Explanation for the Increased Induction Times in Binary Mixed Anionic

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Explanation for the Increased Induction Times in Binary Mixed Anionic Surfactant Mixtures Published as part of a virtual special issue of selected papers presented at the 9th International Workshop on the Crystal Growth of Organic Materials (CGOM9). Atthaphon Maneedaeng,† Adrian E. Flood,*,† Brian P. Grady,‡ and Kenneth J. Haller§ †

School of Chemical Engineering, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand Institute of Applied Surfactant Research, School of Chemical, Biological and Materials Engineering, The University of Oklahoma, Norman, Oklahoma 73019, United States § School of Chemistry, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand ‡

bS Supporting Information ABSTRACT: The induction time for precipitation of pure sodium dodecylsulfate (NaDS) solutions by CaCl2 both below and above the cmc at a specific temperature depends only on the supersaturation ratio of the precipitating species in the bulk solution, rather than the means of achieving the supersaturation (changes in calcium ion concentration or in surfactant concentration). For mixed NaDS/sodium decylsulfate (NaDeS) systems precipitated by CaCl2, the induction time is only a function of the supersaturation ratio calculated based on Ca(DS)2, which is formed from these solutions, since its solubility product is orders of magnitude less than that of Ca(DeS)2. The increase in induction time in mixtures of these surfactants, compared to pure systems of the same total surfactant content, is only due to the change in the concentration of the precipitating species (DS) because of changes in the molar ratio of the surfactants present and thermodynamic changes due to mixed micellization. For mixed NaDS/sodium octylbenzenesulfonate (NaOBS) systems precipitated by CaCl2, the precipitation of calcium surfactant salts can result in either Ca(DS)2 or Ca(OBS)2, depending on the conditions, due to the similar KSP values of these two salts. Precipitation of Ca(OBS)2 occurs in systems of approximately 050 mol % NaDS, and inhibition of precipitation is not found in mixed NaDS/NaOBS systems for this range of surfactant compositions. For precipitation of Ca(DS)2 in systems between 50 and 100 mol % NaDS, the value of the induction time as a function of supersaturation ratio calculated based on Ca(DS)2 is slightly larger than that found in the pure NaDS systems. Inhibition in these mixtures is mainly due to the change in concentration of the precipitating species (monomer DS) because of changes in surfactant composition in the solution phase and changes in the precipitation phase boundary because of the thermodynamic changes resulting from mixed micellization; however, there is also a small amount of kinetic inhibition.

’ INTRODUCTION Precipitation of calcium-neutralized surfactants is one problem for applications of anionic surfactants, in particular laundry detergency. Much research has been directed toward avoiding anionic surfactant precipitation by counterions such as divalent calcium and magnesium ions, or cationic surfactants, to avoid the formation of soap scum. Three notable approaches have been used to reduce the detrimental effects of calcium in anionic surfactant applications. The first method uses considerable amounts of additives (e.g., fatty alcohols) to improve the solubility of the calcium surfactant.1 Another approach uses builders to enhance the surfactant’s tolerance to calcium ions.2 Zeolites, phosphates, or silicates have a large affinity for calcium ions and act as builders by binding calcium ions.3 However, builders generally are not thought of as environmentally friendly. The last method is to develop anionic surfactant formulations that do not precipitate in the presence of calcium ions. The use of mixed surfactant systems can decrease the Krafft temperature and r 2011 American Chemical Society

increase either hardness tolerance or time required to begin precipitation.48 This article concerns the third method and investigates some fundamentals of surfactant precipitation. There have been numerous thermodynamic studies on the equilibrium for precipitation of single anionic surfactants precipitated by divalent ions and cationic surfactants,915 but only a few have studied the kinetics of precipitation.5,6,14 The induction time of anionic surfactants precipitated by calcium ions in surfactant mixtures is a key feature of kinetic studies in the context of inhibition of precipitation in detergency applications. However, there are a few such studies in the scientific literature. This work aims to systematically investigate the inhibition of precipitation of mixed anionic surfactants by calcium ions. The work reports the relationship Received: January 31, 2011 Revised: April 28, 2011 Published: May 04, 2011 2948

dx.doi.org/10.1021/cg200155q | Cryst. Growth Des. 2011, 11, 2948–2956

Crystal Growth & Design between induction time and the degree of solution supersaturation over a wide range of solution molarity, both below and above the cmc of the sodium-neutralized system in order to extend the knowledge of the kinetics of precipitation of binary anionic surfactant mixtures. Models for anionic surfactant precipitation and the activity of counterion binding from previous research16 were used here to calculate the amounts of precipitating species in the intermicellar solution, thereby improving the understanding of the inhibition of the precipitation of anionic surfactants. Moreover, crystallization parameters are estimated to model the behavior of calcium-induced precipitation of single and binary mixed anionic surfactants.

’ MATERIALS AND METHODS Experimental Procedure. Materials. Sodium dodecylsulfate, NaDS (Carlo Erba, Special grade, >92%), and sodium 4-octylbenzenesulfonate, NaOBS (Sigma-Aldrich, >97%), were further purified by recrystallizing twice from deionized water and methanol, respectively, and then dried over silica gel at room temperature for 24 h. Sodium decylsulfate, NaDeS (Fluka, puriss. p.a., >99%) was used without further purification. Calcium chloride dihydrate, CaCl2 3 2H2O (Sigma-Aldrich, analytical reagent grade, >98.0%) was used as received. Deionized water (18 MΩ 3 cm) was used to prepare all aqueous samples. Induction Time Determination. Fresh stock solutions of NaDS were prepared immediately before use to reduce hydrolysis of NaDS. The induction time for precipitation of NaDS by CaCl2 was investigated as an example of a single anionic surfactant system and was chosen since its precipitate (calcium dodecylsulfate, Ca(DS)2) has the lowest solubility product (KSP) of the three calcium surfactant salts. Experiments were performed across the precipitation phase boundary of Ca(DS)2 with varying supersaturation ratios. For mixed (binary) anionic surfactant systems, fresh stock NaDS, NaDeS, and NaOBS solutions both below and above the critical micelle concentration of the mixture (cmcM) were prepared to avoid hydrolysis of the anionic surfactants. The induction times of the two binary systems, NaDS/NaDeS and NaDS/NaOBS, precipitated with CaCl2 were investigated. The experiments were performed with different molar ratios of surfactants and several supersaturation ratios by varying the total surfactant concentration and the CaCl2 concentration. All experiments were carried out at 30 ( 0.5 °C with constant agitation with a magnetic stirrer flea at 200 rpm in an online turbidity device using a green light diode (LED) as a light source. The detector was a small photocell with a range of light resistance of 110 kΩ depending on the light intensity. The mixture in the turbidity device was contained in a 25 mL vial of 2 cm diameter. Ten milliliters of a stock surfactant mixture at an appropriate concentration was pipetted into the vial; immediately following this, 10 mL of a stock CaCl2 solution was pipetted into the vial to create a solution of the correct composition of the surfactants and CaCl2. Stock solutions were maintained at 30 °C using a constant temperature bath. The temperature of the turbidity device was maintained with a constant temperature jacket using water from a temperature-controlled water bath. The voltage signal was recorded every second by a Valleman DVM 345DI digital multimeter with a PC interface. Induction times were determined by finding the time difference between the mixing of the surfactant solution and calcium solution and the point of the turbidity curve where the first small change in turbidity indicates crystal nucleation. The induction time was

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determined three times for each batch to determine reproducibility; however, for precipitations having induction times less than 10 s, the induction time was observed visually once again to confirm the reliability of the device. The amount of precipitate from these experiments is very low due to the low solubility products of the species, and it was insufficient for powder X-ray diffraction analysis. For this reason, the species having the higher value of the supersaturation ratio was assumed to precipitate from solutions where more than one species was supersaturated. Modeling of the Surfactant Precipitation Phase Boundary and Supersaturation. Precipitation occurs when the ion product of a soluble ionic species in solution is in excess of the equilibrium ion product, i.e. the solubility product (KSP) which is defined in eq 1. Below the cmc, all surfactant species are assumed to be in the monomeric form with their dissociated monovalent counterions; thus, counterions are not bound to the micelle. In this case, the concentrations of all species in the bulk solution can be found independently. For precipitating systems above the cmc, there are three coexisting phases (or pseudophases): monomeric or solution phase, micelle phase, and precipitate phase. Pseudophase separation theory for this phenomenon was first proposed by Stainsby and Alexander.17 Surfactant species are present in the solution phase, the micelle phase, and the precipitate phase when it occurs, and counterions are also present in the solution phase, bound to the surface of the micelles, and at least one counterion species must also exist in the precipitate phase. The solubility product relationship for precipitation of the anionic surfactants with calcium ions can be expressed as

2 2þ Þð½S KSP ¼ ð½Ca2þ unb fCa mon f S Þ

ð1Þ

where KSP is the activity-based solubility product of the precipitating anionic surfactant salt, [Ca2þ]*unb is the concentration of unbound calcium ions at the equilibrium state, and [S]*mon is the concentration of the precipitating surfactant ion in the monomeric form at equilibrium. The activity coefficients of * 2þ) at equilibrium can be the surfactant (fS*) and calcium (fCa estimated using an extended DebyeH€uckel expression18 log fi ¼

Aðzi Þ2 I 0:5 0:3I 1 þ Bai I 0:5

ð2Þ

where A and B are constants depending on the solvent and the solution temperature, zi is the valence of the ion, and I is the ionic strength of the solution. The values of A and B for aqueous solutions have been tabulated at 30 °C: A = 0.5239 and B = 3.279 107.19 The parameter ai is an empirical value based on the ion diameter: for DS, DeS, and OBS, ai is equal to 7 108 cm1, and ai is equal to 6 108 cm1 for the calcium ion.5,19,20 Activity coefficients in the solution pseudophase can be estimated by this equation regardless of micellization and counterion binding, since it can be assumed that these phenomena do not contribute significantly to the ionic strength and do not have much effect on the monomer surfactant and unbound calcium ions.5,6,14 The critical micelle concentration is the concentration of surfactant required in order to create a micelle phase. When micelles are present in the system, sodium and calcium ions are bound at the negatively charged surface of the micelles and, hence, the unbound calcium ion concentration is reduced due to counterion binding on the micelle. The micelles also act as a sink for surfactant molecules and, thus, reduce the concentration of surfactant monomer in solution. Modeling micellization and 2949

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Crystal Growth & Design

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related phenomena in order to estimate the activity of the surfactant monomers and counterions can be performed using a series of models to determine the concentration of monomers in the solutionmicelle equilibrium, and the concentration of the counterions in the solution phase required for the precipitation. The compositions of the precipitating species in each phase are estimated using the pseudophase separation theory and regular solution theory, as discussed elsewhere.21,22 The pseudophase separation theory assumes that micelles are a new phase that is in equilibrium with the solution phase. The phase equilibrium can then be modeled with thermodynamic equilibrium models, with the most commonly used for micellar equilibrium being the regular solution theory.23,24 The model is based on the equivalence of the chemical potential in the two phases,23 Ri γi, m cmci ¼ Xi γi, M cmcM

ð3Þ

With the activity coefficients in the micelle phase (for a binary surfactant system) being modeled as γ1, M ¼ expðβM X22 Þ

ð4Þ

γ2, M ¼ expðβM X12 Þ

ð5Þ

The previous equations are on a surfactant-only basis, with Ri representing the mole fraction of surfactant i on a surfactant-only basis in the solution phase, Xi representing the mole fraction of surfactant i in the micelle phase, and γi,m and γi,M representing the activity of the surfactant i in the solution phase and micelle phase, respectively. The activity coefficients for the solution phase are not the same as those used in eq 1, since the expressions in eqs 4 and 5 represent a surfactant only basis. γ1,m and γ2,m may be assumed to be unity (e.g., ideal mixing) for the range of concentrations used here.21 cmci is the critical micelle concentration of the pure surfactant i, and cmcM is the critical micelle concentration of the surfactant mixture at its actual composition. The cmc of the pure surfactants depends on the concentration of ions in solution. The effect of the monovalent ions (in this instance sodium) can be taken into account using the CorrinHarkins model25 ln½cmci ¼ K1, i Kg , i ln½Naþ unb

concentrations are determined simultaneously with bound counterion concentrations and cmc values using a recently proposed counterion binding model for sodium and calcium, the species under consideration in this study.16 The model consists of a measured degree of total counterion binding (eq 9) and an equilibrium between individual counterion species bound to the micelle and in solution (eq 10). βT ¼ βCa2þ þ βNaþ ¼ 0:65 ½Naþ b ½Ca2þ ¼ K 2þ b ½S mon ½Ca unb

½Naþ unb

The nucleation rate (J) can be predicted as a function of supersaturation based on the classical nucleation model. The nucleation rate can be described as the number of nuclei formed per unit of time per volume, and it can be expressed in the form of the Arrhenius reaction velocity equation commonly used for the rate of a thermally activated process28 J ¼ A expðΔG=kB TÞ

½Naþ tot ½Naþ unb ½Naþ ¼ b ½NaStot ½S mon ½S mic

ð7Þ

βCa2þ ¼

2ð½Ca2þ tot ½Ca2þ unb Þ 2½Ca2þ b ¼ ½NaStot ½S mon ½S mic

ð8Þ

In these equations the subscript tot indicates the total amount of the specie in the system in any form. The unbound counterion

ð12Þ

where A is an empirical constant, kB is the Bolzmann constant, and ΔG is the Gibbs free energy change per molecule on formation of a nuclei, defined as ΔG ¼

þ

βNaþ ¼

ð10Þ

In these equations the subscript unb indicates the concentration of ions in the solution pseudophase, b the concentration of bound counterions, and mon the concentration of surfactant in the solution pseudophase. We assume that the counterion binding to the mixed micelles in binary mixed anionic surfactant systems is the same as that in single anionic surfactant systems; that is, eq 9 applies to all systems because both the head groups and the surfactant backbones of the molecules are similar.26,27 Above the supersaturation ratio, this theory allows each individual precipitating surfactant monomer concentration to be calculated for the binary mixed anionic surfactant systems even when a mixed micelle is formed. The supersaturation ratio8 is defined in eq 11 !1=3 ½Ca2þ unb ½S 2mon fCa2þ fS2 ð11Þ S0 ¼ KSP

ð6Þ

where K1,i and Kg,i are model constants and [Na ]unb represents the concentration of sodium ions in the solution phase (those not bound to the micelle phase). The constants depend on the species under consideration. Concentrations of the unbound counterions require modeling of the counterion binding to the negatively charged surface of the micelle. The counterion binding coefficients (βi) reflect the fraction of the negative charge on the surface of the micelles that is negated by the presence of counterions, and therefore, they are defined as

ð9Þ

βγ3 Vm2 f ðθÞ ð2:303kB T log S0 Þ2

ð13Þ

where β is a geometric factor and is equal to 16π/3 for a spherical nucleus, γ is the surface energy in J/m2, and Vm is the molecular volume and is equal to 521.6 Å3 for Ca(DS)2 and 502.8 Å3 for Ca(OBS)2, as predicted by the Connolly molecular volume method in Chem3D Pro 11.0.29 f(θ) is a correction factor; f(θ) = 1 for homogeneous nucleation, and f(θ) = 0.01 for heterogeneous nucleation. Induction time (tind) is a fundamental parameter in crystallization and has frequently been used as a measure of the nucleation event, making the simplifying assumption that it can be considered to be inversely proportional to the rate of nucleation.28 The induction time is a function of the supersaturation ratio (S0); several groups have described investigations into the relationship between the induction time for precipitation and the degree of supersaturation for various crystal forms.6,3032 On the basis of the classical homogeneous nucleation model, the induction time can be written with respect to the 2950



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Figure 2. Dependence of the induction time on the supersaturation ratio for NaDS precipitating by CaCl2 at 30 °C.

energy of the nucleus. If a larger amount of energy is required to form a stable nucleus, then a larger time is required to have sufficient nuclei in the solution to detect. However, prediction using the relationship above has been suggested to be valid only for relatively high supersaturation ratios.35

’ RESULTS AND DISCUSSION Precipitation of Single Anionic Surfactant Systems by CaCl2. NaDS was chosen to investigate single anionic surfactant

Figure 1. Selected turbidity curves by precipitation of NaDS with CaCl2 (a) below and (b) above the cmc at 30 °C with varying supersaturation ratios, S0.

supersaturation ratio as follows28,33 " log tind

# γ3 µ T 3 ðlog2 S0 Þ

ð14Þ

Anionic surfactant precipitation with hardness ions has been found to occur in the range of seconds to minutes.6,34 A study of nucleation rate is very difficult in a conventional laboratory. However, the nucleation rate can be approximated by using the relationship between the induction time and supersaturation ratios, which can be used to approximate the interfacial energy of nuclei and free energy barrier. Equations 1214 suggest that the plot between (log tind) and the inverse of (log2 S0) at a specific temperature yields a linear function with slope related to the nucleation rate, which can also be used to estimate the surface

precipitation systems, since NaDS has been widely used in various surfactant applications and since the solubility product (KSP) of its precipitate, Ca(DS)2, is lower than the KSP of the other two calcium salts, Ca(OBS)2 and Ca(DeS)2, used in this study. Selected experimental results from the online turbidity measurement are shown in Figure 1. This figure shows the responses of the turbidity, as Ca(DS)2 is precipitated both below (a) and above (b) the cmc of the mixture. The induction time is determined as the time elapsed between the addition of calcium (zero seconds) and the appearance of the precipitate, which results in a sudden increase in the turbidity. Both below and above the cmc the induction time increases as the supersaturation ratio decreases. However above the cmc, the induction time is increasing even while the total surfactant concentration is increasing. This can be explained by the reduction in the concentration of the ions in the precipitating species (monomer surfactant and unbound calcium) because of micellization and counterion binding. The induction time results for all systems studied in this work are shown in the Supporting Information. A plot of induction time against the supersaturation ratio of Ca(DS)2 is shown in Figure 2. Figure 2 shows that precipitation in the single surfactant system usually occurs within 2 min or less. The time required to nucleate Ca(DS)2 becomes very small when the supersaturation ratio approaches a high value (for instance when the supersaturation ratio is over 3) whether the system is below or above the cmc. The relationship between the induction time and the supersaturation ratio is the same above and below the cmc, which indicates that the micelles in solution are not 2951



Figure 3. Precipitation phase boundary of NaDS precipitated by CaCl2, lines of constant supersaturation, and the corresponding induction times at 30 °C.

Figure 4. Measurement and modeling of the precipitation phase boundary of Ca(DS)2 at 30 °C in pure NaDS solutions and in NaDS/ NaOBS systems.

acting as a template for nucleation of precipitate. In other words, the time required to precipitate Ca(DS)2 is a function of supersaturation ratio only with respect to the amount of dodecylsulfate monomers ([DS]mon) and unbound calcium ions ([Ca2þ]unb) in the bulk solution rather than the total concentrations of the species. Figure 3 shows points of constant induction time and lines of constant supersaturation, both plotted on the precipitation phase boundary plot. Small induction time curves are far away from the equilibrium curve while large induction times occur closer to the phase boundary (where the supersaturation ratio, S0 = 1). The results indicate that the induction time is the same function of the supersaturation ratio both below and above the cmc even

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Figure 5. Dependence of the induction time on the supersaturation ratio for binary mixed NaDS/NaOBS systems precipitating by CaCl2 for 25% and 50% NaDS molar ratios and a supersaturation ratio based on Ca(OBS)2, at 30 °C.

though induction time contours above the cmc have been shifted slightly higher relative to the phase boundary compared to below the cmc: the shift of the induction time curves is the same as the shift in the constant S0 curves. Precipitation of NaDS/NaOBS Systems by CaCl2. Determination of the precipitating species in mixtures of NaDS, NaOBS, and hardness ions is complex. The solubility products of Ca(DS)2 and Ca(OBS)2 are relatively close to each other at 30 °C (in the same order of magnitude, 1010), and the cmc values of the sodium surfactants are also similar: 7.9 mM and 12.0 mM for NaDS and NaOBS solutions at 30 °C, respectively. In cases where the concentration of NaDS is larger than the concentration of NaOBS, Ca(DS)2 will usually precipitate. Measured and modeled phase boundaries for the mixed surfactant system at 50% NaDS and the pure Ca(DS)2 system (when plotted as the calcium content required for a certain concentration of NaDS to precipitate) are plotted in Figure 4. It can be seen that the boundaries for the pure and mixed surfactant systems differ appreciably above the cmc because of the difference in the cmc values of the pure and mixed systems. This helps demonstrate a major contributing factor between the difference in induction times between pure and mixed surfactant systems for a constant total surfactant loading. Creating a mixed surfactant system not only lowers the solution concentration of the precipitating species (since some of the surfactant is now a different anion than in the crystal lattice) but also modifies the thermodynamics of the system above the cmc, thus also modifying the supersaturation ratio of the precipitating species. It should be noted that the modeled precipitation phase boundary is very close to the experimental data as the concentration of surfactant approaches zero, but the deviation between the model and the measurements increases up to the point of the cmc. It is expected that the extended DebyeHuckel activity coefficient model should be able to fit the activity coefficient of calcium ions across the range of concentrations studied here (since this model was parametrized largely though the use of thermodynamic data for small ions) but may give slightly poorer 2952



Figure 6. Dependence of the induction time on the supersaturation ratio for binary mixed NaDS/NaOBS systems precipitating by CaCl2 for 50%, 75%, and 100% NaDS molar ratios, and supersaturation ratio based on Ca(DS)2, at 30 °C.

estimates for the activities of the surfactant monomers for moderate concentrations (larger than 1 mM) of these species. This suggests accurate activity predictions at low surfactant concentrations (where the required calcium content to achieve precipitation is high) but poorer results closer to the cmc, where the calcium ion activity coefficient approaches unity (since the calcium concentration is of the order of 0.01 mM) but the surfactant monomer concentration is larger. Since either Ca(DS)2 or Ca(OBS)2 may have the larger supersaturation ratio depending on the solution composition, the plot of induction time has been divided into two sets of data based on Ca(OBS)2 precipitation when its supersaturation ratio is larger (Figure 5) and based on Ca(DS)2 precipitation (Figure 6) when its supersaturation ratio is larger. These figures demonstrate the relationship between induction time and supersaturation ratio for binary mixed NaDS/NaOBS systems precipitated by CaCl2 for three different molar ratios of DS/OBS and demonstrating a wide range of calcium chloride concentrations and a wide range of total surfactant concentrations below and above the cmc values. Figure 5 shows the induction time of NaDS/NaOBS systems precipitated by CaCl2 at a range of 25% NaDS and some data from the 50% NaDS system (the cases where a comparison of the supersaturation ratios of the two species supports the precipitation of the OBS salt) versus the supersaturation ratio calculated with respect to Ca(OBS)2. The induction time of the mixed anionic surfactant precipitation at this range of molar ratios of NaDS/NaOBS systems is similar to the pure system of NaDS, so no improvement in the hardness tolerance is suggested for these solutions. Figure 6 shows the induction time of NaDS/NaOBS systems precipitated by CaCl2 versus the supersaturation ratio calculated with respect to Ca(DS)2 at compositions of 75% NaDS, and also the 50% NaDS data where supersaturation ratios suggest the DS salt should precipitate. The induction time for pure Ca(DS)2 precipitation from pure NaDS systems is also plotted in Figure 6 in order to compare the precipitation behavior between pure and mixed systems. It can be observed that the induction time at this range of molar ratios of NaDS/NaOBS systems is slightly larger

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Figure 7. Dependence of the induction time on the supersaturation ratio for binary mixed NaDS/NaDeS systems precipitating by CaCl2 at 30 °C.

than the induction time in pure NaDS systems even for the same supersaturation ratio value. Several points of experimental data, tabulated in the Supporting Information, are not plotted in the figure because their supersaturation ratio is sufficiently small that plotting the point would create too large a range for the induction time axis of this graph. Soontravanich and Scamehorn showed that the 6065% NaDS molar ratio in the binary mixed NaDS/ NaOBS systems is the range of the optimal molar ratio that results in the maximum increase in the induction time.6 An increase in the induction time can also be noted in this work over the range 5075% NaDS molar ratio in the mixed NaDS/NaOBS systems. For clarity, the supersaturation ratios of the individual surfactant species have been calculated separately to observe which surfactant salt is likely to be precipitating, and all experimental data for all systems are tabulated in the Supporting Information. There are some outliers in the data plotted in Figure 6; it is possible that these points are due to the other salt form (Ca(OBS)2) precipitating; however, this salt form has a lower supersaturation ratio than Ca(DS)2 under these conditions. At 75% NaDS (25% NaOBS) the supersaturation ratio with respect to Ca(DS)2 is significantly larger than the supersaturation ratio with respect to Ca(OBS)2. In this case, the induction time is significantly higher than others, even though the supersaturation ratio with respect to Ca(DS)2 is large. The inhibition of binary anionic surfactant mixtures has been observed in most of the experimental data, even though the supersaturation ratio with respect to Ca(DS)2 is relatively high. The precipitation behavior at 75% NaDS molar ratio is interesting with respect to what delays the precipitate forming, because the same behavior was not observed in 75% NaOBS, even though both surfactants have a similar structure and solubility. It should be noted that some data points for the induction time at 75% NaDS molar ratio are strongly scattered, and this could be due to small inaccuracies in the model prediction of the phase boundary at this composition. Precipitation of NaDS/NaDeS Systems by CaCl2. The relationship between induction time and supersaturation ratio is shown for the binary mixed NaDS/NaDeS systems precipitated by CaCl2 in Figure 7. The precipitation trend is similar to 2953



Figure 8. Variation in the induction time as a function of supersaturation ratio for the binary mixed NaDS/NaDeS systems precipitating by CaCl2 at 30 °C.

that of the single anionic surfactant systems because there will be only Ca(DS)2 precipitating out from the mixtures. Only Ca(DS)2 precipitates from any of the mixtures investigated due to the large difference between the solubility products of Ca(DS)2 and Ca(DeS)2, which make all NaDS/NaDeS systems in this work below the precipitation boundary for Ca(DeS)2. Thus, it is only necessary to refer to supersaturation ratios with respect to Ca(DS)2 in the following discussion. Figure 7 shows only one function of induction time with respect to supersaturation ratio for all NaDS/NaDeS molar ratios; this not only implies that the inhibition or disruption of mixed anionic surfactant precipitation due to the different tail length might be wrong, but it also argues against suggestions that the second surfactant monomers interfere with the surface of the Ca(DS)2 nucleus.6,14 Thus, the induction time of binary mixed NaDS/NaDeS systems precipitated with CaCl2 at a particular value of supersaturation is equal (to within the accuracy of the measurements) to the induction time of single NaDS systems precipitated with CaCl2 at the same supersaturation value. The lack of any kinetic inhibition in these systems is possible due to the rapidly formed precipitate crystals being unable to distinguish effectively between the Ca(DS)2 units at the surface of the crystal and the adsorbed Ca(DeS)2 units (due to the aliphatic tails of the surfactant molecules being only semicrystalline in the precipitate), and hence, the decyl sulfate ions do not act effectively as inhibitors. The induction time for precipitation of mixed NaDS/NaDeS systems by CaCl2 tends to be larger as the molar ratio of NaDS is decreased compared to the pure NaDS system of the same total surfactant content. The reduction of the DS molar ratio causes a reduction in the supersaturation ratio due to a smaller amount of DS present in the system, resulting in a larger induction time. Above the cmc of the mixture, there is the added complication that the change in the cmc due to the mixing also changes the supersaturation ratio in the system due to the change in the proportion of surfactant in the monomeric form. Estimation of Kinetic Parameters of Anionic Surfactant Precipitation. Figure 8 shows the relationship between induction time and supersaturation ratio for mixed NaDS/NaDeS

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Figure 9. Variation in the induction time as a function of supersaturation ratio for the binary mixed NaDS/NaOBS systems precipitated by CaCl2 at 30 °C, where S0 is based on Ca(OBS)2.

Table 1. Interfacial Energy Predicted from eq 12 for Calcium Surfactant Salt Precipitation at 30°C interfacial expected

energy,

pre-exp

precipitate

γ (mJ m2)

factor (A)

pure NaDS solution NaDS/NaDeS mixtures

Ca(DS)2

1.84 ( 0.40

15.08

for all molar ratios studied

Ca(DS)2

2.25 ( 0.40

17.13

25% NaDS (OBS based)

Ca(OBS)2

1.87 ( 0.18

9.05

50% NaDS (OBS based)

Ca(OBS)2

2.00 ( 0.18

21.84

50% NaDS (DS based)

Ca(DS)2

3.08 ( 0.40

14.05

75% NaDS (DS based)

Ca(DS)2

3.38 ( 0.40

16.87

system

NaDS/NaOBS mixtures

systems plotted to confirm the relationship in eq 14. The scattered experimental data is probably due to the stochastic nature of nucleation; however, a linear relationship can still be observed from the data, yielding a slope of 0.0581 ( 0.031 with an intercept value of 1.234 ( 0.154. This analysis allows the interfacial energy to be estimated as 2.2 ( 0.4 mJ/m2. Similar analysis of the binary mixed NaDS/NaOBS systems precipitated by CaCl2 has also been performed; however, the analysis in this case depends on the precipitating species (either Ca(DS)2 or Ca(OBS)2) and also on composition in the case of Ca(DS)2 systems. There may be a small effect of composition on induction time (Figure 9) when Ca(OBS)2 is the precipitating species; however, the difference seen in this figure is not statistically significant. Approximate interfacial energy values for all systems can be predicted from the slope of the relationship between induction time and supersaturation ratio, and these are tabulated in Table 1. In these calculations, we have assumed homogeneous nucleation, since the supersaturation values are large for the majority of the experiments, the stock solutions were prepared carefully to avoid 2954


Crystal Growth & Design the presence of foreign particles, and all glassware used was carefully cleaned and dried before each experiment. It should be noted that the accuracy of these values will depend on the validity of the assumptions in classical nucleation theory, and values should be used only as a guide to real surface energies. A large value of interfacial energy indicates a large time required to initiate precipitation of the calcium surfactant salt. For instance, the energies required to form the nuclei of Ca(DS)2 in pure systems and in mixed NaDS/NaDeS are equivalent to each other, given the uncertainty of the interfacial energy value. The energy required to form the nuclei of Ca(OBS)2 at 25% and 50% NaDS (but when the supersaturation ratio is based on Ca(OBS)2) is close to that of Ca(DS)2. Hence, Ca(OBS)2 and Ca(DS)2 precipitation by CaCl2 should follow a similar trend, which may be due to their similar solubility product and structure. The energy required to form the nuclei of Ca(DS)2 from the 5075% NaDS molar ratio system in NaDS/NaOBS mixtures is larger compared to the interfacial energy value with respect to Ca(DS)2 from pure or NaDS/NaDeS systems, and the difference is indicative of the inhibition of precipitation in mixed NaDS/ NaOBS mixtures.

’ CONCLUSIONS The precipitation of single anionic surfactant precipitated by CaCl2 at a specific temperature depends only on the supersaturation of the precipitating species in the bulk solution both below and above the cmc, as can be seen from the induction time being a function only of supersaturation ratio, defined on the basis of calcium concentration. As surfactant concentration increases above the cmc of the sodium form of the surfactant, then the concentration of the anionic surfactant monomers decreases as the unbound sodium ion content increases, due to dissociation from the surfactant molecule; increased sodium ion contents decrease the cmc, as given via the CorrinHarkins relation. In addition, a fraction of calcium ions are bound to the charged micelles, reducing the amount of unbound calcium ions in the bulk solution. For mixtures of NaDS and NaDeS precipitated by CaCl2, the induction time is only a function of the supersaturation ratio, calculated on the basis of Ca(DS)2. From the relationship between the induction time and the supersaturation ratio, it can be concluded that only Ca(DS)2 will precipitate out from the mixtures, because the solubility product of Ca(DS)2 is much smaller than the solubility product of Ca(DeS)2. The difference in the number of carbon atoms in the surfactant backbone in the surfactant mixture does not lead to inhibition, perhaps because the crystal cannot distinguish between the different surfactants. For the mixed NaDS/NaOBS systems precipitated by CaCl2, the precipitation of calcium surfactant salts can be considered on the basis of either Ca(DS)2 or Ca(OBS)2. Precipitation of Ca(OBS)2 occurs in the systems of 050% NaDS molar ratio. The induction times for Ca(OBS)2 precipitation appear to be the same function of induction time whenever Ca(OBS)2 precipitates. In this range, the inhibition of precipitation is not found in the mixed NaDS/NaOBS systems. For precipitation of Ca(DS)2 in the systems of 50100% molar ratio NaDS/NaOBS mixtures, the induction time is not the same function of supersaturation ratio for the pure Ca(DS)2 systems. In this case, some inhibition of precipitation is observed, as the induction time is larger than that in the mixed system at the same degree of supersaturation with respect to Ca(DS)2.

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’ ASSOCIATED CONTENT

bS

Supporting Information. Tables showing a summary of induction times of single NaDS systems precipitated by CaCl2 corresponding to its supersaturation ratio at 30 °C; induction time vs supersaturation ratio for binary mixed NaDS/NaDeS systems precipitated by CaCl2 at 30 °C; and induction time vs supersaturation ratio for binary mixed NaDS/NaOBS systems precipitated by CaCl2 at 30 °C. S0 is given for both possible sodium salts. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Assoc. Prof. Adrian E. Flood, School of Chemical Engineering, Suranaree University of Technology, 111 University Ave., Muang District, Nakhon Ratchasima 30000, Thailand. Phone: 66 44224497. Fax: 66 44224609. E-mail: adrianfl@sut.ac.th.

’ ACKNOWLEDGMENT The authors acknowledge the Thailand Research Fund for a scholarship and research funding for A.M. through the Royal Golden Jubilee Ph.D. program, Grant No. PHD/0177/2547. Funds from the Institute of Applied Surfactant Research at the University of Oklahoma were also used in support of this research; sponsors of the institute are Akzo Nobel, Church & Dwight, Clorox, Conoco/Phillips, Ecolab, Halliburton Services, Huntsman, Oxiteno, Procter & Gamble, Sasol, S.C. Johnson, and Shell Chemical. The authors also thank Professor John F. Scamehorn of the University of Oklahoma for valuable comments regarding micellization in the presence of counterions. ’ REFERENCES (1) Zapf, A.; Beck, R.; Platz, G.; Hoffmann, H. Adv. Colloid Interface Sci. 2003, 100, 349–380. (2) Crutchfield, M. M. J. Am. Oil Chem. Soc. 1978, 55, 58–65. (3) Hollingsworth, M. W. J. Am. Oil Chem. Soc. 1978, 55, 49–51. (4) Rodriguez, C. H.; Scamehorn, J. F. J. Surf. Deterg. 1999, 2, 17–28. (5) Rodriguez, C. H.; Scamehorn, J. F. J. Surf. Deterg. 2001, 4, 15–26. (6) Soontravanich, S.; Scamehorn, J. F. J. Surf. Deterg. 2010, 13, 1–11. (7) Stellner, K. L.; Scamehorn, J. F. Langmuir 1989, 5, 70–77. (8) Stellner, K. L.; Scamehorn, J. F. Langmuir 1989, 5, 77–84. (9) Gerbacia, W. E. F. J. Colloid Interface Sci. 1983, 93, 556–559. (10) Kallay, N.; Pastuovic, M.; Matijevic, E. J. Colloid Interface Sci. 1985, 106, 452–458. (11) Miyamoto, S. Bull. Chem. Soc. Jpn. 1960, 33, 371–375. (12) Noïk, C.; Baviere, M.; Defives, D. J. Colloid Interface Sci. 1987, 115, 36–45. (13) Peacock, J. M.; Matijevi, E. J. Colloid Interface Sci. 1980, 77, 548–554. (14) Rodriguez, C. H.; Lowery, L. H.; Scamehorn, J. F.; Harwell, J. H. J. Surf. Deterg. 2001, 4, 1–14. (15) Shinoda, K.; Hirai, T. J. Phys. Chem. 1977, 81, 1842–1845. (16) Maneedaeng, A.; Haller, K. J.; Grady, B. P.; Flood, A. E. J. Colloid Interface Sci. 2011, 356, 598–604. (17) Stainsby, G.; Alexander, A. E. Trans. Faraday Soc. 1950, 46, 587–597. (18) Davies, C. W.; Shedlovsky, T. J. Electrochem. Soc. 1964, 111, 85–86. (19) Klotz, I. M.; Rosenberg, R. M. Chemical Thermodynamics; John Wiley & Sons: Hoboken, NJ, 2008. (20) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1959. 2955



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