Size Change of the Wormlike Micelles of Pentaoxyethylene

Mar 27, 2008 - C12E7 were characterized by static light scattering (SLS) and dynamic light ... c along with the cross-sectional diameter d from the SL...
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J. Phys. Chem. B 2008, 112, 4648-4655

Size Change of the Wormlike Micelles of Pentaoxyethylene, Hexaoxyethylene, and Heptaoxyethylene Dodecyl Ethers with Uptake of n-Dodecane Maiko Miyake, Ayako Asano, and Yoshiyuki Einaga* Department of Chemistry, Nara Women’s UniVersity, Nara 630-8506, Japan ReceiVed: NoVember 28, 2007; In Final Form: February 6, 2008

Wormlike micelles of the surfactant penta-, hexa-, and heptaoxyethylene dodecyl ethers C12E5, C12E6, and C12E7 were characterized by static light scattering (SLS) and dynamic light scattering (DLS) experiments to examine effects of uptake of n-dodecane on the micellar characteristics. The SLS results have been successfully analyzed by the light scattering theory for micelle solutions to yield the molar mass Mw(c) as a function of concentration c along with the cross-sectional diameter d of the micelle. The apparent hydrodynamic radius RH,app(c) determined by DLS as a function of c has also been successfully analyzed by the fuzzy cylinder theory which takes into account the hydrodynamic and direct collision interactions among micelles, providing us with the values of the stiffness parameter λ-1. It has been found that the micellar length Lw increases with increasing surfactant mass concentration c and the values of d and λ-1 increase with increasing n-dodecane content wd, as in the case of various CiEj micelles containing n-alcohol. On the other hand, the values of Mw, Lw, and RH,app for all the micelles examined decrease with increasing wd contrary to the micelles containing n-alcohol. This finding may be attributed to the fact that the addition of n-dodecane into the micelles weakens hydrophilic interactions among polyoxyethylene chains of the surfactant molecules and water, making the micelles unstable, and then leading them to collapse into smaller micelles.

Introduction For the last several years, we have investigated wormlike micelles of nonionic surfactant polyoxyethylene alkyl ethers H(CH2)i(OCH2CH2)jOH (CiEj) by static light scattering (SLS), dynamic light scattering (DLS), and viscometry.1-14 In the work, we were able to determine the concentration-dependent characteristics of the micelles by separating contributions of the intermicellar thermodynamic and hydrodynamic interactions to the SLS and DLS results with the aid of the corresponding theories. We have determined the weight-average molar mass Mw of the micelles as a function of surfactant mass concentration c along with the cross-sectional diameter d from the SLS data by using a molecular thermodynamic theory15,16 formulated with the wormlike spherocylinder model. It has then found that the molar mass Mw dependence of mean-square radius of gyration 〈S2〉, hydrodynamic radius RH, and intrinsic viscosity [η] for the micelles of pure CiEj with various i and j1-7 and their binary mixtures8,9 is quantitatively represented by the chain statistical17 and hydrodynamic theories18-21 based on the wormlike chain and spherocylinder models, respectively. The analyses have yielded the values of the stiffness parameter λ-1 for the micelles. The studies have been extended to the CiEj micelles containing n-dodecanol or n-octanol in order to explore effects of uptake of n-alcohol into the micelles on the micellar characteristics.10-14 The SLS and DLS results were successfully analyzed in a similar fashion to the micelle solutions of single CiEj and their binary mixtures. In particular, it has been demonstrated that the fuzzy cylinder theory22-25 is favorably applied to analyze the apparent hydrodynamic radius RH,app, which is directly obtained from DLS experiment, as a function of the micelle concentration, thereby yielding the concentration-dependent micellar growth * Corresponding author. E-mail: [email protected]. Fax: +81742-20-3400.

by separating contributions of the enhancement of hydrodynamic interactions among micelles with increasing concentration. It has been found that the values of the micellar length L, d, and λ-1 become larger as the n-dodecanol or n-octanol content in the micelles increases. A number of studies have been made on the C12E5 micelles containing an oil such as n-octane, n-decane, and n-dodecane,26-34 and it has been found that the surfactant with the oil selfassemble in variety of structures depending on surfactant concentration, oil content, and temperature. The C12E5 + oil micelles assume polymer-like or wormlike structure at low concentrations c in the L1 phase in the range of small oil content and then grow in length with increasing c and the entanglement network is formed in the solution at sufficiently high concentrations. Menge et al.26-28 have shown for the n-decane + C12E5 + water system by SLS, DLS, and small angle neutron scattering (SANS) measurements that the apparent molar mass Mapp of the wormlike micelles formed in the L1 phase increases with c at the lower range of c, passing through a maximum, and then decreases with increasing c at higher c. They have also found that the apparent hydrodynamic radius RH,app as a function of c exhibits a similar behavior to Mapp. They, however, treat only the apparent quantities Mapp and RH,app, which include contributions from intermicellar thermodynamic or hydrodynamic interactions and have not evaluated Mw(c) and RH for the micelles in an isolatedstate. In this work, we have studied the micelles in the C12E5 + n-dodecane + water, C12E6 + n-dodecane + water, and C12E7 + n-dodecane + water systems by SLS and DLS measurements. The main aim is to investigate effects of uptake of n-alkane on the variation of the micellar characteristics such as the micellar length, cross-sectional diameter, and stiffness in comparison with the case of uptake of n-alcohol. We follow the technique mentioned above to characterize isolated micelles at finite c by

10.1021/jp7110742 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/27/2008

The Effect of Uptake of n-Dodecane on Micellar Characteristics

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separate evaluation of the thermodynamic and hydrodynamic interactions among micelles. In the above three systems, our previous experimental results10 for the C12E6 + n-dodecane micelles are re-analyzed according to the present scheme in order to explore the dependence of the hydrophilic chain length j of the CiEj molecule.

For the system C12E5 + n-dodecane + water at 10.0 °C e T e 25.0 °C (∂n/∂c)T,p ) 0.134 - 3.43 × 10-4(T - 273.15) (wd ) 0.0501)

(2)

(∂n/∂c)T,p ) 0.137 - 4.07 × 10-4(T - 273.15) (wd ) 0.0991)

(3)

Experimental Section

(∂n/∂c)T,p ) 0.136 - 3.68 × 10-4(T - 273.15) (wd ) 0.150)

(4)

Materials. The surfactant C12E5 and C12E7 samples and n-dodecane were purchased from Nikko Chemicals Co., Ltd. and Nakaraitesque Co., respectively. These materials were used without further purification. The solvent, water, used was high purity (ultrapure) water prepared with Simpli Lab water purification system of Millipore Co. Phase Diagram. Cloud-point temperature of a given micelle solution was determined as the temperature at which the intensity of the laser light transmitted through the solution abruptly decreased when temperature was gradually raised. The emulsification failure boundary was determined by visual observation. The results may be somewhat less precise since the phase transition is often difficult to see. C12E5 and C12E7 micelle solutions were prepared by dissolving them in water and adding appropriate amount of n-dodecane with a microliter syringe (Hamilton). Complete mixing and micelle formation were achieved by stirring the solutions using a magnetic stirrer for at least 1 day. The weight fractions w of micelle solutions were determined gravimetrically and converted to mass concentrations c by the densities F of the solutions given below. Throughout this paper, w and c denote the weight fraction and mass concentration of the micelles containing n-dodecane in their aqueous solutions. n-Dodecane content in the micelle is represented by its weight fraction wd. Static Light Scattering. The scattering intensities were measured for micelle solutions of C12E5 + n-dodecane with varying wd at 15.0 °C, and for those of C12E7 + n-dodecane with varying wd at 40.0 °C. The ratio Kc/∆Rθ was obtained for each solution as a function of the scattering angle θ ranging from 30 to 150° and was extrapolated to zero scattering angle to evaluate Kc/∆R0. Here, c is the mass concentration of surfactant + n-dodecane, ∆Rθ is the excess Rayleigh ratio, and K is the optical constant defined as

For the system C12E7 + n-dodcane + water at 30.0 °C e T e 40.0 °C

K)

4π2n2(∂n/∂c)T,p2 NAλ04

(1)

with NA being the Avogadro’s number, λ0 the wavelength of the incident light in vacuum, n the refractive index of the solution, (∂n/∂c)T,p the refractive index increment, T the absolute temperature, and p the pressure. The plot of Kc/∆Rθ vs sin2(θ/ 2) affords a good horizontal straight line for all the micelle solutions studied. The apparatus used is an ALV DLS/SLS-5000/E light scattering photogoniometer and correlator system with vertically polarized incident light of 632.8 nm wavelength from a Uniphase Model 1145P He-Ne gas laser. The micellar solutions were prepared in the same way as those for the cloud-point measurements described above. The experimental procedure is the same as described before.1-6,8,9,11-14 In the present study, we have treated the micelle solutions as the binary system which consists of micelles containing ndodecane as a solute and water as a solvent. The results for the refractive index increment (∂n/∂c)T,p measured at 632.8 nm with a Union Giken R601 differential refractometer are summarized as (in cm3/g):

(∂n/∂c)T,p ) 0.1337 - 2.088 × 10-4(T - 273.15) (wd ) 0.0502) (5) (∂n/∂c)T,p ) 0.1291 - 1.150 × 10-4(T - 273.15) (wd ) 0.0751) (6) (∂n/∂c)T,p ) 0.1496 - 5.155 × 10-4(T - 273.15) (wd ) 0.0993) (7)

Dynamic Light Scattering. DLS measurements were carried out to determine the translational diffusion coefficient D for the micelles by the use of the same apparatus and light source as used in the SLS studies described above. All the test solutions studied are the same as those used in the SLS studies. From the D values obtained by the cumulant method for the normalized autocorrelation function g(2)(t), the apparent hydrodynamic radius RH,app has been evaluated by the equation11,35-37 RH,app )

( )

(1 - Vc)2MwkBT Kc 6πη0D ∆R0

(8)

where V is the partial specific volume of the solute (micelle), kB is the Boltzmann constant, and η0 is the solvent viscosity. Some comments on the factor (1 - Vc)2 in eq 8 may be in order. When the friction coefficient ζ between micelles and solvent defined in the solvent-fixed frame is used, the diffusion coefficient D in the laboratory-fixed frame (which is relevant to DLS measurements) is related to the concentration gradient (∂µ0/∂c)T,p of the chemical potential µ0 of the solvent by the equation including the factor (1 - Vc) as explicitly given by Berne and Pecora.35 Then, conversion of (∂µ0/∂c)T,p to the osmotic compressibility (∂π/∂c)T,µ0, which is proportional to Kc/ ∆R0, arises another factor (1 - Vc) as shown by Stepa´nek et al.37 The manipulation of the equations, thus, finally results in the factor (1 - Vc)2 in the expression of D and then RH,app as given by eq 8. The friction coefficient ζ in this formulation is pertinent to interpret the observed results on the basis of molecular theories, since in most cases ζ is theoretically calculated in the solvent-fixed frame. It should be, however, emphasized that eq 8 is a defining equation for the apparent hydrodynamic radius RH,app and that other expressions of D including the first power of (1 - Vc) may be derived when different definition of ζ is employed. We note that effects of this factor on the RH,app values are rather small at low concentrations. If the first power of (1 - Vc) were employed in eq 8, it would only increase the present values of RH,app given below by ca. 10% at most in the range of c examined in the present study. It is also to be noted that since the micelles examined may have a distribution in size the values of D and RH,app thus determined should be taken as averages. Density. For the C12E5 + n-dodecane and C12E7 + ndodecane micelle solutions, the solution density F has been found to be independent of micelle weight fraction w and n-dodecane content wd at every temperature examined except for the former micelle solutions with wd ) 0.150. Thus, we

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Figure 1. Three-dimensional representation of the phase diagram for the C12E5 + n-dodecane + water (a) and C12E7 + n-dodecane + water (b) systems: ws, weight fraction of C12E5 or C12E7 in the respective solution; wd, weight fraction of n-dodecane in the C12E5 or C12E7 + n-dodecane mixture. In (a), filled circles and the surface enclosed by the solid lines represent the binodal points and surface, respectively, while the unfilled circles and the surface enclosed by the dashed and dotted lines represent the emulsification failure boundary. In (b), the surface enclosed by the solid and dashed lines represents the binodal surface determined by the cloud points shown by the filled circles. In both (a) and (b), the cloud points for wd ) 0 are the literature results.5

have used the literature values of the density F0 of pure water at corresponding temperatures for F, and the values of V of the micelles have been calculated as F-1 0 for those solutions. For the latter, F (in g/cm3) and V (in cm3/g) have been calculated by the equation: F-1 ) F0-1 + Bw

(9)

3 with B ()V - F-1 0 ) ) 0.0495 cm /g at T ) 15.0 °C, 0.0555 3 cm /g at T ) 20.0 °C, and 0.0585 cm3/g at T ) 25.0 °C.

Results Phase Behavior. Panels a and b of Figure 1 indicate the 3D phase diagrams for the ternary systems C12E5 + n-dodecane + water and C12E7 + n-dodecane + water, respectively, where the data points for the binary systems C12E5 + water and C12E7 + water, i.e., wd ) 0 are the literature results by Shirai and Einaga.5 Here, ws is the weight fraction of the surfactant C12E5 or C12E7 in the solution and filled and unfilled circles represent the cloud points and emulsification failure boundaries, respectively. A series of the data points for the latter near wd ) 0.028 are the results by Hellweg and von Klitzing.34 (For the phase diagram for the C12E6 + n-dodecane + water system, refer to our previous paper.10) We find that at small wd, the cloud point curve shift to lower temperatures with increasing wd and then shift to higher temperatures at larger wd in contrast to the case of the micelle solutions containing n-alcohol,10-14 for which the phase boundaries monotonically shift to lower temperatures as the alcohol content increases. In Figure 1a, the emulsification failure boundary schematically shown by the surface enclosed by dashed and dotted lines indicates that too much n-dodecane cannot be included in the C12E5 micelles at any T and wd. All the light scattering experiments have been performed in the L1 phase below the binodal surface.

Discussion Analysis of the SLS Results. As mentioned in the Introduction, we have analyzed the present SLS data by employing Sato theory for static light scattering from micellar solutions15,16,25 with the wormlike spherocylinder model with the total length L, cross-sectional diameter d, and stiffness λ-1 in order to determine Mw of the micelles at a specific concentration c. In the theory, the weight-average molar mass Mw of the micelles and its distribution have been formulated on the basis of multiple equilibria among various micelles of different sizes and monomer by representing chemical potentials of the micelles as functions of c in a similar fashion to the classical mean-field and recent molecular theoretical approaches.38-40 The intermicellar thermodynamic interactions have also been taken into account in the chemical potential on the basis of a statistical thermodynamic theory for stiff polymer solutions with the wormlike spherocylinder model.16 The interactions also affect the micellar growth to some extent, since they may shift the multiple equilibria among micelles of various sizes through their chemical potentials. The expression for Kc/∆R0 is written by Kc 1 ) + 2A(c)c ∆R0 Mw(c)

(10)

where Mw(c) is the weight-average molar mass of the micelles and A(c) is the apparent second virial coefficient in a sense that it includes the second, third, and the higher virial coefficient terms. Mw(c) and A(c) are functions of c, containing three parameters d, free-energy parameter g2 which controls micellar growth, and depth ˆ of the attractive potential between spherocylinders. In these, g2 represents the difference in Gibbs free energy between surfactant molecules located in the end-capped portion and those in the central cylindrical portion of the micelle. As in the case of the previous work,11-14 we have treated the present micelle solutions as two component systems

The Effect of Uptake of n-Dodecane on Micellar Characteristics

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Figure 3. The results of the curve fitting for the bilogarithmic plots of Kc/∆R0 against c for the C12E6 + n-dodecane + water system with varying n-dodecane content wd as indicated in the micelles at T ) 40.0 °C: The data points have been reproduced from ref 10. The solid and dashed curves represent the calculated values of Kc/∆R0 and 1/Mw(c), respectively.

Figure 2. The results of the curve fitting for the bilogarithmic plots of Kc/∆R0 against c for the C12E5 + n-dodecane + water system with varying n-dodecane content wd as indicated in the micelles at T ) 15.0 °C (a) and for the C12E7 + n-dodecane + water system with varying wd values as indicated at T ) 40.0 °C (b). The solid and dashed curves represent the calculated values of Kc/∆R0 and 1/Mw(c), respectively.

consisting of micelles and solvent, although they include three components: surfactant C12E5 or C12E7, n-dodecane, and water. It has been assumed in the analyses that the composition of (C12E5 or C12E7) + n-dodecane in the micelles is given by wd. The weight-average molecular weight of the (C12E5 or C12E7) + n-dodecane mixture calculated with a given wd was used as the surfactant molecular weight M0 required in the theoretical analysis. Panels a and b of Figure 2 represent the results of curvefitting of the theoretical calculations to the experimental values of Kc/∆R0 for the micelle solutions of C12E5 + n-dodecane at 15.0 °C and C12E7 + n-dodecane at 40.0 °C with various wd indicated, respectively. Figure 3 shows the reanalyzed results for the micelle solutions of C12E6 + n-dodecane at 40.0 °C. The solid and dashed curves in the figures represent the bestfit theoretical values of Kc/∆R0 and 1/Mw(c) at the respective wd values. The former curves are in good coincidence with the respective data points at given wd except for the data at the smallest c and largest wd for each system. The latter results may suggest that the micelles at these compositions are not large enough to assume a wormlike shape. As in the case of the previous findings1-6 for the micelles formed with single surfactant of various type, the data points for the C12E5 + n-dodecane micelles with wd ) 0.0501 and 0.0991 and for the C12E6 + n-dodecane micelles at any wd follow straight lines with a slope of -0.5, showing that Mw increases with c following a relation Mw ∝ c1/2 in the range of

Figure 4. g2 as a function of n-dodecane content wd in the micelles for the micelle solutions of C12E5 + n-dodecane at 15.0 °C (circles), C12E6 + n-dodecane at 40.0 °C (triangles), and C12E7 + n-dodecane at 40.0 °C (squares).

c examined. These results are in good correspondence with simple theoretical predictions for sufficiently long wormlike micelles, derived from the thermodynamic treatments of multiple equilibria among micelles of various aggregation numbers.15,36-40 In contrast to the results, the data points for the C12E5 + n-dodecane micelles with wd ) 0.150 and for all the C12E7 + n-dodecane micelles follow curves convex upward, implying that these micelles are rather small in length. The solid and dashed curves coincide with each other at small c, and the difference between them steadily increases with increasing c. The results indicate that contributions of the virial coefficient terms to Kc/∆R0 are negligible at small c but progressively increase with increasing c as expected. In Figure 4, variation of g2 with wd is shown for the C12E5 (circles), C12E6 (triangles), and C12E7 (squares) micelles containing n-dodecane. The g2 value for each micelle decreases with increasing wd, corresponding to the results that the micelles grow in length with wd, as shown below, contrary to the previous results for the CiEj micelles containing n-alcohol.11,12,14 The Micellar Length. Figure 5 illustrates the weight-average length Lw as a function of the surfactant mass concentration c for the C12E5 + n-dodecane micelles at T ) 15.0 °C (panel a),

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Figure 6. Concentration dependence of the apparent hydrodynamic radius RH,app for the C12E5 + n-dodecane micelles with varying n-dodecane content wd as indicated in the micelles at T ) 15.0 °C (a) and for the C12E7 + n-dodecane micelles with varying wd as indicated at T ) 40.0 °C (b). The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see text).

Figure 5. Weight-average micellar length Lw as a function of concentration c for the micelle solutions of C12E5 + n-dodecane at 15.0 °C (a), C12E6 + n-dodecane at 40.0 °C (b), and C12E7 + n-dodecane at 40.0 °C (c) at indicated wd.

for the C12E6 + n-dodecane micelles at T ) 40.0 °C (panel b), and for the C12E7 + n-dodecane micelles at 40.0 °C (panel c). Here, Lw was calculated by Lw )

4VMw πNAd2

+

d 3

(11)

from the values of Mw and d obtained above from the analyses of the SLS results. For all the micelles with fixed wd, the length Lw increases with increasing c. On the other hand, it decreases with increasing n-dodecane content wd, contrary to the case of the micelles containing

n-alcohol reported in the previous papers.11-14 The former results may indicate that the addition of n-dodecane into the micelles weakens hydrophilic interactions among polyoxyethylene tails of the CiEj molecules forming micelles and water too significantly to maintain the micellar size, as mentioned by Menge et al.,26-28 and leads to collapse of the micelles of smaller size. The latter implies that n-alcohol plays a role of a kind of cosurfactant in the micelles, since it has a hydroxyl group which may work as a hydrophilic group. The decrease of the micellar size with increasing wd is in correspondence with the results for g2 given in Figure 4 and the phase behavior shown in Figure 1 and in ref 10. We see that the Lw values for the C12E5 + n-dodecane micelles with wd ) 0.150 and for all the C12E7 + n-dodecane micelles are quite small as suggested above from the curve fitting results given in Figure 2. Hydrodynamic Radius of the Micelles. Panels a and b of Figure 6 depict bilogarithmic plots of RH,app determined by eq 8 from the D data against c for the C12E5 + n-dodecane micelles of indicated wd at 15.0 °C and the C12E7 + n-dodecane micelles of indicated wd at 40.0 °C, respectively. In Figure 7 are shown the re-analyzed results for the C12E6 + n-dodecane micelles of indicated wd at 40.0 °C.10 The RH,app values for all the micelles at fixed c decrease with increasing wd corresponding to the decrease of the micellar length Lw shown in Figure 5. The results are again in contrast to the findings11-14 for the CiEj micelles containing n-alcohol, where RH,app significantly increases with n-alcohol content. It is seen that, for every micelle of given wd,

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Figure 7. Concentration dependence of the apparent hydrodynamic radius RH,app for the C12E6 + n-dodecane micelles with varying n-dodecane content wd as indicated in the micelles at T ) 40.0 °C. The data points have been reproduced from ref 10. The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see Text).

RH,app increases with increasing c. The RH,app values do not, however, necessarily correspond to those for isolated micelles. The increase of RH,app reflects both micellar growth in size and enhancement of the effects of the intermicellar hydrodynamic interactions with increasing c. RH,app as a function of c may be represented as RH,app(c) ) RH(c)H(c)

(12)

where RH(c) represents the hydrodynamic radius of a isolated micelle, which may grow in size with c and H(c) the hydrodynamic interactions, which may be enhanced with c. In these two functions, RH(c) may be calculated by employing the equations formulated for the translational friction coefficient by Norisuye et al.18 with the wormlike spherocylinder model near the rod limit and by Yamakawa et al.19,20 with the wormlike cylinder model as a function of the micellar length L including d and the stiffness parameter λ-1. Their equation for RH reads RH )

L 2f(λL,λd)

(13)

The expression for the function f is so lengthy that we refer the reader to the original papers.18-20 We are able to calculate RH(c) required in eq 12 by combining eq 13 with eq 11. Here, Lw by eq 11 is used in place of L in eq 13 and the Mw values as a function of c are obtained from the dashed lines in Figures 2 and 3. The function H(c) in eq 12 may be calculated with the formulation given by Sato et al.22-25 They have recently studied the concentration dependence of the intermolecular hydrodynamic and direct collision interactions among wormlike polymer chains by using a fuzzy cylinder model. The fuzzy cylinder is defined as a cylinder which encapsulate a wormlike chain or a wormlike spherocylinder in the present case. Its effective length and diameter are evaluated from the wormlike chain parameters L, d, and λ-1. In the formulation, Sato et al. have taken into account the hydrodynamic interactions among fuzzy cylinders and also the jamming effects of the cylinders on the longitudinal and transverse diffusion coefficients along and perpendicular to the chain end-to-end axis, respectively. The solid curves in Figures 6 and 7 are the best-fit theoretical values of RH,app(c) thus calculated by eq 12 by combining Sato

Figure 8. Bilogarithmic plots of RH,app against Mw for the C12E5 + n-dodecane micelles with varying n-dodecane content wd as indicated in the micelles at T ) 15.0 °C (a), the C12E6 + n-dodecane micelles with varying wd as indicated at T ) 40.0 °C (b), and the C12E7 + n-dodecane micelles with varying wd as indicated at T ) 40.0 °C (c). The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see text).

et al.’s H(c) with RH(c). Here, we have used the d values obtained from the analysis of the SLS data and determined the values of λ-1 so as to achieve the best fit to the observed results. It is to be noted that the theoretical values of RH,app (and also RH) for the C12E5 + n-dodecane micelles with wd ) 0.150 and for the C12E7 + n-dodecane micelles with wd ) 0.0993 do not highly depend on the λ-1 value, which is considered to be higher than a few hundred nanometers, due to the fact that these micelles are rather small in length. The values of λ-1 were not, thus, unequivocally determined for these micelles. The solid

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Figure 9. n-Dodecane content wd (in the micelles) dependence of the cross-sectional diameter d for the C12E5 + n-dodecane (at T ) 15.0 °C) (circles), C12E6 + n-dodecane (at T ) 40.0 °C) (triangles), and C12E7 + n-dodecane (at T ) 40.0 °C) (squares).

(and also the dashed) lines for these micelles in Figure 6 represent the theoretical values calculated with λ-1 ) 400 nm. The dashed lines represent relationships between RH and c for the isolated micelles without any intermicellar hydrodynamic interaction and thus the growth of the micelles with increasing c. We find that the solid and corresponding dashed lines, i.e., RH,app(c) and RH(c), coincide with each other at small c and the difference between them becomes progressively large with c. The latter results imply that a great portion of RH,app results from the hydrodynamic interactions at larger c and that the increase of the micellar size with c is rather moderate. In panels a, b, and c of Figure 8, the same observed and theoretical results for RH,app and RH as those in Figures 6a, 6b, and 7 are shown as functions of Mw in the bilogarithmic plots, respectively. The dashed lines represent the theoretical values of RH and correspond to the relationship between RH and Mw as usually shown for real polymer solutions. They asymptotically approach the data points and the solid curves as Mw is decreased, i.e., as c is lowered, indicating that the effects of the intermicellar hydrodynamic interactions on RH,app become negligible in the asymptotic region of low c as expected. At any given wd, the difference between the solid and dashed curves, which steeply increase with Mw, is due to the enhancement of the intermicellar hydrodynamic and dynamic interactions with increasing c, i.e., the contribution of H(c) to RH,app(c) in eq 12. For all the micelles, the data points and the solid line for fixed wd shift to the smaller Mw and RH,app as wd is increased, contrary to the case of the CiEj micelles containing n-alcohol, implying that the micelles collapse into smaller size with addition of n-dodecane. Variation of Characteristics of the C12E5, C12E6, and C12E7 Micelles with uptake of n-Dodecane. Figure 9 depicts wd dependence of d determined from the analysis of the SLS results for the C12E5 (circles), C12E6 (triangles), and C12E7 (squares) micelles containing n-dodecane. The d values of these micelles increase with increasing n-dodecane content wd in the micelles. The present results are similar to the previous findings for the CiEj micelles containing n-dodecanol or n-octanol.12,14 The dependence of the d values on the hydrophilic chain length is not, however, systematic and thus we cannot derive definite conclusion about the dependence at present. The values of the spacing s between the hydrophilic tails of adjacent surfactant molecules on the micellar surface are evaluated from the values of d, Lw, and the aggregation number Nw calculated from Mw. Here, the surface area of the sphero-

Miyake et al.

Figure 10. n-Dodecane content wd (in the micelles) dependence of the spacing s between adjacent surfactant tails on the micellar surface for the C12E5 + n-dodecane (at T ) 15.0 °C) (circles), C12E6 + n-dodecane (at T ) 40.0 °C) (triangles), and C12E7 + n-dodecane (at T ) 40.0 °C) (squares).

Figure 11. n-Dodecane content wd (in the micelles) dependence of the stiffness parameter λ-1 for the C12E5 + n-dodecane (at T ) 15.0 °C) (circles), C12E6 + n-dodecane (at T ) 40.0 °C) (triangles), and C12E7 + n-dodecane (at T ) 40.0 °C) (squares).

cylindrical micelles was calculated from the values of d and Lw, and then dividing it by the aggregation number Nw yielded the values of the area occupied by each surfactant molecule, from which the spacing s was evaluated. They are plotted against wd in Figure 10 for the three micelles. The s value gradually decreases with increasing wd for all the three micelles, implying that the surfactant molecules are more densely assembled with increasing wd in order to keep n-dodecane inside the micelles. We find that it is substantially independent of the hydrophilic chain length of the surfactant molecules. Figure 11 illustrates wd dependence of λ-1 evaluated from the analysis of the RH,app as function of c for the C12E5 (circles), C12E6 (triangles), and C12E7 (squares) micelles containing n-dodecane. It is to be noted that the data points for the C12E5 micelle with wd ) 0.150 and for the C12E7 micelle with wd ) 0.0993 are missed in this figure, since they are too large as mentioned above. The λ-1 values for all of the three micelles increase with increasing wd. The λ-1 values for the C12E7 + n-dodecane micelles are larger than those for the other two micelles, although the dependence of the d values on the hydrophilic chain length is not systematic. The fact that the micelles become stiffer with uptake of n-dodecane may be correlated with the result that the cross-sectional diameter d of

The Effect of Uptake of n-Dodecane on Micellar Characteristics the micelles become larger as n-dodecane content is increased in the micelles. Conclusions In the present work, we have examined variation of characteristics of the C12E5, C12E6, and C12E7 micelles with uptake of n-dodecane by static light scattering (SLS) and dynamic light scattering (DLS) experiments. As in the previous studies on the CiEj micelles containing n-alcohol,11-14 the SLS results Kc/∆R0 have been successfully analyzed with the aid of the theory15,25 for light scattering of micelle solutions formulated with wormlike spherocylinder model to yield the molar mass Mw(c) as a function of c along with the cross-sectional diameter d of the micelle. The apparent hydrodynamic radius RH,app(c) from DLS as a function of the micellar concentration c has been successfully analyzed by the fuzzy cylinder theory by Sato et al.,22-25 which takes into account the hydrodynamic and direct collision interactions among micelles, that allowed us also to evaluate the stiffness parameter λ-1. It has been found that the micellar length Lw increases with increasing c irrespective of the n-dodecane content wd, as in the case of the CiEj micelles with and without including n-alcohol.1-6,11-14 The d values for all the micelles examined increase with increasing wd, similar to the micelles containing n-dodecanol or n-octanol, accompanying the increase of the stiffness parameter λ-1. On the other hand, the length Lw, molar mass Mw, and hydrodynamic radius RH of the C12E5, C12E6, and C12E7 micelles decrease with increasing weight fraction wd of n-dodecane in the micelles, contrary to the micelles containing n-dodecanol or n-octanol. The results may result from the fact that the addition of n-dodecane into the micelles weakens hydrophilic interactions among polyoxyethylene chains of the surfactant molecules and water, making the micelles unstable and then leading to the collapse of micelles of smaller size. It is surprising that a rather small difference between the end groups of n-dodecane and n-dodecanol, i.e., proton and hydroxyl group, causes significant effects on the characteristics of the CiEj micelles. Acknowledgment. The authors are grateful to Professor T. Sato of Osaka University for valuable discussions and for providing us with the computer program to calculate the apparent hydrodynamic radius. References and Notes (1) Yoshimura, S.; Shirai, S.; Einaga, Y. J. Phys. Chem. B 2004, 108, 15477.

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