Characteristics of Wormlike Pentaoxyethylene Decyl Ether C10E5

It has also been demonstrated that the apparent hydrodynamic radius RH,app(c) as a function of c is well described by a fuzzy cylinder theory which ta...
0 downloads 0 Views 225KB Size
Download PDF
J. Phys. Chem. B 2007, 111, 535-542

535

Characteristics of Wormlike Pentaoxyethylene Decyl Ether C10E5 Micelles Containing n-Dodecanol Maiko Miyake and Yoshiyuki Einaga* Department of Chemistry, Nara Women’s UniVersity Nara 630-8506, Japan ReceiVed: October 1, 2006; In Final Form: NoVember 13, 2006

The wormlike micelles formed with the surfactant pentaoxyethylene decyl ether C10E5 containing n-dodecanol were characterized by static (SLS) and dynamic light scattering (DLS) experiments. The SLS results have been analyzed with the aid of the light scattering theory for micelle solutions, thereby yielding the molar mass Mw(c) as a function of concentration c along with the cross-sectional diameter d of the micelle. The observed Kc/∆R0 as a function of c and the hydrodynamic radius RH as functions of Mw have been well described by the theories for the wormlike spherocylinder model. It has also been demonstrated that the apparent hydrodynamic radius RH,app(c) as a function of c is well described by a fuzzy cylinder theory which takes into account the hydrodynamic and direct collision interactions among micelles. Our previous results for the hexaoxyethylene dodecyl ether C12E6 micelles containing n-dodecanol were reanalyzed in the same scheme. It has been found that the micellar length increases with increasing concentration c or with raising temperature T irrespective of the composition of the C10E5 + n-dodecanol and C12E6 + n-dodecanol systems. The length of the micelles at fixed c and T steeply increases with increasing weight fraction wd of n-dodecanol in both systems. The growth of the micelles accompanies the increase of the cross-sectional diameter d of the micelles and the results that the surfactant molecules are more densely assembled with increasing wd in order to keep n-dodecanol molecules inside the micelles.

Introduction In the previous work on aqueous solutions of nonionic surfactant polyoxyethylene alkyl ethers H(CH2)i(OCH2CH2)jOH (abbreviated CiEj), we have investigated the characteristics of CiEj micelles such as the weight-average molar mass Mw, meansquare radius of gyration 〈S2〉, hydrodynamic radius RH, and intrinsic viscosity [η] as functions of surfactant mass concentration c by static (SLS) and dynamic light scattering (DLS) measurements and viscometry.1-7 We have determined the values of Mw(c) at a specified c along with the cross-sectional diameter d of the micelles from the analysis of the SLS data by using a molecular thermodynamic theory8,9 formulated with the wormlike spherocylinder model. It was then found that molar mass Mw dependence of 〈S2〉, RH, and [η] is 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. Aqueous solutions of the surfactant C12E5 containing an oil such as n-octane, n-decane, and n-dodecane were extensively studied,15-23 and it has been found that the surfactant with the oil self-assemble in variety of structures depending on surfactant concentration, oil content, and temperature. In the range of small oil content, C12E5 forms polymer-like or wormlike micelles at low concentrations c of the surfactant + oil in the L1 phase. The micelles grow in length with increasing c and the entanglement network is formed in the solution at sufficiently high concentrations. As the oil content is increased, the wormlike micelles are transformed to droplet microemulsions and the bicontinuous microemulsion structures are formed in the solution at high oil content. Menge et al.15-17 studied the n-decane + C12E5 + water system by SLS, DLS, and small angle neutron scattering (SANS)

measurements. They have shown that the apparent molar mass Mapp of the wormlike micelles formed in the L1 phase increases with c in the range of small c, passing through a maximum, and then decreases with increasing c at higher c. Here, Mapp includes two contributions, i.e., concentration-dependent molar mass Mw(c) of the micelles and concentration dependent structure factor S(c, q ) 0) (q is the magnitude of the scattering vector) which reflects thermodynamic interactions among micelles. The increase of Mapp at low c, thus, represents the increase of Mw(c), while the decrease of Mapp at high c is due to dominant contribution of S(c, q ) 0) to the SLS results and does not reflect size of the micelles. They have also found that the apparent hydrodynamic radius RH,app as a function of c exhibits a similar behavior to Mapp. Kwon and Kim24,25 have indicated that the aggregation number and the hydrodynamic radius of the micelles in the system phospholipid (DL-R-phosphatidylcoline dimyristoyl) + C12E5 + water increases as the amount of a phospholipid is increased, by forming wormlike micelles. Menge et al. or Kwon and Kim have demonstrated the C12E5 micelles in the L1 phase assume a flexible cylindrical shape and grow in size with increasing c and oil or phospholipid content. They, however, treat only the apparent quantities obtained by SLS and DLS experiments and have not evaluated Mw(c) and RH for the micelles by separating the contributions of the thermodynamic and hydrodynamic interactions to the SLS and DLS results. The concentration-dependent characteristics of the micelles in an isolated state is not determined unequivocally. In the present study, we have studied the micelles in the n-dodecanol + C10E5 + water system by SLS and DLS measurements. As in the case of the micelle solutions of simple CiEj mentioned above, we analyze the SLS and DLS results by using molecular thermodynamic8,9 and hydrodynamic theories26 in order to obtain the micellar characteristics by separating

10.1021/jp0664465 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/23/2006

536 J. Phys. Chem. B, Vol. 111, No. 3, 2007

Miyake and Einaga

contributions of the thermodynamic and hydrodynamic interactions among micelles. Our previous experimental results27 for the system n-dodecanol + C12E6 + water are also reanalyzed according to the present scheme. Experimental Section Materials. The surfactant C10E5 sample and n-dodecanol were purchased from Nikko Chemicals Co. Ltd. and Nakaraitesque Co., respectively, and used without further purification. The solvent water used was high purity (ultrapure) water prepared with SimpliLab 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. C10E5 micelle solutions were prepared by dissolving C10E5 in water with adding an appropriate amount of n-dodecanol 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-Dodecanol is 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 + n-dodecanol in the C10E5 + water + n-dodecanol ternary solutions. n-Dodecanol content in the C10E5 + ndodecanol mixtures is represented by its weight fraction wd. 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 various wd at 20.0 °C and for those of wd ) 0.0156 at various temperatures T. The ratio Kc/∆Rθ was obtained for each solution as a function of the scattering angle θ ranging from 30 to 150° and extrapolated to zero scattering angle to evaluate Kc/∆R0. Here, c is the mass concentration of surfactant + n-dodecanol, ∆Rθ is the excess Rayleigh ratio, and K is the optical constant defined as follows:

K)

4π2n2(∂n/∂c)2T,p 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 straight line with a negligible slope for all the micelle solutions studied. The values of the radius of gyration of the micelles were not able to be determined with sufficient accuracy. 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.1-5,7 In the present study, we have treated the micelle solutions as the binary system which consists of micelles containing n-dodecanol 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 10.0 °C < T < 40.0 °C,

(∂n/∂c)T,p ) 0.133 - 2.20 × 10-4(T - 273.15) (wd ) 0.0156) (2) (∂n/∂c)T,p ) 0.131 - 2.74 × 10-4(T - 273.15) (wd ) 0.0300) (3) (∂n/∂c)T,p ) 0.137 - 4.55 × 10-4(T - 273.15) (wd ) 0.0501) (4) (∂n/∂c)T,p ) 0.132 - 2.03 × 10-4(T - 273.15) (wd ) 0.0587) (5) Dynamic Light Scattering. DLS measurements were carried out to determine the mutual 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. The D values were obtained by the cumulant method for the normalized autocorrelation function g(2) (t). They are related to Kc/∆R0 and to the translational friction coefficient ζ of the solute particles moving relative to the solvent, i.e., the friction coefficient ζ in the solvent-fixed frame, by1,28-31

D)

( )

(1 - Vc)2MwkBT Kc ζ ∆R0

(6)

Here, V is the partial specific volume of the solute (micelle) and kB is the Boltzmann constant. After the Stokes relation, we define the apparent hydrodynamic radius RH,app by

ζ ) 6πη0RH,app

(7)

where η0 is the solvent viscosity. By eqs 6 and 7, we have evaluated RH,app of the C10E5 + n-dodecanol micelles at various wd and T. Note that since the micelles observed may have a range of sizes, the values of D and RH,app should be regarded as an average, but the effects of the distribution on the theoretical data analyses given below are not quantitatively estimated at present. Density. For all the micelle solutions containing n-dodecanol, the solution density F has been found to be independent of micelle weight fraction w and n-dodecanol content wd 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 F-1 0 . Results Phase Behavior. In Figure 1, cloud point curves are shown for the ternary system C10E5 + n-dodecanol + water at various wd. Here, the data points for the binary system C10E5 + water, i.e., wd ) 0 are the literature results by Imanishi and Einaga.3 We find that all the micelle solutions studied represent the phase separation behavior of the LCST (lower critical solution temperature) type and that the phase boundaries significantly shift to lower temperatures as wd increases. Figure 2 depicts the 3D phase diagrams for the micelle solutions containing n-dodecanol constructed from the cloud point data given in Figure 1, along with the literature results at wd ) 0.3 Here, ws is the weight fraction of the surfactant C10E5 in the solution.

Wormlike Pentaoxyethylene Decyl Ether C10E5 Micelles

J. Phys. Chem. B, Vol. 111, No. 3, 2007 537

Figure 1. Cloud point curves for the C10E5 + n-dodecanol + water system: The weight fraction wd of n-dodecanol in the C10E5 + n-dodecanol mixture is 0, 0.0156, 0.0300, 0.0501, and 0.0587 from top to bottom, respectively. The data points for wd ) 0 are the literature results of ref 3.

Figure 3. Plots of (Kc/∆R0) against c for the C10E5 + n-dodecanol + water system at various wd (T ) 20.0 °C) (a) and temperatures T (wd ) 0.0156) (b): (a) O, wd ) 0; K, wd ) 0.0156; y, wd ) 0.0300; k, wd ) 0.0501; Y, wd ) 0.0587; (b) T is 20.0, 25.0, 30.0, and 35.0 °C from top to bottom, respectively. The solid curves represent the theoretical values.

the micelles grow in molecular weight with increasing ndodecanol content or temperature. Discussion

Figure 2. Three-dimensional representation of the binodal surface for the C10E5 + n-dodecanol + water system: ws, weight fraction of C10E5 in the solution; wd, weight fraction of n-dodecanol in the C10E5 + n-dodecanol mixture. The data points for wd ) 0 are the literature results of ref 3.

Surprisingly, the binodal surface of a kind of shelf shape is seen at wd = 0.03 at large ws, although the cloud point curves are smoothly shifted with variation of wd. All the light scattering experiments have been performed in the L1 phase below the binodal surface. Light Scattering Results. In Figure 3a and b, Kc/∆R0 are plotted against c examined at various wd at T ) 20.0 °C and at various T at wd ) 0.0156, respectively. Here, the data points at wd ) 0 in Figure 3a were obtained by extrapolation of the literature data ( ref 3) at higher temperatures to T ) 20.0 °C. The solid curves represent the theoretical values calculated as described below. The data points at fixed wd in Figure 3a and at fixed T in Figure 3b follow a curve convex downward. The Kc/∆R0 value decreases with increasing wd or T, suggesting that

Analysis of SLS Data. In order to determine the Mw values of the micelles at a specific concentration c, we have analyzed the present SLS data by employing a light-scattering theory for micellar solutions formulated by Sato8,9 with 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 stiffness of the wormlike cylinder is represented by the stiffness parameter λ-1. The result for Kc/ ∆R0 reads

Kc 1 ) + 2A(c)c ∆R0 Mw(c)

(8)

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 is comprised of 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 strength ˆ of the attractive interaction between spherocylinders. In these, g2 represents the difference

538 J. Phys. Chem. B, Vol. 111, No. 3, 2007

Miyake and Einaga

Figure 5. The results of the curve fitting for the plots of Kc/∆R0 against c for the C12E6 + n-dodecanol + water system at various wd indicated and at T ) 25.0 °C: The solid and dashed curves represent the calculated values of Kc/∆R0 and 1/Mw(c), respectively.

Figure 4. The results of the curve fitting for the plots of Kc/∆R0 against c for the C10E5 + n-dodecanol + water system at various wd (T ) 20.0 °C) (a) and temperatures (wd ) 0.0156) (b) indicated: The solid and dashed curves represent the calculated values of Kc/∆R0 and 1/Mw(c), respectively.

in Gibbs free energy between surfactant molecules located in the end-capped portion and those in the central cylindrical portion of the micelle. We refer the expressions for the functions Mw(c) and A(c) to the original papers (refs 8 and 9) and our previous papers,1,3 since they are fairly involved. 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, n-dodecanol, and water. It has been assumed in the analyses that the composition of C10E5 + n-dodecanol in the micelles is given by wd. The weight average molecular weight of the C10E5 + n-dodecanol mixture calculated with a given wd was used as the surfactant molecular weight M0 required in the theoretical analysis. Figure 4a and b demonstrate the results of curve-fitting of the theoretical calculations to the experimental values of Kc/ ∆R0 for the micelle solutions of various wd indicated at 20.0 °C (a) and of wd ) 0.0156 at various T indicated (b), respectively. In Figure 5 are shown the results of reanalysis of the previous SLS data27 for the C12E6 + n-dodecanol micelle solutions of various wd at 25.0 °C. The solid curves in the figures represent the best-fit theoretical curves. It is seen that they are in good coincidence with the respective data points at given wd or T. The good agreement implies that the micelles containing n-dodecanol are well represented by the wormlike spherocylinder model. The dashed lines represent the values of 1/Mw(c) at respective wd or T. For all the micelles at any fixed wd and T, 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 findings1-5,7 for the micelles formed with single surfactant of various type. These results are in good agreement with the simple theoretical predictions derived from the thermodynamic treatments of multiple equilibria among micelles of various aggregation numbers.8,33-35 The increase in Mw(c), with increasing c and wd and with raising temperature, is consistent with the findings by Menge et al.15,16 for the C12E5 + n-decane micelles. 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, that is, the second term of the right-hand side of eq 8, to Kc/∆R0 are negligible at small c but progressively increase with increasing c as expected. As to the virial coefficient terms, it is predicted36,37 that the relation A(c)c ∝ c2 holds for the range of moderately concentrated or semiconcentrate solutions of real polymers. To confirm this, Kc/∆R0 - M-1 w is double-logarithmically plotted against c in Figure 6, where the solid straight line shows a slope of 2. We see that the data points for the two micelle solutions at various wd and T tend to a slope of 2 and to converge to a nearly single line at large c. The results may imply that both of the micelle solutions at log c > -1.5 belong to the semiconcentrate solutions. The data points are largely scattered due to the somewhat bad quality of the data. The scattering may be also caused by the variation of the stiffness of the two micelles with wd and T to some extent. The d value determined by the curve fitting was independent of T but varied with wd. The results of d for the C10E5 and C12E6 micelles containing n-dodecanol are listed in Tables 1 and 2, respectively. We find that d gradually increases with increasing wd. The present finding is in qualitative agreement with SANS results by Menge et al.17 for C12E5 micelles containing n-decane. In Figure 7, variation of g2 with wd (a) and with T (b) is shown for the C10E5 and C12E6 micelles containing n-dodecanol. For each micelle, g2 is an increasing function of wd and T, corresponding to the results that the micelles grow in length with increasing wd and raising temperature. The g2 values for the C10E5 micelles at 20.0 °C are slightly smaller than those for the C12E6 micelles at 25.0 °C. Considering from the previous findings that the g2 value for the CiEj micelles becomes larger for larger i or smaller j,5,7 the slight difference may be attributed to the difference in temperature examined. We have found that

Wormlike Pentaoxyethylene Decyl Ether C10E5 Micelles

J. Phys. Chem. B, Vol. 111, No. 3, 2007 539

Figure 6. Double-logarithmic plots of (Kc/∆R0) - M-1 w against c for the C10E5 + n-dodecanol + water at various wd (T ) 20.0 °C) (O), at various T (wd ) 0.0156) (B) and C12E6 + n-dodecanol + water at various wd (T ) 25.0 °C) (squares); O: pip up (wd ) 0.0156), pip right (wd ) 0.0300), pip down (wd ) 0.0501), pip left (wd ) 0.0587); B: pip right (T ) 25.0 °C), pip down (T ) 30.0 °C), pip left (T ) 35.0 °C); 0: pip up (wd ) 0.0261), pip right (wd ) 0.0311), pip down (wd ) 0.0490), pip left (wd ) 0.0755); The solid line represents a slope of 2.

TABLE 1: Characteristics of C10E5 Micelles Containing n-Dodecanol at 20.0 °C wd

d/nm

λ-1/nm

s/nm

0 0.0156 0.0300 0.0501 0.0587

2.6 2.6 2.9 3.0 3.4

35 25 35 35 40

1.12 1.11 1.05 1.03 0.97

a

a

Figure 7. g2 as a function of wd (a) and temperature (b): O, C10E5 + n-dodecanol + water; B, C12E6 + n-dodecanol + water

Cited from ref 3.

dynamic interactions which may be enhanced with c. In these two functions, RH(c) may be calculated by employing the equations formulated by Norisuye et al.11 for the wormlike 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 including d and the stiffness parameter λ-1. Their equation for RH reads

TABLE 2: Characteristics of C12E6 Micelles Containing n-Dodecanol at 25.0 °C

a

wd

d/nm

λ-1/nm

s/nm

0a 0.0261 0.0311 0.0490 0.0755

2.3 2.7 3.0 3.4 4.2

14 22 30 30 40

1.30 1.19 1.12 1.05 0.94

RH )

Cited from ref 1.

ˆ does not show clear systematic dependence on wd and T, taking roughly a constant value ˆ /kBT = 0.2 ( 0.1, although the results are not shown here. Hydrodynamic Radius of the Micelles. The values of RH,app determined by eqs 6 and 7 for the C10E5 + n-dodecanol micelles of various wd at 20.0 °C and of wd ) 0.0156 at various T and for the C12E6 + n-dodecanol micelles of various wd at 25.0 °C are double- logarithmically plotted against c in Figure 8a-c, respectively. It is found that at any given wd and T, 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)

(9)

where RH(c) represents the hydrodynamic radius of a “isolated” micelle which may grow in size with c and H(c) the hydro-

L 2f(λL,λd)

(10)

The expression for the function f is so lengthy that we refer it to the original papers.11-13 The weight-average micellar length Lw is related to Mw by

Lw )

4υ Mw πNAd

2

+

d 3

(11)

Here, the relation is derived from the micellar volume and Lw is used in place of L in eq 10. The Mw values as a function of c are obtained from the dashed lines in Figures 4 and 5. We are, thus, able to calculate RH(c) required in eq 9, by combining eq 10 with eq 11. The function H(c) in eq 9 may be calculated with the formulation given by Sato et al. 26,38,39 They 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 encapsulate a wormlike chain or a wormlike spherocylinder in the present case. Its effective length and diameter are evaluated from the wormlike

540 J. Phys. Chem. B, Vol. 111, No. 3, 2007

Miyake and Einaga

Figure 9. Double-logarithmic plots of RH,app against Mw for the C10E5 + n-dodecanol micelles with various wd indicated (T ) 20.0 °C) (a) and at various T indicated (wd ) 0.0156) (b): The solid and dashed curves represents the theoretical values (see Text).

Figure 8. Concentration dependence of RH,app for the C10E5 + n-dodecanol micelles with various wd indicated (T ) 20.0 °C) (a), for the C10E5 + n-dodecanol micelles at various T indicated (wd ) 0.0156) (b), and for the C12E6 + n- dodecanol micelles with various wd indicated and at T ) 25.0 °C (c): The solid curves represent the theoretical values (see Text).

chain parameters L, d, and λ-1. In the fuzzy cylinder theory, Sato et al. have taken into account the hydrodynamic interactions among fuzzy cylinders and also jamming effects of the cylinders on the longitudinal and transverse diffusion coefficients along and perpendicular to the chain end-to-end axis, respectively. Combining Sato et al.’s H(c), eqs 10 and 11 with the experimental results for Mw(c), we have calculated RH,app(c) by eq 9. The solid curves in Figure 8 are the theoretical values thus calculated. Here, we have used the d values obtained from the analyses of the SLS data and the values of λ-1 determined by the fitting the theoretical relations of RH vs Mw to the experimental results as described below. It should be noted that

the calculations have been accomplished without any adjustable parameter. As found in Figure 8, the theoretical results are favorably compared with the observed ones, although the data points are somewhat scattered and discrepancy between observed and calculated results are found in some cases, especially at large T in Figure 8b and at large wd in Figure 8c. The discrepancy shown in Figure 8b may result from variation of the stiffness of the micelles with temperature, although the theoretical curves are calculated with a constant value of the stiffness parameter λ-1 as seen in Figure 9b. Figures 9a, b, and 10 depict double-logarithmic plots of RH,app against Mw for the data given in Figures 8a-c, respectively. As Mw is decreased, i.e., as c is lowered, RH,app of each micelle with a given wd at fixed T decreases following the curve convex downward shown by the dashed line. In our previous papers, 1-3 it has been shown that in similar plots, the data points at different T asymptotically form a single composite curve at low c, or small Mw, implying that the effects of the intermicellar hydrodynamic interactions on RH,app become negligible in the asymptotic region of low c. The present results are similar to the previous findings. We, therefore, analyze the data points at the smallest Mw at each fixed T in Figures 9 and 10 by regarding them to provide the relationship between RH and Mw for “isolated” micelles. In the present analyses, we have calculated RH as a function of Mw by eqs 10 and 11 for various values of λ-1 with the use of the d values determined above from the SLS results. The solid lines in Figures 9 and 10 represent best-fit curves to the data points for the micelles of the smallest Mw with given wd and T. From the curve fitting, the values of λ-1 were

Wormlike Pentaoxyethylene Decyl Ether C10E5 Micelles

J. Phys. Chem. B, Vol. 111, No. 3, 2007 541

Figure 10. Double-logarithmic plots of RH,app against Mw for the C12E6 + n-dodecanol micelles with various wd indicated and at T ) 25.0 °C: The solid and dashed curves represents the theoretical values (see Text).

determined. The dashed curves indicate the theoretical values of RH,app calculated by eq 9 as mentioned above. It is found that the theoretical curves for RH,app describe the observed behavior fairly well, implying that the micelles may be represented with the wormlike spherocylinder model. The difference between the dashed and solid curves for fixed wd and T, 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). The λ-1 values obtained are summarized in Tables 1 and 2 for the C10E5 and C12E6 micelles containing n-dodecanol, respectively, along with the values of d. It is found that the λ-1 values of the C10E5 micelles are roughly constant or slightly increased with increasing wd, while those of the C12E6 micelles are more greatly increased with wd. The variation of λ-1 with wd seems to parallel the increase in d. It may be, thus, concluded that uptake of n-dodecanol into the micelles make them fat and stiff. Micellar Length. The weight-average length Lw of the C10E5 and C12E6 micelles containing n-dodecanol have been calculated by eq 11 from the values of Mw(c) and d obtained above from the analyses of the SLS data. Figures 11 and 12 show the results for the former micelles at T ) 20.0 °C and for the latter micelles at T ) 25.0 °C, respectively, as functions of the surfactant weight fraction ws and wd. Here, the previous results for the C10E5 and C12E6 micelles are reproduced as the data points at wd ) 0 from the literature.1,3 For both of the micelles at a given wd, Lw becomes larger as ws is increased. As seen in these figures, Lw at fixed ws steeply increases with increasing wd, i.e., with uptake of n-dodecanol into the micelles. The results are consistent with the finding by Menge et al.15 for the C12E5 micelles containing n-decane. Comparing the results in Figures 11 and 12, we find that Lw of the C12E6 micelles is larger than that of the C10E5 micelles. This is in correspondence with the results for g2 given in Figure 7a. The longer alkyl group in the surfactant molecule CiEj facilitate 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 the greater extent at higher temperatures. The difference in Lw between the C10E5 and C12E6 micelles containing n-dodecanol results from these three competitive effects.

Figure 11. ws and wd dependence of the length L for the C10E5 + n-dodecanol micelles at 20.0 °C.

Figure 12. ws and wd dependence of the length L for the C12E6 + n-dodecanol micelles at 25.0 °C.

In Figures 13, Lw of the C10E5 + n-dodecanol micelles with wd ) 0.0156 is plotted against c and T. The length Lw at fixed c significantly increases with raising temperature. This finding is in line with our previous results1-7 for the micelles of the single surfactant CiEj. It is also in qualitative agreement with the results reported by Menge et al. (ref 16) for the C12E5 + n-decane micelles and those by Kwon and Kim (ref 24) for the C12E5 + phospholipid micelles. Variation of the Micellar Characteristics with Uptake of n-Dodecanol. 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

542 J. Phys. Chem. B, Vol. 111, No. 3, 2007

Miyake and Einaga and C12E6 micelles. It has been found that the growth of the micelles accompanies the increase of the cross-sectional diameter d and the results that the surfactant molecules are more densely gathered with increasing wd in order to keep n-dodecanol inside the micelles. Acknowledgment. We 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

Figure 13. concentration and temperature dependence of the length L for the C10E5 + n-dodecanol micelles with wd ) 0.0156.

aggregation number Nw calculated from Mw. They are summarized in Tables 1 and 2 for the C10E5 and C12E6 micelles, respectively, along with the results for d and λ-1. We find that the s value is gradually decreased with increasing wd for both micelles. The results imply that the surfactant molecules are more densely assembled as the n-dodecanol content is increased, in order to keep them inside the micelles. Conclusions In this study, we have investigated the pentaoxyethylene decyl ether C10E5 micelles containing n-dodecanol by static (SLS) and dynamic light scattering (DLS) experiments by employing the same technique as used in the previous studies.1-5,7 The results of Kc/∆R0 from SLS have been analyzed with the aid of the thermodynamic theory8 for light scattering of micelle solutions formulated with wormlike spherocylinder model, thereby yielding the molar mass Mw(c) as a function of c along with the cross-sectional diameter d of the micelle. It is also found that the apparent hydrodynamic radius RH,app(c) as a function of the micellar concentration has been well described by the fuzzy cylinder theory by Sato et al.26,38,39 which takes into account the hydrodynamic and direct collision interactions among micelles. The hydrodynamic radius RH of the individual “isolated” micelles in the sufficiently dilute range have been well described as functions of Mw by the theories for the wormlike spherocylinder models, allowing us to evaluate the stiffness parameter λ-1. The previous results for the C12E6 + n-dodecanol micelles were also successfully reanalyzed in the present scheme. The good agreement found between the calculated and observed results for Kc/∆R0 and RH,app(c) as functions of c and for RH as a function of Mw indicates that the C10E5 and C12E6 micelles containing n-dodecanol assume a shape of flexible spherocylinders in dilute solutions. It has been found that the micellar length increases with increasing surfactant weight fraction ws or with raising temperature T irrespective of the n-dodecanol content wd. The length of the micelles at fixed ws and T steeply increases with increasing weight fraction wd of n-dodecanol in both of the C10E5

(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. Polymer J. 2005, 37, 368. (5) Shirai, Y.; Einaga, Y Polymer J. 2005, 37, 913. (6) Shirai, S.; Yoshimura, S.; Einaga, Y. Polymer J. 2006, 38, 37. (7) Einaga, Y.; Inaba. Y.; Syakado. M. Polymer J. 2006, 38, 64. (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) Menge, U.; Lang, P.; Findenegg, G. H. J. Phys. Chem. B 1999, 103, 5768. (16) Menge, U.; Lang, P.; Findenegg, G. H. Colloid Surf. A 2000, 163, 81. (17) Menge, U.; Lang, P.; Findenegg, G. H.; Strunz, P. J. Phys. Chem. B 2003, 107, 1316. (18) Bernheim-Groswasser, A.; Tlusty, T.; Safran, S. A.; Talmon, Y. Langmuir 1999, 15, 5448. (19) Strey, R. Colloid Polym. Sci. 1994, 272, 1005. (20) Komura, S.; Takeda, T.; Kawabata, Y.; Ghosh, S. K.; Seto, H.; Nagao. M. Phys. ReV. E. 2001, 63, 41402. (21) Hellweg, T.; Langevin, D. Phys. ReV. E. 1998, 57, 6825. (22) Hellweg, T.; Langevin, D. Phys. A 1999, 264, 370. (23) Hellweg, T.; von Klitzing, R. Phys. A 2000, 283, 349. (24) Kwon, S. Y.; Kim, M. W. Langmuir 2001, 17, 8016. (25) Kwon, S. Y.; Kim, M. W. Phys. ReV. Lett. 2002, 89, 258302. (26) Kanematsu, T.; Sato, T. Imai, Y.; Ute, K.: Kitayama, T. Polym. J. 2005, 37, 65. (27) Einaga, Y.; Totake, Y. Matsuyama, H. Polym. J. 2004, 36, 971. (28) Berne, B.; Pecora, R. Dynamic Light Scattering; J. Wiley: New York, 1976. (29) Vink, H. J. Chem. Soc., Faraday Trans. I. 1985, 81, 1725. (30) Stepanek, P.; Brown, W.; Hvidt, S. Macromolecules 1996, 29, 8888. (31) Some comments on the factor (1 - Vc)2 in eq 6 may be in order. When the friction coefficient ζ 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 at constant T and pressure p of the chemical potential µ0 of the solvent by the equation including the factor (1 - Vc) as explicitly given by Berne and Pecora. (ref 28) 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 Stepanek et al.30 and Yamakawa.32 The manipulation of the equations, thus, finally results in the factor (1 - Vc)2 in the expression of D as given by eq 6. 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.32 It is, however, emphasized that eq 6 should be taken as a definition of ζ in a sense and that other expressions of D, including the first power of (1 Vc), may be derived when different definition of ζ is employed. (32) Yamakawa, H. Modern Theory of Polymer Solutions, Chapter 4; Harper and Row: New York, 1971. (33) Blankschtein, D.; Thurston, G. M.; Benedek, G. B. J. Chem. Phys. 1986, 85, 7268. (34) Cates, M. E.; Candau, S, J. J. Phys. Condens. Matter 1990, 2, 6869. (35) Zoeller, N.; Lue. L.; Blankschtein, D. Langmuir 1997, 13, 5258. (36) Casassa, E. F.; Berry. G. C. Polymer Solutions. In ComprehensiVe Polymer Science; Allen. G., Ed.; Pergamon Press: New York, 1988. (37) Berry. G. C. AdV. Polym. Sci. 1994, 114, 233. (38) Ohshima, A.; Yamagata. A.; Sato, T.; Teramoto. A. Macromolecules 1999, 32, 8645. (39) Sato. T.; Ohshima, A.; Teramoto. A. Macromolecules 1998, 31, 3094.