External field-driven property localization in liquids of responsive macromolecules.

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.

Interaction-Limited Aggregation: Fine-Tuning the Size of pNIPAM Particles by Association with Hydrophobic Ions.

We have investigated the formation of stable clusters of poly(N-isopropylacrylamide) (pNIPAM) chains in water at temperatures above the lower critical solution temperature (LCST), induced by the presence of sodium tetraphenylborate, NaPh4B. The hydrophobic Ph4B- ions interact strongly with the pNIPAM chains, providing them with a net effective negative charge, which leads to the stabilization of pNIPAM clusters for temperatures above the LCST, with a mean cluster size that depends non-monotonically on salt concentration. Combining experiments with physical modeling at the mesoscopic level and atomistic molecular dynamic simulations, we show that this effect is caused by the interplay between the hydrophobic attraction between pNIPAM chains and the electrostatic repulsion induced by the associated Ph4B- ions. These results provide insight on the significance of weak associative anion-polymer interaction driven by hydrophobic interaction and how this anionic binding can prevent macroscopic phase separation. Harvesting the competition between attractive hydrophobic and repulsive electrostatic interaction opens avenues for the dynamic control of the formation of well-calibrated polymer microparticles.

Liquid structure of bistable responsive macromolecules using mean-field density-functional theory.

Macromolecular crowding typically applies to biomolecular and polymer-based systems in which the individual particles often feature a two-state folded/unfolded or coil-to-globule transition, such as found for proteins and peptides, DNA and RNA, or supramolecular polymers. Here, we employ a mean-field density functional theory (DFT) of a model of soft and bistable responsive colloids (RCs) in which the size of the macromolecule is explicitly resolved as a degree of freedom living in a bimodal 'Landau' energy landscape (exhibiting big and small states), thus directly responding to the crowding environment. Using this RC-DFT we study the effects of self-crowding on the liquid bulk structure and thermodynamics for different energy barriers and softnesses of the bimodal energy landscape, in conditions close to the coil-to-globule transition. We find substantial crowding effects on the internal distributions, a complex polydispersity behavior, and quasi-universal compression curves for increasing (generalized) packing fractions. Moreover, we uncover distinct signatures of bimodal versus unimodal behavior in the particle compression. Finally, the analysis of the pair structure - derived from the test particle route - reveals that the microstructure of the liquid is quite inhomogeneous due to local depletion effects, tuneable by particle softness.

Controlling the anisotropic self-assembly of polybutadiene-grafted silica nanoparticles by tuning three-body interaction forces.

Recently, the significant improvements in polymer composites properties have been mainly attributed to the ability of filler nanoparticles (NPs) to self-assemble into highly anisotropic self-assembled structures. In this work, we investigate the self-assembly of core-shell NPs composed of a silica core grafted with polybutadiene (PB) chains, generating the so-called "hairy" NPs (HNPs), immersed in tetrahydrofuran solvent. While uncoated silica beads aggregate forming uniform compact structures, the presence of a PB shell affects the silica NPs organization to the point that by increasing the polymer density at the corona, they tend to self-assemble into linear chain-like structures. To reproduce the experimental observations, we propose a theoretical model for the two-body that considers the van der Waals attractive energy together with the polymer-induced repulsive steric contribution and includes an additional three-body interaction term. This term arises due to the anisotropic distribution of PB, which increases their concentration near the NPs contact region. The resulting steric repulsion experienced by a third NP approaching the dimer prevents its binding close to the dimer bond and favors the growth of chain-like structures. We find good agreement between the simulated and experimental self-assembled superstructures, confirming that this three-body steric repulsion plays a key role in determining the cluster morphology of these core-shell NPs. The model also shows that further increasing the grafting density leads to low-density gel-like open structures.

Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions.

We employ Reactive Dynamical Density Functional Theory (R-DDFT) and Reactive Brownian Dynamics (R-BD) simulations to investigate the dynamics of a suspension of active soft Gaussian colloids with binary interaction switching, i.e., a one-component colloidal system in which every particle stochastically switches at predefined rates between two interaction states with different mobility. Using R-DDFT we extend a theory previously developed to access the dynamics of inhomogeneous liquids [Archer et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75, 040501] to study the influence of the switching activity on the self and distinct part of the Van Hove function in bulk solution, and determine the corresponding mean squared displacement of the switching particles. Our results demonstrate that, even though the average diffusion coefficient is not affected by the switching activity, it significantly modifies the non-equilibrium dynamics and diffusion coefficients of the individual particles, leading to a crossover from short to long times, with a regime for intermediate times showing anomalous diffusion. In addition, the self-part of the van Hove function has a Gaussian form at short and long times, but becomes non-Gaussian at intermediates ones, having a crossover between short and large displacements. The corresponding self-intermediate scattering function shows the two-step relaxation patters typically observed in soft materials with heterogeneous dynamics such as glasses and gels. We also introduce a phenomenological Continuous Time Random Walk (CTRW) theory to understand the heterogeneous diffusion of this system. R-DDFT results are in excellent agreement with R-BD simulations and the analytical predictions of CTRW theory, thus confirming that R-DDFT constitutes a powerful method to investigate not only the structure and phase behavior, but also the dynamical properties of non-equilibrium active switching colloidal suspensions.

Effects of Vimentin Intermediate Filaments on the Structure and Dynamics of In Vitro Multicomponent Interpenetrating Cytoskeletal Networks.

We investigate the rheological properties of interpenetrating networks reconstituted from the main cytoskeletal components: filamentous actin, microtubules, and vimentin intermediate filaments. The elastic modulus is determined largely by actin, with little contribution from either microtubules or vimentin. However, vimentin dramatically impacts the relaxation, with even small amounts significantly increasing the relaxation time of the interpenetrating network. This highly unusual decoupling between dissipation and elasticity may reflect weak attractive interactions between vimentin and actin networks.

Active binary switching of soft colloids: stability and structural properties.

We employ reactive dynamical density functional theory (R-DDFT) and reactive Brownian dynamics (R-BD) simulations to study the non-equilibrium structure and phase behavior of an active dispersion of soft Gaussian colloids with binary interaction switching, i.e., we consider a one-component colloidal system in which every particle can individually switch stochastically between two interaction states (here, sizes 'big' and 'small') at predefined rates. We consider the influence of switching activity on the inhomogeneous density profiles of the colloids confined by various external potentials, as well as on their pair structure and phase behavior in bulk solutions. For the latter, we extend the R-DDFT method to incorporate the Percus test-particle route. Our results demonstrate that switching activity strongly modifies the steady-state density profiles and structural (pair) correlations. In particular, the switching rate interpolates from a near-equilibrium binary colloidal mixture of two states at very low rates to a non-equilibrium, 'one-state liquid' at very high rates characterized by one, average interaction size. The latter limit can be described by an equivalent effective one-component (EOC) equilibrium system, for which the exact analytical expression for the effective pair potential is a diffusion-weighted superposition of the active systems' pair potentials. This leads to the interesting fact that under certain conditions an interacting switching system can behave like a non-interacting (ideal) gas in the limit of high switching rates. Moreover, for colloids that are unstable (i.e., demix) near equilibrium, we demonstrate that phase separation and micro-clustering in both confinement and bulk can be dynamically controlled by the switching rate, and vanish for high rates. All R-DDFT results are in excellent agreement with our R-BD simulations.

Scaling Laws in the Diffusive Release of Neutral Cargo from Hollow Hydrogel Nanoparticles: Paclitaxel-Loaded Poly(4-vinylpyridine).

We study the nonequilibrium diffusive release of electroneutral molecular cargo encapsulated inside hollow hydrogel nanoparticles. We propose a theoretical model that includes osmotic, steric, and short-range polymer-cargo attractions to determine the effective cargo-hydrogel interaction, ueff*, and the effective diffusion coefficient of the cargo inside the polymer network, Deff*. Using dynamical density functional theory (DDFT), we investigate the scaling of the characteristic release time, τ1/2, with the key parameters involved in the process, namely, ueff*, Deff*, and the swelling ratio. This effort represents a full study of the problem, covering a broad range of cargo sizes and providing predictions for repulsive and attractive polymer shells. Our calculations show that the release time through repulsive polymer networks scales with q2eßueff*/Deff* for ßueff* ≫ 1. In this case, the cargo molecules are excluded from the shell of the hydrogel. For attractive shells, the polymer retains the cargo molecules on its internal surface and its interior, and the release time grows exponentially with the attraction strength. The DDFT calculations are compared to an analytical model for the mean first passage time, which provides an excellent quantitative description of the kinetics for both repulsive and attractive shells without fitting parameters. Finally, we apply the method to reproduce experimental results on the release of paclitaxel from hollow poly(4-vinylpyridine) nanoparticles and find that the slow release of the drug can be explained in terms of the strong binding attraction between the drug and the polymer.

Controlling the Microstructure and Phase Behavior of Confined Soft Colloids by Active Interaction Switching.

We explore the microstructure and phase behavior of confined soft colloids which can actively switch their interactions at a predefined kinetic rate. For this, we employ a reactive dynamical density-functional theory and study the effect of a two-state switching of the size of colloids interacting with a Gaussian pair potential in the nonequilibrium steady state. The switching rate interpolates between a near-equilibrium binary mixture at low rates and a nonequilibrium monodisperse liquid for large rates, strongly affecting the one-body density profiles, adsorption, and pressure at confining walls. Importantly, we show that sufficiently fast switching impedes the phase separation of an (in equilibrium) unstable liquid, allowing the control of the degree of mixing and condensation and local microstructuring in a cellular confinement by tuning the switching rate.

Nonequilibrium Uptake Kinetics of Molecular Cargo into Hollow Hydrogels Tuned by Electrosteric Interactions.

Hollow hydrogels represent excellent nano- and microcarriers due to their ability to encapsulate and release large amounts of cargo molecules (cosolutes) such as reactants, drugs, and proteins. In this work, we use a combination of a phenomenological effective cosolute-hydrogel interaction potential and dynamic density functional theory to investigate the full nonequilibrium encapsulation kinetics of charged and dipolar cosolutes by an isolated charged hollow hydrogel immersed in a 1:1 electrolyte aqueous solution. Our analysis covers a broad spectrum of cosolute valences ( zc) and electric dipole moments (µc), as well as hydrogel swelling states and hydrogel charge densities. Our calculations show that, close to the collapsed state, the polar cosolutes are predominantly precluded and the encapsulation process is strongly hindered by the excluded-volume interaction exerted by the polymer network. Different equilibrium and kinetic sorption regimes (interface versus interior) are found depending on the value and sign of zc and the value of µc. For cosolutes of the same sign of charge as the gel, the superposition of steric and electrostatic repulsion leads to an "interaction-controlled" encapsulation process, in which the characteristic time to fill the empty core of the hydrogel grows exponentially with zc. On the other hand, for cosolutes oppositely charged to the gel, we find a "diffusion-controlled" kinetic regime, where cosolutes tend to rapidly absorb into the hydrogel membrane and the encapsulation rate depends only on the cosolute diffusion time across the membrane. Finally, we find that increasing µc promotes the appearance of metastable and stable surface adsorption states. For large enough µc, the kinetics enters an "adsorption-hindered diffusion", where the enhanced surface adsorption imposes a barrier and slows down the uptake. Our study represents the first attempt to systematically describe how the swelling state of the hydrogel and other leading physical interaction parameters determine the encapsulation kinetics and the final equilibrium distribution of polar molecular cargo.

Direct determination of forces between charged nanogels through coarse-grained simulations.

In this work, electrostatic forces between charged nanogels are explored through coarse-grained simulations. These simulations allow us to explicitly consider the complex topology of these nanoparticles and provide reliable force values to examine highly charged nanogels of a few tens of nanometers. The results obtained here clearly reveal that the electrostatic interactions between these nanoparticles are not governed by the net charge of the nanogel, which includes not only the charge of the polymer network but also the charge of ions inside. Thus two theoretical procedures for predicting effective charges are also proposed and investigated. Both provide predictions of the same order and capture the behavior found for the effective charge obtained from simulations.

Maximizing the absorption of small cosolutes inside neutral hydrogels: steric exclusion versus hydrophobic adhesion.

In this work the equilibrium absorption of nanometric cosolutes (which could represent drugs, reactants, small globular proteins and other kind of biomacromolecules) inside neutral hydrogels is studied. We specially focus on exploring, for different swelling states, the competition between the steric exclusion induced by the cross-linked polymer network constituting the hydrogel, and the solvent-induced short-range hydrophobic attraction between the polymer chains and the cosolute particle. For this purpose, the cosolute partition coefficient is calculated by means of coarse-grained grand canonical Monte Carlo simulations, and the results are compared to theoretical predictions based on the calculation of the excluded and binding volume around the polymer chains. For small hydrophobic attractions or large cosolute sizes, the steric repulsion dominates, and the partition coefficient decreases monotonically with the polymer volume fraction, ϕm. However, for large enough hydrophobic attraction strength, the interplay between hydrophobic adhesion and the steric exclusion leads to a maximum in the partition coefficient at certain intermediate polymer density. Good qualitative and quantitative agreement is achieved between simulation results and theoretical predictions in the limit of small ϕm, pointing out the importance of geometrical aspects of the cross-linked polymer network, even for hydrogels in the swollen state. In addition, the theory is able to predict analytically the onset of the maximum formation in terms of the details of the cosolute-monomer pair interaction, in good agreement with simulations too. Finally, the effect of the many-body attractions between the cosolute and multiple polymer chains is quantified. The results clearly show that these many-body attractions play a very relevant role determining the cosolute binding, enhancing its absorption in more than one order of magnitude.

Conformation change of an isotactic poly (N-isopropylacrylamide) membrane: Molecular dynamics.

In this work, isotactic Poly (N-Isopropylacrylamide)-PNIPAM-in neat water and in electrolyte solutions is studied by means of molecular dynamics simulations. This is done for an infinitely diluted oligomer and for an assembly of several PNIPAM chains arranged into a planar membrane configuration with a core-shell morphology. We employed two different force fields, AMBER (assisted model building with energy refinement) and OPLS-AA (all atom - optimized potentials for liquid simulations) in combination with extended simple point charge water. Despite the more water insoluble character of isotactic oligomers, our results support the existence of a coil to globule transition for the isolated 30-mer. This may imply the existence of an oligomer rich phase of coil-like structures in equilibrium with a water rich phase for temperatures close but below the coil to globule transition temperature, TΘ. However, the obtained coil structure is much more compact than that corresponding to the syndiotactic chain. Our estimations of TΘ are (308±5) K and (303±5) K for AMBER and OPLS-AA, respectively. The membrane configuration allows one to include chain-chain interactions, to follow density profiles of water, polymer, and solutes, and accessing the membrane-water interface tension. Results show gradual shrinking and swelling of the membrane by switching temperature above and below TΘ, as well as the increase and decrease of the membrane-water interface tension. Finally, concentration profiles for 1M NaCl and 1M NaI electrolytes are shown, depicting a strong salting-out effect for NaCl and a much lighter effect for NaI, in good qualitative agreement with experiments.

Sorption and Spatial Distribution of Protein Globules in Charged Hydrogel Particles.

We have theoretically studied the uptake of a nonuniformly charged biomolecule suitable for representing a globular protein or a drug by a charged hydrogel carrier in the presence of a 1:1 electrolyte. On the basis of the analysis of a physical interaction Hamiltonian including monopolar, dipolar, and Born (self-energy) contributions derived from linear electrostatic theory of the unperturbed homogeneous hydrogel, we have identified five different sorption states of the system, from complete repulsion of the molecule to its full sorption deep inside the hydrogel, passing through metastable and stable surface adsorption states. The results are summarized in state diagrams that also explore the effects of varying the electrolyte concentration, the sign of the net electric charge of the biomolecule, and the role of including excluded-volume (steric) or hydrophobic biomolecule-hydrogel interactions. We show that the dipole moment of the biomolecule is a key parameter controlling the spatial distribution of the globules. In particular, biomolecules with a large dipole moment tend to be adsorbed at the external surface of the hydrogel, even if like-charged, whereas uniformly charged biomolecules tend to partition toward the internal core of an oppositely charged hydrogel. Hydrophobic attraction shifts the states toward the internal sorption of the biomolecule, whereas steric repulsion promotes surface adsorption for oppositely charged biomolecules or for the total exclusion of likely charged ones. Our results establish a guideline for the spatial partitioning of proteins and drugs in hydrogel carriers, tunable by the hydrogel charge, pH, and salt concentration.

Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge.

In this work the equilibrium distribution of ions around a thermo-responsive charged nanogel particle in an electrolyte aqueous suspension is explored using coarse-grained Monte Carlo computer simulations and the Ornstein-Zernike integral equation theory. We explicitly consider the ionic size in both methods and study the interplay between electrostatic and excluded-volume effects for swollen and shrunken nanogels, monovalent and trivalent counterions, and for two different nanogel charges. We find good quantitative agreement between the ionic density profiles obtained using both methods when the excluded repulsive force exerted by the cross-linked polymer network is taken into account. For the shrunken conformation, the electrostatic repulsion between the charged groups provokes a heterogeneous polymer density profile, leading to a nanogel structure with an internal low density hole surrounded by a dense corona. The results show that the excluded-volume repulsion strongly hinders the ion permeation for shrunken nanogels, where volume exclusion is able to significantly reduce the concentration of counterions in the more dense regions of the nanogel. In general, we demonstrate that the thermosensitive behaviour of nanogels, as well as their internal structure, is strongly influenced by the valence of the counterions and also by the charge of the particles. On the one hand, an increase of the counterion valence moves the swelling transition to lower temperatures, and induces a major structuring of the charged monomers into internal and external layers around the crown for shrunken nanogels. On the other hand, increasing the particle charge shifts the swelling curve to larger values of the effective radius of the nanogel.

Swelling of ionic microgel particles in the presence of excluded-volume interactions: a density functional approach.

In this work a new density functional theory framework is developed to predict the salt-concentration dependent swelling state of charged microgels and the local concentration of monovalent ions inside and outside the microgel. For this purpose, elastic, solvent-induced and electrostatic contributions to the microgel free energy are considered together with the free energy of the ions. In addition to the electrostatic interaction, the model explicitly considers both the microgel-ion excluded-volume (steric) repulsion and the ionic correlations, in such a way that the formalism is consistent with the Hypernetted-Chain Closure approximation (HNC). We explore the role that the solvent quality, chain elasticity, salt concentration and microgel bare charge play on the swelling state, the effective charge and on the ionic density profiles. Our results show that the microgel-ion steric exclusion foments the increase of the particle size up to 10%. The role that the steric effect plays on the counterion distribution becomes more important when the microgel approaches the shrunken configuration, developing an accumulation peak at the microgel interface and a reduction in the inner core of the microgel that induce a significant increase of the microgel effective charge. We further find that deep inside the particle charge electroneutrality is achieved and a Donnan potential corrected by the steric exclusion is established.

Further details on the phase diagram of hard ellipsoids of revolution.

In recent work we revisited the phase diagram of hard ellipsoids of revolution (spheroids) by means of replica exchange Monte Carlo simulations. This was done by setting random initial configurations, and allows to confirm the formation of sm2 crystal structures at high densities [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)] for large anisotropies and stretched-fcc for small anisotropies. In this work we employed the same technique but setting the starting cells as sm2 crystal structures having the maximum known packing density [A. Donev, F. H. Stillinger, P. M. Chaikin, and S. Torquato, Phys. Rev. Lett. 92, 255506 (2004)]. This procedure yields a very rich behavior for quasi-spherical oblates and prolates. These systems, from low to high pressures, show the following phases: isotropic fluid, plastic solid, stretched-fcc solid, and sm2 solid. The first three transitions are first order, whereas the last one is a subtle, probably high order transition. This picture is consistent with the fact of having the sm2 structure capable of producing the maximally achievable density.

Self-assembly in two-dimensions of colloidal particles at liquid mixtures.

The aim of this work is to simulate the formation of colloidal rings, circular clusters, and voids induced by oily lenses at the air-water interface. The presence of two liquids with different surface tension leads to the formation of a nonhomogeneous interface. In this case, the total interaction potential is assumed to be composed of only two terms; the first one is due to the (repulsive) pairwise dipolar force between partly immersed charged microspheres, whereas the second depends on the position of the particle at the interface and is connected to the interfacial stress caused by the difference of surface tension between both liquids. This simple potential is able to reproduce the experimental rings, circular clusters and voids found by different authors.

Two-dimensional colloidal aggregation: concentration effects.

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned 2.5 orders of magnitude. In the DLCA case and in the flocculation regime, it was found that the fractal dimension shows a linear-type increase with the concentration phi, following the law: d(f)=d(fo)+aphi(c). For the on-lattice simulations the fractal dimension in the zero concentration limit, d(fo), was 1.451+/-0.002, while for the off-lattice simulations the same quantity took the value 1.445+/-0.003. The prefactor a and exponent c were for the on-lattice simulations equal to 0.633+/-0.021 and 1.046+/-0.032, while for the off-lattice simulations they were 1.005+/-0.059 and 0.999+/-0.045, respectively. For the exponents z and z', defining the increase of the weight-average (S(w)(t)) and number-average (S(n)(t)) cluster sizes as a function of time, we obtained in the DLCA case the laws: z=z(o)+bphi(d) and z'=z'(o)+b'phi(d'). For the on-lattice simulations, z(o), b, and d were equal to 0.593+/-0.008, 0.696+/-0.068, and 0.485+/-0.048, respectively, while for the off-lattice simulations they were 0.595+/-0.005, 0.807+/-0.093, and 0.599+/-0.051. In the case of the exponent z', the quantities z'(o), b', and d' were, for the on-lattice simulations, equal to 0.615+/-0.004, 0.814+/-0.081, and 0.620+/-0.043, respectively, while for the off-lattice algorithm they took the values 0.598+/-0.002, 0.855+/-0.035, and 0.610+/-0.018. In RLCA we have found again that the fractal dimension, in the flocculation regime, shows a similar linear-type increase with the concentration d(f)=d(fo)+aphi(c), with d(fo)=1.560+/-0.004, a=0.342+/-0.039, and c=1.000+/-0.112. In this RLCA case it was not possible to find a straight line in the log-log plots of S(w)(t) and S(n)(t) in the aggregation regime considered, and no exponents z and z' were defined. We argue however that for sufficiently long periods of time the cluster averages should tend to those for DLCA and, therefore, their exponents should coincide with z and z' of the DLCA case. Finally, we present the bell-shaped master curves for the scaling of the cluster size distribution function and their evolution when the concentration increases, for both the DLCA and RLCA cases.