Simple Mechanism for the Observed Breakdown of the Nernst-Einstein Relation for Ions in Carbon Nanotubes.

In this Letter, we present a simple mechanism that explains the recent experimental observation of the breakdown of the Nernst-Einstein (NE) relation for an ion moving in a carbon nanotube of subnanometer diameter. We argue that the friction acting on the ion is largely independent of the ion velocity, i.e.

Theory of the force of friction acting on water chains flowing through carbon nanotubes.

A simple model for the friction experienced by the one-dimensional water chains that flow through subnanometer diameter carbon nanotubes is studied. The model is based on a lowest order perturbation theory treatment of the friction experienced by the water chains due to the excitation of phonon and electron excitations in both the nanotube and the water chain, as a result of the motion of the chain. On the basis of this model, we are able to demonstrate how the observed flow velocities of water chains through carbon nanotubes of the order of several centimeters per second can be accounted for.

Electrical image potential and solvation energies for an ion in a pore in a metallic electrode or in a nanotube.

Electrical image potentials can be important in small spaces, such as nanoscale pores in porous electrodes, which are used in capacitive desalination and in supercapacitors, as argued by Bazant's group at Massachusetts Institute of Technology. It will be shown here that inside pores in porous metallic materials the image potentials can be considerably larger than near flat walls, as a result of the fact that the dielectric constant for an electric field perpendicular to a wall is much smaller than the bulk dielectric constant of water. Calculations will be presented for the image potential in spherical and cylindrically shaped pores.

Effects of electrical image potentials and solvation energy on salt ions near a metallic or dielectric wall.

Electrical image potentials near a metallic or a dielectric wall of higher dielectric constant than that of the solution are attractive, and therefore, could concentrate salt ions near the wall. In fact, ions in room temperature ionic liquids have been observed to precipitate near a metallic surface (but not near a nonmetallic surface). It will be argued that a likely reason for why precipitation of ions in salt water due to electrical image forces has not as yet been observed is that the solvation of the ions is reduced near the wall.

Droplet evaporation residue indicating SARS-COV-2 survivability on surfaces.

We conducted a systematic investigation of droplet evaporation on different surfaces. We found that droplets formed even with distilled water do not disappear with evaporation but instead shrink to a residue of a few micrometers lasting over 24 h. The residue formation process differs across surfaces and humidity levels.

Enhancement of the ion concentration in a salt solution near a wall due to electrical image potentials and enhancement of surface tension due to the presence of salt.

Effects of electrical image potentials on the salt ion concentration near a solid wall are studied using a one-loop approximation treatment of the grand canonical partition function, which is the Debye-Hückel approximation. Electrical image potentials resulting from both metallic and dielectric walls of dielectric constant larger than that of water near the wall are considered. Our treatment of this problem supports the conclusions of an earlier publication by one of the authors which shows that near a solid wall there should be a high concentration of ions, resulting from image potentials.

Effects of electrical image forces on salt dissolved in water.

It will be shown that for a solution of salt dissolved in water in contact with a metallic or dielectric wall, the concentration of salt ions (both positive and negative) near the wall can be large enough to exceed the salt's solubility limit, as a result of electrical image charge forces. In addition, since the dielectric constant of water increases from 2.1 at the wall to 81 at about 1 nm from a solid wall, there will be an attractive image potential near the plane on which this increase of the dielectric constant occurs.

Effects of electronic friction from the walls on water flow in carbon nanotubes and on water desalination.

A mechanism for removal of salt from salt water is discussed, which results from friction due to Ohm's law heating, resulting from motion of an electron charge induced in the tube walls by the water molecules' dipoles and the ions' charges. The desalination occurs because this friction is larger for salt ions than for water molecules. Friction due to Ohm's law heating might also provide an explanation for the observation by Secchi et al.

Diffusion mechanism for highly compressed microgel particles.

It is argued that Voronoi tessellation theory can be used to model the observed diffusion of microgel particles in a highly compressed microgel colloid. It is shown that this model is able to account for the fact that even when the microgel colloid is highly compressed, the particles can diffuse, while the diffusion rate decreases as the degree of compression of the microgel colloid increases, as observed.

Enhancement of the water flow velocity through carbon nanotubes resulting from the radius dependence of the friction due to electron excitations.

Secchi et al. [Nature (London) 537, 210 (2016)10.1038/nature19315] observed a large enhancement of the permeability and slip length in carbon nanotubes when the tube radius is of the order of 15 nm, but not in boron nitride nanotubes.

Effects of Capillary Forces on a Hydrogel Sphere Pressed against a Surface.

A theoretical treatment is provided for effects of capillary forces on a hemispherically shaped hydrogel sample pressed against a solid hydrophilic surface. It is pointed out that the adhesion of a hydrogel to a surface resulting from capillary forces is different from that of a nonporous solid because of the porous nature of the hydrogel. Because of this, the Laplace pressure subtracts from the osmotic pressure inside the gel.

Compression and lubrication of salt free polyelectrolyte microgel particles in highly compressed suspensions by counterion osmotic pressure.

The compression of polyelectrolyte microgel particles in a salt-free highly compressed colloid due to osmotic pressure outside of the particles due to counterions located there is studied for a model based on a quasi-analytic solution of the Poisson-Boltzmann equation and a model for the gel elasticity based on counterion osmotic pressure inside the particles and polymer elasticity (of entropic origin). It is found that for particles of radius of the order of a tenth of a micron, the counterion osmotic pressure should play a significant role in the compression of the particles, especially particles which do not have a corona (i.e.

Multiscale treatment of theoretical mechanisms for the protection of hydrogel surfaces from adhesive forces.

One role of a lubricant is to prevent wear of two surfaces in contact, which is likely to be the result of adhesive forces that cause a pair of asperities belonging to two surfaces in contact to stick together. Such adhesive sticking of asperities can occur both for sliding surfaces and for surfaces which are pressed together and then pulled apart. The latter situation, for example, is important for contact lenses, as prevention of sticking reduces possible damage to the cornea as the lenses are inserted and removed from the eye.

Discrete model studies of two grafted polyelectrolyte polymer hydrogels pressed in contact.

The interaction between two grafted polymer gels was investigated. We studied a defect-free network of diamond-like topology containing 8 tetra-functional nodes linked by 16 non-crossing chains. In order to explain the very low friction coefficient observed for polyelectrolyte hydrogels, we computed the monomer density profile of these polymer gels, the interpenetration between two polymer gels (defined as the percentage of monomers belonging to one gel which have penetrated the second gel), the normal force per unit area, and the radial distribution function of the interacting monomers.

Theory of lubrication due to polyelectrolyte hydrogels with arbitrary salt concentration and degree of compression.

A Poisson-Boltzmann equation solution is used to determine the thickness of a thin fluid lubricating layer predicted to separate two polyelectrolyte hydrogels in contact for arbitrary salt concentration as a function of applied load and fixed charge and salt concentration. We consider loads ranging from 1 Pa, at which the thin fluid layer thickness is of the order of micron, up to loads of the order of a MPa, at which it is estimated to be of the order of an angstrom. This allows us to predict the thickness of this layer over the wide range of loads that can occur in various applications of hydrogels.

Surface roughness and dry friction.

Persson's multiscale contact mechanics theory combined with a multiscale Brillouin-Prandtl-Tomlinson model is used to show that on the basis of these models "dry friction" [i.e., kinetic friction that remains at exceedingly small velocities (but still above the creep range) close to its value at higher velocities] should almost always occur for self-affine surfaces when the dominant interaction between two surfaces in contact is due to interatomic hard core repulsion, except for extremely smooth surfaces (i.

Comparison of the kinetic friction of planar neutral and polyelectrolyte polymer brushes using molecular dynamics simulations.

We have simulated the relative shear motion of both neutral and polyelectrolyte end-grafted polymer brushes using molecular dynamics. The flexible neutral polymer brush is treated as a bead-spring model, and the polyelectrolyte brush is treated the same way except that each bead is charged and there are counterions present to neutralize the charge. We investigated the friction coefficient, monomer density, and brush penetration for both polyelectrolyte and neutral brushes with both equal grafting density and equal normal force under good solvent conditions.

Theory of the short time mechanical relaxation in articular cartilage.

Articular cartilage is comprised of macromolecules, proteoglycans, with (charged) chondroitin sulfate side-chains attached to them. The proteoglycans are attached to longer hyaluronic acid chains, trapped within a network of type II collagen fibrils. As a consequence of their relatively long persistence lengths, the number of persistence lengths along the chondroitin sulfate and proteoglycan chains is relatively small, and consequently, the retraction times for these side chains are also quite short.

Theory of hydrostatic lubrication for polymer hydrogel-coated surfaces with excess salt.

It is argued on the basis of a solution of the Poisson-Boltzmann equation and scaling arguments that for arbitrary salt concentration, the overwhelming majority of the regions of contact of two hydrogel-coated surfaces should be separated by a thin fluid layer. This is likely to be one of the mechanisms responsible for their excellent lubricating capability.

Static and dry friction due to multiscale surface roughness.

It is shown on the basis of scaling arguments that a disordered interface between two elastic solids will quite generally exhibit static and dry friction (i.e., kinetic friction which does not vanish as the sliding velocity approaches zero) because of Tomlinson-model instabilities that occur for small-length-scale asperities.

Theory of the observed ultralow friction between sliding polyelectrolyte brushes.

It is shown using a method based on a modified version of the mean field theory of Miklavic and Marcelja [J. Phys. Chem.

Theory of depinning of monolayer films adsorbed on a quartz crystal microbalance.

In quartz crystal microbalance studies of the friction between an adsorbed monolayer film and a metallic substrate, the films are observed to slide relative to the substrate under inertial forces of order 10(-14) dyn per film atom, a force much smaller than all existing theoretical estimates of the force that surface defects are capable of exerting on the film. We argue that defect potentials with a range comparable to an atomic spacing or more will produce a pinning force below the inertial force.

Theory of the effects of multiscale surface roughness and stiffness on static friction.

It is shown on the basis of simple scaling arguments that an interface between two three-dimensional elastic solids, consisting of completely flat disordered surfaces, which interact with interatomic hard core interactions, will be in a weak pinning regime, and hence exhibit negligibly small static friction. It is argued, however, that the presence of roughness on multiple length scales can lead to much larger friction (i.e.

Adiabatic molecular-dynamics-simulation-method studies of kinetic friction.

An adiabatic molecular-dynamics method is developed and used to study the Muser-Robbins model for dry friction (i.e., nonzero kinetic friction in the slow sliding speed limit).

Theory of lubrication due to collective pinning.

In collective pinning theory, the problem of two three-dimensional solids in contact is at its critical dimension. This implies that when the disordered forces acting between the two solids at the interface are relatively strong, the force of static friction should be large, but at smaller values of these forces, the system switches over to a regime of weak static friction. It is argued that this provides a mechanism for the reduction of friction in boundary lubrication.