Effect of Ion Size

Instead of taking the ions as point charges, as done above, the Debye-Hiickel theory can be extended to ions with finite sizes. Let each of the ions (cations and anions) be modeled as a hard sphere of diameter a with its charge located 

Debye Length in Nanometer for Different Electrolyte Concentrations and Valencies (Aqueous Solutions at 25°C) 

The first term on the right-hand side of Equation 3.34 is obviously the contribution from the reference ion itself (according to the Coulomb law, Equation 3.2). As a result, the second term must be the contribution of all ions outside the reference ion. Hence, the second term is identified as fhe electric potential if cloud from the ion cloud acting on the reference ion. 

We now consider the charge distribution inside the cloud that leads to the potential given by Equation 3.35. 

In addition to nanostructural properties of the conducting polymer, considerable influence on actuation behavior has been demonstrated due to the choice of electrolyte. This has included properties of the solvent employed, and crucially the size of doping ions and their interaction with the conducting polymer. As mentioned above, PPy films doped with moderately small anions (e.g. CP) lead to actuation driven by anion movement. By contrast, it is generally found that the inclusion of a large dopant anion (e.g. DBS) within PPy leads to cation-driven actuation, typically when a smaller cation is employed (e.g. Na ). However, it is not always a simple matter of predicting which movement, anion or cation, will predominate for a particular electrolyte system, and for a particular type of 

The size of the cations in PPy acmators was found to be a cracial factor, with a faster response given for smaller cations for cylindrical films formed in Nap-TS, showing that the bending mechanism was controlled by cation insertion and extraction [107]. For PPy films doped with [Fe(CN)e], a larger deformation was estabhshed with increased solvation of the alkali-metal cation used, in the order Li Na K [122]. This finding was confirmed in a further study using PPy(DBS) tubular films [104]. 

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The above demonstration that in a great many cationic polymerisation systems ion-pairs are of no importance as far as the rate of reaction is concerned, raises the question of how it can be explained that in many such systems the nature of the initiator, which determines essentially the nature of the anion, can influence the DP of the polymer formed. In principle, a change of anion, say from a smaller one, e.g., BF4, to a larger one, such as SbF6 could influence the DP in a number of ways. Flowever, probably the most important way is through the effect of ion-size on KD [equation (i)]. 

The effect of ion size on the rates of intercalation of NH J, CH3NH+, C2H5NH 3, n-C3H7NHt, i-C3H7NHt, (CH3)2NH , (CH3)3NH+, and (CH3) N+ into Z-4A zeolite has also been investigated using the pressure-jump technique (18). The results shown in Table V illustrate that Z-4A acts like an ion-sieve. For ions with a volume... 

We find, from the models that fit the experimental data, that A j/kgT is most often in the range from -0.3 to 0. It varies quite regularly with variation of species in a manner that is consistent with the conclusion that the important effects of ion size are explicitly accounted for in Eq. (9). ( 33,3 0 The most striking regularity is that if i and j are both species that are all or largely hydrophobic then A j tends to be nearly... 

Several attempts have been made to improve the PB by accounting for the effects of ion size, ion correlation, and fluctuations of ion distributions. The resultant modified models have led to improved predictions for the ion effects in RNA/DNA folding stability. 

Ania CO, Pernak J, Stefaniak F, Raymundo-Pinero E, Beguin F. Solvent-free ionic liquids as in situ probes for assessing the effect of ion size on the performance of electrical double layer capacitors. Carbon 2006 44 3113-3148. 

Nishio, T., and Minakata, A. Effects of ion size and valence on ion distribution in mixed counterion systems of a rodlike polyelectrolyte solution. 2. mixed-valence counterion systems. Journal of Physical Chemistry B, 2003, 107, No. 32, p. 8140-8145. 

Su, T Bowers, M.T., Ion-polar molecule collisions the effect of ion size on ion-polar molecule rate constants the parameterization of the average-dipole-orientation theory, Int. J. Mass Spectrom Ion Phys. 1973, 12, 347-356. 

An experimental determination of the effect of ion size upon diffusion was performed by measuring the diffusivity of Rb in KCl. In the temperature region near to the melting point, the results obeyed an Arrhenius relationship ... 

Bohinc K, Kralj-Iglic V, Iglic A (2001) Thickness of electrical double layer. Effect of ion size. Eiectrochim Acta 46 3033-3040... 

In more recent theoretical work Hubbard Colonomos and Wolynes (81) developed a molecular theory of the dynamics of the two depolarization processes which predicts specific effects of ion size reducing to the Hubbard-Onsager result for slip boundary conditions in the limit of large ion radii. Numerical results for methanol were later tested by measurements of Winsor and Cole (82) for five salts which... 

T. Nishio and A. Minakata, /. Chem. Phys., 113, 10784 (2000). Effects of Ion Size and Valence on Ion Distribution in Mixed Connterion Systems of Rodlike Polyelectrolyte Solution. 1. Mixed-Size Counterion Systems with Same Valence. 

This chapter describes the use of SCMFT to predict the structure of RTILs at electrified interfaces and the corresponding EDL capacitance. Special attention is paid to study the effect of ion-size and specific (non-electrostatic) adsorption of ions on the shape of the EDL capacitance curve. Results from this study is used to shed light on the unusual shape of the differential capacitance curve in RTILs observed in experiments. In general, the capacitance curve in RTILs has a shape of inverse parabola or a camel-like with two maxima around the point of zero charge (pzc),(Alam et al., 2007 2008 Lockett et al., 2008) which are in contrast to the parabola-shaped capacitance curve typically found in aqueous electrolytes. 

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