Langmuir 1994,10, 1268-1273
1268
Synergism at a Liquid-Solid Interface. Adsorption of Binary Mixtures of Bile Salts onto a Cholesterol Surface F. Gonz6lez-Caballero*y+and M. L. Kerkebt Department of Applied Physics, Faculty of Sciences, University of Granada, 18071 Granada, Spain, and Department of Physics, Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, Morocco Received August 31, 1993. In Final Form: January 3,1994"
The nonideal solution treatment of molecular interactions in binary mixtures of surfactants at a solidliquid interface elaborated by Rosen et al. has been used to study the synergetic phenomena that can take place at the cholesterol-bile salt solution interface. The three binary combinations of sodium cholate (NaC),sodium deoxycholate (NaDC),and sodium chenodeoxycholate(NaCDC)in aqueous solution were investigated. Synergism was found in NaC-NaDC and NaC-NaCDC mixtures, and no synergetic effect was detected for the NaDC-NaCDC mixture. For all the systems studied there was consistency between synergism found at the solution-air and at cholesterol-solution interfaces. Values of the molecular interaction parameter, 0, at the solution-air and at the cholesterol-solution interface were also calculated. The small values of 101in the three binary systems, especiallyin the NaDC-NaCDC mixture, reflect a weak interaction between the surfactant molecules at the interface. This was ascribed to the similar molecular structures of these surfactants,
Introduction In the scientific literature of the last 30 years, it is possible to find many works concerning physicochemical properties of bile substances.l-8 The contributions of O'Connor,l Salcedo? Carey,L4 Sma11,5p6 and others were very helpful in understanding and explaining to some extent the behavior of these substances in many important biological phenomena, such as bile stone formation, for example. In our own e~perience,'?~ we found, when studying some interfacial energetic properties of cholesterol immersed in bile salt solutions, that these properties were drastically altered by the adsorption of bile salt micelles onto the solid surface. In this process, cholesterol changes from a hydrophobic solid to a hydrophilic one. This phenomenon was reproducible for all the bile salts studied (sodium cholate, sodium deoxycholate, and sodium chenodeoxycholate). On the basis this, we demonstrated that the aggregation process of cholesterol in an aqueous medium is hindered in the presence of bile salt micelles, and favored in their absence. One can doubt, however, if these results, as well as those obtained by other authors, can really be extrapolated to
* To whom correspondence should be addressed a t the Departamento de Ffsica Aplicada, Facultad de Ciencias, Universidad d e Granada, c/. Campus d e Fuentenueva, s/n, 18071 Granada, Spain. + University of Grenada. Abdelmalek Essaadi University. .a Abstract published in Aduance ACS Abstracts, February 15,
analyze the behavior of these surfactants in real systems. The main obstacle resides in the fact that, in biological systems, bile salt molecules are not found individually, but as mixtures. Thus, the efficiency of interfacial free energy reduction by a mixture of bile salts can be higher, lower, or comparable with that obtained for individual bile salts. For this reason, we extended our research to study the effect of the adsorption of binary mixtures of these bile salts onto the cholesterolsurface and the eventual synergetic phenomena that can accompany the adsorption process. For this purpose, we have used the recent theory elaborated by M. J. Rosen et al."12J4J5 In this theory, the authors extended the regular solution treatment of Rubingh for mixed micelles13 to adsorption at the aqueous solution-air and solid-solution interfaces. We will report here only the main features of this study.
Theory Two fundamental properties of surfactants are monolayer formation at the interface and micelle formation in solution. For surfactant mixtures, characteristic phenomena are mixed monolayer formation at the interface and mixed micelle formation in s01ution.l~ According to Rosen et al., the molecular interaction parameter, 8, between two surfactants, 1 and 2,in the mixed monolayer at the interface can be evaluated by the following basic equations:15
1994. (1) OConnor, C. J.; Ch'ng, B. T.; Wallace, R. E. J. Colloid Interface
sei. 4111 - ... 1983.95. - - -I
- - I
(2) Salcedo,J.; Delgado, A.; Gondez-Caballero, F. h o g . Colloid Polym. Sci. 1989, 79, 64. (3) Carey, M. C. In The Liver, Biology and Pathobiology; Arias, 1. M., Schachter, D., Poper, H., Shafritz, D. A., Eds.; Reven Press: New York, 1982; p 429. (4) Carey, M. C. In Clinical Hepathology; Cosmos, G., Thaler, H., Eds.; Springer Verlag: Berlin, 1983; p 53. 15) Small, D. M.: Penkett, S. A.: Chauman D. Biochem. BioDhvs. _ - Acta 1969,173, 178. (6) Small, D. M. In The Bile Acids, Chemistry, Physiology and
Metabolism: Nair,.P. P.,. Kritchevskv, _ .D... Eds.:. Plenum Press: New York. 1971; Vol. 1, p 303. (7) J ~ c z u kB.; , Kerkeb, M. L.; Bialopiotrowicz,T.; Gonzaez-Caballero, F. J. Colloid Interface Sci. 1992, 151, 333. (8) Kerkeb, M. L.; Gondez-Caballero, F.; Jafinuk, B.; Bialopiotrowin, T. Colloids Surf. 1992, 62, 263.
= 1 (1) (9) Rosen, M. J.; Hua, X. Y. J. Colloid Interface Sci. 1982,86, 161. (10) Rosen, M. J.; Hua, X. Y. J. Am. Oil Chem. SOC. 1982,59, 582. (11) Rosen, M. J.; Zhu, B. Y. J. Colloid Interface Sci. 1984,99,427. (12) Zhu, B. Y.;Roeen, M. J. J. Colloid Interface Sci. 1984, 99, 435. (13) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1,p 337. (14) Roeen, M.J. Surfactants and Interfacial Phenomena, 2nd ed.; John Wiley and Sons: New York, Singapore, 1989; p 393. (15) Rosen, M.J.; Gu,B. Colloids Surf. 1987,23, 119.
0743-746319412410-1268$04.50/0 0 1994 American Chemical Society
Synergism at the Cholesterol-Bile Salt Solution Interface ln-- “ClZ
8=
Aav
xc,o
[ l - XAl0
1
+ (1- X)Azo
(1- XY
Langmuir, Vol. 10, No.4, 1994 1269
(2) with
with A, = XA1+ (1- X)A,
(3)
A, is the average area per surfactant moleculein the mixed monolayer at the interface, Al and A2 being the partial molar interfacial areas occupied by surfactants 1 and 2, respectively, a t the solid-mixture solution interface. X is the mole fraction of surfactant 1 at the interface. Precise information on the conditions giving rise to both eqs 1 and 2 can be found in the original work by Rosen et al. (ref 15). In those equations, C1O and Cz0 are the concentrations of surfactants 1 and 2, respectively, in a solution of pure surfactant. a is the mole fraction of surfactant 1in the binary mixture of surfactants dissolved in the solution. AI’ and Azo are, respectively, the molar interfacial areas occupied by surfactants 1 and 2 a t the solid-solution of pure surfactant interface. C ~isZthe total concentration of surfactants in the mixture solution. Equation 1 can be solved iteratively for X when Cl0, Czo,C1z,A1°,AzO,andAavareknown. Thelatter quantities can be obtained from plots of ylv (liquid-vapor interface) or ylv cos 8 (solid-liquid interface) versus surfactant concentration for both pure and mixed surfactant solutions. For this purpose, a selected value of surface tension, ylv, or of ylv cos 8, can be chosen, and then the Cl0, Cz0, and Clz quantities are those needed to obtain such a value of 7lVor ylvcos 8. AI’, Azo, and Aav are obtained from the above plots, using a Gibbs adsorption equation in the same way as described by Rosen et al.’5 X,in turn, can be used in eq 2 to calculate the molecular interaction parameter,
8.
Synergism in the solid-liquid interfacial free energy exists in a solution of mixed surfactants in contact with a solid when a given value of the solid-liquid interfacial free energy, yd, occurs at a total mixed surfactant concentration in the bulk solution phase lower than the concentration of any of the components of the mixture required to obtain the same value of ysl (CIZ< Cl0 and CIZ < CZO). According to Young’s equation (eq 4), for a drop of a pure liquid (1) forming a contact angle, 8, in equilibrium with a surface of a solid (s), the solid-liquid interfacial free energy, ysl, can be expressed as follows: Ysl
= Yav - Ylv cos 8
(4)
where ysv is the surface free energy of the solid in equilibrium with the liquid vapor and ylv the surface tension of the liquid. For a low-energy solid in contact with a liquid solution, the variations of the interfacial free cos energy yI1should be mainly related to variations of 71” e (eq 4). Let us consider a mixture of two surfactants. The presence of a synergetic phenomenon is accompanied by a minimum in the curve corresponding to the variations of the total surfactant concentration, C ~ Zversus , the molar fraction in solution, a ( C ~values Z are selected for the same value of ylV cos 8, for all values of a). This minimum corresponds to the condition for maximal sinergism. Taking this into account and derivating eq 2 with respect to a,it is possible to show that, at the point of maximum synergism,ls
]
Aav (6) XAlo (1- X)Azo Equation 5 indicates that, at the point of maximum synergism, the mole fractions of surfactant 1in solution, a*,and at the interface, X*, are equal. At the point of maximum synergism (a = a*),a value of ylv cos 8, and hence a value of yd, can be obtained for a minimal concentration of the surfactants in the mixture solution, Cl~,mb.This concentration is less than those required for any other value of a # a* to give the same interfacial free energy, ysl. Combining eqs 5 and 2,C12,can be expressed as follows:
[
Bz = yslAZo 1-
+
(7)
If surfactant 1 represents the more surface-active component, the limiting value of the mole fraction of surfactant 1 at the interface, X h , for which synergism exists can be calculated numerically using the following equation:l5 1- X,
exp[8(1-
x,)’ + B1l
=
1-x,
CZo exp(BX,’ Cl
+ B,) (8)
Equation 8 can be solved numerically for Xb. This, in turn, can be used to calculate the corresponding value for a,alim:15
where the other symbols are already known.
Experimental Section Materials. Sodium cholate (NaC), sodium deoxycholate (NaDC),and sodium chenodeoxycholate(NaCDC)were supplied by Sigma (analytical grade, minimum purity 99%) and were used as received from the manufacturer. Cholesterol was a Serva product (analytical grade, minimum purity 99%) and was recrystallized three times from ethanol-water mixtures to ensure purity. Water used in the experiments was twice distilled from an all-Pyrex still and filtered through 0.2-rm Nuclepore membranes (Milli-Q Reagent System, Millipore). The chemical structure of the bile salts is shown in Figure 1, where the nature and position of the different functional groups are given. The molecule of cholesterol is similar to that of the bile salt, the main difference being the existence of a carboxylic group at the end of the hydrocarbon chain, as well as the presence of a double bond at Cm and a hydroxyl group in the molecule of cholesterol at Ca. Measurements. Surface Tension Measurements. Bile salts were dissolved in aqueous 0.01 M NaCl solutions in order to have constant ionic strength conditions. The pH of the solutions was adjusted to 7.0 0.1 using solutions of HCl and NaOH. Surface tension measurements were made by the pendant drop method, using a goniometer (Model 100-00,RamBHart, Inc.). For each solution, the drop was generated by a Hamilton microsyringe in a thermostated environmental chamber (Model 100-07, Ram6-Hart, Inc.) saturated with the solution vapor to
*
Gonzblez-Caballero and Kerkeb
1270 Langmuir, Vol. 10, No. 4, 1994
60 -
I
Bile salt IAbbreviatlonI Substituents sodium cholate R , Rzm R 3 9 OH R i g R2m OH, R 3 9 H sodium deoxycholate sodium chenodeoxycholate R R 2 OH, R 3 = H
1
66
-
60
-
9
Figure 1. Molecular structure of bile salts NaC, NaDC, and NaCDC. retard drop evaporation. For each concentration, the surface tension was measured for at least 20 drops. In all seta of the experiments,the standard deviation did not exceed 0.2 mN/m. Contact Angle Measurements. Cholesterol was dissolved in chloroform, and 3 mL of the solution was poured onto a glass plate. The plates were left in an open area to evaporate the chloroform and then dried in a desiccator at 66 "C for 3 h. The film of cholesterol obtained by this method was found earlier to be a good surface for contact angle measurements.16 Contact angles were measured by the sessile drop method, using the goniometer described above. The glass plates covered with cholesterol were placed in the thermostated environmental chamber saturated with the solutionvapor, and drops of bile salt solutionswere deposited on these surfaces. The contact angles were measured 10 min after the deposition of the drops. For each system, contact angles of at least 20 drops of each solution on the cholesterol surface were measured. In all cases, the standard deviation did not exceed 2 O . Since thie studycould be of biologicalinterest,the temperature in the environmentalchamber was kept constant at 37 OC, i.e., at a value that is within the range of human body temperatures.
Results and Discussion Synergism at the Liquid-Vapor Interface. Curves of surface tension, ylv,versus surfactant concentration are shown in Figure 2 for pure NaC, NaDC, and NaCDC solutions, and in Figure 3 for solutions of the NaC-NaDC binary mixture. Similar curves, not shown here, were obtained for the NaC-NaCDC and NaDC-NaCDC systems. NaC in the NaC-NaDC and NaC-NaCDC mixtures and NaDC in the mixture NaDC-NaCDC are termed as surfactant 1. For a selected value of the surface tension, ylv = 55 mN m-1 (marked in Figure 3 by a dashed line), C 1 O and CZ" values (a = 1 and a = 0, respectively) were determined graphically from the plots in Figure 2. In a similar way, for the same selected ylvvalue as above, C12 corresponding to different values of a were determined from the plots in Figure 3. Figure 4 shows plots of log CIZversus a for the three binary mixtures NaC-NaDC, NaC-NaCDC, and NaDCNaCDC. There, a minimum can be observed on the curves corresponding to the NaC-NaDC and NaC-NaCDC mixtures. In each case, this minimum value indicates that there exists a value of a at which the total concentration of the mixed surfactant is lower than the concentration of the individual surfactants required for the same selected (16) Chibowski, E.: Kerkeb, M. L.; Gonzaez-Caballero, F. Langmuir 1993, 9, 2491.
1o - ~ 1o+ 10-1 Concentration (M) Figure 2. Surface tension of bile salt solutions as a function of the logarithm of the molar concentration: (X) NaC, (+) NaDC, (*) NaCDC.
IO+
69
.............
Concentration (M)
Figure 3. Surface tension of NaC-NaDC mixture solutions as a function of the logarithm of the total molar surfactant a = 0.4, (X) a = 0.6,(+) a = 0.8. concentration: (*) a = 0.2, (0) surface tension to be obtained. This implies the existence of synergetic phenomena in the NaC-NaDC and NaCNaCDC mixtures. The curve corresponding to the NaDCNaCDC mixture (Figure 4) does not show any minimum, so we can conclude from these experiments that no synergetic effect is observed in this system. Accordingto Rosen et al.,16 the conditions for synergism are (1)P must be negative and (2) lln(C1°/CzO)+ 0 3 1 -&)I
< 181.
Table 1lists the g values (calculated from eqs 1and 2) and ln(C10/C20)+ (B1 - Bz) values for the investigated mixtures for the liquid-vapor interface. From this table it can be seen that the two above conditions of synergism are satisfied in the case of the NaC-NaDC and NaCNaCDC mixtures, whereas the second condition is not fulfilled in the case of the NaDC-NaCDC mixture. Thus, we can conclude that there is good agreement between the synergism experimentally found and theoretically predicted by Rosen et al.'s theory. I t is also apparent from the data in Table 1that stronger interaction (higher B values) exists in the cases of NaCNaDC and NaC-NaCDC than in the case of the NaDC-
Langmuir, Vol. 10, No. 4, 1994 1271
Synergism at the Cholesterol-Bile Salt Solution Interface loff
-3.3
c,,
4
I
Table 2. Contact Angles of the NaC-NaDC Mixture Solution on the Cholesterol Surface, at Different Values of the Total Surfactant Concentration contact angle (deg) concn (M)
1
a
5x104
84
lo-' 5 x lo-'
82 80 78 73 69 46
10-9 5 x 1o-s
le2 5X 1k2
a =0
a = 0.2
a = 0.4
a = 0.6
a = 0.8
80 78 74 68 55 50 36
79 78 74 68 55 50 35
80 79 75 69 58 53 39
80 79 76 71 59 54 39
81 80 77 72 62 56 42
40
-4.1
'
0
I
0.1
I
1
0.2 0.3
I
0.4
I
I
I
0.5 0.6 0.7
,
I
I
0.8
0.9
1
a Figure 4. Logarithm of the total surfactant concentrationaa a function of the molar fraction of surfactant 1 in the surfactant mixture dissolved (solution-air interface): (0) NaC-NaDC, (*) NaC-NaCDC, (X) NaDC-NaCDC. Table 1. Values of the Molecular Interaction Parameter of the Bile Salt Binary Mixtures, at Solution-Air and Cholesterol-Solution Interfaces YIv YII (C1°/C2") + interface (mN/m) (mJ/m2) lv 55 81 5.74 55 NaC-NaCDC lv 51 5.74 55 NaDC-NaCDC lv 5.74 51
system NaC-NaDC
(Bl-Bz) 1.54 1.40 1.11 0.37 -0.43 -1.03
15'
-2.33 -1.57 -2.21 -0.90 -0.30 -0.22
NaCDC system. Some explanation of this behavior could be found from the analysis of the surface free energy components of each of these bile salts. In an earlier paper,' we showed that the apolar, Lifshitz-van der Waals contributions to the surface free energy of the three bile salts are nearly identical (around 26 mJ m-2, at 20 "C). However, slight differences were found for the Lewis acidbase parameters of the polar component of the surface free energy of these surfactants.7 Of course, these differences should be responsible for the different magnitudes of the interaction between a pair of bile salts,as manifested by the values obtained for the fl parameter (see Table 1). The origin of this lies in the fact that the NaC molecule has three hydroxyl groups on the steroid nucleus, whereas NaDC and NaCDC have two (see Figure 1). Thus, the polar contribution to the energy of interaction between NaC and NaDC or NaCDC should be slightly different (higher) than that between NaDC and NaCDC. This is in good agreement with the values of fl obtained (-2.33 for NaC-NaDC and -2.21 for NaC-NaCDC, as compared with the very small value of /3 (-0.30) obtained for the NaDCNaCDC binary mixture). In any case the small values of 1/31 indicate that all these interactions are weak, which is reasonable since the surfactants have similar molecular structure and the charges of their ionic groups are of the same sign. The negative value of fl means that the interactions between the surfactant molecules in the interfacial film are of attractive nature.
Concentration (M)
Figure 5. ylvcos 6 values for bile salt solutions aa a function of the logarithm of the molar concentration: (+) NaC, (*) NaDC, (X)
NaCDC.
Synergism at the Solid-Liquid Interface. The results obtained in the previous section show that the synergetic effect between bile salt molecules at a liquidgas interface, when present, is very weak. Let us consider now the cholesterol-bile salt solution interface. The presence of the cholesterol surface can modify the degree of interaction between a pair of bile salt molecules, and hence the possible synergetic effect between these surfactants. In order to study synergetic phenomena a t the solidliquid interface, drops of the solutions described above were deposited onto the cholesterolsurface, and the contact angles were measured. The results are shown in Table 2 (NaC-NaDC mixture). Curves of ylvcos 0 versus surfactant concentration are shown in Figure 5 for pure NaC, NaDC, and NaCDC solutions, and in Figure 6 for solutions of the NaC-NaDC binary mixture. Similar curves were obtained for the NaC-NaCDC and NaDC-NaCDC systems (not shown here). In this case, C12 was obtained graphically from the plots of ylvcos0 vs total concentration of the bile salts in solution (Figures 5 and 61, for the same selected value of ylvcos 0 (30 mJ m-2). As previously, log Clz was plotted as a function of a and represented in Figure 7 for the three binary mixtures. Similarly as for the liquidvapor interface (Figure 4), the results in Figure 7 show a minimum on the curves for the NaC-NaDC and NaCNaCDC mixtures, and no minimum for the NaDC-NaCDC system. So, we can conclude that synergetic phenomena are experimentally observed only in the NaC-NaDC and NaC-NaCDC mixtures. For the three binary systems, and for different a values, the values of the molar fractions of surfactant 1 at the interface, X, were calculated using eq 1. For these
Gonztrlez-Caballero and Kerkeb
1272 Langmuir, Vol. 10, No. 4, 1994
X
Concentration (M) Figure 6. ylv cos 8 values of NaC-NaDC mixture solutions aa a function of the logarithm of the total molar surfactant a = 0.6,(*) a = 0.8. concentration: (+) a = 0.2, (X) a = 0.4, (0)
0
0.1
0.2 0.3 0.4
0.6
0.6
0.7
0.8 0.9
1
a Figure 8. Molar fraction of surfactant 1 at the interface 88 a function of ita molar fractionin the surfactant mixture dissolved
(cholesterol-solution interface): NaCDC, (X) NaDC-NaCDC.
c
-1.2
( 0 ) NaC-NaDC, (*)
NaC-
Table 3. Values of NaC Molar Fraction Corresponding to Maximum Synergism, a*,the Minimum Total Surfactant Concentration To Obtain the Selected Value of 7lVcos 8, and the NaC Molar Fractions in the Surfactant Mixture Dissolved in Solution and at the Interface, under Limiting Synergism Conditions system NaC-NaDC NaC-NaCDC
-2.2
1
I
0
0.1
I
I
I
I
,
I
0.2 0.3 0.4 0.6 0.6 0.7
1
I
I
0.8
0.9
1
o!
Figure 7. Total surfactant concentration as a function of the molar fractionof surfactant 1in the surfactantmixture dissolved (cholesterol-solution interface): (0)NaC-NaDC, (*) NaC-
NaCDC, (X) NaDC-NaCDC.
calculations, yslwas estimated from Young's equation (eq 4), for a value of ysv= 35.74mJ m-2, the surface free energy of ch~lesterol.~ Figure 8 shows variations of X as a function of the molar fraction of this surfactant in the bulk phase, a,for the three binary systems. It appears from this figure that the NaDC-NaCDC mixture behaves in such a manner that the molar fraction of NaDC at the solid (cholesterol)solution interface is higher than the one in the bulk solution. This means that the affinity of NaDC for cholesterol is higher than that of NaCDC. The sample analysis can be made for the other two systems shown in Figure 8. Thus, it results from this figure that the following order of the surface affinity of the bile salts for the cholesterol surface exists: NaDC > NaCDC > NaC. The values of @ and ln(C1O/C2") + (B1-B2) for the three mixtures for the solid-liquid interface are also listed in
a*
4zd(M)
slim
Xli,
0.10 0.29
1.08X 1bz 2.87 X
0.22
0.18 0.530
0.63
Table 1. From the data in this table, and applying the synergism conditions of Rosen's theory cited above, we can confirm the existence of a synergetic effect in the NaCNaDC and NaC-NaCDC mixtures and ita absence in the NaDC-NaCDC mixture. Again, there is quite good agreement between the prediction of Rosen et al.'s theory and experimental findings. It is clear from the data in Table 1that the values of the molecular interaction parameter @ depend on the kind of interface, Le., solid-vapor or solid-liquid. For all three binary systems, /3 decreases in absolute value (it becomes less negative) for the solid-liquid interface. This implies that in the presence of the cholesterol the weak attractive interactions between the surfactant molecules decrease in comparison to those found for the liquid-air interface. So, we can conclude that the nature of the interface has some effect on the extent of molecular interactions of the bile salt in the interfacial film. For two systems which showed synergism (NaC-NaDC and NaC-NaCDC), using eqs 5 and 7-9,the mole fraction of NaC under maximum synergism conditions, a*,the minimum total surfactant concentration to obtain the selected values of ylvor 71" cos 8,Clamh, and the limiting value of the mole fractions of NaC in solution, a b ,and a t the interface, X b ,were calculated. These values are listed in Table 3. From the data in this table, it can be seen that in the surfactant mixture the synergism phenomenon is most noticeable if the NaC mole fraction is almost 10% in the case of the NaC-NaDC mixture, and almost 29 % in the case of the NaC-NaCDC mixture. Under
Synergism at the Cholesterol-Bile Salt Solution Interface
Langmuir, Vol. 10, No. 4, 1994 1273
these conditions, the selected value of the surface free energy can be obtained with a minimum total surfactant concentration, C~Z&,of only 1.08 X M for the NaCNaDC mixture, and 2.87 X le2M for the NaC-NaCDC mixture. From Table 3, we can also conclude, on the basis ,, if the mole fraction of the calculated values of q,,that of NaC exceeds 22% and 63% of the total surfactant content in the NaC-NaDC and NaC-NaCDC mixtures, respectively, no synergetic phenomenon takes place. These percentages correspond to the mole fraction of NaC at the interface (Xb) equal to 0.18 and 0.53, respectively (see Table 3). In conclusion, it can be stated that, a t the liquid-vapor interface, as well as at the solid-liquid interface, no synergism phenomenon was detected in the system of NaDC-NaCDC, unlike the NaC-NaDC and NaC-NaCDC binary mixtures. As can be deduced from the values of 1/31,synergism phenomena in these latter two cases are very weak. As a consequence, the conclusion can be drawn that the molecules of bile salts are mixed in an almost ideal way concerning their surface activity, and the general features of the results obtained with individual bile salts are similar to those obtained with a mixture of these surfactants. In fact, it is not surprising that these mixtures behave almost ideally. It is because of their identical hydrophilic groups, as well as the fact that their hydrophobic chains are of similar molecular structure. Hence, it could be expected that the aggregation process of cholesterol in the bile salt solutions does not depend significantly on the composition of the surfactant solution (individual bile salt concentrations), but on the total surfactant concentration in the aqueous medium.
chemicalpotential of surfactant i at the solid-liquid interface, defined as a monolayer of pure surfactant i at a zero solid-liquid interfacialtension chemical potential of surfactant i at the solidsolution of pure surfactant i interface chemicalpotential of surfactant i in the bulk phase of the surfactant solution chemicalpotential of surfactant i in the bulk phase at a standard state defined as a 1 M solution chemical potential of surfactant i in the bulk phase of a solution of pure surfactant i activity coefficient of surfactant i at the solidmixture solution interface activity coefficient of surfactant i in the bulk of the mixture solution activitycoefficientof surfactant i in the bulk phase of a solution of pure surfactant i partial molar interfacial area occupied by surfactant i at the solid-mixture solution interface molar interfacial area occupied by surfactant i at the solid-solution of pure surfactant i interface average area per surfactant molecule in the mixed monolayer at the interface concentrationof surfactant i in the mixture solution concentration of surfactant i in a solution of pure surfactant i total concentration of Surfactants in the mixture solution minimum total concentration of surfactants required to obtain a given interfacial energy reduction mole fraction of surfactant 1in the binary mixture of surfactants dissolved in the solution mole fraction of surfactant 1 dissolved in the solution surfactant mixture, under maximum synergism conditions limiting mole fraction of surfactant 1 in the surfactant mixture, dissolved in the solution, at which synergism exists mole fraction of surfactant 1at the interface mole fractionof surfactant 1at the interface,under maximum synergism conditions limiting mole fraction of surfactant 1 at the interface, at which synergism exists
Y 7r
e
B Pi4
List of Symbols interfacial free energy interfacialfree energy reduction (surfacepressure) contact angle of a liquid on a solid surface molecular interaction parameter chemical potential of surfactant i at the solidmixture solution interface
&,ao
Pi,b P"i,b Pi,b' fi,
fi fi" Ai Ai"
Ci Ci" c12 C12,min
a a*
X X*
