Surfactant mixtures mixing rules

All formulators use mixed surfactants, particularly since Griffin s HLB concept and its associated mixing rule was introduced 50 years ago as a yardstick for hydrophilicity. There are essentially two reasons either the commercial products they use are already mixtures, or the proper surfactant property is not attainable with a commercial product, and it is attempted by mixing available species. 

Nonionic surfactants can be mixed as well, but in practice most of them, at least the ethoxylated ones, are already a mixture because of the polycondensation mechanism in ethylene oxide adduction. Isomerically pure ethoxylates are extremely expensive and are exclusively reserved for research work. Little work has been carried out with mixture of isomerically pure nonionics and the bulk of the work on mixture deals with mixtures of commercial products, i.e., mixture of mixtures, which obey a linear mixing rule on EON, provided that the base mixtures are not too different [8,35]. 

It is worth noting here that this difference between the interface and in the bulk is not specific to surfactant mixtures. While oil mixtures of very similar substances, such as n-alkanes, exhibit a linear mixing rule written in terms of equivalent alkane carbon number or EACN [62-64], mixtures of oils containing substances with very different polarities behave in a non-ideal way and exhibit a segregation near the interface, which results in an accumulation most polar oil components close to the interface [65]. 

If the mixing is followed (as for ionic surfactants) by carrying out a salinity scan, the aspect of the In S -mixture composition rule is often found to be non-linear as indicated in Fig. 13 left plot. 

The phase behavior of systems containing pH-sensitive surfactants is another example of non-linearity of the mixing rule. If an oil phase containing an amphiphilic molecule, such as an organic acid, as in the case of naphtenic acids in crude oils, is put into contact with an alkaline water phase, the neutralization takes place at interface and results in a mixture of unneutralized acid (the lipophilic component) and its dissociated alkaline salt (the hydrophilic component). Hence, the interface contains a mixture of two surfactants whose relative proportion depends on the ionization (in the water and at interface), and thus of the pH [75]. 

The CMC of this new surfactant is several orders of magnitude lower than the CMC of its parent species. Figure 15 indicates a typical CMC plot versus the composition of the anionic-cationic (e.g., dodecyl sulfate-tetradecyl trimethyl ammomnium chloride) mixture in water. It can be seen that the CMCs of the anionic and cationic species are quite high, e.g., around 0.1 wt. %. As soon as a very small percentage of cationic is added to an anionic solution, the CMC falls several orders of magnitude. The same happens when a very small amount of anionic is added to a cationic solution. In both cases it seems that an equimolar catanionic species forms, and that its very low CMC dominates the mixing rule [84]. 

Nishikido (21) has done a systematic study o-f mixed sur-factant solubilization. In that study, solubilization in mixed systems was compared to that predicted by application o-f a linear mixing rule to the solubilizations in the pure surfactant component micelles. For example, in this "ideal case, a micelle composed of a 50/50 molar mixture of two surfactants would have a solubilization capacity which is an average of that of the two pure surfactants involved. A system showing negative deviation from ideality would have less solubilization than this ideal system a system having positive deviation from ideality would have more. 

Most detergents contain electrolytes, e.g. sulphate, bicarbonate, carbonate or citrate and the presence of these electrolytes increases the adsorption of anionic surfactants at the gas/liquid interface as already mentioned. This leads to a reduction of the surface tension at an equal solution concentration [7] and to a strong decrease of the cmc. The effect can be of several orders of magnitude. Similar to this are the effects of mixtures of surfactants with the same hydrophilic group and different alkyl chain length or mixtures of anionic and non-ionic surfactants as they are mostly used in detergency [8]. Mixtures of anionic and non-ionic surfactants follow the mixing rule (eqn. 3) in the ideal case ... 

Here, C°P ni, C°e i, and C°e 2 are the optimum salinities of the mixture, surfactant components 1 and 2, respectively. The surfactant mole fractions are Xi and X2. Salager et al. also proposed that other characteristic parameters could follow a linear mixing rule. 

Crude oils were found to behave as an equivalent alkane as far as the attainment of optimum formulation was concerned. The equivalent alkane carbon number or EACN was then introduced to characterise pure hydrocarbons or mixtures [26]. The EACN of an oil phase is defined as the ACN of the alkane that results in the satisfaction of the correlation in the same conditions of surfactant, salinity, alcohol and temperature. EACN has been experimentally determined for n-alkanes mixtures, resulting in a linear mixing rule on a molar fraction basis, namely... 

The last technique, which is the best one when there is very little information on the unknown component, is based on the mixing of a pair of known components with the unknown one, and the use of a linear mixing rule. For instance, if the characteristic parameter ((3 = a - EON) of an unknown non-ionic surfactant is to be determined, the correlation to be used for the mixture of the two base products, such as two ethoxylated nonylphenols with different EONs, e.g. EONi and EON2, so that the mixture that results in three-phase behaviour is EONm is as follows ... 

Figure 3.10 Mixing rules for surfactant mixtures, (a) u/k as a function of the average surfactant molecular weight (Msurf) for a mixture of two anionic surfactants, (b) Salinity (S) versus wt.% of non-ionic surfactant in a mixture of an anionic and a non-ionic surfactant, (c) Salinity (S) versus wt.% of cationic surfactant in a mixture of an anionic and a cationic surfactant.

Mixing anionic and cationic surfactants results in the formation of an equimolar catanionic species, which is likely to precipitate even at very low concentration, because it is more hydrophobic (two tails) and less ionic (the charges cancel out at least partially). It was shown, however, that this equimolar catanionic surfactant tends to behave as a hydrophobic amphoteric, i.e. ionic surfactant, which is able to exhibit a linear mixing rule with either of the ionic species provided its proportion remains small, say, less than 20% [57]. For instance, if 5 wt.% of a cationic surfactant is added to 95 wt.% of anionic surfactant, the actual mixture behaves as if it were a mixture of 90 wt.% anionic and 10 wt.% catanionic surfactant. In practice, the pure catanionic species precipitates and hence does not exist as a soluble substance in the microemulsion. Hence, its characteristic parameter has to be estimated by extrapolating the linear trends of the 1 1 mixture, as seen in Fig. 3.10(c). 

The calculation cannot be carried out in an accurate way because, as mentioned before, the mixing rule between anionic and non-ionic surfactants is not actually linear due to a shielding of the ionic group by the polyethylene oxide chain. However, the use of a linear approximation often leads to a fairly good estimate in some cases such as a mixture of alkylbenzene sulphonates and ethoxylated nonylphenols to be considered as an example next [61]. 

If a mixture of these anionic and non-ionic surfactants is prepared with molar fractions %NI and xm at the interface (assumed to be the same than the molar fractions in the system), and if the mixing rule is assumed to be linear, then the optimum formulation of the mixture... 

Another way to attain intermediate or different properties is to use surfactant mixtures. The characteristic parameter (surfactant mixture containing relatively similar substances can be calculated according to a linear mixing rule based on the molar fractions at the interface [73,74]. 

As an essential feature of the HLB scale, it was assumed that the HLB of a surfactant mixture could be calculated from a linear average mixing rule based on weight composition. Thus intermediate HLB could be attained simply by mixing two or more surfactants by using the relation.ship ... 

The churuct eristic parameter of ionic surfactant mixture can be readily calculated from a linear mixing rule on its olK so that i65,67 ... 

Mixtures of two or more svufactants have been used very often to attain some average property with more or less success. The early hydrophilic-Upophilic balance (HLB) rule of formulation assumes that the surfactant mixture at the interface (i.e., the one that produces the result) depends linearly on the mixture composition in the system. This implicitly assumes that there is some kind of collective behavior among all surfactants (i.e., that all surfactant species partition in the same way in all phases and at the interface). This approximation is known to be valid when similar surfactants are mixed, particularly from the hydrophilic—lipophilic tendency point of view [85,86]. However, if a very hydrophiUc surfactant is mixed with a very lipophilic one, there is not necessarily an intermediate hydrophilicity mixture at the interface. In many cases, the most hydrophilic surfactant will partition mostly in water, whereas the most lipophilic one will fractionate into the oil phase, so that they may leave a leftover surfactant mixture of unpredictable hydrophilicity at the interface [46,49]. For example, it has been shown that sometimes a hydrophilic result is attained by adding a lipophilic surfactant, by the so-called retrograde transition [87,88] phenomenon. 

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