- Email: [email protected]
Modeling of the micellar solution - solid surfactant equilibrium
IIlIIMIRI Ir
ELSEVIER
~'
.
Fluid Phase Equilibria 117 (1996) 320-333
Modeling of the Micellar Solution - Solid Surfactant Equilibrium N.A.Smimova
Department of Chemistry, St.Petersburg State University, Universitetskyprosp.2, 198904, St.Petersburg. Russia. INTRODUCTION In many aqueous surfactant systems the lower temperature boundary for the micellar region is determined by the solution - crystal surfactant phase equilibrium (the other main types of lower temperature phase transitions are the ice crystallization and gel formation). A typical shape of the crystal surfactant solubility curve known as the Krafft boundary is shown in Fig. 1 where a fragment of the phase diagram for the surfactant - water binary at constant pressure is presented. The temperature vs. concentration solubility curve goes up steeply in the range of very high dilutions and changes the slope drastically near the Krafft point (the point where the solubility curve and the CMC curve intersect). The "plateau" in the micellar range is characteristic of the curve. For zwitterionic and some nonionic surfactants the Krafft plateau is nearly horizontal, for ionic surfactant a relatively steeper slope is observed (Laughlin, 1994). The temperature slope for the Krafft boundary in surfactant - water binaries was analyzed on the basis of strict thermodynamic relations (Rusanov, 1992) and using the ideal monodispersed micellar solution model (Smirnova, 1994). The model relating mainly to nonionic surfactants permits to connect the slope with the partial enthalpy of the dissolution of the solid surfactant and with the average aggregation number for micelles. Model estimations for the N-dodecanoyl-N-methylglucamine aqueous system were in a satisfactory agreement with experimental data. The results for aqueous surfactant binaries provide the basis for the study of the micellar solution - solid phase equilibrium for multicomponent systems containing additives. Experimental data for such systems are not numerous and relate mainly to ionic surfactants, not much is made in the field of thermodynamic modeling. At the same time the problem of the third component effect on the micellar solution - solid phase equilibrium is of practical interest, in particular, for the search of additives decreasing effectively the surfactant precipitation (dissolution) temperature. General expressions for the Krafft temperature change on the third component addition,as applied to the pseudo phase separation model, were given by Nakayama et al. (1966), Tsujii and Mino (1978). More detailed consideration was performed recently (Smirnova, 1994). In the present communication new results in the modeling of the third component effects are presented. 0378-3812/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378 - 3812(95)02969-9
321
N.A. Smirnova/ Fluid Phase Equilibria 117 (I 996) 320-333
CMC
T
MICELLAR SOLUTION
line
./
L e
•
THE KRAFFT BOUNDARY /
L+S
X!
Fig. 1 A fragment of the phase diagram for surfactant-water system: L- the liquid solution; E - the liquid-crystalline phase; S - the solid phase; x~ the surfactant mole fraction; T - the temperature; the dotted line is the CMC curve.
322
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 3 2 0 - 3 3 3
One can recognize the following main types of behavior of the component 3 added to the surfactant (1) - water (2) solution. a) The additive does not influence the composition of micelles; b) A nonpolar additive (a hydrocarbon for example) is solubilized inside the micelle hydrocarbon core; c) Amphiphilic molecules with small polar groups and short alkyl chains, like light alcohols, fatty acids or amine, are partly incorporated into micelles forming mixed micelles with the basic surfactant; d) The additive itself is apt to micellization, components 1 and 3 have comparable sizes of polar and alkyl groups, the concentration of nonaggregated molecules 3 is negligible. In the cases a-c an additive does not influence the composition of the solid phase, the latter being the pure (possibly hydrated) basic surfactant. These cases are considered in part I where main attention is paid to light amphiphilic additives of the type c. Part II is devoted to systems of the type d, aqueous mixtures of two surfactant homologues are among them. The possibility for two surfactants to form solid solutions is taken into account. It will be assumed that the third component concentration is not very high, this component is only an additive, the solvent remain to a great extent aqueous. The model approach used in the work relate to systems with nonionic surfactants. I. SYSTEMS WITH LIGHT AMPHIPHILIC ADDITIVES Ternary surfactant (1) - water (2) - additive (3) solutions in equilibrium with the pure solid component 1 are under consideration. The following strict thermodynamic relations are valid for such systems: (1) P,xl/x 2
.
.
.
.
where T is the temperature, P is the pressure, x i denotes the mole fraction of the component i in the saturated solution (i=1,2,3), gl stands for the chemical potential, al - for the activity of the surfactant, AH 1 is the partial molar enthalpy of its dissolution. The AH1 value at low additive concentrations does not differ considerably from the heat of dissolution for the binary surfactant - water system and consequently the difference in the (dT/dx3)p.x./x ~ magnitude for various additives should result mainly from different influence of the additives on the surfactant chemical potential. It is not likely that any substantial effect can be exerted by additives not penetrating inside micelles (case a) or solubilized inside the
323
N.A. Srairnova / Fluid Phase Equilibria 117 (1996) 320-333
hydrocarbon micellar core (case b). On the other hand, amphiphilic substances forming mixed micelles with the basic surfactant (case c) may produce significant changes in the g~ value as in this case the micelle itself becomes a solution. If the temperature change along the KrafR plateau in the surfactant - water binary is small, a pseudo phase separation model (Shinoda and Hutchinson, 1962) with its approximation that this plateau is horizontal seems to be a reasonable approach for the description of the third component effects. According to the model, the micellar solution of an overall composition xi, x2, x3 is considered as consisting of micellar (M) and aqueous (W) pseudo phases. Mole fractions xff (/=1,3) and xi w (/--2,3) M M characterize the composition of these phases; x~ +x3 ~ 1; x2~'+x3~'~ 1. Accepting the surfactant activity to be the unity in the micelles composed only of the component 1 and neglecting the AH1 concentration dependence we obtain from eq.(1) that
AH 1
oi(x ')
(2)
where To is the Krafft plateau temperature for the surfactant - water binary, T is the surfactant dissolution temperature for the ternary mixture under study, AT=T- To. If the micellar phase behaves like an ideal solution then
AH1
in0_xe)
(3)
The following applications of the formulae (2) and (3) may be of interest. 1. Determination of the surfactant activity al in multicomponent micellar solutions from AT data. 2. Estimation of the mixed micelles composition ( x Y ) 3. Prediction of the AT(xa,x3) dependencies. 4. Explanation of regularities in the influence of the molecular structure of additives. Applications 1 and 2 are straightforward, points 3 and 4 need special consideration.
324
N.A. Smimova /Fluid Phase Equilibria I17 (19%) 320-333
. .
dependen ce and reguk&.s
The_.&G&
.
m the AT-effect nroduced bv various
homologues. Using the material balance equations one can easily express x3Mthrough the overall mole fractions of the components and through the distribution coefficient KX ~xf”I$~,
K: = lim K,. x3-+0
The limiting slope of the AT(x,),~,,,
curve depends on K : ,x1 and x2 :
.
If Klx,
C-C x2,
RT2 K*
then
=-=I
(4) (5)
x’
It means that the higher is the K: value, the greater is the slope of the AT(x3) curve. In accord with the phase separation model we can write: K,
=Y
3wiY 3”;
K: =yr”/y3Mm= exp --=A& i where activity coefficients
1 y ;“” and y y relate to the same standard
state for the
component 3 (pure liquid); y ,“” and y y” are the activity coefficients in infinitely diluted solutions of the component 3 in the micelles and water; Apt is the change of the reference chemical potential of the component 3 for its transfer from the phase W to the phase A4. The temperature dependence of the K: value is described as AH3W+ M p =
RT2
’
(8)
where AH3W~M is the partial molar enthalpy of the transfer of the component from the aqueous pseudo phase to the micellar one at infinite dilutions.
3
N.A. Smirnova / Fluid Phase Equilibria I 17 (I 996) 320-333
325
One can use the model for the discussion of some regularities in the change of the AT-effect for a homologous row of amphiphilic additives (for example, alkanols). It follows from eqs.(4)-(7) that the AT effect depends on the RT InK~ = Atx30 value. For amphiphilic homologues forming mixed micelles with the basic surfactant (polar groups of the additive molecules are near the micelle polar surface, alkyl tails are inside the micelle hydrocarbon core) the A~30value should correlate with the transfer free energy of alkyl tails from the aqueous to hydrocarbon medium. It is known that the latter, being negative, is less in its absolute value for the branched hydrocarbon chain than for the normal chain of the same length -
(Tanford,1980). Hence the distribution coefficient K~ for amphiphiles with the normal alkyl group appears to be higher than for the isomers with a branched chain. So, the most strong effect on the temperature decrease is to be awaited from additives of a normal structure. The increase of the absolute Alx3o value with the increase of the alkyl tail length permits to await the growth of the AT effect in the row of C2,C3 etc. homologues. However, the lowering of the effect for higher homologues is probable, which may be caused by several reasons. One of them may be the change in the structure of mixed micelles. When alkyl tails of amphiphilic homologues (alkanols, for example) become longer, they behave more and more like nonpolar substances and are apt to be solubilized inside the hydrocarbon core of micelles. In this case their effect on the activity of the basic surfactant becomes weaker. It is possible also that on addition of higher homologues not a precipitation of the crystal basic surfactant, but another phase transition, in particular, gel formation, may occur on the temperature decrease. Illustrations for the N-dodecanovl-N-methvl~lucamine-water-n-alkanol mixtures. The surfactant under consideration (MEGA-12)
CH,
O
OH
OH
OH
OH
OH
is a typical nonionic surfactant with prolonged polar and hydrocarbon parts. In our earlier works the data on the micellar solution - crystal surfactant equilibrium for the MEGA-12 - water binary (Smirnova and Churjusova, 1995) and some results for mixtures containing n-butanol as an additive (Smirnova, 1994) were presented. Here a wider range of additives studied in our laboratory is discussed. It has been found that nonpolar substances like alkanes and benzene, such polar additives as dimethyl formamide, dimethyl sulfoxide, citric acid, glycerol, Na + and K ÷ salts, etc. do not produce any significant change in the N-dodecanoyl-N-methylglucamine dissolution temperature. As one could expect effective additives are among light amphiphilic substances (monocarbonic acids, alkanols, cellosolves).
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N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320-333
The data presented below relate to alkanols. The influence of the alkyl tail length and the isomeric structure of alkanols on the MEGA-12 dissolution temperature is illustrated by Figs.2,3 where AT=T(w3, wJw2) - T(w3=0, wl/w2); w i is the weight percent of the component i (/--1,2,3). One can follow the regularities discussed above: n-alkanols are more effective additives than their isomers, the ATeffect increases with the increase of the alkyl chain length (C2< C3
IATI-
The formulae (2)-(7) were used for the interpretation of the AT (w3, wl/w2) dependences over a wide range of the surfactant and n-alkanol (C2-C4) concentrations. To estimate the AT-value for some mixture one needs to know the To, and K x values. According to the DSC (differential scanning calorimetry) data for the MEGA-12 - water binary (Smirnova and Churjusova, 1995) T0,~320K, AH1=37kJmo1-1. It was found that for mixtures containing up to 10% of C2-C4 alkanols the changes in the AH1 values did not exceed 20% and in the calculations the approximation A/-/~~, const was used. The micellar phase in the concentration range under study was treated as an ideal solution. In this approximation Y ~4 =V ~
•,,,*
W~
Woo
=const; K x = hxy 3/Y 3 • The
Y ~v/~, 3wo~ values for the aqueous alcohol solutions were estimated using UNIFAC (Hansen et al, 1991), temperature dependence of the K x value was neglected. Only one parameter, K * (see Table 1), was adjusted. Examples of the calculated A T(w3) dependences at Wl/W2--const for mixtures with n-PrOH or n-BuOH as an additive are presented in Fig.4 and Table 2. Main features of the experimental behavior are reproduced in the model calculations when the y ~r concentration dependence is taken into account, whereas the approximation K x = K ~ is rather inaccurate, especially for mixtures with low surfactant concentrations. Approximate information on the micellar and aqueous phases compositions can be drawn from the calculations as is illustrated by Table 2. It was also of interest to estimate the alcohol activity coefficient in the micellar phase using the (Table 1). The negative value of the excess relationship y Moo=y WOO/K*x chemical potential R T In Y 3M o¢ presumably is in great part due to the energy contribution.
N.A. Smirnova / Fluid Phase Equilibria I 17 (1996) 320-333
-AT, K
327
n-BuOH _
t6,0'
42.0"
B.o
4.0
O
',
2..o
4..0
6.0
~.o
~o.o
~z.o
w3(%)
Fig.2 The AT = T(w3) - T(w3=0) values vs the n-alkanol w e i g h t concentration (w3) for MEGA- 12(1) - H20(2) - n-Alkanol(3) mixtures; wl/w2 = -AT, K "!0.0
~.o
6.o
2.o
I
-
I
I
I
n
Fig. 3 The AT vs the number of c-atoms in alcohol molecules for the composition: glucamine 38w.%, water 54w.%, alcohol 8w.%. n-alkanols (CnH2n+lOI-I) • - :i-PrOH a - i-BuOH " sec-BuOH 0 - tert-BuOH o
-
N.A. Smirnova/Fluid Phase Equilibria 117 (1996) 320-333
328
-AT, K
4O
n-PrOH
50
t ,.oo I°° j o ob
ZO
....... 4O
I
i
I
I
I
Z
4-
6
8
4O
w3(%)
4
-AT, K
4o
....." ,."
n-BuOH .•
.°
..
,-
t o et
3o
..'"
2o
...
~d'f
~,.-'-_..;'-,.4
...,..'~~~-
f7 ~-,_.~~
~
4-
lO
O
I
Z
'~
4-
I
6
"'l
8
!
40
w3(%),
Fig.4 The AT = T(w3) - T(w3=0) values vs the n-Alkanol weight concentration (w3) for MEGA-12(1) - H20(2 ) - n-Alkanol(3) systems at vl/w2 = 1/30 (1); 1/10(2);1/3 (3); 2/3 (4). - - exp ......... calc;y ~=const .....
W
calc; T 3 (x) dependence is taken into account by UNIFAC
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320-333
329
Table 1. The limiting values of the distribution coefficients K ~ and of the alkanol activity coefficients in aqueous [IT] and micellar [M] phases (t=50°C). *
Woo *
Alkanol
K x
7 3
EtOH n-PrOH n-BuOH
5.9 24.7 63.7
4.65 17.5 48.9
M~
7 3 0.79 0.71 0.77
The y f ~ values are taken from the book by Morachevsky et al., 1982. An extention of the model for mixtures containing salt additives would be of interest. According to our data the influence of many salts (Na2CO3, K2CO3, NaNO3, NaC1 etc.) on the MEGA-12 dissolution temperature is insignificant for aqueous solutions but substantial for aqueous mixtures containing alkanols (EtOH, PrOH, BuOH) AT<0. Table 2. Examples of the experimental and calculated results for saturated micellar solutions MEGA- 12 (1) - water (2) - n-alkanol (3); wl/w2= 1/2. w3
-ATexp
-ATcalc
g x
X3W
Xl M
al
0.003 0.008 0.014 0.020 0.025 0.030
0.92 0.82 0.73 0.65 0.59 0.55
0.92 0.83 0.75 0.67 0.62 0.58
0.001 0.002 0.004 0.008 0.010
0.92 0.85 0.75 0.58 0.52
0.93 0.88 0.76 0.59 0.53
n-PrOH 1.2 3.0 4.9 6.9 8.5 10.1
1.8 4.2 6.5 8.9 10.5 12.2
1.9 4.6 7.2 9.8 11.7 13.5
23.2 21.3 19.5 17.7 16.5 15.3 n-BuOH
0.93 1.75 3.3 6.25 8.1
1.6 2.9 6.4 11.7 14.0
1.95 3.6 6.5 12.1 14.5
61.4 59.5 56.4 50.1 48.8
330
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320 -333
The phenomena may be explained by the increase of the alkanol activity coefficient in the presence of salts (salting out effect). As it is seen from eqs.(4)-(7) the effect should result in the increase of the alcohol distribution coefficient K x and consequently in the higher (dT/dx3)e, xj/x 2 values. Model calculations are in progress. II. SYSTEMS CONTAINING TWO SURFACTANTS It is supposed that the component 3 itself is apt to micellization and beyond the CMC the concentration of nonaggregated molecules in the solution is negligible both for the surfactant 1 and for the surfactant 3. For the average composition of micelles it stands:
Xl M= xl /(x~ + x3) that is the xl M value is determined entirely by the relative overall concentrations of the surfactants and, unlike systems with light amphiphilic additives, which were considered in part I, the changes in the Xl + x3 (or Wl/W2) values at xl/(Xl + x3) = const do not influence the value ofxl M . Using the pseudo phase separation approach we deal with the equilibrium between the two component micellar pseudo phase and the solid phase. For such a system at constant pressure the equilibrium temperature is determined by one variable, that is by the xl M= Xl /(Xl + x3) value. Consequently, the temperature change on addition of a surfactant as the third component should be the function only of the x 1 /(Xl + x3) ratio. Experimental data for MEGA-12 (1) water (2) - MEGA-8 (3) system presented in Fig.5 illustrate this conclusion. Certainly, one should remember that the validity of the conclusion is comparable with the validity of the approximation about the constant temperature along the Krafft plateau for binary micellar aqueous surfactant systems. In our further consideration the possibility for surfactants 1 and 3 to form solid solutions is taken into account, xi s denotes the mole fraction of the component i in the solid phase (i=1,3). For the description of the temperature vs composition dependence for the micellar pseudo phase (M) - solid solution (S) equilibrium we turn to the Van-der-Waals differential equation for two component two phase systems. In the approximation of ideality for the both phases we obtain
( dd_~3m ) _ R T 21 - K p
Q21 x M
(9)
N.A. Smirnova /Fluid Phase Equilibria 117 (1996)
320-333
331
-AT, K 20
16
12
II
|
|
|
0.2
0.4
0.6
0.8
I
1.0
x3/(xl+x3) Fig.5 The AT=T(w3)-T(w~=0) value vs. the relative mole fraction of the surfactant 3 X3/(XI+X3) for MEGA-12 (1) - H20 (2) - MEGA-8 (3) mixtures. The data relate to the following w~+w3 (weight %) values:
10 (o), 20 (.), 30 (o), 40 (A), 50 (,0.
332
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320-333
where K= x3 s/x3 M ; s
s
S Q21 is the differential molar enthalpy of the solid phase formation, Hi, is the partial molar enthalpy of the component i in the phase S, HY denotes the analogous value for the phase M (i=1,3). For systems where the solid phase contains only the component 1 we should accept x3S=0; K=0. The limiting slope of the Y(xM) curve is given by the following relations:
(dT)*
= lim ( dT, 1
RT2
(ll)
where AH1 -- H1M - H1s is the dissolution enthalpy for the surfactant 1 in the 1-2 binary; K*= lim xS3 / x3M. xM--~0
The formulae (9)-(11) may be used for approximate estimations of the solid phasernicellar pseudo phase distribution coefficient from AT(x~) experimental data. For the curve presented in Fig.5 for the MEGA-12 - water - MEGA-8 system
(dT/dx 3M)-P ~ -14. Using the AH1 and Y values for the MEGA-12 - water binary we fred K* ~0.40. Certainly, it would be desirable to support the conclusion on the formation of the MEGA-8 - MEGA-12 solid solutions by some direct measurements.
CONCLUSIONS The main attention in the paper was paid to the effect of the third component added to aqueous surfactant mixures on the temperature of the micellar solution - solid surfactant equilibrium (the AT effect). Systems with light amphiphilic additives and those where the third component is a surfactant forming mixed micelles and solid solutions with the basic surfactant were tinder consideration. In modeling the pseudo phase separation approach was applied. The model has appeared to be successful in the description of main features of AT effects in their dependence on the composition of mixtures containing nonionic surfactants. The possibility to use the data on the temperature of the micellar solution - solid surfactant equilibrium for estimations of the
N.A. Smirnova / Fluid Phase Equilibria I 17 (1996) 320-333
333
surfactant activity and the composition of mixed micelles in multicomponent systems is outlined. ACKNOWLEDGMENTS Support of this research by Procter & Gamble Co is gratefully appreciated. The author is thankful to A.G.Morachevsky, M.V.Alexeeva and T.G.Churjusova for their contribution to the study. REFERENCES Hansen, H.K., Rasmussen, P., Fredenslund, Aa., 1991. Vapor-liquid equilibria by UNIFAC group contribution.5.Revision and extention. Ind.Eng.Chem.Res.30:23522355. Laughlin, R.G., 1994. The aqueous phase behavior of surfactants. Academic Press. London, San Dirgo, N.Y., 558p. Morachevsky, A.G., Smimova, N.A., Balashova, I.M., Pukinsky, I.B., 1982. Thermodinamika razbavlennich rastvorov neelektrolitov. Chimia, Leningrad, 344p.(in Russian) Nakayama, H., Shinoda, K. and Hutchinson, E., 1966. The effect of added alcohols on the solubility and the Kraft~ point of sodium dodecylsulfate. J.Phys.Chem., 70:35023504. Rusanov, A.I., 1992. Micelloobrazovanie v rastvorach poverchnostno-activnikh veschestv. Chimia, St.Petersburg, 288p. (in Russian) Smimova, N.A., 1994. Thermodynamic study of the micellar solution - solid surfactant equilibrium. 13-th IUPAC Conference on Chemical Thermodynamics, ClermontFerrand, France, July 1994. Abstracts. P. 147-148. Fluid Phase Equilibria. (in press) Smirnova, N.A. and Churjusova, T.G., 1995. Thermodynamic study of the temperature-concentration dependence along the Krafft boundary: DSC measurements and modeling for N-dodecanoyl-N-methylglucamine-water system. Langmuir.(in press) Tan_ford, Ch., 1980. The hydrophobic effects: formation of micelles and biological membranes. Wiley.N.Y., 2nd ed.,p.233. Tsujii, K., and Mino, J., 1978. Krafll point depression of some zwitterionic surfactants by inorganic salts. J.Phys.Chem., 82:1610-1614.
ELSEVIER
~'
.
Fluid Phase Equilibria 117 (1996) 320-333
Modeling of the Micellar Solution - Solid Surfactant Equilibrium N.A.Smimova
Department of Chemistry, St.Petersburg State University, Universitetskyprosp.2, 198904, St.Petersburg. Russia. INTRODUCTION In many aqueous surfactant systems the lower temperature boundary for the micellar region is determined by the solution - crystal surfactant phase equilibrium (the other main types of lower temperature phase transitions are the ice crystallization and gel formation). A typical shape of the crystal surfactant solubility curve known as the Krafft boundary is shown in Fig. 1 where a fragment of the phase diagram for the surfactant - water binary at constant pressure is presented. The temperature vs. concentration solubility curve goes up steeply in the range of very high dilutions and changes the slope drastically near the Krafft point (the point where the solubility curve and the CMC curve intersect). The "plateau" in the micellar range is characteristic of the curve. For zwitterionic and some nonionic surfactants the Krafft plateau is nearly horizontal, for ionic surfactant a relatively steeper slope is observed (Laughlin, 1994). The temperature slope for the Krafft boundary in surfactant - water binaries was analyzed on the basis of strict thermodynamic relations (Rusanov, 1992) and using the ideal monodispersed micellar solution model (Smirnova, 1994). The model relating mainly to nonionic surfactants permits to connect the slope with the partial enthalpy of the dissolution of the solid surfactant and with the average aggregation number for micelles. Model estimations for the N-dodecanoyl-N-methylglucamine aqueous system were in a satisfactory agreement with experimental data. The results for aqueous surfactant binaries provide the basis for the study of the micellar solution - solid phase equilibrium for multicomponent systems containing additives. Experimental data for such systems are not numerous and relate mainly to ionic surfactants, not much is made in the field of thermodynamic modeling. At the same time the problem of the third component effect on the micellar solution - solid phase equilibrium is of practical interest, in particular, for the search of additives decreasing effectively the surfactant precipitation (dissolution) temperature. General expressions for the Krafft temperature change on the third component addition,as applied to the pseudo phase separation model, were given by Nakayama et al. (1966), Tsujii and Mino (1978). More detailed consideration was performed recently (Smirnova, 1994). In the present communication new results in the modeling of the third component effects are presented. 0378-3812/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378 - 3812(95)02969-9
321
N.A. Smirnova/ Fluid Phase Equilibria 117 (I 996) 320-333
CMC
T
MICELLAR SOLUTION
line
./
L e
•
THE KRAFFT BOUNDARY /
L+S
X!
Fig. 1 A fragment of the phase diagram for surfactant-water system: L- the liquid solution; E - the liquid-crystalline phase; S - the solid phase; x~ the surfactant mole fraction; T - the temperature; the dotted line is the CMC curve.
322
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 3 2 0 - 3 3 3
One can recognize the following main types of behavior of the component 3 added to the surfactant (1) - water (2) solution. a) The additive does not influence the composition of micelles; b) A nonpolar additive (a hydrocarbon for example) is solubilized inside the micelle hydrocarbon core; c) Amphiphilic molecules with small polar groups and short alkyl chains, like light alcohols, fatty acids or amine, are partly incorporated into micelles forming mixed micelles with the basic surfactant; d) The additive itself is apt to micellization, components 1 and 3 have comparable sizes of polar and alkyl groups, the concentration of nonaggregated molecules 3 is negligible. In the cases a-c an additive does not influence the composition of the solid phase, the latter being the pure (possibly hydrated) basic surfactant. These cases are considered in part I where main attention is paid to light amphiphilic additives of the type c. Part II is devoted to systems of the type d, aqueous mixtures of two surfactant homologues are among them. The possibility for two surfactants to form solid solutions is taken into account. It will be assumed that the third component concentration is not very high, this component is only an additive, the solvent remain to a great extent aqueous. The model approach used in the work relate to systems with nonionic surfactants. I. SYSTEMS WITH LIGHT AMPHIPHILIC ADDITIVES Ternary surfactant (1) - water (2) - additive (3) solutions in equilibrium with the pure solid component 1 are under consideration. The following strict thermodynamic relations are valid for such systems: (1) P,xl/x 2
.
.
.
.
where T is the temperature, P is the pressure, x i denotes the mole fraction of the component i in the saturated solution (i=1,2,3), gl stands for the chemical potential, al - for the activity of the surfactant, AH 1 is the partial molar enthalpy of its dissolution. The AH1 value at low additive concentrations does not differ considerably from the heat of dissolution for the binary surfactant - water system and consequently the difference in the (dT/dx3)p.x./x ~ magnitude for various additives should result mainly from different influence of the additives on the surfactant chemical potential. It is not likely that any substantial effect can be exerted by additives not penetrating inside micelles (case a) or solubilized inside the
323
N.A. Srairnova / Fluid Phase Equilibria 117 (1996) 320-333
hydrocarbon micellar core (case b). On the other hand, amphiphilic substances forming mixed micelles with the basic surfactant (case c) may produce significant changes in the g~ value as in this case the micelle itself becomes a solution. If the temperature change along the KrafR plateau in the surfactant - water binary is small, a pseudo phase separation model (Shinoda and Hutchinson, 1962) with its approximation that this plateau is horizontal seems to be a reasonable approach for the description of the third component effects. According to the model, the micellar solution of an overall composition xi, x2, x3 is considered as consisting of micellar (M) and aqueous (W) pseudo phases. Mole fractions xff (/=1,3) and xi w (/--2,3) M M characterize the composition of these phases; x~ +x3 ~ 1; x2~'+x3~'~ 1. Accepting the surfactant activity to be the unity in the micelles composed only of the component 1 and neglecting the AH1 concentration dependence we obtain from eq.(1) that
AH 1
oi(x ')
(2)
where To is the Krafft plateau temperature for the surfactant - water binary, T is the surfactant dissolution temperature for the ternary mixture under study, AT=T- To. If the micellar phase behaves like an ideal solution then
AH1
in0_xe)
(3)
The following applications of the formulae (2) and (3) may be of interest. 1. Determination of the surfactant activity al in multicomponent micellar solutions from AT data. 2. Estimation of the mixed micelles composition ( x Y ) 3. Prediction of the AT(xa,x3) dependencies. 4. Explanation of regularities in the influence of the molecular structure of additives. Applications 1 and 2 are straightforward, points 3 and 4 need special consideration.
324
N.A. Smimova /Fluid Phase Equilibria I17 (19%) 320-333
. .
dependen ce and reguk&.s
The_.&G&
.
m the AT-effect nroduced bv various
homologues. Using the material balance equations one can easily express x3Mthrough the overall mole fractions of the components and through the distribution coefficient KX ~xf”I$~,
K: = lim K,. x3-+0
The limiting slope of the AT(x,),~,,,
curve depends on K : ,x1 and x2 :
.
If Klx,
C-C x2,
RT2 K*
then
=-=I
(4) (5)
x’
It means that the higher is the K: value, the greater is the slope of the AT(x3) curve. In accord with the phase separation model we can write: K,
=Y
3wiY 3”;
K: =yr”/y3Mm= exp --=A& i where activity coefficients
1 y ;“” and y y relate to the same standard
state for the
component 3 (pure liquid); y ,“” and y y” are the activity coefficients in infinitely diluted solutions of the component 3 in the micelles and water; Apt is the change of the reference chemical potential of the component 3 for its transfer from the phase W to the phase A4. The temperature dependence of the K: value is described as AH3W+ M p =
RT2
’
(8)
where AH3W~M is the partial molar enthalpy of the transfer of the component from the aqueous pseudo phase to the micellar one at infinite dilutions.
3
N.A. Smirnova / Fluid Phase Equilibria I 17 (I 996) 320-333
325
One can use the model for the discussion of some regularities in the change of the AT-effect for a homologous row of amphiphilic additives (for example, alkanols). It follows from eqs.(4)-(7) that the AT effect depends on the RT InK~ = Atx30 value. For amphiphilic homologues forming mixed micelles with the basic surfactant (polar groups of the additive molecules are near the micelle polar surface, alkyl tails are inside the micelle hydrocarbon core) the A~30value should correlate with the transfer free energy of alkyl tails from the aqueous to hydrocarbon medium. It is known that the latter, being negative, is less in its absolute value for the branched hydrocarbon chain than for the normal chain of the same length -
(Tanford,1980). Hence the distribution coefficient K~ for amphiphiles with the normal alkyl group appears to be higher than for the isomers with a branched chain. So, the most strong effect on the temperature decrease is to be awaited from additives of a normal structure. The increase of the absolute Alx3o value with the increase of the alkyl tail length permits to await the growth of the AT effect in the row of C2,C3 etc. homologues. However, the lowering of the effect for higher homologues is probable, which may be caused by several reasons. One of them may be the change in the structure of mixed micelles. When alkyl tails of amphiphilic homologues (alkanols, for example) become longer, they behave more and more like nonpolar substances and are apt to be solubilized inside the hydrocarbon core of micelles. In this case their effect on the activity of the basic surfactant becomes weaker. It is possible also that on addition of higher homologues not a precipitation of the crystal basic surfactant, but another phase transition, in particular, gel formation, may occur on the temperature decrease. Illustrations for the N-dodecanovl-N-methvl~lucamine-water-n-alkanol mixtures. The surfactant under consideration (MEGA-12)
CH,
O
OH
OH
OH
OH
OH
is a typical nonionic surfactant with prolonged polar and hydrocarbon parts. In our earlier works the data on the micellar solution - crystal surfactant equilibrium for the MEGA-12 - water binary (Smirnova and Churjusova, 1995) and some results for mixtures containing n-butanol as an additive (Smirnova, 1994) were presented. Here a wider range of additives studied in our laboratory is discussed. It has been found that nonpolar substances like alkanes and benzene, such polar additives as dimethyl formamide, dimethyl sulfoxide, citric acid, glycerol, Na + and K ÷ salts, etc. do not produce any significant change in the N-dodecanoyl-N-methylglucamine dissolution temperature. As one could expect effective additives are among light amphiphilic substances (monocarbonic acids, alkanols, cellosolves).
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N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320-333
The data presented below relate to alkanols. The influence of the alkyl tail length and the isomeric structure of alkanols on the MEGA-12 dissolution temperature is illustrated by Figs.2,3 where AT=T(w3, wJw2) - T(w3=0, wl/w2); w i is the weight percent of the component i (/--1,2,3). One can follow the regularities discussed above: n-alkanols are more effective additives than their isomers, the ATeffect increases with the increase of the alkyl chain length (C2< C3
IATI-
The formulae (2)-(7) were used for the interpretation of the AT (w3, wl/w2) dependences over a wide range of the surfactant and n-alkanol (C2-C4) concentrations. To estimate the AT-value for some mixture one needs to know the To, and K x values. According to the DSC (differential scanning calorimetry) data for the MEGA-12 - water binary (Smirnova and Churjusova, 1995) T0,~320K, AH1=37kJmo1-1. It was found that for mixtures containing up to 10% of C2-C4 alkanols the changes in the AH1 values did not exceed 20% and in the calculations the approximation A/-/~~, const was used. The micellar phase in the concentration range under study was treated as an ideal solution. In this approximation Y ~4 =V ~
•,,,*
W~
Woo
=const; K x = hxy 3/Y 3 • The
Y ~v/~, 3wo~ values for the aqueous alcohol solutions were estimated using UNIFAC (Hansen et al, 1991), temperature dependence of the K x value was neglected. Only one parameter, K * (see Table 1), was adjusted. Examples of the calculated A T(w3) dependences at Wl/W2--const for mixtures with n-PrOH or n-BuOH as an additive are presented in Fig.4 and Table 2. Main features of the experimental behavior are reproduced in the model calculations when the y ~r concentration dependence is taken into account, whereas the approximation K x = K ~ is rather inaccurate, especially for mixtures with low surfactant concentrations. Approximate information on the micellar and aqueous phases compositions can be drawn from the calculations as is illustrated by Table 2. It was also of interest to estimate the alcohol activity coefficient in the micellar phase using the (Table 1). The negative value of the excess relationship y Moo=y WOO/K*x chemical potential R T In Y 3M o¢ presumably is in great part due to the energy contribution.
N.A. Smirnova / Fluid Phase Equilibria I 17 (1996) 320-333
-AT, K
327
n-BuOH _
t6,0'
42.0"
B.o
4.0
O
',
2..o
4..0
6.0
~.o
~o.o
~z.o
w3(%)
Fig.2 The AT = T(w3) - T(w3=0) values vs the n-alkanol w e i g h t concentration (w3) for MEGA- 12(1) - H20(2) - n-Alkanol(3) mixtures; wl/w2 = -AT, K "!0.0
~.o
6.o
2.o
I
-
I
I
I
n
Fig. 3 The AT vs the number of c-atoms in alcohol molecules for the composition: glucamine 38w.%, water 54w.%, alcohol 8w.%. n-alkanols (CnH2n+lOI-I) • - :i-PrOH a - i-BuOH " sec-BuOH 0 - tert-BuOH o
-
N.A. Smirnova/Fluid Phase Equilibria 117 (1996) 320-333
328
-AT, K
4O
n-PrOH
50
t ,.oo I°° j o ob
ZO
....... 4O
I
i
I
I
I
Z
4-
6
8
4O
w3(%)
4
-AT, K
4o
....." ,."
n-BuOH .•
.°
..
,-
t o et
3o
..'"
2o
...
~d'f
~,.-'-_..;'-,.4
...,..'~~~-
f7 ~-,_.~~
~
4-
lO
O
I
Z
'~
4-
I
6
"'l
8
!
40
w3(%),
Fig.4 The AT = T(w3) - T(w3=0) values vs the n-Alkanol weight concentration (w3) for MEGA-12(1) - H20(2 ) - n-Alkanol(3) systems at vl/w2 = 1/30 (1); 1/10(2);1/3 (3); 2/3 (4). - - exp ......... calc;y ~=const .....
W
calc; T 3 (x) dependence is taken into account by UNIFAC
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320-333
329
Table 1. The limiting values of the distribution coefficients K ~ and of the alkanol activity coefficients in aqueous [IT] and micellar [M] phases (t=50°C). *
Woo *
Alkanol
K x
7 3
EtOH n-PrOH n-BuOH
5.9 24.7 63.7
4.65 17.5 48.9
M~
7 3 0.79 0.71 0.77
The y f ~ values are taken from the book by Morachevsky et al., 1982. An extention of the model for mixtures containing salt additives would be of interest. According to our data the influence of many salts (Na2CO3, K2CO3, NaNO3, NaC1 etc.) on the MEGA-12 dissolution temperature is insignificant for aqueous solutions but substantial for aqueous mixtures containing alkanols (EtOH, PrOH, BuOH) AT<0. Table 2. Examples of the experimental and calculated results for saturated micellar solutions MEGA- 12 (1) - water (2) - n-alkanol (3); wl/w2= 1/2. w3
-ATexp
-ATcalc
g x
X3W
Xl M
al
0.003 0.008 0.014 0.020 0.025 0.030
0.92 0.82 0.73 0.65 0.59 0.55
0.92 0.83 0.75 0.67 0.62 0.58
0.001 0.002 0.004 0.008 0.010
0.92 0.85 0.75 0.58 0.52
0.93 0.88 0.76 0.59 0.53
n-PrOH 1.2 3.0 4.9 6.9 8.5 10.1
1.8 4.2 6.5 8.9 10.5 12.2
1.9 4.6 7.2 9.8 11.7 13.5
23.2 21.3 19.5 17.7 16.5 15.3 n-BuOH
0.93 1.75 3.3 6.25 8.1
1.6 2.9 6.4 11.7 14.0
1.95 3.6 6.5 12.1 14.5
61.4 59.5 56.4 50.1 48.8
330
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320 -333
The phenomena may be explained by the increase of the alkanol activity coefficient in the presence of salts (salting out effect). As it is seen from eqs.(4)-(7) the effect should result in the increase of the alcohol distribution coefficient K x and consequently in the higher (dT/dx3)e, xj/x 2 values. Model calculations are in progress. II. SYSTEMS CONTAINING TWO SURFACTANTS It is supposed that the component 3 itself is apt to micellization and beyond the CMC the concentration of nonaggregated molecules in the solution is negligible both for the surfactant 1 and for the surfactant 3. For the average composition of micelles it stands:
Xl M= xl /(x~ + x3) that is the xl M value is determined entirely by the relative overall concentrations of the surfactants and, unlike systems with light amphiphilic additives, which were considered in part I, the changes in the Xl + x3 (or Wl/W2) values at xl/(Xl + x3) = const do not influence the value ofxl M . Using the pseudo phase separation approach we deal with the equilibrium between the two component micellar pseudo phase and the solid phase. For such a system at constant pressure the equilibrium temperature is determined by one variable, that is by the xl M= Xl /(Xl + x3) value. Consequently, the temperature change on addition of a surfactant as the third component should be the function only of the x 1 /(Xl + x3) ratio. Experimental data for MEGA-12 (1) water (2) - MEGA-8 (3) system presented in Fig.5 illustrate this conclusion. Certainly, one should remember that the validity of the conclusion is comparable with the validity of the approximation about the constant temperature along the Krafft plateau for binary micellar aqueous surfactant systems. In our further consideration the possibility for surfactants 1 and 3 to form solid solutions is taken into account, xi s denotes the mole fraction of the component i in the solid phase (i=1,3). For the description of the temperature vs composition dependence for the micellar pseudo phase (M) - solid solution (S) equilibrium we turn to the Van-der-Waals differential equation for two component two phase systems. In the approximation of ideality for the both phases we obtain
( dd_~3m ) _ R T 21 - K p
Q21 x M
(9)
N.A. Smirnova /Fluid Phase Equilibria 117 (1996)
320-333
331
-AT, K 20
16
12
II
|
|
|
0.2
0.4
0.6
0.8
I
1.0
x3/(xl+x3) Fig.5 The AT=T(w3)-T(w~=0) value vs. the relative mole fraction of the surfactant 3 X3/(XI+X3) for MEGA-12 (1) - H20 (2) - MEGA-8 (3) mixtures. The data relate to the following w~+w3 (weight %) values:
10 (o), 20 (.), 30 (o), 40 (A), 50 (,0.
332
N.A. Smirnova / Fluid Phase Equilibria 117 (1996) 320-333
where K= x3 s/x3 M ; s
s
S Q21 is the differential molar enthalpy of the solid phase formation, Hi, is the partial molar enthalpy of the component i in the phase S, HY denotes the analogous value for the phase M (i=1,3). For systems where the solid phase contains only the component 1 we should accept x3S=0; K=0. The limiting slope of the Y(xM) curve is given by the following relations:
(dT)*
= lim ( dT, 1
RT2
(ll)
where AH1 -- H1M - H1s is the dissolution enthalpy for the surfactant 1 in the 1-2 binary; K*= lim xS3 / x3M. xM--~0
The formulae (9)-(11) may be used for approximate estimations of the solid phasernicellar pseudo phase distribution coefficient from AT(x~) experimental data. For the curve presented in Fig.5 for the MEGA-12 - water - MEGA-8 system
(dT/dx 3M)-P ~ -14. Using the AH1 and Y values for the MEGA-12 - water binary we fred K* ~0.40. Certainly, it would be desirable to support the conclusion on the formation of the MEGA-8 - MEGA-12 solid solutions by some direct measurements.
CONCLUSIONS The main attention in the paper was paid to the effect of the third component added to aqueous surfactant mixures on the temperature of the micellar solution - solid surfactant equilibrium (the AT effect). Systems with light amphiphilic additives and those where the third component is a surfactant forming mixed micelles and solid solutions with the basic surfactant were tinder consideration. In modeling the pseudo phase separation approach was applied. The model has appeared to be successful in the description of main features of AT effects in their dependence on the composition of mixtures containing nonionic surfactants. The possibility to use the data on the temperature of the micellar solution - solid surfactant equilibrium for estimations of the
N.A. Smirnova / Fluid Phase Equilibria I 17 (1996) 320-333
333
surfactant activity and the composition of mixed micelles in multicomponent systems is outlined. ACKNOWLEDGMENTS Support of this research by Procter & Gamble Co is gratefully appreciated. The author is thankful to A.G.Morachevsky, M.V.Alexeeva and T.G.Churjusova for their contribution to the study. REFERENCES Hansen, H.K., Rasmussen, P., Fredenslund, Aa., 1991. Vapor-liquid equilibria by UNIFAC group contribution.5.Revision and extention. Ind.Eng.Chem.Res.30:23522355. Laughlin, R.G., 1994. The aqueous phase behavior of surfactants. Academic Press. London, San Dirgo, N.Y., 558p. Morachevsky, A.G., Smimova, N.A., Balashova, I.M., Pukinsky, I.B., 1982. Thermodinamika razbavlennich rastvorov neelektrolitov. Chimia, Leningrad, 344p.(in Russian) Nakayama, H., Shinoda, K. and Hutchinson, E., 1966. The effect of added alcohols on the solubility and the Kraft~ point of sodium dodecylsulfate. J.Phys.Chem., 70:35023504. Rusanov, A.I., 1992. Micelloobrazovanie v rastvorach poverchnostno-activnikh veschestv. Chimia, St.Petersburg, 288p. (in Russian) Smimova, N.A., 1994. Thermodynamic study of the micellar solution - solid surfactant equilibrium. 13-th IUPAC Conference on Chemical Thermodynamics, ClermontFerrand, France, July 1994. Abstracts. P. 147-148. Fluid Phase Equilibria. (in press) Smirnova, N.A. and Churjusova, T.G., 1995. Thermodynamic study of the temperature-concentration dependence along the Krafft boundary: DSC measurements and modeling for N-dodecanoyl-N-methylglucamine-water system. Langmuir.(in press) Tan_ford, Ch., 1980. The hydrophobic effects: formation of micelles and biological membranes. Wiley.N.Y., 2nd ed.,p.233. Tsujii, K., and Mino, J., 1978. Krafll point depression of some zwitterionic surfactants by inorganic salts. J.Phys.Chem., 82:1610-1614.