Lyotropic numbers

Fig. 13. Preferential iateraction parameter vs lyotropic number for lysozyme on (° ) bovine semm albumin and ( ) Toyopead.

Fig. 40.—Relationships between the lyotropic number, N, and the viscosity of starch gels.

The second empirical correlation that has been observed is between the ion pair enthalpy of hydration and the lyotropic number (Buchner, 23, 24). The lyotropic number was developed by Buchner as a quantitative eicpression of the position of the anion in the Hofmeister series. It... 

Fig. 2. Enthalpies of hydration as functions of the lyotropic numbers of the anions.

Again in the case of the lyotropic number interpolation the accuracy is dependent on the accuracy of the measurement of the lyotropic number, though the sum of the hydration heats only changes slowly with lyotropic number. It must also be stressed that the lattice energies obtained in this way are not theoretical lattice energies in that they are not based on any model of the crystal. Rather they are empirical or experimental in that they are based on a combination of empirical hydration enthalpies and experimental enthalpies of solution. 

Azide Kapustinskii formula Term-by-term calculation (a) Ionic radius (b) Lyotropic number... 

Madelung Term Lattice Energy Ionic Radius Lyotropic Number From Heat of formation ... 

Comparison of Water and Methanol Solutions. Comparison of (-AA(7/RT)j for ions in both water and methanol solutions can be made by using (-AA(7/R2 )ua+ and (-AA(7/R2 )(j2 - as references for the alkali metal cations and halide anions respectively. These have been plotted in Figure 5 with the lyotropic numbers for each ion. Figure 5 shows that with respect to halide ions the correlation of lyotropic number with [ (-AAG/RT)j.-(-AA( /R2 )j,j -] is both linear and identical for both solvents, whereas the corresponding correlations with respect to alkali metal cations are different. In particular, with respect to these latter ions, the change of [ (-AAG/RT) j -(-AA( / )jjg+] with lyotropic number is greater in methanol solutions than in aqueous solutions. This means that for a given membrane, the variations in solute separation for alkali metal halide salts with common anions is much less in aqueous solutions than in methanol solutions, which is consistent with experimental results. Further, in the case of methanol solutions, the solute separation increases with increase in lyotropic number for the alkali metal cation series and decreases with an increase in lyotropic number for the halide series. 

Citrate compounds are salting-out electrolytes — they tie up water molecules in the liquid and as a result help force the formation of liquid crystals or lamellar stmctures. It is sometimes possible to reverse this trend by the addition of salting-in electrolytes, compounds with high lyotropic numbers (>9.5) which can raise the cloud point of a liquid formulation [26], This permits increased concentration without the onset of structuring. 

Here k is the constant depended on the kind of surfactant, electrolyte and temperature. Practically all anions and cations diminish the CMC of ethoxylated nonionics in accordance with their lyotropic numbers of constituting ions following the sequence... 

Figure 9. Relation between the threshold concentration and the lyotropic number of anions. Cation species are indicated in the figure at the right of the respective lines (ref. 19, 20).

Lyotropic numbers N o, Table 5.1, were assigned to ions in the 30s of the last century by Buchner and Voet (Buchner et al. 1932 Voet 1937a, 1937b) according to their effects on colloidal systems. The lyotropic series has nowadays been to some extent superseded by the Hofmeister series, with which it is taken to be practically synonymous, but it is not so exactly. For the alkali metal cations and the halide anions the lyotropic numbers obtained from colloidal phenomena are linearly related to their enthalpies of hydration. Voet (1937a) concluded that the lyotropic series are simply related to the electric field strengths of the ions. Note that the Myo values for the alkali metal cations are not commensurate with those of the alkaline earth cations and with those of the anions. 

Table 5.1 Lyotropic numbers for colloideil systems. (Buchner et al. 1932 ...

Schott H (1984) Lyotropic numbers of anions from cloud point changes of non-ionic surfactants. CoU Surf 11 51-54... 

TABLE 8.11 Lyotropic Numbers, Applicable to Colloidal Systems [89, 90]... 

Inversions of the positions of some anions in the series are noted when several related phenomena are nsed to establish it as reported by Cacace et al. and by Pinna et al. [98, 99], For instance, F was placed at the head of the series according to Hochachka and Somero [101] and to HaU and Drake [102], althongh other authors relegated it to nearer its middle. A related series, whose lyotropic numbers are given in Table 8.11, also has several reversals with respect to the Hofmeister series as pointed out by Schott [103] and by Lo Nostro et al. [104]. 

Salts that are most effective in lowering the consolute temperature of polyoxyethylene in water have cations that tend to form strong crown-ether-like complexes with the polyoxyethylene and anions that are of low lyotropic number. Salts that tend to form cation complexes with polyoxyethylene and have anions with high lyotropic number show high ionic conductivity (24, 25) in the solid phase with poly(ethylene oxide). 

Anion Lyotropic number Formation of biphase with polyethylene glycol... 

The electrical properties of the alkali metal salt complexes are of interest as solid electrodes for batteries (27, 27a). There is particular interest in alkali metal-thiocyanate salt complexes this interest is related to the anion having a high lyotropic number and a correspondingly high conductivity (see Table 4). The complete phase diagram has been published for the potassium thiocyanate/ and sodium/thiocyanate/polyethylene glycol system (28), and various thermodynamic properties have... 

Morris DEC (1958) Lattice energies and related properties dtaived by use of lyotropic numbers. J Inorg Nucl Chem 6 295-302... 

However, it should be mentioned that specific ion effects were found even several decades before Hofineister. In 1847, Poiseuille was probably the first who noted that some salts increase the viscosity of water, whereas others decrease it. Jones and Dole in 1929, Cox and Wolfenden in 1934, and several other groups further refined the specific ion effect on water viscosity. From these viscosity smdies and in particular the Jones-Dole viscosity B coefficients, the expressions for water-structure maker and water-structure breaker were finally derived. They were first introduced in 1945 by Frank and Evans, who showed the relationship between viscosity and entropy of dilution. There is a third concept introduced by A. Voet [see also Eckfeldt ] the ordering ofions according to their lyotropic numbers. It nicely correlates with ion effects on the swelling... 

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