Variation of Characteristics of Pentaoxyethylene Decyl C10E5 and

Jul 26, 2007 - Maiko Miyake, Ayako Asano, and Yoshiyuki Einaga. The Journal of Physical Chemistry B 2008 112 (15), 4648-4655. Abstract | Full Text HTM...
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J. Phys. Chem. B 2007, 111, 9444-9452

Variation of Characteristics of Pentaoxyethylene Decyl C10E5 and Hexaoxyethylene Tetradecyl C14E6 Ether Micelles with Uptake of n-Octanol Maiko Miyake, Megumi Ebihara, and Yoshiyuki Einaga* Department of Chemistry, Nara Women’s UniVersity, Nara 630-8506, Japan ReceiVed: April 18, 2007; In Final Form: May 28, 2007

Wormlike micelles of the surfactant pentaoxyethylene decyl C10E5 and hexaoxyethylene tetradecyl C14E6 ethers were characterized by static (SLS) and dynamic light scattering (DLS) experiments to examine effects of uptake of n-octanol 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 a 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 weight fraction ws and increasing n-octanol content wo in the micelles or with raising temperature T. The values of d and λ-1 are found to increase with increasing wo, whereas the spacing s between hydrophilic tails of adjacent surfactant molecules on the micellar surface decreases with increasing wo. Comparison with our previous results for the C10E5 and C14E6 micelles containing n-dodecanol has revealed the salient features in change of the micellar characteristics with uptake of n-alcohols as follows: (i) The Lw values increase more significantly for the C14E6 micelles containing n-dodecanol than those containing n-octanol, whereas Lw of the C10E5 micelles increases by including n-dodecanol and n-octanol without a significant difference for the two alcohols. (ii) The values of d and λ-1 of the C10E5 and C14E6 micelles increase with uptake of n-octanol and n-dodecanol into the micelles. They are larger for the C10E5 micelles than for the C14E6 micelles, and their increase with alcohol content is less significant for the C14E6 micelles in comparison with the C10E5 micelles. (iii) The s values of the C10E5 and C14E6 micelles decrease with uptake of n-octanol and n-dodecanol into the micelles. They are somewhat larger in the latter micelles than in the former. (iv) The variation in d, s, and λ-1 with uptake of n-alcohol occurs with no difference in the effects for the two alcohols n-octanol and n-dodecanol.

Introduction In this series of work on micelle solutions of nonionic surfactant polyoxyethylene alkyl ethers H(CH2)i(OCH2CH2)jOH (CiEj), we have characterized the CiEj micelles with various i and j by static (SLS) and dynamic light scattering (DLS) measurements1-6 and viscometry.7 It has been demonstrated that the SLS results (the excess Rayleigh ratio) as a function of surfactant concentration c are successfully analyzed by a molecular thermodynamic theory8,9 formulated with the wormlike spherocylinder model to provide us with the molar mass Mw(c) of the micelle at a specified c along with the crosssectional diameter d of the spherocylinder. The molar mass Mw dependence of the mean-square radius of gyration 〈S2〉, hydrodynamic radius RH, and intrinsic viscosity [η] has been found to be quantitatively represented by the chain statistical10 and hydrodynamic11-14 theories based on the wormlike chain and spherocylinder models, respectively, thereby yielding the values of the stiffness parameter λ-1. Following the work on micelle slutions of pure CiEj, we have also studied C12E6, C10E5, C12E5, C10E6, and C14E6 micelles containing n-dodecanol to explore the effects of uptake of an n-alcohol into the micelles on the micellar characteristics.15-18 The SLS and DLS results are well represented by the theories based on the spherocylinder model mentioned above as in the case of the micelle solutions of simple CiEj. It has been shown

that the fuzzy cylinder theory19-21 is applied in a favorable fashion to analyze the apparent hydrodynamic radius RH,app, which is directly obtained from DLS experiment, as a function of the micelle concentration, thereby obtaining the concentrationdependent micellar growth 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 content in the micelles increases. In the present work, we have studied the micelles in the C10E5 + n-octanol + water and C14E6 + n-octanol + water systems by SLS and DLS measurements. The main aim is to investigate effects of species of n-alcohol on the variation of the micellar characteristics such as the micellar length, cross-sectional diameter, and stiffness with uptake of n-alcohol. Experimental Section Materials. The surfactant C10E5 and C14E6 samples were purchased from Nikko Chemicals Co. Ltd. n-Octanol was supplied by Nakaraitesque Co. 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. The cloud-point temperature of a given micelle solution was determined as the temperature at which

10.1021/jp073017d CCC: $37.00 © 2007 American Chemical Society Published on Web 07/26/2007

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the intensity of the laser light transmitted through the solution abruptly decreased when the temperature was gradually raised. C10E5 and C14E6 micelle solutions were prepared by dissolving them in water with the addition of the appropriate amount of n-octanol 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. n-Octanol is substantially insoluble in water and thus completely incorporated into the micelles. 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 (C10E5 or C14E6) + n-octanol in the (C10E5 or C14E6) + water + n-octanol ternary solutions. n-Octanol content in the (C10E5 or C14E6) + n-octanol mixtures is represented by its weight fraction wo. Static Light Scattering. SLS measurements were performed to obtain the weight-average molar mass Mw of the micelles in the L1 phase. The scattering intensities were measured for micelle solutions of C10E5 + n-octanol with various wo at 20.0, 25.0, and 30.0 °C, and for those of C14E6 + n-octanol with various wo at 25.0 °C. The ratio Kc/∆Rθ was obtained for each solution as a function of the scattering angle θ ranging from 0 to 150° and extrapolated to zero scattering angle to evaluate Kc/∆R0. For the C14E6 micelles containing n-octanol, the apparent mean-square radius of gyration 〈S2〉app at a specified c was determined on the basis of the fundamental light-scattering equation for dilute polymer solutions

(

) (

〈S2〉 2 Kc 1 ) + 2A2c + ‚‚‚ + q + ‚‚‚ ∆Rθ Mw 3Mw 4πn sin(θ/2) q) λ0

)

(1) (2)

from the slope of the Kc/∆Rθ versus sin2(θ/2) plot. Here, c is the mass concentration of surfactant + n-dodecanol, ∆Rθ is the excess Rayleigh ratio, A2 is the second virial coefficient, 〈S2〉 is the mean-square radius of gyration, q is the magnitude of the scattering vector, λ0 is the wave length of the incident light in vacuum, and K is the optical constant defined as

K)

4π2n2(∂n/∂c)T,p2 NAλ0

4

(3)

with NA being the Avogadro’s number, n the refractive index of the solution, (∂n/∂c)T,p the refractive index increment, T the absolute temperature, and p the pressure. In the evaluation, we used the Mw values determined as described below at given c, wo, and T. Since 〈S2〉 is possibly affected by intermicellar interactions, it is denoted by 〈S2〉app. We note that the 〈S2〉app values of the C10E5 micelles are not large enough to be determined by SLS measurements. The plot of Kc/∆Rθ vs sin2(θ/2) affords a good 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 In the present study, we have treated the micelle solutions as the binary

system which consists of micelles containing n-octanol 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). For the system C10E5 + n-octanol + water at 15.0 °C eT e 35.0 °C

(∂n/∂c)T,p ) 0.1337 - 2.18 × 10-4(T - 273.15) (wo ) 0.0291) (4) (∂n/∂c)T,p ) 0.1334 - 2.38 × 10-4(T - 273.15) (wo ) 0.0401) (5) (∂n/∂c)T,p ) 0.1321 - 2.33 × 10-4(T - 273.15) (wo ) 0.0502) (6) For the system C14E6 + n-octanol + water at 15.0 °C eT e 25.0 °C

(∂n/∂c)T,p ) 0.142 - 4.475 × 10-4(T - 273.15) (wo ) 0.0315) (7) (∂n/∂c)T,p ) 0.133 - 2.675 × 10-4(T - 273.15) (wo ) 0.0517) (8) (∂n/∂c)T,p ) 0.131 - 3.250 × 10-4(T - 273.15) (wo ) 0.0695) (9) 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 of 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 equation16,22-24

( )

(1 - Vc)2MwkBT Kc RH,app ) 6πη0D ∆R0

(10)

where V is the partial specific volume of the solute (micelle), kB is the Boltzmann constant, and η0 is the solvent viscosity. It should be emphasized that eq 10 is a defining equation for the apparent hydrodynamic radius RH,app which implicitly include the effects of hydrodynamic interactions. 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 all of the micelle solutions containing n-octanol, the solution density F has been found to be independent of micelle weight fraction w and n-octanol content wo at every temperature examined, i.e., from 15.0 to 35.0 °C. Thus we 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 F0-1. Results Phase Behavior. Figure 1, panels a and b, depicts the 3D phase diagrams for the ternary systems C10E5 + n-octanol + water and C14E6 + n-octanol + water, respectively. Here, the data points for the binary systems C10E5 + water and C14E6 +

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Figure 1. Three-dimensional representation of the binodal surface for the C10E5 + n-octanol + water (a) and C14E6 + n-octanol + water (b) systems: ws, weight fraction of C10E5 or C14E6 in the respective solution; wo, weight fraction of n-octanol in the C10E5 or C14E6 + n-octanol mixture. The data points for wo ) 0 are the literature results.1,3

water, i.e., wo ) 0 are the literature results by Imanishi and Einaga3 and Yoshimura et al.1 Here, ws is the weight fraction of the surfactant C10E5 or C14E6 in the solution. We find that all of the micelle solutions at fixed wo represent the phase separation behavior of the LCST (lower critical solution temperature) type and that the phase boundaries significantly shift to lower temperatures as wo increases. All of the light scattering experiments have been performed in the L1 phase below the binodal surface. Discussion Determination of the Molar Mass Mw(c). In order to determine the Mw values of the micelles at a specified concentration c, we have analyzed the present SLS data by employing a light-scattering theory for micellar solutions formulated by Sato8,9 with a wormlike spherocylinder model for polymer-like micelles as in the previous work mentioned in the Introduction. The model consists of a wormlike cylinder of contour length L - d with cross-sectional diameter d and two hemispheres of diameter d which cap both ends of the cylinder, and the stiffness of the wormlike cylinder is represented by the stiffness parameter λ-1. 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.25-27 In the formulation, the free-energy parameter g2, which represents the difference in free energy between the surfactant molecules located in the end-capped portion to those in the central cylindrical portion in the micelles, plays a dominant role in the multiple equilibria and then the micellar growth with concentration. 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.9 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 apparent virial coefficient A(c), which includes the second A2, third A3, and higher virial coefficient terms, has been formulated to describe thermodynamic properties of micelle solutions up to high concentrations by taking into account the hard-core repulsive interactions dominated by the parameter d together with the attractive interactions dominated by the parameter  (the depth of the attractive potential well) among the micelles. In sum, the functions Mw(c) and A(c) and then the excess zero-angle Rayleigh ratio ∆R0 have been given as functions of c with including d, g2, and  as parameters. By the formulation, we are able to evaluate Mw(c) by determining the best-fit theoretical values of Kc/∆R0 as a function of c to the observed data at fixed T with selected proper values of d, g2, and . As mentioned above, we have treated present micelle solutions as two component systems consisting of micelles and solvent, although they include three components: surfactant C10E5 or C14E6, n-octanol, and water. It has been assumed that the composition of (C10E5 or C14E6) + n-octanol in the micelles is given by wo. The weight average molecular weight of the (C10E5 or C14E6) + n-octanol mixture calculated with a given wo was used as the surfactant molecular weight M0 required in the theoretical analysis. Figure 2, panels a and b, demonstrates the results of curvefitting of the theoretical calculations to the experimental values of Kc/∆R0 for the micelle solutions of C10E5 + n-octanol at 20.0 °C and C14E6 + n-octanol at 25.0 °C with various wo indicated, respectively. Here, the results for wo ) 0 are reproduced from the literature.1,16 Figure 3 shows the results for the micelle solutions of C10E5 + n-octanol with wo ) 0.0291

Effects of Uptake of n-Octanol on Micelles

Figure 2. Results of the curve fitting for the bilogarithmic plots of Kc/∆R0 against c for the C10E5 + n-octanol + water system of various n-octanol content in the micelles wo indicated at T ) 20.0 °C (a) and for the C14E6 + n-octanol + water system of various wo indicated at T ) 25.0 °C (b). The solid and dashed curves represent the calculated values of Kc/∆R0 and 1/Mw(c), respectively. The results for wo ) 0 were reproduced from the literature.1,3,16

Figure 3. Results of the curve fitting for the bilogarithmic plots of Kc/∆R0 against c for the C10E5 + n-octanol + water system of n-octanol content in the micelles wo ) 0.0291 at T ) 20.0, 25.0, and 30.0 °C. The solid and dashed curves represent the calculated values of Kc/∆R0 and 1/Mw(c), respectively.

at 20.0, 25.0, and 30.0 °C. The solid curves in the figures represent the best-fit theoretical values. They are in good coincidence with the respective data points at given wo, implying that the micelles containing n-octanol are well represented by the wormlike spherocylinder model. The dashed lines represent

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Figure 4. g2 as a function of octanol content in the micelles wo for the micelle solutions of C10E5 + n-octanol at 20.0 °C (circles) and C14E6 + n-octanol at 25.0 °C (filled circles) (a) and as a function of temperature T for the micelle solutions of C10E5 + n-octanol of wo ) 0.0291 (b).

the values of 1/Mw(c) at respective wo. For all of the micelles at any fixed wo, they are straight lines with a slope of -0.5, showing that Mw increases with c following a relation Mw ∝ c1/2 in the range of c examined, as in the case of the previous findings1-6 for the micelles formed with a single surfactant of various type. These results are in good correspondence with simple theoretical predictions derived from the thermodynamic treatments of multiple equilibria among micelles of various aggregation numbers.8,25-27 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. The d value determined by the curve fitting was independent of T but gradually increased with wo for both C10E5 and C14E6 micelles containing n-octanol as in the case with the micelles containing n-dodecanol. They were 2.60, 2.68, 2.90, and 3.10 nm at wo ) 0, 0.0291, 0.0401, and 0.0502, respectively, for the former micelles and 2.40, 2.45, 2.60, and 2.70 nm at wo ) 0, 0.0315, 0.0517, and 0.0695, respectively, for the latter. In these, the values at wo ) 0 are the literature results.1,3,16 In Figure 4a, variation of g2 with wo is shown for the C10E5 (circles) and C14E6 (filled circles) micelles containing n-octanol. For each micelle, g2 gradually increases with increasing wo, corresponding to the results that the micelles grow in length with wo. The g2 values for the C14E6 micelles at 25.0 °C are significantly larger than those for the C10E5 micelles at 20.0 °C. The great difference in g2 between the two micelles

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Figure 5. Molar mass Mw dependence of the apparent root meansquare radius of gyration 〈S2〉app1/2 for the C14E6 + n-octanol micelles with various n-octanol content in the micelles wo indicated at T ) 25.0 °C. The solid curves represent the theoretical values (see the text).

may correspond to the result that the C14E6 micelles grow in length to a greater extent than the C10E5 micelles with or without containing n-octanol as described below. Figure 4b indicates that g2 for the C10E5 + n-octanol micelle solutions increases linearly with T. The increase of g2 is also in good correspondence with the result that the micelles grow in length with raising temperature as shown below. Mean-Square Radius of Gyration. The molar mass dependence of root mean-square radius of gyration 〈S2〉app1/2 is exhibited in Figure 5 for the C14E6 micelles containing n-octanol with various wo indicated at 25.0 °C. The data points for each fixed wo form a single curve, independent of c, implying that they correspond to the values for the “isolated”micelles, i.e., 〈S2〉1/2. The observed results are quantitatively represented by the theoretical values of 〈S2〉1/2 calculated by the Benoit-Doty equation for wormlike polymers10 as shown by the solid curves. Here, the relation between Mw and the weight-average micellar length Lw derived from the micellar volume

Lw )

4VMw πNAd

2

+

d 3

(11)

has been utilized (Lw was used in place of L). In the calculation, the d values obtained from SLS results in the preceding section were used and then the λ-1 values were determined as 17, 18, and 19 nm for wo ) 0.0315, 0.0517, and 0.0695, respectively, to achieve the best fit to the experimental results. Hydrodynamic Radius of the Micelles. The values of RH,app determined by eq 10 for the C10E5 + n-octanol micelles of various wo at 20.0 °C and for the C14E6 + n-octanol micelles of various wo at 25.0 °C are bilogarithmically plotted against c in Figure 6, panels a and b, respectively. In Figure 7 are shown the results for the C10E5 + n-octanol micelles of wo ) 0.0291 at 20.0, 25.0, and 30.0 °C. It is found that, at any given wo and T, RH,app increases with increasing c. 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, thus, represented as

RH,app(c) ) RH(c) H(c)

Figure 6. Concentration dependence of the apparent hydrodynamic radius RH,app (large symbols) calculated by eq 10 and R/H (small symbols) calculated by eq 13 for the C10E5 + n-octanol micelles with various n-octanol content in the micelles wo indicated at T ) 20.0 °C (a) and for the C14E6 + n-octanol micelles with various wo indicated at T ) 25.0 °C (b). The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see the text).

Figure 7. Concentration dependence of the apparent hydrodynamic radius RH,app for the C10E5 + n-octanol micelles with n-octanol content in the micelles wo ) 0.0291 at T ) 20.0, 25.0, and 30.0 °C. The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see the text).

(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 is enhanced with increasing c. In these two functions, RH(c) may be calculated by employing the equations formulated by Norisuye et al.11 for the wormlike

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spherocylinder model near the rod limit and by Yamakawa et al.12,13 for the wormlike cylinder model, as a function of the micellar length L with the inclusion of d and the stiffness parameter λ-1. We are able to calculate RH(c) as a function of c or Mw, by using eq 11, in which Lw is used in place of L. We note that Lw is a function of c, and the relations between Mw and c shown by the dashed lines in Figures 2 and 3 are utilized. The function H(c) may be calculated with the formulation given by Sato et al.,19-21 who have recently treated with 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 encapsulates a wormlike chain or a wormlike spherocylinder in the present case. Its effective length and diameter are evaluated from the wormlike spherocylinder parameters L, d, and λ-1. Here, eq 11 and the experimental relationship between Mw and c are again utilized. 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 et al.’s H(c) with RH(c). Here, we have used the d values obtained from the analyses of the SLS data and determined the values of λ-1 so as to achieve the best fit to the observed results. 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 large c and that the increase of the micellar size with c is rather moderate. In Figure 6 are included the values of the apparent hydrodynamic radius R/H (small symbols) calculated by the StokesEinstein relation

R/H )

kBT 6πη0D

(13)

It is seen that they are considerably smaller than those for RH,app and nearly constant or rather decreasing with increasing c at high concentrations, say c > 0.03 g/cm3. The results imply that the hydrodynamic interaction term H(c) in eq 12 is roughly compensating for the thermodynamic interaction terms 2A2Mwc + ‚‚‚ which is included in Kc/∆R0 of eq 10.28 However, almost all of the data points for R/H are located even below the dashed lines which represent the hydrodynamic radius RH(c) for the “isolated”micelles, indicating that the use of eq 13, as sometimes done, leads to significant underestimation of the hydrodynamic radius. In Figures 8a,b and 9, the same observed and theoretical results for RH,app and RH as those in Figures 6a,b and 7 are shown as functions of Mw in the bilogarithmic plots, respectively. Here, the literature results for the C14E61 micelles with wo ) 0 are included in Figure 8b. 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. The results are in line with our previous findings for RH of the single CiEj micelles.1-3 At any given wo or T, the difference between the solid and dashed curves, which steeply increase with Mw, is due to the enhancement of the intermicellar hydrodynamic and

Figure 8. Bilogarithmic plots of RH,app against Mw for the C10E5 + n-octanol micelles with various n-octanol content in the micelles wo indicated at T ) 20.0 °C (a) and the C14E6 + n-octanol micelles with various wo indicated at T ) 25.0 °C (b). The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see the text).

Figure 9. Bilogarithmic plots of RH,app against Mw for the C10E5 + n-octanol micelles with n-octanol content in the micelles wo ) 0.0291 at T ) 20.0, 25.0, and 30.0 °C. The solid and dashed curves represent the theoretical values with and without the intermicellar hydrodynamic interactions (see the text).

dynamic interactions with increasing c (i.e., the contribution of H(c) to RH,app(c) in eq 12). The λ-1 values determined are 35, 36, and 40 nm for wo ) 0.0291, 0.0401, and 0.0502 at T ) 20.0 °C, respectively, for the C10E5 micelles and 12 nm for any wo examined at T )

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Figure 10. Surfactant weight fraction ws and n-octanol content in the micelles wo dependence of the weight-average micellar length Lw for the C10E5 + n-octanol micelles at 20.0 °C (a) and for the C14E6 + n-octanol micelles at 25.0 °C (b).

25.0 °C for the C14E6 micelles. They are 35, 30, and 25 nm for the C10E5 micelles of wo ) 0.0291 at 20.0, 25.0, and 30.0 °C, respectively. It should be noted that, for the C14E6 micelles, the λ-1 value from RH,app is significantly smaller than those from 〈S2〉. The difference may be attributed to the fact that there is a distribution in micellar size and different averages are reflected in RH,app and 〈S2〉 as mentioned previously.1,2,5 Micellar Length. Figure 10, panels a and b, illustrates the weight-average length Lw as a function of the surfactant weight fraction ws and the n-octanol content in the micelles wo for the C10E5 micelles at T ) 20.0 °C (a) and for the C14E6 micelles at 25.0 °C (b), respectively. Figure 11 shows Lw as a function of ws and T for the C10E5 micelles of wo ) 0.0291. Here, Lw was calculated by eq 11 from the values of Mw and d obtained above from the analyses of the SLS data. For both of the micelles at a given wo and T, Lw becomes larger as ws is increased. As seen in Figure 10, panels a and b, Lw at fixed ws steeply increases with increasing wo (i.e., with uptake of n-octanol into the micelles). We find that the C14E6 micelles grow in length to a greater extent than the C10E5 micelles. This is in correspondence with the results for g2 given in Figure 4a, where the g2 value for the C14E6 + n-octanol micelles is significantly larger than that for the C10E5 + n-octanol micelles. The finding is also in line with our previous results1-7 for the micelles of the single surfactant CiEj. The longer alkyl group in the surfactant molecule CiEj facilitates growth of the micelles due to the stronger hydrophobic or attractive interactions among CiEj molecules in the micelle. On the other hand, the longer oxyethylene units depress the micellar growth due to the stronger repulsive interactions among the hydrophilic groups of the adjacent CiEj molecules on the micellar surface. The micelles grow in length to a greater extent at higher temperatures. The difference in Lw between the C10E5 and C14E6 micelles containing n-octanol results from these three competitive effects. Figure 11 indicates that the C10E5 micelles containing a fixed amount of n-octanol

Figure 11. Surfactant weight fraction ws and temperature T dependence of the weight-average micellar length Lw for the C10E5 + n-octanol micelles for n-octanol content wo ) 0.0291 in the micelles.

grow in length with raising temperature in correspondence with the increase of g2 as mentioned above. Variation of the Micellar Characteristics with Uptake of n-Alcohol. Figure 12 depicts concentration dependence of Lw for the C10E5 (a) and C14E6 micelles (b) containing n-octanol (circles) or n-dodecanol (filled circles) with wo = (or wd =)

Effects of Uptake of n-Octanol on Micelles

J. Phys. Chem. B, Vol. 111, No. 32, 2007 9451

Figure 14. Octanol content wo or dodecanol content wd (in the micelles) dependence of the spacing s between adjacent surfactant tails on the micellar surface for the C10E5 + n-octanol (at T ) 20.0 °C) (circles), C14E6 + n-octanol (at T ) 25.0 °C) (filled circles), C10E5 + n-dodecanol (at T ) 20.0 °C) (triangles), and C14E6 + n-dodecanol micelles (at T ) 25.0 °C) (filled triangles).

Figure 12. Concentration dependence of the weight-average micellar length Lw: (a) C10E5 + n-octanol (wo ) 0.0502), circles, solid curve; C10E5 + n-dodecanol (wd ) 0.0501), filled circles, dashed curve, (at T ) 20.0 °C); (b) C14E6 + n-octanol (wo ) 0.0517), circles, solid curve; C14E6 + n-dodecanol (wd ) 0.0505), filled circles, dashed curve, (at T ) 25.0 °C).

Figure 15. Octanol content wo or dodecanol content wd (in the micelles) dependence of the stiffness parameter λ-1 for the C10E5 + n-octanol (at T ) 20.0 °C) (circles), C14E6 + n-octanol (at T ) 25.0 °C) (filled circles), C10E5 + n-dodecanol (at T ) 20.0 °C) (triangles), and C14E6 + n-dodecanol micelles (at T ) 25.0 °C) (filled triangles).

Figure 13. Octanol content wo or dodecanol content wd (in the micelles) dependence of the cross-sectional diameter d for the C10E5 + n-octanol (at T ) 20.0 °C) (circles), C14E6 + n-octanol (at T ) 25.0 °C) (filled circles), C10E5 + n-dodecanol (at T ) 20.0 °C) (triangles), and C14E6 + n-dodecanol micelles (at T ) 25.0 °C) (filled triangles).

0.05. The difference in the micellar length Lw between the two cases with uptake of n-octanol and n-dodecanol is negligible for the C10E5 micelles but significant for the C14E6 micelles. In the latter, Lw of the C14E6 + n-dodecanol micelles is larger than that of the C14E6 + n-octanol micelles by a factor about two.

As shown in Figure 13, the d values of the C10E5 and C14E6 micelles increase with increasing n-octanol wo or n-dodecanol content wd in the micelles. We do not find any difference in d between the two kinds of n-alcohol containing in the micelles. It is seen that the increase of d is slightly more significant for the C10E5 micelles than that for the C14E6 micelles and that the d values are larger for the former micelles than those for the latter. 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. They are plotted against wo or wd in Figure 14 for the C10E5 (circles and triangles) and C14E6 micelles (filled circles and triangles). No difference is again found between the species of the n-alcohols contained in the both micelles. We find that the s value is gradually decreased with increasing wo or wd for both micelles. The results imply that the surfactant molecules are more densely assembled as the n-alcohol content is increased, in order to keep them inside the micelles.

9452 J. Phys. Chem. B, Vol. 111, No. 32, 2007 Figure 15 illustrates the wo or wd dependence of λ-1 evaluated from the analysis of the relationship between RH,app and c for the C10E5 and C14E6 micelles containing n-octanol or ndodecanol. The λ-1 values for the C10E5 micelles increase with increasing wo or wd, whereas those for the C14E6 micelles are substantially independent of wo or wd. They are again independent of the species of n-alcohols contained in the micelles. The value of λ-1 is larger for the C10E5 micelles than that for the C14E6 micelles, when compared at the same wo or wd. This result is in line with our previous results5,6 for the micelles of the single surfactant CiEj, where the surfactant molecules of the shorter hydrophobic chain length form stiffer micelles. Conclusions In this work, we have examined variation of characteristics of the C10E5 and C14E6 micelles with uptake of n-octanol by static (SLS) and dynamic light scattering (DLS) measurements. As in the previous studies,1-6,16-18 the SLS results Kc/∆R0 have been successfully analyzed by the theory8 for light scattering of micelle solutions formulated with the 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 has been also successfully analyzed by the fuzzy cylinder theory by Sato et al.19-21 which takes into account the hydrodynamic and direct collision interactions among micelles and allowed us to evaluate the stiffness parameter λ-1. The concentration c dependence of the hydrodynamic radius RH,app was divided into two contributions: growth of the individual “isolated” micelles with c and enhancement of hydrodynamic and direct collision interactions among micelles with c. The micellar length increases with increasing surfactant weight fraction ws or with raising the temperature T irrespective of the n-octanol content wo in the micelles. The length of the micelles at fixed ws and T steeply increases with increasing wo. The length of the C14E6 micelles is extremely larger than that of the C10E5 micelles. Both values of the cross-sectional diameter d and the stiffness parameter λ-1 increase with increasing wo. It has been found that the increase in d and λ-1 is more significant for the C10E5 micelles than for the C14E6 micelles (i.e., for the micelles of the surfactant with shorter hydrophobic chain length). The spacing s between the adjacent hydrophilic tails of the surfactant molecules on the micellar surface has been found to decrease gradually with increasing wo, where the s values of the C14E6 micelles are larger than those of the C10E5 micelles. Comparing the present results with the previous ones16,18 for the C10E5 and C14E6 micelles containing n-dodecanol, we have found salient changes in the micellar characteristics with uptake

Miyake et al. of n-alcohols as follows: (i) The total length Lw increases more significantly for the C14E6 micelles containing n-dodecanol than those containing n-octanol, whereas Lw of the C10E5 micelles increases by including n-dodecanol and n-octanol without a significant difference for the two alcohols. (ii) The values of d and λ-1 of the C10E5 and C14E6 micelles increase, and those of s decrease with uptake of n-octanol and n-dodecanol into the micelles. The increase of d and λ-1 is less significant for the C14E6 micelles in comparison with the C10E5 micelles, and the variation in the three parameters occurs with no difference in the effects for the two alcohols. Acknowledgment. The authors are grateful to Professor T. Sato of Osaka University for valuable discussions and 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. (2) Hamada, N.; Einaga, Y. J. Phys. Chem. B 2005, 109, 6990. (3) Imanishi, K.; Einaga, Y. J. Phys. Chem. B 2005, 109, 7574. (4) Einaga, Y.; Kusumoto, A.; Noda, A. Polym. J. 2005, 37, 368. (5) Shirai, Y.; Einaga, Y. Polym. J. 2005, 37, 913. (6) Einaga, Y.; Inaba, Y.; Syakado, M. Polym. J. 2006, 38, 64. (7) Shirai, S.; Yoshimura, S.; Einaga, Y. Polym. J. 2006, 38, 37. (8) Sato, T. Langmuir 2004, 20, 1095. (9) Koyama, R.; Sato, T. Macromolecules 2002, 35, 2235. (10) Benoit, H.; Doty, P. J. Phys. Chem. 1953, 57, 958. (11) Norisuye, T.; Motowoka, M.; Fujita, H. Macromolecules 1979, 12, 320. (12) Yamakawa, H.; Fujii, M. Macromolecules 1973, 6, 407. (13) Yamakawa, H.; Yoshizaki, T. Macromolecules 1979, 12, 32. (14) Yoshizaki, T.; Nitta, I.; Yamakawa, H. Macromolecules 1988, 21, 165. (15) Einaga, Y.; Totake, Y.; Matsuyama, H. Polym. J. 2004, 36, 971. (16) Miyake, M.; Einaga, Y. J. Phys. Chem. B 2007, 111, 535. (17) Miyake, M.; Einaga, Y. Polym. J. in press. (18) Einaga, Y.; Ebihara, M.; Uchida, U. Polym. J. in press. (19) Kanematsu, T.; Sato, T.; Imai, Y.; Ute, K.; Kitayama, T. Polym. J. 2005, 37, 65. (20) Ohshima, A.; Yamagata, A.; Sato, T.; Teramoto, A. Macromolecules 1999, 32, 8645. (21) Sato, T.; Ohshima, A.; Teramoto, A. Macromolecules 1998, 31, 3094. (22) Berne, B.; Pecora, R. Dynamic Light Scattering; J. Wiley: New York, 1976. (23) Vink, H. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1725. (24) Stepa´nek, P.; Brown, W.; Hvidt, S. Macromolecules 1996, 29, 8888. (25) Blankschtein, D.; Thurston, G. M.; Benedek, G. B. J. Chem. Phys. 1986, 85, 7268. (26) Cates, M. E.; Candau, S. J. J. Phys. Condens. Matter 1990, 2, 6869. (27) Zoeller, N.; Lue, L.; Blankschtein, D. Langmuir 1997, 13, 5258. (28) Combining eq 10 with eq 1 at θ ) 0, we obtain RH,app ) kBT/ 6πη0D (1 - Vc)2(1 + 2A2Mwc + ‚‚‚). The calculation of R/H by eq 13, thus, implies that the terms 2A2Mwc + ‚‚‚ are neglected in this equation (note that (1 - Vc)2 is close to unity at small c as in the present case). If the values of R/H accidentally coincide with those for the “isolated”micelles indicated by the dashed lines in Figure 6, it means that H(c) in eq 12 compensates for the term (1 + 2A2Mwc + ‚‚‚).