An all-atom MD framework is developed to investigate densely grafted polyelectrolyte (PE) brushes. The solvation water of counterions is replaced by charged functional groups on the PE chains. The complex between counterions and the negatively charged PE segments overwhelms water by weight and volume above a critical grafting density, giving rise to a ''water-in-salt''-like scenario. Furthermore, the counterions and water molecules lose most of their mobility within the PE brushes as a result of electrostatic interactions and brush-induced confinement.

In this paper, we study the diffusioosmotic (DOS) transport in a nanochannel grafted with pH-responsive polyelectrolyte (PE) brushes and establish brush-functionalization-driven enhancement in induced nanofluidic electric field and electrokinetic transport. The PE brushes are modeled using our recently developed augmented strong stretching theory. We consider the generation of the DOS transport due to the imposition of a salt concentration gradient along the length of the nanochannel. The presence of the salt concentration gradient induces an electric field that has an osmotic (associated with the flow-driven migration of the ions in the induced electric double layer) and an ionic (associated with the conduction current) component. These two components evolve in a manner such that the electric field in the brush-grafted nanochannel is larger (smaller) in magnitude than that in the brush-less nanochannels for the case where the electric field is positive (negative). Furthermore, we quantify the DOS flow velocity and establish that for most of the parameter choices, the DOS velocity, which is a combination of the induced pressure-gradient-driven chemiosmotic component and the induced electric field driven electroosmotic transport, is significantly larger for the nanochannels grafted with backbone-charged PE brushes (i.e., brushes where the charge is distributed along the entire length of the brushes) as compared to brush-free nanochannels or nanochannels grafted with PE brushes containing charges on their non-grafted ends.

We employ molecular dynamics (MD) simulations to study the spreading and imbibition of a liquid drop on a porous, soft, solvophilic, and responsive surface represented by a layer of polymer molecules grafted on a solvophilic solid. These polymer molecules are in a crumpled and collapsed globule-like state before the interaction with the drop but transition to a “brush”-like state as they get wetted by the liquid drop. We hypothesize that for a wide range of densities of polymer grafting (σg), the drop spreading is dictated by the balance of the driving inertial pressure and balancing viscoelastic dissipation (associated with the spreading of the liquid drop on the polymer layer that undergoes globule-to-brush transition and serves as the viscoelastic solid). Using the well-known idea that the viscoelastic resisting force exerted by the viscoelastic solid on a spreading drop scales as u n (where n is the index of the power-law-like rheology of the polymer layer serving as the viscoelastic solid and u is the spreading velocity of the drop on this viscoelastic solid) and considering n = 2/3, we show that the scaling calculation recovers the MD simulation prediction of r ∼ t 1/4 and r eq ∼ σg –1/3 (where r and r eq are the instantaneous and equilibrium spreading radii, respectively). We further describe the wicking behavior of the drop through the polymer layer by appropriately accounting for the manner in which the progressive time-dependent swelling of the grafted polymer molecules provides larger space for the wicking. Third, we quantify, possibly for the first time, the temporal dynamics of the “brush”-forming process (i.e., capture the dynamics of wetting-mediated globule-to-brush transition). We show that the dynamics of the polymer chain swelling depends on σg and is faster for sparser grafting. Most importantly, we confirm that the height of the relaxed polymer chains approximately scales as σg 1/3, confirming the attainment of brush-like configuration by the polymer molecules as they are wetted by the liquid drop. Finally, we argue that our simulations raise the possibility of designing soft, “responsive”, and widely deployable liquid-infused surfaces where the polymer grafted solid, with the polymer undergoing a globule-to-brush transition, serves as the responsive “surface”.

Abstract

In this paper, we employ the direct numerical simulation (DNS) method for probing three-dimensional, axisymmetric coalescence of microscale, power-law-obeying, and shear-thinning polymeric liquid drops of identical sizes impacting a solid, solvophilic substrate with a finite velocity. Unlike the cases of drop coalescence of Newtonian liquid drops, coalescence of non-Newtonian polymeric drops has received very little attention. Our study bridges this gap by providing (1) the time-dependent, three-dimensional (3D) velocity field and 3D velocity vectors inside two coalescing polymeric drops in the presence of a solid substrate and (2) the effect of the drop impact velocity (on the solid substrate), quantified by the Weber number (We), on the coalescence dynamics. Our simulations reveal that the drop coalescence is qualitatively similar for different We values, although the velocity magnitudes involved, the time required to attain different stages of coalescence, and the time needed to attain equilibrium vary drastically for finitely large We values. Finally, we provide detailed simulation-based, as well as physics-based, scaling laws describing the growth of the height and the width of the bridge (formed due to coalescence) dictating the 3D coalescence event. Our analyses reveal distinct scaling laws for the growth of bridge height and width for early and late stages of coalescence as a function of We. We also provide simulation-based coalescence results for the case of two unequal sized drops impacting on a substrate (nonaxisymmetric coalescence) as well as results for axisymmetric coalescence for drops of different rheology. We anticipate that our findings will be critical in better understanding events such as inkjet or aerosol jet polymer printing, dynamics of polymer blends, and many more.