1.20.4: Surfactants and Miceles: Ionics
An intense debate concerns the structure of micelles, particularly those formed by ionic surfactants such as SDS and CTAB. It seems generally agreed that micelles are essentially spherical in shape. The polar head groups ( e.g. \(– \mathrm{N}^{+} \mathrm{Me}_{3}\)) are at the surface of each micelle, having strong interactions with the surrounding solvent. In close proximity in the Stern layer are counterions (e.g. bromide ions in the case of CTAB); the aggregation number \(\mathrm{n}\) describes the number of cations which form each micelle. The total charge on the micelle is determined the aggregation number and a quantity \(\beta\), the latter being the fraction of charge of aggregated ions forming the micelle neutralized by the micelle bound counter ions. The remaining fraction of counter ions exists as ‘free’ ions in aqueous solution. Both \(mathrm{n}\) and \(\beta\) are characteristic of a given surfactant system, and are obtained from analysis of experimental data [1]. The properties of ionic surfactants have been extensively studied [2-14]. Here we examine four thermodynamic descriptions of these systems.
Ionic Surfactant:1:1 salt: Phase Equilibrium: Dry Neutral Micelle
We consider a dilute aqueous solution of an ionic surfactant; e.g. \(\mathrm{AM}^{+} \mathrm{Br}^{-}\). As more surfactant is added a trace amount of micelles appear in the solution when the concentration of surfactant just exceeds the cmc. The trace amount of surfactant is present as micelles constituting a micellar phase. At defined \(\mathrm{T}\) and \(\mathrm{p}\), the following equilibrium is established in the case of the model surfactant \(\mathrm{AM}^{+} \mathrm{Br}^{-}\);
\[\mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{aq}) \Leftrightarrow \mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{mic}) \nonumber \]
Then,
\[\mu^{\mathrm{cq}}\left[\mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{aq})\right]=\mu^{\mathrm{cq}}\left[\mathrm{AM}^{+} \mathrm{Br}^{-}(\mathrm{mic})\right] \nonumber \]
We assume that the micelles carry no charge. The chemical potential of the surfactant in aqueous solution is related to the cmc using the following equation where \(\mathrm{y}_{\pm}\) is the mean ionic activity coefficient. We set \(\mu^{\mathrm{eq}}\left[\mathrm{AM}^{+} \mathrm{Br}^{-} \text {(mic) }\right]\) equal to the chemical potential of the surfactant in the pure micellar state, \(\mu^{*}\left[\mathrm{AM}^{+} \mathrm{Br}^{-} \text {(mic) }\right]\).
\[\begin{aligned}
\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq} ; \mathrm{c}-\mathrm{scale}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmc} \, \mathrm{y}_{\pm} \, / \mathrm{c}_{\mathrm{r}}\right) \\
&=\mu^{*}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {micellar phase }\right)
\end{aligned} \nonumber \]
Here \(\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq} ; \mathrm{c}-\text { scale }\right)\) is the chemical potential of the salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) in aqueous solution at unit concentration where the properties of the salt are ideal. Thus \(\mathrm{y}_{\pm}\) describes the role of ion-ion interactions in the solution having salt concentration cmc. Because the model states that there is only a trace amount of micelles in the system, we do not take account of salt-micelle interactions. Then
\[\Delta_{\text {mic }} \mathrm{G}^{0}=\mu^{*}\left(\text { micellar phase; } \mathrm{AM}^{+} \mathrm{Br}^{-}\right)-\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {aq; } \mathrm{c}-\text { scale }\right) \nonumber \]
Hence,
\[\Delta_{\text {mic }} G^{0}(\mathrm{aq} ; \mathrm{c}-\text { scale })=2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmc} \, \mathrm{y}_{\pm} / \mathrm{c}_{\mathrm{r}}\right) \nonumber \]
If the salt concentration in the aqueous solution at the cmc is quite low, a useful assumption sets \(\mathrm{y}_{\pm}\) equal to unity. Then,
\[\Delta_{\text {mic }} \mathrm{G}^{0}(\mathrm{aq} ; \mathrm{c}-\mathrm{scale})=2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right) \nonumber \]
The latter equation leads to the calculation of the standard increase in Gibbs energy when one mole of salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) passes from the ideal solution, concentration \(1 \mathrm{mol dm}^{-3}\) to the micellar phase.
There is a modest problem with the latter equation which can raise conceptual problems. As normally stated the cmc for a given salt is expressed using the unit ‘\(\mathrm{mol dm}^{-3}\)‘ so that \(\mathrm{c}_{\mathrm{r}} = 1 \mathrm{~mol dm}^{-3}\). This means that when \(\mathrm{cmc} > 1 \mathrm{~mol dm}^{-3}\), \(\Delta_{\operatorname{mic}} G^{0}(\mathrm{aq} ; \mathrm{c}-\text { scale })\) is positive. For solutes where \(\mathrm{cmc} < 1 \mathrm{~mol dm}^{-3}\), the derived quantity is negative.
Another approach expresses the cmc using the mole fractions, cmx such that equation (c) is written as follows.
\[\begin{gathered}
\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {aq } ; \mathrm{x}-\mathrm{scale}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{cmx} \, \mathrm{f}_{\pm}^{*}\right) \\
=\mu^{*}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {micellar phase }\right)
\end{gathered} \nonumber \]
Here \(\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq} ; \mathrm{x}-\text { scale }\right)\) is the chemical potential of the salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) in an ideal solution where the (asymmetric) activity coefficient \(\mathrm{f}_{\pm}^{*}=1.0\) and \(\mathrm{cmx} = 1.0\). .
By definition \(\operatorname{limit}\left[x\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) \rightarrow 0\right] \mathrm{f}_{\pm}^{*}=1.0 \text { at all } \mathrm{T} \text { and } \mathrm{p}\).} The analogue of equation (f) takes the following form.
\[\Delta_{\text {mic }} \mathrm{G}^{0}(\mathrm{aq} ; \mathrm{x}-\text { scale })=2 \, \mathrm{R} \, \mathrm{T} \, \ln (\mathrm{cm} \mathrm{x}) \nonumber \]
Because cmx is always less than unity, \(\Delta_{\text {mic }} G^{0}(a q ; x-\text { scale })\) is always negative. It is important in these calculations to note the definitions of reference and standard states for solutes and micelles otherwise false conclusions can be drawn [14]. The analysis proceeds to use the Gibbs-Helmholtz equation. Hence,
\[\Delta_{\text {mic }} \mathrm{H}^{0}(\mathrm{aq} ; \mathrm{x}-\text { scale })=-2 \, \mathrm{R} \, \mathrm{T}^{2} \,\{\partial \ln (\mathrm{cmx}) / \partial \mathrm{T}\}_{\mathrm{p}} \nonumber \]
The term \(\left\{\partial \ln (\mathrm{cmx}) / \partial \mathrm{T}_{\mathrm{P}}\right.\) is conveniently obtained by expressing the dependence of cmx on temperature using the following polynomial.
\[\ln (c m x)=a_{1}+a_{2} \, T+a_{3} \, T^{2}+\ldots \nonumber \]
Equation (h) is straightforward, the stoichiometric factor ‘2’ emerging from the fact that each mole of salt \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) produces on complete dissociation 2 moles of ions. A key assumption in this analysis is that the micelles carry no electric charge. In other words a micelle is formed by \(\mathrm{n}\) moles of cation \(\mathrm{AM}^{+}\), \(\mathrm{n}\) moles of counter ions \(\mathrm{Br}^{-}\) being bound within the Stern layer such that the charge on each micelle is zero. This model is a little unrealistic.
Ionic Surfactant: 1:1 salt: Phase Equilibrium: Dry Charged Micelle
A cationic surfactant \(\mathrm{AM}^{+} \mathrm{Br}^{-}\) in aqueous solution forms micelles when \(\mathrm{n}\) cations come together to form a micellar phase. Bearing in mind that \(\mathrm{n}\) might be greater than 20, the idea that there exists micro-phases of macro-cations in a system with an electric charge at least +20 is not attractive. In practice the charge is partially neutralised by bromide ions in the Stern layer. The quantity \(\beta\) refers to the fraction of counter ions bound to cations. Thus the formal charge number on each micelle is \([n \,(1-\beta)]\). In the model developed here we represent the formation of the micro-phase comprising the micelles as follows where n is the number of cation monomers which cluster, the remaining bromide ions being present in the aqueous solution (phase).
\[\begin{aligned}
\mathrm{nAM}^{+}(\mathrm{aq}) &+\mathrm{n} \,(1-\beta+\beta) \mathrm{Br}^{-}(\mathrm{aq}) \\
& \Leftrightarrow\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n} \,(1-\beta)}(\mathrm{mic})+\mathrm{n} \,(1-\beta) \mathrm{Br}^{-}(\mathrm{aq})
\end{aligned} \nonumber \]
We re-express this equilibrium in terms of equilibrium chemical potentials for a system at fixed \(\mathrm{T}\) and \(\mathrm{p}\).
\[\begin{aligned}
&\mathrm{n} \, \mu^{\mathrm{cq}}\left(\mathrm{AM}^{+} ; \mathrm{aq}\right)+\mathrm{n} \,(1-\beta+\beta) \, \mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right) \\
&=\mu^{\mathrm{eq}}\left\{\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n}(1-\beta)} ; \text { micelle }\right\}+\mathrm{n} \,(1-\beta) \mu^{\mathrm{cq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)
\end{aligned} \nonumber \]
We define the chemical potential of the micelle microphase which contains 1 mole of \(\mathrm{AM}^{+}\). This is a key extrathermodynamic step. We also describe the micelle as a pure ‘phase’.
\[\begin{aligned}
\mu^{\mathrm{eq}}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\} \\
&=\mu^{\mathrm{cq}}\left\{\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n}(1-\beta)} ; \text { micelle }\right\} / \mathrm{n}
\end{aligned} \nonumber \]
Hence,
\[\begin{aligned}
&\mu^{\mathrm{eq}}\left(\mathrm{AM}^{+} ; \mathrm{aq}\right)+\mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right) \\
&=\mu^{*}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\}+(1-\beta) \mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)
\end{aligned} \nonumber \]
Or,
\[\begin{aligned}
&\mu^{\mathrm{cq}}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)= \\
&\mu^{\mathrm{eq}}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{-}\right]^{(1-\beta)} ; \text { micelle\} }+(1-\beta) \mu^{\mathrm{cq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)\right.
\end{aligned} \nonumber \]
The term \(\mu^{थ}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)\) is the equilibrium chemical potential of a 1:1 salt in solution at the cmc. The term \(\mu^{\mathrm{eq}}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)\) is the equilibrium chemical potential of the bromide ion in the solution at the cmc of the surfactant. In any event the system is electrically neutral.
\[\begin{aligned}
&\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} \, \mathrm{y}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) / \mathrm{c}_{\mathrm{r}}\right] \\
&=\mu^{*}\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\} \\
&+(1-\beta) \,\left\{\mu^{0}\left(\mathrm{Br}{ }^{-} ; \mathrm{aq}\right)+\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} \, \mathrm{y}\left(\mathrm{Br}^{-}\right) / \mathrm{c}_{\mathrm{r}}\right]\right\}
\end{aligned} \nonumber \]
By definition,
\[\begin{aligned}
\Delta_{\text {mic }} \mathrm{G}^{0}=\mu^{*} &\left\{\left[\mathrm{AM}^{+} \beta \mathrm{Br}^{*}\right]^{(1-\beta)} ; \text { micelle }\right\} \\
&+(1-\beta) \, \mu^{0}\left(\mathrm{Br}^{-} ; \mathrm{aq}\right)-\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-1} ; \mathrm{aq}\right)
\end{aligned} \nonumber \]
Assuming both \(\mathrm{y}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right)\) and \(\mathrm{y}\left(\mathrm{Br}^{-}\right)\) are unity,
\[\Delta_{\text {mic }} \mathrm{G}^{0}=2 \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right]-(1-\beta) \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right] \nonumber \]
or
\[\Delta_{\text {mic }} \mathrm{G}^{0}=(1+\beta) \, \mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{cmc} / \mathrm{c}_{\mathrm{r}}\right] \nonumber \]
The latter equation closely resembles that for non-ionic surfactants for which \(\beta\) is unity. For ionic surfactants it is not justified to assume that \(\beta\) is also unity.
Ionic Surfactant: 1:1 salt: Dry Charged Micelle:Mixed Salt Solutions
As more ionic surfactant is added to a solution having the concentration of surfactant equal to the cmc, so the solution increasingly resembles a mixed salt solution, simple salt, charged micelles and counter ions. Analysis of the properties of such solutions was described by Burchfield and Woolley [2-5]. We might develop the analysis from equation (k). An advantage of writing the equation in this form stems from the observation that both sides of the equation describe an electrically neutral system. Woolley and co-- workers [4,5] prefer a form which removes a contribution \(\mathrm{n} \,(1-\beta) \mathrm{Br}^{-}(\mathrm{aq})\) from each side of equation (k).
\[\mathrm{nAM}^{+}(\mathrm{aq})+\mathrm{n} \, \beta \mathrm{Br}^{-}(\mathrm{aq}) \Leftrightarrow\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{a} \,(1-\beta)}(\mathrm{aq}) \nonumber \]
Nevertheless one might argue that equation (k) does have the merit in comparing two salts whereas equation (t) describes the links between three ions. In terms of equation (k) , there are two salts in solution.
-
\(\mathrm{AM}^{+} \mathrm{Br}^{-}\) where \(v_{+}=1, v_{-}=1, v=2, Q=\left(v_{+}^{v+} \, v_{-}^{v-}\right)^{1 / v}=1, y_{\pm}^{v}=y_{+}^{v+} \, y_{-}^{v-}, \text { or } y_{\pm}^{2}=y_{+} \, y_{-}\) But
\[\begin{aligned}
&\mu\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right)= \\
&\mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right)+2 \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{c}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) \, \mathrm{y}_{\pm}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) / \mathrm{c}_{\mathrm{r}}\right)
\end{aligned} \nonumber \] -
For the micellar salt, \(\left[\mathrm{nAM}^{+} \mathrm{n} \, \beta \mathrm{Br}^{-}\right]^{\mathrm{n} \,(1-\beta)} \mathrm{n} \,(1-\beta) \mathrm{Br} \mathrm{r}^{-}\)
\(\mathrm{v}_{+}=1, \mathrm{v}_{-}=\mathrm{n} \,(1-\beta),\) and \(v=n \,(1-\beta)+1\) and \(\mathrm{Q}^{\mathrm{n}(1-\beta)+1}=\left[1 \,\{\mathrm{n} \,(1-\beta)\}^{\mathrm{n}(1-\beta)}\right]\) with \(\mathrm{y}_{\pm}^{\mathrm{n} \,(1-\beta)+1}=\mathrm{y}_{+}^{1} \, \mathrm{y}_{-}^{\mathrm{n} \,(1-\beta)}\)
Then,\[\begin{aligned}
&\mu(\text { mic. salt }) \\
&\left.=\mu^{0} \text { (mic. salt }\right)+[n \,(1-\beta)+1] \, R \, T \, \ln \left[Q \, c(\text { mic.salt }) \, y_{\pm} / c_{r}\right]
\end{aligned} \nonumber \]
At equilibrium,
\[\mathrm{n} \, \mu^{\mathrm{eq}}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq}\right)=\mu^{\mathrm{eq}}(\text { mic. salt; aq }) \nonumber \]
Hence,
\[\Delta_{\text {mics slt }} \mathrm{G}^{0}=-\mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{K}_{0}\right)=\mu^{0}(\text { mic.salt })-\mathrm{n} \, \mu^{0}\left(\mathrm{AM}^{+} \mathrm{Br}^{-}\right) \nonumber \]
The total concentration of salt ctot in the system is given by equation (y).
\[\operatorname{ctot}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \text {system }\right)=\mathrm{n} \, \mathrm{c}(\text { ch arg ed micelles })+\mathrm{c}\left(\mathrm{AM}^{+} \mathrm{Br}^{-} ; \mathrm{aq}\right) \nonumber \]
The analysis makes no explicit reference to a cmc. Instead the micellar system is described as a mixed salt solution. Application of these equations requires careful computer –based curve fitting for multi-parametric equations. The latter include equations relating mean ionic activity coefficients for salts to the composition of a given solution. A shielding factor \(\delta\) was use by Burchfield and Woolley to reduce the impact of micellar charge of the cationic micelles on calculated ionic strength [2]. Thus the effective charge on the cationic micelles was written as \(n \,(1-\beta) \, \delta\) where \(\delta\) is approx. 0.5.
Ionic Surfactant: Mass Action Model
In general terms the equilibrium between surfactant monomers \(\mathrm{Z}^{+}\), counter anions \(\mathrm{X}^{-}\) and micelles \(\mathrm{M}\) can be represented by the following equation.
\[\mathrm{n} Z^{+}(\mathrm{aq})+\mathrm{mX} \mathrm{X}^{-}(\mathrm{aq}) \Leftrightarrow \mathrm{M}^{(\mathrm{n}-\mathrm{m})+}(\mathrm{aq}) \nonumber \]
Then in terms of the mass action model, the concentration equilibrium constant,
\[\mathrm{K}_{\mathrm{c}}^{0}=\left[\mathrm{M}^{(\mathrm{n}-\mathrm{m})+}\right] /\left\{\left[\mathrm{Z}^{+}\right]^{\mathrm{n}} \,\left[\mathrm{X}^{-}\right]^{\mathrm{m}}\right\} \nonumber \]
By definition,
\[\Delta_{\text {mic }} \mathrm{G}^{0}=-(\mathrm{n})^{-1} \, \mathrm{R} \, \mathrm{T} \, \ln \left(\mathrm{K}_{\mathrm{c}}^{0}\right) \nonumber \]
Then,
\[\Delta_{\text {mic }} \mathrm{G}^{0} /(\mathrm{R} \, \mathrm{T})=-(\mathrm{n})^{-1} \, \ln \left[\mathrm{M}^{(\mathrm{n}-\mathrm{m})+}\right]+\ln \left[\mathrm{Z}^{+}\right]+(\mathrm{m} / \mathrm{n}) \, \ln \left[\mathrm{X}^{-}\right] \nonumber \]
Footnotes
[1] N. M. van Os, J. R. Haak and L. A. M. Rupert, Physico – Chemical Properties of Selected Anionic, Cationic and Non-ionic Surfactants, Elsevier, Amsterdam 1993.
[2] T. E. Burchfield, and E. M. Woolley, J. Phys. Chem.,1984, 88 ,2149.
[3] T. E. Burchfield and E. M. Woolley, in Surfactants in Solution, ed. K. L. Mittal and P. Bothorel, Plenum Press, New Yok, 1987, volume 4 , 69.
[4] E. M. Woolley and T. E. Burchfield, J. Phys. Chem.,1984, 88 ,2155.
[5] T. E. Burchfield and E.M.Wooley, Fluid Phase Equilib., 1985, 20 ,207.
[6] D. F.Evans, M. Allen, B.W. Ninham and A. Fouda, J. Solution Chem.,1984, 13 ,87.
[7] D. G. Archer, J. Solution Chem.,1986, 15 ,727
[8]
- L. Espada, M. N. Jones and G. Pilcher, J.Chem. Thermodyn., 1970, 2 ,1, 333; and references therein.
- M. N. Jones, G. Pilcher and L.Espada, J. Chem.Thermodyn,.,1970, 2 ,333
[9] M. J. Blandamer, P. M. Cullis, L. G. Soldi and M. C. S. Subha, J. Therm. Anal.,1996, 46 ,1583.
[10] R. Zana, Langmuir, 1996, 12 ,1208.
[11] M. J. Blandamer, K. Bijma, J. B. F. N. Engberts, P. M. Cullis, P. M. Last, K. D. Irlam and L. G. Soldi, J. Chem.Soc. Faraday Trans.,1997, 93 ,1579; and references therein.
[12] M. J. Blandamer, W. Posthumnus, J. B. F. N. Engberts and K. Bijma, J. Mol. Liq., 1997, 73-74 ,91.
[13] R. DeLisi, E. Fiscaro, S. Milioto, E. Pelizetti and P. Savarino, J. Solution Chem.,1990, 19 , 247.
[14] M. J. Blandamer, P. M. Cullis, L. G. Soldi, J. B. F. N. Engberts, A. Kacperska, N. M. van Os and M. C. S. Subha, Adv. Colloid Interface Sci.,1995, 58 ,171.
[15] For further references concerning the Stern Layer, see N. J. Buurma, P. Serena, M. J. Blandamer and J. B. F. N. Engberts, J. Org. Chem., 2004, 69 , 3899.