Growth and aging in a few phase-separating active matter systems.

Via computer simulations we study evolution dynamics in systems of continuously moving active Brownian particles. The obtained results are discussed against those from the passive 2D Ising case. Following sudden quenches of random configurations to state points lying within the miscibility gaps and to the critical points, we investigate the far-from-steady-state dynamics by calculating quantities associated with structure and characteristic length scales. We also study aging for quenches into the miscibility gap and provide a quantitative picture for the scaling behavior of the two-time order-parameter correlation function. The overall structure and dynamics are consistent with expectations from the Ising model. This remains true for certain active lattice models as well, for which we present results for quenches to the critical points.

Membrane-Mediated Interactions Between Nonspherical Elastic Particles.

The transport of particles across lipid-bilayer membranes is important for biological cells to exchange information and material with their environment. Large particles often get wrapped by membranes, a process which has been intensively investigated in the case of hard particles. However, many particles in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses, macromolecular condensates, polymer-grafted nanoparticles, and microgels. Vesicles may serve as a generic model system for deformable particles. Here, we study nonspherical vesicles with various sizes, shapes, and elastic properties at initially planar lipid-bilayer membranes. Using the Helfrich Hamiltonian, triangulated membranes, and energy minimization, we predict the interplay of vesicle shapes and wrapping states. Increasing particle softness enhances the stability of shallow-wrapped and deep-wrapped states over nonwrapped and complete-wrapped states. The free membrane mediates an interaction between partial-wrapped vesicles. For the pair interaction between deep-wrapped vesicles, we predict repulsion. For shallow-wrapped vesicles, we predict attraction for tip-to-tip orientation and repulsion for side-by-side orientation. Our predictions may guide the design and fabrication of deformable particles for efficient use in medical applications, such as targeted drug delivery.

Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies.

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer which show interesting, "universal" behavior. For a given NP radius, Rc, and for large enough areal grafting densities, σ, to be in the dense brush regime we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, Mn. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕNP, ϕNP,max = [Rc/(Rc + hmax)]3 ≈ 0.049. Motivated by this conclusion, we measured CO-2 and CH4 permeability enhancements across a variety of Rc, Mn and σ, and find that they behave in a similar manner when considered as a function of ϕNP, with a peak in the near vicinity of the predicted ϕNP,max. Thus, the chain length dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ behave akin to a two-layer transport medium - the region in the near vicinity of the NP surface is comprised of extended polymer chains which speed-up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

Wetting transitions of polymer solutions: Effects of chain length and chain stiffness.

Wetting and drying phenomena are studied for flexible and semiflexible polymer solutions via coarse-grained molecular dynamics simulations and density functional theory calculations. This study is based on the use of Young's equation for the contact angle, determining all relevant surface tensions from the anisotropy of the pressure tensor. The solvent quality (or effective temperature, equivalently) is varied systematically, while all other interactions remain unaltered. For flexible polymers, the wetting transition temperature Tw increases monotonically with chain length N, while the contact angle at temperatures far below Tw is independent of N. For semiflexible polymer solutions, Tw varies non-monotonically with the persistence length: Initially, Tw increases with increasing chain stiffness and reaches a maximum, but then a sudden drop of Tw is observed, which is associated with the isotropic-nematic transition of the system.

Blends of Semiflexible Polymers: Interplay of Nematic Order and Phase Separation.

Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several cases of bending stiffness κ (the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e., NA=16, NB=32 or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (N=32) and large stiffness disparity (κB/κA=4.9 to 8), both isotropic-nematic and nematic-nematic unmixing occur. It is found that the phase diagrams may exhibit a triple point or a nematic-nematic critical point, and that coexisting phases differ appreciably in their monomer densities. The properties of the two types of chains (nematic order parameters, chain radii, etc.) in the various phases are studied in detail, and predictions on the (anisotropic) critical behavior near the critical point of nematic-nematic unmixing are made.

Gas Transport in Interacting Planar Brushes.

Recent experiments on melts of spherical nanoparticles (NPs) densely grafted with polymer chains show enhanced gas transport relative to the neat polymer (without NPs). As a means of understanding this unexpected behavior, we consider here the simpler case of two interacting planar brushes, under conditions representing a polymer melt far below its critical point (i.e., where the "free volume" or holes act akin to a poor solvent). Computer simulations illustrate, in agreement with mean-field ideas, that the density profile far away from the walls is flat but with a value that is marginally larger than the corresponding polymer melt under identical state conditions. We find that tracer particles, which represent the gas of interest, segregate preferentially to the grafting surface, with this result being relatively insensitive to the nature of polymer-surface interactions. These brush layers therefore correspond to heterogeneous transport media: the gas molecules near the grafting surface have accelerated dynamics (presumably parallel to the wall) relative to the corresponding polymer melt, but they have slower dynamics in the central region of the brush. We therefore find that gas molecules perform hop-like motions - they spend a significant part of their time in the regions of fast transport, separated by motions where they "hop" from one surface to the other. These phenomena in combination lead to an overall speedup in gas dynamics in these brush layers relative to a polymer melt, in good agreement with the experimental data.

Tuning Selectivities in Gas Separation Membranes Based on Polymer-Grafted Nanoparticles.

Polymer membranes are critical to many sustainability applications that require the size-based separation of gas mixtures. Despite their ubiquity, there is a continuing need to selectively affect the transport of different mixture components while enhancing mechanical strength and hindering aging. Polymer-grafted nanoparticles (GNPs) have recently been explored in the context of gas separations. Membranes made from pure GNPs have higher gas permeability and lower selectivity relative to the neat polymer because they have increased mean free volume. Going beyond this ability to manipulate the mean free volume by grafting chains to a nanoparticle, the conceptual advance of the present work is our finding that GNPs are spatially heterogeneous transport media, with this free volume distribution being easily manipulated by the addition of free polymer. In particular, adding a small amount of appropriately chosen free polymer can increase the membrane gas selectivity by up to two orders of magnitude while only moderately reducing small gas permeability. Added short free chains, which are homogeneously distributed in the polymer layer of the GNP, reduce the permeability of all gases but yield no dramatic increases in selectivity. In contrast, free chains with length comparable to the grafts, which populate the interstitial pockets between GNPs, preferentially hinder the transport of the larger gas and thus result in large selectivity increases. This work thus establishes that we can favorably manipulate the selective gas transport properties of GNP membranes through the entropic effects associated with the addition of free chains.

Structure of Polymer-Grafted Nanoparticle Melts.

The structure of neat melts of polymer-grafted nanoparticles (GNPs) is studied via coarse-grained molecular dynamics simulations. We systematically vary the degree of polymerization and grafting density at fixed nanoparticle (NP) radius and study in detail the shape and size of the GNP coronas. For sufficiently high grafting density, chain sections close to the NP core are extended and form a dry layer. Further away from the NP, there is an interpenetration layer, where the polymer coronas of neighboring GNPs overlap and the chain sections have almost unperturbed conformations. To better understand this partitioning, we develop a two-layer model, representing the grafted polymer around an NP by spherical dry and interpenetration layers. This model quantitatively predicts that the thicknesses of the two layers depend on one universal parameter, x, the degree of overcrowding of grafted chains relative to chains in the melt. Both simulations and theory show that the chain extension free energy is nonmonotonic with increasing chain length at a fixed grafting density, with a well-defined maximum. This maximum is indicative of the crossover from the dry layer-dominated to interpenetration layer-dominated regime, and it could have profound consequences on our understanding of a variety of anomalous transport properties of these GNPs. Our theoretical approach therefore provides a facile means for understanding and designing solvent-free GNP-based materials.

Entropic Unmixing in Nematic Blends of Semiflexible Polymers.

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

Kinetics of domain growth and aging in a two-dimensional off-lattice system.

We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w}, â„“, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

Phase behavior of flexible and semiflexible polymers in solvents of varying quality.

The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained models, with a bond-angle potential to control chain stiffness, for chain lengths comparable to the persistence length of the chains. We varied both the density of the monomeric units and the effective temperature that controls the quality of the implicit solvent. For very stiff chains, only a single transition from an isotropic fluid to a nematic is found, with a phase diagram of "swan-neck" topology. For less stiff chains, however, also unmixing between isotropic fluids of different concentration, ending in a critical point, occurs for temperatures above a triple point. The associated critical behavior is examined in the MD simulations and found compatible with Ising universality. Apart from this critical behavior, DFT calculations agree qualitatively with the MD simulations.

Segregation in Drying Binary Colloidal Droplets.

When a colloidal suspension droplet evaporates from a solid surface, it leaves a characteristic deposit in the contact region. These deposits are common and important for many applications in printing, coating, or washing. By the use of superamphiphobic surfaces as a substrate, the contact area can be reduced so that evaporation is almost radially symmetric. While drying, the droplets maintain a nearly perfect spherical shape. Here, we exploit this phenomenon to fabricate supraparticles from bidisperse colloidal aqueous suspensions. The supraparticles have a core-shell morphology. The outer region is predominantly occupied by small colloids, forming a close-packed crystalline structure. Toward the center, the number of large colloids increases and they are packed amorphously. The extent of this stratification decreases with decreasing the evaporation rate. Complementary simulations indicate that evaporation leads to a local increase in density, which, in turn, exerts stronger inward forces on the larger colloids. A comparison between experiments and simulations suggest that hydrodynamic interactions between the suspended colloids reduce the extent of stratification. Our findings are relevant for the fabrication of supraparticles for applications in the fields of chromatography, catalysis, drug delivery, photonics, and a better understanding of spray-drying.

Disentangling the Role of Chain Conformation on the Mechanics of Polymer Tethered Particle Materials.

The linear elastic properties of isotropic materials of polymer tethered nanoparticles (NPs) are evaluated using noncontact Brillouin light spectroscopy. While the mechanical properties of dense brush materials follow predicted trends with NP composition, a surprising increase in elastic moduli is observed in the case of sparsely grafted particle systems at approximately equal NP filling ratio. Complementary molecular dynamics simulations reveal that the stiffening is caused by the coil-like conformations of the grafted chains, which lead to stronger polymer-polymer interactions compared to densely grafted NPs with short chains. Our results point to novel opportunities to enhance the physical properties of composite materials by the strategic design of the "molecular architecture" of constituents to benefit from synergistic effects relating to the organization of the polymer component.

Kinetics of Vapor-Solid Phase Transitions: Structure, Growth, and Mechanism.

The kinetics of the separation between low and high density phases in a single component Lennard-Jones model is studied via molecular dynamics simulations, at very low temperatures, in the space dimension d=2. For densities close to the vapor branch of the coexistence curve, disconnected nanoscale clusters of the high density phase exhibit essentially ballistic motion. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filamentlike nonequilibrium structure at a later time, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in the kinetics of phase transitions, is found to be absent. This invalidates the common method, that provides a growth law comparable to that in solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality, quantifies the growth of the characteristic "length" to be a power law with time, the exponent being strongly temperature dependent. The observed growth law is in agreement with the outcome of a nonequilibrium kinetic theory.

Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transition.

Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model has been obtained via the Monte Carlo simulations. The transport properties, viz., the bulk viscosity and the thermal conductivity, are calculated via the Green-Kubo relations, by taking inputs from the MD simulations in the microcanonical ensemble. The critical singularities of these quantities are estimated via the FSS method. The results thus obtained are in nice agreement with the predictions of the dynamic renormalization group and mode-coupling theories.

Droplet growth during vapor-liquid transition in a 2D Lennard-Jones fluid.

Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this purpose, has been obtained via the Monte Carlo simulations. Our focus is on the region very close to the vapor branch of the coexistence curve. Quenches to such region provide morphology that consists of disconnected circular clusters in the vapor background. We identified that these clusters exhibit diffusive motion and grow via sticky collisions among them. The growth follows power-law behavior with time, exponent of which is found to be in nice agreement with a theoretical prediction.

Dimensionality dependence of aging in kinetics of diffusive phase separation: Behavior of order-parameter autocorrelation.

Behavior of two-time autocorrelation during the phase separation in solid binary mixtures is studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions 2 and 3 are obtained empirically. The long-time behavior is found to be power law, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Cahn-Hilliard and Ising models provide consistent results.

Aging in ferromagnetic ordering: full decay and finite-size scaling of autocorrelation.

Nonequilibrium dynamics in Ising and Ginzburg-Landau models were studied for a nonconserved order parameter that mimics ordering in ferromagnets. The focus was on the understanding of the decay of the two time (t, t(w); t > tw) order-parameter correlation function. For this quantity, a full form has been obtained empirically which, for t ≫ t(w), provides a power-law ∼ (ℓ/ℓ(w))(-λ), ℓ and ℓ(w) being the characteristic lengths at t and tw, respectively. This empirical form was used for a finite-size scaling analysis to obtain the exponent λ in space dimensions d = 2 and 3. Our estimates of λ and understanding of the finite-size effects, for the models considered, provide useful information on the relevance of thermal noise. The values of λ obtained are in good agreement with the predictions of a theory based on Gaussian auxiliary field ansatz.