) to determine the vapor-liquid spinodal phase diagram of smooth and rough colloidal particles interacting through square-well attraction. Additionally, we use Gibbs Ensemble Monte Carlo (GEMC) simulations to locate their vapor-liquid coexistence curves. We model a rough colloidal particle as a spherical core with small beads embedded on its surface. The critical point of smooth spherical particle systems predicted by theory and simulations is in quantitative agreement. An increase in surface roughness due to an increase in either the number of beads or the diameter of the beads has a modest effect on the local structure of the system in the supercritical region. In contrast, increasing surface roughness consistently shifts the vapor-liquid coexistence curves to higher temperatures. The critical temperature is found to be a quadratic function of the number of beads. At a fixed bead size and number of beads, the critical temperature does not vary with the arrangement of beads on the core. Both IET and GEMC simulations predict that unlike critical temperatures, critical packing fractions vary non-monotonically with surface roughness. We find that the feasibility and accuracy of the integral equation theory depend sensitively on the chosen closure combination.

Self-assembly of polymer-linked nanoparticles and scaling behavior in the assembled phase.

An entropic depletion-driven phase separation is known to be observed for mixtures of polymers and nanoparticles. While polymer-linked nanoparticles have been synthesized, their phase behavior has only been predicted for chemically specific interactions. We use integral equation theory to determine the structure and phase behavior of chemically isotropic polymer-linked nanoparticles at high densities. When each end of a linear polymer is grafted to a nanoparticle, we predict an entropy-driven microphase separation of locally segregated polymer-rich and nanoparticle-rich domains. The formation of these self-assembled structures is purely a consequence of the shape of the polymer-linked particle species. The depletion-driven demixing of ungrafted polymer-nanoparticle composites (with small amounts of nanoparticles) is enhanced as particle diameter (D) grows compared to the polymer radius of gyration (Rg). However, this study shows that for polymer-linked nanoparticle systems, the transition from a liquid to microphase separated state shifts to higher densities (i.e. is inhibited) as D/Rg increases. The transition volume fractions attain a unique value (of ∼0.69) at D/Rg ∼ 1.13. The repeating length scale (L*) is 1.4-2.2 times the size of the entire species (D + Rg). Surprisingly, L*/(D + Rg) is a non-monotonic function of the polymer radius of gyration. The repeating length scale also displays a remarkable scaling behavior, as a function of the particle diameter and the polymer density. Additionally, our study implies that two different mechanisms of transitioning to the microphase separated state are possible for these systems, which has important implications for the transition density and the kinds of structures formed.

Theoretical study of the structure and assembly of Janus rods.

Microscopic integral equation theory is applied to investigate the real and Fourier space structure and phase behavior of compositionally symmetric AB Janus rods that interact via hard core excluded volume interactions and competing repulsive and attractive tail potentials. If the spatial range of the latter are short and equal, chemical asymmetry results in attraction-driven assembly into a cylindrical micellar structure of spatial periodicity between one and two rods lengths. The apparent microphase spinodal ordering temperature increases with attraction range and rod length, and the microdomain coherence length strongly grows upon cooling. However, as the tail repulsion range increases significantly, the micellar morphology is destroyed and a new repulsion-driven ordering emerges at high volume fractions characterized by a much smaller spatial periodicity. We also find a tight correlation between the local attraction-induced clustering (quantified by the excess number of nearest neighbors) and the microdomain-scale ordering (measured by the amplitude of the intense low wavevector peak of the collective structure factor). Moreover, the former converges to a unique value at the microphase spinodal temperature for all volume fractions, repulsion strengths, and tail repulsion ranges studied, in qualitative contrast to the behavior of the repulsive-interaction driven ordering phenomena. The phase behavior trends of the integral equation approach are compared to a computationally and conceptually simpler mean field hybrid formulation based on a random phase approximation treatment of tail potentials, thereby allowing the role of physical clustering, interparticle correlations, and microdomain scale concentration fluctuations to be assessed.

Activated dynamics in dense fluids of attractive nonspherical particles. I. Kinetic crossover, dynamic free energies, and the physical nature of glasses and gels.

We apply the center-of-mass versions of naïve mode coupling theory and nonlinear Langevin equation theory to study how short-range attractive interactions modify the onset of localization, activated single-particle dynamics, and the physical nature of the transiently arrested state of a variety of dense nonspherical particle fluids (and the spherical analog) as a function of volume fraction and attraction strength. The form of the dynamic crossover boundary depends on particle shape, but the reentrant glass-fluid-gel phenomenon and the repulsive glass-to-attractive glass crossover always occur. Diverse functional forms of the dynamic free energy are found for all shapes including glasslike, gel-like, a glass-gel form defined by the coexistence of two localization minima and two activation barriers, and a "mixed" attractive glass characterized by a single, very short localization length but an activation barrier located at a large displacement as in repulsive-force caged glasses. For the latter state, particle trajectories are expected to be of a two-step activated form and can be accessed at high attraction strength by increasing volume fraction, or by increasing attraction strength at fixed high enough volume fraction. A new classification scheme for slow dynamics of fluids of dense attractive particles is proposed based on specification of both the nature of the localized state and the particle displacements required to restore ergodicity via activated barrier hopping. The proposed physical picture appears to be in qualitative agreement with recent computer simulations and colloid experiments.

Activated dynamics in dense fluids of attractive nonspherical particles. II. Elasticity, barriers, relaxation, fragility, and self-diffusion.

In paper II of this series we apply the center-of-mass version of Nonlinear Langevin Equation theory to study how short-range attractive interactions influence the elastic shear modulus, transient localization length, activated dynamics, and kinetic arrest of a variety of nonspherical particle dense fluids (and the spherical analog) as a function of volume fraction and attraction strength. The activation barrier (roughly the natural logarithm of the dimensionless relaxation time) is predicted to be a rich function of particle shape, volume fraction, and attraction strength, and the dynamic fragility varies significantly with particle shape. At fixed volume fraction, the barrier grows in a parabolic manner with inverse temperature nondimensionalized by an onset value, analogous to what has been established for thermal glass-forming liquids. Kinetic arrest boundaries lie at significantly higher volume fractions and attraction strengths relative to their dynamic crossover analogs, but their particle shape dependence remains the same. A limited universality of barrier heights is found based on the concept of an effective mean-square confining force. The mean hopping time and self-diffusion constant in the attractive glass region of the nonequilibrium phase diagram is predicted to vary nonmonotonically with attraction strength or inverse temperature, qualitatively consistent with recent computer simulations and colloid experiments.

Janus particle synthesis and assembly.

Janus particles, colloid-sized particles with two regions of different surface chemical composition, possess energetic interactions that depend not only on their separation but also on their orientation. Research on Janus and colloidal particles that are chemically patchy in even more complicated fashion has opened a new chapter in the colloid research field. This article highlights recent progress in both experiment and theory regarding synthesis and self-assembly of Janus particles, and tentatively outlines some areas of future opportunity.

The influence of shape on the glassy dynamics of hard nonspherical particle fluids. I. Dynamic crossover and elasticity.

We extend and apply the center-of-mass version of the microscopic naive mode coupling theory to study the ideal kinetic glass transition of dense fluids and suspensions composed of broad families of one-, two-, and three-dimensional hard nonspherical particles. A kinetic arrest diagram is constructed which indicates a dynamical crossover or onset of activated barrier hopping controlled transport. We find (quasi-) one-dimensional rods and rings form ideal glasses at the lowest volume fractions which decrease strongly with aspect ratio. Two-dimensional disks form ideal glasses at intermediate volume fractions which decrease slowly with the number of particles comprising the planar objects. Compact three-dimensional cluster particles exhibit a subtle nonmonotonic variation of the onset volume fraction that depends on their detailed shape, surface corrugation, and intraparticle interstitial volume. A strong correlation between the ideal kinetic arrest volume fraction and dimensionless compressibility (amplitude of density fluctuations) is predicted. The elastic shear modulus (transient localization length) grows (decreases) exponentially with volume fraction in a manner that becomes stronger as particle dimensionality increases.

The influence of shape on the glassy dynamics of hard nonspherical particle fluids. II. Barriers, relaxation, fragility, kinetic vitrification, and universality.

We extend and apply the nonlinear Langevin equation theory of activated barrier hopping dynamics in glassy fluids and colloidal suspensions to study broad families of one-, two-, and three-dimensional hard nonspherical particles. Beyond the ideal kinetic arrest volume fraction, entropic barriers emerge with heights (alpha relaxation times, inverse diffusion constants) that increase nonlinearly (nonexponentially) with volume fraction and in a manner that becomes stronger with particle dimensionality. Partial collapse of the volume fraction dependence of barrier heights and reduced relaxation times of different particle shapes within a fixed dimensionality class are achieved based on a difference volume fraction variable that quantifies the distance from the ideal mode coupling theory dynamic crossover. However, the barrier, alpha relaxation time, and self-diffusion constant results of all shapes are remarkably well collapsed onto a single universal master curve based on a theoretically motivated coupling constant which quantifies the renormalized mean square force on a tagged particle. The latter is determined mainly by the square of the intermolecular site-site contact value of the pair correlation function, thereby providing an explicit microscopic connection between local packing, binary collisions, and slow dynamics. A large variation of the dynamic fragility with particle shape is found with compact cluster particles being the most fragile. A kinetic glass transition map is constructed that is relevant to vitrification of laboratory colloidal suspensions. The possible relevance of the hard particle results for understanding the dynamic fragility of thermal van der Waals liquids is discussed.