1. Introduction Many applications of surfactants involve the formation of copious amounts of foam. However in applications such as shampooing and the hand washing of clothes and dishes, foam formation is adversely affected by the presence of triglyceride-based oily soils which can function as effective antifoams. These soils include sebum in the case of shampooing and clothes washing and fat-based food residues in the case of dishwashing. They variously

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contain both saturated and unsaturated triglycerides together with free fatty acids, wax esters and other relatively minor components1,2. Understanding of the antifoam behaviour of these complex mixtures is limited. Zhang et al3 however describe a study of the antifoam behaviour of triolein/oleic acid mixtures – two ingredients usually present in oily soil. This mixture is without significant antifoam effect except if the aqueous phase contains free Ca2+ ions and is at a high enough pH to ionize the fatty acid and cause the precipitation of calcium oleate particles at the oil-water interface. The resulting oil/particle mixture exhibits the synergistic antifoam behaviour characteristic of such mixtures4. In this series of papers we are concerned to establish the role of pH and Ca2+ in the antifoam behaviour of the more complex mixtures which comprise realistic oily soils. Unlike triolein/oleic acid mixtures, such soils are solid/liquid mixtures5,6 at the temperatures prevalent in many emerging markets during washing and shampooing. It is therefore possible that they exhibit an intrinsic oil/particle antifoam synergy under those circumstances even in the absence of Ca2+ and at low pH. We explore this possibility in Part 27 using both a model sebum and simple mixtures of triolein with either a saturated triglyceride or a saturated fatty acid. Both the triglyceride and fatty acid were selected to be sparingly soluble in triolein. The behaviour of the triolein-based mixtures is compared with the bridging mechanisms of antifoam action4 in the as yet unpublished Parts 3 and 48,9. Use of sodium alkyl benzene sulphonate surfactants for washing both clothes and dishes by hand is ubiquitous in emerging markets. The study of the antifoam behaviour of oily soil, to be described in Part 27, therefore concerns solutions of sodium alkyl benzene sulphonates as surfactants but at an ionic strength typical of that present during clothes washing by hand where arguably the most important oily soil is human sebum. Of particular interest is the role of calcium interaction with fatty acids in determining the antifoam action of the latter. However the presence of Ca2+ also influences the physical properties of the surfactant solution. For example increase in the Ca2+ ion concentration decreases the critical micelle concentration and the equilibrium air-water and oil-water surface tensions of both submicellar and micellar solutions10,11. Such changes could potentially reduce the effectiveness of the oily soil antifoam as a result of changes to both entry and bridging coefficients4,12. At a high enough Ca2+ concentration the so-called precipitation boundary is reached in solutions of sodium alkyl benzene sulphonates where a precipitate of calcium alkyl benzene sulphonate begins to form. Foamability declines at that point13,14 which effect is also potentially superimposed upon the effects of oily soil antifoam. The position of this boundary is often moved in applications to higher Ca2+ concentrations by the addition of co-surfactants or chelating agents (so-called builders), which we have omitted. In this paper we are concerned to establish the cause of the diminution in foamability at the precipitation boundary in the absence of oily soil antifoam. This boundary is important in the application of sodium alkyl benzene sulphonates for the washing of clothes where foam is a marker for completion of rinsing which becomes problematic in circumstances where water shortage is

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an issue. The combined adverse effects on foamability of oily soil antifoam and precipitate formation upon addition of excess Ca2+ to solutions of sodium alkyl benzene sulphonates are considered in Part 27. In establishing the cause of the decline in foamability at the precipitation boundary we have selected both a single sodium dodecyl benzene sulphonate isomer and a commercial sodium alkyl benzene sulphonate blend. As with Matheson et a115,16, 18,19 we characterise these surfactants by measurement of critical micelle concentrations and the respective precipitation phase diagrams where the latter is defined by plots of log(surfactant concentration) against log(calcium ion concentration). A concentration of 17mM sodium chloride at pH 10.5 models the ionic strengths typical of those prevailing in hand washing of clothes. We also measure the foam behaviour in a scan of increasing Ca2+ ion concentration through the micellar region into the precipitate + micellar region of the phase diagram at constant surfactant concentration. The transport behaviour of surfactant to the air-water surface across this scan has also been measured. We will show, as indicated in our preliminary advance publication17 that the decline in foamability at the precipitation boundary is revealed by the latter to concern the replacement of labile micelles by large, relatively stable, lamellar entities so that surfactant transport to the rapidly forming airwater surfaces during foam generation is too slow to ensure foam film stability. Here we present the relevant details and evidence for that proposition.

2. Materials and Methods

2.1 Materials - Surfactant, Electrolytes and Water Two surfactants were used in this study – a nominally pure (~99%) sodium p-dodecyl 4phenyl sulphonate (C12 4-phenyl SO3Na) and a commercial sodium linear alkyl benzene sulphonate paste (NaLAS). Both were obtained from Procter & Gamble, Newcastle Technical Centre, and used as received. The anionic surfactant content of this NaLAS was 84.1% by weight with the specified chain length and phenyl isomer distribution, shown in detail in Table S1 (Supplementary material). This material consisted of a blend of C10 – C12 chain lengths including the 2-phenyl up to the 6-phenyl isomers for each chain length. Non-surfactant impurities in the surfactant pastes were 15.13% water, 0.75% Na2SO4 and Na2CO3 with equal alkalinity as 0.02% NaOH by weight. Sodium chloride (NaCl), of a minimum purity 99.5% and calcium chloride dihydrate (CaCl2.2H2O) of purity 99% were used as received from Sigma-Aldrich UK. Sodium hydroxide (NaOH) at a purity of 97% and hydrochloric acid (HCl) with an activity of 37% were also purchased (from Sigma-Aldrich) and were used for pH adjustment. All solutions were prepared in 17mM NaCl.

2.2 Preparation of Ca2+- Surfactant Precipitation Phase Diagram The Ca2+-Surfactant phase diagram is composed of a CMC boundary, a monomerprecipitate boundary and a micellar-precipitate boundary. The precipitation boundaries were defined by the onset of turbidity.

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In each measurement, a range of sample solutions of a given surfactant concentration in 17mM NaCl at pH 10.5 were prepared. [Ca2+] was increased by 0.5×10-4 M through the turbidity boundary. The resulting solutions were equilibrated at 25oC for 24 hours to ensure complete precipitation. The precipitation boundary was visibly sharp, occurring clearly between two increments of [Ca2+]. The boundary was therefore determined as the mean between the two relevant increments with a maximum error ± 0.25×10-4 M. Precipitates could be removed by filtration using a Millipore filter (0.2 μm purchased from Millipore Corporation, USA).

2.3 Measurement of Foamability and Foam Stability

2.3.1 Tumbling Cylinder Method20 This method employed mechanical rotation of polymethyl-methacrylate cylinders about their mid-height (after Procter and Gamble). These cylinders, each of height 30cm and diameter 9cm of total volume 1875 cm3, were rotated at 0.47 Hz for 10 or more rotations at 25±1oC. Foamability was measured as the volume of air entrained in the foam immediately after completion of the cycles of rotation. Cylinders contained either 500 cm3 or 250 cm3 of solution. Foam stability was measured as the volume of air in foam after standing for 10 minutes. All measurements were replicated twice with an estimated error of ± 63 cm3.

2.3.2 Bartsch Method20,21 Foamabilities were measured as the volume of air entrained in foam immediately after shaking 100 cm3 graduated cylinders containing 25 cm3 of solutions at a frequency of ~3 Hz in cylinders for 10 seconds. Cylinders were pre-equilibrated in a thermosat bath at 25oC. The cylinders were of 18cm height and diameter 2.7cm. Foam stability was measured as volume of air in the foam after the cylinders were allowed to stand for 10 minutes in a thermostat water bath at 25 0C. All the measurements were twice replicated. The error measured by this method is ± 1.5 cm3.

2.4 Equilibrium and Dynamic Surface Tensions All air-water surface tensions were measured at 25oC in solutions of 17 mM NaCl at pH 10.5. The Wilhelmy plate method (CDCA-100 Commercial Surface Tensiometer, Camtel Ltd., UK) was used to measure the near-equilibrium air-water surface tensions of solutions of both surfactants. Critical micelle concentrations were determined from Gibbs plots of these surface tensions against the logarithm of the surfactant concentration. Presence of minor contaminants, which transport slowly to the air-water surface, for both NaLAS and nominally pure C12 4-phenyl SO3Na meant that true equilibrium required in excess of 24 hours. Practical considerations meant that the near-equilibrium surface tensions required for Gibbs plots were therefore measured after only one hour of equilibration. Dynamic surface tensions used a maximum bubble pressure tensiometer (BPA-1S SINTERFACE Technologies, Germany).

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2.5 Optical Microscopy An optical microscope with crossed polars (Jenaval from Carl Zeiss Ltd.) was used to observe the precipitates formed by addition of Ca2+ ions to aqueous micellar solutions of sodium alkyl benzene sulphonate solutions.

3. Results and Discussion

3.1 Ca2+- Surfactant Precipitation Phase Diagrams The precipitation phase diagram for the system C12 4-phenyl SO3Na/Ca2+ in 17 mM NaCl at pH 10.5 and 25oC is shown in Figure 1a where log10[C12 4-phenyl SO3Na] is plotted against log10[Ca2+]. Here the line AB represents the CMC boundary between monomeric and micellar surfactant solutions. We note that the CMC in the absence of Ca2+ is ~ 6.3 x 10-3M, which is significantly greater than, for example, that in the presence of 10-4M Ca2+ shown in the figure. The line BC in Figure 1a represents the lower precipitation boundary between monomeric surfactant solutions and a region containing both monomers and calcium dodecyl 4-phenyl sulphonate precipitate. This line has a gradient of ~ -0.43± 0.02 which is close to, but not equal to the value of 0.5 expected by stoichiometric equivalence. The line BD represents the upper precipitation boundary between a micellar surfactant solution and a region containing calcium dodecyl 4-phenyl sulphonate precipitate and micellar solution. This line is convex with respect to the abscissa as a consequence of the function describing the increase in binding of Ca2+ to surfactant micelles as the concentration of the latter increases. The lines AB, BC and BD are seen to converge on a singularity at point B where a monomer solution phase is in equilibrium with both micelles and precipitate (and where the phase rule indicates zero degrees of freedom at constant T&P provided we can consider micelles as constituting a separate phase). The precipitation phase diagram for NaLAS/Ca2+ (where NaLAS is a commercial sodium alkyl benzene sulphonate blend), also in 17 mM NaCl at pH 10.5 and 25oC, is shown in Figure 1b. Comparison with Figure 1a reveals a close similarity despite the complexity of the commercial NaLAS mixture. This sample of NaLAS therefore appears to be showing ``pseudo-monocomponent'' behaviour with respect to the precipitation phase diagram. The average molecular weight of the NaLAS is 344 with a hydrocarbon chain length distribution (see Table S1) which peaks at C12. This compares with a molecular weight of 348 for C12 4-phenyl SO3Na. Some similarity between the equilibrium precipitation phase behaviour of these two surfactants is perhaps therefore to be expected. In the NaLAS precipitation phase diagram of Figure 1b the monomer-precipitate line BC has a gradient of ~ -0.42±0.02. This compares with gradients of ~ -0.5 reported by Matheson et al15 for the corresponding line for each of commercial NaLAS samples of average chain lengths C11.4, C12 and C13 in both deionized water and 10mM Na2SO4

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solution both at 25oC. Curiously Matheson et al15 report that the presence of 10mM Na2SO4 increases the solubility of the precipitate. Verge et al22 also report gradients of -0.5 for various blends of NaLAS in the absence of any additional indifferent electrolyte. Unlike the micellar-precipitate boundary line BD in both Figures 1a and b, which is convex with respect to the abscissa, Matheson et al15 report that the equivalent line is concave with respect to the abscissa in the absence of added electrolyte and linear in the presence of 10mM Na2SO4 for each of the commercial NaLAS samples considered by them. By contrast Verge et al22 present precipitation phase diagrams with a linear micellar-precipitate boundary line BD in the absence of added electrolyte. There would appear to appear to be little agreement here.

3.2 The Nature of the Precipitate Peacock and Matijevic23 have determined the precipitation phase diagrams of two pure sodium alkyl benzene sulphonates – sodium p-decyl 2-phenyl sulphonate (C10 2-phenyl SO3Na) and sodium p- tetradecyl 7-phenyl sulphonate (C14 7-phenyl SO3Na). In both cases the gradient of the monomer-precipitate line (BC in Figures 1a and b) is reported to be -0.5. In the case of C10 2-phenyl SO3Na the precipitate was clearly crystalline – moreover analysis revealed a ratio of C10 2-phenyl SO3Na /Ca2+ = 2. All of this is consistent with a crystal of stoichiometry Ca(C10 2-phenyl SO3Na)2. Although the gradient of the monomerprecipitate line for C14 7-phenyl SO3Na is also reported to be -0.5 no analysis of the precipitate is given. It is also simply described as consisting of ``compact particles of less than one micron diameter'' which could mean mesophase rather than crystal formation. Smith et al16 have in fact shown that the precipitate formed from the interaction of Ca2+ with various commercial LAS- blends is a mesophase. Sein at al24 have prepared a sample of the compound Ca(LAS)2, from a commercial blend of alkylbenzene sulphonic acid and show that it forms only lamellar phase with water ``even at very low concentrations (< 0.1 wt%)''. We have also examined the precipitates formed from both C12 4-phenyl SO3Na and NaLAS in aqueous solutions of 17mM NaCl at pH 10.5 containing Ca2+ using optical microscopy with crossed polarizers to observe the precipitates after centrifuging The resulting images are shown in Figure 2. They confirm the formation of lamellar mesophases rather than crystals. In summary then we find that all reported observations of the interaction of Ca2+ with commercial LAS blends reveal the formation of lamellar mesophase. We also find lamellar mesophase to be formed in the case of pure C12 4-phenyl SO3Na as apparently do Peacock and Matijevic23 in the case of pure C14 7-phenyl SO3Na. Moreover we note that all reported observations of the monomer-precipitate line (line BC in Figures 1a and b), in solutions which contain no indifferent electrolyte, reveal a gradient of -0.5. This includes the C14 7phenyl SO3Na/Ca2+ system reported by Peacock and Matijevic23 despite the absence of corrections for ionic non-ideality (presumably justified by the low [Ca2+] range involved). However our observations involved the presence of significant concentrations of indifferent

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electrolyte (17mM NaCl) for which however we find a gradient of the monomer-precipitate line of ~ -0.43 for the C12 4-phenyl SO3Na/Ca2+ system and ~ -0.42 for the NaLAS/Ca2+ system. In this we differ from the findings of Matheson et al15 who report a gradient of -0.5 for the monomer-precipitate line for various commercial NaLAS samples in the presence of 10mM NaSO4. This difference may concern equilibration although both our results and those of Matheson et al15 involved 24 hours equilibration time. We should note however that Matheson et al15 make no corrections for ionic activities in estimating solubility coefficients and do not actually present data points on their plots equivalent to the line BC in Figure 1. A possible explanation for low values of the gradient of monomer-precipitate line in the case of the C12 4-phenyl SO3Na/Ca2+ and NaLAS/Ca2+ systems reported here could concern ionic non-ideality. Thus, allowing for non-ideality, the solubility product, K sp , for a stoichiometric calcium alkyl benzene sulphonate precipitate should be written 2

K sp  f 3 Ca 2   ABS   (1)

where  ABS   is any alkyl benzene sulphonate anion and f  is the mean ionic activity coefficient. Taking logs and differentiating with respect to dlog Ca 2  we obtain for the gradient of the monomer-precipitate line

    log  ABS    logf          0.5 3   1 2 2    log Ca      log Ca         Na ,Cl      Na ,Cl       where we assume that the presence of a large excess of NaCl means that the changes in [Na+] and [Cl-] accompanying changes in [Ca2+] and [ABS-] can be neglected. The mean ionic activity coefficient may be estimated using the extended Debye-Hückel law25 which in this case can be written as log f   

2A s 1 B s

where A  0.509  mol. kg-1 

(3) 1/2

and B is a constant (taken26 to be ~1.5 (mol. kg-1)-1/2). s is

the ionic strength (in mol. kg-1) which for the system considered here is given by s   Na    3 Ca 2 

(4)

(2)

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where due allowance is made for electro-neutrality and the presence of the counter ions ABS-, Cl-, and OH-. Differentiating eq. 3, and combining the result with eqs. 2 and 4, yields

 9 A Ca 2  / s   log  ABS           0.5 1   (5) 2 2  log Ca     1  2 B s  B s        Na ,Cl   The gradient log  ABS /log Ca 2  is seen from eq.5 to be a function of [Ca2+]. This means that in general a plot of log[ABS-] against log[Ca2+] will only be linear with a gradient of -0.5 when the contribution of the indifferent electrolyte to the ionic strength is so high that any contribution from changes in [Ca2+] and [ABS-] is negligible. Otherwise the modulus of the gradient will be <0.5 and plots will be non-linear. That the contribution of Ca2+ to the ionic strength is not negligible is revealed if we note that s changes from ~18mM to ~ 23 mM along the line BC in Figure 1, for both alkyl benzene sulphonates, as the concentration of Ca2+ is increased. We can calculate the gradient ∂log[ABS − ]/ ∂log[Ca2+ ] using the coordinates for each of the Ca2+ concentrations corresponding to the data points on the monomer-precipitate line BC for the system C12 4-phenyl SO3Na/Ca2+ shown in Figure 1a. Calculated values of those gradients are not constant and their moduli decrease from 0.50 to 0.48 with increasing [Ca2+] with a mean of 0.49. Similar values can be calculated for the system NaLAS/Ca2+. However as we have seen lines drawn through those data points have gradients as low as – (0.42-0.43). We therefore have to conclude that if these precipitates possessed the stoichiometry CaABS2 then the effect of ionic non-ideality is not sufficient to reduce log  ABS  /log  Ca 2  to the experimental values exhibited by the monomer-precipitate

boundary lines BC shown in Figure 1. Another possible explanation concerns the partial substitution of bound Ca2+ by Na+ in the lamellar phase precipitating from solutions which contain relatively high concentrations of the latter. Thus we can show, using a simple mass action argument presented as an appendix in Supplementary material, that displacement of about 12% of the Ca2+binding sites with Na+ is sufficient to account for the low gradients of ∂log[ABS − ]/ ∂log[Ca2+ ]. Such displacement would however seem unlikely in view of the high tendency of Ca2+ to bind chemically to charged surface sites. This is exemplified in a recent paper by Anachkov et al10 who show that increasing the concentration of NaCl as indifferent electrolyte from zero to 47mM NaCl has little effect on air-water surface tensions in a Gibbs plot for a solution of a technical grade sodium dodecyl benzene sulphonate in the presence of 1.2 mM Ca2+. It rather suggests that Ca2+ binding to the adsorbed surfactant dominates and that no tendency for displacement by Na+ is occurring. Indeed Anachkov et al10 show that Na+ occupancy of the Stern layer of the adsorbed surfactant is almost completely eliminated by the presence of 1.2mM Ca2+. Perhaps then

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the most likely explanation for the low gradients of ∂log[ABS − ]/ ∂log[Ca2+ ] concerns incomplete achievement of equilibrium in these very dilute, slowly precipitating, systems. We therefore conclude that the precipitate formed when calcium ions are added to these solutions of sodium alkyl benzene sulphonates in 17mM NaCl at pH 10.5 is a lamellar phase of probable composition Ca(ABS)2.

3.3 Effects of pH and Calcium on Foam and Dynamic Surface Behaviour of C12 4phenyl SO3Na Solutions The foam behaviour of solutions of both C12 4-phenyl SO3Na and NaLAS in 17mM NaCl at 25oC has been studied in order to establish the cause of the well-known decline in foamability accompanying the formation of calcium alkyl benzene sulphonate precipitates13,14. A surfactant concentration of 2mM was selected as typical of those used during clothes washing by hand. In the case of C12 4-phenyl SO3Na foam behaviour was measured as a function of Ca2+ concentration and pH using only the Bartsch method20,21. In effect a scan EFGH was made through both the micellar region and beyond into the region of the phase diagram where precipitate forms as shown in Figure 1. Here we remember that the region EF concerns clear micellar solutions. Along the line FG micellar solution coexists with precipitate. However constant concentration of surfactant removes a degree of freedom and the phase rule therefore predicts an invariant system where the chemical potential of the relevant species should be constant. Increasing [Ca2+] simply decreases the ratio of micellar surfactant to precipitate. At point G the free surfactant drops below the cmc and micelles are no longer present. Along the line GH monomeric surfactant exists only with precipitate. Here we should note that the position of the point G should be regarded as subject to significant uncertainty. It was inferred from near equilibrium airwater surface tensions (at surface age 10s), measured in a scan EFGH. Constant equilibrium surface tensions in the region FG imply constant chemical potential of the surfactant monomer. Results of foam measurements by the Bartsch method20,21 are shown in Figure 3. The foamability is seen to decline markedly with increasing [Ca2+] from the micellar-precipitate boundary which corresponds to point F (where [Ca2+] = 0.53 mM at 2.0 mM C12 4-phenyl SO3Na) in Figure 1. The foams were however stable for at least 10 minutes. There was no effect of pH (pH 3 vs. pH 10.5) on either foamability or foam stability. Removal of the precipitate formed at 4 mM Ca 2+ by filtration produced no significant change in foamability or foam stability as shown in Table 1. This strongly implies the absence of any antifoam effect by this lamellar phase precipitate. Absence of any antifoam effect is likely to be due to the hydrophilic nature of the surfaces of the lamellar phase particles where the surfactant head groups will dominate exposure to the aqueous phase4. We have therefore explored the possibility that the diminished foamability, accompanying precipitation of lamellar phase, simply concerns replacement of labile monomer and micellar surfactant with relatively stable, slowly diffusing mesophase particles. The latter would be able to

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only slowly transport to the rapidly expanding air-water surfaces formed during foam generation. Measurement of dynamic surface tensions represents a convenient means of studying the transport of surfactant to air-water surfaces. Such measurements are presented in Figure 4 for surface ages of 0.1s, 1s and 10s. It is obvious from the figure that presence of up to ~ 0.53 mM calcium causes a decrease in surface tension at all surface ages. This is presumably due to enhanced surface activity in this clear micellar region of the phase diagram. However at calcium concentrations > ~ 0.53 mM, the solutions become turbid due to precipitation of lamellar phase particles. At the relatively high surface age of 10s the surface tension is presumably close to equilibrium and is initially almost constant with increasing calcium ion concentration up to ~1.2 ± 0.2 mM Ca2+ despite the presence of increasing amounts of lamellar phase. As we have seen consideration of the phase rule suggests that for a pure surfactant in the region FG of the phase diagram shown in Figure 1 (at constant total surfactant concentration in the presence of micelles and precipitated lamellar phase) the system should be invariant at equilibrium. The dynamic surface tensions at a surface age of 10s shown in Figure 4 do in fact permit an estimate of the position of the point G in the precipitation phase diagram of Figure 1. It seems likely however that measurements of surface tensions at longer surface ages would move the estimated position of G to higher [Ca2+]. At surface ages of 0.1 - 1s and calcium concentrations of > ~ 0.53 mM, dynamic surface tensions are shown in Figure 4 to increase markedly with increasing [Ca2+]. This is presumably a consequence of an increase of precipitation in this region from a micellar state to particles of lamellar phase. Such particles are likely to have extremely low diffusion coefficients, slow breakdown rates27 and no tendency to adhere to air-water surfaces. The effect is particularly striking at [Ca2+] ≥ 2 mM and a surface age of 0.1s. The surface is then almost denuded of surfactant as indicated by a dynamic surface tension nearly equal to that of pure water. The significant departure from equilibrium adsorptions under dynamic conditions revealed by Figure 4 suggests a correlation with declining foamability. Direct comparison with dynamic surface tension is of course arguably too simplistic. However we should note that as surface tensions increase under dynamic conditions and adsorption declines, surface tension gradients decrease, Plateau border capillary pressures increase and disjoining pressures decrease rendering foam films more susceptible to spontaneous rupture28. However we would also expect film rupture to be stochastic with some foam films surviving and their stability subsequently reinforced by further adsorption as surfaces age and approach equilibrium after aeration as ceased. Low foamability then does not, as we see in Figure 3, necessarily mean low stability for any surviving foam.

3.4 Effects of Calcium and pH on Foam and Dynamic Surface Behaviour of NaLAS Solutions

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The foam and dynamic surface tensions corresponding to a similar scan, EFGH, have been made across the precipitation phase diagram of the NaLAS/Ca2+ shown in Figure 1b. Again the surfactant concentration was held constant at 2 mM in 17 mM NaCl but at pH 3, 7 and 10.5. An approximate estimate of the position of point G at 1.6±0.4 mM Ca2+ was again estimated from the relevant dynamic surface tension measurements at a surface age of 10s. Availability of this surfactant meant that measurements of foam behaviour could be made with two techniques – the Bartsch method20,21 and the tumbling cylinder method20. The foamability using the Bartsch method20,21, shown in Figure 5, is similar to that of the C12 4-phenyl SO3Na/Ca2+ system. Again it reveals a marked decline with increasing Ca2+ from the micellar-precipitate boundary corresponding to the point F on the phase diagram of Figure 1b. However since NaLAS is a commercial blend of almost 20 homologues and isomers (see Table S1) unsurprisingly the gradient of the decline is significantly less marked, presumably as a consequence of the effect of fractionation on the extent of lamellar phase precipitation. The effect of pH is seen to be slight with perhaps some indication of diminished foamability with increasing pH. This possibly concerns the effect of the changes in ionic strength attendant upon changes in pH, which are likely to be greater than is the case with the pure C12 4-phenyl SO3Na solutions as a consequence of the presence of inorganic impurities in this NaLAS sample. As with the C12 4-phenyl SO3Na/Ca2+ system foam is seen to be essentially stable for at least 600s regardless of Ca2+ concentration or pH. The foamabilities of this NaLAS/Ca2+ system, measured with the tumbling cylinder method and also shown in Figure 5, did not reveal the onset of a marked decline in foamability at the micellar-precipitate boundary (point F in Figure 1b). The decline in foamability with increasing [Ca2+] is seen in the figure to be more gradual than is the case using the Bartsch method20,21. However, as with the latter, foam is essentially stable up to at least 10 minutes regardless of pH or [Ca2+]. Removal of the lamellar phase precipitate by filtration had little effect on foamability as was found with the system C12 4-phenyl SO3Na/Ca2+. Similar results for NaLAS/Ca2+ are also presented in Table 1. We must therefore conclude that the relevant diminution of foamability in that system also does not concern an antifoam effect. Dynamic surface tensions for 2 mM NaLAS solutions in 17 mM NaCL at pH 10.5 as a function of [Ca2+] are shown in Figure 6. This again represents a scan EFGH through the relevant precipitation phase diagram shown in Figure 1b. Comparison with the corresponding plots for C12 4-phenyl SO3Na shown in Figure 4 reveals some similarities. In both cases dynamic surface tensions mostly decrease with increasing [Ca2+] up to the micellar-precipitate boundary (point F in Figure 1a and b). With increasing [Ca2+] above the concentration at that boundary, where solutions are turbid due to the precipitation of lamellar phase, dynamic surface tensions increase markedly at a surface age of 0.1s in both systems. However the gradient of the dynamic surface tension against [Ca2+] in the NaLAS/Ca2+ is obviously less than that in the corresponding C12 4-phenyl SO3Na/Ca2+

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system. At surface ages of 1s and 10s the difference in such gradients between the two systems is even more marked. We should remember that, in the case of the pure C12 4-phenyl SO3 Na solution, the micellar-precipitate region (region FG in Figure 1a) is invariant according to the phase rule. The equilibrium surface tension should therefore be constant in that region. Surprisingly then we see in Figure 6 that at a surface age of 10s, near constant dynamic surface tensions are also apparent for the NaLAS solution from the micellar-precipitate boundary up to [Ca2+] ~ 1.6 mM, despite the multicomponent nature of this commercial surfactant. It seems probable that the increasing gradients of dynamic surface tensions against [Ca2+] for both NaLAS/Ca2+ and C12 4-phenyl SO3 Na systems are due to the conversion of labile micellar material to non-labile lamellar precipitate. That the gradients are less marked for the commercial NaLAS/Ca2+ system probably reflects the effect of fractionation. Thus onset of precipitation at the micellar-precipitate boundary concerns a mixed lamellar phase containing relatively high proportions of the longer chain homologues. Precipitation of the remaining micellar material, rich in shorter chain homologues, will therefore require higher concentrations of Ca2+. Relative to a pure surfactant of similar molecular weight we would therefore expect the proportion of labile micellar material to be higher in a commercial blend as the Ca2+ concentration increases beyond the precipitation boundary. Fractionation then means that dynamic surface tensions at [Ca2+] in the micellar-precipitate region at surface ages of 0.1s and 1s for NaLAS become significantly lower than those for the corresponding C12 4-phenyl SO3Na/Ca2+ system despite similar molecular weights. This would therefore imply that transport of surfactant to air-water surfaces in the case of the commercial NaLAS solution is faster in these circumstances than is the case with the pure surfactant. We would therefore expect this difference to lead to differences in foamability if the decline in foamability is mainly due to the effect of precipitation of lamellar phase on surfactant transport to air-water surfaces. In Figure 7 we compare the foamabilities of the two systems by the Bartsch method20,21. The foamability of the NaLAS solution is indeed significantly higher than that of the C12 4-phenyl SO3Na solution at Ca2+ concentrations above that of the micellar-precipitate boundary. In the same figure we compare the dynamic surface tensions of these two systems at a surface age of 0.1s. The dynamic surface tension of the NaLAS solution is lower than that of the C12 4-phenyl SO3Na solution in the relevant region. However both dynamic surface tensions tend to converge as [Ca2+]  4 mM as do the foamabilities. It is tempting to suggest therefore that a surface age perhaps close to ~0.1s is characteristic of this Bartsch method20,21 of foam generation. By contrast the foamability of NaLAS solutions measured using the tumbling cylinder method20, shown in Figure 5, reveals a more gradual decrease with increasing [Ca2+] than is observed with the Bartsch method20,21. Since dynamic surface tensions shown in Figure 6 for these solutions indicate a gradual increase with increasing [Ca2+] at

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higher surface ages this may therefore suggest that such ages, perhaps close to 1s, are then relevant for that methodology.

4. Summary and Conclusions Addition of Ca2+ to aqueous micellar solutions of the sodium alkyl benzene sulphonate solutions considered here produced precipitates of lamellar phase of probable composition Ca(ABS)2 (where ABS is either C12 4-phenyl SO3- or LAS-). This precipitation of mesophase is accompanied by declines in foamability where we have shown that the latter cannot be restored to any extent by removal of the precipitate. This confirms the absence of any antifoam effect. The onset of precipitation of mesophase is however accompanied by marked declines in the rate of transport of surfactant to air-water surfaces as indicated by measurements of dynamic surface tensions. It seems likely that such declines derive from the low diffusion coefficients and slow breakdown rates characteristic of lamellar phase particles27. Slow transport to air-water surfaces means low surfactant adsorption at airwater surfaces leading to diminished contributions of disjoining forces to foam film stability and enhanced capillary pressures which oppose disjoining forces and increase foam film thinning rates as do the concomitant reductions in surface tension gradients4. These factors all conspire to diminish the stability of foam films during the rapid aeration accompanying foam generation. However subsequent slow adsorption of surfactant to the film surfaces of any surviving foam appears to stabilize the latter. Therefore foamability may be diminished by mesophase precipitation in these surfactant solutions but any foam formed may be stable. Similar observations have been reported involving precipitation of lamellar phase upon addition of zwitterionic surfactant to solutions of sodium C12 6-phenyl sulphonate28. Comparison of the foam and dynamic surface tension behaviour of a pure sodium alkyl benzene sulphonate with a commercial blend of similar average molecular weight revealed qualitatively similar behaviour. However significant quantitative differences were apparent. Solutions of the commercial surfactant blend tended to show more rapid transport to airwater surfaces in the micellar-precipitate region of the precipitation phase diagram. Higher foamability was therefore observed. This effect would appear to be a consequence of fractionation in the commercial blend as precipitation of the lower molecular weight components requires higher Ca2+ concentrations. As a result the foamability of the commercial LAS blend is higher in the micellar-precipitate region. It is apparent that there are no definitive measurements of the complete Ca2+ - precipitation phase diagram for these important sodium alkyl benzene suphonates, as a function of ionic strength in the presence of indifferent electrolyte, involving pure surfactants where extreme care has been taken to ensure equilibrium and due allowance made for ionic activity coefficients. Accurate measurement of the monomer-precipitate boundary, allowing for ionic activity coefficients should afford a means of unambiguously establishing whether any substitution of Ca2+ in the bilayers of any lamellar phase with other counter ions can

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occur. However of arguably greater significance is the determination of the monomermicelle-mesophase precipitate composition in the three phase region (FG in Figure 1) and the quantitative interpretation of the resulting dynamic surface tensions from a knowledge of the relevant micelle and lamellar kinetic behaviour. Our yet to be published papers7-9 are not however concerned with those challenges but rather with the effects of triglyceridebased antifoams, which are superimposed upon the foam behaviour intrinsic to these solutions of sodium alkyl benzene sulphonates. The mode of action of such antifoams, including the role of Ca2+and pH in the presence of indifferent electrolyte, forms the focus of those studies. One application of the issues raised here concerns rinsing after washing of for example clothes. This can be particularly problematic in case of water shortages or even long distances from water sources. Foam is used as a marker during rinsing. Dilution with hard water can then lead to precipitation of anionic surfactant as concentrations of calcium complexing agents (``builders'') decline. The comparison of foamabilities between commercial NaLAS and pure C12 4-phenyl SO3Na shown in Figure 7 suggests that minimizing fractionation by tightening the specification of the commercial surfactant can reduce foamabilities at [Ca2+] above the precipitation boundary. In conclusion we should emphasise the distinction between the absence of antifoam effects due to dispersed lamellar phase and the well-known antifoam effects in aqueous solutions associated with hydrophobic particles, oils and mixture of such oils and particles4. Consider then for example the, often weak, antifoam effects realized by hydrophobic particles alone. Such effects occur when the particles are added to an aqueous surfactant solution, leaving the physical properties of the surfactant in solution unchanged. The effects require that the particles be sufficiently hydrophobic so that the contact angle is greater than a critical value which is determined by the geometry of the particles30-33. Particles with sharp edges are particularly effective in this context33. Hydrophobicity is in turn associated with the presence of low energy methyl and methylene groups or their perfluoro derivatives at the surfaces of such particles34. By contrast lamellar phase particles formed in an aqueous medium usually consist of stacked bilayers (multi-walled vesicles for example) where the hydrophilic head groups are exposed to the aqueous phase and the hydrophobic methylene chains are confined to the interiors of the bilayers (see for example35). Such structures are therefore likely to be hydrophilic leading to the observed absence of antifoam effects. Here we should note that addition of mono and divalent counterions to aqueous solutions of anionic surfactants does not always produce lamellar phase precipitate. Crystalline precipitates are also formed. The crystal habits of such precipitates may involve sharp edges together with exposure of hydrocarbon chains to the aqueous surface resulting in finite contact angles36, all of which means potential antifoam effects. There is for example some limited evidence that surfactants such as sodium dodecyl sulphate form crystalline precipitates below the Krafft temperature in the presence of excess [Na+] which exhibit antifoam effects in addition to reduction in rates of transport to air-water surfaces20,37. It

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would therefore be of interest to compare the observations reported here with the effect of Ca2+ on the foamabilities and dynamic surface properties of solutions of C10 2-phenyl SO3Na which apparently forms a stoichiometric crystalline precipitate rather than a mesophase above the precipitation boundary23. Acknowledgement Financial support for Li ran and P.R.Garrett is gratefully acknowledged from EPSRC (UK) and Procter and Gamble through EP/F000499/1. References (1). Nikkari, T.;1; Comparitive Chemistry of Sebum. J. Invest. Dermatol. 1974, 62, 257-267. [2]. Wood, J.D.; Enser, M.; Fisher, A.V.; Nute, G.R.; Sheard, P.R.; Richardson, R.I.; Hughes, S.I.; Whittington, F.M.;1; Fat deposition, Fatty Acid Composition and Meat Quality: A Review. Meat Sci. 2008, 78, 343-358. [3]. Zhang, H.; Miller, C.A.; Garrett, P.R.; Raney, K.H.;1; Mechanism for Defoaming by Oils and Calcium Soap in Aqueous Systems. J. Colloid Interface Sci. 2003, 263, 633-644. [4]. Garrett, P.R.;1; Mode of Action of Antifoams in The Science of Defoaming; Theory, Experiment and Applications; CRC Press, New York,Surfactant Science Series 2013, Vol.155, Chp. 4. [5]. Stefaniak, A.B.; Harvey, C.J.;1; Dissolution of Materials in Artificial Skin Surface Film Liquids. Toxicol. in Vitro. 2006, 20, 1265-1283. [6]. Motwani, M.R.; Rhein, L.D.; Zatz, J.L.;1; Differential Scanning Calorimetry Studies of Sebum Models. J.Cosmetic Sci. 2001, 52(4), 211-224. [7]. Garrett, P.R.; Ran, L.;1; The Effect of Calcium on the Foam Behaviour of Aqueous Sodium Alkyl Benzene Sulphonate Solutions. 2. In the Presence of Triglyceride-based Antifoam Mixtures. Unpublished results. [8]. Garrett, P.R.; Ran, L.;1; The Effect of Calcium on the Foam Behaviour of Aqueous Sodium Alkyl Benzene Sulphonate Solutions. 3. The Role of the Oil in Triglyceride-based Antifoam Mixtures.Unpublished results. [9]. Garrett, P.R.; Ran, L.; Morris, G.D.M.;1; The Effect of Calcium on the Foam Behaviour of Aqueous Sodium Alkyl Benzene Sulphonate Solutions. 4. The Role of the Particles in Triglyceride-based Antifoam Mixtures. Unpublished results. [10]. Anachkov, S.E.; Tcholakova, S.; Dimitrova, D.T.; Denkov, N.D.; Subrahmaniam, N.; Bhuna, P.;1; Adsorption of linear alkyl benzene Sulphonates on Oil-Water Interface: Effects of Na+, Mg2+ and Ca2+ ions. Coll.Surf. A: Physicochem. Eng. Aspects. 2015, 466, 18-27. [11]. Hall, D.G.;1; Personal communication.

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[12]. Denkov, N.D.;1; Mechanisms of Foam Destruction by Oil-Based Antifoams. Langmuir 2004, 20, 9463-9505. [13] Cohen, L.; Moreno, A.; Berna, J.L.;1; Influence of Anionic Concentration and Water Hardness on Foaming Properties of a Linear Alkylbenzene Sulphonate. J.Amer. Oil Chem.Soc. 1993,70(1), 75-78. [14]. Cohen, L.; Moreno, A.; Berna, J.L.;1; Influence of Anionic Concentration and Water Hardness on Foaming Properties of a Linear Alkylbenzene Sulphonate – Erratum to reference12. J.Amer. Oil Chem.Soc. 1993, 70(7), 735. [15]. Matheson, K.L.; Cox, M.F.; Smith, D.L.;1; Interactions between Linear Alkylbenzene Sulfonates and Water Hardness Ions. I. Effect of Calcium Ion on Surfactant Solubility and Implications for Detergency Performance. J.Amer. Oil Chem.Soc.1985, 62(9), 1391. [16]. Smith, D.L.; Matheson, K.L.; Cox, M.F.;1; Interactions between Linear Alkylbenzene Sulfonates and Water Hardness Ions. III. Solubilization and Performance Characteristics of Ca(LAS)2. J.Amer. Oil Chem.Soc.1985, 62(9), 1399. [17]. Ran,L.; Jones, S.A.; Embley, B.; Tong, M.M.; Garrett, P.R.; Cox, S.J., Grassia, P.; Neethling, S.J. Characterisation,;1; Modification and Mathematical Modelling of Sudsing. Colloids Surf. A Physicochem. Eng. Aspects, 2011, 382, 50. [18]. Matheson, K.L.;1; Detergency Performance Comparison between LAS and ABS using Calcium Sulfonate Precipitation Boundary Diagrams. J. Amer. Oil Chem. Soc. 1985, 62(8), 1269. [19]. Cox, M.F.; Matheson, K.L.;1; Interactions between Linear Alkylbenzene Sulfonates and Water Hardness ions. II. Reducing Hardness Sensitivity by the Addition of Micelle Promotion Agents. J. Amer. Oil Chem. Soc. 1985, 62(9), 1396. [20]. Garrett, P.R.;1; Experimental Methods for the Study of Foam and Antifoam action in The Science of Defoaming; Theory, Experiment and Applications; CRC Press, New York,Surfactant Science Series 2013, Vol.155, Chp. 2. [21]. Bartsch, O.;1; Über Schaumsysteme. Kolloidchem. Beihefte. 1924, 20, 1-49. [22]. Verge, C.; Moreno, A.; Bravo, J.; Berna, J.L.;1; Influence of Water Hardness on the Bioavailability and Toxoicity of Linear Alkylbenzene Sulphonate (LAS). Chemosphere 2001, 44, 1749-1757. [23]. Peacock, J.M.; Matijević, E.;1; Precipitation of Alkylbenzene Sulfonates with Metal ions. J. Colloid Int. Sci. 1980, 77(2), 548-554.

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[24]. Sein, A.; Engberts, B.F.N.; van der Linden, E.; van de Pas, J.C.;1; Lyotropic Phases of Dodecylbenzenesulfonates with different Counterions in Water. Langmuir 1996, 12(12), 29132923. [25]. Atkins, P.W.;1; Physical Chemistry; Oxford University press, Oxford, 1990, 4th edition, Chp. 10. [26]. Kumar, A.; Sanghavi, R.; Mohandas, V.P.;1; Solubility Pattern of CaSO4.2H2) in the System NaCL + CaCl2 + H2O and Solution Densities at 35oC: Non-ideality and Ion Pairinng. J. Chem. Eng. Data. 2007, 52, 902-905. [27]. Farquhar, K.D.; Misran, M.; Robinson, B.H.; Steytler, D.C.; Morini, P.; Garrett, P.R.; Holzwarth, J.F.;1; The Kinetics and Mechanism of Micelle-Vesicle Transitions in aqueous Solution. J. Phys. Condens. Matter, 1996, 8, 9397-9404. [28]. Garrett, P.R.; Gratton, P.L.;1; Dynamic Surface Tensions, Foam and the Transition from Micellar Solution to Lamellar Phase Dispersion. Colloids Surf. A Physicochem. Eng. Aspects, 1995, 103, 127-145. [29]. Garrett, P.R.;1; Some General Properties of Foams in The Science of Defoaming; Theory, Experiment and Applications; CRC Press, New York,Surfactant Science Series 2013, Vol.155, Chp. 1. [30]. Garrett, P.R.;1; The Effect of Polytetrafluoroethylene Particles on the Foamability of Aqueous Surfactant Solutions. J. Colloid Int. Sci. 1979, 69(1), 107-121. [31]. Dippenaar, A.,;1; The Destabilisation of Froth by Solids. I The Mechanism of Film Rupture. Int. J. Miner. Process. 1982, 9, 1-14. [32] .Aveyard, R.; Binks, B.P.; Fletcher, P.D.I.; Rutherford, C.E.;1; Contact Angles in Relation to the Effect of Solids on Film and Foam Stability. J. Dispersion Sci. Technol. 1994, 15(3), 251- 271. [33]. Frye, G.C.; Berg, J.C.;1; Antifoam Action by Solid Particles. J.Colloid Int. Sci. 1989, 127(1), 222-238. [34]. Shafrin, E.G.; Zisman, W.A.;1; Constitutive Relations in the Wetting of Low Energy Surfaces and the Theory of the Retraction method of Preparing Monolyers. J. Phys. Chem. 1960, 64, 519 – 524. [35]. Fennell Evans, D.; Wennerström, H.;1; Bilayer Systems in The Colloid Domain; WileyVCH, 2nd Edn., 1999, Chp. 6, 299 – 350. [36]. Luangpirom, N.; Dechabumphen, N.; Saiwan, C.; Scamehorn, J.;1; Contact Angles of Surfactant Solutions on Precipitated Surfactant Surfaces. J.Surfactants Deterg., 2001, 4(4), 367 – 373.

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[37]. Peck, T.G.,;1; The Mechanisms of Foam Breakdown by Oils and Particles, PhD Thesis, University of Hull, 1994.

Figure1. Precipitation phase diagram for alkyl benzene suphonates + Ca2+ in 17mM NaCl at pH 10.5 and 25oC. (a). Sodium dodecyl 4-phenyl sulphonate (C12LAS). (b). Commercial sodium alkyl benzene sulphonate (NaLAS). In both (a) and (b) the dotted line EFGH indicates the scan employed in this work for both foam and dynamic surface tension measurements. The point G is at the approximate transition from a region where micelles and precipitate are in equilibrium with surfactant monomer to a region where only precipitate is in equilibrium with monomer. Figure 2. Photomicrographs with crossed polarizers of precipitates, after centrifuging, formed in (a). System C12 4-phenyl SO3Na/Ca2+ (b). System NaLAS/Ca2+. Both in 2 mM surfactant, 4mM Ca2+ and 17mM NaCl at pH 10.5 and 25oC. The scale bar represents 100 micron. Figure 3. Foamability and foam stability by the Bartsch method20,21 in 2mM C12 4-phenyl SO3Na, in 17mM NaCl at 25±1oC. (a) immediately after shaking for 10s; (b) after standing for 10 min;  pH 3;  pH 10.5. Figure 4. Dynamic surface tensions at various surface ages of solution of 2mM C12 4-phenyl SO3Na in 17mM NaCl, at pH 10.5 and 25±1 oC;  0.1 s;  1 s; ▲ 10 s. The line coresponding to the boundary at point G (shown in Figure 1) is at the approximate transition from a region where micelles and precipitate are in equilibrium with surfactant monomer to a region where only precipitate is in equilibrium with monomer. Figure 5. Foamability and foam stability of 2mM NaLAS in 17mM NaCl, at 25±1oC. By the Bartsch method20,21; (a) immediately after shaking for 10s; (b) after standing for 10 min. By tumbling cylinder method20; (c) immediately after 10 rotations; (d) after standing for 10 min.  pH 3;  pH 7; ∆ pH 10.5. Figure 6. Dynamic Surface Tensions at different surface ages of 2mM NaLAS in 17mM NaCl, at pH 10.5 and 25±1oC; 0.1s; ■ 1s; ▲ 10s. The line corresponding to the boundary at point G (shown in Figure 1b) is at the approximate transition from a region where both micelles and precipitate are in equilibrium with surfactant monomer to a region where only precipitate is in equilibrium with monomer. Table 1. The effect of removal, by filtration (using a 0.2 μm Millipore filter), of lamellar phase precipitate on foamability and foam stability for 2 mM solutions of both C12 4-phenyl SO3Na

19

and NaLAS in 4 mM Ca2+ and 17 mM NaCl at pH 10.5 and 25±1oC. Foam behaviour by Bartsch method20,21. System C12 4-phenyl SO3Na/Ca2+ NaLAS/Ca2+

TDENDOFDOCTD

Foamability Foam stability after 600s Foamability Foam stability after 600s

Volume air in foam/cm3 Before filtration After filtration 26 24 25.5 23 25 28 23 26