Viscosity modeling, ionic liquids

Tochigi K, Yamamoto H (2007) Estimation of ionic conductivity and viscosity of ionic liquids using a QSPR model. J Phys Chem C 111 15989-15994... 

Clearly, many structural parameters affect the viscosity of ionic liquids and a more exhaustive study is needed to rationalize flie different trends and to establish a correlation model for prediction. 

A well-known effect of water impurities in ionic liquids is the viscosity decrease. " However, also ionic liquids were reported, in which water impurities induces gelation. Spohr and Patey have shown with ionic liquid model systems that water tends to replace the counter ions from the ion solvation shell in ionic liquids with small ion size disparity, leading to a faster diffusion of the lighter ion-water clusters. However, water can increase viscosity of ionic liquids if the ion size disparity is too large, or if strong directional ion pairs are found. Spohr and Patey attributed this behavior to extended water-anion chains and strongly bound water-anion-cation clusters. A classical molecular dynamics study by Raju and Balasubramanian observed that the anion diffuse faster than the cation in water ionic liquid mixtures in contrast to neat ionic liquids. The larger... 

The highly detailed results obtained for the neat ionic liquid [BMIM][PFg] clearly demonstrate the potential of this method for determination of molecular reorienta-tional dynamics in ionic liquids. Further studies should combine the results for the reorientational dynamics with viscosity data in order to compare experimental correlation times with correlation times calculated from hydrodynamic models (cf [14]). It should thus be possible to draw conclusions about the intermolecular structure and interactions in ionic liquids and about the molecular basis of specific properties of ionic liquids. 

The calculation of viscosities of electrolyte mixtures can be accomplished with the method of Andrade (see Ref. [40]) extended with the electrolyte correction by Jones-Dole [44]. First, the pure component viscosities of molecular species are determined by the three-parametric Andrade equation, which allows a mixing rule to be applied and the mixture viscosity of an electrolyte-free liquid phase to be obtained. The latter is transformed into the viscosity of the liquid phase using the electrolyte correction term of Jones and Dole [44], whereas the ionic mobility and conductivity are used as model parameters. 

The conductivity of ionic liquids can be modeled in the same manner as the viscosity, i.e. despite the high ionic strength of the liquid, ionic migration is limited by the availability of suitably sized voids [130]. Since the fraction of suitably sized holes in ambient temperature ionic liquids is effectively at infinite dilution, migration should be described by a combination of the Stokes-Einstein and Nernst-Einstein equations. This is explained in greater detail in Chapter 11.3 on process scale-up but it is sufficient to say that an expression can be derived for the conductivity, k... 

After asserting the nanostructured nature of ionic liquids, the structural analysis of these fluids continued in two different directions. The first was to check how the built-in flexibility of the isolated ions of the model affect (or are affected by) the nanostructured nature of the ionic liquid, and how that can influence properties like viscosity, electrical conductivity, or diffusion coefficients. It must be stressed that the charges in the CLAP model are fixed to the atomic positions, which means that the most obvious way to probe the relation between the structure of the ionic liquid as a whole in terms of the structure of its individual ions is to investigate the flexibility (conformational landscape) of the latter. The second alternative direction was to probe the structure of ionic liquids not by regarding into the structure of the component ions but by instead using an external probe (for example, a neutral molecular species), solubility experiments with selected solute molecules being the most obvious experimental approach. 

Overall the density of ionic liquids is somewhat easier to model than the viscosity. In general the change of density with temperature has been fitted to linear equations of the form... 

The film thickness obtained in the glass microchannels of 0.2 mm ID seems to be under-predicted by all the models, although the Ca numbers range for this work (0.007 < Ca < 0.159) falls within the Ca numbers range that the models are valid as shown in Table 2.2. The large film thickness values in the case of the small channel may be due to the high Ca numbers achieved at relatively low mixture velocities because of the high viscosity of the ionic liquid. 

It was proposed that the reason that ionic liquids fit this model so accurately is due to the small number of suitably sized holes available at ambient temperatures that are able to accommodate the exceptionally large ions [21]. Under these conditions, the holes are effectively at infinite dilution, and this is the reason that Equation 1.3 becomes valid. It was shown that the viscosity of an ionic liquid could be accurately modelled using a gas-like model where mobility was hindered by the probability of finding a hole large enough for an ion to move into. The liquids that do not fit hole theory tend to be those whose ions are less spherical. Modifications to this theory have been made by Zhao et al., who took into account the asymmetric nature of the cation, and this significantly inproved the prediction of the conductivity of long chain salts [22]. 

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. 

This model is essentially derived from classical thermodynamics and fluid mechanics, treating the diffusing species as a spherical particle in a continuum of fluid. Further development of this model has also seen it modified to involve other geometries however, its main purpose is to highlight the relationship between diffusion and viscosity. The main disadvantage in applying this model to ionic liquids is that it assumes that there are no interactions between the ions/molecules, but it has been found to show some correlation [51, 55]. 

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