hlliq,.

X.Y.

".0 "

~

, .\XD P.\TTI.(l~l.l\.

.:.':,'" 'I~,Ii.. .1. .

:.\x."no,,)--.;), J.

All/cr.

Free-Energy Changes on Transfer of Surface-Active Agents between

Various Colloidal and Interfacial States

1,INl AND P. SOMASUNDARAN

lIcnry Kr1l11J, ~.J,.y..l uf -'lints, Columbia UnivtT&it1J, New York, New York 10017

Received February 4, 1971; accepted June 9, 1971

So..'. It,

J.. to

'E~, K

~larked changes in the various physical properties of systems containing aqueoussurfactant solutions, due to the transfer of the surfactant species from one colloidalor interfacial state to another, have been reported in the literature to occur at cer-tain critical surfactant concentrations. An examination of the various procesaes;::¥olving such transfer and the related free-energy changes is made in this work forn better understanding of the mechanisms involved.

The values for transfer energy per CH:group for various phenomena such as micelli-zation, hemimicellization, emulsification, adsorption at the solution-gas interface,adsorption at the solution-hydrocarbon interface, dissolution, and evaporationranged from -0.6 kT for micellization of ionic surfactants to -2.0 kT for evapora-tion. These values are discussed in tenDS of the interactions of the surfactant specieswhile in different states between themselves as well as with the other species in the::ystem. For the calculation of the transfer energy for micellization of ionic sur-"etants, it was necessary to apply an important correction based on Shinoda's! ;I:'atment for the "kinetic micelles" containing the counterions.

.\KER. J. 8.SM (1952).

INTRODUCTION concentrations at which they occur are of~h:lIV changes in the various physical considerable interest since they indicate

properties of S)'stems containing aqueous the extent of the van der WaaIs interaction-Urf:lct a nt solutions have been reported between hydrocarbon chains under various

: by numerous workers to occur at specific conditions and their entropies in solution! -lIrf:lct:!!t concentrations. While changes as \vell as in the associated states. An in-

in iil\ch jiroperties as surface tension, equiva- terpretation of the results and a correlationlellt CUllductance refructive index densit". bet,,'een them is, ho\vever, complicated, ,J'

: \i:'CO~it:,', transport number, turbidity, and since several other factors ~uch as size andi 'I,.;motic coefficient of the surfactant solu- charge of the polar heads of the surfactant,: ti\)l1~ h:lve been attributed to the association concentration of salts in the solution and

~ in th~ bulk of small molecules or ions into the influence, if any, of hydrocarbon chains" micellei;, ch:mges in i;Olid-liquid interfacial on the structure of' the bulk water and

~rI)~rtii" such as zeta potential and those thereby on its entropy, will influence theIn int~l'i:lcial phenomena such as froth above phenomena to different extents inftotntion and flocculation have been ascribed different cases.

; \l) th~ :I..').~ci(l.tion at the solid-liquid inter- Since the basic reason for both the mice 1-r~ of the surfactant species to fonn t\VO- lization and hemimicellization is consideredditnen"i 1 t 11d h . .

11i - ~ ona aggrega es ca e eInlUllCe es to be the same attempts were made earlier(1-.)). These phenomena and the surfactant to correlate th~ two phenomena "ith some

success (4). In both the phenomena, the

Jounaal 01 Colll1il aa4CIIW/- SciIIIa. Vol. 37. No.4, Deoemw 1971

731

.'.

!~ :~ . '-~

- #,:

f

IOn le:lve from Technion, Haifa, Israel

~j~

t;or73-:1: LIN A~l) ~()~I.\,..:t.~I).\":..\:"-

TABLE II,".!.LUES OBT.\.INED roa ... USIXG K~owx 1\. ,'.\I,I't;,. FOR F.\'fTY ACtl) ~f)\PS .\XI)

n-ALKTLTa1KETBYL.\.3IKONIUK BaOYtD}:tO \~I' Till"'. O14T\I~t:P Fnl: 1\, {'"tXGA V AWE OF -l.tl.~ J: T . f'14 (t--- .-

T~rCI K, o~ ~:Surfact&nt II..,"

---l.m A-T

-l.~A'r.-1...~ A.T-1.<18 .7'-1.11 kT-I.~ kT-1.I~LT

254525-IS2560,,-;:4)

".!IIi

II..T."

II.;;'

0.58"

0.65

O.fH

0.61'

1:t1Fatty acid soapsAlkyl sulfatesAlkylammonium chloridesAlkylammonium chloridesn-Alkyltrimethylammonium bromidesn-Alkyltrimethylammonium bromidesn-Alkyltrimethylammonium chlorides

('20)

rtPOrted in the IipJicelle for1\\:ttit)11... V;\!"" tll:,t (':\1

of tht' ::\\11)(' rill

cbaill' !; 111\ t I,,"fiquid ~:\" I lit I

!till It'-' 111:,1\ II~n('.1 ,':\rli.'r i.

$1\ aqueous to nIt is likely that

t,,~I,.1,'I'.\"Oren\O'- ut till'the e~; .,..:"lIrf' Ilf

ch3in~ on thl'aqueous ph:l.Seinside the miltrapped inside. .

dimers and othemolec1.!les do f(the - ~iactantrange:;. ..\.ccordconcentration (

I be high enougJ, the possibility

senti~lly frommonomers, In ~

for CH2 groupterio: ,)£ the nsince those pchains it\ conIdimers is alrefentering thepo~sibility thvside ~\ micelle\iquirl hydro.

' d " )51 ert \.11 ,

trnn,;ier ene~help of Traut

I' ~en8ion datf\In this casec:\n be con8In its moven

. bulk of ~ hyc

4 References for K. values. ~ '~ K. values calculated on the basis of an average value of -1.08 kT obtained for ~..' for fut t \" acid ~soaps and n-alkyltrimethylammonium bromides. . .;;: t~

.."

Equation [5] then becomes: to micelle excluding the term w.. Tbilog CMC = (log A) v~\lue of. Kg for fatty. acid soaps \V'~ given

b~. Cornn and Harkins (13) as O.;>u and "+ (nj2.303 kT)(w. + ~..). [6J for alk-yltrimethylammonium bromid{'s bY ~

T 1 h 1 f B:.lm. ct al. (20) as 0.6;3. If no inorganic ;.he va ues that one gets for t e s ope 0 lt :, .-.J

ded ' c . 1to C' IC d .ii;h 1 C~'IC li . h f 11 sa 1:;.~ , i IS equa -, an \\"e '

t e og l.~ VB n ne 18, t ere ore, actua ybt .. f E [8J .

+ d . h f .. 0 a1n rom q. .

w. ~.. an not ~- In t e case 0 Iorncsurfactants. log C~[C

It has been pointed out by Corrin and = [~ j? 303 (1 + K )kT] + K" (9JHarkins (13) and Shinoda (14) that C~IC ...n .. g .

of long-chain salts is a function of the con- Comparison of Eqs. [9] and [3] yieldscent~ati°n. of the counterions. The actual b = [cP..,j2.303 (1 + K )kT] [101relatIonshIP has been reported by several g

workers (15-19) to be of the form: T::sing the values available in the liter:.\ture10 CMC = - K 10 C. + K' [7] (~1) for Kg for f~tty acid ~aps and n-:\lkyl.

g g g, , tr1methylammornum bromides, cP..' 18 reo

,vhere C, is the total counterion concentra- c:.tlculnted from the values of b given intion in moles/liter, K is an empirical Table I. The rationale behind the use ofconstant, and Kg is the ratio of the number the slopes of the log C~IC vs log C i curves '

of counterions to long-chain ions in the for calculating the free energy of micellemicelle and is always less than unity (17). formation has been discussed recent i). byAccording to Shinoda (16), a plot of log ~[ukerjee et al. (22, 23). The results thatC~IC in the presence of salt as a function ,ve obtained in the above manner for ~..of the number of carbon atoms in an alk)1 are given in Table II along \\ith the value:;chain is also linear. Equation [7] for such 1\ of Kg used in the calculations. Furthermore,ca"e becomes: b:.\.~ed on values of b available in liter:~turelog CMC = -Kg log C, - Kln + K", [8] for :arious reagents and an average \t\lu:

obtamed for cP..' from the above result:;,,..-here Kl is a constant and is equal v:\lues of Ku are evaluated for various sur-to cP..,j2.303 kT, and K" is another em- fact ants and presented in Table II.pirical constant. ~.., is the transfer energy The values, -1.04 kT and -1.13 /.:.T,per CH2 group from aqueous environment obtained for ~.' are in agreement with those

JourtlGl 0/ CoUui4 aU /"",- &i8f\C-. Vol. 31, No, 4, Deoember 19..1

:\[arked (

nuneral-aq U(

tam critic.'\lt'"

736 LIN AND SO~I.\SUNDARAN

.

~~ 10

1z2'Cc..z.. 10~u

..oJoJ..u

i.:. to2~

~\..! IO'r....~toC~to~ -,... t:u~8

\1-0.4128 ~I'\ 2.503kT

~\

\\

...

10 ... . . . . . . . . 18 10 12 .. 16 18 ZO

NUM8£R OF CARlON ATOMSIN TIC ALKYL CHAIN. .

FIG. 2. Least-equare plot of log HMC of alkyl-ammonium acetates from 8treaming potentialdata (2) as a function of the number of carbonatoms in the chain.

IO~-- ~. IC

FIG. 4. Least-of SQdium alkylfrom electrophordat.'\ (0) of Wa\fuur\ ,n of thechaill.

formation; it will be referred to as ~ ~.

for the case of hemimicelle formation"the solid-liquid interface and as I/>A(1c) forthat at the solid-gas interface. tV 0' is ~electrical part of the free energy of .micelle formation, and A' is anconstant. The value that we obtainedthe least-square method for 1/>1&(81) from:2 is -0.95 kT. Electrophoreticand adsorption data of WakarnatsuFuerstenau (29) for alumina insolutions of all..-yl sulfonates at aionic strength of 2 X 10. Nin a similar manner. The hemimicellecentrations obtained from the two setsdata are given in Fig. 3 as a functionnumber of carbon atoms in the alkylThe value obtained for 1/>1(81) from the --

trophoretic mobility data is -0.77 kTiand that obtained from the adsorptiondata is -0.71 kT. In all cases 1/>1(01) is hi~than the value -0.6 kT obtained for tot81free energy per CH, group for the formatio~of micelles of ionic surfactants.obtained for 1/>1(51) under conditions of ,

."

zeta potential of the mineral and henceconstant adsorption density of the sur~:

...,.,10

fnct~t specieas reported eatreatment ofFuerstenau '$urfactants Thtentil of tbionic strengthfor 4>1(81) ,vhilconcentrationsho\v a chan!tion isothermpos.~ble chat

. potential of tlkT (1';{7 4) .

. "eo.be neglecteddellSities of "concentratiolhave been ifzero at thes..ever be said

obtained for the formation of micelles ofionic surfactants. Free energy of hemi-micelle formation in the case of alkyl-ammonium acetates \vas calculated bytreating in the following manner the stream-ing potential data reported earlier ( 2)for quartz in aqueous solutions containingthe above surfactant. Hemimicelle con- ~centrations (HMC) were first obtained ~from these data by graphically locating i 10'the concentrations at which the extrapola- ~tions of the straight line portions of the ~8t.reaming potential curve intersected the icun'e for ammonium acetate. A least-square ~.. .,plot of log H~IC VB the number of carbon ~ 10 l ~~~_~_~-_.~~. ntoms in the alkyl chain is giv~n in Fig. 2. !Slope of this line is the free energy of co- ;hesion per CHz group in the hemimicelle,~1ccording to the equation -I

I I 10 . 10 12 14 'I 'I

H~IC = A exp [(We + n4>,,)/kT] [11] NUM.~ROFCAR.ONA"OMS'N "H~ ALKYL CHAIH..

developed earlier (4) for hemimicelle for- FIG. 3. Least-square plot of log HMC of sod.i~m.mation by analogy to micelle formation. alkyl sulfonates !rom eleetrophoretic mobUlt)

. . . (B) and adsorption data (0) of WakamatsU41" In the above equatIon 18 the transfer and Fuerstenau (29) as a function of the numberenerg)' per CHz group for hemimicelle of carbon atoms in the chain.

Journal o/CoiloU au r"t.../oce &.:.-, Vol. 37, No.4, December 19..!

0.30" ~

~

,~

~ 737Fl:I.:E E:\"El:l;Y Of ~lrltFACTAJ.~TS

red to ;\." ..(11)

Ie fOrllJati'm at.

md :1:; Q,..c' for,

r:~cc. 11.,' i8 the '~

energy "i hefni. $:. " ~18 ml l'mplneal ~

,ve obtailll'd by ~

r ~\.IJ frt\m fil. l

horetic mobility'

Wakamatsu and

.1in~~ ill al\Ueoua~:

~S at :'1 ("llIIstan~;;0-r ''-as also treated :\'

hemimicelle con.the t,vo sets of '.

a function or the ~

Ii the alkyl chains.

~I) .from t~~ elee. i~ 18 -0.11 kT "

the adS<lrption Tses 41.(01) is higber.{'

.btained ror totalZ

for the rormation~-

factants. Valuea::

onditions or zero ,

.neml and hence ;ity or the sur-;

00'" TABLE IIIIILB GROUP NUMBBRS FOR HYDROPHILIC .%.XD

HYDROPHOBIC GROUPS (32)

I H7dropbobie

38.7 -CH- 0.47521.1 -cBs- 0.47519.1 -CHI 0.-17511.0 -CH- 0.4759.42.11.1.3

Hydrophilic ItoaP8

; .0'..: ..:

~ I, .a0"

Na+K+

Na+Na+

~~\.';-;

-80.--CO<.r-COO--sOa-N (tertiary amine)-COOH-oH-0-

.' c

'\

\if10-

-.j . . . . , : . .~ . .\10 I 10 It 14 16 'I

NUMKR OF CARBON ATOMSIN THE ALKYL CHAIN, .

FIG. 4. Le88t-square plot of log concentrationof sodium alkyl sulfonates at zero zeta potentialfrom electrophoretic mobility (8) and adsorptiondata (0) of Wakamatsu and Fuerstenau (29) 88 a(unction of the number of carbon atoms in thechain.

t;AC81) under conditions of zero zeta potentialare in general lower than those obtainedfor the nonelectrical free energy per CHIgroup, t;-, for transfer from aqueous solu-tion into micelle. This might partly bedue to the possible higher restriction inthe movement of the molecules in the hemi-micelles than in the micelles. The largerexposure to the aqueous environment ofthe portions of the a.lkyl chains in the hemi-micelle than in the micelle must also cer-tainly be taken into account.

The value obtained for ~(sa) by treatingthe data obtained for Hl\IC from flotation

factant species at solid-liquid interface is, data was 1.01 kT (4, 5). It has been shownas reported earlier, -0.98 kT (2). A similar earlier (5, 30) that the adsorption of thetreatment of the data of Wakamatsu and surfactant species at the liquid-air interfaceFuerstenau (29) for concentrations of is the most important factor under conditons$urfactants needed to make the zeta po- of incipient flotation. Surfactant speciestential of the mineral zero at constant forming hemimicelles can be consideredionic strength yielded a value of -0.82 kT during the flotation to be essentially at thefor t;h(81) while treatment of their data for solid-air interface with its alkyl chainsconcentrations of surfactants needed to located in the gaseous environment of thesho\v a change in the slope of the adsorp- bubble that is in contact with the mineraltion isotherm which has been ascribed to a particle. In this connection it might bepossible change in the sign of the zeta noted that the above value for t;A(a&) is inPOtential of the mineral particles gave -0.80 agreement with that obtained for transferkT (Fig. 4). The latter value may, ho\vever, energy per CH2 group with the help ofbe neglected since the reported adsorption Traube rule from the surface-tension datadensities of various surfactant at the above for the surfactant solution-air interface.concentrations are not constant, as it should .have been if the zeta potential was actually H ydrophile-l~pophile Balance

zero at these concentrations. It can, how- Surfactants have been classified accordingever be said that the values obtained for to the Sizes and strengths of the hydrophilic

JovrMl 01 CoilM llftl.rl- &NtIce, VoL 37. No.4, Det'8mber 19i1

~,.~:'

~

R- ATOMSCHAIN. .

If log HMC of sodiumtropboretic mobility(0) of Wakamal8Unotion of the number

738 LL.~ AND SOMASUNDAR.~~

T.\.BLE IVHLB "'.\LUE8 FOB SODIU1I F.\TrY ACID SO.\PS, SODIUM ALKYL SULI'.\TES, .\ND SODIUK

AL~YL SULPONATES -HLB {Eq. tub.rmula CAlC (mole liler-l)

21.35~.-IO19.-'518.5017.0041.90-10.95-to.OO

39.0538.1037.1513.2512.3011.3510.0109.4.~

1.0 X 10""1 (~OC)2.4 X 10""' (~OC)4.~ X 10""a (~OC)9.0 X 10"". (~OC)1.8 X 10-. (~OC)1.1 X 10""1 (45°C)2.9 X 19-' (-46°C)7.5 X 10-a (-'5°C)1.9 X 10""a (-46°C)5.0 X 10""4 (-46°C)1.3 X 10""4 (45°C)3.0 X 10""' (35°C)9.8 X 10""1 (35°C)2.7 X 10""1 (35°C)1.0 X 10""1 (35°C)3.4 X 10-- (35°C)

CH,(CHt),cOOXaCH,(CHt)I.COOXnCHs(CHt)11COOX aCH,(CHt),tCOO~ nCH,(CHt)ltCOOX ;1C,H11W.NaC1OHtl~.~1IC11Ht..'o\O.~ IIC1.H1tSO.XI\C1.H~.~uC1,Hs7HO.XI\CltH,ISO,.,-"aCttH,oI8(),NaC1.H,~..~aC1,H~,N aC1IH'7S0~'\'a

C"CISCt.Ct.Ct.C.Ct.Ct.c,.C'ICt.('"CISCHCtlCt.

and lipophilic group:-; ill their molecule~.Balance of the above t\\.o opposing kindof groups has been c:llled "h:-,'drophile-lipophile balance" or HLB. The HLBvalue of a surfactant is obtained :\8 follo"..-;on the btL.'5is of kno,,"tl group values de-fined empiric:uly by C;riffin (31) :\ndDa,;es (32) and listed in Tl.Lble III.

HLB = ~('-alues for hydrophilic groUP8\- 2: (values for hydrophobic. groups) + 7 [12)

On the basis of the :\bo\e, a lipophilic surf:\ceactive agent is tL.~igtled :\ 10\" HLB numberand :) h~'drophilic one is :\."ISigned I.L highnumber. HLB values for ~me ordintll1"surfactants are given in Ttlblc 1'-. It mightbe noted that the vl.Lriation of HLB valueper CHi group in the alk~'l chtun of thesurfactant is -0.475 ",hich ",hen multipliedby 2.303 kT again ~'ield., -1.09 kT, com-parable "ith the value obt:uned for trl\nsferfrom aqueous :o;olution to :;ol\ttion-II~"dl"O-carbon interface.

SulubilitySolubilit~" d:\ta for \l~rious long-ch:\in

surfactants are plotted in fig. .5. The rela-

J0VnI4/ 01 CoII.u 4"~ ("",,/ae# Scie"".. Vol. 37. Nn. ~. I)e.,.mbel

\.

1~

;:I=" llOinted ou 1..,~:~llSe while\tl'tlded confi-I\:litlS, in the,'Ililitig t\8 a re~

II~ between,-I II:; (10). S

:..i' tIt portion,"I\Il'OUS en~;r("II:lllge that i11\I»t'cular Val!r:III~£ering frcl'Ill' ~lope of tI,ility in \Vatel,I 1\lIlction of\\ ile the sol

, .'n d n:111'","" .h"ln\\' their ('Illl' tLlkyl sul,\':uue:i. The-:11 uration c~;

III l'qwlibriu:,,\irelles andI.,r the euergI'; ~ill sulfou;I t that sor;11 I Ile form 0IHI..."ess some,'\'l'll while i

ll:\.., in eqw;t r:ms£er ener,liITl'rence bltll:lt \vas obi,,' ionic su

!.S-! kT ;1

I;. the abo'11:ITure of t

-IH'cies into,Iimers, mic

It mightI ...,Iubility c

,t ,-.o°C (g

-1.21 k, I've for"

I II it" the f.I,~"iv~ ene.I\lth lUcre:

tionship is linear in all cases at least up to avalue of 14 for n. The slope of the lincafportion for alk)-l amines at 22°C (11111:\lcohols at 25° can be treated to give,respectively, -1.53kT and -l.34kT fOf

the transfer energy per CHI group fnll1\

aqueous solutions to liquid stat{'. \,"l'

will indicate this energy as ~l' The

corresponding value for fatty acids at 2fioC

is -1.4;3 kT. Since these acids have ~L m{'lt-

ing point above 25°C, this energy is for thc

transfer of CH2 group from the aqUCO\L.;

solution to the solid state and this \\ill ~

referred to as ~. . This is compart\ble \"ith

the value mentioned earlier for the encrg.\'

for complete transfer from :\n aqueous to ~L

hydrocarbon environment. Dissolution of ~L

surfactant in water might indeed be 0011-

sidered as a transfer of the molecule~ from :L

hydrocarbon interior to an aqueous en-

vironment. It might be noted that if the

surftLctant is solid, then the energ)' of dis-

solution should include also a term tu

account for the "fusion" of the solid, TIle

peculiar change ill solubility in the regioll of

C1,-C1S is in line with the smaller ch:\llg{'~

in the corresponding partition coefficiellt~

and the dimerlsation constants. )lukerjee

r 1971

FREE ENERGY OF SURFACTANTS 739

. 'ATTY ACIDS. Z"C I I

. 'ATTY ACIDS. 5O"C -t1O

. 'N££ AMO.£.ZZ'C I

. ALCOHOLS. Z"C i

. No ALKYL ,OUT£s.:Z"C I

8ULI'.\.TES, .\.ND SODIU~

::~ IlUinted out thnt this might possibly be",'(':IIL.~ ,vhile SD\nll chains remain in :m 10\(I,tlded configuration in \vnter, vef}' long'::Iill", in the C1rC1S range, tend to\vt\rds.,':1111; t\S a result of the hydrophobic bond.

;ll't\Veen portions of the s.'\me :\Ikyl:,; (10). Such bondillg bet,,-een the «if.

".llt portions of the same chain \\"hile in,'lllt'IIIIS en"ironment "ill reduce the energy,;I:III~e that is possible due to the inter-:11'11,'('ultLr Vim der ""I\:.Lls cohemon tLfter'r:lll~fcring from an aqueous en"ironment.1111' ~Iopc of the lin~ obtained for the solu-i,iiit," in \vater of :-o<lium tLlkyl sulfonateM :1.8, "Iction of the chlLin length is -1.00 kT. "\\ "the solubilities of tLlkyl nmines, fatty I

II',I~, t\nd alcohols diseu.~l above nre:",i(I\\' their Ci\IC values, the 8OIubilities oftill' :Llkyl su1foruLte~ t\re above their C)[C,:Illle~. The solid "ulfolli\te surfactant at-ltllr:Ltion Ct\n, therefor~, be con"idered to beIII 1'lluilibriun1 "ith mOI\(Imer.-; 1\8 \vell :\8Illi"l'lles t\nd possibly «imcrs. .\ lo\\-er value:" file energy transfer in the CMe of long-," :1 sulfonntes is th~n po~ibly due to the::': tluLt some of the di"'..olv~d species nre " ".. EIII 1 11f' form of micelle~ and dimers Imd hence Correlat~ between Ii arlOUS free ll,;r!JYi"I';"'('s.~ some intermolecular cohesive energy Changes. OP& Tr~8fer /rol'&. an .~que'J'~"1,,("1 \vhile in ,vater. If the .o;olid surfactant Soltd£on to Different Fll&al .~tates

\1:1... in equilibrium "ith micelles only, the Energy change due to the trnnsfer ofIr:lll"fer energy could be expected to be the t\lkyl chains from aqueous .'1Olutions is found.liIY.'rence between -1.44 J.:T and -0.6 kT to be in the range of -0.6 kT to -1..j kT11,11 'V:\S obtained for the micelle formation per CH2 group dependillg on \\"hether the" itmic surfl\Ctunts. The v~lue between tratl~fer of the chaiI1S i~ into a micelle, h~mi-

"i-1 kT and -1.44 kT that 'VILS obtained micelle, hydrocarbon medium, or liquid or111 tile ~ve C3..~e possibly depends on the solid state, the amount of internction that is

11:11 lire of the distribution of the dissolved possible bet,veen chains (\S '\"ell ~ other

",,'('ies into variou.~ states such us monomers, factors such ~\S entropy of the molecule,; in,lil'I('~, micelles, etc. each ~tat? being different from c~ t.o case.

I t might be noted th~Lt tile 81ope of the The ml\X1~um .tot~\l energy of cohes1on be-I b.l.t f I I . f tt ...1. tween chams WIll l\Ctu~lly be the value th~~t'" II 11 Y curve or ong-c It~m a y acl~ . .- -()OC ( . . F. . ) . 1,1' 1 can be obtained from evaporatIon dt\h\.I' I given m '1g. OJ Vle umg u va ue. . . ".) . v Th18 value WhICh we '~"111 call ~. 18 gIven

" -1.-1 kT for~. 18 lo\ver thl~n that of the by Debye (26) ~ -2 kT. Energy tran"fer

'01,1 \(~ for solubility ~t ;:?;jOC. Thi~ is in line per CHI group during dis.'SOlution, ~. ur

\'II~I the fact that the van der WMls co- transfer to hydrocarbon medium from an11""we energy bet\ve~n chains \\;11 decret\Se :\queous environment, .. is about -0.6 kTI,ith increase in temperature of the system. less than the above value, pos,'3ibly due to

JoWlIG1 01 Col~4 an41nlcr""'. Sri""" Vol, 37, ~no ~. l)ecpml~r 1971

HLB <£q. (Ill>--

21

~

19

18

17

41

40

-to

39

38

37

13

12

11

10

9

\ +. I c-0..3' T'iOm -10

-+, I-0."" -z 3O3-T i. I

II

10

~....i...: -= 10.~

~

+,-o.52"~

~\.

\\ \

\\-~\+. .-0.131' i:'jO"jOT . '\L -0.581' on:Ja,

~ , , II 15 15 17 ItN_R OF CM- ATOMSIN THE ALKYL CHAIN. .

FIG. 5. Least-square plot of solubilities ill waterof medi\tm chain alcohols (34), lollg-ch.'\in amines(35). long-chain fatty acids (36), and long-r:haillsuI foliates (37) as a fUllctioll of the num~r ofcarbon atoms in the chain.

, in nil c~es at le:\...t lip tll :,

,~, The ~Iope of th(' linl':,r,.'-1 nmin~s at 2:?O(~ :11«1. can be trented to ~ivr,

l,53~~T mid -lo:{.J"'T fllr

~r~' per CH2 grollp fnllllIUS to liqlud ~tat('o \\"t':his energ}' IlS q". 1111'llue for f:rtty :Lcid:) :,t :!;j"Cice these acids huvc :, IllI'lt.!;)oC, thi.'! energ)' is fllr tIlt'! group from the :I.11I1I'CIII"~lid :)tnte and thi" "oill Ix', , Thi.'! is comp:Lr:lhlt. "oilhoILed eurlier for tilt, t'IICfJt'°II...fer from :Ln :LqU('(III~ to :L..ironment, Di:):)()IIltitlll Ilf :1

tLter might indeed bt' 1'1111'~fer of the molecul('~ fnllll :1t~rior to un :UIII('('II~ t""IU~llt be noted tll:lt if tIlt'

id, then th~ ~n('r~o" tlf cli~.include al~ ~L I,'rlll tll

"fu...ion" of the ""lit!. TIlt!in ~lubility in till' rl'~iorl I,f

l~ "ith the smnllcr loh:LII~t'"nding pnrtition C()('ffi('il"'I~-ution constnnts. :\ Illkt'rjt'~

.3.'j

.4t1

.".'j

.i)O

.55

.00

.\15

.00

.05

.10

.1.~.)-

.;:0>

.:~I

.3:)

.4t1

~

...38 40 -&)4 ..

fJ

the inter-.lction bet\\'een hydrocarbon chainsand \vater molecule~ and due to the possiblelo\ver entropy of the hydrocurbon chains inthe t\(lueous solution8 than in its gt\.~u.~ ~state. If the dissolution is from t~ ."Olid I'tt~te :;;then the energy trt\osfer per CH:! gnlllp, ;~ cml be expected to be different fn)m 1/10 ;,

.10by till amount equ.~1 to the ene~' ch.Lnge ;due to fusion per CH2 group. Furthermore, iif tL major portion of the di!':;olv~d ~pecies :;:

exi"t~ at saturation .~ micell~s or dime~, ~1/1. \\'ill be minimized by .Ln .Lmolmt that is i 10

repr(',;entative of the enel'g.\' of coh('~ion of ~chain~ in these micelle~ lLnd dimers .Lnd th~ i.ufr-dction of the specie.'! pre.-;ent in the.'!eform~. Belo\v the Kraft poil1t, tile ener~'change \\;ll be due to tlle \Vettillg of tIle8urfactant, primarily the hydr.Ltioll of thepol.\r heads. According to Sllirum.L et al.(3;3 i the heat of \vetting of ~ium n-.~lkylsulft\te:J is -4,2 kcalfmole and th.Lt ofsodium n-alkyl sulfotlates i~ -8.6 kcalfmole.The ene~' for trallSfer per CH;! group froman aqueous solution to micelle, 1/1.. is signi-ficantly less than 1/1. or C;o dllt' to 8everalfactors described earlier I'uch .\8 the pr~s-t'nce of counterions in the "kinetic micelle",the ~lectrical repulsion bet\Veetl the pohLrheuds, the pos.'!ible expo~ure of portiotls ofthe alkyl ChaiIlS to the t~IUeOl1.~ environmetltand the possible restrictioll of tIle movementof the chains in the micelle. TIle ene~' oftran8fer from .\0 nqueou.~ environment tothe air-liquid interface, 1/11. ,\;th chtlillspractically out of water is, on the basis ofsurface tension data, of the ord~r of -1,08kT. The movement of the alkyl chuin cunbe considered in this ca..~ also to be some-\"hat limited than in .L hydrocurbon me-dium. In addition, the higher repulsionbet\veen polar he:td~ \vhile the surfuctantis .\t the liquid-gas interfuce mu:;t tLl:50 beconsidered. The value for trunsfer ene~robtained for hemimicelle formution, 1/1.(1.) ,from flotation data i... close to the above value-1.08 kT obtained \vith the help of Trnuberule. This is in line \vith the fact that thestate of the alkyl chains in u hemimicelle

Jovrllal rJIC~/0i4 UIla'l..wl- &i_, Vrn. 31, ~o. i. ~lDber 1911

-..

j...,

~'=i

~~~

I I /1tI

~

?I f !1

-SOOtUM .CO... I

SULPHO"ArES')~1._'UM ALOTL

SULPHATEs'g'oc -SODIUM 'ATTT

ACID SOAPS. 10"(

~)

...

.:c

$;-: !.

i¥

&..--".0 .

., ...FIG. 6. CMC of sodium alkyl sulfates, .'SI1dilllll

rt.lkyl sulfonates, and sodium fatty acid !I()IIII~plotted as a flmction of the correspondinlt 111.11values.

-z-

:1-:::~ ~. ::7::-.

"\.\

~\

~3

..-= .=.z =

%~~ -r;

~~";j x~ ~0; ~on =- -

.": -

-<:

-

at the solid-gas interface and the ~t.Lte tlfthose absorbed at the liquid-gas interf.Lrrcould be considered to be more simil.Lr t \Ieach other than most other possible :;t.Lt('~of the hydrocarbon chains discussed .Lb<I,r.Values obtained for ~~(Ii) by treating tiledata for solid-liquid interfacial propertir:;,such us zeta potential, is in gencr.ll le:;.'!th.Ln -1.08 kT possibly due to the I.Lrgrrexposure to the aqueous environment of till:alkyl chains of a hemimicelle at the ~liu'liquid interface than those of a hemimiccllt!at the solid-gas interface.

The value for transfer energy on the b:L:.;:;of "hydrophile-lipophile balance" of variol~surfuctants are identical to the -1.o.~ kTobtained by applying Shinoda's tre:Ltmclltto C~IC data. In fact, this correl.LtiOlI i:ievident \,hen one examines the follo\\.illgp°1;..,iblc interrelation bet"oeen C~IC :11ldHLB derived on the basis that chain lengthis .L common detennining parameter for bothC)IC and HLB:

log C)IC = a' + b' (HLB). l131

It might be noted at this point th.\t Olle

FIIEE EXER<;¥ OF .'IURFACTAJ.~TS741

~4,4 .-~ -~~~::

I §:.¥:;~

l~-

-~

~-~~-~ ~

'=i-~~

~~~

7:E-

-~- ..;: :- ~

~t

'"'

~ Q::.

~

:!;

-- ~::i-=:;?!

~

1

i _"¥

~~

., ~.;.;

.=

-~..:c

t:

0

I

.

i'

l

-~~.,.,.,.,

~:;:--

s.t..t..-:c-:c

~~, I

8SOOtUM A.OYlSUl~"O_A r(5. )"t:

8SOD1UM A,OTl ;SUl T£s' g.'OC ._IUU 'ATTY

ACID SOAPS. lOOC

" ZI ')

-~~-c-c-===

:i:iI I

.....

~..:c

0:-I

~.:cIe"':-

-:c

e:

~-:c

~

-t:: t

-.;c""- ~:o;~~..,7~7-

~-:ot:-~-

...

.:c

~

~-:ce-I

\8,..

"..

.." II

:e:II

.II II

...

-l

t:I

.

-4?-i

~

.:e:.lkyl sulrlll~. ",..Iillhl1m fatt.y IIrill "'1111"~ l'orresprll,llihlt 111.1\ i

..§~

'5S

~

'::-°

~O;:

;.,~

~

- .~ ...:J -

-:'"..= -%-= % c:;-:;-~:: .~

>.=:

=ii~~. = =

~i1- = ~.- -

.._~~ ..: .E-

,,-

1=i~

~.;4

Z

!

:-..;4-<

~ ~\nd tll(' .--t:LII' Ilf

quid-g:I.~ illtl'rf:II'"

>e more ~il11ilar If I

her poHsibl~ ~t:LIf'"

IS di~ul!.-;ed :11)41\1'.

II by tre:l.tillg 1111'~rf~\ciul pnlllt'ri ii""is in gcl1l'r:LI It"""

dut' to tIll' l:u".ICI'r

'nvironmt'111 'Ir II..,

celIe :\t.. till' NlliJ

t' (If .\ 1Il'mimit,,'lh'

~

.E.

::;.

~a;

£

~""

~

~~

--

~

-.~

;:

'--:-,I~

-

~

- x;.; :.

1~=,.=

~ ~ -: "#x - - ,-":-x-

~ '~ ;.-~,;,!- ~= " II - 'I=.::' =':-=~=~

;:~ ;:

~;2

-

~- =. = ":

x :~ - ~ -.:. II =-::.j~i~--: -"

~I

t!.

j

i:

~.

3~I

-::;:i

C~

.2?

1

~

~-:i

~

.-

7;!..~ .- -..,,::.. -

-- - -

.::- . =

~I

-;~~

~

nerg)' on tile b:l."i,.

,nlnnce" of v:~rillll..,to the -1.o.~ 1;1'

inuda','i tr(':~t.IlII'IItthis c()rr(~I:~t illil j"

ne~ till' ti,llo\\'i.llo:t'V(,~11 (::\1(' :11111that ch:~il1 1t'I1J(t II

laramet('r for t>Clt II

c;-= ;;"i -=

%1

~-i

x..

--- -.- :;- -- -- -

-= .--z

-l 1

~.~-

': 7:- - - - -- - -.;:.;: .;: .§ .§ ~ .;: .~

~:§ :§ :§ :§~ :§ ~~ ~ ~ ~ ~- 7: 7:

~ ~ ~ ~ ~~ ~ ~~ 0 ~ ~ = .: :: ::=: g =: =: 5:: $: =;.;. ;. ;. Co.: Co ;.

-<.or: -< --: -< -< .or:

J"urn,1l 01 Colloi~ "n~ Inter-fl,". s.,;..."r, ,",01. :17. N.t. ~. /)".,.,Inl"" 19.1

C)

-;;m~iim

.~;..,

;;

~~<

~

~f.;:

""

b' (HLll). [1:11

1is point th:lt lIlli'

~ot4

~QI

%

:;~

=7:".C:; "T: ~

~

u~

~.../I~

.~

il

~

~.

~

"',~

1/~

~"

~-~.,=

.; =- I

-~.,~ IIj ;:

=

se;

~

3

~~

,.:-

1

-g

]~~- -:.'=

~x

~

-<

\~~

/

LIN .\..~D SO~IASUNDARA..~742

GASEOUS STATE

~

.vjut' :~ m

11'1111\ tn,!.-u tllt'!1IIImol.

u'

AQUEOUS SOLUTION

r~'Ii I, 1I i. .

! .

, ..; \,;l'XU.\I:

! 1'lIy... C, ,1 \,;I;XD.U;

I'I'E~TEX. ..) (1"'" ,~.- """

, ',1 \"rXU\I;

I 'Elt$TE';

i 11.55: , IC"TEX.\r

~. '\I.\:iCXD

I !"IIH) ." ,... .\: \,;t:!\"D,\.E

'(,aM. .-iI,. ...!.I!I,Jda. K

I!I,~J); J.. 1'!.,llipI, J.

, 1!15.)., ' ..\rf'oee. ,\

.. .,fll,'e A..

1.lx, I. J...'.1'; Soluti

rlll':sis. Te)" ,I"g.\', H,.\. (unpub.

I., :\l.\RKIX...

,If ).,., KLEVEXS

30. ;Of; (19.5: H\ltR\'. B

i.I.I., G. F

(1970'! I, '\'£1(. !

, ;'/'11. 66.

'. .\I!Kt:RJEE.

1. :!"1 (1111II ~II'KERJEE. I.: III.!I\"E, P..

,1"'11/.51.. I "!,RIX, )1

.; "ll'r, rh.

\:'-'U.\., K

'lJ\RD, r

T. G., TrG

I ~'"

can determine a' and b' in the follo\\ingmanner, \vhich l'ru~bles the detem1in:\tion ofCMC for a homologous ~erie~ of any 8urface:1Ctive agent from knO\"l HLB v:\lu~ I\ndvice versa. Substituting Eqo [1:!J in [1:3J wehave

log CMC

= a' + b' [~ {hydl"(lphilic ~rclllp)

- ~ (hydl'Clphobic J{rmlp)

+ iJ. [14)

Equations [3) :\nd [14), on the b:\Sis of thedata given in T:~ble III, yield the follo\\ingrelationship bet\'Oeen a, b, a', and b':

bib' ~ O.4i;),

~to

MICELLE (IONIC)

HEMI-MICELLE AT SoL

MICELLE (NON-IONIC)AOSQftPTION AT L-GHEM I-MICELLE AT S-G

:md(0 - o')jb'

- ~ (hydrophilic grtIUp:i:1 + i. [15]

Once 0 and b t\re kilo",} (Tt\ble 1'-), 0'and b' are readily evalu:\teu. For example,for n compound of the UCOOXa type,

, ", ..

HY~~~ROUN-

LI~ID STATESOLID STATE .

FIG. i. Illustration of free-energy chuIIKI'" III"'CHI group involved in the transfer of nlk~.II~bnih'between various colloidal and interfnci:.1 ,.I:~'M.

"\

~~\

,;..S

values of a alld bare 2.41 mid 0.341, re-spectively. Using the~e values a value of-16.33 is obtailled for a' and 0.718 for b'.The final relationship is then

log C~IC = -lG.33 + O.il.~ HLB. [G)

Data based on T~\ble I for the C:\IC ofof sodium fatty ~\Cid 1!(}~lp~, ~ium alk")-lsulfates, and :oIOdium alkyl .'!lllfon~\tes ~\replotted in Fig. ij as ~\ function of the cor-responding HLB values obtained by \lSingEq. [12); linearity bet"'een the two param-eters is evident in both c:\.-;e8.

Sumillary1. The values for free enel"g.\' per CHi

group involved in the trallSfer of ~\lkylchains from one state to ~uiother duringvarious phenomena :,;uch ~'-~ micellization,hemimicellization, adsorption at the liquid-gas interface, and evnporntion are found tobe in the range of -0.6 kT to -2 kT (TableV). A schematic illUstration of these freeenergy changes is shown in Fig. 7.

J-Z o/ColioOl OM l..w, &icftCe. Vul. 31. ~o.~. I)..,.mber

2. The differences between tht' v:lri",.,

values obtained for the free-ener~' Ch:llljtl"can be explained by considering th~ ,'xl rIll

of interaction that is possible bet""{,{,11 I III'

chains in the various cases upon rrm'I\":11from the aqueous environment, :\1111 "IIII'r

such factors as the presence of :\ny i~lt,'r:I"tion between the CH% groups ,vhil,' ill I h.' "aqueous solutions due to the fon":~ti'II1 "i

dimers, etc" and possible expo.'\ure "£ till'chains, ,vbile in various states, pt\rti:llly III

the aqueous environment, as ,veIl :1.0; tilt'

presence of any repulsion betwet'11 IJlII:trheads and t\ny restriction on the m"V~I1\t'111

of the alk-yl chains while in these :;t:ltr 3. For the ca.lculation of eohesi,~ PI\t'I"!!.~

per CHI group for micelle fom1:lti'JI1 "i

ionic surfactants, it ,vas found nec~"...:I~. IIIapply a correction based on n trentml:'/lt "i

Shinoda for the "kinetic micelles" CII/lt:lill'

ing the counterions.4. Finally n correlation bet"'t'£'11 tit,.

HLB values used in emulsion teclllI"l'I~~tmd the corresponding C)IC data "":1" f(llIlItl

19i1

7-13FREE ENERGY OF SURFACTANTS

.!"."ide a method to llumeric:uly evt\lunteIl' from the HLB v:uues (\vhich call be

I:tted theoretically) and ,-ice ve~'\ for,: 1 homologous series of surft\Ct:\nt~.

~+,

rll:IIII("" I"'r!\lk~-I "lIni".:iill ..1 ;LII'IC.

REFERENCES~. \;\SUNDAR.\N, P., .\ND FL'Z""TE~.\l', D. W..

.! - Phy.. Chern. 70, 00 (1966)..-'. ~!\SUNDAR.\N, P., HE.\LY, T, W., .\XI>

rl'ERSTZN.\U, D. W., J. PhyJt. Chenl. 68.

:'.~2 (1964).~.,~_\:;UNDA.R.\N, P., HE.\LY, T. W., .\NI>

fl'ERSTZNAU, D. W., J. CullfJid Inlerfa,'e,..,i. 22,559 (1966).

: i :ERSTBNAU, D. W., Hz_\LY, T. W., .~~I>~.:,~.\.SUND.~RAN, P., Tram. AIJIE 229. 321

119M).-, .-'.."~$UNDARA..."f, P., .~ND FUZRSTE~.\f:, D. W.,

Trcma. AIME W. 102 (1968).,. .-'hiIJoda, K., Bull. Chem. &c. Jap. 26. 101

: 1~153); J. Phy.. Chem. &8. 1136 (1954).- l'l1llipe, J. N., Tram. Faraday SUI'. 51. 561

11\155).- '_, rence, A. S. C., et al., Proc. Int. C&ngr,

"',rface Actil1., 2nd, 19571.385 (1958).Ll~, I. J.," Adsorption of Gases from .\qlle-

.,IIS Solutions on Mineral Surface," D,.,;;c.Thesis, Technion, urael Institute of Tech-I.,/logy, Haifa (1968); LIX, I. J., \~D METZER.A, (unpublished results).

.1" :\1.\RK:l~A, Z. X. et at. Kolloid. Zh. 26. i6

(lfM}-l).,'J KLEVZNS, H. B.. J. Anler. Oil Chc>n. Soc.

30. 76 (19,13).j B\RRY, B. W., :\IORRISON, J. C., .~XD Rf:S-

-ELL. G. F. J., J. Colloid Intcrface S..i. 33.H (1970).

t- HOYER. H. W., .~ND }L\1t.\to, A., J. Phys.'-he,n. 65. 1807 (1001).

It I ~rl'KEa.rZK, P., .!dron. Colloid Interfllce Sci.1. 2-&1 (l96i).

II ~1,KEa.rZK, P., J. Phy.. Chem. 69, 2821 (1005).I~ I>EliYE, P., .~ND AX.\CKER, E. W., J. Phy.,.

,-"'tln. 51. 18 (1~7).1 1-"!lRl~, M. L.. _\XD H_\1tKl~S, W. D., J.

A,lier. Chem. Suc. 69. 683 (l~i).i -IIIXODA, K., J. Phy.. Chem. 58.541 (1954).I.. ',-,.D.\RD, E. D., HARV\, 0., .~~D JO~ES,

T. G., Tram. Faraday &c. D. 980 (195.1).

16. SHINOD~, K., J. Phya. C~. 59, -132 (1955).11. CoRRIN, M. L., J. Colloid Sci. 3,333 (1948).18. ~IYSEL8, E. K. .\.~D MYSELS, K. J., J. Colloid

Sci. m, 315 (1965).19. PZTHICA, B. .\.., Proc. Int. Congr. Stlrfal.e

A("til1., 3rd, Cologne, 1900 1, 212 (1900).20. Bc\RRY, B. W., MORRISON, J. C., .\.ND RUSSELL,

G. F. J., J. Colloid Interface SI'i. 33, ~

(19iO).21. Cit~ in Refs. (13) and (20).~. ~1t:KERJEB, P., ~lYSELS, K. J., .\.NDKAP.\.UNA~,

P., J. Playa. CAe/no n, 4100 (l96i).'23. MUKBRJEB, P., J. Playa. Chern. 6&, 13i5 (1962).2-1. D.\.VIES, J. T., Trana. Faraday Soc. 6&, 1052

(1952).25. STIGTKR, D. .\ND OVERDBEK, J. Th. G., Proc.

Ilal. Cltngr. Surface Actil1., 2nd, 1957 1, 311

(1958).~. DEBYE, P., J. Phy8. Colloid Chern. 53, 1 (19-19).27. B.\NGS, L., "Surfactant Dimers and their Ad-

sorption," Pill Thesis, M.I.T. (196-1).28. .\.PL.\.N, F., AND FVBRSTBN.\.U, D. W., Froth

Flotation, 1962, 1iO (1962).29. W.\K.\3o1.\.TSU, T., .\..~D FUZRSTEN.\.U, D. W.,

Adllan. Chef/to Ser. 79, 161 (1008).30. SO1l.\.SUND.~RAN, P.. Trana. AI.1IE HI, 105

(1968).31. GRIFFIN, W. C., J. Soc. Cosmetic Chern. 1, 311

(1949); "Encyclopedia of Chemical Tech-nology" (R. E. Kirk and D. F. Othmer,eds.), Vol. 5, p. 692. New York (1950); J. So(".C08met. C~. 5 (1954).

32. D.\VIES, J. T., Proc. Ilal. Congr. Surface Act.,2nd, 195i 1. -!26 (1958).

33. Shinoda, K., Hirota, S., and .\maya K., J.Culloid Interface Sci. 21. 102 (1~).

3-1. SEIDELL, A., "Solubilities of Organic Com-pounds," 3rd ed., Vol. 2, pp. 316, 400, 56':.Rnd 622. D. Van ~08trand, New York (1941).

:15. BRO\\"N, D. J., .-\EC Progress Report, NYO-3678 (:\UTS-~) (1953).

36. JOH~, L. M., A~D ~lcBA1N, J. W., J. Amer.Oil Chern. So(". 25, -11 (1948).

3i. ltEED, It. M. _\~D T.\.RTAR, H. V., J. Amer.Chefn. Soc. 5&, 323 (1936).

38. L.\~G3o1uIR. I., J. A mer. Chent. Soc. 39. 1848

(1917).39. HAYDON, D. A. .\.:-'D TAYLOR, F. H., Phil.

TranI. Roy. Soc. London, 252, 225 (1900).40. D\VIE!!. J. T., Trana. Faraday Soc. 6&, 1052

(1952) .

et\vef' II thl~

L teclllll,!I,I,.'."tn \va... fount!

fovrMl 0/ Colloi~ aa~ I"""_~, Vol 37. No. t. December 1971