Dynamic Coupling in Unentangled Liquid Coacervates Formed by Oppositely Charged Polyelectrolytes

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates

We develop a scaling theory for the structure and dynamics of "hybrid" complex coacervates formed from linear polyelectrolytes (PEs) and oppositely charged spherical colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. At low concentrations, in stoichiometric solutions, PEs adsorb at the colloids to form electrically neutral finite-size complexes. These clusters attract each other through bridging between the adsorbed PE layers. Above a threshold concentration, macroscopic phase separation sets in. The coacervate internal structure is defined by (i) the adsorption strength and (ii) the ratio of the resulting shell thickness to the colloid radius, H/R. A scaling diagram of different coacervate regimes is constructed in terms of the colloid charge and its radius for Θ and athermal solvents. For high charges of the colloids, the shell is thick, H ≫ R, and most of the volume of the coacervate is occupied by PEs, which determine its osmotic and rheological properties. The average density of hybrid coacervates exceeds that of their PE-PE counterparts and increases with nanoparticle charge, Q. At the same time, their osmotic moduli remain equal, and the surface tension of hybrid coacervates is lower, which is a consequence of the shell's inhomogeneous density decreasing with the distance from the colloid surface. When charge correlations are weak, hybrid coacervates remain liquid and follow Rouse/reptation dynamics with a Q-dependent viscosity, η _Rouse ∼ Q ^4/5 and η _rep ∼ Q ^28/15 for a Θ solvent. For an athermal solvent, these exponents are equal to 0.89 and 2.68, respectively. The diffusion coefficients of colloids are predicted to be strongly decreasing functions of their radius and charge. Our results on how Q affects the threshold coacervation concentration and colloidal dynamics in condensed phases are consistent with experimental observations for in vitro and in vivo studies of coacervation between supercationic green fluorescent proteins (GFPs) and RNA.

Force-driven active dynamics of thin nanorods in unentangled polymer melts

Recent advances in the functional material and biomedical applications of nanorods call for a fundamental understanding of the active motion of nanorods in a viscoelastic medium. Molecular dynamics simulations are performed to investigate a model system consisting of force-driven active thin nanorods in a melt of unentangled polymers. The activeness of a thin nanorod arises from a constant external force applied uniformly along the rod. The simulations demonstrate that the active force overcomes the randomness of the diffusive motion and results in a ballistic motion along the direction of the applied force at long timescales. The constant speed of the force-driven ballistic motion is determined by the balance of the active force and the friction from the coupling of the nanorod with the polymer viscosity. The friction coefficient, which is computed as the ratio of the active force and the speed, decreases as the active force increases. The origin of the reduction in the friction coefficient is the high speed that allows the nanorod to renew its local environment faster than the relaxation time of melt chains. A scaling theory is developed to quantify the dependence of the friction coefficient on the strength of the active force. The simulations also demonstrate that the force-driven ballistic motion suppresses the rotational diffusion of the rod and cuts off the de-correlation of the rod axis with time. On the scaling level, the long-time trajectory of a force-driven active nanorod piercing through unentangled polymers may be described as a stretched array of "active blobs", where the short-time random-walk trajectory within an active blob is unperturbed by the active force.

DNA dynamics in complex coacervate droplets and micelles

Single stranded DNA (ssDNA), or another polyanion, can be mixed with polycations to form liquid-like complex coacervates. When the polycations are replaced by cationic-neutral diblock copolymers, complex coacervate core micelles (C3Ms) can be formed instead. In both complex coacervates and C3Ms, dynamics plays an important role. Yet, to date, the effect of chain length on the dynamics effect is still not fully understood. The DNA complexes provide a versatile platform to further elucidate these chain length effects because the DNA is monodisperse and its length can be easily adapted. Therefore, we study in this paper the dynamics of fluorescently labelled ssDNA in both complex coacervate droplets and micelles. The DNA dynamics in the complex coacervate droplets is probed by fluorescence recovery after photobleaching (FRAP). We observe that the DNA diffusion coefficient depends more strongly on the DNA length than predicted by the sticky Rouse model and we show that this can be partly explained by changes in complex coacervate density, but that also other factors might play a role. We measure the molecular exchange of C3Ms by making use of Förster resonance energy transfer (FRET) and complement these measurements with Langevin dynamics simulations. We conclude that chain length polydispersity is the main cause of a broad distribution of exchange rates. We hypothesise that the different exchange rates that we observe for the monodisperse DNA are mainly caused by differences in dye interactions and show that the dye can indeed have a large effect on the C3M exchange. In addition, we show that a new description of the C3M molecular exchange is required that accounts among others for the effect of the length of the oppositely charged core species. Together our findings can help to better understand the dynamics in both specific DNA systems and in complex coacervate droplets and micelles in general.