Friction force ionic liquids

An ion in polar liquids is under continuous Brownian motion, and the frictional force exerted on the Brownian particle is proportional to its velocity. The proportional constant, or the friction coefficient, has been a focus of intensive research for almost 100 years both in experimental and theoretical studies [61-65]. According to the simple Stokes law which is based on the hydrodynamic theory, the friction should increase proportionally to ionic radii. However, the experimental observations for small ions such as alkali-halide ions in water show the ion-size dependence which is just opposite to the Stokes law [61-64]. 

Smith et al. [74] have measured the friction force between atomically smooth solid surfaces across IL films of controlled thickness in terms of the number of ion layers (Fig. 19.6). Multiple friction-load regimes emerge, each corresponding to a different number of ion layers in the film. In contrast to molecular liquids, the frictirai coefficients differ for each layer due to their varying composition. The high resolution measurements have revealed the following notable features for the first time in ionic liquid ... 

Nonequilibrium molecular dynamics for the interactimi parameters between alkylammonium alkylsulfonate ILs and an iron surface have been used [92] to develop a procedure for a quantitative prediction of the friction coefficient. Changes in the frictional force are explained in terms of the specific arrangements and orientations of groups forming the ionic liquid at the surface vicinity. 

Classical diffusion can be described by Equation 1.3 when the radius of the sphere is small conpared with the mean free path. With ionic liquids, the mean free path can be less than the radius of the ion, and hence the ion can be considered as moving via a series of discrete jumps where the correlation length is a measure of the size of the hole into which the ion can junp. Appreciating why deviations from the Stokes-Einstein equation occur shows why a model based on holes becomes appropriate. The approximate nature of the Stokes-Einstein equation is often overlooked and is discussed in detail by Bockris and Reddy [5, p. 379]. There are numerous aspects that need to be taken into account, including that it is derived for non-charged particles, it is the local viscosity rather than the bulk that is required, and the ordering effect of the ions exhibits an additional frictional force that needs to be explained. 

Capillary electrophoresis (CE) is used to separate ionic species by exploiting their frictional forces and differences in the charges of the respective species. In traditional electrophoresis, electrically charged analytes move in a conductive liquid medium under the influence of an electric field. CE has proved to be highly successful in enabling the analysis of DNA fragments and other... 

Here we address the problem from a different point of view, namely, in terms of a response of collective excitations in solvent to the ionic field. In Sec. 5.3 we have succeeded in abstracting the collective excitations in a model diatomic liquid which can be identified as acoustic and optical modes. The two modes arise essentially from the translational and rotational motions of solvent molecules. Since the Stokes and dielectric frictions originate basically from the energy dissipation due to the translational and rotational motions of solvent molecules, respectively, it is reasonable to ask how the ionic field couples with the collective excitations and/or how the two drag forces are related to the two col-... 

In polar liquids, a polar solute experiences an additional friction, called the dielectric friction, produced by a lag in the electrostatic forces as the solute dipole rotates away from its equilibrium orientationT " " ° " " " " " ° The reduced polarity at the liquid-vapor and water-organic liquid interfaces is thus expected to slow energy relaxation and speed up reorientation. However, surface roughness, capillary fluctuations, and the ability of an ionic solute to keep its hydration shell can complicate this picture. 

We have implicitly allowed the friction coefficients to be independent of the magnitude and the nature of applied forces, that is to say these coefficients are completely defined by the equilibrium properties of the solution as shown for example by Bearman for self-diffusion processes in binary liquid solutions [14]. Nevertheless, for ionic solutions polarization effects resulting from the application of an external field of forces may give rise to distorted ionic atmospheres and the identification of a unique interaction parameter in electrical and self-diffusion processes becomes questionable. However, it has been proved that as far as polyelectrolytes are concerned, the perturbation of the counter-ion distribution with respect to the equilibrium situation is fairly small despite the high polarizability of polyelectrolyte solutions [18]. Moreover, linear forces - fluxes relations have usually been reported from experimental investigations and for both polyelectrolyte and pure salt solutions electrical and self-diffusion determinations have led to nearly identical frictional parameters [19-20]. The friction model might therefore be used with confidence as long as systems not too far from equilibrium are concerned. 

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