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.

Nonequilibrium free energy during polymer chain growth.

During fast diffusion-influenced polymerization, nonequilibrium behavior of the polymer chains and the surrounding reactive monomers has been reported recently. Based on the laws of thermodynamics, the emerging nonequilibrium structures should be characterizable by some "extra free energy" (excess over the equilibrium Helmholtz free energy). Here, we study the nonequilibrium thermodynamics of chain-growth polymerization of ideal chains in a dispersion of free reactive monomers, using off-lattice, reactive Brownian dynamics computer simulations in conjunction with approximative statistical mechanics and relative entropy (Gibbs-Shannon and Kullback-Leibler) concepts. In the case of fast growing polymers, we indeed report increased nonequilibrium free energies ΔFneq of several kBT compared to equilibrium and near-equilibrium, slowly growing chains. Interestingly, ΔFneq is a non-monotonic function of the degree of polymerization and thus also of time. Our decomposition of the thermodynamic contributions shows that the initial dominant extra free energy is stored in the nonequilibrium inhomogeneous density profiles of the free monomer gas (showing density depletion and wakes) in the vicinity of the active center at the propagating polymer end. At later stages of the polymerization process, we report significant extra contributions stored in the nonequilibrium polymer conformations. Finally, our study implies a nontrivial relaxation kinetics and "restoring" of the extra free energy during the equilibration process after polymerization.

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.

Modulating internal transition kinetics of responsive macromolecules by collective crowding.

Packing and crowding are used in biology as mechanisms to (self-)regulate internal molecular or cellular processes based on collective signaling. Here, we study how the transition kinetics of an internal "switch" of responsive macromolecules is modified collectively by their spatial packing. We employ Brownian dynamics simulations of a model of Responsive Colloids, in which an explicit internal degree of freedom-here, the particle size-moving in a bimodal energy landscape self-consistently responds to the density fluctuations of the crowded environment. We demonstrate that populations and transition times for the two-state switching kinetics can be tuned over one order of magnitude by "self-crowding." An exponential scaling law derived from a combination of Kramers' and liquid state perturbation theory is in very good agreement with the simulations.

Thermal Compaction of Disordered and Elastin-like Polypeptides: A Temperature-Dependent, Sequence-Specific Coarse-Grained Simulation Model.

Elastin-like polypeptides (ELPs) undergo a sharp solubility transition from low-temperature solvated phases to coacervates at elevated temperatures, driven by the increased strength of hydrophobic interactions at higher temperatures. The transition temperature, or "cloud point", critically depends on sequence composition, sequence length, and concentration of the ELPs. In this work, we present a temperature-dependent, implicit solvent, sequence-specific coarse-grained (CG) simulation model that reproduces the transition temperatures as a function of sequence length and guest residue identity of various experimentally probed ELPs to appreciable accuracy. Our model builds upon the self-organized polymer model introduced recently for intrinsically disordered polypeptides (SOP-IDP) and introduces a semi-empirical functional form for the temperature dependence of hydrophobic interactions. In addition to the fine performance for various ELPs, we demonstrate the ability of our model to capture the thermal compactions in dominantly hydrophobic IDPs, consistent with experimental scattering data. With the high computational efficiency afforded by the CG representation, we envisage that the model will be ideally suited for simulations of large-scale structures such as ELP networks and hydrogels, as well as agglomerates of IDPs.

Controlling solvent quality by time: Self-avoiding sprints in nonequilibrium polymerization.

A fundamental paradigm in polymer physics is that macromolecular conformations in equilibrium can be described by universal scaling laws, being key for structure, dynamics, and function of soft (biological) matter and in the materials sciences. Here we reveal that during diffusion-influenced, nonequilibrium chain-growth polymerization, scaling laws change qualitatively, in particular, the growing polymers exhibit a surprising self-avoiding walk behavior in poor and θ solvents. Our analysis, based on monomer-resolved, off-lattice reaction-diffusion computer simulations, demonstrates that this phenomenon is a result of (i) nonequilibrium monomer density depletion correlations around the active polymerization site, leading to a locally directed and self-avoiding growth, in conjunction with (ii) chain (Rouse) relaxation times larger than the competing polymerization reaction time. These intrinsic nonequilibrium mechanisms are facilitated by fast and persistent reaction-driven diffusion ("sprints") of the active site, with analogies to pseudochemotactic active Brownian particles. Our findings have implications for time-controlled structure formation in polymer processing, as in, e.g., reactive self-assembly, photocrosslinking, and three-dimensional printing.

Activity Coefficients of Aqueous Sodium, Calcium, and Europium Nitrate Solutions from Osmotic Equilibrium MD Simulations.

Osmotic and activity coefficients of three aqueous electrolyte solutions with cations of similar ionic radius, but different charges, are described by molecular dynamics with the help of the osmotic equilibrium method using polarizable force fields up to high concentration. Simulations of vapor-liquid interfaces of aqueous solutions of NaNO3, Ca(NO3)2, and Eu(NO3)3 at different concentrations and at 298.15 K provide time-averaged number density profiles and consequently the quantity of solvent molecules in the vapor phase. These three cations of similar ionic radii exhibit an increasing amount of water in their first coordination sphere due to their increasing charge. The solvent activity is directly determined by the vapor phase density at different salt concentrations with respect to the vapor phase density of the pure solvent. The obtained densities of the liquid bulk and the osmotic and activity coefficients for the three different nitrate salts are in good agreement with the experimental results. Time-averaged concentration profiles and the interpretation of radial distribution functions are used to explain the role of coordination on the thermodynamic properties of aqueous electrolyte solutions.

Simulating Osmotic Equilibria: A New Tool for Calculating Activity Coefficients in Concentrated Aqueous Salt Solutions.

Herein, a new theoretical method is presented for predicting osmotic equilibria and activities, where a bulk liquid and its corresponding vapor phase are simulated by means of molecular dynamics using explicit polarization. Calculated time-averaged number density profiles provide the amount of evaporated molecules present in the vapor phase and consequently the vapor-phase density. The activity of the solvent and the corresponding osmotic coefficient are determined by the vapor density at different solute concentrations with respect to the reference vapor density of the pure solvent. With the extended Debye-Hückel equation for the activity coefficient along with the corresponding Gibbs-Duhem relation, the activity coefficients of the solutes are calculated by fitting the osmotic coefficients. A simple model based on the combination of Poisson processes and Maxwell-Boltzmann velocity distributions is introduced to interpret statistical phenomena observed during the simulations, which are related to evaporation and recondensation. This method is applied to aqueous dysprosium nitrate [Dy(NO3)3] solutions at different concentrations. The obtained densities of the liquid bulk and the osmotic and activity coefficients are in good agreement with the experimental results for concentrated and saturated solutions. Density profiles of the liquid-vapor interface at different concentrations provide detailed insight into the spatial distributions of all compounds.

A predictive model of reverse micelles solubilizing water for solvent extraction.

Herein, a minimal model for the common case of W/O solubilization of badly soluble compounds present in an excess phase by reverse micellar aggregates in chemical equilibrium with its single compounds is introduced. A simple model of such liquid-liquid extractions is crucial for obtaining predictive parameter for the modelling of nuclear waste management and hydrometallurgic recycling strategies. The standard Gibbs free energy of aggregation and the concentration of the corresponding aggregate is calculated within a multiple-equilibria approach for a set of aggregate compositions of solute and amphiphilic extractant molecules. This minimal model provides potential surfaces estimating the stability of different aggregate compositions with 6.2kJmol(-1) as a generalized bending constant. The complete concentrations of free and aggregated extractant species as well as the favored aggregation numbers, the polydispersity, the activity of the organic solvent, and the critical concentrations are captured by this thermodynamic model. An increase of the apparent critical micelle concentration for an increasing solute content in the aqueous phase is detected by this method.