sta

ABSTRACT: Isoperibol calorimetry was used to measure therates of precipitation for aqueous solutions of several anionicsurfactants with calcium and of anionic and cationic surfac-tants. A monomer concentration-dependent supersaturationratio was used to describe the relative rates of precipitationfor the surfactant systems studied. This supersaturation ratioallows for the relative rates of precipitation of any surfactantsolution to be compared whether micelles are present in solu-tion or not. In general, as the supersaturation ratio increases,the rate of precipitation decreases and the induction timedecreases, both above and below the critical micelle concen-tration (CMC). The rate of precipitation of sodium dodecyl sul-fate (SDS) with dodecyl pyridinium chloride is much slowerthan the rate of precipitation of the anionic surfactants withcalcium for similar supersaturation ratios. The rate of precipi-tation of SDS with calcium is slightly faster than the rate of pre-cipitation of sodium octyl benzene sulfonate for similar super-saturation ratios. Studies of precipitate crystals, conductedusing image analysis, showed that size and shape dependedon the initial supersaturation, the precipitating surfactant mol-ecule, and the extent of aging (until an equilibrium size andshape was reached). Also, differences in the appearance ofcrystals formed from solutions above and below the CMCwere observed. These were most likely due to the differencein supersaturation of these solutions. The crystals formed dueto precipitation of SDS with calcium at a concentration abovethe CMC formed flat trapezoidal, rhombic, and hexagonalshapes. These aged into clusters by 1 wk. For a solution thatwas precipitated at concentrations beginning below the CMC,the crystals began as elongated and rhombic flat plates andaged into trapezoidal, rhombic, and needle-like structures.

Paper no. S1123 in JSD 4, 114 (January 2001).

KEY WORDS: Anionic surfactants, calorimetry, cationic sur-factants, kinetics of precipitation, surfactant precipitation.

An important characteristic of ionic surfactants, which caninhibit their use in many applications, is their tendency toprecipitate from aqueous solutions. In detergency, surfac-tants are used to aid in the removal of oily soil and in thesuspension of solids in a washing liquid. In hard water(water containing multivalent cations), anionic surfactantstend to precipitate, and then they are no longer available to

participate in the cleaning process. Builders are commonlyused to prevent precipitation in anionic surfactant deter-gency systems (1,2). In all-purpose laundry detergents,washing and softening the clothes simultaneously in thewash cycle is a goal. Anionic surfactants are generally neces-sary for the removal of some soil types, and cationic surfac-tants for fabric softening. These dissimilar surfactants canprecipitate together from solution leading to a residue anda decrease in cleaning action. Other applications wheresurfactant precipitation can be detrimental are surfactant-based separations (3) and enhanced oil recovery (4). Sur-factant precipitation can be advantageous in some applica-tions such as surfactant recovery by crystallization (5,6).Because of the tendency for ionic surfactants to precipitate,surfactant precipitation behavior and the ability to manipu-late this behavior are extremely important.

Numerous research efforts have studied the thermody-namics of surfactant precipitation (e.g., Krafft temperatureor hardness tolerance studies) (4); but few studies havebeen directed at understanding the kinetics of the precipi-tation reaction. Precipitation kinetics, not thermodynamics,can dictate the influence of precipitation in processes whichutilize surfactants. For example in laundry detergency,whether surfactants actually precipitate in a wash cycle (e.g.,20 min) is important, not whether precipitation occurs atequilibrium (which may not occur for much longer times).

In this work, the rates of precipitation of single-compo-nent anionic surfactant/calcium and anionic surfactant/cationic surfactant systems are measured using calorimetry.The effect of micelles on the precipitation rate is deducedfrom experiments above and below the critical micelle con-centration (CMC). Image analyses are used to characterizethe crystals formed in these systems. This is the first of a se-ries of three papers. In the second paper, rates of precipita-tion of well-defined mixtures of anionic surfactants are pre-sented. In the third paper, atomic force microscope scansof these single components and mixed systems are pre-sented and used to interpret rate results.

EXPERIMENTAL PROCEDURES

Materials. The two anionic surfactants used in this studywere sodium dodecyl sulfate (SDS) and sodium octyl ben-zene sulfonate (SOBS). The cationic surfactant used was

Copyright 2001 by AOCS Press Journal of Surfactants and Detergents, Vol. 4, No. 1 (January 2001) 1

*To whom correspondence should be addressed at the University ofOklahoma, The Energy Center, 100 E. Boyd, Norman, OK 73019-1004.E-mail: [email protected]

Kinetics of Precipitation of Surfactants. I. Anionic Surfactantswith Calcium and with Cationic Surfactants

Cheryl H. Rodriguez, Lori H. Lowery, John F. Scamehorn*, and Jeffrey H. HarwellInstitute for Applied Surfactant Research, University of Oklahoma, Norman, Oklahoma 73019

dodecyl pyridinium chloride (DPC). Electrophoresis/high-performance liquid chromatography-grade SDS was at least99% pure and was obtained from Fisher Scientific (Pitts-burgh, PA). It was further purified by recrystallization fromwater, then from methanol, followed by drying under avacuum at 30C. The SOBS was obtained from Aldrich (Mil-waukee, WI) at a purity of 97%. The SOBS was recrystallizedfirst from methanol, and then from water. It was then rinsedwith cold methanol and dried under vacuum at 30C. Tech-nical-grade DPC was purchased from Pfaltz & Bauer (Water-bury, CT). The DPC was purified by recrystallization froman 80:20 mixture of petroleum ether/ethanol (Fisher Sci-entific). This was repeated three times, yielding white crys-tals when dried under vacuum at low heat. Reagent-gradecalcium chloride was obtained from Fisher Scientific andwas used as received. Water was double-deionized.

Methods. (i) Precipitation phase boundaries. For the SOBS/CaCl2 system, a series of solutions was made for each surfac-tant concentration with varying CaCl2 concentrations. Thetemperature of these solutions was first lowered to nearly0C for 24 h to force precipitation (711). Surfactant solu-tions can stay supersaturated for long periods of time(12,13) resulting in nonequilibrium apparent hardness tol-erances. The temperature was then held constant at 30Cfor 4 d while gently shaking the samples daily to ensureequilibrium (8). For each series of solutions of increasingcalcium concentration, some samples would still containcrystals at the end of 4 d, whereas others would have be-come clear. The average of the highest calcium concentra-tion yielding clear solutions and the lowest calcium concen-tration yielding turbid solutions is considered the hardnesstolerance at that surfactant concentration (on the phaseboundary). The SDS/CaCl2 precipitation phase boundarywas obtained from Stellner and Scamehorn (8). TheSDS/DPC precipitation phase boundary was obtained fromStellner et al. (10).

(ii) Calorimetry. A Tronac (Orem, UT) model 458/558calorimeter was used in isoperibol mode to measure theheat of reaction as a function of time. Isoperibol calorime-try is a nearly adiabatic process. However, a small amount ofheat is transferred from the reaction vessel to the water bathand is added to the reaction vessel by the stirrer and ther-mistors. Over short lengths of time, this heat leak can bemodeled as a linear function of the reaction vessel tempera-ture. The temperature of the water bath at 30C can bemaintained within 0.025C using a Tronac PTC-41 temper-ature controller. A diagram of the reaction vessel setup isshown in Scheme 1. The rates of precipitation of SDS orSOBS with calcium and of mixtures of SDS with DPC weremeasured. Approximately 48 g of anionic surfactant solu-tion was placed in the reaction vessel, and approximately 2g of concentrated calcium chloride solution or concen-trated DPC solution was injected into a soft glass ampoule,which was then sealed with a Microflame (Foxboro, MA) bu-tane torch and placed in the ampoule holder-stirrer. The re-action vessel was clamped into place, and the system allowedto equilibrate with the water bath temperature. The am-

poule could then be broken with the hammer to allow in-stantaneous mixing of its contents with the solution in thereaction vessel by vigorous stirring. A program written byLopata (14) to run the calorimeter for buret titration wasmodified to run the calorimeter with the ampoule method(15).

(iii) Heats of reaction. When an anionic surfactant solutionis mixed with a counterion, the apparent experimental heatof reaction is the total heat released from the precipitationreaction, dilution of the ampoule contents, dilution of thereaction vessel contents, breaking of the ampoule, and insome cases, micelle formation and dissociation. Additionalexperiments must be done to determine these extraneousheats. The heat of breaking the ampoule is measured bybreaking an ampoule containing water into the reaction ves-sel containing water. Heat of dilution of the ampoule solu-tion is measured by breaking either the CaCl2 or DPC (belowthe CMC) ampoule solution into water. The heat of demicel-lization of DPC is found by breaking an ampoule of micellarDPC solution into water, and then subtracting the heat of di-lution from the total heat obtained. The heat of dilution ofthe reaction vessel solution is measured by breaking waterinto the appropriate reaction vessel solution below the CMC.The heat of micellization upon introduction of CaCl2 ismeasured by breaking a CaCl2 ampoule solution into a sur-factant solution that is above the CMC but outside the pre-cipitation region. This results in the formation of additionalmicelles without precipitation. Heat of mixed micelle forma-tion occurs in the SDS/DPC system and can be measured bybreaking a DPC ampoule solution into an SDS solution thatis above the CMC and outside of the precipitation phaseboundary. Heats of surfactant precipitation are measured bybreaking an ampoule containing a counterion or cationicsurfactant solution into the reaction vessel surfactant solu-tion. The decrease in the CMC upon addition of a counte-rion is calculated using a model presented by Stellner andScamehorn (9). A Microscribe 450 (San Jose, CA) chartrecorder was used to plot the temperature difference be-

2 C.H. RODRIGUEZ ET AL.

Journal of Surfactants and Detergents, Vol. 4, No. 1 (January 2001)

SCHEME 1

tween the reaction vessel and the water bath, in voltage, vs.time.

For each run, the average heat capacity, Cp, is obtainedby adding a known amount of heat for a known amount oftime before and after the reaction. Then, by using this heatcapacity, the overall heat occurring during a reaction, QT,can be obtained:

QT = Cp T [1]

where T is the total temperature change during a reactionminus the temperature change due to the heat leak fromthe reaction vessel. For systems that start above the CMC,demicellization occurs as the precipitation reaction pro-ceeds. The heat associated with this process is subtractedfrom QT as a function of time. The concentration of mi-celles in solution can be found at each point during areaction using the same model as that by Stellner andScamehorn (9) along with a model of the precipitation re-action pathway (10,16,17). The heat due only to precipita-tion at each point along the reaction pathway can thus beseparated from all of the extraneous heats associated with acalorimeter run.

(iv) Conductivity. Conductivity can be used to follow theprecipitation reactions of some of the systems studied andto verify the calorimetric results qualitatively. As precipita-tion occurs, ions are removed from the system, which de-creases the total conductivity of the system. An SDS solutionwas placed in a side arm flask kept at 30C. The solution wasstirred and nitrogen was blown into the flask to reduce theabsorption of carbon dioxide into the solution (18). A con-centrated, 30C CaCl2 or DPC solution was quickly addedto the SDS solution. An Orion (Beverley, MA) conductivitymeter model 1-1 with a total conductivity probe was used tomeasure the conductivity of the solution as a function oftime during the precipitation reaction.

(v) Optical analysis. A qualitative study of the crystal sizesand shapes at various times after mixing was conducted byimage analysis. The reactants were mixed at 30C. After mix-ing the reactants, crystal size and shapes were analyzed at 4min of vigorous stirring via image analysis. The crystals werethen allowed to age for 1 d and 1 wk before analysis was donewith image analysis. A Nikon (Tokyo, Japan) microscope in-terfaced with a Gateway (North Sioux City, SD) computerutilizing Optimas (Edmonds, WA) software was used.

RESULTS AND DISCUSSION

Precipitation phase boundaries. Establishment of precipitationphase boundaries is necessary to determine the regionwhere precipitation will occur for each system, and they canbe used to determine the theoretical equilibrium conditionfor each precipitation reaction (i.e., solution compositionwhen precipitation is complete). The precipitation phaseboundaries for SDS and SOBS with calcium are shown inFigures 1 (8) and 2. Both experimental and theoreticalmodel results are shown on these phase boundaries. It iswell-known that hardness tolerance reaches a minimum at

the CMC. Below the CMC, as the total anionic surfactantconcentration increases, the concentration of calcium re-quired for precipitation to occur decreases. The solubilityproduct relationship that describes this precipitation for amonovalent surfactant with calcium is shown in Equation 2:

KSP = [S]2 [Ca2+] fS

2 fCa [2]

where KSP is the activity-based solubility product, [S] is the

anionic surfactant concentration, and [Ca2+] is the calciumion concentration. The parameters fS and fCa are the activ-ity coefficients of the surfactant and calcium, respectively.Along the precipitation phase boundary and above theCMC, a simultaneous equilibrium exists between the surfac-

ANIONIC SURFACTANT PRECIPITATION. PART I 3


FIG. 1. Initial conditions used for the precipitation reactions of sodiumdodecyl sulfate (SDS) with CaCl2 in relation to the SDS/CaCl2 precipi-tation phase boundary (from Ref. 8). Prec., precipitation.

FIG. 2. Initial conditions used for the precipitation reactions ofsodium octyl benzene sulfonate (SOBS) with CaCl2 in relation to theSOBS/CaCl2 precipitation phase boundary.

tant as monomer, in micelles, and in precipitate. This equi-librium for an anionic surfactant with Ca2+ is illustrated inScheme 2. There are also sodium ions in solution due to thedissociation of the surfactant salt, which for clarity are notshown in Scheme 2. Sodium was found not to precipitatethe anionic surfactants studied at the concentration levelsemployed in this paper owing to a lower KSP with calciumthan with sodium (on the order of 1010 as opposed to 104). Precipitation occurs above the CMC when the surfac-tant monomer concentration, along with the unboundcounterion concentration, multiplied by appropriate activ-ity coefficients exceeds the solubility product as shown inEquation 3 (19):

KSP = ([S]mon)

2 [Ca2+]un fS2 fCa [3]

where [S]mon is the anionic surfactant monomer concen-tration and [Ca2+]un is the unbound calcium concentration(calcium not bound to micelles).

Micelles act as sequestering agents for the calcium ions(i.e., the calcium ions bind to the micelles). As more surfac-tant is added to the system, the additional surfactant tendsto form more micelles, reducing [Ca2+]un even further. Thisresults in a minimum in the precipitation phase boundaryat the CMC. From the precipitation phase boundaries inFigures 1 and 2, the CMC for SDS is 0.0067 M (14) and forSOBS is 0.012 M. These values are consistent with the CMCvalues obtained from surface tension measurements: 0.0072M for SDS and 0.012 M for SOBS (20). Several reviews havediscussed the thermodynamics (e.g., phase diagrams orKrafft temperatures) of anionic surfactant precipitationwith metal ions (4,21,22).

The parameters fS and fCa in Equations 2 and 3 can bedescribed by the extended Debye-Huckel expression (23):

log f = A (z)2 I 0.5/(1 + B a I 0.5) 0.3 I [4]

where f can be fS or fCa and the constants A and B are de-pendent on the solvent and the temperature of the solu-

tion. The parameter z is the ion valence, and the parametera is an empirical value based on the diameter of the ion. Val-ues for A and B are tabulated (24), as well as for the con-stant a (24,25). The parameter I is the ionic strength of thesolution, defined as:

I = 0.5 ci zi2 = [NaS] + 3[CaCl2] [5]where ci is the total concentration of ion i in solution, zi isthe valence of ion i, [NaS] is the total anionic surfactantconcentration in solution, and [CaCl2] is the total CaCl2concentration in solution. Below the CMC, the surfactantmonomer can be treated as a simple, strong electrolyte inthe calculation of the ionic strength and activity coeffi-cients. However, there is no universally accepted practicefor the calculation of activity coefficients in a micellar solu-tion. In this study, the anionic surfactants and the CaCl2 inthe micellar solutions are treated as simple, strong elec-trolytes, as our group has done previously (11). Severalother methods have been proposed. One considers the mi-celles as a separate species in solution, contributing only aportion of the actual micelle valence (a shielded micelle)(26). Another treats the micelles as a separate phase, whichtherefore does not contribute to the ionic strength of theaqueous solution (27). Burchfield and Woolley (26) alsodiscuss the work of other researchers who have treated thesurfactant in solution as a simple, strong electrolyte as wehave done here.

If solution concentrations are not large enough to satisfythe solubility product (Eq. 3) and the surfactant concentra-tion lies above the eutectic point, or CMC, the solution willcontain monomer and micelles but will not precipitate atequilibrium. If the solubility product is not satisfied (Eq. 2)and the surfactant concentration is below the CMC, the sur-factant will be present only as monomer. If a solution con-tains a concentration of surfactant and calcium that exceedsthe solubility product, then that solution is supersaturatedand, theoretically, will precipitate until the solution concen-tration lies somewhere along the precipitation phaseboundary (solubility product is exactly satisfied; Eq. 2 or 3is valid). The supersaturated points inside the precipitationphase boundaries in Figures 1 and 2 are the initial condi-tions for the precipitation reactions studied here.

The equilibrium relationships that exist in an anionic/cationic surfactant solution are shown schematically inScheme 3 for a micellar solution in which precipitation hasoccurred. In this case, both the sodium and chloride ionscan be bound onto the micelles, but for clarity they are notshown in this figure. Cationic and anionic surfactant can bepresent as monomer and in mixed micelles. Above the solu-bility product, anionic and cationic surfactant monomerscombine to form precipitate. The solubility product rela-tionship for SDS-DPC precipitation is:

KSP = [S]mon [DP

+]mon f2 [6]

where [DP+]mon is the monomer concentration of the do-decyl pyridinium ion and f is the mean activity coefficientof the solution (10). Below the CMC, all of the surfactant is



SCHEME 2

present as monomer; and as the concentration of one of thesurfactants increases, a lesser concentration of the opposite-charged surfactant is needed to cause precipitate to form.Above the CMC, there are an SDS-rich region and a DPC-rich region as seen in Figure 3 from Stellner et al. (10).Along the SDS-rich branch of the precipitation phaseboundary, as SDS-rich mixed micelles form, they act as se-questering agents for the surfactant monomers, and morecationic surfactant is needed for precipitation. This sametrend is true for the DPC-rich branch. The points lying in-

side the precipitation phase boundary in Figure 3 representthe initial conditions used to measure the kinetics ofSDS/DPC precipitation reactions. Owing in part to thecomplex surfactant mixtures in detergent formulations, re-searchers have experimentally determined precipitationphase boundaries for mixtures of anionic/cationic surfac-tants. Scowen and Leja (28) determined the phase bound-aries for various alkyl quaternary ammonium bromides withdifferent anionic surfactants.

The initial conditions shown in Figures 13 are supersat-urated solutions. Supersaturation is a measure of the excessconcentration of the reactants above the equilibrium solu-bility concentrations (2931). A supersaturated solution canbe prepared by cooling the solution below its saturationtemperature, evaporating the solvent in the solution, or bydirect mixing of two reactants which are of higher concen-tration than their equilibrium solubility (which is done inthis study) (29). The degree of supersaturation and thepresence of foreign materials, or seed crystals, affect theability of the supersaturated solution both to form nucleiand to grow crystals. In this paper, a supersaturation ratio(So) is used to describe the excess concentration of reac-tants above the precipitation phase boundary for an anionicsurfactant precipitating with Ca2+, as follows:

So = ([Ca2+]un ([S

]mon)2 fCa fS

2/KSP)1/3 [7]

Equation 7 only takes into consideration the monomersurfactant concentration and the unbound calcium concen-tration. If the initial solution conditions exactly satisfy thesolubility product, then So = 1. Therefore, the more that Soexceeds unity, the more supersaturated the solution be-comes. The initial presence of micelles removes the surfac-tant and calcium from the monomer phase. The supersatu-ration ratio for the SDS/DPC system is defined as:

So = ([DP+]mon ([S

]mon) (f)2/KSP)

1/2 [8]

Equation 8 is a special case of the general supersaturationratio for monovalent reactants (32).

The supersaturated solutions depicted in Figures 1 and 2will theoretically precipitate until the surfactant and cal-cium concentrations in solution reach some point on theprecipitation phase boundary (solubility product is satis-fied, or So = 1). Since the stoichiometry of the precipitate isinvariant, for defined initial conditions, as precipitation oc-curs the concentration of each precipitating species can becalculated from material balances (defining the reactionpathway). For calcium/SDS, the reaction pathway is de-scribed by Equations 911 (10,16,17):

2[NaS] = 2[S]unr + 2[S]ppt [9]

[CaCl2] = [Ca2+]unr + [Ca

2+]ppt [10]

2[S]ppt = [Ca2+]ppt [11]

where [NaS] is the initial surfactant concentration, [CaCl2]is the initial CaCl2 concentration, [S

]unr is the unreacted(or unprecipitated) surfactant ion concentration, [S]ppt is



SCHEME 3

FIG. 3. Initial conditions used for the precipitation reactions of SDSwith dodecyl pyridinium chloride (DPC) in relation to the SDS/DPCprecipitation phase boundary (from Ref. 10). For other abbreviationsee Figure 1.

the precipitated surfactant concentration, and [Ca2+]unr isthe unreacted calcium concentration. Equations 9 and 10are material balances on surfactant and calcium, respec-tively. Equation 11 defines the stoichiometry of the precipi-tation reaction. Note that [S]unr includes surfactant inboth monomeric and micellar form and [Ca2+]unr includesunbound and bound calcium. Combining these equationsgives the reaction pathway constant, D :

D = 2[NaS] [CaCl2] = 2[S]unr [Ca

2+]unr [12]

The constant D is calculated for the initial conditions. Then,[S]unr is assumed to decrease as the precipitation reactionproceeds. From Equation 12, [Ca2+]unr can be calculatedfor every value of [S]unr given. This continues until the re-action pathway intersects the appropriate precipitationphase boundary (either Eq. 2 or Eq. 3 is satisfied depend-ing on whether micelles are present on the phase bound-ary). At each point along the reaction pathway, the un-reacted component concentrations can be put into thepseudo-phase separation model to calculate the concentra-tion of surfactant in the micelles at that point. This allowsfor the subtraction of the heat of demicellization from theoverall process heat as the surfactant precipitates. The reac-tion pathways for SOBS precipitating with calcium areshown in Figure 4. Similar reaction pathways for SDS pre-cipitating with calcium can be depicted.

The corresponding material balances and reaction path-way equation for a precipitation reaction of a monovalentanionic surfactant with a monovalent cationic surfactant areas follows:

[NaS] = [S]unr + [S]ppt [13]

[DPC]i = [DP+]unr + [DP

+]ppt [14]

[S]ppt = [DP+]ppt [15]

D = [S]unr [DP+]unr [16]

where [DPC]i is the initial DPC concentration, [DP+]unr is

the unreacted DPC concentration, and [DP+]ppt is the pre-cipitated DPC concentration.

Nucleation.There is extensive literature describing crys-tallization as a general phenomenon. Most of these articlesor books address precipitation of inorganic salts, but theycan be extrapolated to other precipitation systems. We willbriefly review some aspects which are relevant to the precip-itation of surfactant salts.

The induction period is the period between the attain-ment of supersaturation and the onset of precipitation, asdetermined visually or by the measurement of some appro-priate physical property. A solution can remain supersatu-rated for a long time. Also, concentrations may have to besome distance above the precipitation phase boundary be-fore spontaneous precipitation will occur in real situations.Many authors have described a metastable zone directlyabove a precipitation phase boundary in which spontaneousnucleation does not readily occur (33). Many factors, suchas thermal history, mechanical action and presence of solidparticulates, affect the metastable zone width (34). Nucle-ation can be either homogeneous (spontaneous), hetero-geneous, or secondary. Homogeneous nucleation occurswhen the nuclei are made up of the precipitating compo-nents. Usually, large supersaturation ratios are required forhomogeneous nucleation to occur (33,35,36). One of thefew studies on the kinetics of surfactant precipitation foundthat, for calcium laurate below the CMC, a supersaturationratio of 5 was required for homogeneous nucleation (35).Subnuclei, or embryos, are thought to form and dissipateconstantly in supersaturated solutions, and an energy bar-rier must be overcome in order for a subnucleus to form acritical nucleus (the smallest nucleus that can grow into acrystal). A critical nucleus can form as a result of randomfree energy or concentration fluctuations in local regionsof a solution (29,37). The structure of a critical nucleus isthought to be either a tiny replica of the crystal it will formor a diffuse body of ions, not yet in the rigid lattice of a crys-tal. Since very few ions are thought to form a critical nu-cleus, it is likely that the critical nucleus does not have thecharacteristics of the bulk crystal (35).

Secondary nucleation occurs when nucleation sites arepresent due to the loss of weak outer layers or weak out-growths of the crystals of the precipitating species, duemostly to collisions with other crystals or the reaction vesselhardware (36,38). There is an adsorbed layer of solute onthe surface of a growing crystal (38), which can be easilyseparated to form new nuclei.

Heterogeneous nucleation occurs when small particlespresent in the system act as nucleation sites for the deposi-tion of the precipitating components. The most active nu-clei are probably in the range of 0.1 to 1.0 m (36). In thiswork, the shattered glass of the ampoule, the stirring rod,thermistors, and reaction vessel walls could act as nucle-ation sites. Thorough discussions of the thermodynamics ofnucleation are given in reviews, including Nyvlt et al. (34)and Adamson (39).



FIG. 4. Reaction pathways for SOBS precipitating with calcium at sev-eral initial solution compositions. The four sets of data show how thecomposition varies from an initial value to the end, where it intersectsthe theory line. For abbreviation see Figure 2.

Crystal growth. Crystal growth can be either diffusion-controlled or surface reaction-controlled. In diffusion-controlled growth, the rate-limiting step is the diffusion ofthe precipitating components from the bulk to the crystalsurface. A model that describes the diffusion mechanismhas been used to describe crystal growth of inorganic saltprecipitation (40) and anionic surfactant precipitation withcalcium (35).

There are three possible mechanisms for surface reac-tion-controlled growth: mononuclear growth, polynucleargrowth, and growth due to a screw dislocation. A new layerof a crystal is started when the precipitating componentsnucleate onto the crystal surface. The first site to become oc-cupied on the surface is a high-energy site and is more diffi-cult to fill than the adjacent sites. If the precipitating com-ponents nucleate onto the surface of a crystal very slowlycompared to the growth of a layer, then each layer is com-pleted before a new layer begins. This is called mononucleargrowth and is the most constrained growth mechanism. Ifsurface nucleation is fast, new layers begin before the old lay-ers are complete. This is called polynuclear growth. A screwdislocation is a surface dislocation that forms when a slip ina crystal plane occurs, pushing up part of the surface layer.This creates a lower-energy site adjacent to the raised layer,removing the need for surface nucleation. The Frank mech-anism (41) describes this mechanism in which the crystal isformed from a single layer, spiraling upward as the precipi-tating species occupy the sites at the step of the screw dislo-cation. A crystal forming due to a screw dislocation can con-tinue growing without inhibition until the supersaturationof the system is satiated. The Frank mechanism is widely ac-cepted and has been seen in several instances (13,42). Thespiral pattern that forms is in many instances representativeof the molecular pattern in the lattice (43), and the stepheights have been found to be some multiple of the unit cellheight (42,43). Atomic force microscopy has been used todetermine the surface structure of Ca(DS)2 crystals (whereDS = dodecyl sulfate anion) precipitated from a 0.020 MSDS, 0.01 M CaCl2 solution, and spiral growth was found(20). The surface structure of Ca(OBS)2 crystals was alsostudied for the same concentrations of surfactant and cal-cium, and many steps representing differing heights werefound on the surface being scanned (20).

Calorimetry. The average heat of micellization upon theintroduction of CaCl2 to an anionic surfactant solution is 812 cal/mol of surfactant-forming micelles. The heat ofdilution of the CaCl2 ampoule solutions was found to be 423 cal/mol CaCl2. The heat of dilution of the DPC am-poule solutions was +275 cal/mol DPC. The heat of demi-cellization of the DPC ampoule solution was found to be+1700 cal/mol demicellized DPC. The heats of reaction ves-sel solution dilution and ampoule breaking were found tobe negligible. The average heat of reaction for SDS precipi-tating with Ca2+ is 7,500 cal/mol surfactant precipitated,for SOBS precipitating with Ca2+ is 4,600 cal/mol surfac-tant precipitated, and for SDS precipitating with DPC is 20,000 cal/mol precipitate formed.

Figure 5 shows the rate of precipitation of SDS with cal-cium for several initial conditions below the CMC, and Fig-ure 6 for initial conditions above the CMC. In both cases, asthe initial supersaturation ratio is decreased, the overall rateof precipitation decreases. Also in both cases, a decrease inthe initial supersaturation ratio results in an increase in theinduction time. Above the CMC, the initial supersaturationratio is based on the monomer SDS concentration and un-bound calcium concentration (Eq. 7). Figure 7 shows a com-parison of the rates of precipitation for a range of supersatu-ration ratios both above and below the CMC. The general



FIG. 5. Precipitation rate curves of SDS with CaCl2 below the criticalmicelle concentration (CMC) at 30C. So, supersaturation ratio; forother abbreviation see Figure 1.

FIG. 6. Precipitation rate curves of SDS with CaCl2 above the CMC at30C. For abbreviations see Figures 1 and 5.

trend is an increase in the precipitation rate as the initial su-persaturation ratio is increased, regardless of whether mi-celles are present. In all of the kinetic data shown in thispaper, mole fraction surfactant precipitated is the amountprecipitated divided by the amount precipitated at equilib-rium; hence, this variable will always approach unity at longenough times. The effect of increasing the degree of super-saturation on the precipitation rate of SOBS precipitatingwith calcium is shown in Figure 8. The initial conditions foreach of these rate curves are above the CMC. The sametrend is seen here as was seen for the precipitation of SDSwith calcium. As the supersaturation ratio increases, the rate

of precipitation increases and the induction time decreases.The rate of precipitation of SOBS with calcium is more than1 min slower than for the precipitation of SDS with calciumfor an initial supersaturation ratio of 5.4.

The effect of increasing the degree of supersaturation onthe precipitation rate of SDS precipitating with DPC isshown in Figure 9. The rate of precipitation for theSDS/DPC surfactant precipitation is much slower than forthe SDS/CaCl2 and the SOBS/CaCl2 systems. The SDS/DPC surfactant precipitation took more than 12 min com-pared with 3 min or less for the SDS/CaCl2 and SOBS/CaCl2 surfactant precipitation rates for similar supersatura-tion ratios. Increasing the degree of supersaturation in theSDS/DPC system increases the rate of precipitation. Also,as seen for the precipitation of the two anionic surfactantswith calcium, as the supersaturation ratio decreases, the in-duction time increases.

The half-lives of the precipitation reactions decrease asthe initial supersaturation ratios increase. Figure 10 showsthis trend for each system studied. Reduced time is definedin this paper as time divided by the half-life. Figures 1113show the extent of precipitation plotted as a function ofreduced time for the SDS/CaCl2, SOBS/CaCl2, and SDS/DPC systems, respectively. This results in a universal pre-cipitation rate curve. For a given system, this universal ratecurve is remarkably independent of supersaturation or thepresence or absence of micelles.

Conductivity. Another method to measure the kinetics ofa precipitation reaction involving ionic species is to measurethe change in the conductivity of the solution with time.When ions form complexes or are incorporated into crystallattices, the conductivity of the solution must decrease.Turnbull (32) outlines a procedure to calculate the concen-tration of an ionic solution from conductivity measure-



FIG. 7. Precipitation rate curves of SDS with CaCl2 at 30C. For ab-breviations see Figures 1 and 5.

FIG. 8. Precipitation rate curves of SOBS with CaCl2 above the CMCat 30C. For abbreviations see Figures 2 and 5.

FIG. 9. Precipitation rate curves of SDS with DPC above the CMC at30C. For abbreviations see Figures 1, 3, and 5.

ments. A qualitative comparison between the reaction ki-netics as determined by isoperibol calorimetry and the con-ductivity of these same solutions is shown in Figures 1416(for SDS/CaCl2) and 17 (for SDS/DPC). One of the mostimportant variables in the determination of the kinetics ofprecipitation is the agitation of the solution. Agitation forthe conductivity experiments was provided by a magneticstir bar. The stirring rate was arbitrarily set at 240 rev/mincompared to 400 rev/min in the calorimeter. Owing to vari-ations in the shape and size of both the reaction vessels andthe stirring mechanisms of the two experimental methods,the exact agitation in the calorimeter could not be simu-

lated in the conductivity experiments. Therefore, slight dis-crepancies may be due to these inconsistencies in the con-ditions rather than inaccuracies in the calorimetric methodfor determining precipitation rates. Figure 14 comparesconductivity and calorimeter runs for an SDS/CaCl2 systembelow the CMC for an initial supersaturation ratio of 3.7.Figures 15 and 16 show the comparisons between calorime-ter runs and conductivity for SDS/CaCl2 systems above theCMC. Other researchers have followed the precipitation



FIG. 10. Half-life as a function of initial supersaturation ratio for allsystems studied at 30C. For abbreviations see Figures 13 and 5.

FIG.11. Extent of precipitation plotted against reduced time for SDSwith CaCl2 at 30C. For abbreviations see Figures 1 and 5.

FIG. 12. Extent of precipitation plotted against reduced time forSOBS with CaCl2 above the CMC at 30C. For abbreviations see Fig-ures 2 and 5.

FIG. 13. Extent of precipitation plotted against reduced time for SDSwith DPC above the CMC at 30C. For abbreviations see Figures 1, 3,and 5.

kinetics of BaSO4 using conductivity and have reported sim-ilar results (31,32). The shapes of the curves from calorime-try and from conductivity are very similar for Figures 1416(though opposite in direction due to the detection meth-ods). These results verify that the precipitation is beingmeasured by calorimetry, not some spurious phenomenonor artifact of the experimental procedure.

A comparison of the calorimetry results with the conduc-tivity for an SDS/DPC system is shown in Figure 17. For thissystem, the presence of swamping electrolyte (0.15 M NaCl)in the solution made the change in the conductivity due toprecipitation very small and therefore difficult to detect.The calorimetric and conductivity results show approxi-

mately qualitative agreement even for this high-ionicstrength system.

Optical analysis of crystals. Image analysis and microscopywere used to obtain visual information about the crystalsfrom single surfactant solutions at various lengths of timeafter precipitation took place. Table 1 relates initial anionicsurfactant and counterion concentrations to aging time, ini-tial supersaturation, and the initial relation of each solutionto the CMC. The solutions listed in this table correspond tothe image analysis pictures shown in Figures 1823. Imageanalysis at 40 magnification was used to view Ca(DS)2 andCa(OBS)2 crystals at 4 min after the surfactant and calciumhad been mixed together. These pictures are shown in Fig-



FIG. 14. Comparison of precipitation rate curves between isoperi-bol calorimetry and conductivity for SDS/CaCl2 below the CMC atSo = 3.7 and 30C. For abbreviations see Figues 1 and 5.

FIG. 15. Comparison of precipitation rate curves between isoperibolcalorimetry and conductivity for SDS/CaCl2 above the CMC at So =4.5 and 30C. For abbreviations see Figures 1 and 5.

FIG. 16. Comparison of precipitation rate curves between isoperibolcalorimetry and conductivity for SDS/CaCl2 above the CMC at So =7.0 and 30C. For abbreviations see Figures 1 and 5.

FIG. 17. Comparison of precipitation rate curves between isoperibolcalorimetry and conductivity for SDS/DPC above the CMC at So = 5.1and 30C. For abbreviations see Figures 1, 3, and 5.

ures 18 and 19 for 0.01 M SDS with 0.008 M CaCl2 and 0.075M SOBS with 0.01 M CaCl2, respectively. The crystals fromthe pure SDS solution are mostly trapezoidal and rhombicin shape, with a few hexagonal shapes. Many crystals fromthe pure SOBS solution are elongated flat plates, many withjagged edges. Some broken-edged trapezoidal shapes arepresent as well. Image analysis was also used to view the crys-tals after aging for 1 wk in solution as shown in Figures 20and 21 at 40 magnification. The crystals from 0.01 M SDSsolution and 0.008 M CaCl2 are mostly clusters as shown inFigure 20. The crystals from 0.075 M SOBS solution and0.01 M CaCl2 are long, clear, and needle-like. The initialconditions for Figures 1820 are below the CMC. Figures 22and 23 show crystals from a 0.001 M SDS and 0.008 M CaCl2solution aged for 4 min and 1 wk, respectively. These con-ditions are above the CMC. The Ca(DS)2 crystals aged for 4 min are mostly elongated with a few rhombic shapes.

Crystals aged for 1 wk are trapezoidal, rhombic, with someneedle-like shapes. There are some broken edges as well, asseen in Figure 22. Several microscope pictures of Ca(DS)2crystals (not included here) have also been taken for an ini-tial SDS concentration of 0.004 M and 0.007 M CaCl2 (ap-proximately at the CMC). After 1 d, mostly needle-like,trapezoidal, and rhombic shapes are seen at 10 and 40magnification. The crystal sizes range from 10 to 150 m.After 1 wk, the crystals have not changed significantly in sizeor shape. Development of crystals below the CMC is differ-ent from the development of crystals above the CMC. Crys-tals forming in a less supersaturated system have been seenpreviously to develop differently from crystals forming in a



FIG. 18. Image analysis picture of Ca(DS)2 crystals at 40 precipitatedfrom a 0.010 M SDS/0.008 M CaCl2 solution; taken 4 min after mixingat 30C. For abbreviations see Figures 1 and 3.

FIG. 19. Image analysis picture of Ca(OBS)2 crystals at 40 precipi-tated from a 0.075 M SOBS/0.010 M CaCl2 solution; taken 4 min aftermixing at 30C. OBS, octyl benzene sulfonate; for other abbreviationsee Figure 2.

FIG. 20. Image analysis picture of Ca(DS)2 crystals at 40 precipitatedfrom a 0.010 M SDS/0.008 M CaCl2 solution after 1 wk at 30C. For ab-breviations see Figures 1 and 3.

TABLE 1

Time of Analysis, Initial Supersaturation, and Initial

Relation to Critical Micelle Concentration (CMC)

for Image Analysis Solutions

a

Initial anionicsurfactant Initial counterion Relationconcentration concentration Time So to CMC

010 M SDS 0.008 M CaCl2 4 min 6.59 Above0.075 M SOBS 0.010 M CaCl2 4 min 5.54 Above0.010 M SDS 0.008 M CaCl2 1 wk 6.59 Above0.075 M SOBS 0.010 M CaCl2 1 wk 5.54 Above0.001 M SDS 0.008 M CaCl2 4 min 1.90 Below0.001 M SDS 0.008 M CaCl2 1 wk 1.90 Below0.004 M SDS 0.007 M CaCl2 1 d 4.58 Below0.004 M SDS 0.007 M CaCl2 1 wk 4.58 Below0.0003 M SDS 0.015 M DPC 1 d 3.83 Above0.0003 M SDS 0.015 M DPC 1 wk 3.83 AboveaSDS, sodium dodecyl sulfate; SOBS, sodium octyl benzene sulfonate;DPC, dodecyl pyridinium chloride; So, supersaturation ratio.

more supersaturated system (29). It is uncertain if the dif-ferences seen in this paper between the crystals formed inmicellar solutions and submicellar solutions are related tothe presence of micelles. Lee and Robb (44) presented an electron micrograph of Ca(DS)2 crystals formed underunspecified conditions. Several shapes were seen in this mi-crograph including trapezoidal and rhombic shapes, whichare similar to some of the crystals seen in this project. Thesizes ranged between 1 and 10 m.

Crystals from a 3.0 104 M SDS, 1.5 103 M DPC, and0.15 M NaCl solution at 1 d old and 1 wk old at 40 magni-fication are very thin and plate-like. The crystals have veryirregular shapes that look similar to the clumped-togetherSDS/CaCl2 crystals above the CMC after 1 wk. The 1-d-oldand 1-wk-old SDS/DPC crystals range in diameter from lessthan 15 m to about 20 to 50 m, with no significantchanges occurring within this time span.

Modeling. The only other papers in the literature of whichwe are aware that address kinetics of surfactant precipitationdirectly (35,44,45) are in general agreement with our resultson the rate of precipitation of the Ca(DS)2 system. The rateof precipitation increased as supersaturation increased, as re-ported in those papers, consistent with results reported here.

A model using the diffusion mechanism to describe crys-tal growth was unsuccessful in describing the kinetics of pre-cipitation in this paper. However, the structures for Ca(DS)2and Ca(OBS)2 crystals are quite different from atomic forcemicrographs. So, more sophisticated future kinetic modelsmust incorporate these crystal structure aspects.

ACKNOWLEDGMENTS

Financial support for this work was provided by the industrial spon-sors of the Institute for Applied Surfactant Research includingAkzo Nobel Chemicals Inc., Albemarle Corporation, Amway Cor-poration, Clorox Company, Colgate-Palmolive, Dial Corporation,Dow Chemical Company, DowElanco, E.I. DuPont de Nemours &Company, Halliburton Services Corporation, Henkel Corporation,Huntsman Corporation, ICI Americas Inc., Kerr-McGee Corpora-tion, Lever Brothers, Lubrizol Corporation, Nikko Chemicals,Phillips Petroleum Company, Pilot Chemical Company, Procter &Gamble Company, Reckitt Benckiser North America, Schlum-berger Technology Corporation, Shell Chemical Company, SunChemical Corporation, Unilever Inc., and Witco Corporation.



FIG. 21. Image analysis picture of Ca(OBS)2 crystals at 40 precipi-tated from a 0.075 M SOBS/0.010 M CaCl2 solution after 1 wk at 30C.For abbreviations see Figures 2 and 19.

FIG. 22. Image analysis picture of Ca(DS)2 crystals at 40 precipitatedfrom a 0.001 M SDS/0.008 M CaCl2 solution, taken 4 min after mixingat 30C. For abbreviations see Figures 1 and 3.

FIG. 23. Image analysis picture of Ca(DS)2 crystals at 40 precipitatedfrom a 0.001 M SDS/0.008 M CaCl2 solution after 1 wk at 30C. For ab-breviations see Figures 1 and 3.

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[Received December 16, 1998; accepted December 1, 2000]

Cheryl Rodriguez is a scientist in the Corporate Technology Depart-ment of the Clorox Services Company. She received her B.S. andPh.D. in chemical engineering at the University of Oklahoma. Her



awards include the 1995 Ralph H. Potts Memorial Fellowship fromthe American Oil Chemists Society (AOCS) and an OutstandingPaper Presentation at the 1996 AOCS Annual Meeting.

Lori Lowery is an engineer with Shell Oil Co. She received herB.S. at the University of Kansas and her M.S. at the University ofOklahoma, both in chemical engineering.

John Scamehorn holds the Asahi Glass Chair in Chemical En-gineering and is Director of the Institute for Applied Surfactant Re-search at the University of Oklahoma. He received his B.S. andM.S. at the University of Nebraska and his Ph.D. at the Universityof Texas, all in chemical engineering. Dr. Scamehorn has workedfor Shell, Conoco, and DuPont, and has been on a number of edito-rial boards for journals in the area of surfactants and of separa-

tion science. He has coedited four books and coauthored over 140technical papers. His research interests include surfactant proper-ties important in consumer product formulation and surfactant-based separation processes.

Jeffrey Harwell holds the Conoco/DuPont Professorship inChemical Engineering and is Associate Dean of Engineering at theUniversity of Oklahoma. He received his B.S. at Texas A&M Uni-versity in chemistry, his M.S. at Texas A&M University in chemi-cal engineering, and his Ph.D. at the University of Texas in chemi-cal engineering. Dr. Harwell has coedited three books and coau-thored over 100 technical papers. His research interests include theuse of surfactants in environmental remediation, microemulsionformulation, and nanotube production.

