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Surface tension minimum in ionic surfactant systems II. The effect of oil reservoirs
Calfoiifs and Surfaces, 4 (1982) 61-75 Envier SeiientNii Publishing Company,
Amsterdam -
Printed tn The Netherlands
SURFACE TENSION MINIMUM IN IONIC SURFAdXANT II. THE EFFECI’ OF OIL RESERVOIRS JOSEPH A. BEUNEN+ apartment
51
SYSTEMS
and LEE R. WHlTE++
of Applied Mathematics; Research School of Physical Sciences, Australian
National Uiziuersify,Canbezm, ACT (rlustralb~
(Received June 17tb, 1930; accepted in final form September 23rd. 1981)
ABSTRACT A model b developed to examine the efkt of an oil teseenroiron the surface tensbn of the air-water interface in the presence of Ionfzabte suzfactant. 7&e minimum In the surface ten&n as a function of pH previously found for the case where there t no oil (and mrlbed to the presence at low pH of undissolved surfactant) can atso occur fn the presence of an oil phase even when the system does not have an aqueous Eolubility edge. The oil-water interface is also disced. ‘I&e theory predicts the spontaneous emufsification of the oil-water syskrns over a rangeof PH.
1. INTRODUtX’ION If has been
found
aqrlmus soiuSws
experimentally
that the surface tension in dilute
of certai~~surfactants goes through a minimum as the pH of the solution is varM [Il. Both acidic [ 11 and basic [2] surfactants exhibit this phenomenon which depends sensitively on the surfactant concentration and the ionic strength of the solution. While impurities are a frequent cause of such minima [3] we have shown in a previous vrrork[4] (hereinafter referred to as Paper I) that it is possible for a minimum to occur even in puxe systems. In Paper I a model was developed for the surface tension variation of oleic acid, for which experimental results were obtained by Kulkami and Somasundaran [lJ. The minimum in fhe surface tension may be understood qualitatively in the folIowing terms. At Iow pH ther+ is a precipitate of oleic acid which maintains the concentration in solution at the saturation value. An essentially neut& (associat8zd)
*Present address: Department of Chemkal Engineering,State University of New York at Buffdo. Amherst, NY 14260, U.S.k **Resent addles: Department of Physical Chemistry, Uoivemiy of Melbourne, ParkvilXe 3052,lEctoria. Autralia~ 0136-6622~82l000~000~$02.76
Q) 1982
F,hevier Scientific Publishing Campaay
monolayer is present at the air-water Inkrfacz giving rise to a surface tension less than that of pure water by an amount equaI to the equilibrium spreading pressure of the acid. As the pH is increased-the number of oleate species in solution rises as ions form by dissociation and mole neutral mokcuIes dissolve from the precipitate. This Ieads to Increasedadsorption at the interface and hence a further reduction in 7. At the solubility edge the precipitate has entireIy dissolved and there l:an be no further increase in *he concentration of oleate species. There is thus no tendency for 7 to decrease further. In fact, the dkociatkn of acid molezrles causes the monoIayer to become increasingly charged. The eIectrost&c revulsion of okate ions leads to desorption from the nlonotayer and a resultant i:crease in 7. kom the above, it can be seen that the precipitate glays a vital role in bringing about the initial ~-Iuction in the surface tensiranas the pH in creases. Its function is to act as a resenroir which mainttins the concentration of neutraI surfacfant molecules at n constant value despite the formation of an increashg number of iona. This raises the qur!ation of the existence of surface tension minima in systems where there is some form of = sexvoir other than a precipitate, Such a reservoir* could be provfded by an olt phase in which the surfactant was soluble, Cn thfs paper, we wiU consider a situation in which the aqueous solution is in contact over part of its surface with a Iayer of hydrocarbon, e.g_ paraffin oil atso containing surfactant. The made1 developed in Paper L wiIl be adapted for the caIcuIation of the surface tension of that part of the water surface open to the air. Once again r will be found to have a minimum as a function of pH, This resuit ohviousIy suggests an investigation of the Interfacial tension between the oil and &r as the pH changes. This is more difficult because it requires a model of the adsorption of surfuctant at the oil-water interface for which fittIe data is avaitabte. However, in view of the current interest in multicomponent watet-oil-surfactanf systems, which are found to exhibit Law interfacial tinsions, an attempt will be made to extend the calculations in this direction. The main departure from the treatment in faper I lies in the solution ch~W~.r, -This is disc-d In the following section. The model of the monolayer adsorption is essentially unaltered and wiI1 be reviewed briefIy in section 3. +Jm -fiction 4 results for the surface tension at the air-water interface are presented and discussed. Finally, the extension to the oil-water interface is given in section 5,
As ir, Paper I, the starting point for the caIcuIatIon of the surface tension is the Gibbs adsorption isotherm: dr = - c r&Q C=) i
63
where Q is the adsorption excea of species I and pi is its chemical potential. If the interface is chosen sr, that the adsorption excess of water is zero, the sum in (2.1) extends over the dissoIved species-surfactant molecules RH and ions R-, monovalent electrolyte M+X- and of C~MUS~H+ and OH-. Now
(2.2) where Ci is the concentration (mol - dm-’ ) of species i in the aqueous phase- Tbis equation assumes that the variation in activity coefficient. can be neglected. This is allowable for the inert ions M* and X- since their concentrations change littIe over the pH range of the experiments. It is also a good approximation for the other species since their concentrations are always small. To make use of eqn (2.1) we must therefore determine the variation with pH of the concentrations Ci and the adsorption excesses L’i*In the aqueous solution CH+COH-
=
Kw
(2.3)
where of course CHf
= ~o-PH
12~4)
iind
where Ka is the dissociation constant of the surfactant (assumed acid) and Cix is the concentration of neutral surfactant In the aqueous phase. If there is a precipitate present then we have also CH+CR- = KS
G-1
where KS is the soLubili& product of the surfactant, Equations (2,3), (2.5) and (2.6) are sufficient to determine the aqueous concentrations of aU cornponents. In this case the oil reservoir has no effect. In the absence of a precipitate, however, eqn (2.6) is replaced by a surfactant mass balance in which there is a term for the reservoir. if C denotes the total amount of surfactant expressed as mol dm-’ of water, this condition takes the form (2.7) where VSq, Vho are the voIumes of .water and oilrespectively. The concentration CEH of surfactant in the oil phase can be related to that in the water by a condition of distribution equilibrium. This must take into account the fact that even at 10~ concentrations the surfactant is atmost com-
64
pXetelydimerised in the oil phase [cl. Thus the following retationship can be expected to hold [6l
where Kd is an equiIibrium constant for dimerisation. Equation (2-7) can now be written in the form
and where we have dropped the now unnecessary superacxiptThe soIub3ity edge, at which the precipitate disappears, is calculated by assuming(2.6) and 12.9) both hold and using {2-E): PHS = PK..
+ Iog,,
[
c - -KS
&l
(
1+e
KS
G
)I
(2.10)
The solubility edge thus occurs at a pH value lower than that at which it would In the absence of oil (0 = 0). For given values of pH and C, the aqueous concentration of neutral surfactant is lower because some dissokes In the oil. TO raise the concentration sufficiently for a precipitate to form, more RH must be formed from R- and so a Iower pH Is needed. Equation (2.10) aI9csshows that for a SuitabIy Iarge 0 there is never a precipitate. interffrce the adsorption exIf we wish trl catcufate 7 for *e Water cesses I’i of eqn 42.1) are those at &at part of the water surface not In contact with oiI, One contibutirm k thase comes from the monolayer of Rand RH molecules at the surface. The numbers of these per unit ares are denoted by CL- and Py respectively. The corresponding surfme charge density is u0 = -qrsR-. 4% IS MS up a doubIe Iayer extending Into the soWion which contributes ionic excesses. To calculati these we use the zeroth-order Stem layer m&eel d&bed in Paper I. In this model there is a layer of width 0 adjacent to the surface from which eIectroIyte ions are excluded. The potential $d at the edge of this Iayer is reMed to #at at the suxface q& bY #I3 = $0 + no 4 M/Q
(2.11)
where e1 Is the dS:ectric constant in the layer. The surface charge density can be related to ,+$ L\yusing the fiit @&@ of the Po@ou-Boltzmanrt equation satisfied by +he potential together with the usual bouridary condition at a charged date. _.
65
00
=
-
EukT
sinh q &f2 kT
2 ml
(2.12)
As usual
(2.13) where N is Avogadro’s number and E is the dielectric constant of the bulk soWion.. The cationic species K-i*, M4 have a positive adsorption excess due to their attraction to the negative monolayer: B-4= cir4
(2.14)
where (2.15) >O Similarly
@XCBsseS
the anionic species OH-,
X-, R- have negative double layer
ri = cir-
(2.16)
where (2.17) For our monovalent system it can be shown [4] that
r4 + r- =
-i-g-
c&p + c&p
(2.18)
tanh q &3/4kT
The adsorption excesses of the non-surfactant species are thus defined. That
of the surfactant ion has two components, and that in the double layer:
rir-_ = i--i- +
CR-r-
the adsorption
in the monolayer
(2.19)
whereas the adsorption excess of the neutral species has only the monolayer componenf: rRH
= %i
(2.20)
66
the surface charge density of the monolayer, and hence all Given I$, double layer quantities, are determined, Thus from (2.11) and (2.12) e. and $,r can be caIcuIated. The latter allows the sum F+ + L‘- to be evaIuated from (2.18)_ As will become evident below it is through this quantity only that double layer excesses affect dy. To complete the calculation of 7 the monolayer excesses I?i- and I?& must be determined. This requires a theory of monolayer adsorption which is described in the following section, Before this is done we expand (2.1) by making use of some of the foregoing equations_ Thus from eqn (2.2)
dr EF
= -lL(dCH+
+ dC&
- r_(dCx-
+ dCoH-
- I-L,
+ dGR-) - r;--
dCRCR-
d&Ii --
(2.21)
CRkZ
using definitions (2.14) and (2.16) and eqns (2.19) and (2.20). Thus dY
kT
= -(I-*
+ r_‘)ac,+
-
I-k-
d CR-‘--
C.r,-
-
I‘&
dGR,
(2.22)
CRH
This follows from ths charge neutrality of the bulk solution where we have assumed that the pH is varied by adding acid to an inilia!Iy b&c solution so that C&f+ is constant. ISy diffd?rentiating(2.5) and substituting the result in (2.22) we have fiaIIy
dr -
kT
= [rS,-
- (I-*
+ r_)cH+J
dCH+ - 4;k+
- (r-i-
+ %HI
dCRH
CCcH
(2.23)
This equation can be used to examine the quaIitative behaviour of surface tension without detailed c&uIafion. Firstly, if there in a precipitate present, the solution chemistry is unaffW*_d by the oil reservoir, except of course that the position of the soIubiIity edge is altered. The analysis of Paper I shows that
dr --
(2.24) < 0 for PH -= PI-I, dpH The existence of a minimum will now depend on whether it is possible for the surface tension to increase when there is no precipitate and the oil reservoir comes into play. Differcntiatiug (2.5) and (2.9) and using the results in i2.23) leads to 2.303 kT d+ =r&H(eQQ*CT(l f 2 8CRH) - 1) dpH CRH CR_ (1 l 2 @CRH) f+ (2.25)
67
where we have also anticipati a result of section 3 (eqn (3.10)). From (2.18) it can be seen that r, + I’L is posi?;ive since the potential ## is negative. Thus the second term in the square brackets above is positive. Furthermore, at high pH when most of the surfactant is dissociated, the monolayer will be highly charged and the surface potential therefore huge. The tit term will then be negative provided the vaIue of 0 is not too great*. Thus once again dr/dpH > 0 and there is a minimum. At low pH, where & $# and hence r, + r- are smaller in magnitude, it is possibIe that the first term is positive and larger than the second so that dy/dpH < 0 even without a precipitate, When there is an oil resemoir the behaviour of y in the range pH > pH, may thus be quite varied, depending on the value of 0: (i) the surface tension may increase monotonically for pH > pHS so that the minimum occurs at the solubility edge as before; (ii) 7 may decrease at first so that a minimum QCCWS not at pH = p& but at some higher value; (iii) for very large 3. y may even be monotonically decreasing in the pH range of interest. The exact behaviour is dependent on the variation of potentizd with pH and to that extent is affected by the model chosen for the adsorption of surfacbnt molecules. This is the subject of the following section. 3. THE
ADSORPTLON
ISOTHERM
Our concern here is the asorption of surfactant at the air-water interface. In Paper I we obtained equations governing this adsorption by modelIing the monolayer as a two-dimensional van der Waals gas. The values of parameters appe&ng in the model were determined by fitting the eta isother!n at low pH to published data. The agreement between theoretical and experimental isotherms was adequate at tow areas per molecuIe but not graodat Iarge values. The made1 is still usabIe however,since, over most of the pH range, the surface pressurg is greater than the equitibrium spreading pressure 83 that the monolayer is den&y packed. Zn addition it is not our putpose to develop an accurate model of the monolayer. The van der Wadis equations provide a reasonable and convenient parameterisation of the adsorption behaviour and this is all that is requixed. We have considered another model elsewhere [7!. but it gives results that are little different. Hence for the sake of conformity with Paper L we will use the van der Waals model here. We give only a brief outline, refer&g the reader to the earlier work for details. Consider a unit area of the surface at which No neutral surfactant molecutes and IV_ ions are adsorbed. The thermodynamic behaviour of this portion of the monolayer can be obtained once its Helmhottz free energy ?6xe d&a of Aveyard and Mitchell [Sl
can he used to determine an upper bound for 2 KA of 2*6 .% 10“. However. since the votume ratio of oil and water can be varied widety, 8dIer values of 8 are easiIy attained.
68
F(&,N-,T) is know-u. To the same degree of approximation as that involved in the double-layer modeZ of section 2, we cm decompose this free energy in the following way.
Here PO(N&L,T) is the free energy when the electrostatic interaction between the charged groups has been switched off. The second term is the work done in charging the inkrface, &, (0’) being the electrostatic potential at a charged head group when the surface charge density is u’. The free energy F,, can be determined by cakulating the corresponding partition fu.?r;k~: (3-2) In the present model U has the form U = m if any two molecuXeooverlap = J&u0Af f N-U%
+ ‘A(&
+ N_)zuint~O otherwise
(3.31
Here t@lf (u_*If ) are the non-ekctrirstatic energies of a moIecule {ion) in an infinitely ditub monolayer and the third term represents the interactions among molecUI_ evaluated in a mean fieId approximation. The quantity uinnt is the interaction felt by a given molecule when the monolayer is cIosepacked (area per molecule equal b a,), Equation (3.3) is substituted into (3.2) and the integral evaluated in the van der Waals approximation to yield the free energy PO Fo(No,N-,T)
= kT(Na In No - No + N_ In N_ - N_ + (NO + NJ
- (No + N-1 In (1 - (& +
U(No + N_-)‘uktao
+ nr_)u,) + &u$~
In A2)
+kPv (3.4)
By differentiation of F(N&N_,T) with respect to NO,N_ we obtain the chemical potentials of the surfacknt species in the monolayer. Since this b in equilibrium with the underlying soIution these chemical poteutiak are equal to the correspo~~dingbu& values pz + kT Ln C&/M, ~0 + kT In C&If where M is the number of moles of s&&ion per Utre of solution (-55.5). Equating the chemical potent&& leads to the following equations
69
satisfied by the equiIibrium
+ r”,-bo)
cRH(l - (r;,
h(KM)=fn
-
a0
l
vaIues of &JV..
tr -
rhH
viz. I&,
+i-(l-(r&H
L‘&:
+r&-
MO)-’ (3.5)
tr;H
and
In (KM) = tn
CR-(1 - (r&H +
r:-bO)
u. rsR-
+-
q $0 kT
+i -
(1 -
(r&
+ r&-)ao1-l
(3.6)
(3.7) The
constant K plays the role of the disgociation constant for the reactioll
sotution species
+
vacant surface site
~
adsorbed species
(3-W
and kT ln K can be seen to be the free energy change in transferring a
neutral aurfactant molecute from bulk sotution to the c&e-pa&e3 monolayer. The first terns on the r&h&hand side of eqns (3.5) and (3-6) is the usual product of concentrations accting in the milss-action equation corresponding to the reaction (3.8). All the other ~~EIIISon the right-hand side represent the activity coefficient terms which apperbrin the mass-action equation when the species involved interact with ewh other. The sunw constant K appears in both (3.6) and (3.5) 88 a result or‘the approximation
wo which implies that the non-coufombic f&e energy change on transferring a mokcuZe f&om bulk sotution to the surface is independent of the state of charge of the head group. The validity of this appnbximation is of little importance since the free energy change on transfer of the hydrocarbon chain is the dominant contribution to K. Subtracting (3.6) fkom (3.6) we obtain
r;CR-
=-
riH %H
eq +eIkT
(3.10)
70
a result which was used in the previous section. This equation expresses the fact that because the negative R- species in the monolayer interact repuE sively with one another, they are tess readily adsorbed than the neutral BH species under identical solution conditions_ Equation (3-5) can be used with the Gibbs adsorption isotherm (2.1) to show [4) that at low pH the surface pressure n in the monolayer satisfies a two-dimensional wan der Waals equation: l&&t
f
R-
2af
1(a
-a*)=kT
(3.11)
)_ By fitting this cylation to pubwhere 0: is the area per molecuIe (= l/r& lished ICa data for oleic acid, values for % t e constants ao. Us were determined. These are a0 = 21,3 AZ and uinb = -3.7 kT, The constant K can be determined by considering a situation in which there is a precipitate at tow pH. Then the surface pressure of equ& the equilibrium spreading pressure xW = 30.5; dyn cm-‘. The corresponding v&m of 4 can he taken directly from the fithd x-~1 curve. The adsorption excess of surfactant is thus knowrl and can be substituted into the low pH limit of (3.5) to give K. The result is K = 10”“-3, 4. RESULT3
With the rleterminatian of the adsorption isotherm, anIy one other model parametcr needs to be specified before y(pH) can be c&ulated. This is the *‘inner layer capacitancd’ g/d afl of section 2. We make the simpfest pcs-
sible assumption and take eI to ae equal to the bulk dielectric constant e = 80 for a temperature T = 294%. As in Paper 1 the Stem layer thicknes fl is given the value 3 Ai The soWion paxamr?ters for oteic acid are taken fmrn Jung [Sl and are K, = 10--4-9s, K, = 10-‘11*5s_ The methad of calculation is as follow?* tf the amount af surf&ant C Is greater than K,/K,(l + O(K,/Ka)) a precipitate is present at low pti. The surface tension is then known from the equilibrium spreading pressure-of oleic acid. A small increment in pH is made and the concentrations of all species in the aqueous phase determined from (2.3)-(2.6). Equations (2.11), (2.12). (3.5) and (3.10) can then be sotwed simuItaneousty for #,,,$ t?&-,f& ‘JXe total double layer excess r+ + I?_ can be determined from (2-a) and the increment in r obtained from (2.23). By increasing the pH in small steps and incrementing 7 s.ccordingIy we calculak r(pH) up to the soIubiL ity edge. Above this pH the procedure is continued except that eqn (2.6) is replaced by (2.9) which holds in the absence of a precipitate. vlhe individual -raIues of cc and # are matters of personal ?&osyncracy the ratio q/# anly being of hsportame. Ihe wahmschosea above give the beat vaIue of the ratio for a c:uboxyCate latex coUoid (see ref. 4 of paper I).
71
If C is less than KS/&(1 + U(KS/I’a) there is never a precipitate. The initial concentration of surf&ant in the water will he less than the saturation v&e and so y at low pH will not he r. - w- but some higher value. This can be determined by using the low pH limit of the adsorption equation (3.5) to calculate the zireaper molecule corresponding to the known initial ~urfactant concentration CRH. This is then substituted into the m-u isotherm (3.11) to give the initial vaIue of m. The cakulation then proceeds as described above except of course that eqn (2.9) is used throughout in place of (2.6). 4s was ftiund ill Paper I it is instructive when examining the surface tension behaviour to consider also the v&&ion with pH of the monolayer density. Figures 1 and 2 give respectively the surface tension anti nonnalised ) at a fixed value of 0 for a series of conEzz!~~_d;~%~~:k;~ %I e no precipitate for C vaIues less than about 1.6 x IO- 4. As anticipated in the discussion of section 2, there is nevertheless atUl a minimum in the surface tension, The minimum is smooth because it does not occur at the transition between two pH ranges characterised by different sotutfon chemistry. Its physical origin however is much the same as in the presence of prrecipitate. The oil acZ as a reservoir, maintaining the concentration of neutral species in the aqueous phase in the face of increasing conversion to the ion&d form. 60-C+-
1.0
0-e
c
0.6
0.2 t
t
3.0
I
5.0
I
7.0
t
9.0
I
11.0
VH PH Fig. 1. Surface tension variation at 0.2 mol dmmf M* ions for B = 2 6 X 10" and vari‘(c) c = 9 x 10-s; ous oteate concentrations C. (a) C = 2-S x lo-*; (b) C = 5 X lo-‘; (d)Cl.6 X lo-';(o)C= 2-S x 10". F;s_ 2. Nomahedruonolayer densityu*(rk+ RI&) as a functlood of pH at 0.2 mol dm-’ M+ tons foe3 = 2-s x 10” and various okate coacentratbns C. (a) C = 9 x LO-'; (d)C= 1.6 X 10v4;(e)C= 23 x x0-s; (b) C- S x tO-g;(c)C= 2s x lo-':
72 Consider the case C = 2.5 X fO_ sI At low pH the concentration of neutral surfactant in the water is 1 X LOa , i.e. (C119)~ and that of the dissociated form e%entiaUy zero. At pH 8.0 the concentration of the former has fallen only to 7.7 X 10D9 White that of the latter has rJsen to 1 X 10B5_ This increase in the total concentration of surfactant in the water results in rising adsorption (Pig, 2) and a lowering of the surface tension. The surfactant in the water now accounts for about 40% of the total so that as the pH is increased further the resenroir starts to become depleteci and the concentration of neu&aI species drops rapidly. Although the aqueous concentration of surPac&nt continuw to increase, ionkd species cannot remru’n in the monolayer against the increasing surface potential J&sorption takes place as indicated by Fig. 2 and y rises. For a hJgher tom amount of surPa&ant (C = 5 X lo-‘) the initial adsorption Esgreater and so the surface t4xwJon at tow pH L iower. For the large& two concentrations a precipitate is present inJtiaJJy~This Pwnr the aqurous concentration of neutral surfactant and Jmplies that that of the ion&i species is independent of the total amount of swpactant (see eqn (2.6)). With the sot&ion chemistry thereby de&mined, the resuIts for these concentrations must lie on a common curve JAow their respective volubility edges_ Another feature of Merest is that the surface tension continues to decrease after the soIubiJity edge. For the case C = 1.6 X 10mQ
1.0
a4
10.0
c -
0.2 t t
--_I-
3.0
5.0
7.0 PH
9.0
11.0
I
‘I1
3.0
5.0
7.0
9.0
11.0
PH
&. 3. Sucfacc tenabn wrlatioa at 0.2 mol dm- ’ M* Ions tot oleate concentrationC = 5 x 1O-s ar.d various vahes of 8, (aa)0 = I x 10"; (b) e - 6 x 10”; (cc) B = 2.6 x 10”; (d)@ = 7.5 x UP;(e)8 = 73 x UP- Cume (e) is virtually IndistlnguhhabIe from that obtained in the absence of oil,
Fii 4. NormaLed monolayer densitya~(r~- + ~~~)wcuf8pH~t0.2mol drn-' M+ and warSousvahws of B. (a) 8 - 1 X 10"; (b) 8 - 5 x 10"; ioMfurC=5X10-' (c)e = 2-S x 10ml;(d)e =7.S x 1O1o;(e)8 = 7.5 X lO*,
13
PHS = 6.9 and at pH = pH, more than 98% of the surfactant is still in the oil phase which can therefore continue to act as a reservoir. In Figs. 3 and 4 are plotted results for a fixed total amount of surfactant (C = 5 X lo-‘) and vruying 0. For the given value of C precipitates wiu occur if0 is less than about 7.9 X lo**. For 0 = 7.5 X lo’*, the surface tension continues to decrease after the precipitate has disappeared. The higher the value of 8, the greater the effective oil voIume and hence the lower the initial concentration of suxfactant in either phase. So the starting dues for 7 increase with 0. At high pH however the surfactant is essentially al1in the water and completely ion&d. The oil then no longer affects the solution chemistry and so the curves for different vahxes of 8 merge. As 8 increases the position of the minimum in the absence of a solubility edge shifts to higher pH. The oil volume is grez&et and therefore contains a greater proportion of the surfactant- It can thus continue to act as a rem%void up to higher pH vatues. It is also apparent that the minimum becomes more shallow suggesting that for sufficiently high B the surface tension decreases monotonicaMy and levels out at high PH. ri. THE OIkWATER
INTERFACE
In this final section w8 will examine the interfacial tension between water and the oil itself- Although we are now concerned with the oil-water bound;uy, the atliltysis of section 2 still applies. The effect of the oil at the interface appears only in the adsorption isotherm which is modified by the attractive interaction between oil and surfactant molecules- Unfortunately, there is little exparimental data for oleic acid monolayers at an oit-water interface on which to base a theory of adsorption. This difficulty can how-zverbe circumv@Jrtedby adapting the model developed for the air-water Mzrface. We will assume that the oil is a structureless solvent, the main effect of luhich is to cause the hydrocarbon chain of a surfactant molecule to feel the same attractive interaction at all areas per molecule. Thus at the oitwater interface the free energy of a surfactant monolayer is given by (3.l) with the PO(Na,N-,T) of (3.4) replaced by F,“iw(N,,,N_.T) -
(No
+ N_)
= kT(.Po
In No - No + N
In (1 - (No
The energies uy,
ue
l
N-)a,))
In N_ - N- •C(N,
+N,UrE
+ N’)
in A’
+ N-uy
and uht are taken to b8 the same as for the e
74
water interface. The fkat two are the energies of isolated uudissociated and dissociated molecules at the air-water interface. The effect of the surrounding oil molecules is of course taken into account by the & term. Use of the same self-energies does however neglect any changes in the energy or entropy of the interface due to the displacement of oil molecules from the surface_to the bulk and their replacement by surfactant. Similarly use of the same urnt assumes that the non-coulombic part of the head group interacCan, which is area dependent, is minor compared with the contribution of the hydracarhon chains. With the above form for the free energy the adsorption equation corresponding to (3.5) is cRH(l.In (KM)
(Cl&+ + r&-MO3
= In
+ I-
(1 - (r”,,
+ r3,-)cr,)-’
a~ “&H
Equation (3.6) being modified acc*Jrdingly.The effect of this change in tha adsorption model is to replace the R-U isotherm eqn (3,ll) by 4a - UQ) = kT an equation which has seen some use [9]
(5.3)
as a representation of the behawiby monolayers at oit-wnter interfaces. The vaIue used for a0 is the same as before, since this is basically a reflectbn OP tie dimensions of the oleic acid matecule and is unlikely to be affected by the presence of the oil. Purthermote, the equitibrium coustmt K of (6.2) is given by an Ed-
our exhibited
pression identical to (3.7) and so the same value is usedThe ca.IcuIationpraceeds as described for the air-wa teerinterface except &at in determining the initial interfacial tension, the surface pressure cafcdated from the initial (tow pH) value of 11using (6.3) is subtracted from r,“b = 61.0 dyn cm?, Figure 6 gives the surface tension variition for parameQr values similar to
;-9-, , 3.0
50
7*0
I
1
9.0
11.0
PH Fii- 5, Variatba ia interfacial tension at the oibwrater 8 = 5 x 10" and 0.2 ma1 aim-’ M+ iona
bouhciary
for C = 2.6
X
lo-*;
7s
those of Figs,1-4. It is immediatily obvious that the extra attractive interaction provided by the oil molt%uIes in the monolayer yeatly lowers the surface tension, Indeed for moderate and high pH the calculated value for 7 is actually negative. Droplets of oleic acid-paraffin oil mixtures in dilute alkali have been observed [lo] to undergo spontaneous emulsification over part of the pH range. Prior to the emulsification very low values of the interfacial tension are recorded. The present analysis assumes a single plane interface. It does not consider the possibility of phases in which the oil (or water) is dispersed throughout the water (or oil) in the form of small droplets with a surface film of surfactant. It can therefore not treat the emulsification process and must yietd erroneous results when this occurs, While results such as Fig. 6 cannot thus be taken at face value, they may nevertheless be regarded as the manifestation, within a simpk theoretical model, of the tendency of the system to emulsify, CONCLUSION fn the present work the role of solution chemistry in determining the behaviour of the surface tension of a surf&&ant monoIayer adsorbed on aqueous electrolyte is further examined. It is found that the presence of a precipitate at low pH is not a necessary condition for a minimum to occur. This can also happen when there is an oil layer containing dissoked surfactant- It is then this layer, rather than a precipitate, which acts as a reservoir of suxfactant and brings about an initial decrease in 7 as the pff is increased. The resuk for the oil-water interfaciaI tension must be interpreted with caution. Kowflver, one may say that the spontaneous emulsification observed in oil-water-surfactant systems appears to have a counterpart in the present model in the negative values calculated for the interfacial tension.
REFERENCES 1
2 3
RIB- Kulkami and P_ Ebmasundaran, Am, Inst. Chem. Eng. Symp_ Set., II (1975) 124. J.A. Finch and G-W. Smith, J. Coltoid interface Scl., 45 (1973) 81. kW. Adamson, “P&ysicaI Chemfhy of Surfaces”, 3rd eda, Wdey, New York, 1976,
Cb. 2, 4 68
J.A. Beunen, D.J. Mitchall and L-R, white, J.C.S. Faraday I, 74 (1978) 2601. R Aveyard =d R,W. Mitchell, Trans. Faraday Sot., 66 (1970) 37. 8. GIasatoue, “Textho& of Phytical C%em&try‘, 2nd edn, Macmilian, 1955, p_ 737. J.A, Reuueq Ph.D. Thesis. Australiaa National University, 1979. Ft.F. Jung, MSc. Tfmsis, Universityof Melbourne. 197% G.L. Gahtes Jr., TnsotubIe Monol8yers at LiquZd-Gas Interfaces”, Knnterscience,
10
New York, 1966, Ch. 4, 0 WA See W.W. MansfCeld, Au& J_ ScL Rea, AS (1962) 331, and referencestherein.
Amsterdam -
Printed tn The Netherlands
SURFACE TENSION MINIMUM IN IONIC SURFAdXANT II. THE EFFECI’ OF OIL RESERVOIRS JOSEPH A. BEUNEN+ apartment
51
SYSTEMS
and LEE R. WHlTE++
of Applied Mathematics; Research School of Physical Sciences, Australian
National Uiziuersify,Canbezm, ACT (rlustralb~
(Received June 17tb, 1930; accepted in final form September 23rd. 1981)
ABSTRACT A model b developed to examine the efkt of an oil teseenroiron the surface tensbn of the air-water interface in the presence of Ionfzabte suzfactant. 7&e minimum In the surface ten&n as a function of pH previously found for the case where there t no oil (and mrlbed to the presence at low pH of undissolved surfactant) can atso occur fn the presence of an oil phase even when the system does not have an aqueous Eolubility edge. The oil-water interface is also disced. ‘I&e theory predicts the spontaneous emufsification of the oil-water syskrns over a rangeof PH.
1. INTRODUtX’ION If has been
found
aqrlmus soiuSws
experimentally
that the surface tension in dilute
of certai~~surfactants goes through a minimum as the pH of the solution is varM [Il. Both acidic [ 11 and basic [2] surfactants exhibit this phenomenon which depends sensitively on the surfactant concentration and the ionic strength of the solution. While impurities are a frequent cause of such minima [3] we have shown in a previous vrrork[4] (hereinafter referred to as Paper I) that it is possible for a minimum to occur even in puxe systems. In Paper I a model was developed for the surface tension variation of oleic acid, for which experimental results were obtained by Kulkami and Somasundaran [lJ. The minimum in fhe surface tension may be understood qualitatively in the folIowing terms. At Iow pH ther+ is a precipitate of oleic acid which maintains the concentration in solution at the saturation value. An essentially neut& (associat8zd)
*Present address: Department of Chemkal Engineering,State University of New York at Buffdo. Amherst, NY 14260, U.S.k **Resent addles: Department of Physical Chemistry, Uoivemiy of Melbourne, ParkvilXe 3052,lEctoria. Autralia~ 0136-6622~82l000~000~$02.76
Q) 1982
F,hevier Scientific Publishing Campaay
monolayer is present at the air-water Inkrfacz giving rise to a surface tension less than that of pure water by an amount equaI to the equilibrium spreading pressure of the acid. As the pH is increased-the number of oleate species in solution rises as ions form by dissociation and mole neutral mokcuIes dissolve from the precipitate. This Ieads to Increasedadsorption at the interface and hence a further reduction in 7. At the solubility edge the precipitate has entireIy dissolved and there l:an be no further increase in *he concentration of oleate species. There is thus no tendency for 7 to decrease further. In fact, the dkociatkn of acid molezrles causes the monoIayer to become increasingly charged. The eIectrost&c revulsion of okate ions leads to desorption from the nlonotayer and a resultant i:crease in 7. kom the above, it can be seen that the precipitate glays a vital role in bringing about the initial ~-Iuction in the surface tensiranas the pH in creases. Its function is to act as a resenroir which mainttins the concentration of neutraI surfacfant molecules at n constant value despite the formation of an increashg number of iona. This raises the qur!ation of the existence of surface tension minima in systems where there is some form of = sexvoir other than a precipitate, Such a reservoir* could be provfded by an olt phase in which the surfactant was soluble, Cn thfs paper, we wiU consider a situation in which the aqueous solution is in contact over part of its surface with a Iayer of hydrocarbon, e.g_ paraffin oil atso containing surfactant. The made1 developed in Paper L wiIl be adapted for the caIcuIation of the surface tension of that part of the water surface open to the air. Once again r will be found to have a minimum as a function of pH, This resuit ohviousIy suggests an investigation of the Interfacial tension between the oil and &r as the pH changes. This is more difficult because it requires a model of the adsorption of surfuctant at the oil-water interface for which fittIe data is avaitabte. However, in view of the current interest in multicomponent watet-oil-surfactanf systems, which are found to exhibit Law interfacial tinsions, an attempt will be made to extend the calculations in this direction. The main departure from the treatment in faper I lies in the solution ch~W~.r, -This is disc-d In the following section. The model of the monolayer adsorption is essentially unaltered and wiI1 be reviewed briefIy in section 3. +Jm -fiction 4 results for the surface tension at the air-water interface are presented and discussed. Finally, the extension to the oil-water interface is given in section 5,
As ir, Paper I, the starting point for the caIcuIatIon of the surface tension is the Gibbs adsorption isotherm: dr = - c r&Q C=) i
63
where Q is the adsorption excea of species I and pi is its chemical potential. If the interface is chosen sr, that the adsorption excess of water is zero, the sum in (2.1) extends over the dissoIved species-surfactant molecules RH and ions R-, monovalent electrolyte M+X- and of C~MUS~H+ and OH-. Now
(2.2) where Ci is the concentration (mol - dm-’ ) of species i in the aqueous phase- Tbis equation assumes that the variation in activity coefficient. can be neglected. This is allowable for the inert ions M* and X- since their concentrations change littIe over the pH range of the experiments. It is also a good approximation for the other species since their concentrations are always small. To make use of eqn (2.1) we must therefore determine the variation with pH of the concentrations Ci and the adsorption excesses L’i*In the aqueous solution CH+COH-
=
Kw
(2.3)
where of course CHf
= ~o-PH
12~4)
iind
where Ka is the dissociation constant of the surfactant (assumed acid) and Cix is the concentration of neutral surfactant In the aqueous phase. If there is a precipitate present then we have also CH+CR- = KS
G-1
where KS is the soLubili& product of the surfactant, Equations (2,3), (2.5) and (2.6) are sufficient to determine the aqueous concentrations of aU cornponents. In this case the oil reservoir has no effect. In the absence of a precipitate, however, eqn (2.6) is replaced by a surfactant mass balance in which there is a term for the reservoir. if C denotes the total amount of surfactant expressed as mol dm-’ of water, this condition takes the form (2.7) where VSq, Vho are the voIumes of .water and oilrespectively. The concentration CEH of surfactant in the oil phase can be related to that in the water by a condition of distribution equilibrium. This must take into account the fact that even at 10~ concentrations the surfactant is atmost com-
64
pXetelydimerised in the oil phase [cl. Thus the following retationship can be expected to hold [6l
where Kd is an equiIibrium constant for dimerisation. Equation (2-7) can now be written in the form
and where we have dropped the now unnecessary superacxiptThe soIub3ity edge, at which the precipitate disappears, is calculated by assuming(2.6) and 12.9) both hold and using {2-E): PHS = PK..
+ Iog,,
[
c - -KS
&l
(
1+e
KS
G
)I
(2.10)
The solubility edge thus occurs at a pH value lower than that at which it would In the absence of oil (0 = 0). For given values of pH and C, the aqueous concentration of neutral surfactant is lower because some dissokes In the oil. TO raise the concentration sufficiently for a precipitate to form, more RH must be formed from R- and so a Iower pH Is needed. Equation (2.10) aI9csshows that for a SuitabIy Iarge 0 there is never a precipitate. interffrce the adsorption exIf we wish trl catcufate 7 for *e Water cesses I’i of eqn 42.1) are those at &at part of the water surface not In contact with oiI, One contibutirm k thase comes from the monolayer of Rand RH molecules at the surface. The numbers of these per unit ares are denoted by CL- and Py respectively. The corresponding surfme charge density is u0 = -qrsR-. 4% IS MS up a doubIe Iayer extending Into the soWion which contributes ionic excesses. To calculati these we use the zeroth-order Stem layer m&eel d&bed in Paper I. In this model there is a layer of width 0 adjacent to the surface from which eIectroIyte ions are excluded. The potential $d at the edge of this Iayer is reMed to #at at the suxface q& bY #I3 = $0 + no 4 M/Q
(2.11)
where e1 Is the dS:ectric constant in the layer. The surface charge density can be related to ,+$ L\yusing the fiit @&@ of the Po@ou-Boltzmanrt equation satisfied by +he potential together with the usual bouridary condition at a charged date. _.
65
00
=
-
EukT
sinh q &f2 kT
2 ml
(2.12)
As usual
(2.13) where N is Avogadro’s number and E is the dielectric constant of the bulk soWion.. The cationic species K-i*, M4 have a positive adsorption excess due to their attraction to the negative monolayer: B-4= cir4
(2.14)
where (2.15) >O Similarly
@XCBsseS
the anionic species OH-,
X-, R- have negative double layer
ri = cir-
(2.16)
where (2.17) For our monovalent system it can be shown [4] that
r4 + r- =
-i-g-
c&p + c&p
(2.18)
tanh q &3/4kT
The adsorption excesses of the non-surfactant species are thus defined. That
of the surfactant ion has two components, and that in the double layer:
rir-_ = i--i- +
CR-r-
the adsorption
in the monolayer
(2.19)
whereas the adsorption excess of the neutral species has only the monolayer componenf: rRH
= %i
(2.20)
66
the surface charge density of the monolayer, and hence all Given I$, double layer quantities, are determined, Thus from (2.11) and (2.12) e. and $,r can be caIcuIated. The latter allows the sum F+ + L‘- to be evaIuated from (2.18)_ As will become evident below it is through this quantity only that double layer excesses affect dy. To complete the calculation of 7 the monolayer excesses I?i- and I?& must be determined. This requires a theory of monolayer adsorption which is described in the following section, Before this is done we expand (2.1) by making use of some of the foregoing equations_ Thus from eqn (2.2)
dr EF
= -lL(dCH+
+ dC&
- r_(dCx-
+ dCoH-
- I-L,
+ dGR-) - r;--
dCRCR-
d&Ii --
(2.21)
CRkZ
using definitions (2.14) and (2.16) and eqns (2.19) and (2.20). Thus dY
kT
= -(I-*
+ r_‘)ac,+
-
I-k-
d CR-‘--
C.r,-
-
I‘&
dGR,
(2.22)
CRH
This follows from ths charge neutrality of the bulk solution where we have assumed that the pH is varied by adding acid to an inilia!Iy b&c solution so that C&f+ is constant. ISy diffd?rentiating(2.5) and substituting the result in (2.22) we have fiaIIy
dr -
kT
= [rS,-
- (I-*
+ r_)cH+J
dCH+ - 4;k+
- (r-i-
+ %HI
dCRH
CCcH
(2.23)
This equation can be used to examine the quaIitative behaviour of surface tension without detailed c&uIafion. Firstly, if there in a precipitate present, the solution chemistry is unaffW*_d by the oil reservoir, except of course that the position of the soIubiIity edge is altered. The analysis of Paper I shows that
dr --
(2.24) < 0 for PH -= PI-I, dpH The existence of a minimum will now depend on whether it is possible for the surface tension to increase when there is no precipitate and the oil reservoir comes into play. Differcntiatiug (2.5) and (2.9) and using the results in i2.23) leads to 2.303 kT d+ =r&H(eQQ*CT(l f 2 8CRH) - 1) dpH CRH CR_ (1 l 2 @CRH) f+ (2.25)
67
where we have also anticipati a result of section 3 (eqn (3.10)). From (2.18) it can be seen that r, + I’L is posi?;ive since the potential ## is negative. Thus the second term in the square brackets above is positive. Furthermore, at high pH when most of the surfactant is dissociated, the monolayer will be highly charged and the surface potential therefore huge. The tit term will then be negative provided the vaIue of 0 is not too great*. Thus once again dr/dpH > 0 and there is a minimum. At low pH, where & $# and hence r, + r- are smaller in magnitude, it is possibIe that the first term is positive and larger than the second so that dy/dpH < 0 even without a precipitate, When there is an oil resemoir the behaviour of y in the range pH > pH, may thus be quite varied, depending on the value of 0: (i) the surface tension may increase monotonically for pH > pHS so that the minimum occurs at the solubility edge as before; (ii) 7 may decrease at first so that a minimum QCCWS not at pH = p& but at some higher value; (iii) for very large 3. y may even be monotonically decreasing in the pH range of interest. The exact behaviour is dependent on the variation of potentizd with pH and to that extent is affected by the model chosen for the adsorption of surfacbnt molecules. This is the subject of the following section. 3. THE
ADSORPTLON
ISOTHERM
Our concern here is the asorption of surfactant at the air-water interface. In Paper I we obtained equations governing this adsorption by modelIing the monolayer as a two-dimensional van der Waals gas. The values of parameters appe&ng in the model were determined by fitting the eta isother!n at low pH to published data. The agreement between theoretical and experimental isotherms was adequate at tow areas per molecuIe but not graodat Iarge values. The made1 is still usabIe however,since, over most of the pH range, the surface pressurg is greater than the equitibrium spreading pressure 83 that the monolayer is den&y packed. Zn addition it is not our putpose to develop an accurate model of the monolayer. The van der Wadis equations provide a reasonable and convenient parameterisation of the adsorption behaviour and this is all that is requixed. We have considered another model elsewhere [7!. but it gives results that are little different. Hence for the sake of conformity with Paper L we will use the van der Waals model here. We give only a brief outline, refer&g the reader to the earlier work for details. Consider a unit area of the surface at which No neutral surfactant molecutes and IV_ ions are adsorbed. The thermodynamic behaviour of this portion of the monolayer can be obtained once its Helmhottz free energy ?6xe d&a of Aveyard and Mitchell [Sl
can he used to determine an upper bound for 2 KA of 2*6 .% 10“. However. since the votume ratio of oil and water can be varied widety, 8dIer values of 8 are easiIy attained.
68
F(&,N-,T) is know-u. To the same degree of approximation as that involved in the double-layer modeZ of section 2, we cm decompose this free energy in the following way.
Here PO(N&L,T) is the free energy when the electrostatic interaction between the charged groups has been switched off. The second term is the work done in charging the inkrface, &, (0’) being the electrostatic potential at a charged head group when the surface charge density is u’. The free energy F,, can be determined by cakulating the corresponding partition fu.?r;k~: (3-2) In the present model U has the form U = m if any two molecuXeooverlap = J&u0Af f N-U%
+ ‘A(&
+ N_)zuint~O otherwise
(3.31
Here t@lf (u_*If ) are the non-ekctrirstatic energies of a moIecule {ion) in an infinitely ditub monolayer and the third term represents the interactions among molecUI_ evaluated in a mean fieId approximation. The quantity uinnt is the interaction felt by a given molecule when the monolayer is cIosepacked (area per molecule equal b a,), Equation (3.3) is substituted into (3.2) and the integral evaluated in the van der Waals approximation to yield the free energy PO Fo(No,N-,T)
= kT(Na In No - No + N_ In N_ - N_ + (NO + NJ
- (No + N-1 In (1 - (& +
U(No + N_-)‘uktao
+ nr_)u,) + &u$~
In A2)
+kPv (3.4)
By differentiation of F(N&N_,T) with respect to NO,N_ we obtain the chemical potentials of the surfacknt species in the monolayer. Since this b in equilibrium with the underlying soIution these chemical poteutiak are equal to the correspo~~dingbu& values pz + kT Ln C&/M, ~0 + kT In C&If where M is the number of moles of s&&ion per Utre of solution (-55.5). Equating the chemical potent&& leads to the following equations
69
satisfied by the equiIibrium
+ r”,-bo)
cRH(l - (r;,
h(KM)=fn
-
a0
l
vaIues of &JV..
tr -
rhH
viz. I&,
+i-(l-(r&H
L‘&:
+r&-
MO)-’ (3.5)
tr;H
and
In (KM) = tn
CR-(1 - (r&H +
r:-bO)
u. rsR-
+-
q $0 kT
+i -
(1 -
(r&
+ r&-)ao1-l
(3.6)
(3.7) The
constant K plays the role of the disgociation constant for the reactioll
sotution species
+
vacant surface site
~
adsorbed species
(3-W
and kT ln K can be seen to be the free energy change in transferring a
neutral aurfactant molecute from bulk sotution to the c&e-pa&e3 monolayer. The first terns on the r&h&hand side of eqns (3.5) and (3-6) is the usual product of concentrations accting in the milss-action equation corresponding to the reaction (3.8). All the other ~~EIIISon the right-hand side represent the activity coefficient terms which apperbrin the mass-action equation when the species involved interact with ewh other. The sunw constant K appears in both (3.6) and (3.5) 88 a result or‘the approximation
wo which implies that the non-coufombic f&e energy change on transferring a mokcuZe f&om bulk sotution to the surface is independent of the state of charge of the head group. The validity of this appnbximation is of little importance since the free energy change on transfer of the hydrocarbon chain is the dominant contribution to K. Subtracting (3.6) fkom (3.6) we obtain
r;CR-
=-
riH %H
eq +eIkT
(3.10)
70
a result which was used in the previous section. This equation expresses the fact that because the negative R- species in the monolayer interact repuE sively with one another, they are tess readily adsorbed than the neutral BH species under identical solution conditions_ Equation (3-5) can be used with the Gibbs adsorption isotherm (2.1) to show [4) that at low pH the surface pressure n in the monolayer satisfies a two-dimensional wan der Waals equation: l&&t
f
R-
2af
1(a
-a*)=kT
(3.11)
)_ By fitting this cylation to pubwhere 0: is the area per molecuIe (= l/r& lished ICa data for oleic acid, values for % t e constants ao. Us were determined. These are a0 = 21,3 AZ and uinb = -3.7 kT, The constant K can be determined by considering a situation in which there is a precipitate at tow pH. Then the surface pressure of equ& the equilibrium spreading pressure xW = 30.5; dyn cm-‘. The corresponding v&m of 4 can he taken directly from the fithd x-~1 curve. The adsorption excess of surfactant is thus knowrl and can be substituted into the low pH limit of (3.5) to give K. The result is K = 10”“-3, 4. RESULT3
With the rleterminatian of the adsorption isotherm, anIy one other model parametcr needs to be specified before y(pH) can be c&ulated. This is the *‘inner layer capacitancd’ g/d afl of section 2. We make the simpfest pcs-
sible assumption and take eI to ae equal to the bulk dielectric constant e = 80 for a temperature T = 294%. As in Paper 1 the Stem layer thicknes fl is given the value 3 Ai The soWion paxamr?ters for oteic acid are taken fmrn Jung [Sl and are K, = 10--4-9s, K, = 10-‘11*5s_ The methad of calculation is as follow?* tf the amount af surf&ant C Is greater than K,/K,(l + O(K,/Ka)) a precipitate is present at low pti. The surface tension is then known from the equilibrium spreading pressure-of oleic acid. A small increment in pH is made and the concentrations of all species in the aqueous phase determined from (2.3)-(2.6). Equations (2.11), (2.12). (3.5) and (3.10) can then be sotwed simuItaneousty for #,,,$ t?&-,f& ‘JXe total double layer excess r+ + I?_ can be determined from (2-a) and the increment in r obtained from (2.23). By increasing the pH in small steps and incrementing 7 s.ccordingIy we calculak r(pH) up to the soIubiL ity edge. Above this pH the procedure is continued except that eqn (2.6) is replaced by (2.9) which holds in the absence of a precipitate. vlhe individual -raIues of cc and # are matters of personal ?&osyncracy the ratio q/# anly being of hsportame. Ihe wahmschosea above give the beat vaIue of the ratio for a c:uboxyCate latex coUoid (see ref. 4 of paper I).
71
If C is less than KS/&(1 + U(KS/I’a) there is never a precipitate. The initial concentration of surf&ant in the water will he less than the saturation v&e and so y at low pH will not he r. - w- but some higher value. This can be determined by using the low pH limit of the adsorption equation (3.5) to calculate the zireaper molecule corresponding to the known initial ~urfactant concentration CRH. This is then substituted into the m-u isotherm (3.11) to give the initial vaIue of m. The cakulation then proceeds as described above except of course that eqn (2.9) is used throughout in place of (2.6). 4s was ftiund ill Paper I it is instructive when examining the surface tension behaviour to consider also the v&&ion with pH of the monolayer density. Figures 1 and 2 give respectively the surface tension anti nonnalised ) at a fixed value of 0 for a series of conEzz!~~_d;~%~~:k;~ %I e no precipitate for C vaIues less than about 1.6 x IO- 4. As anticipated in the discussion of section 2, there is nevertheless atUl a minimum in the surface tension, The minimum is smooth because it does not occur at the transition between two pH ranges characterised by different sotutfon chemistry. Its physical origin however is much the same as in the presence of prrecipitate. The oil acZ as a reservoir, maintaining the concentration of neutral species in the aqueous phase in the face of increasing conversion to the ion&d form. 60-C+-
1.0
0-e
c
0.6
0.2 t
t
3.0
I
5.0
I
7.0
t
9.0
I
11.0
VH PH Fig. 1. Surface tension variation at 0.2 mol dmmf M* ions for B = 2 6 X 10" and vari‘(c) c = 9 x 10-s; ous oteate concentrations C. (a) C = 2-S x lo-*; (b) C = 5 X lo-‘; (d)Cl.6 X lo-';(o)C= 2-S x 10". F;s_ 2. Nomahedruonolayer densityu*(rk+ RI&) as a functlood of pH at 0.2 mol dm-’ M+ tons foe3 = 2-s x 10” and various okate coacentratbns C. (a) C = 9 x LO-'; (d)C= 1.6 X 10v4;(e)C= 23 x x0-s; (b) C- S x tO-g;(c)C= 2s x lo-':
72 Consider the case C = 2.5 X fO_ sI At low pH the concentration of neutral surfactant in the water is 1 X LOa , i.e. (C119)~ and that of the dissociated form e%entiaUy zero. At pH 8.0 the concentration of the former has fallen only to 7.7 X 10D9 White that of the latter has rJsen to 1 X 10B5_ This increase in the total concentration of surfactant in the water results in rising adsorption (Pig, 2) and a lowering of the surface tension. The surfactant in the water now accounts for about 40% of the total so that as the pH is increased further the resenroir starts to become depleteci and the concentration of neu&aI species drops rapidly. Although the aqueous concentration of surPac&nt continuw to increase, ionkd species cannot remru’n in the monolayer against the increasing surface potential J&sorption takes place as indicated by Fig. 2 and y rises. For a hJgher tom amount of surPa&ant (C = 5 X lo-‘) the initial adsorption Esgreater and so the surface t4xwJon at tow pH L iower. For the large& two concentrations a precipitate is present inJtiaJJy~This Pwnr the aqurous concentration of neutral surfactant and Jmplies that that of the ion&i species is independent of the total amount of swpactant (see eqn (2.6)). With the sot&ion chemistry thereby de&mined, the resuIts for these concentrations must lie on a common curve JAow their respective volubility edges_ Another feature of Merest is that the surface tension continues to decrease after the soIubiJity edge. For the case C = 1.6 X 10mQ
1.0
a4
10.0
c -
0.2 t t
--_I-
3.0
5.0
7.0 PH
9.0
11.0
I
‘I1
3.0
5.0
7.0
9.0
11.0
PH
&. 3. Sucfacc tenabn wrlatioa at 0.2 mol dm- ’ M* Ions tot oleate concentrationC = 5 x 1O-s ar.d various vahes of 8, (aa)0 = I x 10"; (b) e - 6 x 10”; (cc) B = 2.6 x 10”; (d)@ = 7.5 x UP;(e)8 = 73 x UP- Cume (e) is virtually IndistlnguhhabIe from that obtained in the absence of oil,
Fii 4. NormaLed monolayer densitya~(r~- + ~~~)wcuf8pH~t0.2mol drn-' M+ and warSousvahws of B. (a) 8 - 1 X 10"; (b) 8 - 5 x 10"; ioMfurC=5X10-' (c)e = 2-S x 10ml;(d)e =7.S x 1O1o;(e)8 = 7.5 X lO*,
13
PHS = 6.9 and at pH = pH, more than 98% of the surfactant is still in the oil phase which can therefore continue to act as a reservoir. In Figs. 3 and 4 are plotted results for a fixed total amount of surfactant (C = 5 X lo-‘) and vruying 0. For the given value of C precipitates wiu occur if0 is less than about 7.9 X lo**. For 0 = 7.5 X lo’*, the surface tension continues to decrease after the precipitate has disappeared. The higher the value of 8, the greater the effective oil voIume and hence the lower the initial concentration of suxfactant in either phase. So the starting dues for 7 increase with 0. At high pH however the surfactant is essentially al1in the water and completely ion&d. The oil then no longer affects the solution chemistry and so the curves for different vahxes of 8 merge. As 8 increases the position of the minimum in the absence of a solubility edge shifts to higher pH. The oil volume is grez&et and therefore contains a greater proportion of the surfactant- It can thus continue to act as a rem%void up to higher pH vatues. It is also apparent that the minimum becomes more shallow suggesting that for sufficiently high B the surface tension decreases monotonicaMy and levels out at high PH. ri. THE OIkWATER
INTERFACE
In this final section w8 will examine the interfacial tension between water and the oil itself- Although we are now concerned with the oil-water bound;uy, the atliltysis of section 2 still applies. The effect of the oil at the interface appears only in the adsorption isotherm which is modified by the attractive interaction between oil and surfactant molecules- Unfortunately, there is little exparimental data for oleic acid monolayers at an oit-water interface on which to base a theory of adsorption. This difficulty can how-zverbe circumv@Jrtedby adapting the model developed for the air-water Mzrface. We will assume that the oil is a structureless solvent, the main effect of luhich is to cause the hydrocarbon chain of a surfactant molecule to feel the same attractive interaction at all areas per molecule. Thus at the oitwater interface the free energy of a surfactant monolayer is given by (3.l) with the PO(Na,N-,T) of (3.4) replaced by F,“iw(N,,,N_.T) -
(No
+ N_)
= kT(.Po
In No - No + N
In (1 - (No
The energies uy,
ue
l
N-)a,))
In N_ - N- •C(N,
+N,UrE
+ N’)
in A’
+ N-uy
and uht are taken to b8 the same as for the e
74
water interface. The fkat two are the energies of isolated uudissociated and dissociated molecules at the air-water interface. The effect of the surrounding oil molecules is of course taken into account by the & term. Use of the same self-energies does however neglect any changes in the energy or entropy of the interface due to the displacement of oil molecules from the surface_to the bulk and their replacement by surfactant. Similarly use of the same urnt assumes that the non-coulombic part of the head group interacCan, which is area dependent, is minor compared with the contribution of the hydracarhon chains. With the above form for the free energy the adsorption equation corresponding to (3.5) is cRH(l.In (KM)
(Cl&+ + r&-MO3
= In
+ I-
(1 - (r”,,
+ r3,-)cr,)-’
a~ “&H
Equation (3.6) being modified acc*Jrdingly.The effect of this change in tha adsorption model is to replace the R-U isotherm eqn (3,ll) by 4a - UQ) = kT an equation which has seen some use [9]
(5.3)
as a representation of the behawiby monolayers at oit-wnter interfaces. The vaIue used for a0 is the same as before, since this is basically a reflectbn OP tie dimensions of the oleic acid matecule and is unlikely to be affected by the presence of the oil. Purthermote, the equitibrium coustmt K of (6.2) is given by an Ed-
our exhibited
pression identical to (3.7) and so the same value is usedThe ca.IcuIationpraceeds as described for the air-wa teerinterface except &at in determining the initial interfacial tension, the surface pressure cafcdated from the initial (tow pH) value of 11using (6.3) is subtracted from r,“b = 61.0 dyn cm?, Figure 6 gives the surface tension variition for parameQr values similar to
;-9-, , 3.0
50
7*0
I
1
9.0
11.0
PH Fii- 5, Variatba ia interfacial tension at the oibwrater 8 = 5 x 10" and 0.2 ma1 aim-’ M+ iona
bouhciary
for C = 2.6
X
lo-*;
7s
those of Figs,1-4. It is immediatily obvious that the extra attractive interaction provided by the oil molt%uIes in the monolayer yeatly lowers the surface tension, Indeed for moderate and high pH the calculated value for 7 is actually negative. Droplets of oleic acid-paraffin oil mixtures in dilute alkali have been observed [lo] to undergo spontaneous emulsification over part of the pH range. Prior to the emulsification very low values of the interfacial tension are recorded. The present analysis assumes a single plane interface. It does not consider the possibility of phases in which the oil (or water) is dispersed throughout the water (or oil) in the form of small droplets with a surface film of surfactant. It can therefore not treat the emulsification process and must yietd erroneous results when this occurs, While results such as Fig. 6 cannot thus be taken at face value, they may nevertheless be regarded as the manifestation, within a simpk theoretical model, of the tendency of the system to emulsify, CONCLUSION fn the present work the role of solution chemistry in determining the behaviour of the surface tension of a surf&&ant monoIayer adsorbed on aqueous electrolyte is further examined. It is found that the presence of a precipitate at low pH is not a necessary condition for a minimum to occur. This can also happen when there is an oil layer containing dissoked surfactant- It is then this layer, rather than a precipitate, which acts as a reservoir of suxfactant and brings about an initial decrease in 7 as the pff is increased. The resuk for the oil-water interfaciaI tension must be interpreted with caution. Kowflver, one may say that the spontaneous emulsification observed in oil-water-surfactant systems appears to have a counterpart in the present model in the negative values calculated for the interfacial tension.
REFERENCES 1
2 3
RIB- Kulkami and P_ Ebmasundaran, Am, Inst. Chem. Eng. Symp_ Set., II (1975) 124. J.A. Finch and G-W. Smith, J. Coltoid interface Scl., 45 (1973) 81. kW. Adamson, “P&ysicaI Chemfhy of Surfaces”, 3rd eda, Wdey, New York, 1976,
Cb. 2, 4 68
J.A. Beunen, D.J. Mitchall and L-R, white, J.C.S. Faraday I, 74 (1978) 2601. R Aveyard =d R,W. Mitchell, Trans. Faraday Sot., 66 (1970) 37. 8. GIasatoue, “Textho& of Phytical C%em&try‘, 2nd edn, Macmilian, 1955, p_ 737. J.A, Reuueq Ph.D. Thesis. Australiaa National University, 1979. Ft.F. Jung, MSc. Tfmsis, Universityof Melbourne. 197% G.L. Gahtes Jr., TnsotubIe Monol8yers at LiquZd-Gas Interfaces”, Knnterscience,
10
New York, 1966, Ch. 4, 0 WA See W.W. MansfCeld, Au& J_ ScL Rea, AS (1962) 331, and referencestherein.