Roland R. Netz

Neutral and charged polymers at interfaces

Abstract Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a summary of recent progress in this rapidly evolving field. Because many experimental studies are performed with rather stiff biopolymers, we discuss in detail the case of semi-flexible polymers in addition to flexible ones. We first review the behavior of neutral and charged chains in solution. Then, the adsorption of a single polymer chain is considered. Next, the adsorption and depletion processes in the many-chain case are reviewed. Profiles, changes in the surface tension and polymer surface excess are presented. Mean-field and corrections due to fluctuations and lateral correlations are discussed. The force of interaction between two adsorbed layers, which is important in understanding colloidal stability, is characterized. The behavior of grafted polymers is also reviewed, both for neutral and charged polymer brushes.

Shear-induced unfolding triggers adhesion of von Willebrand factor fibers

von Willebrand factor (VWF), a protein present in our circulatory system, is necessary to stop bleeding under high shear-stress conditions as found in small blood vessels. The results presented here help unravel how an increase in hydrodynamic shear stress activates VWFs adhesion potential, leading to the counterintuitive phenomena of enhanced adsorption rate under strong shear conditions. Using a microfluidic device, we were able to mimic a wide range of bloodflow conditions and directly visualize the conformational dynamics of this protein under shear flow. In particular, we find that VWF displays a reversible globule-stretch transition at a critical shear rate γ̇crit in the absence of any adsorbing surface. Computer simulations reproduce this sharp transition and identify the large size of VWFs repeating units as one of the keys for this unique hydrodynamic activation. In the presence of an adsorbing collagen substrate, we find a large increase in the protein adsorption at the same critical shear rate, suggesting that the globule unfolding in bulk triggers the surface adsorption in the case of a collagen substrate, which provides a sufficient density of binding sites. Monitoring the adsorption process of multiple VWF fibers, we were able to follow the formation of an immobilized network that constitutes a “sticky” grid necessary for blood platelet adhesion under high shear flow. Because areas of high shear stress coincide with a higher chance for vessel wall damage by mechanical forces, we identified the shear-induced increase in the binding probability of VWF as an effective self-regulating repair mechanism of our microvascular system.

Molecular Origin of Fast Water Transport in Carbon Nanotube Membranes: Superlubricity versus Curvature Dependent Friction

In this paper, we study the interfacial friction of water at graphitic interfaces with various topologies, water between planar graphene sheets, inside and outside carbon nanotubes, with the goal to disentangle confinement and curvature effects on friction. We show that the friction coefficient exhibits a strong curvature dependence; while friction is independent of confinement for the graphene slab, it decreases with carbon nanotube radius for water inside, but increases for water outside. As a paradigm the friction coefficient is found to vanish below a threshold diameter for armchair nanotubes. Using a statistical description of the interfacial friction, we highlight here a structural origin of this curvature dependence, mainly associated with a curvature-induced incommensurability between the water and carbon structures. These results support the recent experiments reporting fast transport of water in nanometric carbon nanotube membranes.

Interfacial water at hydrophobic and hydrophilic surfaces: slip, viscosity, and diffusion.

The dynamics and structure of water at hydrophobic and hydrophilic diamond surfaces is examined via non-equilibrium Molecular Dynamics simulations. For hydrophobic surfaces under shearing conditions, the general hydrodynamic boundary condition involves a finite surface slip. The value of the slip length depends sensitively on the surface water interaction strength and the surface roughness; heuristic scaling relations between slip length, contact angle, and depletion layer thickness are proposed. Inert gas in the aqueous phase exhibits pronounced surface activity but only mildly increases the slip length. On polar hydrophilic surfaces, in contrast, slip is absent, but the water viscosity is found to be increased within a thin surface layer. The viscosity and the thickness of this surface layer depend on the density of polar surface groups. The dynamics of single water molecules in the surface layer exhibits a similar distinction: on hydrophobic surfaces the dynamics is purely diffusive, while close to a hydrophilic surface transient binding or trapping of water molecules over times of the order of hundreds of picoseconds occurs. We also discuss in detail the effect of the Lennard-Jones cutoff length on the interfacial properties.

Statics and dynamics of strongly charged soft matter

Abstract Soft matter materials, such as polymers, membranes, proteins, are often electrically charged. This makes them water soluble, which is of great importance in technological application and a prerequisite for biological function. We discuss a few static and dynamic systems that are dominated by charge effects. One class comprises complexation between oppositely charged objects, for example the adsorption of charged ions or charged polymers on oppositely charged substrates of different geometry. Here the main questions are whether adsorption occurs and what the effective charge of the resulting complex is. We explicitly discuss the adsorption behavior of polyelectrolytes on substrates of planar, cylindrical and spherical geometry with specific reference to DNA adsorption on supported charged lipid layers, DNA adsorption on oppositely charged cylindrical dendro-polymers, and DNA binding on globular histone proteins, respectively. In all these systems salt plays a crucial role, and some of the important features can already be obtained on the linear Debye–Huckel level. The second class comprises effective interactions between similarly charged objects. Here the main theme is to understand the experimental finding that similarly and highly charged bodies attract each other in the presence of multi-valent counterions. This is demonstrated using field-theoretic arguments as well as Monte-Carlo simulations for the case of two homogeneously charged bodies. Realistic surfaces, on the other hand, are corrugated and also exhibit modulated charge distributions, which is important for static properties such as the counterion-density distribution, but has even more pronounced consequences for dynamic properties such as the counterion mobility. More pronounced dynamic effects are obtained with highly condensed charged systems in strong electric fields. Likewise, an electrostatically collapsed highly charged polymer is unfolded and oriented in strong electric fields. All charged systems occur in water, and water by itself is not a very well understood material. At the end of this review, we give a very brief and incomplete account of the behavior of water at planar surfaces. The coupling between water structure and charge effects is largely unexplored, and a few directions for future research are sketched. On an even more nanoscopic level, we demonstrate using ab initio methods that specific interactions between oppositely charged groups (which occur when their electron orbitals start to overlap) are important and cause ion-specific effects that have recently moved into the focus of interest.

Reversed Anionic Hofmeister Series: The Interplay of Surface Charge and Surface Polarity

We describe a two-scale modeling approach toward anion specificity at surfaces of varying charge and polarity. Explicit-solvent atomistic molecular dynamics simulations at neutral hydrophobic (i.e., nonpolar) and neutral hydrophilic (i.e., polar) self-assembled monolayers furnish potentials of mean force for Na(+) and the halide anions F(-), Cl(-), and I(-) which are then used within Poisson-Boltzmann theory to calculate ionic distributions at surfaces of arbitrary charge for finite ion concentration. On the basis of calculated long-ranged electrostatic forces and coagulation properties, we obtain the direct anionic Hofmeister series at negatively charged hydrophobic surfaces. Reversal takes place when going to negative polar or to positive nonpolar surfaces, leading to the indirect series, while for positive polar surfaces the direct series is again obtained. This is in full accordance with a recent experimental classification of colloidal coagulation kinetics and also reflects the trends of the ion specific solubility properties of proteins. A schematic Hofmeister phase diagram is proposed. Partial series reversal is understood as a transient phenomenon for surfaces of intermediate polarity or charge.

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions

Abstract:We formulate the exact non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point of the field-theoretic action, and the effects of counter-ion fluctuations are included by a loop-wise expansion around this saddle point. The Poisson equation is obeyed at each order in this loop expansion. We explicitly give the expansion of the Gibbs potential up to two loops. We then apply our field-theoretic formalism to the case of a single impenetrable wall with counter ions only (in the absence of salt ions). We obtain the fluctuation corrections to the electrostatic potential and the counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. The effective interactions and correlation functions between charged particles close to the charged wall are obtained on the one-loop level.

Rational design of ion force fields based on thermodynamic solvation properties

Most aqueous biological and technological systems contain solvated ions. Atomistic explicit-water simulations of ionic solutions rely crucially on accurate ionic force fields, which contain most commonly two adjustable parameters: the Lennard-Jones diameter and the interaction strength. Assuming these parameters to be properly optimized, the plethora of parameters one finds in the literature for one and the same ion is surprising. In principle, the two parameters should be uniquely determined by matching two ionic properties obtained for a particular water model and within a given simulation protocol with the corresponding experimental observables. Traditionally, ion parameters were chosen in a somewhat unsystematic way to reproduce the solvation free energy and to give the correct ion size when compared with scattering results. Which experimental observable one chooses to reproduce should in principle depend on the context within which the ionic force field is going to be used. In the present work we suggest to use the solvation free energy in conjunction with the solvation entropy to construct thermodynamically sound force fields for the alkali and halide ions for the simulation of ion-specific effects in aqueous environment. To that end we determine the solvation free energy and entropy of both cations and anions in the entire relevant parameter space. As an independent check on the quality of the resulting force fields we also determine the effective ionic radius from the first peak of the radial ion-water distribution function. Several difficulties during parameter optimization are discussed in detail. (i) Single-ion solvation depends decisively on water-air surface properties, which experimentally becomes relevant when introducing extrathermodynamic assumptions on the hydronium (H(3)O(+)) solvation energy. Fitting ion pairs circumvents this problem but leaves the parameters of one reference ion (here we choose chloride) undetermined. (ii) For the halides the problem is almost underdetermined, i.e., there is a whole set of degenerate parameters that equally well describe, e.g., chloride and bromide ions. (iii) For the heavy cations the problem is overdetermined, i.e., no combination of Lennard-Jones parameters is able to reproduce simultaneously energy and entropy of solvation. We discuss various possibilities to deal with these problems and finally present an optimized force field for the halide anions that reproduces the free energy and the entropy of solvation. For the alkali metal cations there is no unambiguous choice of parameters. Therefore, we give three different parameter sets for every ion with a small, intermediate, or large Lennard-Jones interaction strength, where the Lennard-Jones diameters are optimized to reproduce the solvation free energy. The ionic radius is reproduced with acceptable accuracy by this optimization strategy, meaning that the proposed force fields are reliable beyond the target observables (i.e., free energy and entropy of solvation).

Electrostatic Interactions in Strongly-Coupled Soft Matter

Charged soft-matter systems—such as colloidal dispersions and charged polymers—are dominated by attractive forces between constituent like-charged particles when neutralizing counterions of high charge valency are introduced. Such counter-intuitive effects indicate strong electrostatic coupling between like-charged particles, which essentially results from electrostatic correlations among counterions residing near particle surfaces. In this paper, the attraction mechanism and the structure of counterionic correlations are discussed in the limit of strong coupling based on recent numerical and analytical investigations and for various geometries (planar, spherical and cylindrical) of charged objects.

Anionic and Cationic Hofmeister Effects on Hydrophobic and Hydrophilic Surfaces

Using a two-step modeling approach, we address the full spectrum of direct, reversed, and altered ionic sequences as the charge of the ion, the charge of the surface, and the surface polarity are varied. From solvent-explicit molecular dynamics simulations, we extract single-ion surface interaction potentials for halide and alkali ions at hydrophilic and hydrophobic surfaces. These are used within Poisson-Boltzmann theory to calculate ion density and electrostatic potential distributions at mixed polar/unpolar surfaces for varying surface charge. The resulting interfacial tension increments agree quantitatively with experimental data and capture the Hofmeister series, especially the anomaly of lithium, which is difficult to obtain using continuum theory. Phase diagrams that feature different Hofmeister series as a function of surface charge, salt concentration, and surface polarity are constructed from the long-range force between two surfaces interacting across electrolyte solutions. Large anions such as iodide have a high hydrophobic surface affinity and increase the effective charge magnitude on negatively charged unpolar surfaces. Large cations such as cesium also have a large hydrophobic surface affinity and thereby compensate an external negative charge surface charge most efficiently, which explains the well-known asymmetry between cations and anions. On the hydrophilic surface, the size-dependence of the ion surface affinity is reversed, explaining the Hofmeister series reversal when comparing hydrophobic with hydrophilic surfaces.