Polymer Journal, Vol. 37, No. 5, pp. 368–375 (2005)
Effects of Hydrophobic Chain Length on the Micelles of Heptaoxyethylene Hexadecyl C16E7 and Octadecyl C18E7 Ethers
y Yoshiyuki EINAGA, Ai KUSUMOTO, and Akane NODA
Department of Chemistry, Nara Women’s University, Kitauoya Nishi-machi, Nara 630-8506, Japan
(Received January 4, 2005; Accepted February 1, 2005; Published May 15, 2005)
ABSTRACT: Micelles of heptaoxyethylene hexadecyl C16E7 and octadecyl C18E7 ethers in dilute aqueous solu- tions were characterized at finite surfactant concentrations c by static (SLS) and dynamic light scattering (DLS) experi- ments at several temperatures T below the critical points, in order to examine the effects of hydrophobic chain length on size, shape, structure, etc., of the micelles. The SLS results were successfully analyzed by the thermodynamic theory
formulated with wormlike spherocylinder model for SLS of micelle solutions, thereby yielding the molar mass Mw of the micelles as a function of c and the cross-sectional diameter d, indicating that the micelles assume a flexible spher- 2 1=2 ocylindrical shape. The radius of gyration hS i and hydrodynamic radius RH of the micelles as functions of Mw were found to be also well described by the corresponding theories for the wormlike spherocylinder or wormlike chain mod- els. The micelles grow in size with increasing T to greater length for longer hydrophobic chain, i.e., alkyl group of the surfactants. They were rather flexible compared to the micelles formed with other polyoxyethylen alkyl ethers. The cross-sectional diameter d and spacings s between adjacent hexaoxyethylene chains on the micellar surface were sim-
ilar in the C16E7 and C18E7 micelles. [DOI 10.1295/polymj.37.368] KEY WORDS Polyoxyethylene Alkyl Ether / Micelle / Light Scattering / Diffusion Coefficient / Hydrodynamic Radius / Radius of Gyration / Wormlike Chain /
Nonionic surfactants polyoxyethylene mono-alkyl lutions by SLS and DLS measurements. The SLS data ether H(CH2)i(OCH2CH2)jOH, hereafter abbreviated have been analyzed by using the thermodynamic theo- 17,18 as CiEj, form polymerlike micelles in dilute aqueous ry of light scattering for micellar solutions to yield solution (L1 phase) below the lower consolute phase the molar mass Mw of the micelle as a function of sur- boundary. The micelles are known to grow in size factant concentration, along with values of the cross- with increasing surfactant concentration and raising sectional diameter d. The results of the hydrodynamic 2 temperature, in particular when approaching the phase radius RH and mean-square radius of gyration hS i as boundary. The polymerlike micelles have certain sim- functions of Mw have been found to be well described ilarities to real polymers and have been, thus, charac- by the corresponding theory19–22 with wormlike spher- terized with the use of experimental techniques em- ocylinder or chain model, providing the information ployed in the polymer solution studies, such as static of the micellar size, structure, and intrinsic flexibility. (SLS) and dynamic light scattering (DLS),1–6,9 small- In this work, we have applied the same method to 10–12 12,13 angle neutron scattering (SANS), viscometry, micelles of heptaoxyethylene tetradecyl C16E7 and oc- 2–5 pulsed-field gradient NMR, and so forth. However, tadecyl C18E7 ethers, in order to investigate effects of the micelles possess the essential difference from the hydrophobic chain length of the surfactant mole- polymers that the micellar size and its distribution, cules on the micellar characteristics. in general, depend on surfactant concentration, tem- perature, intermicellar thermodynamic interactions, EXPERIMENTAL and other factors. It is formidably difficult to achieve separate evaluation of the micellar growth and the en- Materials hancement of the intermicellar interactions as func- High-purity C16E7 and C18E7 samples were pur- tions of surfactant concentration. Therefore, the inter- chased from Nikko Chemicals Co. Ltd. and used with- pretations given hitherto for the observed results out further purification. The solvent water used was especially by the SLS and DLS experiments are not high purity (ultrapure) water prepared with Simpli unequivocal. Lab water purification system of Millipore Co. In the previous papers, we have studied C12E6 and 14 15 C14E6 micelles, C14E8,C16E8, and C18E8 micelles, Phase Diagram 16 and C10E5 and C10E6 micelles, in dilute aqueous so- Cloud-point temperatures of given test solutions
yTo whom correspondence should be addressed (E-mail: [email protected]).
368 Micelles of Heptaoxyethylene Hexadecyl and Octadecyl Ethers
were determined as the temperatures at which intensi- measured at 25.0, 35.0, and 45.0 C for C16E7 micelle ty of the laser light transmitted through the solution solutions, and at 38.0, 42.0, and 46.0 C for C18E8 mi- abruptly decreased when temperature was gradually celle solutions, at 632.8 nm with a Union Giken R601 raised, by the fact that the originally transparent solu- differential refractometer. The results were 0.1314 3 3 tions became turbid. cm /g for C16E7 solutions and 0.1116 cm /g for C18E7 solutions, irrespective of temperature. Static Light Scattering SLS measurements were performed to obtain the Dynamic Light Scattering weight-average molar mass Mw of the C16E7 and DLS measurements were carried out to determine C18E7 micelles. The scattering intensities were meas- the translational diffusion coefficient D for the mi- ured for each solution and for the solvent water at celles in water at various temperatures in the one scattering angles ranging from 30 to 150 and at phase (L1 phase) region below or between the phase temperatures T ranging from 30.0 to 45.0 C for C16E7 separation boundaries shown below by the use of solutions and from 38.0 to 44.0 C for C18E7 solutions. the same apparatus and light source as used in the The ratio Kc=ÁR was obtained for each solution as a SLS studies described above. The normalized autocor- function of and extrapolated to zero scattering angle relation function gð2ÞðtÞ of scattered light intensity to evaluate Kc=ÁR0. Here, c is the surfactant mass IðtÞ, i.e., concentration, ÁR is the excess Rayleigh ratio at , hIð0ÞIðtÞi and K is the optical constant defined as gð2ÞðtÞ¼ ð2Þ hIð0Þi2 2 2 2 4 n ð@n=@cÞT;p K ¼ 4 ð1Þ was measured at scattering angles ranging from 30 NA0 to 150. with NA being the Avogadro’s number, 0 the wave- All the test solutions studied are the same as those length of the incident light in vacuum, n the refractive used in the SLS studies. From the data for gð2ÞðtÞ,we index of the solution, ð@n=@cÞT;p the refractive index determined D by the equation increment, T the absolute temperature and p the pres- ð2Þ 2 ð1=2Þ ln½g ðtÞÀ1¼ð1=2Þ ln f À K1t þÁÁÁ ð3Þ sure. The plot of Kc=ÁR vs. sin ð=2Þ affords a good 2 straight line for all the micelle solutions studied. The D ¼ lim K1=q ð4Þ apparent mean-square radius of gyration of the mi- q!0 celles was determined from the slope of the straight Here, f is the coherent factor fixed by the optical sys- line as described below. tem, K1 is the first cumulant, and q is the magnitude of The apparatus used is an ALV DLS/SLS-5000/E the scattering vector defined as light scattering photogoniometer and correlator sys- 4n tem with vertically polarized incident light of q ¼ sinð=2Þð5Þ 632.8 nm wavelength from a Uniphase Model 1145P 0 He–Ne gas laser. For a calibration of the apparatus, It should be noted that the D values should be regard- the intensity of light scattered from pure benzene ed as the z-average, since the micelles observed may was measured at 25.0 C at a scattering angle of 90, have distribution in size. where the Rayleigh ratio RUvð90Þ of pure benzene for unpolarized scattered light with polarized incident Density light at a wavelength of 632.8 nm was taken as The solution density required for the calculation 11:84  10À6 cmÀ1.23,24 of c and the partial specific volume v was measured The micellar solutions were prepared by dissolving at 25.0, 35.0, and 45.0 C for C16E7 micelle solutions, appropriate amount of the surfactant in water. Com- and at 38.0, 42.0, and 46.0 C for C18E7 micelle solu- plete mixing and micelle formation were achieved tions with a pycnometer of the Lipkin–Davison type. by stirring using a magnetic stirrer at least for one For both C16E7 and C18E7 micelle solutions, was day. The solutions thus prepared were optically puri- independent of w. Thus, we have used literature val- fied by filtration through a membrane of 0.20 mm pore ues of the density 0 of pure water at corresponding size and transferred into optically clean NMR tubes of temperatures for , and the v values of the micelles À1 10 mm diameter which was used as scatterring cells. have been calculated as 0 . The weight concentrations w of test solutions were de- termined gravimetrically and converted to mass con- RESULTS AND DISCUSSION centrations c by the use of the densities of the solu- tions given below. Phase Behavior The refractive index increment ð@n=@cÞT;p was Figure 1 depicts phase diagrams of the C16E7 +
Polym. J., Vol. 37, No. 5, 2005 369 Y. EINAGA,A.KUSUMOTO, and A. NODA
60 3.0 ° ° : 30.0 C : 40.0 C C16E7 2.5 : 35.0 °C : 45.0 °C
C E -1 55 16 7
2.0 /mol g ) 50 0 R ∆ 1.5 / Kc
45 ( 6 1.0 C 10 ° / T 40 0.5
C18E7 0.0 35 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 102c/g cm-3 30 Figure 2. Plots of (Kc=ÁR0) against c for the C16E7 micelle solutions at various T indicated. 25 0.0 0.01 0.02 0.03 0.04 0.05
w 4.0 : 38.0 °C : 42.0 °C C18E7 3.5 : 40.0 °C : 44.0 °C
Figure 1. Cloud Point Curves of the C16E7 + water (filled -1 circles) and C18E7 + water (unfilled circles) systems. 3.0 /mol g
) 2.5 0 R
∆ water (filled circles) and C E + water (unfilled cir- / 2.0
18 7 Kc ( cles) systems. The cloud point curves for both the 7 1.5 10 C16E7 and C18E7 micelle solutions represent phase 1.0 separation boundaries of the LCST (lower critical so- 0.5 lution temperature) type, above which the solutions 0 phase-separate into two phases. The LCST of the for- 0 2 4 6 8 10 12 mer system is higher by about 5 C than that of the lat- 103c/g cm-3 ter. The C18E7 + water system has another phase boundary of the UCST (upper critical solution temper- Figure 3. Plots of (Kc=ÁR0) against c for the C18E7 micelle ature) type in addition to that of the LCST type. Thus, solutions at various T indicated. the C18E7 micelles are stable only in the limitted tem- perature range in between the two phase boundaries. monomer, by representing chemical potentials of the micelles as functions of c with the free energy param- Static Light Scattering eter g2 which controls micellar formation and growth, Kc=ÁR0 for all the solutions of the C16E7 and and the strength ^ of the attractive interactions be- C18E7 micelles at various temperatures are plotted tween spherocylindrical micelles, in a similar way to against c in Figures 2 and 3, respectively. The data the classical mean-field and recent molecular theoret- 25–27 points at fixed T follow a curve convex downward ical approaches. As a result, the number-Nn and whose curvature becomes slightly less significant as weight-average aggregation number Nw of the mi- T is increased. The Kc=ÁR0 value at fixed c decreases celles have been formulated as functions of c along with increasing T. with the micellar size distribution functions. Then, As mentioned in the Introduction, we have analyzed he has derived the equation for light scattering of mi- the present SLS data by employing a light-scattering celle solutions by using the chemical potentials. The 17 theory for micellar solutions formulated by Sato result for Kc=ÁR0 reads with wormlike spherocylinder model for polymerlike Kc 1 micelles, in order to determine the M values of the ¼ þ 2AðcÞc ð6Þ w ð Þ micelles at finite concentrations c. The model consists ÁR0 Mw c of a wormlike cylinder of contour length L À d with where MwðcÞ is the weight-average molar mass of the cross-sectional diameter d and two hemispheres of di- micelles and AðcÞ is the apparent second virial coeffi- ameter d which cap both ends of the cylinder. Stiff- cient in a sense that it is comprised of the second, ness of the wormlike cylinder is represented by the third, and the higher virial coefficient terms. Both À1 stiffness parameter . Sato has dealt with multiple are functions of c, containing three parameters d, g2, equilibrium between micelles of different sizes and and ^. We refer the expressions for the functions
370 Polym. J., Vol. 37, No. 5, 2005 Micelles of Heptaoxyethylene Hexadecyl and Octadecyl Ethers
17,18 MwðcÞ and AðcÞ to the original papers or our pre- have determined the Mw values of each micelles as a vious paper,14 since they are fairly involved. function of c. The dashed lines represent the values of In Figures 4 and 5 are demonstrated the results of 1=MwðcÞ at respective temperatures. For all the mi- curve-fitting of the theoretical calculations to the ex- celles at any fixed T, they have a slope of À0:5, show- 1=2 perimental values of Kc=ÁR0 for the C16E7 and C18E7 ing that Mw increases with c as Mw / c in the range micelle solutions, respectively. Here, the solid curves of c examined, as in the case of the previous findings 14 represent the best-fit theoretical values calculated by for the C12E6 and C14E6 micelles, C14E8,C16E8, and 15 16 eq 6 by choosing the proper values of d, g2, and ^. C18E8 micelles, and C10E5 and C10E6 micelles. It is seen that the solid curves are in good coincidence These results are in good correspondence with simple with the respective data points at given temperatures. theoretical predictions derived from the thermody- The agreement between the calculated and observed namic treatments of multiple equilibria among mi- 17,25–27 results implies that the C16E7 and C18E7 micelles in celles of various aggregation numbers. The sol- dilute aqueous solutions are represented by the worm- id and dashed curves tend to coincide with each other like spherocylinder model. From the curve fitting, we at small c and the difference between them steadily in- creases with increasing c. The results indicate that contributions of the virial coefficient terms to −5.5 Kc=ÁR0 are small at small c but progressively in- C16E7 ] crease with increasing c as expected. -1 −6.0 The d value chosen in the curve-fitting procedure is
/mol g 2.5 nm for both C16E7 and C18E7 micelles at any T ) 0
R studied. The values of g2 and ^ determined are plotted ∆ −
/ 6.5 against T in Figures 6 and 7, respectively. It is found Kc ( that when compared at fixed T, the g2 value is larger − log [ 7.0 in the C18E7 micelles than in the C16E7 micelles. For each micelle, g2 is an increasing function of T, though
−7.5 degree of the increase is small in the former micelles. −3.0 −2.5 −2.0 −1.5 These results for g2 may reflect the fact that alkyl log (c/g cm-3) group of the surfactant molecules is longer in C18E7 than in C16E7 but the length of oxyethylene group is Figure 4. The results of the curve fitting for the plots of Kc= the same for both the surfactant. The values of ^ for ÁR0 against c for the C16E7 micelle solutions at various T: Sym- the C18E7 micelle solutions are larger than those for bols have the same meaning as those in Figure 2. The solid and the C16E7 micelle solutions, although the differences dashed curves represent Kc=ÁR0 and 1=MwðcÞ, respectively. Tem- are rather small. peratures T are 30.0, 35.0, 40.0, and 45.0 C from top to bottom, respectively. Molar Mass Dependence of Radius of Gyration We have determined the apparent mean-square 2 radius of gyration hS iapp for the C16E7 and C18E7 − 2 6.5 C18E7 micelles from the slope of the Kc=ÁR vs. sin ð=2Þ ] -1
23 /mol g ) 0 R
∆ / −7.0 22 Kc (
log [ 21 2 g 20 −7.5 −3.0 −2.5 −2.0 -3 log (c/g cm ) 19
Figure 5. The results of the curve fitting for the plots of 18 Kc=ÁR0 against c for the C18E7 micelle solutions at various T: 30 35 40 45 Symbols have the same meaning as those in Figure 3. The solid T/°C and dashed curves represent Kc=ÁR0 and 1=MwðcÞ, respectively. Temperatures T are 38.0, 40.0, 42.0, and 44.0 C from top to bot- Figure 6. Temperature dependence of g2 for the C16E7 + tom, respectively. water (filled circles) and C18E7 + water (unfilled circles) systems.
Polym. J., Vol. 37, No. 5, 2005 371 Y. EINAGA,A.KUSUMOTO, and A. NODA
0.35 2.5 : 38.0 °C : 42.0 °C : 40.0 °C : 44.0 °C
0.34 ) /nm 1/2 app
^ ε 〉 2.0
0.33 2 S (〈 log 0.32
C18E7
1.5 0.31 6.8 7.0 7.2 7.4 7.6 30 35 40 45 log M T/°C w
Figure 9. Double-logarithmic plots of hS2i1=2 against M for Figure 7. Temperature dependence of ^ for the C16E7 + app w the C E micelles at various T indicated. The solid curve repre- water (filled circles) and C18E7 + water (unfilled circles) systems. 18 7 sents the theoretical values calculated by eqs 8 and 9. plot, on the basis of the fundamental light scattering L 1 1 1 equation 2hS2i¼ À þ À ð1 À eÀ2LÞð8Þ 6 4 4L 82L2 Kc 1 1 2 2 ¼ 1 þ hS iq þ 2A2c þÁÁÁ ð7Þ Here, the values of Lw calculated by ÁR MwðcÞ 3 4vM d at finite concentrations by using the M ðcÞ values de- L ¼ w þ ð9Þ w w 2 NAd 3 termined as described above. Here, A2 is the second 2 2 virial coefficient and hS i is denoted by hS iapp, since were used in place of L in eq 8. it may possibly be affected by intermicellar interac- In the calculation, the d value 2.5 nm obtained in tions and then concentration-dependent. Molar mass the preceding section was used and then the value of 2 1=2 À1 Mw dependence of hS iapp is exhibited in Figures 8 was determined as 25.0 nm for the C16E7 micelles and 9 for the C16E7 and C18E7 micelles, respectively, and 22.0 nm for the C18E7 micelles to achieve the at various T indicated. All the data points for each mi- best-fit to the observed results. It is found that the cal- celle form a single composite curve irrespective of culated results well explains the observed behavior of 2 1=2 temperature and concentration, implying that the val- hS iapp, although the theoretical curves deviate up- 2 1=2 ues of hS iapp determined at finite c correspond to ward from the observed values at small Mw especially those for the individual micelles free from inter- and for the C16E7 micelles for the reason that cannot be intra-micellar interactions or excluded volume effects. specified at present. The agreement again shows that The solid curves show the best-fit theoretical values of the C16E7 and C18E7 micelles assume a wormlike hS2i for the wormlike chain model calculated by22 shape in dilute aqueous solution.
Hydrodynamic Radius of the Micelle 3 From the mutual diffusion coefficient D determined : 30.0 °C : 40.0 °C : 35.0 °C : 45.0 °C from DLS results by eq 4, the apparent hydrodynamic
) radius RH,app as a function of c has been evaluated 14,28,29 /nm by
1/2 2 app
〉 ð1 À vcÞ M @ 2 2
S D ¼ ð10Þ
(〈 60NARH,app @c T;p log where M is the molar mass of the solute, 0 is the sol- vent viscosity, and ð@=@cÞ is the osmotic compres- C16E7 T;p sibility. In this evaluation, we have used the SLS data 1 6 7 8 for ð@=@cÞT;p together with the values of MwðcÞ ob- tained in the previous section in place of M. The val- log Mw ues of RH,app thus determined at various T are plotted 2 1=2 against c in Figures 10 and 11 for the C E and Figure 8. Double-logarithmic plots of hS iapp against Mw for 16 7 the C16E7 micelles at various T indicated. The solid curve repre- C18E7 micelles, respectively. It was found that at sents the theoretical values calculated by eqs 8 and 9. any given T, RH,app increases with increasing c.It
372 Polym. J., Vol. 37, No. 5, 2005 Micelles of Heptaoxyethylene Hexadecyl and Octadecyl Ethers
1600 5 ° ° : 30.0 °C : 40.0 °C : 30.0 C : 40.0 C C16E7 1400 : 35.0 °C : 45.0 °C : 35.0 °C : 45.0 °C 1200 4 Å / 1000 H,app /nm
800 R 3 H,app log R 600
400 2
200
0 1 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 6.0 6.5 7.0 7.5 8.0 2 -3 10 c/g cm log MW
Figure 10. Concentration dependence of RH,app for the C16E7 Figure 12. Double-logarithmic plots of RH,app against Mw for micelles at indicated T. the C16E7 micelles at various T indicated. The solid curve repre- sents the theoretical values calculated by eqs 9 and 11.
300 : 38.0 °C : 42.0 °C : 40.0 °C : 44.0 °C : 38.0 °C : 42.0 °C 250 C18E7 : 40.0 °C : 44.0 °C 3.5 200 Å / /nm 150 H,app H,app R
R 3.0
100 log
50 2.5
0 0 2 4 6 8 10 12 103c/g cm-3 7.0 7.2 7.4
log Mw Figure 11. Concentration dependence of RH,app for the C18E7 micelles at indicated T. Figure 13. Double-logarithmic plots of RH,app against Mw for the C18E7 micelles at various T indicated. The solid curve repre- sents the theoretical values calculated by eqs 9 and 11. should be noted that the RH,app values do not necessa- rily correspond to those for ‘‘isolated’’ micelles. The 19 increase of RH,app may reflect two effects; micellar lated by Norisuye et al. for the wormlike spherocy- growth in size and enhancement of the effects of the linder model and by Yamakawa et al.20,21 for the intermicellar hydrodynamic interactions with increas- wormlike cylinder model, as a function of L with in- ing c. cluding the parameters d and À1. From these theo- In Figures 12 and 13, RH,app are double-logarithmi- ries, we may derive the expression for RH as a func- À1 cally plotted against Mw for C16E7 and C18E7 mi- tion of L, d, and over the entire range of L celles, respectively. In our previous papers,14–16 it including the sphere, i.e., the case L ¼ d. It reads has been shown that in similar plots, the data points L at different T asymptotically form a single composite R ¼ ð11Þ H 2f ðL;dÞ curve at small Mw, or at small c, suggesting that the effects of the intermicellar hydrodynamic interactions The expression for the function f is so lengthy that we 19–21 on RH,app become less significant as c is lowered and refer it to the original papers. By eqs 9 and 11, the are negligible in the asymptotic region of low c. The theoretical values of RH have been calculated as a À1 present results are similar to the previous findings. function of Mw for various values of with the Thus, we analyze the data points at small Mw at each use of the d values 2.5 nm determined above for the fixed T in Figures 12 and 13 by regarding them to C16E7 and C18E7 micelles. Here, the Lw values calcu- give the relationship between RH and Mw for the ‘‘iso- lated by eq 9 were again used in place of L in eq 11. lated’’ micelles. In Figures 12 and 13, the solid lines are best-fit curves The translational diffusion coefficient D is formu- to the data points for which the effects of the intermi-
Polym. J., Vol. 37, No. 5, 2005 373 Y. EINAGA,A.KUSUMOTO, and A. NODA cellar hydrodynamic interactions are considered to be for each of the micelles at a few or several tempera- negligible. We note that the data of RH,app for the tures examined in this study. The weight-average con- C16E7 micelles at 45.0 C are not avilable at small tour length Lw was calculated by eq 9 from the values Mw or in other word at low c in Figure 12. It is found of MwðcÞ and d obtained above. For each micelle, Lw that the theoretical curves well describe the observed becomes larger as c is increased or T is raised. It is behavior of RH as a function of Mw, implying that the found that the micelles grow to a greater length as micelles observed may be represented with the worm- longer the alkyl chain length of the surfactant mole- like spherocylinder model. The data points at fixed T cules. This result may come from the thermodynamic steeply increase with Mw deviating upward from the reason that attractive interactions among C18E7 mole- solid curve due to the enhancement of the intermicel- cules are stronger than among C16E7 molecules as lar hydrodynamic interactions with increasing c. demonstrated above by the values of g2 (see Figure 6). The curve fittings yield a À1 value of 6.0 nm for The spacings s between the hydrophilic tails of ad- À1 both C16E7 and C18E7 micelles. These values jacent surfactant molecules on the micellar surface are are considerably smaller than those obtained above evaluated from the values of d, Lw, and the aggrega- 2 from the analysis of hS i. These differences may be at- tion number Nw calculated from Mw. The s value ob- tributed to the fact that there is a distribution in micel- tained is ca. 1.37 nm for the C16E7 micelles and ca. 2 1=2 lar size and different averages are reflected in hS iapp 1.41 nm for the C18E7 micelles irrespective of c and 17,27 and RH. It has been theoretically shown that the T. The result indicates that the micelles are formed highly extended micelles have the most probable dis- and grow in the way that the hydrophilic groups of tribution in size and the distribution affords a value ca. the CiE7 molecules are located at intervals of these s 2 as the ratio of the weight-average aggregation num- values on the micellar surface on the average. These ber Nw to the number-average Nn irrespective of T and s values are not significantly different from each other, c. It is anticipated that the ratio Nw=Nn ¼ 2 is realized presumably reflecting that the hydrophilic groups are at the limit of extensive micellar growth, which can be the same in the two surfactants. 1=2 ascertained by the setup of the relation Mw / c as observed in Figures 4 and 5 in the present case. Thus, CONCLUSIONS the micelles observed in this study are considered to have the most probable distribution in size and the dis- In the present work, we have determined shape, À1 2 1=2 tribution affects the evaluation of from hS i size, and flexibility of the C16E7 and C18E7 micelles and RH. at finite surfactant concentrations c from SLS and À1 The value from RH indicate that the present mi- DLS experiments by employing the same method as 14–16 celles of C16E7 and C18E7 are rather flexible compared used in the previous study for the CiEj micelles. to the micelles of other CiEj molecules studied previ- The results of Kc=ÁR0 from SLS have been analyzed ously.14–16 with the aid of the thermodynamic theory17 for light scattering of micelle solutions formulated with worm- Micelle Structure like spherocylinder model. The analyses have yielded Figure 14 shows concentration dependence of Lw the molar mass MwðcÞ as a function of c and the cross- sectional diameter d. The good agreement between the calculated and observed Kc=ÁR0 as a function of c in- 15 dicates that the present micelles assume a shape of wormlike spherocylinders in dilute solutions. The mean-square radius of gyration hS2i and the hy- 45.0 10 T/ °C = 44.0 drodynamic radius RH of the individual ‘‘isolated’’ mi- /nm 40.0 celles as functions of M ( M ðcÞ) have been suc-
w w w L
-3 cessfully described by the corresponding theories for 10 40.0 the wormlike chain and the wormlike spherocylinder 5 models, respectively. The values of the stiffness pa- rameter À1 evaluated from the fitting of the calculat- 30.0 2 ed values for hS i or RH to the experimental results 0 have revealed that the micelles are far from rigid rods 0 1 2 3 4 but rather flexible. 102c/g cm-3 It has been found that the C18E7 micelles grow in
Figure 14. Concentration dependence of Lw for the C16E7 length to a greater extent than the C16E7 micelles. (filled circles) and C18E7 (unfilled circles) micelles at various T The finding may imply that attractive interactions indicated. among surfactant molecules, by which micelles are
374 Polym. J., Vol. 37, No. 5, 2005 Micelles of Heptaoxyethylene Hexadecyl and Octadecyl Ethers formed, are stronger in the C18E7 micelles with longer Langmuir, 12, 2894 (1996). hydrophobic chain of alkyl group, as clearly evi- 11. G. Jerke, J. S. Pedersen, S. U. Egelhaaf, and P. denced by the large differences in the free energy pa- Schurtenberger, Langmuir, 14, 6013 (1998). 12. O. Glatter, G. Fritz, H. Lindner, J. Brunner-Papela, R. rameter g2. On the other hand, the cross-sectional di- ameter d of the cylindrical micelles and the spacings s Mittelbach, R. Strey, and S. U. Egelhaaf, Langmuir, 16, of the adjacent hydrophilic chains on the micellar sur- 8692 (2000). 13. T. R. Carale and D. Blankschtein, J. Phys. Chem., 96, 455 face have been found to have approximately the same (1992). values for the C16E7 and C18E7 micelles. 14. S. Yoshimura, S. Shirai, and Y. Einaga, J. Phys. Chem. B, 108, 15477 (2004). Acknowledgment. The authors are grateful to 15. N. Hamada and Y. Einaga, J. Phys. Chem. B, in press. Prof. Takahiro Sato at Osaka University, Japan and 16. K. Imanishi and Y. Einaga, J. Phys. Chem. B, in press. also to members of the NKO Academy for valuable 17. T. Sato, Langmuir, 20, 1095 (2004). discussions and comments. 18. R. Koyama and T. Sato, Macromolecules, 35, 2235 (2002). 19. T. Norisuye, M. Motowoka, and H. Fujita, Macromolecules, 12, 320 (1979). REFERENCES 20. H. Yamakawa and M. Fujii, Macromolecules, 6, 407 (1973). 21. H. Yamakawa and T. Yoshizaki, Macromolecules, 12,32 1. A. Bernheim-Groswasser, E. Wachtel, and Y. Talmon, (1979). Langmuir, 16, 4131 (2000). 22. H. Benoit and P. Doty, J. Phys. Chem., 57, 958 (1953). 2. W. Brown, R. Johnson, P. Stilbs, and B. Lindman, J. Phys. 23. E. R. Pike, R. W. Pomeroy, and J. M. Vaughan, J. Chem. Chem., 87, 4548 (1983). Phys., 62, 3188 (1975). 3. T. Kato and T. Seimiya, J. Phys. Chem., 90, 1986 (1986). 24. Y. Einaga, T. Mitani, J. Hashizume, and H. Fujita, Polym. J., 4. W. Brown and R. Rymden, J. Phys. Chem., 91, 3565 (1987). 11, 565 (1979). 5. W. Brown, Z. Pu, and R. Rymden, J. Phys. Chem., 92, 6086 25. D. Blankschtein, G. M. Thurston, and G. B. Benedek, (1988). J. Chem. Phys., 85, 7268 (1986). 6. T. Imae, J. Phys. Chem., 92, 5721 (1988). 26. M. E. Cates and S. J. Candou, J. Phys.: Condens. Matter, 2, 7. W. Richtering, W. Burchard, and H. Finkelmann, J. Phys. 6869 (1990). Chem., 92, 6032 (1988). 27. N. Zoeller, L. Lue, and D. Blankschtein, Langmuir, 13, 5258 8. T. Kato, S. Anzai, and T. Seimiya, J. Phys. Chem., 94, 7255 (1997). (1990). 28. B. J. Berne and R. Pecora, ‘‘Dynamic Light Scattering,’’ 9. H. Strunk, P. Lang, and G. H. Findenegg, J. Phys. Chem., John Wiley & Sons, New York, N.Y., 1976. 98, 11557 (1994). 29. P. Stepanek, W. Brown, and S. Hvidt, Macromolecules, 29, 10. P. Schurtenberger, C. Cavaco, F. Tiberg, and O. Regev, 8888 (1996).
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