Micellar lifetime, or stability, is a fundamental property of surfactants that can influence many of the processes where surfactants are used. Although micelles are drawn in textbooks as well defined, static aggregates, in reality most micelles have very short lives, completely disintegrating and reforming from surfactant monomers often in time scales of milliseconds.

The influence of micellar stability on technological processes has been an active area or research for the group of Professor Shah for a decade now, as reviewed in [Huibers et al., 1996a] (Figure 4-1). Following in the footsteps of several researchers before me, especially Dr. Seoung-Geun Oh, I have conducted a number of studies on the influence of certain additives on the micellar stability of sodium dodecylsulfate (SDS), as well as studies on the influence of micellar stability on processes of technological interest, such as foaming, solubilization, detergency, fabric wetting, and emulsification [Huibers et al., 1996a]. These micellar lifetime investigations were carried out using the pressure-jump technique with conductivity detection. We study micellar stability because of its potential to influence many such processes, and knowledge of the effects of certain types of additives on micellar stability helps make our understanding more complete.
 

(Figure 4-1. Effect of micellar lifetime (slow relaxation time) on technological processes.)
 

All initial work on micellar lifetime was to establish the magnitude of the change in lifetime with the concentration of the surfactant. It was shown that lifetime could change by several orders of magnitude, depending on concentration. For several anionic surfactants, micellar lifetime was shown to increase by orders of magnitude up to a critical concentration (200 mM for SDS), and fall after that point [Huibers et al., 1996a; Lessner et al., 1981]. For several cationic surfactants, the increase in stability with concentration is more gradual, and then plateaus without displaying an obvious maximum stability value (see Cationic Surfactants section). Finally, for nonionic surfactants, micellar lifetime seems to drop with an increase in concentration [Lang et al., 1972a, b; Platz, 1981; Strey and Pakush, 1986]. Additionally, the influence of temperature has been studied, demonstrating a strong decrease in micellar lifetime with increasing temperature [Inoue et al., 1978; 1980].

Since all practical applications of surfactant involve the presence of other species besides surfactant and solvent, it is important to establish what the effect of these will be on micellar lifetime, in order to have a better understanding of the influence of these additives on the technological processes affected by micellar lifetime. Initial work by Leung and Shah [1986] studied the influences of short chain alcohols and water soluble polymer on SDS micellar stability, and Oh and Shah [1991] later studied SDS and some additional alcohols. Lessner et al. [1981a, b] studied the influence of salt on micellar lifetime, in this case NaClO₄ on SDS and sodium tetradecyl sulfate micelles.

I have extended these additive investigations, by studying the influence of longer chained alcohols (octanol through dodecanol), glycerol, large counterions of the tetraalkyl ammonium bromide class, nonionic surfactants (Tween 80) and electrolytes (NaCl, glycine, sodium octanoate) on SDS micellar lifetime.

Influence of Alcohol Cosurfactants on Micellar Lifetime

Earlier studies of the addition of alcohols to SDS micelles focused on the shorter alcohols. Generally, these shorter alcohols tend to destabilize the micelles. Leung and Shah [1986] added different concentrations of methanol through pentanol to 100 mM SDS micelles (Figure 4-2) [Huibers et al., 1996a]. Methanol, ethanol and propanol have a small effect on micellar lifetime, with t₂ slowly decreasing with concentration. Given the solubility of the alcohols in water (Table 4-1), it appears that these alcohols do not partition extensively into the micelle, and the lower stability may be due to the nature of the solvent (water/alcohol) mixture. Butanol seems to have an effect of decreasing micellar lifetime, by over an order of magnitude for concentrations over 300 mM, but pentanol is the most interesting of the shorter alcohols, increasing micellar stability in 100 mM SDS by over a factor of two at 50 mM pentanol, but then sharply decreasing micellar lifetime for concentrations over 150 mM. Oh and Shah [1991] showed that hexanol increased the micellar stability of 50 mM SDS, up to a 70 mM hexanol concentration, and decreased t₂ above that. From Table 4-1 it can be seen that the solubility of hexanol in water is 59 mM at 25^oC, so it may be reasonable to assume that alcohol will stabilize the SDS micelles, as long as the alcohol will partition into the micelles (not the case for methanol through propanol),
 

(Figure 4-2. Variation of the slow relaxation time (t₂) of 100 mM SDS as a function of alcohol concentration [Leung and Shah, 1986].)
 

and as long as the ratio of alcohol to surfactant is not too high, as can happen when low alcohol solubility in water forces the alcohol to partition to a large extent into the micelles at higher alcohol concentrations.

Results. New measurements were taken of the micellar lifetime of SDS mixed with the higher alcohols, octanol, decanol, and dodecanol, were tested using the pressure jump technique. All were shown to increase the micellar lifetime of 100 mM solutions (alcohol + SDS concentration total of 100 mM). Due to the low solubility of decanol and dodecanol, it is expected that these alcohols will partition entirely into the micelles. Octanol has a low solubility of 3.8 mM, and this may partly explain the reason for the initial decrease in micellar lifetime of the mixture at 5 mM octanol + 95 mM SDS (Figure 4-3) [Huibers et al., 1996a]. From these results, combined with the previous work, some conclusions can be drawn about the influence of alcohol on micellar stability, as summarized in Table 4-2.
 

(Figure 4-3. Slow relaxation time for mixtures of SDS and higher alcohols. The concentration of the mixtures remains constant at 100 mM (SDS+alcohol).)
 

One issue in working with SDS solutions are questions about the apparent ‘aging’ of the solution. No satisfactory measurements have been published on the changes over time that have been seen in solution properties. It is interesting to note that the micellar lifetime of 5 mM dodecanol + 95 mM SDS is essentially the same as 100 mM SDS. The hydrolysis of SDS over time has been attributed to a change in observed properties over time, with SDS decaying into dodecanol and sulfate ions. This micellar lifetime result suggests that the decay of even a few percent of the SDS will not influence processes using SDS that are influenced by micellar lifetime.

Influence of Glycerol on Micellar Lifetime

The stability of SDS micelles, as measured by the slow relaxation time, has been well characterized [Huibers et al., 1996a; Oh et al., 1996]. Micelle stability increases with concentration above CMC to 200 mM, then decreases. When glycerol/water mixtures are used as the solvent, one would expect changes due to the increased viscosity of the mixture, as well as the weaker solvent interaction as measured by a decrease in surface tension. The effect of additives on micellar properties has been well established for just one property, the CMC. van Os et al. [1993] has tabulated literature values of micellar properties, for pure surfactants in aqueous solution, as well as for solutions with solvent and electrolyte additives. Such additives change the nature of the solvent, by changing the structure of water. Water normally forms a complex and dynamic hydrogen-bonding network, and additives modify this by requiring that some of these hydrogen bonds be broken, and new interactions formed with the additive. These changes have been accounted for in models by a change in the dielectric constant of solubility parameter of the solvent.

For a related compound, ethylene glycol, the solubilization parameter increases for glycol/water mixtures, resulting in increased solubility of the surfactant monomer and thus a higher CMC. This can also be determined from the surface tension of the solvent mixture, which is lower than that of pure water. This indicates that the solvent intermolecular forces are weaker, which will also allow an increased solubility of the surfactant.

As far as the author is aware, no previous work has been done on the effect of solvent mixtures on micellar stability. In this thesis the micellar stability of SDS at different concentrations is presented for 50/50 glycerol/water mixtures, and the effect of glycerol/water ratio is examined for 100 mM SDS.

Viscosity of glycerol/water mixtures. Glycerol is a solvent similar to water in that it engages in extensive hydrogen bonding with itself, resulting in a surface tension of 63 dyne/cm, comparable to 72 dyne/cm for water, and much higher than the 22-30 dyne/cm of a typical organic solvent. The addition of glycerol to water increases viscosity, but with a very nonlinear relationship to the volume fraction. Glycerol has a viscosity of 1000 cp at 25^oC, and water has 0.89 cp. If the influence of adding glycerol to water on micellar stability was only a viscosity effect, essentially slowing the transport of surfactant monomers to and from the micelle, then one would expect changes in micellar lifetime would be proportional to changes in viscosity. When measured, however, the change in micellar lifetime with the addition of glycerol is not so simple.

One can model the strong nonlinear nature of the viscosity of glycerol/water mixtures. The hyperbolic formula proposed by Waterman et al. [1960] for vapor-liquid equilibrium models provides an excellent fit to the data [CRC Press, 1980] when the log of the viscosity is considered. The resulting equation is

where h_g is the viscosity of glycerol at 20^oC (1412 cp), h_w is the viscosity of water (1.01 cp), and x is the weight fraction of water in the mixture. As can be seen in Figure 4-4, the fit to the data is quite good, and a sharp rise in viscosity is seen as the mixture approaches pure glycerol.

The addition of glycerol to the solvent causes a significant decrease in the conductivity of the micellar solution (Figure 4-5). One might expect that addition of a second solvent that lowers the intermolecular interactions in the solvent (as can be measured by glycerol/water surface tension) would cause an increase in CMC, and also an increase in conductivity. The viscosity also plays a role, with increasing viscosity causing a decrease in conductivity, and this must be the dominating factor.

Micellar lifetime. Addition of short chain alcohols such as methanol, ethanol and propanol, which are completely soluble in water, have been shown to decrease micellar
 

(Figure 4-4. Viscosity of glycerol/water mixtures [CRC Press, 1980].)
 

(Figure 4-5. Conductivity of glycerol/water/SDS mixtures.)
 

lifetime (Figure 4-2) [Huibers et al., 1996a]. It was expected that glycerol would do the same, and measurements at 1-10 wt% glycerol in water show the same trend (Figure 4-6). The micellar lifetime for 100 mM SDS is approximately 200 ms in water, falling to 30 ms for 10% glycerol in water as the solvent. The most unexpected result is the appearance of an apparent third lifetime, which appears above 10% glycerol. The initially observed decay time, which we will call t₂, continues to decrease above 10% glycerol, with an apparent linear relationship between the glycerol weight fraction and the logarithm of the decay time. The t₂ is too short to measure with more than 30% glycerol, as it falls below 1 millisecond. The new decay time, which we will call t₃, rises slightly and appears to plateau at approximately 1.0 sec, and was not detected at concentrations below 10% glycerol.

At a constant 1:1 glycerol/water ratio, the micellar lifetime vs. SDS concentration also show some interesting features. When compared to SDS in pure water (Figure 4-7), the peak in micellar lifetime observed at 200 mM appears shifted to lower concentrations. This shift causes the glycerol/water t₂ values to be higher than pure water in some cases, and to be lower in other concentrations, as seen in the Figure. The lifetime measured here for the glycerol/water mixtures is probably t₃, as the t₂ as measured for 100 mM SDS is probably too short to measure.

The physical meaning of t₃ is not readily apparent. Some initial film stability tests for glycerol/water/SDS mixtures show that film stability greatly increases with the addition of glycerol. A micellar role in film stability has been established [Patel et al., 1996], with a decrease in micellar stability causing an increase in film stability. One would also
 

(Figure 4-6. Slow relaxation time of 100 mM SDS with different glycerol/water ratios.)
 

(Figure 4-7. Slow relaxation time of SDS at a 1:1 glycerol/water ratio.)
 

expect that an increase in the bulk viscosity of the film liquid by addition of glycerol would also act to increase film stability. Measurements of film stability suggest that the break time increases several times greater than the increase in viscosity, suggesting a role for micellar stability. As it is the t₂ that decreases and not t₃, this suggests that the former is the micellar lifetime as measured in previous studies, related to the time involved in complete formation or destruction of micelles from monomer, and thus the physical meaning of t₃ is still unexplained. It is not surprising that this t₃ has not been seen before, with no apparent solvent mixture data besides the short chain alcohols in the literature. It may be that t₃ can be seen in alcohol/water mixtures, although the concentrations in previous studies were probably too low for it to become apparent. From Figure 4-2, alcohols were added at up to 300 mM, which amounts to 0.96, 1.38 and 1.80 wt% for methanol, ethanol and propanol, respectively, well below the 10 wt% where t₃ was first observed in glycerol.

Influence of Counterion Size on Micellar Lifetime

The counterion plays a role in the micellar stability of ionic surfactants. Until recent years, little has been done to study this phenomenon. Oh and Shah [1993a] first measured the effect of counterions on SDS micelles. Blute et al. [1994] studied the influence of large counterions on foam stability, establishing that the tetraalkyl ammonium salts can be effective antifoaming agents for anionic surfactant solutions. We seek to explain this effect in terms of micellar stability.

Effect of antifoaming agents on micellar stability. The tetraalkyl ammonium salts have a demonstrated foam destabilizing ability. This has been attributed to their large size, which alters the packing of surfactant head groups at the foam interface. If this change in packing serves to decrease the surface viscosity, foams will be less stable. The role of micellar stability on foamability has also been demonstrated, where more stable micelles result in less stable foams. The micelles act as a reservoir of surfactant, which may be drawn upon by thinning foam films. If the micelles are too stable, then the foam films do not receive the necessary surfactant and may break.

The effect of addition of tetraalkyl ammonium chloride (3, 30 mM) on the micellar stability of SDS micelles (150 mM) is investigated, with alkyl groups ranging from one to five carbons. These large cations act to destabilize micelles to a much greater extent than addition of an equivalent amount of sodium ions to solution. This can be attributed to the effect of their size on decreasing the packing density of the sulfate head groups at the micellar surface, and the resulting decrease in surface viscosity. Micellar stability thus has a less significant contribution to foam stability than surface viscosity.

Recent work has demonstrated that foam properties can be effected by micellar stability [Oh and Shah, 1991]. Blute et al. [1994] have demonstrated that large organic counterions can act as better antifoam agents than more traditional antifoamers such as tributyl phosphate and 2-ethylhexanol. They attribute the antifoaming ability of these large counterions to the decrease in packing density of the surfactant head groups, resulting in a less condensed film with lower surface viscosity.

Normally, addition of counterions leads to two counteracting effects: foam stability is decreased by addition of ions which reduce the electrical repulsion between the ionic double layers on both sides of the liquid film, and is increased by the decrease in repulsion between adjacent surfactant head groups, causing a more condensed film of higher surface viscosity [Bikerman, 1973; Rosen, 1989].

To understand the impact of micellar stability on the action of antifoaming agents, we undertook a study of the effect of these large organic counterions on the micellar stability of SDS solutions. Micelles form a reservoir of surfactant in solution. When a foam film is thinned to the point where there is a depletion of surfactant at the interface, replenishment can occur from the micelles in solution. If the micelles are too stable, this process may be too slow, and the foam film can break. It would be expected that the addition of any species that stabilizes the micelles would contribute to less stable foam.

Experimental. Sodium dodecyl sulfate (99%, Sigma Chemical Co., St. Louis, MO), tetramethyl ammonium chloride (97%, Fisher Scientific, Fair Lawn, NJ), tetraethyl ammonium chloride, tetrabutyl ammonium chloride, and tetrapentyl ammonium chloride (Eastman Fine Chemicals, Rochester, NY) were used as received.

Pressure jump measurements were performed using an apparatus from Dia-Log GmbH, Düsseldorf, Germany. The surfactant/tetraalkyl ammonium chloride samples were pressurized to 130 bar for 30 seconds, allowing micellar equilibrium to be reached. The critical micellar concentration at this pressure should be higher, resulting in fewer micelles and more monomer surfactant than at one atmosphere pressure. After equilibrium is achieved, the pressure is released by overpressuring and bursting of a foil at one end of the pressure chamber. The conductivity of the surfactant solution held in a conductivity cell attached to the pressure chamber is compared to a reference cell loaded with a KCl solution of the same conductivity. The change in the conductivity is monitored over time (Figure 1 in Huibers et al. [1996a]), and the observed exponential decay of the conductivity signal is related to the micellar stability. All measurements were taken at 25^oC.

Results and discussion. To best understand the effect of the addition of tetraalkyl ammonium counterions to SDS micelles, one may compare the changes to that seen by the addition of an equivalent amount of sodium counterions. The effect of addition of Na⁺ counterion to the stability of SDS micelles can be predicted. From the data of Lessner et al. [1981], the following relationships can be determined relating micellar stability as measured by the slow relaxation time constant, t₂, to the counterion concentration, c_g, for the SDS/NaClO₄ system at 25^oC.

These equations apply over a range of 25 to 350 mM SDS, given a salt free solution. Applying these equations to the 150 mM SDS cases studied here, the following estimates are given (Table 4-3):

Addition of the tetraalkyl ammonium chloride salts to SDS micelles has two effects. The first is the compression of the electrical double layer and thus the reduction of the repulsion between the sulfate head groups at the micellar surface. The second is the substitution of tetraalkyl ammonium (TAA⁺) ions for sodium ions, and the resulting change in packing of the sulfate groups, due to the difference in size between the Na⁺ and the TAA⁺ ions. Both of these phenomena will occur at the micellar interface as well as the foam film interface.

Pressure jump measurements with conductivity detection were performed on 150 mM SDS solutions, with the addition of 3 or 30 mM of tetraalkyl ammonium chloride (TAA⁺). The alkyl groups studied were methyl, ethyl, butyl and pentyl. For 150 mM SDS alone, the micellar slow relaxation time, t₂, was measured to be 1.38 sec.

On addition of 3 mM tetraalkyl ammonium ions, micellar stability increased for the methyl, ethyl and butyl cases, and no significant increase was observed for tetrapentyl ammonium chloride (Figure 4-8). One would expect an increase in micellar stability of approximately 30% for the addition of 3 mM Na⁺, to a t₂ value of 1.79 sec (Table 4-3). Thus, at a 50:1 Na⁺:TAA⁺ ratio, tetramethyl ammonium through tetrabutyl ammonium cations stabilize micelles better than the addition of an equivalent amount of Na⁺.

On addition of 30 mM TAA⁺, the situation is completely different. For all cases, a decrease in the micellar stability is observed. This decrease is greater for the larger counterions. For the tetrabutyl ammonium and tetrapentyl ammonium ions, the reduction in micellar lifetime is approximately three orders of magnitude. There are still many more
 

(Figure 4-8. Slow relaxation time (t₂) vs. size of counterion, for 3 and 30 mM concentrations of tetraalkyl-ammonium chloride salts, where the alkyl group varies from methyl to pentyl.)
 

sodium ions present than TAA⁺ ions, for this case the ratio is 5:1 Na⁺:TAA⁺. Sufficient amount of the TAA⁺ counterions are present to affect the packing of the sulfate head groups at the micellar surface.

To establish more precisely what concentrations favor micellar stability, the effect of tetraethyl-ammonium chloride concentration was studied up to 50 mM (Figure 4-9) in 150 mM SDS. Concentrations up to 5 mM TEAC showed increasing t₂, with t₂ returning to the 0 mM level only above approximately 15 mM TEAC. In this case greater than 1:10 TEAC/SDS (molar basis) is required for micellar stability to be reduced. A comparison of molar ratio to micellar stability for different alkyl sizes shows that the smaller alkyl groups stabilize micelles to a greater extent (Figure 4-10).

One would expect that any addition leading to less stable micelles would result in a more stable foam. This is not the case with the addition of tetraalkyl ammonium ions, however. One may conclude that there are two counteracting changes taking place. The decrease in packing of the micelle sulfate head groups must also occur at the foam film interface. This destabilizing effect is overwhelming the foam stabilizing effect caused by the increase in micellar stability.

Conclusion. Addition of tetraalkyl ammonium counterions to SDS solutions in proportions as small as 5:1 SDS:TAA⁺ causes a significant reduction of micellar stability, where an increase would be expected for the equivalent addition of Na⁺ ions. This reduction of micellar stability is attributed to the decreased surface viscosity of the micelles due to the alteration of packing of the sulfate head groups by the bulky tetraalkyl ammonium
 

(Figure 4-9. Slow relaxation time vs. concentration, for tetraethylammonium chloride in 150 mM SDS.)
 

(Figure 4-10. Slow relaxation time vs. concentration, for tetraethylammonium chloride in 75 mM SDS.)
 

counterions. The large decrease in micellar stability achieved by the addition of these TAA⁺ ions would normally be expected to stabilize foams. The foam destabilizing effect of a decrease in head group packing at the foam film interface appears to be the dominant factor over micellar stability.

Influence of Added Nonionic Surfactant on Micellar Lifetime

The pressure jump technique with electrical conductivity for the detection method is an ideal means for the measurement of ionic surfactant micellar stability, but is not suitable for the measurement of nonionic surfactant micellar stability due to the low conductivity (Table 4-4), and insignificant conductivity change with a change in CMC. The Dia-Log pressure jump apparatus is limited in the conductivity of the solutions that it can measure, from a minimum of 100 to a maximum of 10000 mho/cm. To explore the limits of studying nonionic surfactant micelles with pressure jump, I measured the micellar lifetimes of some mixed ionic/nonionic surfactants. The systems studied were SDS/Tween 80 and AOT/Arlacel 20.

Results. The effect of the nonionic surfactant, Tween 80 (polyoxyethylene 20 sorbitan monooleate), on SDS micellar lifetime was measured by substituting SDS by Tween 80 on an equimolar basis. The two surfactants couldn’t be more different, especially in the hydrophilic domains. SDS has a dodecyl (C₁₂) alkyl tail, while Tween 80 has an oleate (C₁₈ with a double bond at the 9th carbon) tail. SDS has a small, polar head group (SO₄^-), while the Tween has an extremely large head group, a sorbitan ring (cyclic six carbon sorbitol carbohydrate), and 20 ethylene oxide residues (-C₂H₄O-) polymerized onto the hydroxyl groups of the sorbitan.

Starting with 100 mM SDS, t₂ of mixtures were measured down to 70 mM SDS + 30 mM Tween 80. Initially, there appears to be no effect on t₂, but above 5% (molar basis) Tween 80, the micellar lifetime of the mixtures greatly increases (Figure 4-11). This increase tails off at greater than 20% Tween. As the mixtures studied are equimolar, the stability increase can truly be attributed to synergism between the two surfactants. The stability of 80 mM SDS + 20 mM Tween 80 is even greater than the maximum for pure SDS at 200 mM.

The increase of SDS stability on the addition of Tween 80 is similar to the influence of long chain alcohols (Figure 4-3). The initial lack of increase with the addition of Tween is similar to octanol, and the magnitude of the increase at 25% is similar to that of decanol. One clear advantage of Tween 80 over the long chain alcohols for enhancing micellar stability is the solubility of the Tween. Tween 80 has no apparent limit to its aqueous solubility, and forms micelles by itself. Contrarily, the long chain alcohols have extremely limited solubility, just 3.8 mM for octanol and 0.234 mM for decanol (Table 4-1), and in mixed micelles no more than 25 mM decanol and 15 mM octanol can be solubilized in a 100 mM SDS + alcohol mixture.

There are limits to the amount of nonionic surfactant added to SDS that can be studied using the pressure-jump technique. As the amount of Tween 80 is increased, the magnitude of the conductivity change with the change in CMC is diminished. Figure 4-12 shows typical traces seen from a pressure-jump experiment. The initially high conductivity level drops instantaneously after the bursting of the foil on overpressuring of the autoclave. The initial drop is due to the fast relaxation time (t₁), and the time constant for this drop cannot be measured, as it is expected to be in the microsecond range. The second decay, due to the slow relaxation time (t₂), is readily observable as an exponential decay and the time constant for this curve is easily obtainable. As the Tween 80 concentration is increased, the drop in amplitude of both the t₁ and t₂ signals are apparent. In Figure 4-12, the amplitudes drop from 10 mV to 2.5 mV for t₁ going from 90/10 to 70/30 SDS/Tween (molar basis), and from 6 mV to 2.5 mV for t₂. Below a 2 mV change in signal for t₂ it is very difficult to determine the time constant. Although we know the conductivity of the solution is falling in this case with added Tween (Table 4-4), the same loss of signal results from the addition of electrolyte, such as NaCl, limiting the amount of added electrolyte that can be studied with
 

(Figure 4-11. Slow relaxation time of mixed anionic and nonionic surfactants, for different mixtures of 100 mM combined SDS + Tween 80.)
 

(Figure 4-12. Typical electrical conductivity vs. time traces for pressure-jump experiments. These examples show the decrease in signal as the proportion of nonionic surfactant increases.)
 

(Figure 4-13. Slow relaxation time (t₂) for mixed anionic and nonionic surfactants, for different mixtures of 0.5 wt% combined AOT + Arlacel 20.)
 

the pressure jump technique. For 150 mM SDS, the signal levels had dropped to 2 mV for the addition of 30 mM NaCl.

Another anionic surfactant was studied, Aerosol OT (also known as AOT, sodium bis-2-ethylhexyl-sulfosuccinate), a twin tailed surfactant. AOT is most commonly used to make reverse micelles, because of its bulky hydrophobic group relative to its hydrophilic group. Normal micelles can be made by mixing with a surfactant with a bulky head group, such as Arlacel 20 (sorbitan laurate). The micellar lifetime of mixtures of these two surfactants in 0.5 wt% solutions has been measured for 1:3 and 3:1 AOT/Arlacel 20 mixtures. From Figure 4-13, the micellar stability is seen to be higher for mixtures with more Arlacel 20. One surprising result was the measurement of a 2 second micellar lifetime for 3:1 AOT/Arlacel 20 at 0.17 wt% surfactant. This is a very high t₂ for such a low concentration of surfactant, which amounts to just 2.8 mM AOT (MW=444 g/mol) and 1.2 mM Arlacel 20 (MW=344).

Influence of Added Electrolyte on Micellar Lifetime

It has been demonstrated in this thesis that alcohols, glycerol, and tetraalkyl-ammonium chloride salts all influence micellar lifetime, with a variety of results. Considering other electrolytes, there is one study in the literature with a thorough study of the effect of NaClO₄ concentration on both SDS and sodium tetradecyl sulfate micellar solutions [Lessner et al., 1981a; b], where the maximum in the micellar stability was correlated to the counterion concentration (assuming some of the initial surfactant counterion is bound), resulting in a model where the micellar stability graphs for SDS with different salt concentrations lie on top of each other. From this it appears that the reason for the decline in micellar stability after the maximum at 200 mM is caused by a change in the surfactant head group interactions, possibly due to the collapse of the electrical double layer with sufficient electrolyte in solution. It should be noted that the micellar lifetime vs. concentration for nonionics is always decreasing, which may be due to the lack of stabilizing ionic interactions.

Results. I have studied the effect of a few different counterions on micellar stability of 100 mM SDS, with the combined results for glycine, glycerol, and sodium octanoate in Figure 4-14, and the NaCl results in Table 4-5. All of the ionic species examined here act to increase micellar stability. The salt NaCl and the zwitterionic glycine increase micellar stability, but be less than a factor of two. The sodium octanoate, on the other hand, has a great stabilizing effect. It is itself a surfactant, although it has a very high CMC of 140 mM [Rosen, 1989] because of its short alkyl group (as confirmed in Figure 4-16). The initial increase, below 10 mM NaC₈OO is approximately 0.037 sec/mM, with t₂ doubling on addition of 4.6 mM NaC₈OO. At the concentrations studied, sodium octanoate would not form micelles on its own.

(Figure 4-14. Slow relaxation time vs. additive concentration for 100 mM SDS with the additives glycerol, glycine and sodium octanoate.)
 

(Figure 4-15. Slow relaxation time vs. concentration for mixed sodium octanoate/SDS micelles, compared with pure SDS micelles.)
 

(Figure 4-16. Surface tension vs. concentration for sodium octanoate.)
 

The slight increase in micellar lifetime with the addition of electrolytes may be explained in the context of Lessner et al. [1981a; b], where the counterion concentration was shown to have a stabilizing influence at concentrations below the maximum, and destabilizing effects at concentrations above the maximum in micellar lifetime (200 mM for SDS). The stabilizing effect of the sodium octanoate may be explained by similar ionic considerations, as if it is ionic repulsion in the head groups that stabilizes micelles, then the surface active sodium octanoate will partition into the micelles and mixed micelles with two anionic components will be formed. This result is supported by the comparison in Figure 4-15, where the SDS/ NaC₈OO combination is compared with SDS, with a 1:1 substitution of SDS for NaC₈OO (ie. 100 mM SDS + 50 mM NaC₈OO is compared to 150 mM SDS). The resulting micellar lifetimes are very close, showing that the NaC₈OO essentially acts as additional SDS on an equimolar basis.
 

Effect of Molecular Structure on Dynamic Surface Tension

Besides these studies of the effects of various additives, I pursued the study of the SDS micellar system using several new techniques. Our goals were to find supporting evidence for the existence of a fundamental change in the micellar state at 200 mM, where SDS micellar lifetime is a maximum and a sphere to cylinder transition has been proposed [Oh and Shah, 1993b].

Equilibrium measurements of surface tension have been performed for many surfactant systems. The understanding of dynamic surface tension is of importance in any technological application where a new gas/liquid interface is being created in the presence of a surfactant solution, because often the equilibrium surface tension value is never reached, and the actual dynamic surface tension value will be much higher. This effect is often more important for solutions containing large surfactants, which have a lower rate of diffusion to the interface. Measurements of dynamic properties are relevant to such technological processes as foaming and fabric wetting, as well as situations where surfactants diffuse to a new liquid/liquid interface, such as emulsification, or to a solid/liquid interface, such as detergency. The maximum bubble pressure technique was developed over a century ago as reviewed by Mysels [1990], although it became more useful only in recent decades with the availability of fast pressure transducers and the electronics necessary to monitor the varying pressure signal. It is the most common technique for the measurement of dynamic surface tension, and has been applied to a variety of surfactants (Table 1, [Huibers and Shah, 1996b]).

Two contributions to dynamic surface tension measurements are presented in this thesis. A new method of calibration using solvent mixtures is presented, addressing some important issues faced when dissimilar solvents are used in many cases cited in the literature. Second, measurements were performed on a family of commercial surfactants, the Brij 7x series of octadecyl ethoxylates, establishing cases where the traditional methods of analysis developed for maximum bubble pressure measurements cannot be applied satisfactorily [Huibers and Shah, 1996b]. Finally, some of the measurements are presented to establish the quality of the measurements taken with this homemade MBP instrument, with comparisons to results in the literature for SDS and Triton X-100. This section also highlights the large variability found in the literature for identical or similar experiments.

Acetone/water mixtures for calibration of maximum bubble pressure instruments

Calibration of maximum bubble pressure instrumentation involves correlation of pressure transducer signals to surface tensions of various liquids. It is proposed that the use of acetone/water solvent mixtures can lead to more accurate measurements. The surface tensions of these calibration solvent mixtures can span the measurement range of 45 to 70 dyne/cm, where no pure solvent is available for calibration. Many surfactant solutions of interest have dynamic surface tension values in this range. Other considerations, such as solvent viscosity and wetting of the capillary material, may also make solvent mixtures a better choice.

The traditional method of calibration of maximum bubble pressure instrumentation for the measurement of dynamic surface tension involves correlation of the maximum voltage signal measured from a pressure transducer with the expected surface tension of a pure liquid. It is expected that this transducer signal will remain constant over the entire range of bubble rates for the instrument, as there should be no dynamic effect of the interface lifetime on surface tension for these liquids.

The primary limitation of this method is in the nature of the liquids used for calibration. Most organic solvents have surface tensions in the 20 to 30 dyne/cm range, and there are very few with higher values (see Table 4-7). There are only a handful of solvents with surface tensions in the 35 to 45 dyne/cm range, and then there is quite a large gap until the surface tension of water of 72.75 dyne/cm is reached (at 20^oC). In the literature, several references cite the use of either a two point [Woolfrey et al., 1986] or multiple point calibration [Tamura et al., 1995; Hua and Rosen, 1988]. A multiple point calibration was done, comparing surface tension values measured by the Wilhelmy plate method to transducer voltage levels. The solvents used are listed in Table 4-6. Voltage signals in the transducer are normalized by subtracting the baseline voltage at zero differential pressure. The measured values in the table result from a linear regression of the six solvent transducer readings to the literature values, using this equation to predict what the measured (MBP) value was.

Materials and methods. Acetone was HPLC grade, purchased from Fisher Scientific (Fair Lawn, NJ). Water was distilled, deionized water. Static surface tension measurements were done using the Wilhelmy plate technique and a Rosano tensiometer. Dynamic surface tensions were done using a maximum bubble pressure apparatus. A differential pressure transducer (Model PX164-010D5V) covering the range 0" to 10" H₂O (2500 Pa) was purchased from OMEGA Engineering (Stamford, CT). A steel needle was used as a capillary, with inner radius of 0.132 mm. A single capillary is used, submerged 1.0 cm into the sample solvent. The apparatus is capable of measuring interface lifetimes of 20 milliseconds to 10 seconds.

Discussion. One concern about the pure solvent calibration procedure is that for the investigation of dynamic surface tension of surfactant solutions at small interface lifetimes (high bubble rates), many measurements of interest will occur in the 45 to 70 dyne/cm range. This is especially true for the nonionic surfactants. For ethoxylated alkyl ethers, the equilibrium surface tension values for longer EO numbers (n<15 for C₁₂E_n) are greater than 40 dyne/cm and dynamic values approach 55 dyne/cm for short (20 millisecond) interface lifetimes, while shorter EO number surfactants may have equilibrium values as low as 30 dyne/cm, but approach 70 dyne/cm for short interface lifetimes [Tamura et al., 1995].

Another unknown factor in the use of many different pure solvents is the wetting characteristics of those solvents with the capillary material. Some organic solvents may wet the capillary in a different manner than water, depending on the hydrophobicity of the capillary material [Mysels, 1990]. This difference in wetting may affect bubble formation, and thus potentially affect the observed maximum bubble pressure for a given liquid surface tension.

Viscosity effect. Another potential problem with the use of a variety of solvents is the mismatch in viscosity. It can be demonstrated that the maximum bubble pressure apparatus can give higher apparent surface tension readings with viscous liquids. Figure 4-17 shows the dynamic surface tension of glycerol. It is expected that glycerol would have a constant surface tension of 63.4 dyne/cm at all bubble rates. At higher bubble rates, however, the apparent surface tension is higher because the viscous resistance to the expansion of the bubble out of the capillary tip requires the inclusion of another pressure term in the calculation.

Another problem occurs when the bubble breakage process leaves behind a bubble attached to the capillary that has a larger radius than the capillary radius, rather than breaking off completely and leaving no bubble attached to the tip. This causes a problem because the maximum pressure is reached for a hemispherical bubble at the capillary tip that has a larger radius than the capillary radius, and will depend on gas flowrate. The assumption that the maximum pressure will occur due to the Laplace pressure of a hemispherical bubble at the capillary tip is violated. This obviously prevents the correlation of maximum bubble pressure with the surface tension of the liquid, because the radius of curvature at the maximum pressure is unknown. This process is demonstrated by Garrett and Ward [1989] for high gas flowrates in water.

Garrett and Ward [1989] also describe the inverse relationship between capillary radius and dead time. A larger radius is desirable to achieve a shorter dead time and thus a higher bubble rate, but there is a tradeoff because of the increased influence of the viscosity effect for larger capillaries. The viscosities of the solvents used for calibration are presented in Table 4-7.

Surface tension of solvent mixtures. The static and dynamic surface tension values of acetone/water mixtures were investigated. This pair was chosen because they are completely miscible, the mixtures cover the surface tension range of interest, and the viscosities are relatively matched.

The static surface tension values for acetone/water mixtures are presented in Figure 4-18. For these mixtures there is no change as a function of interface lifetime for the entire dynamic range of the maximum bubble pressure instrument. This is critical to the use of these mixtures for the calibration of MBP equipment, as there should be no dynamic behavior of diffusion of one solvent to the interface, where it may change the surface tension over very short interface lifetimes. There may be a surface excess of one solvent, ie. one solvent prefers the interface to the bulk, but it must be that there is such a large fraction of that solvent that there is no diffusion limiting the transport of that solvent to newly formed interface, because of the large amount of that solvent in the bulk solvent mixture.

Conclusion. There appears to be no disadvantage to the use of acetone/water mixtures for calibration of maximum bubble pressure instrumentation, as opposed to using a number of pure solvents of varying surface tensions. The acetone/water mixtures show no dynamic behavior, and the dynamic and static values of surface tension correlate well. The mixtures have a definite advantage in allowing calibration of the instrumentation over the 45-70 dyne/cm surface tension range, where many measurements of interest are taken, but no suitable solvent is available for calibration. The mixtures may have an additional advantage over the use of several solvents, because of the close values of the viscosities and densities of the acetone/water mixtures, as well as a similarity in their wetting characteristics of capillary material.
 

(Figure 4-17. Apparent dynamic surface tension of glycerol.)
 

(Figure 4-18. Equilibrium surface tension of methanol/water mixtures.)
 

Results. There have been relatively few measurements of dynamic surface tension (using maximum bubble pressure) of nonionic surfactants. To this date, only the dodecyl ethoxylates, the nonylphenol polyglycol ethers, and the octylphenol polyglycol ethers (Triton X-100) have been studied (see Table 1, [Huibers and Shah, 1996b]). The quantity of dynamic surface tension data is greatly dwarfed by the body of literature on static surface tension measurements, which is a primary method of critical micelle concentration (CMC) determination. The contribution of this thesis is to demonstrate MBP measurements on surfactants that are larger than any studied to date (Brij 700), and to show that the established analysis techniques, both empirical formulas and diffusion coefficient determination, do not work for commercial surfactants, which are polydisperse mixtures by nature.

Effect of Micellar Structure on ²³Na NMR Measurements

Two distinct measurements come from NMR measurements, a shift and a decay lifetime. These are influenced by the environment of the nuclei probed. Both measurements are available for different nuclei, depending on the operation of the NMR apparatus. It is well known that the CMC can be measured using hydrogen NMR, as both the shift and the lifetime change with the chemical environment as some fraction of the surfactant molecules go from the monomer state (surrounded by water) to micellar aggregates, where they are in close association with other surfactant molecules. ²³Na NMR has been used for various biological studies, and some surfactant studies [Lindman et al., 1984; Yoshida et al., 1986; Soderman et al., 1987; Monduzzi et al., 1990; Ceglie et al., 1991; Romsted and Yoon, 1993], but not over the ranges of SDS concentrations that we were interested in. ¹H NMR has been used to show that a transition occurs in SDS micelles at 70-80 mM, which was attributed to a shape transition from spherical to cylindrical micelles [Zhao and Fung, 1993]. As it has been proposed that the maximum in micellar lifetime at 200 mM is due to this shape transition, we thought it could be productive to investigate ²³Na NMR measurements from premicellar to greater than 200 mM concentrations, to see what transitions were observable. It can be expected that counterion binding would change with the collapse of the electrical double layer, and the onset of the spherical-to-cylindrical micellar shape transition. This change of counterion binding, with a resulting change in the sodium environment, should be apparent in the ²³Na NMR measurements.

The definition of the second CMC is not very clear. The first CMC is well established, being the onset of micellization, and observed as a sharp change in slope in several solution properties, notably the surface tension [Rosen, 1989]. The presence of a second CMC implies that there is a second distinct change in slope in some properties at some higher concentration. Shah and coworkers have well established such a sharp change in the micellar lifetime of SDS at 200 mM, and corresponding technological processes that are influenced by micellar lifetime [Huibers et al., 1996a; Oh et al., 1996]. This inflection has also been designated the second CMC, and attributed to the transition of spherical to cylindrical micelles [Oh and Shah, 1993b].

It was believed that NMR measurements should support the existence of a transition at 200 mM for SDS, given the nature of the measurement, and clues from the literature. ²³Na nuclear magnetic resonance spectroscopy allows us to discover something of the dynamic state of the sodium ion in a micellar solution. The chemical shift (d) provides information about the local environment of the sodium atom by the influence of the electron clouds of neighboring atoms in shielding the sodium atom signal. The spin-lattice relaxation time (T₁) will decrease with the corresponding decrease of the motion of the sodium ion, providing some dynamic information on the system. These NMR measurements provide information on the microenvironment of sodium ions, which exist both in solution as well as closely bound to monomers and micelles of SDS.

Evidence from the literature of some change at 200 mM is somewhat contradictory. Gustavsson and Lindman [1978] appeared to show an inflection in ²³Na NMR chemical shifts at approximately this concentration, though they do not discuss it in their text, as they were interested in changes near the first CMC. Zhao and Fung [1993] used ¹H NMR to study SDS, showing a ‘second CMC’ in the range of 70-84 mM using chemical shift data, and 50-67 mM using relaxation rate data. They did not perform measurements at sufficiently high concentrations to observe any inflections at 200 mM. Given these reports in the literature, it was judged useful to take careful measurements near 200 mM for SDS solutions, to establish whether any inflections were observable to lend support to the hypothesis that the second CMC lies there.

Experimental. Sodium dodecyl sulfate (99%) was purchased from Sigma Chemical Co. (St. Louis, MO) and used as received. The water used was deionized and distilled. ²³Na NMR spectra were obtained using a Varian XL spectrometer (300 MHz) under a deuterium internal lock operating in the Fourier transform mode. The ²³Na spin-lattice relaxation time (T₁) was measured by the Inversion Recovery Fourier Transform method. All measurements were taken at 26^oC.

Results and discussion. Measurements of ²³Na NMR chemical shifts (Figure 4-19) and relaxation times (Figure 4-20) were made at concentrations ranging from 2 mM to 400 mM. No obvious inflection in the data is seen in the vicinity of 200 mM. For the relaxation time data, the apparently significant measurement at 80 mM was not repeatable in a second set of NMR measurements, nor was any other change apparent from additional measurements in the 60-150 mM range.

When plotted vs. the inverse of concentration, as is common in NMR studies, the CMC is quite obvious, occurring near the third data point from the right (8 mM), in both chemical shift (Figure 4-21) and relaxation time (Figure 4-22). There also appears to be a change in slope between the 40 mM and 80 mM, which is gradual in the d data but apparently more well defined in the T₁ data, although the T₁ data point at 80 mM is believed to be anomalous. This apparently supports the ¹H NMR evidence for some transition in the 50-90 mM range, although this may not be significant given the magnitude of the error in the ²³Na NMR measurements. Examining the NMR measurements vs. the inverse of concentration near 200 mM also shows some apparent change in slope near 200 mM and 250 mM, although again this may be insignificant when the error in the measurements is considered.
 

(Figure 4-19. ²³Na chemical shift (d ) vs. SDS concentration for the entire range from 2 to 400 mM.)
 

(Figure 4-20. Spin-lattice relaxation time (T₁) vs. SDS concentration for the entire range from 2 to 400 mM.)
 

(Figure 4-21. ²³Na chemical shift (d ) vs. the inverse of the SDS concentration for the entire range from 2 to 400 mM.)
 

(Figure 4-22. Spin-lattice relaxation time (T₁) vs. the inverse of the SDS concentration for the entire range from 2 to 400 mM, showing linear relationship of T₁ to 1/[SDS] over certain concentration ranges.)
 

Conclusion. I am reluctant to draw a conclusion that there are no changes above CMC apparent in ²³Na NMR d and T₁ data. The application of ²³Na NMR to micellar systems continues in the literature and I believe that additional careful studies may show some evidence for transitions in SDS micellar systems above 8 mM.

In order to extend the work of this group beyond studies of SDS, I undertook some measurements of the micellar lifetime of cationic micelles, including cetyltrimethyl ammonium bromide (CTAB), myristyltrimethyl ammonium chloride (MTAB), and cetyl pyridinium chloride (CPC). It was expected that a similar situation to SDS would be seen - an increase in lifetime with concentration up to some maximum, and then a decrease. For the three systems studied, this is not the case, as a much slower rise in t₂ was observed with concentration, followed by a plateau, and no apparent drop. Investigations were also made into the correlation between micellar lifetime and two technological processes, foamability for MTAB and fabric wetting for both MTAB and CTAB.

Micellar Lifetime

Using the pressure-jump technique, I measured the micellar lifetime of several cationic surfactants. There are literature references for such studies in the review articles mentioned at the beginning of this chapter, although these focus only on the concentrations near CMC. My goal was to go to much higher concentrations, and determine whether a maximum micellar stability was observable, as with the SDS system. I studied three common cationic surfactants, CPC, MTAB and CTAB.

The concentrations studied were all well above CMC, as can be determined from surface tension measurements (Figure 4-23) or from the literature. The CMC values for these three surfactants are 0.9, 3.6 and 0.9 mM respectively at 25^oC. Care must be taken when working with CTAB, as its Krafft point is reported in the literature as 25^oC [van Os et al., 1993] or 26^oC [Rosen, 1989], and can crystallize out of solution if the temperature is lowered below this point. If the surfactant crystallizes out of solution in the pressure-jump sample cell, then the surfactant concentration of the measurements would be much lower than expected. The conductivity of these solutions increases with concentration in a linear manner, as can be seen with MTAB (Figure 4-24), which follows a formula C = a + b [MTAB].

Results. Micellar lifetime is plotted for CPC (Figure 4-25), MTAB (Figure 4-26) and CTAB (Figure 4-27). As can be seen in these figures, the micellar lifetime increases with concentration, and then plateaus, with no clear maximum. The MTAB case is the most unusual, with lifetimes of 25 sec at 75 mM. Concentrations were tested up to 300 mM, but no decrease was seen. This long t₂ of 25 sec approaches the upper limit of what can be measured with the digital storage oscilloscope used at the pressure-jump recording device. Results could not be determined at higher concentrations, as the amplitude of the conductivity signal difference as seen by the pressure-jump bridge circuit drops with the increase in ionic strength of the solution (Figure 4-28). The concentration where the signal drops to a minimum observable value happens at a lower surfactant concentration and a lower conductivity than the SDS solutions.

Discussion. These cationic systems have certain clear differences from the SDS system. First, the rise in micellar lifetime with concentration is not as large. Second, there is no clearly defined maximum, but rather a large plateau region. What does this tell us about these cationic micelles? Certainly the influence of surfactant head group charge is a factor in stabilizing the micelles as concentration increases, similar to the anionic SDS, but to a lesser extent, and opposed to the nonionic surfactants, where micellar lifetime drops with increasing concentration. The plateau is reached at a concentration of the order of 100 mM, well below the ionic strength of the SDS solutions (200 mM) where the maximum is found. If the SDS maximum is due to the collapse of the electrical double layer, and the onset of cylindrical micelles, then there is still roughly 100 mM more surfactant needed to bring about a double layer collapse in the cationic systems. Why then would there be a plateau, instead of the steady rise seen in the SDS system? The only possible explanations for this are either a fundamental difference in repulsion between positive charges in aqueous solutions vs. negative charges (this seems unlikely to be significant) or the influence of the size of the head group. The sulfate head group in SDS is smaller and more highly charged than the head groups of trimethylammonium or pyridinium. It is possible that this distributed head group charge plays a strong role on the magnitude of the interactions between micelles, and thus the slope of the micellar lifetime with concentration.
 

(Figure 4-23. Surface tension vs. concentration for CPC, establishing a CMC of 0.9 mM.)
 

(Figure 4-24. Electrical conductivity vs. concentration for MTAB.)
 

(Figure 4-25. Slow relaxation time (t₂) vs. concentration for CPC.)
 

(Figure 4-26. Slow relaxation time vs. concentration for MTAB.)
 

(Figure 4-27. Slow relaxation time vs. concentration for CTAB.)
 

(Figure 4-28. Slow relaxation time conductivity signal amplitude vs. concentration for CPC.)
 

For further studies of this system, it would be interesting to see the effect of added electrolyte on these cationic micellar systems, as they may show a maximum at 100 mM or below given enough electrolyte added. Of course, there are limits to the amount of electrolyte that can be added and still have an observable signal using the conductivity detection method with the pressure-jump apparatus. It should also prove useful to study shorter chained surfactants. Especially for the CTAB studies, it would be better to take measurements at higher temperatures, as the literature value for the Krafft point of CTAB is 25-26^oC, and the CTAB solutions will often spontaneously crystallize out of solution (and potentially in the pressure-jump cells) even hours after the solution has been prepared and appears stable. These measurements could be done at higher temperatures, but one must be aware that the micellar lifetime falls sharply with temperature [Inoue et al., 1980]. Another option is to use the chloride, as I have observed that CTAC has a lower Krafft point and is thus more soluble.

Effect of Micellar Lifetime on Processes

Investigations were made into the correlation between micellar lifetime and two technological processes, foamability for MTAB and fabric wetting for both MTAB and CTAB. For SDS solutions, fabric wetting time was shown to increase with concentration up to a maximum at 200 mM, and then fall (Figure 5.9 in Oh et al. [1996]). Foamability was shown to decrease to 200 mM SDS, then increase (Figure 5.5 in Oh et al. [1996]). An analogous correlation for cationic surfactants would lead to much more general conclusions about the influence of micellar stability on such technological processes.

Fabric wetting time. The fabric wetting experiments were conducted by dropping a 1 cm x 1 cm square of cotton fabric onto the surface of a micellar solution. The wetting time is the time it takes for the fabric to break below the surface of the liquid. As a piece of fabric has a large surface area and many small pores, one can imagine that the dynamic surface tension of the liquid plays an important role in the wetting of this large new surface area and in the penetration of the liquid into small pores.

Fabric wetting results show a decrease in wetting time with an increase of concentration, both for MTAB (Figure 4-29) and CTAB (Figure 4-30). These results are contrary to the SDS results (Figure 5.9 in [Oh et al., 1996]), where the wetting time increased initially with increasing concentration. This leads to the conclusion that a correlation cannot generally be drawn between this process of decreased fabric wetting time and an increase in micellar stability. It may be possible that the comparison between cationic and anionic surfactant binding to the fabric may not be valid, due to differences in the specific molecular interactions between the surfactant and the fabric. One assumes that the cotton fabric is essentially ‘nonionic’, having a carbon backbone and exposed hydroxyl groups. A positively charged cationic surfactant or a negatively charged anionic surfactant may be expected to have approximately the same charge-dipole interaction with these hydroxyl groups, so no obvious difference in the two surfactants can be seen.

Foamability. Foamability experiments are conducted by blowing air through a glass frit at the bottom of a long tube, containing a sample of surfactant solution. The air passes through the solution and foam is formed. By maintaining a constant air flowrate from
 

(Figure 4-29. Fabric wetting time vs. concentration for MTAB.)
 

(Figure 4-30. Fabric wetting time vs. concentration for CTAB.)
 

(Figure 4-31. Foam height vs. concentration for MTAB.)
 

(Figure 4-32. Foamability vs. concentration for MTAB.)
 

sample to sample, foamability can be measured by determining the foam height as a function of time for the initial foam formation. It is important to measure the initial foam creation rate, since as the foam ages, drainage and collapse start to take place and the foam height increases more slowly, eventually reaching an equilibrium height.

Foamability was measured for MTAB solutions, over the concentration range of 10 to 100 mM. The foam height increased linearly with time (Figure 4-31), with very little difference between the different concentrations. When the slope (foamability) is plotted vs. concentration (Figure 4-32), small changes are seen between the solutions, with an apparent minimum in foamability in the 30 to 70 mM range. As with the fabric wetting experiments, the results are contrary to SDS (Figure 5.5 in [Oh et al., 1996]), where a decrease in the foamability is seen with increase in concentration (increase in micellar stability). In this experiment no such complicating factors are present such as the possibility of the different surfactants interacting differently with the fabric material, as in this case the newly formed interface is an air/solution surface. Again, no clear conclusion can be drawn from these experiments with cationic surfactants that the micellar lifetime has a dominant influence on these processes.

Nonionic surfactant micellar lifetime cannot be measured with the same apparatus as the ionic surfactants (pressure-jump with electrical conductivity detection) simply because the nonionics are nonconducting in comparison to the ionics, and thus conductivity changes cannot be measured with a change in micellar state. New methods must be developed, and the most promising is temperature-jump with ultraviolet light absorbance as the detection method. Since nonionic surfactant aggregation number is so temperature dependent, a small change in temperature will cause a detectable change in aggregation number (Figure 4-33). In the UV, absorption due to losses from Rayleigh scattering should be detectable. In the visible, if a solvatochromic dye is present, a shift in absorbance peak may be detectable with a change in the micellar shape. Both of these detection methods for nonionic surfactant micellar stability determination are investigated in the following sections.

Solvatochromism in Nonionic Surfactants

It has been established decades ago that certain dyes have shifts in their UV/visible absorbance spectral peaks with the polarity of their environment [Zollinger, 1987]. Thus, such dyes have been used as an empirical means to quantify the polarity of solvents, one of the applications being solvent selection for organic synthesis. Two popular indices are the Kosower [1958] index, based on the dye 1-ethyl-4-methoxycarbonyl-pyridinium iodide, and the E_T(30) index, based on Reichardt’s dye, 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridinium)-phenoxide [Reichardt, 1994]. A large number of compounds exhibiting solvatochromism are tabulated by Reichardt [1994].

Dyes have been used for several micellar core polarity studies; for example Zhu and Schelly [1992] studied the interior of Triton X-100 reverse micelles in cyclohexane with Methyl Orange, Ueda and Schelly [1989] studied AOT reverse micelles in benzene using the dye 1-methyl-8-oxyquinolinium betaine. Several studies used Reichardt’s dye as a
 

(Figure 4-33. Nonionic surfactant micellar kinetics via temperature-jump.)
 

probe; Varadaraj et al. [1993] studied the interior of SDS/acrylamide polymer micelles, Varadaraj et al. [1990] and Warr and Evans [1988] studied micelles from several different surfactant types, Zachariasse et al. [1981] studied micelles, microemulsions and bilayers made from several different surfactants, and Lay et al. [1989] studied W/O microemulsion interfaces. Several other studies using Reichardt’s dye on organized media besides micelles are tabulated in his review [Reichardt, 1994].

Results. A number of oil soluble dyes were screened for possible solvatochromism by measuring the wavelength of the primary absorption peaks in isobutanol and decane, thus covering a range of solvent polarities. From Table 4-8, it can be seen that Sudan Black B had the largest shift in pure solvents. Dyes Sudan II and Orange OT are interesting, as they show multiple peaks, which shift differently (and also change in height) with solvent polarity. Aniline Blue is interesting, being insoluble in water and oil (decane), but soluble in an intermediate solvent, isobutanol, and also shows potential for solvatochromism in micellar solutions.

To see whether this dye would be sensitive to the polarity of the micellar interior, the maximum absorbance peak in several different micelles with different hydrophobic tail structures was measured (Table 4-9). The maximum shift of 10 nm between the micelles sampled here indicates that this dye has potential as a micellar probe. The absorbance peaks for Sudan Black B were higher than for the isobutanol, indicating a more polar environment in the micellar core than in the alcohol.

Conclusions. Several commonly available oil soluble dyes have demonstrable solvatochromism. The dye with the greatest spectral shift among those studied, Sudan II, also shows spectral shift from one type of nonionic micelle to another, suggesting that a shift may be observable for aggregation number changes in a given micelle.

Determination of Aggregation Number by UV Rayleigh Scattering
The aggregation number, or mean number of surfactant molecules in a micelle, has been determined by several means. The primary methods include dye fluorescence and micellar diffusion measurements.

The standard method of using fluorescence involves solubilizing pyrene into the micellar solution [Zana, 1987; Lianos and Zana, 1981]. Pyrene is a fused ring aromatic hydrocarbon, water insoluble, and partitions into the micellar interior. Given a number of pyrene molecules roughly of the same order as the number of micelles, the pyrene will partition among the micelles, with some having no pyrene, some having one molecule per micelle, some having two, etc. in a Poisson population distribution. It has been established that the ratio between two fluorescent (vibronic) peaks in the spectrum depend on whether the fluorescing pyrene is isolated, or closely associated with another pyrene molecule, probably through pi-electron overlap. Through the ratio of these two peaks it can be determined what fraction exists as monomer, and from the Poisson statistics it can then be determined, knowing the pyrene to surfactant molar ratio, what the aggregation number is. This method has been applied to many surfactant systems. One question with any dye method is whether the dye itself influences the micellar property that we are interested in measuring, and Tondre et al. [1975] have addressed this by establishing the minimum surfactant/dye ratio allowable for the dye to have no influence on the system, for a variety of surfactants. A disadvantage of this method is the need to maintain a high purity of the sample, as many compounds act to quench the fluorescence, resulting in too weak or erroneous readings. One quencher is oxygen, so the prepared samples must be purged with nitrogen and nitrogen must be maintained as the head space gas of the cuvette during the measurement.

The standard method using micellar diffusion involves the examination of a micellar solution using quasi-elastic (dynamic) light scattering. Using this technique, the diffusion of light scattering objects in solution (micelles in this case) can be directly measured. Applying the Stokes-Einstein equation, the particle size can be determined, assuming that the objects are spheres, are not interacting with neighboring spheres, and the size distribution of the scatterers is uniform. These requirements are not strictly met for micellar solutions, but it is often assumed that they are true. Another factor causing this to be a less than ideal method is that the hydrodynamic radius of the diffusing micelle includes whatever water is entrained or closely associated with the hydrophilic domains of the surfactants, and the extent of this water is not known.

Both of these methods for aggregation number determination require expensive instrumentation. I have come across a means for determining aggregation number accidentally by studies of nonionic micellar solutions using a relatively more common and inexpensive UV/vis spectrophotometer.

All micellar solutions appear clear and colorless, thus absorbing no visible light. Assuming that no UV chromophore is present, such as a phenyl ring or double bonds, one might assume that the solution will be transparent in the ultraviolet spectrum also. This is not the case if light scattering objects, such as the micelles in solution, are large enough, as they will scatter light through the Rayleigh scattering mechanism. This mechanism is interesting, as the scattering intensity has an inverse fourth power with wavelength, so if scattering will occur it will be seen most prominently in the UV. This mechanism is more commonly thought of as molecular scattering, and is the reason why the sky is blue (blue light scatters from the atmospheric gas molecules much more than red) and sunsets are red. Using a UV/vis spectrophotometer, an apparent absorption can be measured with a sensitive instrument. This absorption will not be due to actual molecular absorption, which is responsible for most colors, but actually is due to scattering losses (Figure 4-34). I have established that this absorption loss can be determined for nonionic micelles, as two size factors are in our favor - the micelles have a quite large aggregation number, and the individual surfactant molecules are also large. This method of aggregation number determination is more appropriate for relative determinations, such as what the effect of an additive or temperature change will do to the micelles, unless a calibration can be performed. Calculations of the scattering intensity from first principles are possible, but require an estimate for the index of refraction of the micelle, which at best can only be estimated assuming an oil-drop model for the micellar interior.

Results. Figure 4-35 is an example of the absorbance spectrum of a typical (Brij 78) nonionic surfactant micellar solution. When plotted as log absorbance vs. log wavelength (Figure 4-36), the slope of approximately -4 strongly suggests that the absorbance is due to Rayleigh scattering. The same absorbance spectrum for SDS (Figure 4-37), whose aggregation has been well established as approximately 64, shows a much weaker scattering signal. This is expected, as the micelles are much smaller than nonionic micelles, and the SDS molecules themselves are small compared to most nonionic surfactants. In the UV region, water starts to absorb as well (Figure 4-38). To determine the absolute amount of light attributed to Rayleigh scattering, this baseline water absorption must be subtracted.

For surfactants with strong absorbing features, such as alkylphenyl ethoxylates (Figure 4-39), the UV absorption band of the phenyl ring at 245-290 nm is a complicating feature of the spectrum. Other molecular features can also cause UV absorption, such as individual double bonds (Figure 4-40). It may be possible to see changes in the aggregation number from Rayleigh scattering by considering regions above 290 nm, if the scattering signal is strong enough. It may be possible to extend this to lower wavelengths, by precisely measuring the molar absorptivity of the surfactant, and correcting the absorption measured for the micelles by the molecular absorption from the surfactant.

This method of aggregation number determination holds out a possibility for a detection method for nonionic surfactant micellar lifetime measurements using temperature-jump. Since it has been well established that aggregation number for the nonionics increases so strongly with temperature (Table 4-10), an increase in the UV absorbance due to Rayleigh scattering should be measurable after a temperature-jump, and the kinetics of this change should be related to the micellar kinetics, as the micelles must rearrange from more smaller micelles at the original temperature to fewer, larger micelles at the higher temperature.

(Figure 4-34. Measuring light scattering with absorbance spectroscopy.)
 

(Figure 4-35. Absorbance spectrum of Arlasolve 200.)
 

(Figure 4-36. Log absorbance vs. log wavelength for Brij 78.)
 

(Figure 4-37. Absorbance spectrum of SDS.)
 

(Figure 4-38. Ultraviolet absorbance spectrum of water vs. temperature.)
 

(Figure 4-39. Absorbance spectrum of Igepal CO-720.)
 

(Figure 4-40. Absorbance spectrum of Brij 97.)
 

Conclusion. There are clearly observable changes in UV absorption with temperature, which appear to be Rayleigh scattering from the functional dependence of absorption on wavelength. As the Rayleigh scattering signal should be proportional to the size of the micelle, and scattering is readily measured in the 190-230 nm region, UV absorption appears to be an ideal, unobtrusive method for the measurement of changes in micellar aggregation number with temperature-jump perturbations.

The following comments are the conclusions from this research on micellar stability: