14032
J. Phys. Chem. 1995,99, 14032-14038
Behaviors of Sodium Deoxycholate (NaDC)and Polyoxyethylene tert-Octylphenyl Ether (Triton X-100) at the AirNater Interface and in the Bulk Md. Emdadul HaqueJ Akhil Ranjan Das,**+and Satya Priya Moulik8 Polymer Science Unit, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India, and Centre for &#ace Science, Department of Chemistry, Jadavpur University, Jadavpur, Calcutta 700 032, India Received: December 19, 1994; In Final Form: July 1, 1995@
The interfacial and bulk properties of sodium deoxycholate (NaDC) and polyoxyethylene tert-octylphenyl ether (Triton X-100, TX-100) and their binary mixtures in aqueous solution have been investigated by means of surface tension, conductance, calorimetric, and fluorescence methods. The experimental results are utilized to evaluate critical micelle concentration (cmc), counterion binding, mean aggregation number, thermodynamics of micellization, interfacial adsorption, and the microenvironment of the surfactant systems. The enthalpy of micellization ( m ~ has )been found to be negligible for TX-100 and mixed combinations containing its higher proportion. The entropy of micellization (ASOM)is the predominant factor in the micellization process. The polarity of the mixed micelles obtained from 11/13 and the lifetime of the pyrene monomer fluorescence shows that the solubilization site of pyrene changes with mole fraction. The concentration dependence of Z1/Z3 indicates that the mixed micellar size and composition vary with total surfactant concentration, and the initial micelles near the cmc contain higher mole fractions of TX-100 compared to the experimental ones. The mean aggregation number is seen to decrease with the increase of the mole fraction of NaDC in the mixed micelle. The composition of the mixed systems have been estimated using regular solution theory, excess thermodynamic quantities, and the molecular thermodynamic model. The mole fractions of NaDC in micelles are found to be lower than those of analytical mole fractions.
Introduction Mixed micellar systems composed of binary surfactant combinations are very important from the viewpoint of fundamental, technological, pharmaceutical, and biological considerations. Extensive studies have been reported on the mixed systems of ordinary surfactants.'-8 In recent years, much attention has been paid to the investigations of mixed micellar properties of synthetic and natural detergents. Thus, considerable effort has been devoted to the study of mixed aggregates of bile salts with synthetic surfactants as well as lipids to understand the nature of interaction in the bulk and at the air1 water i n t e r f a ~ e . ~ - 'The ~ bile salts are biologically very important molecules and play vital roles in a number of physiological processes.13 Some of them are known to dissolve cholesterol gallstones,I4 and their mixed aggregates with biological lipids such as lecithin facilitate emulsification and absorption of lipids. In combination with ordinary detergents, bile salts are used in biochemistry and pharmaceutical preparations as solubilizers for medicine. The interaction of synthetic ionic surfactants and conjugated as well as nonconjugated bile salts have been studied from the standpoint of critical micelle concentration (cmc), surface, and bulk phase proper tie^.^^-^^ However, investigations of binary mixtures of bile salts and nonionic detergents are conspicuously limited.20*21Recently two paper^^^.*^ have reported studies on the mixed systems of a nonionic surfactant, octaethelene glycol n-decyl ether with sodium cholate and sodium glycocholate, using fluorescence probing methods to obtain the aggregation number and polarity of the interior of the micelle. We have undertaken a detailed program of investigations on the mixed micellar properties of bile salts with synthetic
' Indian Association for the Cultivation of Science. @
Jadavpur University. Abstract published in Aduunce ACS Absrructs, August 15, 1995.
0022-365419512099-14032$09.0010
nonionic surfactants. The present paper deals with the interaction of sodium deoxycholate (NaDC) and polyoxyethylenetertoctylphenyl ether (Triton X-100, TX-100) in aqueous solution with reference to mixed micelle formation, counterion binding, aggregation number, thermodynamics of micellization, and behavior at the aidwater interface and in the bulk using surface tension, conductance, calorometric, and fluorescence probing technics. The aggregation number and polarity of the micellar interior have been explored by pyrene fluorescence. Intramicellar interactions and the composition of the mixed micelles are also compared on the basis of recent theoretical treatm e n t ~ . ~ ~The - * ~rationale for the selection of TX-100 is due to its wide use for stabilization and solubilization in chemical, biochemical, pharmaceutical, and industrial fields. Experimental Section Materials. NaDC, Sigma Chemicals, was 99% pure. It was further purified by crystallization several times from the mixed solvents of acetone and water and soxhlet extraction with acetone for 72 h. TX-100was obtained from Aldrich and used as received. Pyrene (Aldrich) as a probe was purified by gel chromatography with cyclohexane. Cetyl pyridinium chloride (CpCl), the quencher, was purified several times by recrystallization from the mixed solvents of acetone and isopropyl alcohol after decolorization with activated carbon in the mixed solvents. Aqueous solutions of surfactants were prepared in phosphate buffer (NaH2P04, NazHP04 of BDH Chemicals), adjusting pH in the range 8.0-8.2 except for conductance measurements. Methods. All measurements were recorded at 296 f 0.01 K in a thermostated water bath. Water at constant temperature was circulated around the cell chamber in fluorescence measurements. The calorimetric runs were taken at 303 f 0.0002 K. 0 1995 American Chemical Society
NaDC and Triton X-100 at the AirNater Interface
J. Phys. Chem., Vol. 99, No. 38, I995 14033
Surface Tension Measurements. The surface tensions of the solutions were measured with a du Nouy tensiometer Model K8 of KRUSS Garmany using a platinum ring. The tensiometer was calibrated against water. The measured surface tension values were corrected according to the procedure of Harkins and Jordan.27 In an experimental run, the surfactant solution was added gradually to water in the glass vessel at constant temperature and the data for surface tensions were taken at 15min intervals after thorough mixing with the help of a Teflon coated magnetic stirrer. The instrumental accuracy was f 0 . 1 dydcm. Conductivity Measurements. Conductance measurements were taken in a Jenway conductometer at 10 mHZ. A dip type cell of cell constant 1.39 cm-’ was used. The error limits in measurements were within &OS%. In the actual procedure, the surfactant solution was gradually added to water by a microsyringe, and the conductance of the solution was recorded after attaining temperature equilibrium and thorough mixing. Calorimetric Measurements. A Tronac Isoperibol titration calorimeter was used for measuring heats of micellization at 303 f 0.0002 K. The heat of reaction of HCl and NaOH was measured for checking the calibration of the calorimeter. The accuracy of the apparatus was 0.5% on 2 cal. The measurement procedure was the same as that described elsewhere.’8 For evaluation of the heat of micellization, the thermograms were processed following the procedure of Kreshek and Hargraves.28 The standard deviation in the measured enthalpy of micellization (AHOM)was 4~4%. Fluorescence Measurements. Fluorescence measurements were taken in a Perkin Elmer (Model MPF 44B)fluorescence spectrometer. The excitation wavelength was 1 = 335 nm, and the pyrene concentration was around low5mol dm-3. The ratio of the intensity of the pyrene emissions at 373 and 383 nm, defined as IllI3, provides information on the polarity of the m i c r o e n v i r ~ n m e n t . ~ ~A- ~single ~ photon counting apparatus (Applied Photophysics single photon counting setup with pulsed nitrogen lamp) was used for the time resolved fluorescence quenching studies. The decay curves (fluorescence intensity I ( r ) vs time t ) of micelle solubilized pyrene was computer fitted to the decay f u n c t i ~ n ~(eq ~ -1)~using ~ a nonlinear least squares weighted procedure, where z and KE are the lifetime and rate constant of fluorescence decay phenomenon.
I ( t ) = I(0) eXp{ -(t/t) - R[1 - eXp(KEt)]}
(1)
The following results were obtained from the fluorescence data analysis: (a) the fluorescence lifetime z of the pyrene in its microenvironment; (b) the rate constant KE for intramolecular excimer formation; (c) the ratio R = CJM (C, is the molar concentration of the micelle solubilized pyrene, and M is the micelle concentration in moles per liter); and (d) the aggregation number related to the above ratio by the relationship
where C and cmc are the concentration of the surfactant and its critical micelle concentration, respectively.
Results and Discussion Critical Micelle Concentration, The cmc values of individual and mixed surfactant solutions obtained by different methods are given in Table 1. Graphical representations are omitted to save space. The cmcs determined by different methods showed reasonably good agreement. Surface tension and fluorescence measurements yielded rather close cmc values,
TABLE 1: Cmc Values of NaDC-TX-100 Mixed Systems by Different Methods (Temperature = 296 K; 303 K (Cdorimetry)Y cmc/(mmol dm-l) surface tension
aNaDC
1.0@ 0.90 0.75 0.50 0.25
2.34 (2.75,18 1.17 (1.32) 0.69 (0.80) 0.43 (0.48) 0.32 (0.35) 0.10 0.29 (0.29) 0.00‘ 0.27 (0.26j7)
fluorescence
conductance
calorimetry
2.45 (2.405*) 1.50 0.72 0.50 0.42 0.32 0.25
5.55 (3.97’9 4.62 2.26 1.15 0.63
5.83 3.58 3.05 2.46
a Values in parentheses indicate the cmc from the Clint equation. The values with a reference number in the parentheses indicate cmcs from literature. The cmc of NaDC (mmol dm-3) by the solubility method: 5.0;555.0.56 The cmc of TX-100 (mmol dm-3) by the spectroscopic (UV) method: 0.26;17 0.29.53
i)U
FORI
IFOR
. . l
1
I
4.5
I 4.0
9:1
I 3.5
I
3.0
I120 2.5
Figure 1. Surface pressure (JC) as a function of log C for pure and mixed systems of NadC and TX-100 at 296 K. The type of system and the ordinate scale are indicated in each plot. The first component in the ratio is TX-100.
which were lower compared to those obtained from conductance and calorimetry. The temperature may have a minor effect on the cmc. The reproducibility and consistency of the results realized by different methods ruled out the error induced discrepancies among them. The calorimetric cmc determination of bile salts with synthetic surfactants has been rarely rep ~ r t e d . The ~ ~ measured ,~~ cmc values have shown a comparable trend with bile salts (other than NaDC)-nonionic detergent combinations recently r e p ~ r t e d . ~ ’It- ~is~a general experience that the cmc is a method d e ~ e n d e n t ~property. ~.~’ The results of other workers on NaDC and TX-100 by different methods are compared in Table 1. Surface Pressure of the Single and Mixed Surfactants. The surface pressure (n) as a function of log C of the individual and mixed aqueous solutions of NaDC and TX-100 is shown in Figure 1. The observed breaks in the surface pressure curves of the studied mixtures indicate that micelle formation occurs above a critical concentration. These cmcs and the values of the surface pressure at the cmc (ncmc) are given in Table 2. In order to calculate the amount of surfactant adsorbed per unit area of the airlaqueous solution interface at various concentrations, the Gibb’s adsorption equation was used. For a binary surfactant combination, the Gibb’s surface excess of surfactants relative to a zero excess of water per unit area of the surface is given by the equation
dJc = C r , R T d In a,
(3)
Haque et al.
14034 J. Phys. Chem., Vol. 99, No. 38, 1995
TABLE 2: rmax, Amin,AGOM,and AGOadfor the NaDC-TX-100 System from Surface Tension Measurements (Temperature = 296 K)" aNaDC cmcl(mmo1dm-3) lo6 x T,,,/(mol cm-2) A,iJnm2 AGo~/(kJmol-') AGo,d(kJ mol-') .n,,,/(erg cm-2) 1.OO 0.90 0.75 0.50 0.25 0.10 0.00
0.91 1.45 1.61 1.65 1.18 1.64 1.61
2.34 1.17 0.69 0.43 0.32 0.29 0.27
- 14.9
1.82 1.14 (1.44) 1.03 (1.62) 1.OO ( 1.42) 0.91 (1.22) 1.01 (1.10) 1.02
-45.0 -46.2 -47.9 -50.0 -50.5 -45.9 -45.6
- 16.6 - 17.9 -19.1 -19.8 -20.0 -20.2
26.1 37.6 40.4 40.9 42.6 41.9 41 .O
Values in parentheses were obtained from eq 9. AGo,d was calculated from eq 7 using AGOMestimated from surface tension data without counterion biniing. where dn is the change in the surface pressure of the solution relative to pure water, Ti is the surface excess (adsorption density), ai is the activity of the ith component in the mixed film, T is the absolute temperature, and R is the gas constant. When the composition of the surfactant components in the aqueous solution is constant and C is the total concentration of the surfactant in solution,
r = 1/4.61Rfl&/(d
log C
+ d log Y*)]
(4)
where Y+ is the mean activity coefficient of the surfactant in solution. The maximum adsorption density (rmax (mol cm-2)) and the minimum area per molecule (Amin(nm2)) was calculated from the relationships
rmax = 1/4.61RT lim C-cmc
where N is the Avogadro number. The d log vi was neglected in the calculation since the surfactant solutions were always dilute. Here, Ami,, refers to the average of the combinations of both NaDC and TX-100, assuming 1:l composition of the surfactants at the interface. The rmax, Amin, and ncmc obtained from surface pressure plots values (nagainst log 0 are also contained in Table 2. rmax are of the same order as those of the nonionic surfactant n-dodecyl P-D-maltoside mixed with n-dodecyl octaethylene glycol ether and also of cationic surfactants of various chain
length^.^^,^^
rmax for the pure surfactants were lower than those of the mixtures; the Ami,, values of the pure surfactants were obviously greater than their mixtures. The individual components occupied a greater area per molecule due to mutual repulsion; the presence of the nonionic TX-100 molecules at the interface reduced it. With flat orientation, a saturated monolayer interface of deoxycholate was reported to correspond to 1.80 nm2/ molecule. The estimated area per molecule of TX-100 is 1.10 nm2. Thermodynamics of Interfacial Adsorption and Micelle Formation. The standard free energy of adsorption at the air/ saturated monolayer interface (AGoad)was obtained from the relationship (7)
where ncmc is the surface pressure at the cmc and rmax is the surface excess at the maximum adsorption level. . The free energy of micelle formation per mole of monomer unit (AGO,) was evaluated by applying the equation
+j)RT In cmc
"a
f
1.00 0.90 0.75 0.50 0.25 0.10 0.00
0.08 0.20 0.26 0.30 0.29
AGOMI (kJ mol-')
AHOM/ (kJ mol-')
ASOM/ (J K-I mol-')
-16.1 -19.9 -22.6 -24.8 -25.5 -20.0 -20.2
-0.70 -2.76 -2.48 -0.41 0.0
52.0 57.9 68.0 82.4 86.1 67.6 68.2
0.0 0.0
a A G o ~ was calculated using 8, considering counterion binding. AHOM was considered invariant between 296 and 303 K for the estimation of ASOMat 296 K by the Gibbs equation (AGOM= A H O M TASOM).
TABLE 4: Polarity of the Micelle Interior and Aggregation Number (% for the NaDC-TX-100 Combinations at 296 K
(&/d log C)
Amin= 10'8/NTmax
AGO, = (1
TABLE 3: AGOM,A H O M , A S O M , and Counterion Binding v) of the NaDC-TX-100 System at 296 K (ConsideringA H O M Values from Calorimetric ResultsY
(8)
-
aNaDc
11/13
tdns
N
1.OO 0.90 0.75 0.50 0.25 0.10 0.00
0.77 0.90 1.14 1.26 1.32 1.39 1.40
300 285 244 239 222 215 21 1
10 36 54 69 85 109 139
KE x 10-7/~-1 1.33 1.23 1.48 1.08 0.93
0.44 2.00
where f is the fraction of micelle bound counterions (f was obtained from conductance-concentration results according to the Evans method40). Low values of counterion binding of the bile salts were reported in the The f values of the mixed systems (Table 3) were used to calculate AG'M. The Evans method of evaluation off (although not very accurate) is frequently used to estimate f for its simplicity and easy adoptibility. This was the rationale for its use in the present study. According to our e ~ p e r i e n c e , 'this ~ . ~did ~ minimaly affect the results. This model has been used in limited mixed surfactant systems.'* We considered it applicable to the present NaDC-TX-100 combinations. The f values were found to vary in the range of 0.20-0.30; there was a minor trend of increase with decreasing a N a C in the mixture. The f obtained for pure NaDC micelle was significantly low (0.08). The observed trend in f may appear to be unusual. f is intrinsically related to the surface charge density of the micelles, which in turn becomes a function of the aggregation number. It will be subsequently seen (Table 4)that the micellar aggregation number was found to increase with decreasing (XNaDC in the mixture. Although the proportion of NaDC in the mixed micelles decreased with an increased proportion of TX-100, the variation of their number in the micellar assembly might have on the average kept the effective charge density constant to yield practically mildly variedf. The aggregation number of pure NaDC micelle was significantly low; thefwas also at least 50% lower. The values of AGOad, AGO,. ncmc, and rmax are given in Table 2.
NaDC and Triton X-100 at the Airwater Interface I
J. Phys. Chem., Vol. 99, No. 38, 1995 14035
C
0 0
n
1.31
-’4
W
.
TT XX -- 11 00 00 00 1:3 11:1 :1 “
2 v
3
* O -0
t
300 I
n
VI
250 0.71
I
I
0
20
40
[C 3
I
I
60 80 / m m o l dm-3
I
C Y
t.”
100
Figure 2. Plot of 11/13 vs surfactant concentration of pure and mixed systems of NaDC and TX-100 at 296 K. The first component of the ratio is TX-100.
The AGoad values indicated that the adsorption process was more favorable for the surfactant combinations compared to individual surfactants; i.e., the interaction was more spontaneous at the interface. Drummond et al.38reported comparable AGoad values for pure as well as mixed nonionic surfactant combinations. In addition to AGOM,A H O M is essential for a comprehensive thermodynamic analysis of the micellization process. The values of AWMobtained from calorimetry are considered most suitable for the purpose. The Kreshek and Hargraves method28 used by us recentlyi8 was followed to determine A H O M of surfactant systems from the thermograms. The A ~ P M values for a few surfactant mixtures were very low and, therefore, taken as zero. The entropy of micellization ASOM values were obtained from the Gibbs-Helmholtz equation in terms of AGOM and AWM. The results are presented in the Table 3. The ASOM values are usually observed to be positive.M. The positive ASOM values are considered to be due to the disorder or randomness as a result of melting of “icebergs” or “flickering clusters” around the nonpolar tail45 of the surfactant monomers along with the residence of hydrophobic ends in similar environments in the micelle interior. Partially neutral micelle formation takes place due to counterion binding, leading to reduced wateddipole interaction thus resulting in enhanced entropy. In all the surfactant combinations investigated, increasing proportions of NaDC manifested a decreasing effect on ASOM. The AWMat aNaDC < 0.25 was insignificant; the micellization process was entropy guided. The spontaneity of the process maximized at (XNaDC = 0.25 with maximization of ASOM; thereafter the energetic behavior of the mixed system was found to be identical with that of the pure TX-100 system. Besides orientation and packing of the surfactants, hydration and microenvironments may influence the ASOMvalues. A quantitative interpretation of all the factors involved in the process seems to be a very difficult proposition and will be kept pending for future assessment. Microenvironment. The ratio of the first and third vibronic peaks, 11/13, in a monomeric pyrene fluorescence emission spectrum is known to be sensitive to the local polarity of the probe microenvironment and the solubilization ~ i t e . ~ ~The ,~’ dependence of 11/13 of pure and mixed micellar combinations of NaDC and TX-100 on the total surfactant concentration is shown in the Figure 2. In the low amphiphile concentration, the 11/13values for the mixed systems are comparable with that of TX-100. This indicates that the solubilization sites of pyrene and the microenvironment of the micelles are very close to those
200 ,,
0
0.5
1.0
Figure 3. Plot of 11/13 and the lifetime (to)against the mole fraction of NaDC at 296 K (at a total surfactant concentration of 0.1 mol dm-3).
of TX-100 micelles and the ratio of the NaDC in the mixed micelle is much lower compared to the stoichiometric mole fraction of the surfactant. The 11/13 and to48 (lifetime) values of pyrene fluorescence at different mole fractions of NaDC at constant [NaDC] of 100 mol dm-3 are shown in Table 4 and Figure 3. The low 11/13 and large to values indicate the microenvironment of pyrene solubilized in NaDC to be nearly as nonpolar as hydrocarbon s0lvents.~8 The 11/13 values for the nonionic micelle TX-100 and its mixtures with a N a C 5 0.25 were close to those of the polar solvents, e.g., ethanol. The solubilization sites of pyrene in NaDC and TX-100 micelles were different. Similar to the behavior of aromatic hydrocarbons, owing to its slight surface activity, pyrene resides in the palisade layer of ordinary surface active agents.49 The magnitudes of 11/13 and to indicated pyrene solubilization in the palisade layers of TX-100 micelles and in the interior of NaDC micelles. Similar observations were reported by Zana et al.48 In Figure 3 a break point is observed in the curve, and beyond this point 11/13values decrease sharply. A break point is also observed in the r o - a N a D c curve at the same mole fraction. A sharp decrease in 11/13and an increase in to values in the aNaDC of 0.75-1.0 reflect a large increase in the hydrophobicity in the micelle and the pyrene solubilization site. The break points in both the curves suggest a transition of the pyrene solubilization site from the palisade layer to the micelle interior. Aggregation Number. The mean aggregation numbers of the pure and mixed surfactant systems were determined at a total surfactant concentration of 100 mol dm-3. The plot of N of all the mixed combinations vs a” at a total surfactant concentration of 100 mol dm-3 is shown in Figure 4. An abrupt
14036 J. Phys. Chem., Vol. 99, No. 38, 1995
150 0.90 0.75 0.50 0.25 0.10
100
-0.521/-0.521 -0.7091-1.086 -1.0001- 1.899 -1.325/-1.621 -0.939/- 1.545
0.882410.6604 0.713510.4890 0.510410.3617 0.3418/0.2695 0.4233/0.2169
0.8732D.6493 0.934110.8127 0.968U0.9173 0.986810.9754 0.999110.9957
Y N ~ D C ( R )and YTX.~W(PB) stand for activity coefficients of NaDC and TX- 100 from the Rubingh theory and the Puvvada-Blankschtein
I2
50
0
0.51/0.3210.51 0.3110.24/0.35 0.1810.29/0.26 0.10/0.10/0.12 0.0310.0510.05
model, respectively. results, and good agreement was observed at a N a D C < 0.75. Similar behaviors were also observed for NaDC alkyl sulfate mixture^.^ The cmcs were derived from conductance and calorimetry; although agreed among them, they were all perceptibly higher than the ideal values. A more quantitative approach toward mixed micelle formation was put forward by Rubingh on the basis of regular solution theory.24 Rubingh's derivation permitted evaluation of an interaction parameter p (based on experimental cmc data) and micelle composition in the mixed system. Also Motomura et al.25had shown that mixed micellar composition of surfactants can be derived in terms of excess thermodynamic functions. The values of interaction parameter /?,the activity coefficients of the surfactants, and the mole fraction of NaDC in micelles XR and XM calculated from the treatments of Rubingh and Motomura et al., respectively, are listed in Table 5 . Negative values of the interaction parameter p indicate attractive interaction between the surfactants. Amin values for the mixed combinations (Table 2) also supported this observation. Negative p values were also reported in the mixed systems of anionic-nonionic and nonionic-nonionic detergents, including bile in the former. In several recent publications Puvvada and Blankschtein26 have proposed a theoretical model for computing the cmc of binary surfactant mixtures, their interaction, and activity coefficients in the micelle, micellar composition, and their aggregation number on the basis of hydrophobic, structural, and electrical interactions between the binary components. Equation 10 is thus modified to
I 0.5
1
&
1.
-
Figure 4. Plot of the mean aggregation number (N) vs the mole fraction of NaDC at 296 K.
decrease in is observed in the low a N a C region of 0.1. A small quantity of NaDC considerably inhibits the aggregation behavior. This abrupt change in F may be due to widely differing cohesions and shapes of the two molecules forming the mixed species. The % of the pure NaDC micelle is small compared to that of the pure TX-100micelle. The of mixed micelles were of intermediate values. Zana et al.22reported similar behavior of the mixed micelles of the bile salts. Interaction of Surfactants. Assuming ideal mixing of the interacting surfactants, the minimum areas per molecule of the mixed entities can be expressed by the relationship
A::
+
TX-100 = aA$F (1 - a)Ami,
(9)
where the new terms Y N ~ Cand ~ ~ x . 1 0are 0 the activity coefficients of NaDC and TX-100in the micelle. Y N ~ Cand ~ ~ ~ - are 1 0 given 0 by the relations
a being the mole fraction of NaDC in the binary surfactant mixture. The A:!: values obtained by the above equation are included in the parentheses in Table 2. The experimental A:: values of the mixed micelles were observed to be lower than those calculated using eq 9 and reflected the degree of interaction of bile salt anion DC- with TX-100. Clint' proposed the following equation to evaluate the cmc of the mixed system on the basis of ideal mixing of the binary surfactant combinations. 1 cmcmix
-
a CmCNaDC
+ 1-a cmcTX-lOO
(10)
The calculated cmcs corresponding to various ratios are shown in the parentheses in Table 1. The calculated ideal cmc values were found to be lower than those obtained from experimental measurements. They were, however, close to the surface tension
where P N ~ c - T X stands . ~ ~for the, specific interaction between NaDC and TX-100, a * is the optimal micellar composition (where the free energy of micellization attains its minimum value), k is the Boltzmann constant, and T is the absolute temperature. In regular solution theory, P N ~ C - TisXempirical . ~ ~ (obtained from fitting of the cmc data), but in the molecular thermodynamic theory of Puvvada and Blankschtein26 the specific interaction term is predicted. It reflects the free energy contribution of the core (arising out of hydrophobic interaction) and the electrostatic contribution (arising out of electrostatic interaction between the charged hydrophilic moieties of the surfactants). To get ~ N ~ D C - T X - I O Ofor the estimation of YNDC and ~ T X - I Wthere , are other relations26that are to be solved which
NaDC and Triton X-100 at the Air/Water Interface
m
J. Phys. Chem., Vol. 99,No. 38, 1995 14037 5 . The enthalpy of micellization of TX-100 is practically zero; with increasing proportion of NaDC, the process becomes more and more endothermic with a fair degree of entropy increase. 6. The activity coefficients of the surfactants derived by the Puvvada and Blankschtein method are lower than those by the Rubingh method. In the mixed condition, Y N is considerably ~ lower than y~x-100.
I
0
E
Acknowledgment. The authors thank Prof. M. Chowdhury and Dr. K. Bhattacharya, Department of Physical Chemistry, IACS, for fluorescence measurement facilities.
E \
References and Notes
V
Clint, J. H.; J . Chem. Soc., Faraday Trans. I 1975, 76, 1327. Lange, H.; Beck, K. H. Kolloid. Z. 2. Polym. 1973, 251, 424. Rosen, M. J.; Hua, X. Y. J. Colloid Interface Sci. 1982, 86, 164. Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1982, 90, 212. (5) Moroi, Y.; Nishikido. N.; Matuua, R. J . Colloid Intetface Sci. 1975, 50, 344. (6) Moroi, Y.; Nishikido, N.; Saito, M. J. Colloid Interface Sci. 1975, 52, 356. (7) Ueno, M.; Obata, M.; Kimoto, Y. J. Jpn. Med. SOC.Bid. Interface 1982, 15, 45. (8) Lucassen-Rynders, E. H. J . Colloid Interface Sci. 1982, 85, 178. (9) Kawamura, H.; Manabe, M.; Saio, H.; Takahasi, H.; Tokunaga, S . Niihama Kogyo Koto Senmon Gakko Kiyo, Rikogaku-hen 1989, 25, 86. (10) Kellaway, I. W.; Marriot, C. Can. J. Pharm. Sci. 1977, 12, 70. (11) Kellaway, I. W.; Marriot, C. Can. J . Pharm. Sci. 1977, 12, 74. (12) Small, D. M. In The Bile Acids; Padmanabhan, P. N., Kritchevsky, D., Eds.; Plenum: New York, 1971; Vol. 1, p 249. (13) Carey, M. C. In The Liver: Biology and Pathobiology; Arias, M., Poper, H., Schachter, D., Shafritz, D. A., Eds.; Raren Press, New York, 1982; Chapter 27, p 429. (14) Igimi, H.; Carey, M. C. J. Lipid Res. 1981, 22, 254. (15) Barry, B. W.; Gray, G. M. T. J . Colloid Interface Sci. 1975, 52, 3 14. (16) Barry, B. W.; Gray, G . M. T. J . Colloid Interface Sci. 1975, 52, 327. (17) Hofmann, A. F.; Small, D. M. Annu. Rev. Med. 1967, 18, 333. Felmeister, A. J. Pharm. Sci. 1972, 61, 151. (18) Jana, P. K.; Moulik, S . P. J . Phys. Chem. 1991, 95, 9525. (19) Martin, S . V.; Mats, A. E. M.; Bahadur, P. Langmuir 1992,8,2396. (20) Green, F. A. J. Colloid Interface Sci. 1971, 35, 475. (21) Pal, S . ; Das, A. R.; Moulik, S. P. Ind. J . Bicohem. Biophys. 1982, 19, 295. (22) Ueno, M.; Kimoto, Y.; Ikeda, Y .; Momose, H.; Zana, R. J . Colloid Interface Sei. 1987, 117, 179. (23) Asano, H.; Aki, K.; Ueno, M. Colloid Polym. Sci. 1989, 267, 935. (24) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 339. (25) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948. (26) Sarmoria, C.; Puvvada, S . ; Blankschtein, D. Langmuir 1992, 8, 2690. Puvvada, S . ; Blankschtein, D. J . Phys. Chem. 1992, 96, 5567. Puvvada, S.; Blankschtein, D. J . Phys. Chem. 1992, 96, 5579. Puvvada, S.; Blankschtein, D. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, Dc. 1992; p 96. (27) Harkins, W. D.; Jordan, H. F. J . Am. Chem. SOC.1930, 52, 1751. (28) Kreshek, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (29) Biks, J.; Lamb, M.; Munro, I. Proc. R. Soc. London A 1964, 280, 289. (30) Henderson, C.; Selinger, B. J . Photochem. 1981, 16, 215. (31) Malliaris, A,; Le Moigne, J.; Sturm, J.; Zana, R. J . Phys. Chem. 1985, 89, 2709. (32) Tachiya, M. Chem. Phys. Lett. 197533.289. Tachiya, M. J . Chem. Phys. 1982, 76, 340. (33) Atik, S . S.; Nam, S . ; Singer, L. A. Chem. Phys. Lett. 1979, 67.75. (34) Infelta, P. P. Chem. Phys. Lett. 1979, 61, 88. Mukhejee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; NSRDS NBS36; National Bureau of Standards: Washington, DC, 1971. (35) Nagadome, S.; Miyoshi, H.; Sugihara, G.; Ikawa, Y . ; Igimi, H. Yukagaku 1990, 39, 18. (36) Birdi, K. S . Macro-Microemulsion Theory and Application; ACS Symposium Series 272; American Chemical Society: Washington, DC, 1983; p 67. (1) (2) (3) (4)
0
0.5 o(
1.o
Figure 5. Profiles of predicted, (- * -), ideal (- -), and experimental (-) cmcmlxas a function of NaDC mole fraction in aqueous solution at 296 K.
are not presented here. Following the procedure adopted by Puvvada and Blankschtein for ionic-nonionic combinations, we computed the parameters in eqs 11-13 for the present NaDC-TX-100 binary mixtures. The results are presented in the Table 5 . It is observed that the values of XR, XM, and a* are low compared to the corresponding stoichiometric mole fractions. The values of the mole fraction by the three methods are close up to a N a c = 0.25, while, in the range of higher mole fraction, XR and a* are more or less the same but different from XM. The theoretical treatments indicate that the micelles formed initially consist of fewer NaDC molecules. We also observed in the fluorescence studies that the initial micelles were found to be organized by higher mole fractions of TX-100. The Y N ~ D Cand ~ ~ x - 1values 00 were lower than those predicted by the regular solution theory of Rubingh. The cmcmix are compared with the Clint (ideal) and experimental values in Figure 5. At a N a c > 0.25, the deviation from the ideal behavior became significantly prominent and the molecular thermodynamic theory showed greater deviation than the measured values. It is to be noted that to arrive at the cmcmix, several relations have to be solved and appropriate constants of molecular dynamics are to be used. Imperfection of the parameters may be the reason for the deviations of the predicted cmc values from the observed results. Conclusions The following conclusions can be drawn from the results: 1. The surface tension and fluorescence derived cmc values are comparable; the conductometrically and calorimetrically determined cmcs are also comparable. The former set is lower than the latter. 2. The minimum areas of the mixed surfactants (TX-100 and NaDC) at the airniquid interface are lower than the pure components because of reduction of the repulsion interactions among the anionic species, NaDC. 3. The polarity of the interior of the mixed micelles varies with the composition; it decreases with increasing TX-100 in the mixture. 4. The micellar aggregation number also decreases with the increase of NaDC in the mixture.
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