A theoretical study of Gemini surfactant phase behavior

JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER 13 1 OCTOBER 1998

A theoretical study of Gemini surfactant phase behaviorKristine M. Layn, Pablo G. Debenedetti, and Robert K. Prud’hommea)

Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544

~Received 14 November 1997; accepted 8 April 1998!

Gemini surfactants are a relatively new type of surface active material, characterized by multiplehydrophilic head groups. The phase behavior of a Gemini surfactant lattice model is studied byMonte Carlo simulations and quasichemical~QC! calculations. The predictions of these methods arein excellent agreement, justifying use of the analytical QC theory. The dependence on temperature,surfactant solubility, surfactant rigidity, and oil chain length of the global phase behavior of ternarymixtures of Gemini surfactant, oil, and water is investigated. Three-phase equilibrium exists only atlow temperatures, with a transition to two-phase equilibrium as temperature is increased. Surfactantswith moderate solubilities~i.e., those which do not have a strong preference for either solvent!exhibit three-phase equilibrium at low temperatures, while surfactants with extreme solubilitypreferences yield two-phase equilibrium only. When a flexible surfactant exhibits three-phaseequilibrium, imposing rigidity promotes a transition from three- to two-phase equilibrium.Increasing molecular size of the hydrophobic solvent~oil! causes a transition from two- tothree-phase equilibrium, and finally back to two-phase equilibrium, but with reversed relativesurfactant solubility in the oil and water phases. ©1998 American Institute of Physics.@S0021-9606~98!51127-0#

f ailsa

sald

paan

rest

ysser-

eieme

th

uca

nifi

us.ur-nic

p-ersetionand

ps

ntsrestics.eskesisthend

ela-an

ofdellults

tifieseyin-

ur-

I. INTRODUCTION

While conventional, or simple, surfactants consist osingle hydrophilic head and one or two hydrophobic taGemini surfactants are characterized by multiple hegroups. The name Gemini was first applied to surfactant1991, at which time it referred exclusively to two identicsimple surfactants joined by a spacer between the hea1

Since then, the label Gemini has broadened to encomany surfactant having two or more head groups andnumber of tails. Several Gemini surfactants are shownFig. 1.

Experimental studies of Gemini surfactants havevealed intriguing behavior of significant practical intereCritical micelle concentration~CMC! and C20 ~surfactantconcentration required to reduce surface tension by 20 dcm! values for Geminis are generally much lower than thoof the corresponding monomers. Typical behavior is illutrated in Table I, which shows differences of several ordof magnitude between CMC and C20 data for selected Geminis and their analogous simple surfactants.5 CMC and C20

values are indicators of surface activity, with smaller valucorresponding to greater surface activity and a more efficsurfactant. Another property for which Geminis differ frosimple surfactants is aggregation morphology. As oneample, aqueous solutions of the Gemini shown in Fig. 1~c!assemble into highly branched, threadlike micelles, whilecorresponding monomer forms only spherical micelles.6 Inaddition to high surface activity and branched microstrtures, Geminis exhibit such interesting phenomenaanomalous CMC dependence on hydrophobicity and sig

a!Author to whom correspondence should be addressed; Phone~609! 258-4577; Fax~609! 258-0211; Electronic mail: [email protected].

5650021-9606/98/109(13)/5651/8/$15.00

Downloaded 22 Aug 2001 to 128.112.35.162. Redistribution subject to A

,din

s.ssy

in

-.

n/e-s

snt

x-

e

-s-

cant hydrophobe solvation at the air–water interface.1

The number of potential Gemini structures is enormoIn addition to structural variables associated with simple sfactants~such as tail length and degree of branching, ionature of the head group, and counterion type!, Geminis arealso characterized by the number of heads~dimer, trimer,tetramer, etc.!, spacer solubility~i.e., hydrophilic or hydro-phobic!, spacer length, and molecular rigidity. This last proerty is determined largely by spacer type. Flexible spac~such as methylene chains! allow the head groups to movrelative to one another, and to adopt a preferred separadistance and orientation based on solvation energeticsentropic considerations. Inflexible spacers~such as stilbenederivatives1! restrict the relative positions of the head grouand result in rigid molecules.

The novel properties associated with Gemini surfactahave motivated efforts to synthesize new Gemini structuwith the hope that they will possess desirable characterisWhile the large number of Gemini structural variables maksuch a trial and error approach inefficient, efforts to majudicious choice of the surfactant structure prior to syntheare hindered by a lack of fundamental understanding ofqualitative relationships between molecular structure amacroscopic properties. Our goal is to develop these rtionships, via theoretical and computational methods, inattempt to guide future synthetic efforts.

The focus of the present work is the phase behaviorGemini surfactant systems. Section II describes the moand two methods~one computational and one theoretica!used to calculate phase diagrams. A comparison of resfrom these methods shows excellent agreement and jususe of the analytical theory. Section III summarizes the kresults of a detailed theoretical study of phase behavior,cluding the effect of temperature, surfactant solubility, s

1 © 1998 American Institute of Physics

IP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

esu

ion

res.iedep-h ofcal

d

a-a

l-ter-aretem,

ngaditsto

than

oci-ns,the

pleth-

ree–

rom

mms isitre-

oreed

lesthe

ncyen-

o-

tail

5652 J. Chem. Phys., Vol. 109, No. 13, 1 October 1998 Layn, Debenedetti, and Prud’homme

factant rigidity, and oil chain length. Section IV concludwith a summary and Sec. V identifies relevant questions crently under investigation.

II. MODEL AND METHODS

A. The model

The goal of this study is to investigate general trendsglobal phase behavior; the model therefore incorporates

FIG. 1. Representative Gemini surfactants.~a! Xylylene diphosphate~Ref.1!; ~b! Diphosphate with rigid stilbene spacer~Ref. 2!; ~c! Bis~dimethyl-alkylammonium bromide! dimer~Ref. 3!; ~d! Trimeric analog of~c! ~Ref. 4!~e!,~f! Disulfate ~Ref. 5!; Y5OCH2CH2O, O, OCH2CH2O, O~CH2CH2O!2.

TABLE I. CMC and C20 data for several Gemini surfactants and their mnomeric~simple surfactant! analogs~Ref. 2!.

Y CMC ~mM! C20 ~mM!

Gemini Figure 1~e! – OCH2CH2O– 0.013 0.0010monomer C12H25SO4Na . . . 8.2 3.1Gemini Figure 1~f! –O– 0.033 0.008Gemini Figure 1~f! – OCH2CH2O– 0.032 0.0065Gemini Figure 1~f! –O~CH2CH2O!2– 0.060 0.0010

monomer C12H25SO3Na . . . 9.8 4.4


r-

nly

the most essential features of Gemini surfactant mixtuThe system consists of a simple cubic lattice fully occupby surfactant, water, and oil molecules. A surfactant is rresented by a connected string of head and tail units, eacwhich occupies a single lattice site. Figure 2 shows typimodel structures. Surfactants are labeledTiH jTk wherei andk refer to tail lengths andj is the combined number of heaand hydrophilic spacer units.

A surfactant head unit is energetically equivalent to wter and a tail unit is energetically equivalent to oil. Thussurfactant is represented by a string of ‘‘waterlike’’ and ‘‘oilike’’ particles, and each site may be energetically characized as hydrophilic or hydrophobic. These interactionsexpected to capture the basic features of a surfactant sysbut are unrealistic in several important ways. No driviforce is imposed to favor the preferential solvation of heunits with water as opposed to other heads, or of tail unwith oil rather than other tails. This allows surfactantsreduce unfavorable contacts by self-aggregating ratherpartitioning to oil–water interfaces.7 In addition, attractivehead interactions neglect the electrostatic repulsion assated with ionic head groups. Despite such simplificatiothese interaction energies have proven successful instudy of monomeric surfactants.7–9

B. Computational method

Previous efforts to predict the phase behavior of simsurfactant systems have involved two computational meods. Early work by Larson and co-workers estimated fenergy through numerical integration of the GibbsHelmholtz equation using average energies obtained fcanonical ensemble Monte Carlo simulations.7,8 Althoughthis approach is thermodynamically rigorous, it suffers froan inability to distinguish two- and three-phase equilibriuand is computationally expensive as a series of simulationrequired to generate a single tie line. Most importantly,requires that the model surfactant be symmetric, which pcludes application of the method to Gemini surfactants. Mrecently, Panagiotopoulos and co-workers have utilizGibbs ensemble simulations.9 While this method is very con-venient for the investigation of systems of small molecuwhich do not have a tendency to form ordered structures,connected nature of microemulsions reduces its efficieand raises concerns regarding adequate sampling of lowergy states.

FIG. 2. Model Gemini surfactants. Open circles represent hydrophobicsegments and filled circles represent hydrophilic segments~head or spacer!.


ensil

ior

a

t tsequeitiica. Isakoesacm

isntntauiltaeemgl

tn

mdtioiste-

edto

pu-es

lting-

f

hetoe

nt

yco

n

d

5653J. Chem. Phys., Vol. 109, No. 13, 1 October 1998 Layn, Debenedetti, and Prud’homme

These considerations motivated the use of a differcomputational method in this work, namely block compotion distributions.10,11 Following equilibration of a canonicaensemble Monte Carlo simulation, the composition ofsmall subcell placed at a random position in the simulatbox is sampled over a large number of configurations. Foternary system~oil, water, and surfactant!, the probabilitydistribution of subcell composition is a three-dimensionsurface. When the bulk~overall system! composition is in asingle-phase region, this surface exhibits a single peak abulk composition. When the bulk composition is in a phaseparated region, local composition fluctuations reflect elibrium phase compositions, resulting in a multimodal frquency surface with each peak centered at the composof an equilibrium phase. With this method, a single canonensemble simulation may yield the endpoints of a tie linepractice, several simulations are sometimes necessary abulk composition must be chosen such that multiple peare of roughly the same height. If the bulk composition is tclose to the composition of one of the equilibrium phasthe peak for this phase will dominate the frequency surfand may alter the positions of other peaks, or in extrecases, render a second peak undetectable.

One of the most significant limitations of this methodan inability to provide a precise estimate of the critical poiAs the bulk composition moves closer to the critical poiequilibrium phases approach the same composition. Becpeaks in the frequency surface are centered at the equrium phase compositions, peaks begin to overlap beforecritical point is reached. Although estimates of the criticpoint may be extracted from finite-size scaling techniqusuch an approach requires long simulations of large systand is computationally expensive even for simple, sincomponent systems.12,13

Simulations are performed on ann3 simple cubic lattice,with a cubic subcell of sizeb3. The efficiency of surfactanmoves is improved by a standard Rosenbluth configuratiobias scheme.14 The optimal ratio of subcell to overall systesize is dependent on surfactant length and is determinetrial and error. If the subcell is too large, phase separawill occur within the cell. While a small subcell avoids thand reduces computation time, the subcell size is limifrom below by composition resolution~the smaller the subcell the fewer compositions which may be observed! and bypeak resolution~when the subcell is too small, multiplpeaks overlap!. The majority of simulations were performefor a T2H2T2 surfactant, for which 15 and five were foundbe adequate values ofn andb, respectively.

FIG. 3. Configurations ofT2H2T2 that are allowed by an imposed rigiditconstraint. When this molecule is treated as rigid, the intramoleculartacts marked by dashed lines are not available for solvation and areincluded in the counting of contacts in the QC treatment.


t-

ana

l

he-i-

-onl

nthes

o,ee

.,se

ib-hels,

se

al

byn

d

C. Theoretical method

The quasichemical~QC! theory of Guggenheim15 wasinvestigated as a simple, analytical alternative to the comtational block distribution method. The QC theory assumindependence of contact pairs and maximizes the resuconfigurational partition function to yield the following relation between the number ofi j contacts,Xi j :

Xi j2

Xii Xj j54e22« i j /kT, ~1!

where « i j is the exchange energy of ani j pair @i.e., e i j

5Ei j 20.5(Eii 1Ej j ), whereEi j is the interaction energy oan i j pair#.

The free energy of mixing obtained by integrating tGibbs–Helmholtz equation is differentiated with respectmole number to yield the following expression for thchange in chemical potential of speciesi upon mixing:

Dm i

kT5 ln q i1

1

2zqi ln

j i

q i1

1

2zqihi ln

hi~12kt !

h~12k i t i !

11

2zqi t i ln

t i~12kh!

t~12k ihi !, ~2!

where z is the coordination number,zqi is the number ofcontacts for each molecule of speciesi , hi is the fraction ofspeciesi contacts which are hydrophilic,t i512hi , q i is thevolume fraction of speciesi , j i is the fraction of all contactswhich originate fromi molecules,h5(j ihi , andt5(j i t i .k is the root of 12k5k2ht(e2«/kT21) which lies betweenzero and two andk i is the same quantity for pure compone

n-ot

FIG. 4. Comparison of QC and simulation results.~a! T2H2T2 and water;z526; T* 5kT/e; solid line, QC, circles, simulation (n515, b55). ~b!T2H2T2, water, and oil;z56; T* 51.33; solid lines, QC, dashed lines ancircles, simulation (n515, b55).


bed

es,inesm.ree-er-pe,i-m.nve-ta-ulk

reef tietherfree

mhearetantone


TABLE II. Summary of systems studied.

rs hs zqs T* rangeThree-phaseequilibrium

T1H2T1 4 0.49 98 3.8 – 10.0 xT2H2T1 5 0.39 122 3.3 – 10.0 xT1H3T1 5 0.59 122 3.8 – 10.0T2H2T2 6 0.33 146 3.3 – 11.1T2H3T1 6 0.49 146 3.3 – 10.0 xT1H4T1 6 0.66 146 2.9 – 10.0T2H3T2 7 0.42 170 4.0 – 10.0 xT2H4T2 8 0.49 194 4.0 – 10.0 xT3H3T3 9 0.33 218 2.9 – 10.0T3H4T2 9 0.44 218 4.0 – 10.0 xT2H5T2 9 0.55 218 4.0 – 10.0 xT2H6T1 9 0.66 218 4.0 – 10.0T1H7T1 9 0.77 218 4.0 – 10.0T3H4T3 10 0.40 242 4.0 – 10.0 xT4H4T3 11 0.36 266 4.0 – 10.0T3H5T3 11 0.45 266 4.0 – 10.0 xT3H6T2 11 0.54 266 4.0 – 10.0 xT2H7T2 11 0.63 266 4.0 – 10.0T2H8T1 11 0.72 266 4.0 – 10.0T1H9T1 11 0.81 266 4.0 – 10.0T6H4T5 15 0.27 362 4.0 – 10.0T5H5T5 15 0.33 362 4.0 – 11.0T5H6T4 15 0.40 362 4.0 – 10.0T4H7T4 15 0.46 362 4.0 – 10.0 xT4H8T3 15 0.53 362 4.0 – 10.0 xT3H9T3 15 0.60 362 4.0 – 10.0 xT3H10T2 15 0.66 362 4.0 – 10.0


i . k i is obtained by replacingh by hi , t by t i , and e ~theexchange energy of a hydrophilic–hydrophobic pair! by zeroif species i has only one type of contact~i.e., is oil orwater!.16 The molecular structure variables which mustspecified arezqi , hi , and r i , the number of sites occupieby each molecule of speciesi .

When a single system exhibits multiple phase envelopthe nature of overlap between the envelopes determwhether the system is in two- or three-phase equilibriuPartial overlap of phase envelopes is characteristic of thphase equilibrium. Because the composition at which ovlap first occurs is the endpoint of a tieline in each envelothis composition is in equilibrium with two other compostions, and therefore all three compositions are in equilibriuWhen multiple phase envelopes overlap such that one elope is completely within the other, one envelope is mestable. The stable envelope is identified by choosing a bcomposition in the overlap region and comparing the fenergy of the system assuming separation along one set olines to the free energy assuming separation along the oset of tie lines. The stable phase envelope yields a lowerenergy.

As mentioned previously, Gemini surfactants range frovery flexible to very rigid, depending on the nature of tspacer. In the limit of a completely flexible spacer, thereno intrinsic barriers to configurational changes; the surfacis free to adopt any configuration, and the most favorable

FIG. 5. The effect of temperature on the phase behavior ofT2H5T2; r s59, zqs5218,hs50.55.



FIG. 6. The effect of surfactant solubility on the phase behavior of Geminis occupying nine sites;r s59, zqs5218,T* 54.0.

xi

te

-la

tnd

re-s.ra-for

ameol-

is

will be determined by solvation effects. In the opposite etreme of a completely rigid spacer, intramolecular motionrestricted and the configuration of the surfactant is dictaby rigid bonds rather than neighboring solvent contacts.

For simplicity, we limit this study to the cases of completely flexible or completely rigid surfactants. As molecurigidity originates from bonds in the spacer, we choosedefine configurations by the relative positions of all head aspacer units and the tail units directly bonded to the hea


-sd

rods.

The positions of the remaining tail segments are notstricted as they represent flexible long chain hydrocarbon

Because a flexible molecule may adopt any configution, all of the contacts along the chain are availablesolvation. In contrast, a completely rigid molecule exists insingle configuration exclusively, and this may prevent socontacts along the chain from interacting with solvent mecules. Figure 3 shows several configurations ofT2H2T2 thatare allowed by a particular rigidity constraint. When th


ho

bytalaooes

ti-isth

oathonf

cts

cuenw

ese

dthineosnra

tioca

icaanilit

erintes

reetea

e

sees.

nd

tri-limi-

m-able

im-

6.tes

ce


molecule is treated as rigid, the contacts marked by daslines are no longer available for solvation. In the contextthe QC theory, the rigidity constraint is introduced simplyexcluding these fixed intramolecular contacts from the tonumber of contacts. This simple result is due to the calcution of equilibrium phase compositions via free energiesmixing; the fixed intramolecular contacts resulting from mlecular rigidity are equivalent in both pure and mixed statand hence make no contribution to mixing energies.

Although this treatment of surfactant rigidity is theorecally rigorous within the framework of the QC theory, itsimplistic in regard to surfactant connectivity. BecauseQC theory accounts only for contact pairs, the structurethe chain molecule is considered only in the counting of pinteractions. Thus the actual configuration adopted bysurfactant is reflected only through the intramolecular ctacts which become fixed and consequently unavailablesolvation. The relative positions of the remaining contaare neglected, as are any entropic effects which may refrom constraining the chain configuration.

D. Method comparison

A comparison of phase diagrams from QC theory callations and block composition distributions shows excellagreement between the two methods. A comparisonmade for binary~surfactant and water! and ternary~surfac-tant, water, and oil! systems, for several surfactant structurover a range of temperatures, and for coordination numbof six ~nearest-neighbor interactions only! and 26~nearest-and diagonal nearest-neighbor interactions!. Figure 4 showsessentially exact quantitative agreement between the pretions of both methods for binary and ternary systems ofGeminiT2H2T2. At least qualitative agreement was foundall cases considered, suggesting that the analytical QC thcaptures the essential features of the problem. This veryisfactory agreement between theory and simulations isexpected to hold for longer molecules and lower tempetures, where a significant amount of molecular associawill occur. The quasichemical theory, which takes into acount nearest-neighbor interactions only, is incapable of cturing long-range association.

In light of the agreement between the quasichemtheory and the Monte Carlo simulations and the significCPU demands of the computational approach, the detastudy discussed in the following section was performed wthe quasichemical theory theory.

III. RESULTS

Results are presented to illustrate the effect of tempture, surfactant solubility, surfactant rigidity, and oil chalength on phase separation. Table II summarizes the sysand conditions studied; results discussed below are repretative of the behavior observed for all systems consideAll calculations are performed with a coordination numbof 26. Water is a single site species. Unless otherwise stathe oil molecule is a single site species and surfactantscompletely flexible ~all contacts along the chain arcounted!.


edf

l-f-,

ef

ire-

orsult

-t

as

,rs

ic-e

ryat-ot-n-p-

lt

edh

a-

msen-d.rd,re

A. Temperature

Figure 5 illustrates the phase behavior ofT2H5T2 over aseries of dimensionless temperatures (T* 5kT/e). At lowtemperatures@Fig. 5~a!#, the system exhibits a three-phatriangle surrounded on two sides by two-phase envelopThere is a miscibility gap along both the oil–surfactant awater–surfactant axis. An increase in temperature@Fig. 5~b!#yields a third two-phase region below the three-phaseangle, decreases the size of the three-phase region, and enates the surfactant–water miscibility gap. At higher teperatures, the three-phase triangle is replaced by a sttwo-phase region@Fig. 5~c!, large envelope# and a metastableregion@Fig. 5~c!, small envelope#. At high [email protected]~d!# both the metastable region and the surfactant–oilmiscibility are eliminated.

B. Surfactant solubility

The effect of surfactant solubility is illustrated by Fig.All of the surfactant structures depicted occupy nine si(r s59) and have the same number of contacts (zqs

5218). Theonly remaining variable ishs , the fraction ofsurfactant contacts that are hydrophilic. Physically,hs is rep-resentative of the molecule’s hydrophilic–lyophilic balan

FIG. 7. The effect of surfactant rigidity on the phase behavior ofT1H2T1;T* 55.55, r s54. ~a! Flexible T1H2T1; zqs598, hs50.49. ~b! RigidT1H2T1; zqs592, hs50.50.


le.


FIG. 8. The effect of oil chain length on the phase behavior ofT2H2T1; r s55, hs50.39,T* 55.56; r o is the number of sites occupied by an oil molecu

st

h-d

iha

eisth

blta

esi

ooasheili

setheoree

incesext

pa-s

.

e-

d.-r ofove

cted

~HLB!; the surfactant becomes more hydrophobic ashs isdecreased below 0.5 and more hydrophilic ashs is increasedabove 0.5.

The progression from Fig. 6~a! to Fig. 6~e! is an increasein the ratio of hydrophilic to hydrophobic units. The mohydrophobic surfactant@Fig. 6~a!# exhibits only two-phaseequilibrium, with the surfactant more soluble in the oil-ricphase. Increasinghs by replacing a tail segment by a hydrophilic spacer unit results in a three-phase triangle surrounby two-phase envelopes@Fig. 6~b!#. The larger two-phaseregion is the one for which the surfactant is more solublethe oil-rich phase, as expected due to the hydrophobic cacter of the surfactant (hs,0.5). Increasinghs to 0.55 yieldsa slightly hydrophilic surfactant which again exhibits a threphase triangle@Fig. 6~c!#. The dominant two-phase regionnow the one for which the surfactant is more soluble inwater-rich phase. An increase inhs to 0.66@Fig. 6~d!# causesa transition to two-phase equilibrium with a small metastaregion near the edge of the stable envelope. The metasregion is eliminated by a further increase inhs @Fig. 6~e!#.

The combined behavior of all systems studied suggthat three-phase equilibrium will exist at low temperaturesthe surfactant is only moderately hydrophilic or hydrophbic. Extreme surfactant solubility preferences yield twphase equilibrium, with an essentially pure oil or water phin equilibrium with surfactant and the remaining solvent. Tphysical cause of this behavior is clear; three-phase equ


ed

nr-

-

e

eble

tsf--e

b-

rium is the result of partial overlap of two separate phaenvelopes, one for which the surfactant is more soluble inwater-rich phase and one for which the surfactant is msoluble in the oil-rich phase. Such behavior will occur if thsurfactant has only a weak preference for one solvent.

C. Surfactant rigidity

As discussed previously, imposing rigidity on a chamolecule fixes intramolecular contacts and thereby reduthe number of contacts available for solvation. In the contof the QC theory, this results in a decrease inzqs , the num-ber of surfactant contacts. In general, this may be accomnied by a change inhs , the fraction of surfactant contactwhich are hydrophilic.

The effect of imposing rigidity is illustrated by Fig. 7Figure 7~a! corresponds to a completely flexibleT1H2T1

(zqs598, hs50.49! and Fig. 7~b! to a completely rigidT1H2T1 which is constrained to lie in the configuration dpicted (zqs592, hs50.50!. The flexible molecule exhibits athree-phase region which is lost when rigidity is imposeAlthough hs for the rigid case is slightly larger, the difference is small compared to the difference in the numbecontacts. The surfactant solubility study discussed absuggests that such a small difference inhs is not likely tohave a significant impact on phase behavior; the expe


um

fo

be

nin

il-

iotho

e-th

ree

haodtivichrin

o

uoas

tgehiemlimg

tao-Init

ee-lib-

m-fea-ca-il–

ionich

s to

war-

en-at

elf-QCts,en-inof

ty.talsys-ata

the

ortd ae

inf a

r


cause of the transition from three- to two-phase equilibriis loss of contacts.

Phase diagrams of rigid surfactants were calculatedall possible configurations ofT1H2T1 andT2H2T1. With theexception of one configuration ofT1H2T1, all rigid configu-rations studied showed similar behavior~loss of the three-phase region exhibited by the flexible molecule!; the excep-tion was for the case of the smallest decrease in the numof contacts (zqs598 for the flexible molecule and 96 for thrigid!.

D. Hydrophobic solvent chain length

Figure 8 shows the effect of the hydrophobic solve~oil! chain length on the phase behavior of the GemT2H2T1. A single site oil molecule@Fig. 8~a!# results in two-phase equilibrium with the surfactant partitioning to the orich phase. Increasing the oil length to two@Fig. 8~b!# resultsin a three-phase triangle with the larger two-phase regcorresponding to the surfactant existing preferentially inoil-rich phase. The three-phase region is retained for anlength of three@Fig. 8~c!#, but the dominant two-phase envlope corresponds to the surfactant being more soluble inwater-rich phase. For sufficiently long oil [email protected]~d!#, the system reverts to two-phase equilibrium withversed surfactant solubility~surfactant is more soluble in thaqueous phase!.

IV. SUMMARY

The phase behavior of Gemini surfactant systemsbeen investigated by computational and theoretical methThe predictions of both methods are generally in quantitaagreement, justifying extensive use of the simpler theoretapproach. A detailed study of relevant system variablesled to general conclusions regarding the effect of tempeture, surfactant solubility, surfactant rigidity, and oil chalength on phase behavior.

Gemini surfactants which are moderately hydrophilichydrophobic~0.39<hs<0.60 for the systems studied! ex-hibit three-phase equilibrium at low temperatures, while sfactants with extreme solubility preferences yield only twphase equilibrium. For systems which exhibit three-phequilibrium, at low temperatures the three-phase regionsurrounded on two sides by two-phase envelopes andsurfactant is immiscible with both water and oil over a larcomposition range. An increase in temperature yields a ttwo-phase region below the three-phase triangle. As the tperature is increased further, the three-phase region is enated, resulting in a stable two-phase region overlappinsmaller metastable envelope. For hydrophilic~hydrophobic!surfactants, the miscibility gap with water~oil! is eliminatedfirst, followed by loss of immiscibility with oil~water! athigher temperatures. Decreasing the number of surfaccontacts available for solvation by imposing rigidity prmotes a transition from three- to two-phase equilibrium.creasing the oil chain length for a system which exhib


r

er

ti

neil

e

-

ss.ealasa-

r

r--eishe

rd-i-a

nt

-s

two-phase equilibrium first results in emergence of a thrphase triangle, followed by a reversion to two-phase equirium with reversed surfactant solubility.

V. FUTURE WORK

As discussed in Sec. II, the interaction energies eployed for this study are expected to capture the basictures of surfactant systems, but contain several simplifitions. For example, they do not promote water–head or otail interactions and they neglect electrostatic repulsbetween ionic head groups. A more detailed model whallows arbitrary head and tail interactions~i.e., does not re-quire heads to be energetically equivalent to water or tailbe energetically equivalent to oil! and a study of Geminisurfactant phase behavior as a function of energetics areranted.

The complete phase diagram of a surfactant system gerally consists of two distinct regions; phase separationlow surfactant concentrations and microstructure sassembly at higher surfactant concentrations. As thetheory is incapable of incorporating long-range order effecmicrostructure studies should be performed by canonicalsemble Monte Carlo simulations. Questions of importancethis area are the final equilibrium structures as a functiontemperature, composition, surfactant structure, and rigidi

A comparison of our theoretical results to experimendata are not provided as the phase behavior of Geminitems has not been studied extensively and insufficient dare available. Experimental studies designed to verifymodel predictions should be pursued.

ACKNOWLEDGMENTS

The authors gratefully acknowledge financial suppfrom the Rhone-Poulenc Complex Fluids Laboratory anNational Science Foundation fellowship to K.M.L. After thsubmission of this manuscript K.M.L. was tragically killedan accident. This paper is dedicated to the memory owonderful student, scholar, and person.

1F. M. Menger and C. A. Littau, J. Am. Chem. Soc.115, 10083~1993!.2H. Eibl, J. McIntyre, E. Fleer, and S. Fleischer, Methods Enzymol.98, 623~1983!.

3R. Zana, M. Benrraou, and R. Rueff, Langmuir7, 1072~1991!.4D. Danino, Y. Talmon, H. Levy, G. Beinert, and R. Zana, Science269,1420 ~1995!.

5M. Rosen, CHEMTECH.30, 30 ~1993!.6R. Zana and Y. Talmon, Nature~London! 362, 228 ~1993!.7R. Larson, L. Scriven, and H. Davis, J. Chem. Phys.83, 2411~1985!.8R. Larson, J. Chem. Phys.89, 1642~1988!.9A. Mackie, K. Onur, and A. Panagiotopoulos, J. Chem. Phys.104, 3718~1996!.

10K. Binder, Z. Phys. B43, 119 ~1981!.11K. Kaski, K. Binder, and J. Gunton, Phys. Rev. B29, 3996~1984!.12K. Binder and D. Heermann,Monte Carlo Simulation in Statistical

Physics-An Introduction~Springer, Berlin, 1988!.13M. Rovere, D. Heermann, and K. Binder, J. Phys.: Condens. Matte2,

7009 ~1990!.14M. Rosenbluth and A. Rosenbluth, J. Chem. Phys.23, 356 ~1953!.15E. Guggenheim,Mixtures ~Oxford University Press, New York, 1952!.16H. Tompa,Polymer Solutions~Academic, New York, 1956!.


Date post:	20-Nov-2023
Category:	Documents
Upload:	princeton
View:	1 times
Download:	0 times

A theoretical study of Gemini surfactant phase behavior

Documents