J. Phys. Chem. 1994, 98, 10208-10215
10208
Structure and Interaction of Lithium Dodecyl Sulfate Micelles in the Presence of Li-Specific Macrocyclic Cage: A Study by SANS Y. C. Liu? P. Baglioni,' J. Teixeira,s and S. H. Chen*J Department of Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139, Department of Chemistry, University of Florence, 50121 Florence, Italy, Luboratoire Leon Brillouin, C. E. Saclay, 91I91 Gif-Sur-Yvette Cedex, France, and Department of Nuclear Engineering, MIT, Cambridge, Massachusetts 02139 Received: April 8, 1994@ We study by small-angle neutron scattering ( S A N S ) the interaction of macrocyclic cage CESTO (C17H37N5) with lithium dodecyl sulfate micelles (LDS) in solution. At pH = 12.7 the CESTO molecule in aqueous solution is neutral and can complex one Li+ ion, incorporating it into its cage. The result is the formation of a positively charged cage, and it is attracted by the negatively charged head groups of dodecyl sulfates in the micelle. We show that there is a strong tendency for the CESTO-Li+ complex to be incorporated into the outer layer of the micelle with a consequence of a drastic reduction of the effective charge of the micelle. Using a two-layer model for the micellar structure factor and a multicomponent ionic solution theory of Khan and Ronis for the intermicellar structure factor, we have satisfactorily fitted all the S A N S data at different surfactant concentrations and various molar ratios of CESTO to LDS. The extracted parameters include the micellar aggregation number, the effective micellar charge, and the fraction of CESTO incorporated into the outer layers of the micelle.
1. Introduction
C"3
During the past 20 years, the aggregational behaviors of various surfactant systems have been extensively studied using surface tensiometry, fluorescence, NMR, conductivity, and scattering techniques.' The surfactants, traditionally classified as ionic, nonionic, and zwitterionic amphiphiles, are known to form micelles in aqueous solution above cmc, namely, the critical micellar concentration. During the last decade, small angle neutron scattering ( S A N S ) has been used as a powerful technique to determine the micellar structures and the intermicellar correlations resulting from interactions between micellar aggregates.* Surfactants with special functions have been synthesized recently. Crown ethers, a class of macrocyclic compounds, for example, show a strong affinity and high selectivity toward alkali, alkaline earth, and transition metal ions.3 The macrocyclic compounds can thus function as complex agents applicable to varieties of processes, such as separation of ions and isotopes, transport across oil-water interfaces, liquid-liquid and liquid-solid phase transfer reactions, dissolution of apolar solvents, organic salts, and ion-selective electrodes, et^.^ The presence of a macrocyclic compound in a micellar solution can in principle alter the aggregational behaviors of the micelles by interaction with the hydrophilic outer layers of the micelles. In this paper we shall describe the use of SANS as an effective tool to study the structure and interaction of micelles formed by an anionic surfactant, lithium dodecyl sulfate (LDS), in aqueous solution in the presence of a macrocyclic crown ether called by us CESTO. A preliminary result of this work has been presented in a brief note.5 Crown ether 5,12,17-trimethyl- 1,5,9,12,17-pentaazabicyclo[7.5.5]nonadecane (CESTO) is synthesized as a specific complex agent for Li' ions. Its chemical structure is illustrated in Figure Department of Materials Science and Engineering, MIT.
* University of Florence. 5 @
Laboratoire Leon Brillouin. Department of Nuclear Engineering, MIT. Abstract published in Advance ACS Absrracts, September 1, 1994.
I
CHf
Figure 1. Cage structure of the CESTO molecule. Note the radius of the semisphere is 5.5 A, large enough to accommodate the Li+ ion.
1. This crown ether is called CESTO (Italian word for basket) because its molecular shape resembles a semispherical basket of radius 5.5 A. This macrocyclic ligand at high basicity can be protonated in aqueous solution. It can capture small ions (H+, Li+, Cu2+, Co2+, and Zn*+) with a high degree of selectivity.6 Preliminary results7 have shown that, in a micellar solution of lithium dodecyl sulfate, the effective micellar charge and the ability to incorporate the free lithium ions in the hydrophilic layer can be controlled in spite of the steric hindrance of the CESTO-Li+ complex. One can use the pH value of the solution to control this effect. At pH > 12 the CESTO molecules are neutral and complex Li+ ions selectively from the anionic surfactants. The counterion distribution in the vicinity of a micelle and in the hydrophilic layer of the micelle is thus profoundly altered due to the complexation process.
2. Experiments The CESTO macrocyclic cage was synthesized as previously reported.8 Lithium dodecyl sulfate (LDS) was purchased from Kodak, recrystallized three times from ethanol, washed with ethyl ether, and dried at 45 O C under moderate vacuum. Solutions were prepared as follows. Stock micellar solutions of LDS were prepared in 99.99% D20. A solution of CESTO was prepared in D20, and the pH was adjusted to 12.7 by using NaOH. At this pH CESTO is neutral and complexes selectively
0022-365419412098-10208$04.50/0 0 1994 American Chemical Society
Lithium Dodecyl Sulfate Micelles
J. Phys. Chem., Vol. 98, No. 40, 1994 10209
Figure 2. Model for the micellar structure. The inner core contains hydrophobic tails of LDS, and the outer layer contains the hydrophilic head of the molecules.
lithium counterions,6 even in the presence of a high concentration of Na+. These solutions were used to produce micellar solutions of 1, 4, and 8% weight LDS concentrations and [CESTO]/[LDS] mole ratios of 0, 0.5, 1, and 1.5. All the solutions were stored in a nitrogen or argon atmosphere to avoid pH change. S A N S measurements were performed at Laboratoire Leon Brillouin, Saclay, France, using a PAXE spectrometer in an OPHEE reactor. Neutrons with an average wavelength A = 6.5 A and a wavelength spread AA/A =‘ 10% were used. The sample-to-detector distance was fixed at 2.04 m, covering the range of the magnitude of scattering vector Q from 0.02 to 0.28 kl. Samples were contained in flat quartz cells with a path length of 1 mm. All measurements were made at a room temperature of 25 “C. The two-dimensional intensity distributions were corrected for the background and the empty cell contributions and then normalized to absolute intensities by dividing them with a scattering intensity of a secondary standard of known cross section. By integrating the normalized 2-D intensity distributions with respect to the azimuthal angle, 1-D scattering intensity distributions Z(Q) in the unit of a differential cross section per unit volume (cm-l) were obtained. The absolute intensities scale determined this way is reliable to within 20%, although the relative intensities among a set of measurements done at the same condition are consistent to within 5%. At MlA = lo%, the correction due to the finite Q resolution in the peak region of the intensity distribution can be safely neglected. SANS data in an absolute scale were analyzed quantitatively with a two-shell micellar model for the particle structure factor P(Q) together with an analytical solution of a multicomponent ionic liquid in a mean spherical approximation (MMSA) for the interparticle structure factor S(Q) of the charged micelles in solution. In fitting data with the theory, we use an overall amplitude factor to account for the calibration factor determined by the secondary standard. This factor can fluctuate up to 25% from unity for different instrumental settings, but at a given instrumental setting it should remain constant to within 5%. In this sense all the fittings we present in this paper are in an absolute scale, which places a great deal of constraint on the applicability of the theory.
3. Modeling of the Micelles The micellar solution is assumed to be composed of a small amount of monomeric surfactants with concentration equal to cmc and uniform-$zed spheroidal micelles with a mean aggregation number N and an effective chsge Z . The fractional ionization is therefore denoted by a = WN. The micelles have a hydrophobic core composed of close-packed hydrocarbon tails of the dodecyl sulfate and a hydrated hydrophilic shell composed of head groups (SO4-), some fraction of counterions (Li+), the complexed ligands (CESTO+Li+), and the solvent molecules (D20). We assume that the hydrophobic core is of spheroidal shape with principal axes a,b,b and the hydrophilic layer has a thickness d. The scattering contribution from the counterions in the vicinity of the micelle is orders of magnitude weaker than that from the macroions for neutron scattering. Consequently, the scattering from the species other than the macroions is treated as a flat background added to the incoherent scattering from all the hydrogen atoms in the solution. The schematic composition of a micelle is shown in Figure 2. Given the geometry of the micelles, the total scattering intensity Z(Q) can be written as9
I = C & x b i - Vme,>2&Q>&Q)+ &kgd
(1)
where fi is the aggregation number and CM = C - cmc, with C the concentration of LDS. P(Q) is the orientationally averaged normalized form factor of a micelle, and s ( Q ) is the orientationally averaged center-center structure factor between micelles. We define the orientation dependent form factor F(Q,p) where p is the direction cosine between the direction of the symmetry axis of the spheroid and the Q vector:
+ (1 - p )b ] v = Q [ ~ ’ ( u+ d)2 + (1 - p2)(b+ d)’I1” u = Q[p2a2
2
2 112
10210 J. Phys. Chem., Vol. 98, No. 40, 1994 &Q) and
Liu et al.
s(Q)are then calculated aslo
to observe the counterion scattering directly and compare it with the analytical solution. In this work we only report the effect of reduction of the fractional ionization due to complexation of CESTO onto the micellar surface.
4. Multicomponent Mean Spherical Approximation and Partial Structure Factors where Sm(Q) is the macroion-macroion structure factor calculated by the MMSA. The dry volumes of LDS and CESTO are VLDS= 410 A3 and VCESTO = 385 A3. The monomer volume is defined as V , = VLDS-I- NCVCESTO,where Nc is the number of CESTO associated with each LDS molecule. The scattering density of the solvent esis given by the scattering length of D20 divided by the volume of a water molecule, 30.27 A3. The total scattering length Cbi is the sum of the scattering lengths of all atoms in the monomer including the atoms of the associated CESTO molecules. The tail volume Vt and the short principal axis length b are given by empirical relations Vt = (27.4 26.9)n A3 and b = (1.50 1.265)n A, where n is the number of the hydrocarbons inside the core." The long principal axis is determined by equating the volume of the inner core Mtto the volume of the ellipsoid 4z/3b2a. The hydrocarbon number n is normally 12 for a pure LDS micelle. However, n is reduced upon addition of CESTO, especially at high ratios. This means that the first couple of hydrocarbons of dodecyl sulfate may be exposed to the solvent because of the complexation of bulky CESTO into the outer layer. The scattering length density of the hydrophobic core el is equal to the total scattering length of the hydrocarbon chain divided by the volume of the core. The scattering density of the hydrophilic outer layer, i.e. the shell, can be written as
+
+
e2 = (bl
+ b2 + b3 + b4 + bS)/V&,l
+
(5)
+
where vsheu = 4 ~ / 3 [ ( a d)(b d)2 - ab2] denotes the volume of the outer layer. The five scattering lengths correspond to the LDS head group, bl = Nbm; the counterions remaining in the shell, b2 = N (1 - a)ki+; CESTO associated with the LDS, b3 = NNcbCest,;the exposed hydrocarbon, b4 = (12 - n)bcaz; and the solvent molecules, b5 = fiNsbsolvent, respectively. The hydration number Ns is determined by
N, =
In this LDS-CESTO system, the scattering lengths of the head group, CESTO, Li+, and the solvent D2O are evaluated as 2.4165 x IOp4, 2.389 x -1.90 x and 1.9153 x 10-4 A, respectively. The fractional ionization a = ZJRis a function of concentration, additional salts, pH value, etc., generally around 0.2 for LDS micellar solution. This means the number of free counterions Li+ surrounding each macroion is 2, while the remaining fi - 2 counterions are inside the outer layer. The distribution of the free counterions around the macroion can be described by the macroion-counterion correlation function, which is the Fourier transform of the macroion-counterion structure factor. Traditionally, the counterion distribution is calculated by numerical methods, such as the solution of the Poisson-Boltzmann integration.'* We can show that the counterion distribution can be analytically solved from the macroion-macroion structure factor, although the scattering contribution from the counterion part is invisible to SANS. In a future experiment small-angle X-ray scattering will be used
4A. Introduction. Consider a polyelectrolyte system composed of macroions with charge ZM, their counterions with charge Zc, and salt ions. In the primitive model,I3 the solvent is regarded as a dielectric medium with a permitivity E . The dominant interactions in the system are the excluded volume and electrostatic interactions, while the van der Waals interaction is neglected. The ratio of the macroion charge to the counterion charge and the ratio of the macroion size to the counterion size are usually as large as 20-100 in a typical micellar solution. The large ratios imply significant asymmetry both in spatial dimensions and in charges between the macroions and counterions. Historically, the problem described above was approached by solving coupled integral equations in the HNC (hypemetted-chain) appr~ximation'~ or in the Rodger and Young (RY) approximation.l5 However, cumbersome numerical computations often diverge at large asymmetry of charges and sizes and are not suitable for analysis of small-angle neutron or X-ray scattering data. It has been known that an analytical solution exists in the so-called mean spherical approximation under the assumption of point-like counterions and salt ions. We call this a multicomponent mean spherical approximation (MMSA), which is a linear description of interactions. The difficulties arising from nonlinearity due to the presence of highly charged macroions can be avoided by a rescaling procedure together with a nonadditivity of macroion-counterion diameter. The MMSA leads to an analytical solution of the effective macroionmacroion direct correlation function and thus its corresponding structure factor. The macroion-macroion structure factor is useful in fitting S A N S data of micellar solutions using the effective macroion charge as an empirical parameter. Knowing an accurate macroion-macroion structure factor from S A N S data, one can then use exact relations provided by the theory to calculate other correlation functions such as the macroioncounterion and couterion-counterion correlation functions. The well-known one-component macroion (OCM) theory of Hayter and Penfold16 and the modification of it, known as the generalized one-component macroion theory (GOCM),l7 have been developed to model the macroion-macroion interactions in solution and used successfully to fit the scattering data. However, these two theories cannot give correlation functions between other ionic species in the solution. On the other hand, the MMSA as formulated by Khan and Ronisl8 gives not only the effective one-component correlation function but also the correlation functions between the other species under the condition of nonadditivity. 4B. MMSA and Rescaled MMSA Theory. MMSA starts from the system of coupled Onstern-Zemike (OZ) equations: (7) with closure relations
+
gij(r)= hij(r) 1 = 0 for r
-= oij
(8)
where q is the diameter for i, j species. For additive diameter
Lithium Dodecyl Sulfate Micelles
J. Phys. Chem., Vol. 98, No. 40, 1994 10211
+
alJ = uAU, with a definition aAy= (ai 4 1 2 . For nonadditive . is the Bjerrum length of the solvent diameter, uij f a A ~LB defined as e2kkBT, where E is the dielectric constant of the solvent. The normalized partial structure factors are defined as
where @T is the total number density of ions, xi is the fraction of ith species, and 6 i j is the Kronecker delta. The rescaled diameter for a one-component theory (OCM) is determined in the following way: OCM requires that g(r) = 0 when r < u. But unrescaled MSA theory sometimes results in g(r) < 0 before r reaches a value a. In this case one picks a slightly larger diameter a m such that g ( a m ) = 0 and beyond which g(r) > 0. The effective diameter of macroions is therefore a m (Gillan’s condition).lg This is often called a rescaled MSA (RMSA).20 4C. Reduction of a Multicomponent System to an Effective One-Component System. The multicomponent polyelectrolyte system that we consider contains macroions with density @M and charge ZM,their original counterions’ el and Z1, and added salt ions’ ei and Zi ( i = 2...1). By diagonalization of a 1 x 1 matrix E(Q), the multicomponent system can be reduced to a three-component system of macroions, counterions, and neutral ions. The densities and charges of the point-like counterions and neutral particles are given as
aL
I 0.05
b
0.1
aA-7
0.15
0.2
I
’b
I i= 1
2, = -
e1
4 !5
@12212
QIA-’l Figure 3. (a) Scattering intensity Z(Q) for 1 wt % LDS at pH = 12.7. The circles are data points, and the solid line and dashed line are the fitted curves using OCM and MMSA, respectively. It is reasonable to conclude the two theories are both capable of fitting the S A N S data but with different effective charges, being higher for the latter. (b) Normalized particle structure factors and interparticle structure factors extracted from the fit to the data in Figure 3a.
e, = i= 1
I
en = &i
- Qc
i= 1
The three-component (M, c, n) system can be further reduced to a two-component (M, c) system under the condition of nonadditivity. The two-component system is finally reduced to an effective one-component system with a Yukawa closure.21
cm(r) = Ae-K(r-a’lrfor r > a,
(13)
where K = [4dB@&2]1’2is the inverse Debye screening length. Defining X = do,,, RM, = OMC/OMM,and k = K Q m , the above correlation function can be rewritten as exp[-k(x-
Cm(X)
= -Q
l)] forx > 1
X
where the dimensionless potential
(14)
B is given as
and
C = exp(-k)[sinh(kR,,)
D = k exp(-kR,,)(
- kR,,
1
cosh(kR,,)]
+ kR,,)
(16)
TABLE 1: Fitting Results of 1 wt % LDS by OCM and MMSA parameters OCM h4MSA aggregation number 88 89 effective charge 12 16 shell thickness (A) 5.5 5.5 short axis length (A) 16.8 16.7 amplitude 1.17 1.17 background 0.14 0.13
v = 24?7MMJm
d w exp[-k(x ~ - 1)lgm(x)
~ M is M the volume fraction of the one-component system. The dimensionless potential Q bears similarity to the DLVO potential22 under certain conditions. Stell showed that MSA with a Yukawa closure has an analytical solution.23 By solving a quartic equation and selecting the physical root, the only unknown parameter, v, can be determined.24 The macroion structure factor Sm(Q) can be calculated using a revised version of Hayter-Penfold’s FORTRAN packageI6 developed by us and used to fit SANS data. In Figure 3a we show the fitted curves for a 1% LDS solution with the structure factor calculated from OCM and from MMSA. The quality of the fits is equally good for both models. The normalized particle structure factor P(Q) and interparticle structure factor S(Q) fitted with the OCM and MMSA procedures are shown in Figure 3b. The particle
Liu et al.
10212 J. Phys. Chem., Vol. 98, No. 40, 1994 1%
[CESTO]/[LDS]=OS
2.5
1
0.5
"0
0.05
0.1
0.15
0.2
0.25
aA-'1 1%
0.05
QIA-ll
[CESTOY[LDSl=l .O
0:l
0.15
1%
0.h5
012
0.05
pH=12
0.2
0.15
0:1
0.;5
QWI
Q[A-']
b
[CESTO]/[LDS]=1.5
LDS1 %
1%
i -2.1
1
.
[CESTO]/[LDS]=OS 2
1
1
0.2. '0
0.05
1%
0:l
0.15
0.2
[CESTO]/[LDS]=l.O
1.2.
1 % [CESTOJ/[LDS]=lS - 12 . 1
QW'I Figure 4. (a) Scattering intensities Z(Q) for LDS = 1% at four [CESTO]/[LDS] ratios, 0, 0.5, 1.0, and 1.5, respectively. Symbols are the data, and solid lines are theoretical results with MMSA. The extracted parameters are listed in Table 2. (b) Normalized particle structure factors and interparticle structure factors extracted from the fit to the data in Figure 4a. It should be noted that as CESTO to LDS increases, the interactions between micelles decrease markedly, as shown by the interparticle structure factors, approaching unity at low Q.
structure factors &Q) extracted are nearly identical from both procedures. The structure factor S(Q) obtained from these two fittings are also quite close to each other, except the effective charge obtained by MMSA is considerably higher than from OCM, as can be seen from Table 1. We have previously shown that the effective charges obtained by OCM and by GOCM at this concentration are nearly identical."
5. Data Analysis and Discussion S A N S data for three different LDS concentrations, 1%, 4%,
and 8% in D20, each at four different molar ratios of [CESTO]/ [LDS], namely, 0, 0.5, 1.0, and 1.5, have been analyzed using a statistically weighted least squares fitting procedure. A FORTRAN code was developed to calculate I(Q) (eq 1) and compare it with the experimental intensity distribution in an absolute scale, by using five fitting parameters. The five parameters are the aggregation number (N,the effective charge (Z), the number of CESTO molecules adsorbed on the LDS micellar surface per head group (PIc), the number of hydrocarbons inside the micellar core &), and the shell thickness (4.
J. Phys. Chem., Vol. 98, No. 40, 1994 10213
Lithium Dodecyl Sulfate Micelles
a
pH=12 LDS4%
4% [CESTO]/(LDS]=O.5
- 41
1
4
4
2
2
0'
0.05
0.1
0.15
0.2
0.25
0'
4
0.05
~[A-li
0.1
7
0.15
0.25
0.2
PIA-'] 4%
4% [CESTOY[LDS]=l.O
[CESTO]/[LDS]=1.5
l(Q)Icm-'l
0'
0.05
011
0.15
0.2
0.25
QLA-'l
b
pH=12
LDS4%
4% [CESTO]/[LDS]:O.5
1
.
2
t
i
4 % [CESTOJ/[LDS]=1.5
4% [CESTO]/[LDS]=l .O
i
1* 2 l
"0
0.05
0.1
0.15
0.2
Q[A-'l Figure 5. (a) Scattering intensities Z(Q) for LDS = 4% at four [CESTO]/[LDS] ratios, 0, 0.5, 1.0, and 1.5, respectively. Symbols are the same as in Figure 4a. The extracted parameters are listed in Table 3. (b) Normalized particle structure factors and interparticle structure factors extracted from the fit to the data in Figure 5a. See caption for Figure 4b.
These fitting parameters are allowed to vary within reasonable ranges to get the minimum x2. The material parameters, including the volumes of the LDS, CESTO, and water molecules and the cmc of LDS (1.32 mh4 for pH = 12.7), are previously known and used as fixed constants. All other parameters, such as the number density of the micelles, the volume fraction of the micellar aggregates, the fractional ionization, the average diameter and axial ratio of the ellipsoidal micelle, the hydration number, the Debye screening length, and the potential of the interaction between micelles, are determined by the internal relationships (volume conservation constraint, etc.) between the fitting parameters and the known materials parameters. The
12 original S A N S Z(Q) data and their corresponding fitted curves along with extracted P(Q) and S(Q) are shown in Figures 4, 5, and 6, in the order of LDS concentration of 1%, 4%, and 8%, respectively. The characteristic parameters are tabulated in Tables 2-4. Three dominating parameters geed to be discussed in detail. Firstly, the aggregation number N increases significantly upon addition of CESTO to LDS @cellar solution. However, except for the 1% dilute solution, N is not monotonically increasing with the [CESTO]/[LDS] ratio, but reaches a maximum value near the molar ratio 0.5. Further experiments are suggested to find the molar ratio corresponding to the maximum aggregation.
Liu et al.
10214 J. Phys. Chem., Vol. 98, No. 40, 1994 a
LDS 8% (CESTO]/[LDS]=0.5
LDS 8% 151
5
‘0
0.05
0.1
0.15
0.2
0.25
LDS 8% [CESTOY(LDS]=1.5
1
5
7
QfA-7
b
LDS 8%
LDS 8% [CESTO)/[LDS]=O.B
LDS 8% [CESTOY[LDS]=lS
LDS 8% [CESTO!/[LDS]=l.O 1.4 1.2
1.21
1
SlOI
0.05
Oil
. 0.15
0.2
n r X-11
Kln 1
Figure 6. (a) Scattering intensities I(Q) for LDS = 8% at four [CESTO]/[LDS] ratios, 0, 0.5, 1.0, and 1.5, respectively. See caption for Figure 4a. The extracted parameters are listed in Table 4. (b) Normalized particle structure factors and interparticle structure factors extracted from the fit to the data in Figure 6a. See caption for Figure 4b.
The enhanced aggregation results in a more elongated ellipsoid. Secondly, the effect charge Z of micelles decreases monotonically with increasing [CESTO]/[LDS] ratio. It is clear that the complexation of CESTO onto the micellar surface reduces the ionic interaction. As a result, the cause for stabilization of the surfactant system has changed from the electrostatic repulsion to the steric repulsion by the CESTO molecules on the micellar surface or a combination of these two effects. Thirdly, the complexation ratios are more or less constants at a fixed [CESTO]/[LDS]ratio, regardless of the surfactant concentration. Furthermore, the trend for the binding ratios indicates a
saturation of this particular complex agent with LDS. The saturation binding ratio is estimated to be around 0.6 CESTO molecules per LDS molecule at room temperature and pH value of 12.7. Several other important effects should be mentioned. The hydration number decreases as the [CESTO]/[LDS] ratio increases. This dehydration effect of the hydrophilic layer of the micelle is caused by the incorporation of excess CESTO molecules since the outer layer of the CESTO molecule is hydrophobic. This is consistent with the observation of the enhanced aggregation and enlarged axial ratio of the ellipsoid,
J. Phys. Chem., Vol. 98, No. 40, 1994 10215
Lithium Dodecyl Sulfate Micelles
TABLE 2: Fitted and Deduced Parameters of LDS = 1% in the Presence of CESTO [CESTO]/[LDS] aggregation number ionization carbon in core shell thickness (A) asso. [CESTO]/[LDS] hydration number axial ratio of ellipsoid averaged diameter (A) background amplitude
0
0.5
1.o
1.5
89 0.17 12 5.5 0 12 1.4 50.3 0.13 1.17
93 0.15 12 6.7 0.48 10 1.5 53.4 0.16 1.25
95 0.07 11.7 6.8 0.54 9.0 1.6 53.2 0.18 1.24
97 -0 11.9 7.0 0.54 8.6 1.7 53.6 0.18 1.23
TABLE 3: Fitted and Deduced Parameters of LDS = 4% in the Presence of CESTO [CESTO]/[LDS] aggregation number ionization carbon in core shell thickness (A) asso. [CESTO]/[LDS] hydration number axial ratio of ellipsoid averaged diameter (A) background amplitude
0
0.5
1.o
1.5
97 0.15 12 5.5 0 11 1.6 51.4 0.13 1.18
183 0.10 10 6.6 0.48 5.1 3.4 62.8 0.22 1.28
156 -0 9.3 6.8 0.54 4.4 3.3 59.6 0.27 1.22
151 -0 8 7.1 0.55 3.8 3.9 58.6 0.27 1.21
TABLE 4: Fitted and Deduced Parameters of LDS = 8% in the Presence of CESTO
Acknowledgment. We are grateful to Laboratoire Leon Brillouin, C. E. Saclay, for providing neutron beam time and the PAXE spectrometer for this work. This research is supported by U.S. DOE Grant DEFG02-90-ER4.5429. Y.C.L. acknowledges the financial support from Texaco Research Center during the period of this research. P.B. acknowledges the Italian CNR and HURST for financial support. References and Notes
[CESTO]/[LDS] aggregation number ionization carbon in core shell thickness (A) asso. [CESTO]/[LDS] hydration number axial ratio of ellipsoid averaged diameter (A) background amplitude
molecules in the outer layers. The intermicellar correlations are calculated according to a multicomponent primitive model in a mean spherical approximation with nonadditive diameters. It is found that the CESTO-Li+ complexes interact strongly with the micelles by adhering to the hydrophilic layers of the micelles. As more CESTO is added to the solution, the aggregation number of micelles increases and the micelles become more elongated. The effective charge of the micelle is markedly reduced (nearly 0 for 1:1 molar ratio of CESTO to LDS). The micellar system is stabilized more sterically rather than electrostatically as the molar ratio of CESTO to LDS increases. There is a saturation binding ratio to CESTO to LDS for this system. Quantitative information on the incorporation of CESTO and Li+ ions, either complexed or uncomplexed, to the surface of micelles and the resultant aggregational behavior of the micelles is obtained for the fiist time by a careful analysis of smallangle neutron scattering data. The fundamental parameters so obtained can be compared with the results obtained from other methods, such as NMR, conductivity, surface tension, and ESR, in a separate or a combined way.’
0
0.5
1.o
1.5
105 0.21 12 5.5 0 11 1.7 52.5 0.13 1.17
164 0.10 10 6.9 0.47 6.6 3.1 61.3 0.29 1.24
143 -0 8.1 7.2 0.54 4.6 3.6 58.0 0.36 1.22
130 -0 6.7 7.2 0.55 2.5 4.4 55.2 0.38 1.20
Another notable feature is the exposure of the hydrocarbon chains to the solvent due to the presence of the complexes. In pure surfactant micellar solutions, it is usually assumed that all 12 hydrocarbons of the dodecyl sulfate are inside the hydrophobic core, with only the first hydrocarbon exposed partially to the solvent. This picture certainly breaks down when some bulky complexes are added to the outer layer. The fitting result shows that the numbers of exposed hydrocarbon units to water depend strongly on the [CESTO]/[LDS] ratio. Taking the 8% concentration for example, at the [CESTO]/[LDS] ratio of 0, 0.5, and 1.0,roughly zero, two, and four, respectively, hydrocarbon units attached to the head group are fully exposed to the solvent.
6. Conclusion We have studied the interaction of CESTO-Li+ complexes with LDS micelles in aqueous solution. The micelles are modeled as two-layered ellipsoids, incorporating counterions, CESTO-Li+ complexes, and the associated hydrated water
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