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COLLOIDS AND ELN EV I E R
Colloids and Surfaces A: Physicochemicaland Engineering Aspects 104 ( P~95) 157 163
A
SURFACES
The properties of mixtures of ionic and nonionic surfactants in water at the water/air interface B. Jaficzuk 1, j. M. Bruque *, M. U Gonzfilez-Martin, C. Dorado-Calasanz Departamento de Fisica, Universidad de Extremadura, 06071 Badajoz, Spain Received 26 October 1994: accepted 23 May 1995
Abstract Surface tension measurements were carried out fl)r systems containing mixtures of sodium dodecyl sulphonate and Triton X-100. From the results of these measurements we evaluated the molecular interactions parameters for the formation of mixed micelles and mixed monolayers at the water/air interface. Also, the values of the surface tension of the systems studied have been calculated using a relation derived by Joos (Bull. Soc. Chim. Belg., 76 (1967) 591) and compared with the measured values. From this comparison, the adsorption behavior of the mixture of SDS and TX-100 can be predicted by the Joos relation, and the effect of the molecular interactions in the adsorbed layer at low surface pressure can be neglected; however, near the cmc these interactions should be taken into account particularly if the ratio of TX-100 to SDS in the mixture is low. This is confirmed by the negative values assumed for the interaction parameters. However, no synergism is present in the adsorbed monolayers and in the micelle formation. ICevwords: Ionic surfactants; Nonionic surfactants; Water: Water/air interface
1. Introduction In most practical applications mixtures of surfactants, rather than individual surfactants, are used. Therefore the influence of the interaction between surface active substances on the physicochemical properties of such mixtures, including the adsorption behavior and micelle formation, are of fundamental importance. Mixed surfactant systems are also of great theoretical interest in their own right. In solutions containing mixtures of surfactants, the tendency to form aggregates is substantially different from that in solutions of single surfactants. The surface behavior of the mixtures of surfac* Corresponding author. ~()n Sabbatical leave from the Department of Physical Chemistry, Faculty of Chemistry, Maria Curie-Sktodowska University, 20-031 kublin, Poland. 0927-7757/95/$09.50 (t;~1995 Elsevier Science B.V. All rights reserved SSDI 0927-7757(95)03287-8
tants has been investigated by many authors [ 1 - 1 2 ] . Some of them suggest that there are no extra surface interactions in the composed system compared with the data for individual surfactant systems [6,9-12]. On the other hand, in most cases, when different types of surfactants are purposely mixed, what is sought is synergism, i.e., the condition when the properties of the mixture are better than those attainable with the individual components by themselves [5]. From the relevant properties of the individual surfactants and the values of the molecular interaction parameters, it is possible to predict whether synergism will exist in a mixture of surfactants by using the equations derived by Rubingh [ 3 ] and Rosen and Hua [13]. The adsorption behavior of mixed layers of surfactants can be described by the equation derived by Joos [ 14].
158
B. Jahczuk et aL/Colloids Surjaces A: Physicochem. Eng. Aspects 104 (1995) 157 163
Mixtures of anionic-nonionic surfactants are very often used in many branches of industry. For our study we chose mixtures of Triton X-100 (TX-100) and sodium dodecyl sulphonate (SDS). The surfactants from the Triton series are used in liquid, paste and powdered forms in many cleaning compounds, ranging from heavy-duty industrial products to gentle detergents for fabrics. However, SDS is used in the flotation processes of many minerals. Thus the properties of mixtures of TX-100 and SDS surfactants should be interesting from both practical and theoretical points of view. Therefore the surface tension of these mixtures has been measured at different temperatures and with different ratios of TX-100 to SDS in the mixture.
2. Experimental
TX-100, p-( 1,1,3,3-tetramethylbutyl)phenoxypolyoxyethylene glycol containing an average of 9.5 oxyethylene units per molecule [15], and SDS were supplied by Merck with a high grade of purity (99%, for tensile tests). Solutions of the TX-100+SDS mixtures at different ratios of TX-100 to SDS were prepared using doubly distilled and deionized water. The surface tension of water was always controlled before the preparation of the solutions. The surface tension measurements were made at 15, 25 and 35°C under atmospheric pressure, by the ring method. The apparatus was connected to a computer which automatically controlled the measurement process and analyzed the obtained results. In all cases more then 10 successive measurements were carried out. The temperature was controlled within __+0.1°C. For this purpose the container with the sample solution was surrounded with a jacket through which thermostated water flowed from a Haake-C thermostat.
3. Evaluation of the molecular interaction parameters
Two fundamental properties of the solutions of surfactants are the formation of micelles in the bulk, and monolayers at the solution/air interface.
For surfactant mixtures, the characteristic phenomena are the formation of mixed monolayers at the interface and mixed micelles in the bulk solution. The molecular interaction parameters for these latter phenomena can be evaluated using the equations derived by Rubingh and Rosen. The molecular interaction parameter for mixed micelle formation, tiM, can be expressed by the relation [3,5,13] /~M =
ln(~C~z/X~ C~) {1 - x ~ ' ) :
(1) '
where CM1,C~2 are the critical micelle concentrations (CMC) of the individual surfactant 1, and the mixture of surfactants 1 and 2, respectively, is the mole fraction of surfactant 1 in the solution phase, and X~' is the mole fraction of surfactant 1 in the mixed micelle. X~ can be evaluated from the equation (X~) 2 ln(~C~2/X~C~) (1 -X1~)2 l n [ ( 1 - ~)C~2/(1 -X]a)C~] = 1,
(2)
where C~ is the CMC of the individual surfactant 2. In the case of the molecular interaction parameter in the mixed monolayer, ~a, it is possible to determine this value from the relation [3,5,13] M =
In(~C12/X1C°)
(3)
( 1 - X1)2
where X1 is the mole fraction of surfactant 1 in the mixed monolayer, Co and C12 are the molar concentrations in the bulk of surfactant 1 and of the mixture of surfactants 1 and 2, respectively, required to produce a given surface tension value. X1 can be obtained from: (X 1 )2
ln(~C~2/X~C°)
(1 - X1)2 ln[(1 - 0~)C12/(1 -- X 1 ) C O]
=1
(4)
where Co is the molar concentration of surfactant 2 in the bulk, required to produce a given surface tension.
4. Equation of state to describe mixed adsorption behavior
To describe the adsorption behavior of mixed layers the generalized Langmuir isotherm has often
159
R Jahczuk et al./Colloids Surfaces A: Physicochem. Eng. Aspects 104 (1995) 157 163
been used. However, a much better possibility from the point of view of applying parameters from the individual surfactant adsorption to the equation of state consists in the relation derived by Joos [ 14]. This relation for surfactants in concentrations up to about 10 -' tool 1- 1 can be written [11,14] exp , ~
+ exp
+ exp | ~ | \~112
-H ' -H exp ( R ~ F ~ ) + [ e x p ( R ~ F ~ )
+exp
(~,~-~75
Figs. 1-4 show the dependence of the surface tension (?9 for the TX-100 + SDS mixtures at 15, 25 and 35"'C on the total concentration of surfactants in solution for ~ (:~ is the mole fraction of surfactant 1 in the mixture) equal to 0.2, 0.4, 0.6 and 0.8, respectively. The lines reflect the dependence of 7 on log C12 calculated from Eq. (7) using the values of F ~ and a of the individual components. The values of F ~ , F ~ , F ~ , a 1 and a~' used in Eq. (7) were evaluated from Eq. (6) from the data for individual surfactants (SDS and TX-100) on the assumption that CI = 0 or C~ = 0 and are listed
-H
---]
so I
q
I
i
70~
1
! 60-
:
Z
+exp
i
i
50}-
~,
,
(6)
2R~;-~=1,
]
40-
[ I
where
-7.5
°
65 log
= exp t 2 V- ) Assuming
that
(7)
5. R e s u l t s and d i s c u s s i o n
)
)+
=1
(5)
= 1, / a2
where /Ls is the chemical potential in the surface under standard conditions, /~B is the chemical potential in the bulk under standard conditions, and ~o is the number of the moles of water per litre. Eq. (5) should give good results for systems of nonionic or ionic surfactants in the presence of a swamping electrolyte. If one of the surfactants is a 1 : 1 electrolyte type A + and B , then its activity is close to C 2 for C < 10 2M [5]. Therefore, for an aqueous solution including one nonionic and one ionic surfactant type 1:1 electrolyte in the absence of a swamping electrolyte, Eq. (5) at a first approximation. can be written in the form • -H
~T~
~1 a
Eq. (7) can be applied to describe the data determined for surfactant mixtures.
--al
where FI~, F ~ and F [ are the maximum adsorption of the solvent, and surfactants 1 and 2, respectively, H is the surface pressure, R is the gas law constant and T is the absolute temperature. The parameters a: and a2 can be expressed as
.l--expt
C1 + C2 = Ct(1 + b), gives
C2/Cl=b=const.,
and
Ctot
=
-55 45 (C,2/rqol i-')
-55
1
, I :'°'°i
25
Fig. 1. Dependence of the surface tension of aqueous solutions of the mixture of SDS and TX-100 surfactants on log C~z at 15, 25 and 35 Cforc~=0.2.
B. Jahczuk et al./Colloids Surfaces A." Physicochem. Eng. Aspects 104 (1995) 157-163
160
80
,
80
70
70
60
T E Z E
7
E z
E
60
"~ 5O
5O
°!
40
50 -7.5
,
i
I
-6.5
~
I
i
I
i
-5.5 -4.5 log (C12/mol 1-1)
•/
•
40
•
50 -7.5
-35
Fig. 2. D e p e n d e n c e of the surface tension of a q u e o u s solutions of the mixture of SDS a n d TX-100 surfactants on log C12 at 15, 25 and 3 5 ° C for ~ = 0 . 4 .
....
25 ~C
-6.5
N\~,
-5.5 109 (C12/mol
-4.5
-5.5
t-1)
Fig. 4. D e p e n d e n c e of the surface tension of a q u e o u s solutions of the mixture of SDS a n d TX-100 surfactants on log C12 at 15, 25 and 3 5 ' C for a = 0 . 8 .
80
Table 1 Parameters in Eq. (6) for TX-100 and SDS Temperature
70
Substance
F~ (tool m 2)
A (nm)
a (moll -t)
Water TX-100 SDS
16.6 x 10 ~' 3.188 x 10 6 6.105 x 10 6
0.10 0.52 0.27
2.036 x 10 -6 2.988 x 10 3
25
Water TX-100 SDS
16.6 x 10 6 3.059 x 10 6 5.113 x 10 6
0.10 0.54 0.32
1.841 x 10 6 2.657 x 10 3
35
Water TX-100 SDS
16.6 x 10 -0 2,928 x 10 6 4,964 x 10 6
0.10 0.57 0.33
1.775 x 1 0 - " 2.564 x 10 3
("C) 15
T 8 Z E
60
"~ 5O
40
. . . . . ~9
5O -7.
-6.5
;c
-5.5 -4.5 log (C12/mol 1-1)
\\\
-3.5
Fig. 3. D e p e n d e n c e of the surface tension of a q u e o u s s o l u t i o n s of the mixture of SDS a n d TX-100 surfactants on log C12 at 15, 25 and 3 5 ° C for :~ = 0.6.
in Table 1. In all cases it was assumed that the area occupied by a water molecule in the adsorbed monolayer is about 10,~2 and thus F ~ = 16.6 x 10 -6 mol m 2.
From Table 1 it appears that the values of the area per molecule, A, for TX-100 and SDS equivalent to F °~ increase with increasing temperature from 15 to 35°C. The values of A for TX-100 are considerably higher than those for SDS. It seems to us that the values of A for both TX-100 and SDS which correspond to F °~ are reasonable. The results presented in Figs. 1-4 show that the surface tension, o/, depends on temperature and c~. However, the changes in y as a function of log C12,
161
B. Jahczuk et al./Colloids" Surfaces A. Physicochem. Eng. Aspects' 104 (1995) 157 163
for a given ~, have the same shape at 15, 25 and 35°C. Of course, near the C M C there is a linear dependence of 7 on log C12. For a given concentration C12, the surface tension decreases as :t increases. From Figs. 1-4 it also appears that at low concentrations there is a very good agreement between the measured and the calculated values of 7 for the mixtures. However, for ct = 0.2, 0.4 and 0.6 in the range of concentrations where there is a linear dependence of 7 on log C12, deviations of the theoretical values of the surface tension from the measured ones can be observed. These deviations decrease from ~t = 0.2 through c~= 0.4 to :t = 0.6, and for c~= 0.8 the measured and the calculated values of 3, are the same. Thus it can be used to predict the adsorption behavior of mixtures of TX-100 + SDS at low concentrations, if the values of F ~ and a of the individual components are known. However, for concentrations near the C M C where the calculated 7 values are higher than the measured ones, the influence of the intermolecular interactions between SDS and TX-100 molecules on the pressure of the monolayer is evident, particularly for solutions in which the concentration of the ionic surfactant is higher than the nonionic one (lower values of ~). The fact that the deviation at high concentrations between the measured and calculated ), values decreases with the increase in the molar fraction of TX-100 in solution, suggests that the free energy of interaction between SDS and TX-100 molecules (AG12) is close to that between the SDS ones (AG22). The free energy of interaction, kGt,, can be determined from the relation [3,16,17]
interactions, there is a synergism in the mixture between two different surfactants, both in the monolayer and in the micelle formations. Synergism in the monolayer formation in aqueous systems containing two surfactants exists when a given surface tension can be attained at a total mixed surface concentration lower than that required for either surfactant by itself [5]. The values of the surface tension for TX-100 and SDS and their mixtures at 15, 25 and 35 C are presented in Fig. 5 (solid curves). From this figure it is clear that there is no synergism in the mixtures of SDS and TX-100. For these systems, except at one point (curve 1), no value of the surface tension of the mixture is lower than ;, for the individual surfactant. Also in this figure are plotted the values of the surface tension of the mixtures at the C M C calculated from Eq.(7) (dashed curves). It can be clearly seen that, for a given temperature, both curves differ considerably for the lowest values of :< which confirms the conclusions drawn from Figs. 1 4. It was possible to calculate the value of fla from Eq. (3) only for :z = 0.2 without considerable errors, because if X 1 is close to zero or one, a large error is made in the calculations of the fia value (Table 2 ). This value is negative and < Iln C ° / C ° l . To show whether synergism in the formation of mixed micelles of SDS and TX-100 is present or not, Fig. 6 presents the dependence of l o g C M C
I/Jal
40 I
58!
ooooo
15 °C
u
tiM = AGll + AG22 - 2AG12 kT
'
(8)
where k is Boltzmann's constant. Using in Eq. (8) the value of tiM (_ 3.22) is calculated from Eq. (1), and the values determined earlier for AGI1 (-33.51 × 10-21J) and AG22 (-19.18 x 10 21j), the A G 1 2 value was calculated to be 19.83 × 10 21 j. This value is only a little lower than that for SDS SDS interactions, confirming the above conclusion. In many cases, as result of the intermolecular
+$56 7 zE ,34 E 'm
5!
C,.O
0.2
04
06
0.8
"r)
Fig. 5. Dependenceof the surface tension of aqueous solutions of the mixtures of SDS and TX-100 on :~ for CMC at 15 {curves 1 1'), 25 {curves 2 2't and 35C (curves 3 Y). The curves 1'. 2', and 3' were determined from Eq. (7).
162
B. Jahczuk et al./Colloids Surfaces A: Physicochem. Eng. Aspects 104 (1995) 157-163
Table 2 Values of the molecular interaction parameters for the mixtures of SDS and TX-100 calculated from Eqs. (3) and (4)
- l o g CMC
Temperature
X2
_rio
Table 3 Values of the molecular interaction parameters for the mixtures of SDS and TX-100 calculated from Eqs. (1) and (2) Temperature
CMC
- l o g CMC
X~
-fia
C~ C~ C~z(0.2TX-100 ) C~ (0.4 TX-100) CtM2(0.6 TX-100) C~: (0.8 TX-100)
3.67 2.02 3.22 3.42 3.54 3.62
0.7232 0.8048 0.8618 0.9179
3.25 3.24 3.29 3.31
C~ C2M C~z (0.2 TX-100) C~z (0.4 TX-100) C72 (0.6 TX-100) CxM/(0.8TX-100)
3.58 1.98 3.14 3.33 3.45 3.53
0.7149 0.8026 0.8605 0.9174
3.21 3.10 3.15 3.20
(°C)
(°C) cO co
35
4.32 2.09 3.70 4.26 2.06 3.65
C12 (0.2 TX-100 co co
Ca2 (0.2 TX-100 co
25
0.8698 2.62
0.8586 2.50
4.13 2.02 3.51 4.02 1.96 3.41
co
CIz (0.2 TX-100 c~o
15
35
co
C12 (0.2 TX-100
25 0.8667 2.18
0.8544 2.24
-1.5
equation of state [-14], with the exception of concentrations near the CMC for low values of ~.
-2.0
ooooo
• ,,,,
i
E
15 °C 2 5 °C
-2.5
Acknowledgements
"~, o
~
-3,0
3.5
-- 4"~),10
I
0.2
I
0.4
I
0.6
0.18
Fig. 6. Dependence of log CMC on a for aqueous solutions of the mixtures of SDS and TX-100 at 15, 25 and 35°C.
on ~ at 15, 25 and 35°C. From this figure it appears that the values of the CMC decrease continuously from the CMC of pure SDS down to the CMC of pure TX-100, and therefore no synergism in the micelle formation is present [5]. The parameter tim of the micelle formation for the mixtures of SDS and TX-100 has been calculated from Eq. (1) and listed in Table 3. In all cases tim is negative and IflM[ < Iln C~/C~l. In conclusion, the mixtures of SDS and TX-IO0 do not present synergism in either the monolayer or micelle formation, and the surface tension of the aqueous solutions of these mixtures of surfactants can be predicted by the modified Joos
One of the authors (BJ) very much appreciates the support obtained from the Spanish Ministerio de Educaci6n y Ciencia for his sabbatical stay at the Departamento de Fisica, Universidad de Extremadura, Spain. Financial support for this work by DGICYT under project No. PB89-0519 is gratefully acknowledged.
References [1] M. Abe and K. Ogino, in K. Ogino and M. Abe (Eds.), Surfactant Science Series, Vol. 46, Dekker, New York, 1992, pp. 1 20. [2] N. Nishikido, in K. Ogino and M. Abe (Eds.), Surfactant Science Series, Vol. 46, Dekker, New York, 1992, pp. 23 61. [3] D.N. Rubingh, in K.L. Mittal (Ed.), Solution Chemistry of Surfactants, Vol. 1, Plenum, New York, 1979, pp. 337-354. [4] H. Lange and K.H. Bech, Kolloid Z. Polym., 251 (1973) 424. [5] J.M. Rosen, in Surfactants and Interfacial Phenomena, Wiley Interscience, New York, 1989, pp. 393-420.
B. Jatlczuk et al./Colloids Surfaces A. Physicochem. Eng. Aspects 104 (1995) 157 163 [6] J. Rodakiewicz-Nowak, J. Colloid Interface Sci., 84 ( 1981 ) 562. [7] P.A. Jacobs, H.E. Leeman and J.B. Uyter, J. Catal., 33 11974) 17. [8] N. Nishikido, J. Colloid Interface Sci., 112 (1986) 87. [9] J. Rodakiewicz-Nowak, J. Colloid Interface Sci., 85 ~1982) 586 [ 101 J. Rodakiewicz-Nowak, Colloids Surfaces, 6 ~1983) 143. [11] R. W~stneck and R. Miller, Colloids Surfaces, 47 1990) 15.
163
[12] D. G6ralczyk and B. Waligura, J. Colloid Interface Sci., 82 (1981) 1. [13] M.J. Rosen and X.Y. Hue, J. Colloid Interface Sci., 86 (1982) 164. [14] P. Joos, Bull. Soc. Claim. Belg., 76 11967) 591. [15] V.K. Sharma, R. Bhat and J.C. Akluwalia, J. Colloid Interface Sci., 112 (1986) 195. [16] P.M. Holland and D.N. Rubing. J. Phys. Chem., 87 (1983) 1984. [17] P.M. Holland, Adv. Colloid Interface Sci., 26 (19861 111.
Colloids and Surfaces A: Physicochemicaland Engineering Aspects 104 ( P~95) 157 163
A
SURFACES
The properties of mixtures of ionic and nonionic surfactants in water at the water/air interface B. Jaficzuk 1, j. M. Bruque *, M. U Gonzfilez-Martin, C. Dorado-Calasanz Departamento de Fisica, Universidad de Extremadura, 06071 Badajoz, Spain Received 26 October 1994: accepted 23 May 1995
Abstract Surface tension measurements were carried out fl)r systems containing mixtures of sodium dodecyl sulphonate and Triton X-100. From the results of these measurements we evaluated the molecular interactions parameters for the formation of mixed micelles and mixed monolayers at the water/air interface. Also, the values of the surface tension of the systems studied have been calculated using a relation derived by Joos (Bull. Soc. Chim. Belg., 76 (1967) 591) and compared with the measured values. From this comparison, the adsorption behavior of the mixture of SDS and TX-100 can be predicted by the Joos relation, and the effect of the molecular interactions in the adsorbed layer at low surface pressure can be neglected; however, near the cmc these interactions should be taken into account particularly if the ratio of TX-100 to SDS in the mixture is low. This is confirmed by the negative values assumed for the interaction parameters. However, no synergism is present in the adsorbed monolayers and in the micelle formation. ICevwords: Ionic surfactants; Nonionic surfactants; Water: Water/air interface
1. Introduction In most practical applications mixtures of surfactants, rather than individual surfactants, are used. Therefore the influence of the interaction between surface active substances on the physicochemical properties of such mixtures, including the adsorption behavior and micelle formation, are of fundamental importance. Mixed surfactant systems are also of great theoretical interest in their own right. In solutions containing mixtures of surfactants, the tendency to form aggregates is substantially different from that in solutions of single surfactants. The surface behavior of the mixtures of surfac* Corresponding author. ~()n Sabbatical leave from the Department of Physical Chemistry, Faculty of Chemistry, Maria Curie-Sktodowska University, 20-031 kublin, Poland. 0927-7757/95/$09.50 (t;~1995 Elsevier Science B.V. All rights reserved SSDI 0927-7757(95)03287-8
tants has been investigated by many authors [ 1 - 1 2 ] . Some of them suggest that there are no extra surface interactions in the composed system compared with the data for individual surfactant systems [6,9-12]. On the other hand, in most cases, when different types of surfactants are purposely mixed, what is sought is synergism, i.e., the condition when the properties of the mixture are better than those attainable with the individual components by themselves [5]. From the relevant properties of the individual surfactants and the values of the molecular interaction parameters, it is possible to predict whether synergism will exist in a mixture of surfactants by using the equations derived by Rubingh [ 3 ] and Rosen and Hua [13]. The adsorption behavior of mixed layers of surfactants can be described by the equation derived by Joos [ 14].
158
B. Jahczuk et aL/Colloids Surjaces A: Physicochem. Eng. Aspects 104 (1995) 157 163
Mixtures of anionic-nonionic surfactants are very often used in many branches of industry. For our study we chose mixtures of Triton X-100 (TX-100) and sodium dodecyl sulphonate (SDS). The surfactants from the Triton series are used in liquid, paste and powdered forms in many cleaning compounds, ranging from heavy-duty industrial products to gentle detergents for fabrics. However, SDS is used in the flotation processes of many minerals. Thus the properties of mixtures of TX-100 and SDS surfactants should be interesting from both practical and theoretical points of view. Therefore the surface tension of these mixtures has been measured at different temperatures and with different ratios of TX-100 to SDS in the mixture.
2. Experimental
TX-100, p-( 1,1,3,3-tetramethylbutyl)phenoxypolyoxyethylene glycol containing an average of 9.5 oxyethylene units per molecule [15], and SDS were supplied by Merck with a high grade of purity (99%, for tensile tests). Solutions of the TX-100+SDS mixtures at different ratios of TX-100 to SDS were prepared using doubly distilled and deionized water. The surface tension of water was always controlled before the preparation of the solutions. The surface tension measurements were made at 15, 25 and 35°C under atmospheric pressure, by the ring method. The apparatus was connected to a computer which automatically controlled the measurement process and analyzed the obtained results. In all cases more then 10 successive measurements were carried out. The temperature was controlled within __+0.1°C. For this purpose the container with the sample solution was surrounded with a jacket through which thermostated water flowed from a Haake-C thermostat.
3. Evaluation of the molecular interaction parameters
Two fundamental properties of the solutions of surfactants are the formation of micelles in the bulk, and monolayers at the solution/air interface.
For surfactant mixtures, the characteristic phenomena are the formation of mixed monolayers at the interface and mixed micelles in the bulk solution. The molecular interaction parameters for these latter phenomena can be evaluated using the equations derived by Rubingh and Rosen. The molecular interaction parameter for mixed micelle formation, tiM, can be expressed by the relation [3,5,13] /~M =
ln(~C~z/X~ C~) {1 - x ~ ' ) :
(1) '
where CM1,C~2 are the critical micelle concentrations (CMC) of the individual surfactant 1, and the mixture of surfactants 1 and 2, respectively, is the mole fraction of surfactant 1 in the solution phase, and X~' is the mole fraction of surfactant 1 in the mixed micelle. X~ can be evaluated from the equation (X~) 2 ln(~C~2/X~C~) (1 -X1~)2 l n [ ( 1 - ~)C~2/(1 -X]a)C~] = 1,
(2)
where C~ is the CMC of the individual surfactant 2. In the case of the molecular interaction parameter in the mixed monolayer, ~a, it is possible to determine this value from the relation [3,5,13] M =
In(~C12/X1C°)
(3)
( 1 - X1)2
where X1 is the mole fraction of surfactant 1 in the mixed monolayer, Co and C12 are the molar concentrations in the bulk of surfactant 1 and of the mixture of surfactants 1 and 2, respectively, required to produce a given surface tension value. X1 can be obtained from: (X 1 )2
ln(~C~2/X~C°)
(1 - X1)2 ln[(1 - 0~)C12/(1 -- X 1 ) C O]
=1
(4)
where Co is the molar concentration of surfactant 2 in the bulk, required to produce a given surface tension.
4. Equation of state to describe mixed adsorption behavior
To describe the adsorption behavior of mixed layers the generalized Langmuir isotherm has often
159
R Jahczuk et al./Colloids Surfaces A: Physicochem. Eng. Aspects 104 (1995) 157 163
been used. However, a much better possibility from the point of view of applying parameters from the individual surfactant adsorption to the equation of state consists in the relation derived by Joos [ 14]. This relation for surfactants in concentrations up to about 10 -' tool 1- 1 can be written [11,14] exp , ~
+ exp
+ exp | ~ | \~112
-H ' -H exp ( R ~ F ~ ) + [ e x p ( R ~ F ~ )
+exp
(~,~-~75
Figs. 1-4 show the dependence of the surface tension (?9 for the TX-100 + SDS mixtures at 15, 25 and 35"'C on the total concentration of surfactants in solution for ~ (:~ is the mole fraction of surfactant 1 in the mixture) equal to 0.2, 0.4, 0.6 and 0.8, respectively. The lines reflect the dependence of 7 on log C12 calculated from Eq. (7) using the values of F ~ and a of the individual components. The values of F ~ , F ~ , F ~ , a 1 and a~' used in Eq. (7) were evaluated from Eq. (6) from the data for individual surfactants (SDS and TX-100) on the assumption that CI = 0 or C~ = 0 and are listed
-H
---]
so I
q
I
i
70~
1
! 60-
:
Z
+exp
i
i
50}-
~,
,
(6)
2R~;-~=1,
]
40-
[ I
where
-7.5
°
65 log
= exp t 2 V- ) Assuming
that
(7)
5. R e s u l t s and d i s c u s s i o n
)
)+
=1
(5)
= 1, / a2
where /Ls is the chemical potential in the surface under standard conditions, /~B is the chemical potential in the bulk under standard conditions, and ~o is the number of the moles of water per litre. Eq. (5) should give good results for systems of nonionic or ionic surfactants in the presence of a swamping electrolyte. If one of the surfactants is a 1 : 1 electrolyte type A + and B , then its activity is close to C 2 for C < 10 2M [5]. Therefore, for an aqueous solution including one nonionic and one ionic surfactant type 1:1 electrolyte in the absence of a swamping electrolyte, Eq. (5) at a first approximation. can be written in the form • -H
~T~
~1 a
Eq. (7) can be applied to describe the data determined for surfactant mixtures.
--al
where FI~, F ~ and F [ are the maximum adsorption of the solvent, and surfactants 1 and 2, respectively, H is the surface pressure, R is the gas law constant and T is the absolute temperature. The parameters a: and a2 can be expressed as
.l--expt
C1 + C2 = Ct(1 + b), gives
C2/Cl=b=const.,
and
Ctot
=
-55 45 (C,2/rqol i-')
-55
1
, I :'°'°i
25
Fig. 1. Dependence of the surface tension of aqueous solutions of the mixture of SDS and TX-100 surfactants on log C~z at 15, 25 and 35 Cforc~=0.2.
B. Jahczuk et al./Colloids Surfaces A." Physicochem. Eng. Aspects 104 (1995) 157-163
160
80
,
80
70
70
60
T E Z E
7
E z
E
60
"~ 5O
5O
°!
40
50 -7.5
,
i
I
-6.5
~
I
i
I
i
-5.5 -4.5 log (C12/mol 1-1)
•/
•
40
•
50 -7.5
-35
Fig. 2. D e p e n d e n c e of the surface tension of a q u e o u s solutions of the mixture of SDS a n d TX-100 surfactants on log C12 at 15, 25 and 3 5 ° C for ~ = 0 . 4 .
....
25 ~C
-6.5
N\~,
-5.5 109 (C12/mol
-4.5
-5.5
t-1)
Fig. 4. D e p e n d e n c e of the surface tension of a q u e o u s solutions of the mixture of SDS a n d TX-100 surfactants on log C12 at 15, 25 and 3 5 ' C for a = 0 . 8 .
80
Table 1 Parameters in Eq. (6) for TX-100 and SDS Temperature
70
Substance
F~ (tool m 2)
A (nm)
a (moll -t)
Water TX-100 SDS
16.6 x 10 ~' 3.188 x 10 6 6.105 x 10 6
0.10 0.52 0.27
2.036 x 10 -6 2.988 x 10 3
25
Water TX-100 SDS
16.6 x 10 6 3.059 x 10 6 5.113 x 10 6
0.10 0.54 0.32
1.841 x 10 6 2.657 x 10 3
35
Water TX-100 SDS
16.6 x 10 -0 2,928 x 10 6 4,964 x 10 6
0.10 0.57 0.33
1.775 x 1 0 - " 2.564 x 10 3
("C) 15
T 8 Z E
60
"~ 5O
40
. . . . . ~9
5O -7.
-6.5
;c
-5.5 -4.5 log (C12/mol 1-1)
\\\
-3.5
Fig. 3. D e p e n d e n c e of the surface tension of a q u e o u s s o l u t i o n s of the mixture of SDS a n d TX-100 surfactants on log C12 at 15, 25 and 3 5 ° C for :~ = 0.6.
in Table 1. In all cases it was assumed that the area occupied by a water molecule in the adsorbed monolayer is about 10,~2 and thus F ~ = 16.6 x 10 -6 mol m 2.
From Table 1 it appears that the values of the area per molecule, A, for TX-100 and SDS equivalent to F °~ increase with increasing temperature from 15 to 35°C. The values of A for TX-100 are considerably higher than those for SDS. It seems to us that the values of A for both TX-100 and SDS which correspond to F °~ are reasonable. The results presented in Figs. 1-4 show that the surface tension, o/, depends on temperature and c~. However, the changes in y as a function of log C12,
161
B. Jahczuk et al./Colloids" Surfaces A. Physicochem. Eng. Aspects' 104 (1995) 157 163
for a given ~, have the same shape at 15, 25 and 35°C. Of course, near the C M C there is a linear dependence of 7 on log C12. For a given concentration C12, the surface tension decreases as :t increases. From Figs. 1-4 it also appears that at low concentrations there is a very good agreement between the measured and the calculated values of 7 for the mixtures. However, for ct = 0.2, 0.4 and 0.6 in the range of concentrations where there is a linear dependence of 7 on log C12, deviations of the theoretical values of the surface tension from the measured ones can be observed. These deviations decrease from ~t = 0.2 through c~= 0.4 to :t = 0.6, and for c~= 0.8 the measured and the calculated values of 3, are the same. Thus it can be used to predict the adsorption behavior of mixtures of TX-100 + SDS at low concentrations, if the values of F ~ and a of the individual components are known. However, for concentrations near the C M C where the calculated 7 values are higher than the measured ones, the influence of the intermolecular interactions between SDS and TX-100 molecules on the pressure of the monolayer is evident, particularly for solutions in which the concentration of the ionic surfactant is higher than the nonionic one (lower values of ~). The fact that the deviation at high concentrations between the measured and calculated ), values decreases with the increase in the molar fraction of TX-100 in solution, suggests that the free energy of interaction between SDS and TX-100 molecules (AG12) is close to that between the SDS ones (AG22). The free energy of interaction, kGt,, can be determined from the relation [3,16,17]
interactions, there is a synergism in the mixture between two different surfactants, both in the monolayer and in the micelle formations. Synergism in the monolayer formation in aqueous systems containing two surfactants exists when a given surface tension can be attained at a total mixed surface concentration lower than that required for either surfactant by itself [5]. The values of the surface tension for TX-100 and SDS and their mixtures at 15, 25 and 35 C are presented in Fig. 5 (solid curves). From this figure it is clear that there is no synergism in the mixtures of SDS and TX-100. For these systems, except at one point (curve 1), no value of the surface tension of the mixture is lower than ;, for the individual surfactant. Also in this figure are plotted the values of the surface tension of the mixtures at the C M C calculated from Eq.(7) (dashed curves). It can be clearly seen that, for a given temperature, both curves differ considerably for the lowest values of :< which confirms the conclusions drawn from Figs. 1 4. It was possible to calculate the value of fla from Eq. (3) only for :z = 0.2 without considerable errors, because if X 1 is close to zero or one, a large error is made in the calculations of the fia value (Table 2 ). This value is negative and < Iln C ° / C ° l . To show whether synergism in the formation of mixed micelles of SDS and TX-100 is present or not, Fig. 6 presents the dependence of l o g C M C
I/Jal
40 I
58!
ooooo
15 °C
u
tiM = AGll + AG22 - 2AG12 kT
'
(8)
where k is Boltzmann's constant. Using in Eq. (8) the value of tiM (_ 3.22) is calculated from Eq. (1), and the values determined earlier for AGI1 (-33.51 × 10-21J) and AG22 (-19.18 x 10 21j), the A G 1 2 value was calculated to be 19.83 × 10 21 j. This value is only a little lower than that for SDS SDS interactions, confirming the above conclusion. In many cases, as result of the intermolecular
+$56 7 zE ,34 E 'm
5!
C,.O
0.2
04
06
0.8
"r)
Fig. 5. Dependenceof the surface tension of aqueous solutions of the mixtures of SDS and TX-100 on :~ for CMC at 15 {curves 1 1'), 25 {curves 2 2't and 35C (curves 3 Y). The curves 1'. 2', and 3' were determined from Eq. (7).
162
B. Jahczuk et al./Colloids Surfaces A: Physicochem. Eng. Aspects 104 (1995) 157-163
Table 2 Values of the molecular interaction parameters for the mixtures of SDS and TX-100 calculated from Eqs. (3) and (4)
- l o g CMC
Temperature
X2
_rio
Table 3 Values of the molecular interaction parameters for the mixtures of SDS and TX-100 calculated from Eqs. (1) and (2) Temperature
CMC
- l o g CMC
X~
-fia
C~ C~ C~z(0.2TX-100 ) C~ (0.4 TX-100) CtM2(0.6 TX-100) C~: (0.8 TX-100)
3.67 2.02 3.22 3.42 3.54 3.62
0.7232 0.8048 0.8618 0.9179
3.25 3.24 3.29 3.31
C~ C2M C~z (0.2 TX-100) C~z (0.4 TX-100) C72 (0.6 TX-100) CxM/(0.8TX-100)
3.58 1.98 3.14 3.33 3.45 3.53
0.7149 0.8026 0.8605 0.9174
3.21 3.10 3.15 3.20
(°C)
(°C) cO co
35
4.32 2.09 3.70 4.26 2.06 3.65
C12 (0.2 TX-100 co co
Ca2 (0.2 TX-100 co
25
0.8698 2.62
0.8586 2.50
4.13 2.02 3.51 4.02 1.96 3.41
co
CIz (0.2 TX-100 c~o
15
35
co
C12 (0.2 TX-100
25 0.8667 2.18
0.8544 2.24
-1.5
equation of state [-14], with the exception of concentrations near the CMC for low values of ~.
-2.0
ooooo
• ,,,,
i
E
15 °C 2 5 °C
-2.5
Acknowledgements
"~, o
~
-3,0
3.5
-- 4"~),10
I
0.2
I
0.4
I
0.6
0.18
Fig. 6. Dependence of log CMC on a for aqueous solutions of the mixtures of SDS and TX-100 at 15, 25 and 35°C.
on ~ at 15, 25 and 35°C. From this figure it appears that the values of the CMC decrease continuously from the CMC of pure SDS down to the CMC of pure TX-100, and therefore no synergism in the micelle formation is present [5]. The parameter tim of the micelle formation for the mixtures of SDS and TX-100 has been calculated from Eq. (1) and listed in Table 3. In all cases tim is negative and IflM[ < Iln C~/C~l. In conclusion, the mixtures of SDS and TX-IO0 do not present synergism in either the monolayer or micelle formation, and the surface tension of the aqueous solutions of these mixtures of surfactants can be predicted by the modified Joos
One of the authors (BJ) very much appreciates the support obtained from the Spanish Ministerio de Educaci6n y Ciencia for his sabbatical stay at the Departamento de Fisica, Universidad de Extremadura, Spain. Financial support for this work by DGICYT under project No. PB89-0519 is gratefully acknowledged.
References [1] M. Abe and K. Ogino, in K. Ogino and M. Abe (Eds.), Surfactant Science Series, Vol. 46, Dekker, New York, 1992, pp. 1 20. [2] N. Nishikido, in K. Ogino and M. Abe (Eds.), Surfactant Science Series, Vol. 46, Dekker, New York, 1992, pp. 23 61. [3] D.N. Rubingh, in K.L. Mittal (Ed.), Solution Chemistry of Surfactants, Vol. 1, Plenum, New York, 1979, pp. 337-354. [4] H. Lange and K.H. Bech, Kolloid Z. Polym., 251 (1973) 424. [5] J.M. Rosen, in Surfactants and Interfacial Phenomena, Wiley Interscience, New York, 1989, pp. 393-420.
B. Jatlczuk et al./Colloids Surfaces A. Physicochem. Eng. Aspects 104 (1995) 157 163 [6] J. Rodakiewicz-Nowak, J. Colloid Interface Sci., 84 ( 1981 ) 562. [7] P.A. Jacobs, H.E. Leeman and J.B. Uyter, J. Catal., 33 11974) 17. [8] N. Nishikido, J. Colloid Interface Sci., 112 (1986) 87. [9] J. Rodakiewicz-Nowak, J. Colloid Interface Sci., 85 ~1982) 586 [ 101 J. Rodakiewicz-Nowak, Colloids Surfaces, 6 ~1983) 143. [11] R. W~stneck and R. Miller, Colloids Surfaces, 47 1990) 15.
163
[12] D. G6ralczyk and B. Waligura, J. Colloid Interface Sci., 82 (1981) 1. [13] M.J. Rosen and X.Y. Hue, J. Colloid Interface Sci., 86 (1982) 164. [14] P. Joos, Bull. Soc. Claim. Belg., 76 11967) 591. [15] V.K. Sharma, R. Bhat and J.C. Akluwalia, J. Colloid Interface Sci., 112 (1986) 195. [16] P.M. Holland and D.N. Rubing. J. Phys. Chem., 87 (1983) 1984. [17] P.M. Holland, Adv. Colloid Interface Sci., 26 (19861 111.