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., dry friction, and demonstrate, based on the Langevin equation for a particle subject to both dry and viscous friction, that the NE relation is violated when dry friction dominates. We predict that the ratio of the diffusion constant to the mobility of the ion is a few orders of magnitude smaller than the value predicted by the NE relation, in quantitative agreement with experiment.

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. If the hydrogen bonds between the water molecules are broken (as would occur if there were an electric field oscillating with a frequency equal to the resonant frequency of the hydrogen bonds present), it is shown that the friction experienced by the water flowing in the tube can be much smaller.

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. The calculations for cylindrical pores can also be applied to nanotubes. It was believed for a long time, on the basis of molecular dynamics simulations, that in order to push a salt solution through a small radius nanotube, work must be done against the solvation energy of the ions, which is larger inside a narrow nanotube than it is in the bulk. The relatively large image charge potential energy in narrow nanotubes, however, tends to oppose this increase in the solvation energy. The degree to which the image potential facilitates the flow of the salt ions into nanotubes will be discussed.

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. This results in an energy barrier. This reduction occurs because of the large decrease near the wall of the dielectric constant of water normal to the wall. The conditions under which ions are able to get past the resulting energy barrier and concentrate at a solid wall, either as a result of a reduction in this barrier due to screening at high ion concentration or as a result of thermal activation over the barrier will be explored.

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. Specifically, under 40% relative humidity, 80% of droplets form residues on plastic and uncoated and coated glass, while less than 20% form on stainless steel and none on copper. The formation of residues and their variability are explained by modeling the evaporation process considering the presence of nonvolatile solutes on substrates and substrate thermal conductivity. Such variability is consistent with the survivability of SARS-CoV-2 measured on these surfaces. We hypothesize that these long-lasting microscale residues can potentially insulate the virus against environmental changes, allowing them to survive and remain infectious for extended durations.

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. We have also applied our treatment to the increase of the surface tension of a liquid that occurs when salt is dissolved in the liquid. Our treatment gives the -c_{s}log(c_{s}) dependence of the surface tension found by Onsager and Samarasa in the small c_{s} limit, where c_{s} is the salt concentration.

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. Such large ion concentrations could possibly be used in water desalination.

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. [Nature 537, 210 (2016)10.1038/nature19315] that the flow velocity of water in carbon nanotubes for a given pressure gradient increases rapidly as the tube radius decreases from 50 to 15 nm, which does not occur for boron nitride nanotubes, which are insulators. This friction can have the right magnitude to produce the slip lengths reported by Secchi et al. One possibility is that the nanotubes in this experiment were metallic, and their conductivity becomes large as their radius decreases, due to ballistic conduction. Another possibility is that when the tube circumference drops below the electron mean-free path, the wall switches from behaving as a two-dimensional conductor to behaving as a one-dimensional conductor for which the electrons are more strongly localized. When the conductivity is sufficiently small, small displacements of the localized electron states can provide the dominant contribution to the motion of the induced charge, rather than current flow, thus reducing the friction due to Ohm's law heating.

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. It will be pointed out that none of the parameters that appear in the usual molecular dynamics treatments of water flow in carbon nanotubes have a length scale comparable to 15 nm, which could account for the observed flow velocity enhancement. It will be demonstrated here, however, that if the friction force between the water and the tube walls in carbon nanotubes is dominated by friction due to electron excitations in the tube walls, the enhanced flow can be accounted for by a reduction in the contribution to the friction due to electron excitations in the wall, resulting from the dependence of the electron energy band gap on the tube radius.

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. For neutral gels, it can exceed the osmotic pressure, causing the gel to deswell. For charged gels, since the counterions inside the gel generally provide much higher osmotic pressure than that due to monomers alone (which is the only source of osmotic pressure in neutral hydrogels), the Laplace pressure is less likely to make the gel deswell. The Laplace pressure can, however, be large enough to deswell asperities (due to surface roughness) on the gel surface, increasing the contact area. This could result in an increase in the friction and ionic electrical conductivity between the gel and the surface (if the surface is an electrical conductor).

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., nonlinked polymer chains attached to their surface). The presence of a corona of monomer density smaller than that of the core of the microgel reduces the contribution of the osmotic pressure due to counterions outside of the microgel. It is also demonstrated that counterion osmotic pressure outside the particles can provide a significant contribution to the lubrication of the interface between the particles and a surface along which the compressed colloid is made to slide, for sufficiently slow velocities.

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. Contact lenses are made from both neutral and polyelectrolyte hydrogels. It is demonstrated here that sticking of neutral hydrogels can be prevented by repulsive forces between asperities in contact, resulting from polymers attached to the gel surface but not linked with each other. For polyelectrolyte hydrogels, it is shown that osmotic pressure due to counterions, held at the interface between asperities in contact by the electrostatic attraction between the ions and the fixed charges in the gel, can provide a sufficiently strong repulsive force to prevent adhesive sticking of small-length-scale asperities.

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.e., surfaces with a Hurst index very close to 1).

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. We argue that, as a consequence of this, they will not significantly inhibit the reptation of the hyaluronic acid chains. Scaling arguments applied to this model allow us to show that the shortest of the mechanical relaxation times of cartilage, that have been determined by Fyhrie and Barone to be due to reptation of the hyaluronic acid polymers, should have a dependence on the load, i.e., force per unit interface area P, carried by the cartilage, proportional to P(3/2).

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. This provides a possible explanation for why static and dry friction are virtually always observed, and superlubricity almost never occurs.

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. 92, 6718 (1988)] that it should be possible for osmotic pressure due to the counterions associated with the two polyelectrolyte polymer brush coated surfaces to support a reasonable load (i.e., about 10(6) Pa) with the brushes held sufficiently far apart to prevent entanglement of polymers belonging to the two brushes, thus avoiding what is believed to be the dominant mechanisms for static and dry friction.

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.