Polyelectrolyte Brushes: MD Simulation and SCF Theory

Correlation between viscoelastic response and frictional properties of hydrated zwitterionic polymer brush film in narrowing shear gap

HYPOTHESIS

A hydrated 2-methacryloyloxyethyl phosphorylcholine (MPC) polymer brush exhibits exceptional lubricity. This lubrication mechanism has traditionally been attributed to either the inherent fluidity of the brush or the water film that forms owing to its hydrophilic nature. Given previous findings that the frictional properties of the MPC polymer brush film show load dependence, we hypothesize that the lubrication mechanism can be elucidated by examining the shear gap (varies owing to the load) dependence of the brush's viscoelastic response.

EXPERIMENTS

MPC polymer brush films with different thicknesses were prepared. Their viscoelastic responses were evaluated across different shear gap widths, and the frictional properties were subsequently compared across states with distinct viscoelastic behaviors.

FINDINGS

The observed shear viscoelasticity demonstrated a clear gap dependence that correlated with frictional attributes. Our data suggests that the lubrication mechanism shifts based on the shear gap. Specifically, two states exhibited low coefficients of friction: one where the osmotic pressure supports the load while allowing flexible deformation of the brush film, and the other where the brush film undergoes compression and transitions to a fully elastic state.

Machine learning enabled quantification of the hydrogen bonds inside the polyelectrolyte brush layer probed using all-atom molecular dynamics simulations

The configuration of densely grafted charged polyelectrolyte (PE) brushes is strongly dictated by the properties and behavior of the counterions that screen the PE brush charges and the solvent molecules (typically water) that solvate the brush molecules and these screening counterions. Only recently, efforts have been made to study the PE brushes atomistically, thereby shedding light on the properties of brush-supported ions and water molecules. However, even for such efforts, there are limitations associated with using a generic definition to estimate certain properties of water and ions inside the brush layer. For example, water-water hydrogen bonds (HBs) will behave differently for locations outside and inside the brush layer, given the fact that the densely closely grafted PE brush molecules create a soft nanoconfinement where the water connectivity becomes highly disrupted: therefore, using the same definition to quantify the HBs inside and outside the brush layer will be unwise. In this paper, we address this limitation by employing an unsupervised machine learning (ML) approach to predict the water-water hydrogen bonding inside a cationic PE brush layer modeled using all-atom molecular dynamics (MD) simulations. The ML method, which relies on a clustering approach and uses the equilibrium coordinates of the water molecules (obtained from the all-atom MD simulations) as the input, is capable of identifying the structural modification of water-water HBs (revealed through appropriate clustering of the data) inside the PE brush layer induced soft nanoconfinement. Such capabilities would not have been possible by using a generic definition of the HBs. Our calculations lead to four key findings: (1) the clusters formed inside and outside the brush layer are structurally similar; (2) the margin of the cluster is shorter inside the PE brush layer confirming the possible disruption of the HBs inside the PE brush layer; (3) the average "hydrogen-acceptor-oxygen-donor-oxygen" angle that defines the HB is reduced for the HBs formed inside the brush layer; (4) the use of the generic definition (definition usable for characterizing the HBs in brush-free bulk) leads to an overprediction of the number of HBs formed inside the PE brush layer.

Strongly enhanced dynamics of a charged Rouse dimer by an external magnetic field

While the dynamics of dimers and polymer chains in a viscous solvent is well understood within the celebrated Rouse model, the effect of an external magnetic field on the dynamics of a charged chain is much less understood. Here, we generalize the Rouse model for a charged dimer to include the effect of an external magnetic field. Our analytically solvable model allows a fundamental insight into the magneto-generated dynamics of the dimer in the overdamped limit as induced by the Lorentz force. Surprisingly, for a dimer of oppositely charged particles, we find an enormous enhancement of the dynamics of the dimer center, which exhibits even a transient superballistic behavior. This is highly unusual in an overdamped system for there is neither inertia nor any internal or external driving. We attribute this to a significant translation and rotation coupling due to the Lorentz force. We also find that magnetic field reduces the mobility of a dimer along its orientation and its effective rotational diffusion coefficient. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.

Ion size effect on electrostatic and electroosmotic properties in soft nanochannels with pH-dependent charge density

We report a theoretical study of the ion size effect on various properties in a soft nanochannel with pH-dependent charge density.

Simulations of polymer brushes with charged end monomers under external electric fields

Using Langevin dynamics simulations, the response of neutral polymer brushes with charged terminal monomers to external electric fields has been investigated. The external electric field is equivalent to the field generated by the opposite surface charges on two parallel electrodes. The effects of charge valence of terminal monomers on the structure of double layers and overall charge balance near the two electrodes were examined. Using the charge density distributions obtained from simulations, the total electric field normal to the electrodes was calculated by numerically solving the Poisson equation. Under external electric fields, the total electric field across the two electrodes is highly non-uniform and in certain regions within the brush, the total electric field nearly vanishes. The probability distribution of electric force acting on one charged terminal monomer was obtained from simulations and how it affects the probability density distribution of terminal monomers was analyzed. The response of polymer brushes with charged terminal monomers to a strongly stretching external electric field was compared with that of uniformly charged polymer brushes.

Polyelectrolyte brushes in external fields: molecular dynamics simulations and mean-field theory

A mean-field model is developed to predict the layer-thickness of sparse and salt-free polyelectrolyte brushes, exposed to an external electric field, which attracts the polyelectrolytes to the substrate. In molecular dynamics simulations, it is shown that a fraction of polymers collapses entirely to screen the charge of the substrate. The remaining brushes are then treated as field-free brushes at reduced grafting density. The mean-field model may thus be applied to field-free brushes, both in their osmotic and their weak charge regimes. It yields simple, closed equations for the brush height and for the partition of counterions in- and outside the brushes, and accurately reproduces simulation data of the collapse of the brushes during the crossover between both charge regimes.

Anion-specific effects on the behavior of pH-sensitive polybasic brushes

The anion-specific solvation and conformational behavior of weakly basic poly(2-dimethylamino)ethyl methacrylate (poly(DMA)), poly(2-diethylamino)ethyl methacrylate (poly(DEA)), and poly(2-diisopropylamino)ethyl methacrylate (poly(DPA)) brushes, with correspondingly increasing inherent hydrophobicity, have been investigated using in situ ellipsometric and quartz crystal microbalance with dissipation (QCM-D) measurements. In the osmotic brush regime, as the initial low concentration of salt is increased, the brushes osmotically swell by the uptake of solvent as they become charged and the attractive hydrophobic inter- and intrachain interactions are overcome. With increased ionic strength, the brushes move into the salted brush regime where they desolvate and collapse as their electrostatic charge is screened. Here, as the brushes collapse, they transition to more uniform and rigid conformations, which dissipate less energy, than similarly solvated brushes at lower ionic strength. Significantly, in these distinct regimes brush behavior is not only ionic strength dependent but is also influenced by the nature of the added salt based on its position in the well-known Hofmeister or lyotropic series, with potassium acetate, nitrate, and thiocyanate investigated. The strongly kosmotropic acetate anions display low affinity for the hydrophobic polymers, and largely unscreened electrosteric repulsions allow the brushes to remain highly solvated at higher acetate concentrations. The mildly chaotropic nitrate and strongly chaotropic thiocyanate anions exhibit a polymer hydrophobicity-dependent affinity for the brushes. Increasing thiocyanate concentration causes the brushes to collapse at lower ionic strength than for the other two anions. This study of weak polybasic brushes demonstrates the importance of all ion, solvent, and polymer interactions.

Structure of polyelectrolyte brushes subject to normal electric fields

Molecular dynamic simulations of salt-free polyelectrolyte brushes subject to external fields applied normal to the grafting substrate reveal the three-dimensional monomer and counterion distributions. It is found that below a critical electric field, local electroneutrality holds for densely grafted brushes and the brush height remains independent of field intensity. Above this critical field (which scales as 1/3 with grafting density) brush height increases smoothly, and the fraction of condensed counterions decreases. The brush bifurcates into two subpopulations of stretched and collapsed chains when the grafting density is not low. At intermediate grafting densities, the majority of chains are stretched and the minority are nonstretched. At high grafting densities bifurcation and brush height growth occur consecutively. The majority of the chains are nonstretched at high grafting densities. Although not observed prior to overstretching of the chain model, it is predicted that the two subpopulations will re-merge to a single highly stretched phase when field intensity reaches a third critical value. The ability to control subpopulations of chains suggests that utilizing electric fields normal to polyelectrolyte brushes holds potential as controllable gates in microfluidic devices.

Interaction between brush layers of bottle-brush polyelectrolytes: molecular dynamics simulations

Interactions between tethered layers composed of aggrecan (charged bottle-brush) macromolecules are responsible for the molecular origin of cartilage biomechanical behavior. To elucidate the role of the electrostatic forces in interaction between bottle-brush layers, we have performed molecular dynamics simulations of charged and neutral bottle-brush macromolecules tethered to substrates. In the case of charged bottle-brush layers, the disjoining pressure P between two brush layers in salt-free solutions increases with decreasing distance D between substrates as P ∝ D(-1.8). A stronger dependence of the disjoining pressure P on the surface separation D was observed for neutral bottle-brushes, P ∝ D(-4.6), in the same interval of disjoining pressures. These scaling laws for dependence of disjoining pressure P on distance D are due to bending energy of the bottle-brush macromolecules within compressed brush layers. The weaker distance dependence observed in polyelectrolyte bottle-brushes is due to interaction between counterion clouds surrounding the bottle-brush macromolecules preventing strong brush overlap.