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J. Phys. Chem. 1992,96 , 6839-6843 6839(6)Spanhel, L.; Henglein, A.; Weller, H. Ber. Bunsen-Ges. Phys. Che m.(7)Henglein, A.; Gutilrrez, M.; eller, H.; Fojtik, A.; Jirkovsky, J. Ber.(8)Rabani, J. J . Phys. Chem. 1989, 93, 707.(9)Gerischer, H.; Labkc, M. J . Electroanal. Chem. 1986, 04, 225.(10)Vogel, R.; ohl, K.; Weller, H. Chem. Phys. Lett. 1990,174, 241.(11) Hotchandani, S.; amat, P. V. Chem. Phys. Lett. 1992, 191, 320.(12)Levy, B. In Photochemical Conversion and Storage oJSola r Energy;Pelizzetti, E., Schiavello, M., Eds.; Kluwer Academic Publishers: Boston,1991; 337.(13)Kam at, P. V.; D imitrijeviE; Fessenden, R. W. J . Phys. Chem. 1989,92, 324.(14) panhel, L.; Anderson, M. . J . A m . Chem. SOC.1991,113,2826.(15)Hotchandani,S.;Kamat, P. V. J. Electrochem.Soc. 1992,139, 630.(16)Kamat, P. V.; Patrick, B. J. Phys . Chem. , preceding paper in this(17)Kamat, P. V.; Das, S.; eorge Thomas, K.; George, M. V. Chem.

1987,109,6632.Bunsen-Ges. Phys. Chem. 1989, 3, 93.

issue.Phys. Lett. 1991, 78 , 75.

(18)Baral, S.; ojtik, A.; Weller, H.; Henglein, A. J . A m . Chem. Soc.(19)Kamat, P. V.; Ebbesen, T. W.; DimitrijeviE, N. M.; Nozik, A. J.(20)Kaschke, M.; rnsting, N. P.; Muller, U.; Weller, H. hem. Phys.

1986, 08, 375.Chem. Phys. Lett. 1989, 157, 84.Lett . 1990, 68, 43.(21)Hodes, G.; lbu-Yaraon, A.; Decker, F.; Motisuke, P. Phys. Rev. B

(22)Vlachopoulos. N.; Liska, P.; Auustynski, J.; Gritzel, M. J . Phys.(23)ORegan, B.; Moser, J.; Anderson, M.; Griitzel, M. J . Phys. Chem.(24)ORegan, B.; Griitzel, M.; Fitzmaurine, C. Chem. Phys. Lett . 1991,(25)Mening, R. Top. Curr. Chem. 1988, 43, 1.(26) a) Fan, F.-R.; Faulkner, L. J. Chem. Phys. 1978, 69, 3341. (b)Slgui, S.; otchandani, S.; addou, D.; Leblanc, R. M. J . Phys. Chem. 1991,95, 8807.

1987, 6,4215.Chem. 1988, 110, 1216.1990, 94, 720.183, 9.

Concentration Dependence of Micellar Size and Composltion in Mixed Anionlc/CationicSurfactant Solutions Studied by Light Scattering and Pulsed-Gradient FT-NMRSpectroscopy

Tadashi Kato,* Hidetomo Takeuchi, and Tsutomu SeimiyaDepartment of Chemistry, Faculty of Science, Tokyo Metropolitan University, Minamiohsawa, Hachioji,Toky o 192-03, Japan (Received: March 13, 1992)

Light scattering and pulsed-gradient lT-NMR spectroscopy (PGNMR) have been measured for aqueous solutions of sodiumdecanesulfonate (Cl,,S03)/octyltrimethylammoniumromide (OTAB ) and sodium octanesu lfonatefOTA B as a functionof total surfa ctant concentration,c , at different mixing ratios (the mole fraction of OTAB in the to tal mixed solute, x 2, is0 .1 4 5 ) . From the analysis of self-diffusion coefficients of su rfactant s obtained by P GN MR , the mole fraction of OTABin the mixed micelle, xZm,s determined. At concentrations much higher than the critical micelle concentration (cmc), xlmis close to x 2 . As c is decreased toward the cmc, x2"' is increased toward equimolar composition. These results suggest tha tmicelles grow with decreasing concentration. Light-scattering results are consistent with this prediction. It is also shownthat in the CI,,S03/OTABsystem, the mixed micelles grow rapidly when x~~ exceeds about 0.4.

IntroductionIt iswell-known that de ct ra ta ti c repulsion between like chargesof hea dgr oup of ionic surfacta nts is a major factor which inmasesthe free energy of micelle formation.' If other surfactants withoppositely charged headgroups are incorporated in to the micelles,the micelle aggregation number is therefore expected to increase.So he composition of mixed micelles is important for discussingmicellar properties in mixed anionic/c ationic surfacta nt solutions.In our previous s t ~ d ie s ,~ * ~e have measured the light-scatteringintensities and self-diffusion coefficients of su rfactants in dilutesolutions (below 0.035 m ~ l d m - ~ )f a sodium dodecyl sulfate(SDS)/octyltrimethylammonium romide (OTAB) system. Inthis system, precipitation occurs in th e range c =(1-3) Xor x2=0.35-0.95 where c is the total surfactant con-centrationand x2 is the mixing ratio expressed by the mole fractionof OTAB in the total mixed solute. So the measurements havebeen made in one phase region, Le., a mixed micelle region. Fromthe a nalyses of th e self-diffusion coefficients and light-scatteringintensities, it has been shown that in the SDS-rich side, as thephase boundary between the mixed micelle region and t he pre-cipitation region is approached, i.e., as x 2 is increased or c isdecreased, the fract ion of OT AB in m ixed micelles,xZm,ncreasesand micellar growth occurs. It has been also shown that the m ixedmicelles grow rapidly when x~~exceeds about 0.25.Although intereating phase behaviom of anionic/cation ic systemhave been reportedIc8 there are only a few papers dealing withmicellar properties,e12 nd none of them discusses the dependenceof micellar composition on the total surfactant concentration. Inthe present study, therefore, we extend the above line of approach0022-3654/92/2096-6839$03.00/0

to sodium decanesulfonate (Cl$3 03) /0T AB and sodium octa-nesulfonate (C8 S03 )/0T AB systems in order to examine thegenerality of our previous results. These systems were chosenbecause precipitation does not occur, so the critical m icelle con-centration (cmc) can be observed a t room temperature. At thesame time, the procedu re for determining m icellar compositionis partly modified.Experimental Section

Materials. Th e sample of OTAB was purchased from TokyoKasei Co. Ltd. (>98%) and purified by recrystallization fromacetone/diethyl ether mixed solvent. The samples of C l& 0 3andC 8 S 0 3were purchased from Tokyo Kasei Co. Ltd. for ion pairchromatography and were used without further purification.Water triply distilled from alkaline permanganate was used forthe light-scattering measurements. For P GN MR measurements,deuterium oxide purchased from Showa Denko Co. Ltd. (99.75%)was used.Light Scattering. Light-scattering intensities were measuredby using a H t N e aser (NEC GLC 601) and a photon-countingsystem composed of photomultiplier (Hamamatsu R649),homem ade discriminator, and univ ersal counter.13 A bsolute in-tensities were calculated using the Rayleigh ratio of benzene at632.8 nm, 1.184 X cm-l.14PulSed-Grpdkat ET-NMR. PG NM R measurements were madeon protons at 99.6 MH z using an internal D 2 0 ock on a JEOLFX-100 Fourier transform N M R spectrometer. Th e details ofthe measurements are similar to those already r e~ 0 rt ed .l ~heabsolute magnitude of the field gradient was calibrated ag ainst

0 1992 American Chemical Society


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6840 The Journal of Physical Chemistry, Vol. 96, No. 16, 1992the value of the self-diffusion coefficient of water a t 25 " C, 2 .30X m2 s-l, as reported by M ills.I6The selfd iffusion coefficient of O TAB , D2, was obtained fromthe echo signals for methyl gro ups bonded to nitrogen by usingthe equation

'42(6)/A2(0)=exP[-B(6)D21 (1)B(6) ( Y C ~ ) ~ ( A6/3)

where A2(S) /A2(0) re the ratio of peak heights in the presenceand absence of the gradient, 7 is the gyromagnetic ratio, G is themagnitude of the g radient, 6 is the duration of each g radient pulse,and A is the time between the two gradient pulses. In our ex-periments, G and A were kept constant at abo ut 0.087 T m-l and40-60 ms, respectively, and 6 is changed.The selfdiffusion coefficient of Cl,$03 (or C8 S0 3),D,, cannotbe determined directly because there are no peaks which ca n beassigned to C$O3 (C8S03)alone in the observed spin-echospectra. So we measured the peak heights of the methylene (orsometimes methy l) signals of the alkyl groups which can be ex-pressed as

A12(6)/A12(0) =(1 -Y z ) exP[-B(6)DI1 +Yz exp[-B(W21(2 )where y 2 epresents the contribution from OTAB . In the presentsystems, however, the observed AI2(6)/AI2(O) alues could be fittedto a single-exponential function within experimen tal errors. Thisindicates tha t th e differen ce between D1 and D2 is sm all and/o reither y, or y 2 is much smaller than unity.Equation 2 can be rearranged as

A12(6)/Al2(0) - Y2 exP[-B(6)D211 - Y 2 =exp[-Bt6)D11 (3)

If y 2 is known, D, can be calculated by plotting the left-hand sideof eq 4 against B(6) (D2 can be determined from eq 1). Takinginto account that the echo amplitude in the absence of the gradientis proportional to exp(-2A/ T2) (T,: he spi nsp in relaxation time)and th at the line width is inversely proportional to T,, 2 can beexpressed as

Kat0 et al.

where xZ Hs the fraction of methylene protons of OTAB and T2(1)and T2(2) are the Tis or CI,$03 (C8S 03) and O TAB, respec-tively. Unfortu nately, it is not possible to determine T2(1)andT2(2) in mixed systems. Therefo re, we calculated D, by usingeq 3 for two cases; i.e., y 2=0 and y 2=yZH. n both cases, theleft-hand side of eq 3 could be fitted to a single-exponentialfunction within experim ental error. However, the form er givesbetter fittings than th e latter does, suggestin g that y 2 s muchsmaller than x ~ ~ .his may be explained as follows. In theSDS/OTAB system, the self-diffusion coefficient of SDS an bedetermined directly from the signals of methylene gr o up bondedto oxygen. In this system, y 2 was found to be much smaller thanx ~ ~ .his comes from the fact tha t most of the O TAB m oleculesform micelles while there exist many SDSmonomers; that is, T2(1)>>T J 2 ) where 1 and 2 represent S DS a nd O TAB , respectively.Th is does not always hold true in the present systems. However,the a nalysis of diffusion coefficients obtained for y 2 =0 showsthat the fraction of OTAB in micellar states is larger than thatof C 1 8 0 3 r C 8 S 0 3 Plm/P2m 1, see later) for x 2


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Mixed A nionic/Cationic Surfactant Solutions The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6841

5 t

0 ' I0 5 10 15 20 25C / lO- 'm~l .dm-~

Figure 3, Self-diffusion coefficients of CI&303 closed symbols) andOTA B (open symbols)vs total surfactant concentration at x2=0.2 (0 ,0 ) , .3 (A, ), an d 0.5 (m, ) .

I , I

0' ' ' ' 1 '0 10 20 30C/ 10-' mol 0 dm-3

Figure 4. Self-diffusion coefficients of C&O, (closed symbols) andOTA B (open symbols)vs otal surfactant concentration at x 2=0.1 (0 ,0 ) , .3 (A, ), an d 0.5 (m, 0 ) .

0.6

0.5

R NX 0.4

0.3

0.20 5 10 15 20 25C/ 1 - mol. dm-3

Figure 5. Mole fraction of OTA B in a mixed micelle vs total surfactantconcentration a t different mixing raitos for the C l& 303 /0T AB system.The symbols are the same as in Figure 1.rapidly with concentration, suggesting that the existence of OT ABmolecules in the monomeric state cannot be neglected. However,we have found that x2"' ca n be determined without assumptionb for most systems. The modified procedu re is described in theAppendix.

F ' i i 5 shows the concentration d e p e n d " of x p at differentmixing ratios for the Cl& 03 /O TA B systems.21 It can be seenfrom the figure that at higher concentrations,x2"' is close to x2.As he total concentration is decreased toward the cmc, however,x2"' is increased toward the equimolar composition.22 Similarresults have been obtained in the C8S 03 /OT AB ystem althoug h

00 10 20 30C / 10-' mol dm-3

Figure 6. Mole fraction of OTA B in a mixed micelle vs otal surfactantconcentration a t different mixing raitos for the C8 S03 /OT AB system.The symbols are the same as in Figure 2.30

25In2 0>* 15z

10

500 10 20 30 40 50

c-c,,/10-~ g.cmq3Figure 7. Debye plot for the Cl&301 ystem . The symbols are the sameas in Figure 1.the extrapolation of xtm s c- mc seems ower than 0.5 exceptfor x 2 =0.5.*'DiscussionThe observed concentration dependences of x2"' in Figures 3and 4 uggest that micelles grow with decreasing concentrationexcept for x2=0.5. Similar results have been obtained in ourprevious tudy on the SDS /OT AB system. In this system, in fact,the light-scattering intensity increas es with decreasing concen-tration and diverges below a certain concentration. In the presentsystems, on the o ther hand , such an an omalo us behavior is notobserved in the light-scattering intensity itself. However, theexistence of points of inflection in the h - c curves in the Cl$03system may be correlated with the change in micelle aggregationnumber. So we tried to c alculate the reciprocal of the apparen tmicellar weight, W , btained from the Debye equation:

( 5 )/W =H ( c - CO)/(& - RwO)H =( 7r2$/h4NA)dv/dc)

where c and co are the total su rfactant concentration and th e cmctn g ~ m - ~ ,espectively, Rwo is the Rayleigh ratio a t the cmc, v1s the refractive index, X, is the wavelength under vacuum, andNA is Avogadro's number. Figure 7 hows the plots of 1 / Wagainst c - o for the Cl $0 3 system. If the micellar weight andcomposition are independent of conce ntration, 1 W can be ex-pressed as

( 6 )where k is proportional to the second virial coefficient of th eosmotic pressure. In the Cl$ 03/ OT AB system, the plots for x 2=0.2 nd 0.3have break points at c * 0.023 a nd 0.015 g - ~ m - ~(0.1 and 0.06 moldm -'), respectively. From the initial slopes for

1 / M * =( l /M ) [ l +k ( c - c o ) +...I


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6842 The Journal of Physical Chemistry, Vol. 96,No. 16, 1992 Kat0 et al.

50 0600 r V I

. 9 1* I I I

2001100i 100.2 0.3 0 .4 0 .5x;

Figure 8. Apparent aggregation number vs mole fraction of OTAB ina mixed micelle for the C,,+303 ystem. The symbols are the same as inFigure 1.x2 =0.2 and 0.3 in the Cl$03/O TA B system, k values wereobtained to be about 80 an d 110cm 3 g1 , espectively, using eq6. For pure C1$03 solutions, on the other hand, k is obtainedto be about 120 cm3.g-l from the data of Tart ar an d Lelong."For sph erical micelles of radius a, k may be expressed as23

k =u (8 +2 4 i p dx (1 +~ ) ~ [ 1e-u(x ) / (kn]) (7)x = ( r - 2a)/(2a)

where u is the specific volume in a micelle,r is the d istance betweenthe centers of two micelles, and V(x) s the intermicellar interactionpotential. Equation 7 demonstrates that k takes positive valueswhen repulsive interaction s between micelles are dom inant. Ifrepulsive interactions become weak, k is ther efore decreased. Inthe SDS solutions, for example, addition of only 0.01 m ol ~d m -~NaC l reduces the k value to half its in itial value.24 The additionof surfacta nts with oppositely charged headgroups d ecreases theelectrostatic repulsion between micelles far more effectively thanan inorg anic salt does. If the initial slope is determine d by in-termicellar interactions alone, it is therefore expected that k isdecreased rapidly with increasing x2.25 However, the k valuesobtained from the initial slope for x 2=0.3 is larger than that forx2=0.2 and nearly qu a l to that for pure Cl$03 solutions. T hesame holds true in the C8 S0 3 ystem. The k values for x 2=0.1and 0.3 were obtained to be about 30 and 50c"&, espectively,which ar e nearly equal to or larger than that in the pure C8 S0 3system" (about 30 cm3*g-l). These results can be explained ifthe m icellar weight itself decreases with increasing concentration.The slope above the break points in Figu re 7 may correspond tointermicellar repulsion because micellar com position depends onconcentration only slightly (see Figure 5 ) and hence the m icellarweight is considered to be alm ost constant in this co ncentratio nrange.In Figure 8, the apparent aggregation number obtained fromeq 5 and26

(8)is plotted against the micellar composition for the Cl $0 3/O TA Bsystemwhere MIand M2 re the molecular weight of C ,& 03 andOTAB, respectively. In spite of the fact that the data on variousmixing ratios and total surfactant co ncentratio ns are included ,most of the m fall on almost the sa me line; when xZm xceeds acertain value, about 0.4, the app arent aggregation number in-creases rapidly. We have already reported such a plot for theSDS/O TAB system. In this system, the apparent aggregationnumber begins to increase at x2, =0.25, which is lower than inthe Cl$0 3/0T AB system.Thus, he dependences of composition and aggregation numberof micelles on the concentrationobserved for thes e systems seemgeneral in mixed anionic /cationic surfactan t solutions. At con-centrations much higher than the cmc, x2, is close to x2 . As c

m* =M*/[ ( l - x J M I +x2M21

isdecreased toward the cmc, x2" is increased toward the equimolarcomposition. When the micellar composition exceeds a certainvalue, the micelle aggregation number increases rapidly. In somesystems where hydrophobic interactions between surfactantmolecules are strong, like the SDS/O TA B system, further changesin the micellar composition induce the precipitation.Conclusions

We have measured the light-scattering intensities and self-diffusion coefficients of su rfactant molecules in C l$0 3/O TA Band C8S03/O TAB ystems ( x2=0.14.5) here precipitationdoes not occur. Th e results may be summ arized as follows.1. The micellar composition (xZm)s nearly equal to the bulkcomposition ( x 2 )at concentrations much higher than the cmc.As the concentration decreases toward the cmc, however, thefraction of cationic sur facta nt in mixed micelles increases towardthe eq uimo lar composition.2. Such a change in micellar composition suggests micellargrowth with decreasing concentration. Light-scattering resultsare consistent with this prediction.3. Taking into account the results in the previous study on theSDS/OTAB system, the above results seem general in mixedanionic/cationic s urfac tant solutions whether precipitation occursor not.

Acknowledgment. This work was partially supported by aGrant-in-Aid for ScienMic Research (No. 02740235) to T.K. fromthe Ministry of Education (Japan). The present PGN MRmeasurements were cam ed out a t the Instrumental Center of IM S.Appendixcomposition ( x 2 9 can be written asIn a mixed micelle composed of surfactants 1 and 2, the micellar

X2" =PpX2/ [P lm(l - x2 ) +PpX2]=X2/[(PI"/P2")(1 - x2) +xzl ('41)

where Pi m i =1, 2) is the fraction of su rfactant m olecule i ina micellized state. When only one type of mixed micelle exists,the self-diffusion coefficient of each surf acta nt can be written asDI =( 1 - Plm)Dlf+PI"Dm (A2a)0 2 =(1 - P2")D,' +P2"Dm (A2b)where D,' ( i =1,2) and D , are th e self-diffusion coefficients ofthe m onomeric and m icellized surfac tant molecules, respectively.For pure surfa ctant solutions, below the cm c, the self-diffusioncoefficient of the surfactant ion, Dp, is almos t independent ofconcentration. So D, in eqs A2a an d A2b may be replaced byDp. Combining e q s A2a and A2b, we obtain

1

The 0: values are observed to be 5.73 X 1O-Io, 5.41 X and5.86 X lo-" m 2 d or C 8S0 3,cI $0 3, and OTAB, respectively.In t he present system s, the value of D I o D I is much larger thanthat of D20- D loat higher concentrations. Even a t the lowestamcentrationnear the cmc, these two values are in the sam e order.Taking into account that P I ms much smaller than unity near thecmc, we can replace eq A3 by the following equation with a goodapproximation:

PIm DIo- DIP2" D2O - D2 644)=-

Inserting eq A4 into eq Al, we can determine x2, from theobserved values of D 1 ,D2,DI o , nd D20.Registry No. OTAB, 2083-68-3; sodium decanesulfonate, 13419-61-9;sodium octanesulfonate, 5324-84-5.

References and Notes( 1 ) For example: Tanford, C . The Hydrophobic Effecf . Formarion ofMicelles & Biological Membranes; Why-Interscience: New York, 1980.


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J . Phys. Chem. 1992, 96,6843-6848 6843(2) Kato, T.; Iwai, M.; Seimiya, T. J . Colloid Interjace Sci. 1989,130,439(3) Kato, T.; Takeuchi, H.; Seimiya, T. J . Colloid Interface Sci. 1990,140,(4) Chen. D. H.; Hall, D. G. Kolloid Z . Z . Polym. 1973, 251, 41.(5) Barker, C. A,; Saul, D.; Tiddy, J. T.; Wheeler, B. A.; Willis. E. J .(6) Jolela, P.; Jonsson, B.; Wennerstrom, H. Prog. Colloid Polym. Sci.( 7 ) Stellner, K. L.; Amante, J. C.; Scamehorn, J. F.; Harwell, J. H. J .(8) Jokela, P.; Jonsson, B.; Khan, A. J . Phys. Chem. 1987, 91, 3291.(9) Anacker, E. A.; Underwood, A. L. J . Phys. Chem. 1987, 85, 2463.(10) Malliaris, A.; Binana-Limbele, W.; Zana, R. J . Colloid Interface Sci.(1 1) Hoffmann, H.; Klaus, J.; Schwander, B. Ber. Bunsen-Ges. Phys.(12) Yu, Z . ; Zhao, G. J. Colloid Interface Sc i. 1989, 130, 414.(13) Kato, T.; Anzai, S.; eimiya, T. J . Phys. Chem. 1990. 94, 7255.(14) Pike, E. R.; Pomeroy, W. R.; Vaughan, J. M. J . Chem. Phys. 1975,(15) Kato, T. J . Phys. Chem. 1985.89, 5750.(16) Mills, R. J . Phys. Chem. 1973, 77, 685.(17) Tarter, H. V.; Lelong, A. L. M. J . Phys. Chem. 1956, 59, 1185.(18) Klevens, H. B. J . Phys. Colloid Chem. 1948,52, 130.(19) Zhu, B. Y.; Rosen, M. J. J. Colloid Interface Sci. 1984, 99, 435.

and references therein.253.Chem. SOC.,Faraday Tram. I 1974, 70 , 154.1985, 70 , 17.Colloid Interface Sc i. 1986, 123, 186.

1986, 110, 114.Chem. 1987, 91 , 99.

62, 3188.

(20) Holland, P. M.; Rubingh, D. N. In Cationic Surjactants. PhysicalChemistry: Holland, P. M., Rubingh, D. N., Eds.; ekker: New York, 1991;p 141.(21) It should be noted that these xZm alues are calculated using D , valuesobtained for y 2=0 (see the Experimental Section). We have also calculatedxZm alues using D , values obtained for y 2 =x2". The differences betweenthese two x2"' values were 2-27% and 6-12% for the Cl$Ol/O TAB andC8SOl/O TAB systems, respectively. How ever, the conce ntration dependencesof xZm re almost the same, and the discussion in the following section is notaffected by these differences.(22) Motomura et al. have developed a method to determine the micellarcomposition at the cmc from the depende nce of the cmc on x2 using the phaseseparation model (Motomura, K.; amanaka, M.; Aratono, M. Colloid Po-lym. Sci . 1984, 262, 948). It may be interesting to compare xZmvaluesobtained by their method with the extrapolated value of x Zm s c - mc.However, the data points in the present study are not enough to calculate( & t n c / a ~ ~ ) ~ , ~hich is necessary for determining xZm.(23) Corti, M.; Degiorgio, V. J . Phys. Chem. 1981, 85, 711.(24) Calcu lated from the data of Huisman: Huisman, H. F. Proc. K. ed .Aka d. Wet. Ser. B Phys. Sci. 1964, 67 , 388.(25) In the C,$OI/O TAB system, the concentration of OTAB is increasedfrom 0.003 to 0.018 mol-dm-' as c is increased from the cmc to 0.06moldm"at x z =0.3.(26) In eq 8, xz should be replaced by xZm.However, this replacement doesnot affect tn* values very much because M, nd M 2 are not so different.

Relaxation Spectr a and Dipolar Correlations for Flexible Polymers with Bulky SideGroups

Ricardo Dhz-Calleja ,f Evaristo Riande,*.* and Julio Sa n R o m h *Departamento de Quimica- F@a. ETSI!, Universidad PolitScnica de Valencia, 46071 Valencia, Spain, andInstituto de Ciencia y Tecnologia de Polimeros (C SIC ). 28006 Madr id, Spain (Received: January 24, 1992)

The experimental intramolecular correlation coefficient gintra=1 +C i z j (os y,,) for poly(2-biphenyl acrylate) (PBP A)chains, where yv is the angle between the dipoles d a t e d with the i andj epeating units, is 0.694 at 30 OC and its temperaturecoefficient, d In gi,,/dT, has a value of 1.9 X lo-' K in the interval 30-60 OC. A two rotational states scheme developedearlier for poly(pheny1acrylate) (PP A) gives a goodaccount of the experimental values of gin, and d In gh,/dT for PBPAchains. The correlation coefficientg tha t includes inter- and intramolecular interactions is only somewhat lower than gin,,suggesting that intermolecular correlations are not very important in this polymer. The dielectric spectrum for the polymerin the bulk presents a glass-rubber relaxation, named a bsorption, followed by two processes in th e subglass region calledy and @ secondary absorptions. Results obtained by using thermally stimulated discharge (TSDC) techniques indicate thatthe mechanisms involved in the lower temperature process (y peak) have an activation energy that is significantly smallerthan that corresponding to the mechanisms that produce the @ relaxation. The dielectric strength of the combined subglassrelaxations ar e discussed in terms of conformational changes associated with the side groups. The coupling scheme is usedto interpret the dielectric and mechanical glass-rubber relaxations . On one hand, important conclusions are obtained relatedwith the relative complexity of the dielectric and mechanical a elaxations; on the other hand, the anomalous temperaturedependence of the glass-rubber relaxation is discussed in terms of the bulkiness of the side group.

IntroductionA relaxation process is characterized by its strength and locationin the time tem per atu re domain. In general, relaxation lossesin th e frequency domain ar e described by th e Kohlrauch-Wil-

liams-Watts (KWW)4(t) =exP(-t/.o)g (1)

in which the exponent 9 seems to be dependenton he nature ofthe physical proc es involved in the relaxation. Most of the resultsat hand seem to suggest that t he value of this quantity is largerfor a dielectric glass-rubber process tha n for a mechanical oneas a consequence of the comparatively wider distribution of re-laxation times exhibited by the amechan ical relaxation! On theother hand, whereas secondary relaxations exhibit Arrheniusbehavior, the temperature dependence of the relaxation times ofglass-rubber relaxations is governed by the free volume andUniversidad Polit&nica de Valqcia.*Institute de Ciencia y Tecnologia de Polimeros (CSIC).

therefore is described by the Vogel-Fulcher-Tammann-Hesse(VFTH)quation5(2 )

where T , is a reference tempe rature and B is proportional t o boththe reciprocal of the volume of the segmen t intervening in th erelaxation and the minimum required volume for a relaxationprocess to take place.6 Ther efore, B must be dependent on boththe material and th e nature of the physical process that intervenesin the relaxation.In recent years, a model has been developed tha t predicts tha tthe product TB for a given material must be invariant (independentof the probe),'-*so hat an important relaxationship is establishedbetween two variables that define the location of the a! processin the timete mperatu re domain. Testing the validity of this theoryrequires, using different physical methods, the study of theglass-rubber transition of polymers with different struc tures . Thisis one of th e aims of th e present work where the dielectric andmechanical glass-rubber relaxa tions of polymers with bulky sidegroups such as poly(Zbipheny1 acrylate) (PBPA ) are studied and

T =70 exp[B/(T - T , ) ]

0022-365419212096-6843$03.00/00 1992 American C hemical Society

micellar growth

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