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Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching states, and are an integral property for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory (DDFT) for a model of responsive colloids (RCs) to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics (BD) computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tuneable by the ratio of translational and conformational diffusion time scales. Our work paves thus the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations., Comment: 14 pages, 8 figures

Single-detector 3D dynamic light scattering (3D-DLS) emerges as a reliable technique to determine the drift velocity of out-of-equilibrium colloidal particles. In particular, our investigation reveals the appearance of oscillations of a well-defined frequency in the autocorrelation function of the scattered intensity when particles are immersed in a medium exposed to thermally induced convection. These oscillations arise as a consequence of the directed motion of particles due to the convective motion of the fluid. The experimental results obtained for different colloidal systems are corroborated by a theoretical model and thoroughly validated with fluid dynamics and Brownian dynamics simulations. The excellent agreement between experimental, theoretical and simulation data allows us to provide a solid and comprehensive explanation of the observed physical phenomena. This study via advanced dynamic light scattering (DLS) technique offers insights into the field of non-equilibrium particle dynamics, applicable not only to colloidal suspension affected by steady-state diffusion-convection but also to other non-equilibrium situations, such as systems driven by external fields (gravitational, electric or magnetic fields, among others)., Comment: 5 pages, 4 figures

The transport of biomolecules, drugs, or reactants encapsulated inside stimuli-responsive polymer networks in aqueous media is fundamental for many material and environmental science applications, including drug delivery, biosensing, catalysis, nanofiltration, water purification, and desalination. The transport is particularly complex in dense polymer media, such as collapsed hydrogels, where the molecules strongly interact with the polymer network and diffuse via a hopping mechanism. In this study, we employ Dynamical Density Functional Theory (DDFT) to investigate the non-equilibrium release kinetics of non-ionic subnanometer-sized molecules initially uploaded inside collapsed microgel particles. The theory is consistent with previous molecular dynamics simulations of collapsed poly($N$-isopropylacrylamide) (PNIPAM) polymer matrices, accommodating molecules of varying shapes and sizes. We found that, despite the intricate physico-chemical properties involved in the released process, the kinetics is predominantly dictated by two material parameters: the diffusion coefficient of the molecules inside the microgel ($D^*$) and the interaction free energy of the molecules with the microgel ($\Delta G$). Our results reveal two distinct limiting regimes: For large, slowly diffusing molecules weakly attracted to the polymer network, the release is primarily driven by diffusion, with a release time that scales as $\tau_{1/2} \sim 1/D^*$. Conversely, for small molecules strongly attracted to the polymer network, the release time is dominated by the interaction, scaling as $\tau_{1/2} \sim \exp(-\Delta G/k_{\textrm{B}} T)$. Our DDFT calculations are directly compared with an analytical equation for the half-release time, demonstrating excellent quantitative agreement. This equation represents a valuable tool for predicting release kinetics of non-ionic molecules from collapsed microgels., Comment: 15 pages, 6 figures

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 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., Comment: 15 pages, 7 figures

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 reaction-diffusion approach based on a reactive dynamical density-functional theory (R-DDFT) and study the effect of a binary (two-state) switching of the size of colloids interacting with a Gaussian pair potential. The rate of switching interpolates between a near-equilibrium binary Gaussian mixture at low rates and an effective monodisperse liquid for large rates, hence strongly affecting the one-body density profiles, adsorption, and pressure at confining walls. Importantly, we demonstrate that sufficiently fast switching impedes the phase separation of an (in equilibrium) unstable liquid, allowing the dynamic control of the degree of mixing/condensation and local micro-structuring in a cellular confinement by tuning the switching rate., Comment: 5 pages, 3 figures, 1 supplemental material (pdf) file

In this work, we use a combination of a phenomenological effective cosolute-hydrogel interaction potential and Dynamic Density Functional Theory to investigate the full non-equilibrium 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 z_c and electric dipole moments mu_c, 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 z_c and the value of mu_c. 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 z_c. 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 only depends on the cosolute diffusion time across the membrane. Finally, we find that increasing mu_c promotes the appearance of metastable and stable surface adsorption states. For large enough mu_c, the kinetics enters a "adsorption-hindered diffusion", where the enhanced surface adsorption imposes a barrier and slows down the uptake., Comment: 35 pages, 11 figures

We study the partitioning of cosolute particles in a thin film of a semi-flexible polymer network by a combination of coarse-grained (implicit-solvent) stochastic dynamics simulations and mean-field theory. We focus on a wide range of solvent qualities and cosolute-network interactions for selected polymer flexibilities. Our investigated ensemble (isothermal-isobaric) allows the network to undergo a volume transition from extended to collapsed state while the cosolutes can distribute in bulk and network, correspondingly. We find a rich topology of equilibrium states of the network and transitions between them, qualitatively depending on solvent quality, polymer flexibility, and cosolute-network interactions. In particular, we find a novel `cosolute-induced' collapsed state, where strongly attractive cosolutes bridge network monomers albeit the latter interact mutually repulsive. Finally, the cosolutes' global partitioning `landscape', computed as a function of solvent quality and cosolute-network interactions, exhibits very different topologies depending on polymer flexibility. The simulation results are supported by theoretical predictions obtained with a two-component mean-field approximation for the Helmholtz free energy that considers the chain elasticity and the particle interactions in terms of a virial expansion. Our findings have implications on the interpretation of transport processes and permeability in hydrogel films, as realized in filtration or macromolecular carrier systems., Comment: Macromolecules (2017)

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., Comment: 15 pages, 8 figures

We have theoretically studied the uptake of a non-uniformly charged biomolecule, suitable to represent a globular protein or a drug, by a charged hydrogel carrier in the presence of a 1:1 electrolyte. Based on 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 meta- 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 towards the internal core of an oppositely-charged hydrogel. Hydrophobic attraction shifts the states towards internal sorption of the biomolecule, whereas steric repulsion promotes surface adsorption for oppositely-charged biomolecules, or the total exclusion for likely-charged ones. Our results establish a guidance for the spatial partitioning of proteins and drugs in hydrogel carriers, tuneable by hydrogel charge, pH and salt concentration., Comment: 16 pages, 5 figures

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 [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 [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., Comment: 10 pages, 10 figures, to be published in JCP