effects of protonation on the viscoelastic properties of tetradecyldimethylamine oxide micelles

8
Effects of Protonation on the Viscoelastic Properties of Tetradecyldimethylamine Oxide Micelles Hiroshi Maeda,* Atsushi Yamamoto, ² Makoto Souda, ² Hideya Kawasaki, ² Khandker S. Hossain, Norio Nemoto, and Mats Almgren § Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan, Department of Molecular and Material Sciences, IGSES, Kyushu UniVersity, Fukuoka 812-8581, Japan, and Department of Physical Chemistry, Uppsala UniVersity, Uppsala, S-751 21 Sweden ReceiVed: January 9, 2001; In Final Form: March 22, 2001 Marked effects of protonation (ionization) of tetradecyldimethylamine oxide on the viscoelastic properties of the micelle solutions were found. The effect strongly suggests the short-range attractive interaction between the headgroups of the nonionic (deprotonated) and the cationic (protonated) species. The zero shear viscosity reached a maximum at the half-ionized state (the degree of ionization R) 0.5) and the value was larger than that of the nonionic species (R) 0) or the cationic species (R) 1) by more than 2 orders of magnitude. At a surfactant concentration C of 0.1 mol/kg, approximately single Maxwell behavior was observed as R approached 0.5 from either side. For the half-ionized micelles (R) 0.5) in 0.1 mol/kg NaCl solutions, the steady-state compliance J e 0 decreased with C with an exponent of 2.1 ( 0.2, suggesting the presence of an entangled network of flexible threadlike micelles. The relaxation time, on the other hand, exhibited a nonlinear dependence on C. It was about 0.1 s and remained nearly constant in the range C > 0.1 mol/kg (regime I), whereas it increased with C in the range of C < 0.09 mol/kg (regime II) with an exponent slightly larger than 1. The single Maxwell behavior was observed in regime I. The regime shift was not controlled by the ratio C/m s , m s representing the NaCl concentration. Effects of NaCl concentration and the temperature on the viscoelastic properties were also examined at R) 0.5. Cryo-transmission electron micrographs clearly showed a highly entangled network in the solution for R) 0.5, while much smaller micelles for R) 0. Contrary to the expectation from the rheological results, a highly entangled network was also observed in the solution for R) 1. Introduction Viscoelastic surfactant solutions have been intensively studied over many years, both theoretically and experimentally. 1-19 These solutions contain long flexible or semiflexible micelless often referred to as threadlike or wormlikesthat become entangled at high concentrations. The transient networks formed by entangled long threadlike micelles exhibit properties similar to those of semidilute and concentrated polymer solutions, with an important difference in that micelles can pass through each other, under certain conditions, by opening and reclosing (phantom network). It has been suggested that in some micelle solutions the networks are cross-linked. The micelle threads are branched and fused with one another. The joints are character- ized by high fluidity. 9,10 Strongly viscoelastic micelle solutions have been found to form on the interaction of cationic micelles with certain groups of counterions, mostly aromatic counterions such as salicylate, 4,5,18,19 tosilate, 14 and naphthalenesulfonates. 17 In some systems, cosurfactants play an essential role for high viscoelasticity to appear. 20 Viscoelastic properties of micelle solutions have been reviewed by Hoffmann 20,21 and others. 22 Theoretical aspects of the rheological properties of micelle solutions have been extensively developed by Cates and others. 23-29 Evidence for entanglement and branching of thread- like micelles has also been obtained from self-diffusion measurements 30-32 and cryo-electron microscopy. 33-34 Alkyldimethylamine oxide has been used mostly as a nonionic surfactant but it exists as either a nonionic or a cationic (protonated form) species, depending on the pH of the aqueous solution. The properties of the solution vary with pH. The effects of protonation have been extensively studied on dodecyldim- ethylamine oxide (C12DAO) and tetradecyldimethyamine oxide (C14DAO) and the results are summarized in a recent review. 35 In the half-ionized or half-protonated state, a number of properties differ significantly from those expected as average properties of an 1:1 mixture of the nonionic and the cationic species. The aggregation number or micelle size exhibited a maximum 36-40 and the critical micelle concentration (cmc) showed a minimum 40-42 around the half-ionized state (R) 0.5). The degree of ionization (protonation) is denoted as R. The peculiar behavior observed at R) 0.5 indicates that a strong attractive interaction occurs between the nonionic and the cationic headgroups, and this has led to the hypothesis of the hydrogen bonding between the nonionic and the cationic species at the surface of the micelles. 37,43-44 This in turn indicates that protonation takes place more readily on the surface of nonionic micelles than for the monomeric state in solutions. 45-47 The effects of protonation on the aqueous-phase behavior, 48 on the solid-phase behavior, 49,50 and the aggregate morphology formed on mica surfaces 51 were also examined. Recently, a cooperative diffusion mode was observed in the dynamic light scattering of solutions of C14DAO at the half-ionized composition (R) 0.5), indicative of the presence of entangled long micelles. 40 Long threadlike micelles were also suggested from a SANS study. 52 In the present study, viscoelastic properties of tetradecyldim- ethylamine oxide (C14DAO) solutions are examined with * Author to whom correspondence should be addressed. E-mail: h. [email protected]. ² Department of Chemistry, Faculty of Sciences, Kyushu University. Department of Molecular and Material Sciences, IGSES, Kyushu University. § Department of Physical Chemistry, Uppsala University. 5411 J. Phys. Chem. B 2001, 105, 5411-5418 10.1021/jp0101155 CCC: $20.00 © 2001 American Chemical Society Published on Web 05/18/2001

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Page 1: Effects of Protonation on the Viscoelastic Properties of Tetradecyldimethylamine Oxide Micelles

Effects of Protonation on the Viscoelastic Properties of Tetradecyldimethylamine OxideMicelles

Hiroshi Maeda,*,† Atsushi Yamamoto,† Makoto Souda,† Hideya Kawasaki,†Khandker S. Hossain,‡ Norio Nemoto,‡ and Mats Almgren§

Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan, Department ofMolecular and Material Sciences, IGSES, Kyushu UniVersity, Fukuoka 812-8581, Japan, and Department ofPhysical Chemistry, Uppsala UniVersity, Uppsala, S-751 21 Sweden

ReceiVed: January 9, 2001; In Final Form: March 22, 2001

Marked effects of protonation (ionization) of tetradecyldimethylamine oxide on the viscoelastic properties ofthe micelle solutions were found. The effect strongly suggests the short-range attractive interaction betweenthe headgroups of the nonionic (deprotonated) and the cationic (protonated) species. The zero shear viscosityreached a maximum at the half-ionized state (the degree of ionizationR ) 0.5) and the value was larger thanthat of the nonionic species (R ) 0) or the cationic species (R ) 1) by more than 2 orders of magnitude. Ata surfactant concentrationC of 0.1 mol/kg, approximately single Maxwell behavior was observed asRapproached 0.5 from either side. For the half-ionized micelles (R ) 0.5) in 0.1 mol/kg NaCl solutions, thesteady-state complianceJe

0 decreased withC with an exponent of 2.1( 0.2, suggesting the presence of anentangled network of flexible threadlike micelles. The relaxation time, on the other hand, exhibited a nonlineardependence onC. It was about 0.1 s and remained nearly constant in the rangeC > 0.1 mol/kg (regime I),whereas it increased withC in the range ofC < 0.09 mol/kg (regime II) with an exponent slightly larger than1. The single Maxwell behavior was observed in regime I. The regime shift was not controlled by the ratioC/ms, ms representing the NaCl concentration. Effects of NaCl concentration and the temperature on theviscoelastic properties were also examined atR ) 0.5. Cryo-transmission electron micrographs clearly showeda highly entangled network in the solution forR ) 0.5, while much smaller micelles forR ) 0. Contrary tothe expectation from the rheological results, a highly entangled network was also observed in the solution forR ) 1.

IntroductionViscoelastic surfactant solutions have been intensively studied

over many years, both theoretically and experimentally.1-19

These solutions contain long flexible or semiflexible micellessoften referred to as threadlike or wormlikesthat becomeentangled at high concentrations. The transient networks formedby entangled long threadlike micelles exhibit properties similarto those of semidilute and concentrated polymer solutions, withan important difference in that micelles can pass through eachother, under certain conditions, by opening and reclosing(phantom network). It has been suggested that in some micellesolutions the networks are cross-linked. The micelle threads arebranched and fused with one another. The joints are character-ized by high fluidity.9,10 Strongly viscoelastic micelle solutionshave been found to form on the interaction of cationic micelleswith certain groups of counterions, mostly aromatic counterionssuch as salicylate,4,5,18,19tosilate,14 and naphthalenesulfonates.17

In some systems, cosurfactants play an essential role for highviscoelasticity to appear.20 Viscoelastic properties of micellesolutions have been reviewed by Hoffmann20,21 and others.22

Theoretical aspects of the rheological properties of micellesolutions have been extensively developed by Cates andothers.23-29 Evidence for entanglement and branching of thread-like micelles has also been obtained from self-diffusionmeasurements30-32 and cryo-electron microscopy.33-34

Alkyldimethylamine oxide has been used mostly as a nonionicsurfactant but it exists as either a nonionic or a cationic(protonated form) species, depending on the pH of the aqueoussolution. The properties of the solution vary with pH. The effectsof protonation have been extensively studied on dodecyldim-ethylamine oxide (C12DAO) and tetradecyldimethyamine oxide(C14DAO) and the results are summarized in a recent review.35

In the half-ionized or half-protonated state, a number ofproperties differ significantly from those expected as averageproperties of an 1:1 mixture of the nonionic and the cationicspecies. The aggregation number or micelle size exhibited amaximum36-40 and the critical micelle concentration (cmc)showed a minimum40-42 around the half-ionized state (R )0.5). The degree of ionization (protonation) is denoted asR. Thepeculiar behavior observed atR ) 0.5 indicates that a strongattractive interaction occurs between the nonionic and thecationic headgroups, and this has led to the hypothesis of thehydrogen bonding between the nonionic and the cationic speciesat the surface of the micelles.37,43-44 This in turn indicates thatprotonation takes place more readily on the surface of nonionicmicelles than for the monomeric state in solutions.45-47 Theeffects of protonation on the aqueous-phase behavior,48 on thesolid-phase behavior,49,50and the aggregate morphology formedon mica surfaces51 were also examined. Recently, a cooperativediffusion mode was observed in the dynamic light scattering ofsolutions of C14DAO at the half-ionized composition (R ) 0.5),indicative of the presence of entangled long micelles.40 Longthreadlike micelles were also suggested from a SANS study.52

In the present study, viscoelastic properties of tetradecyldim-ethylamine oxide (C14DAO) solutions are examined with

* Author to whom correspondence should be addressed. E-mail: [email protected].

† Department of Chemistry, Faculty of Sciences, Kyushu University.‡ Department of Molecular and Material Sciences, IGSES, Kyushu

University.§ Department of Physical Chemistry, Uppsala University.

5411J. Phys. Chem. B2001,105,5411-5418

10.1021/jp0101155 CCC: $20.00 © 2001 American Chemical SocietyPublished on Web 05/18/2001

Page 2: Effects of Protonation on the Viscoelastic Properties of Tetradecyldimethylamine Oxide Micelles

emphasis on the effect of protonation. The solutions weredirectly observed by CryoTEM.

Experimental Section

Material and Sample Preparation.C14DAO samples wereprepared as reported previously.40 The surfactant concentrationC and the NaCl concentrationms were in mol kg-1 or molal.The oscillatory shear, the shear flow, and shear creep measure-ment were performed with a stress-controlled rheometer (Carri-MED CSL-100 England) with a cone plate (plate diameter 6cm, 2° angle) and a parallel plate type geometry (plate diameter4 cm). The storage modulusG′(ω) and the loss modulusG′′-(ω) were measured as functions of angular frequencyω from100 to 0.1 rad/s at temperatures varying from 25 to 55°C. Thedynamic measurements were made at strain amplitude levelswhere the dynamic moduli are strain independent. A solventtrap equipped with the rheometer was used to protect the samplefrom evaporation. Solutions were kept for at least 1 day beforemeasurements. The temperature was controlled within 0.1°C.

Results

Effects of Ionization. In Figure 1, the dynamic shear storagemodulus G′(ω) and the loss modulusG′′(ω) of C14DAOsolution (C ) 0.1 mol kg-1) in 0.1 mol kg-1 NaCl are shown

as functions of the degree of ionization of micelles in the rangeof frequency ω between 0.4 and 100 rad/s. For both thenonionic(R ) 0) and the cationic (R ) 1) micelles, viscoelas-ticities were very low. As the degree of ionizationR approached0.5 from either side,G′ andG′′ both increased and reached therespective maximum values atR ) 0.5.

In Figure 2, the Cole-Cole plots of the data are shown. Asclearly indicated by a hemicircle in this type of plot, singleMaxwell type of relaxation is observed atR ) 0.5, whereas thebehavior was non Maxwellian atR values smaller than 0.4 andgreater than 0.6. In the case of the Maxwell behavior,G′ andG′′ are given as follows in terms of the relaxation timeτΜ andthe elastic modulusGM:

The viscosityη was given byη ) τMGM. The data exhibitingnon-Maxwell behavior obtained atR values other than 0.5 werefitted to the following relations in the low-frequency range (theterminal relaxation region).

Viscosities were evaluated by eq 3. We evaluated the terminalrelaxation time by eq 2 and the values are given in Figure3B.The steady-state shear complianceJe

0 was evaluated by eq4 and is shown in Figure 3A.

At R ) 0.5,τ exhibits a maximum andJe exhibits a minimum.We measured the viscosity of the solutions also by creepmeasurements and the flow measurements by a rotating vis-cometer. The viscosity showed reversible shear-thinning orthixotropy atR ) 0.5. Zero-shear viscositiesη0 were evaluatedby extrapolating the data to zero shear rate. Viscosities fromthe three different methods gave essentially identical results andthey all showed the maximum atR ) 0.5. The data obtainedfrom oscillatory shear method are shown in Figure 3C. It isnotable that the viscosity increased by nearly 3 orders ofmagnitude for a change ofR from eitherR ) 0 or 1 to R )0.5.

Effects of the Surfactant Concentration. Effects of thesurfactant concentration,C, were examined atR ) 0.5 in 0.1mol kg-1 NaCl in the range of 0.04 and 0.5 mol kg-1, as shownin Figure 4. The corresponding Cole-Cole plots are shown inFigure 5 and we could discriminate two concentration regimes

Figure 1. Angular frequencyω dependence of (A) storage shearmodulusG′, and (B) loss shear modulusG′′ for C14DAO solutionswith different degree of ionizationR at C ) 0.1 mol kg-1, ms ) 0.1mol kg-1. Symbols forR are (b) 0, (0) 0.24, (4) 0.4, (O) 0.5, (3) 0.6,(]) 0.75, (2) 1.

Figure 2. Cole-Cole plots for C14DAO solutions with differentR atC ) 0.1 mol kg-1, ms ) 0.1 mol kg-1. Symbols forR are (b) 0, (0)0.24, (4) 0.4, (O) 0.5, (3) 0.6, (]) 0.75, (2) 1.

G′(ω) ) GMω2τM2/(1 + ω2τM

2),

G′′(ω) ) GM ωτM/(1 + ω2τM2) (1)

G′(ω) ) ητω2 (2)

G′′(ω) ) ηω (3)

Je0 ) τ/η (4)

5412 J. Phys. Chem. B, Vol. 105, No. 23, 2001 Maeda et al.

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characterized of different relaxation mechanisms. In the con-centrated solutions (regime I,C > 0.2 mol kg-1), single Maxwellrelaxation behavior is found, while no such behavior is seen inthe range of low concentrations (regime II,C < 0.09 mol kg-1).In regime I, the data were analyzed by eq 1 andτM and GM

were evaluated. Zero-shear viscosity was evaluated byGMτM.In regime II, the data were analyzed by eqs 2-4. TheJe

0 andGM

-1 decrease withC with an exponent 2.1( 0.2 over thewhole range ofC examined, as shown in Figure 6A.

This scaling relation indicates the presence of a networkformed by the entanglement of long threadlike micelles in thesolution. It is likely that this scaling holds over the whole rangeof C, irrespective of the concentration regimes. Accordingly, atransient network is expected to be present also in regime II. Inregime II, however, there is a possibility that the observedexponent close to-2 might arise from the effect of polydis-persity with respect to the micelle length. The relaxation time,on the other hand, exhibits a nonlinear behavior as shown inFigure 6B, different in the two regimes. The relaxation time inregime I,τM, was about 0.1 s and nearly constant independentof C. The data in regime II represent terminal relaxation timesobtained by eq 2 and increase withC. The slopes of the twostraight lines in this figure (d logτ)/(d log C) were 1.2( 0.1for 0.04< C/mol kg-1 < 0.1(regime II) and 0( 0.2 for 0.2<C/mol kg-1 < 0.5(Regime I). The zero-shear viscosity alsoshows a nonlinear dependence in a double logarithmic plot,Figure 6C. The slope (d logη)/)d log C) changes from 3.2(0.3 for the lowC range (0.04< C < 0.1) to 2.0( 0.3 for thehigh C range (0.2< C/mol kg-1).

Effect of Ionic Strength at 25 °C. The effects of ionicstrength were examined at three surfactant concentrations, 0.05,0.10, and 0.20 mol kg-1, in the range of NaCl concentrationms

between 0.05 and 0.3 mol kg-1. At ms ) 0.4 mol kg-1, phaseseparation took place. The steady-state shear compliancedecreased monotonically withms as shown in Figure 7A. Chainflexibility is expected to increase withms due to a decrease ofthe electrostatic persistence length. Micelle growth withms isalso expected to contribute to the decrease ofJe

0. At C ) 0.1mol kg-1, deviation from single Maxwell behavior becameprogressively large asms either increased or decreased from0.1 mol kg-1. We have seen above that the crossover concentra-tion C* between the two regimes is around 0.1 mol kg-1 in 0.1mol kg-1 NaCl. This does not imply, that the crossover iscontrolled by the condition that ratioC/ms ) 1, however, asshown below. We observed approximately single Maxwell typebehavior forC ) 0.05 mol kg-1 at ms ) 0.2 mol kg-1. Therelaxation times shown in Figure 7B suggest that the crossovertakes place atC/ms ) 1/4-1/2, 1, and 2 forC ) 0.05, 0.1, and0.2 mol kg-1, respectively. The data shown in Figure 7B suggestthat the concentration-independent relaxation time in regime Ionly weakly depended onms in the rangems < 0.1 mol kg-1,whereas it decreased withms

-2 in the rangems > 0.1 mol kg-1.We can summarize thems dependence of the relaxation time inregime I as follows in a highly approximate way:

In regime II, on the other hand, the relaxation time increased

Figure 3. The R dependence of (A) the steady shear complianceJe0, (B) the relaxation timeτ, and (C) the zero shear viscosityη for C14DAO

solutions atC ) 0.1 mol kg-1, ms ) 0.1 mol kg-1.

Je0 or GM

-1 ∝ C-2.1 (5)

τ ∝ ms-2 (ms > 0.1 mol kg-1 : regime I) (6)

τ ) constant independent ofms

(ms < 0.1 mol kg-1 : regime I)

Viscoelastic Properties of C14DAO Micelles J. Phys. Chem. B, Vol. 105, No. 23, 20015413

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with ms and its power was between 1 and 2. The relaxationtime at lowC thus showed a maximum at aboutms ) 0.1 mol

kg-1. In conclusion, the effect of NaCl concentration can bedescribed withms instead of the ratioC/ms. This is reasonablebecause no specific Cl- counterion binding has been suggestedin the case of C14DAO.

Effect of Temperature.The effects of the temperatureT wereexamined in a range 25-55 °C on the solutions of 0.1 mol kg-1

NaCl for the half-ionized surfactant (R ) 0.5) at two concentra-tions C. Steady-state shear compliances were nearly constant,(2.5-3.5) × 10-3 Pa-1, in this range ofT for C ) 0.5 molkg-1, whereas they showed a tendency to increase withT at C) 0.1 mol kg-1. The viscosity decreased withT according toη∼ exp(-0.13T) for both concentrations (Figure 8A). AtC )0.5 mol kg-1, the relaxation time decreased withT, andτ/ηsolv

Figure 4. Angular frequencyω dependence of (A) the storage shearmodulusG′ and (B) the loss shear modulusG′′ for C14DAO solutionswith different md at R ) 0.5, ms ) 0.1 mol kg-1. Symbols forC are(×) 0.04, (4) 0.05, (1) 0.07, (0) 0.09, (+) 0.10, (]) 0.13, (b) 0.16,(O) 0.20, ([) 0.30, (3) 0.40, (O) 0.50 mol kg-1.

Figure 5. Cole-Cole plots for C14DAO solutions with differentmd

at R ) 0.5,ms ) 0.1 mol kg-1. Symbols forC are (×) 0.04, (0) 0.05,(]) 0.07, (2) 0.09, (O) 0.10 (A), and (O) 0.10, (4) 0.20, (]) 0.30,(1) 0.40, (b) 0.50 mol kg-1 (B).

Figure 6. TheC dependence of (A) the steady-state shear complianceJe

0, (B) the relaxation timeτ, and (C) the zero shear viscosityη ofC14DAO solutions atR ) 0.5 in 0.1 mol kg-1 NaCl.

5414 J. Phys. Chem. B, Vol. 105, No. 23, 2001 Maeda et al.

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vs 1/T plot gives a straight line (Figure 8B).

We obtained the activation energyE of 21.2 ( 2 kcal mol-1.In comparison, a value of 25-30 kcal mol-1 was reported forcetyltrimethylammonium bromide (CTAB) in 0.25 M KBr.7

Hence, the relaxation mechanism in regime I is not expected todiffer much from that of CTAB insofar as the activation energyis concerned.

Cryo-transmission Electron Micrography (CryoTEM).Figure 9 (A-C) presents cryoTEM micrographs obtained from0.1 mol kg-1 NaCl solutions ofR ) 0 (A), 0.5 (B), and 1(C).To understand what is shown in these micrographs, we mustfirst consider some aspects of the cryoTEM technique. Theaqueous samples are rapidly vitrified in the form of very thinfilms spanning holes in a polymer support. The vitrified filmsare directly examined in transmission mode at liquid nitrogen

temperature. The thickness of the films varies over the holes,from maybe about 500 nm close to the support to a few nm inthe middle of the hole. The thickness must not be much largerthan 500 nm for anything to be observed, scattering of electronsfrom the vitrified water is otherwise excessive. The variationof the thickness results in that the middle portions of themicrographs often are void of structures whereas the projectionsfrom thick parts show a multitude of overlapping structures thatin reality may be present at different heights and cannot bedistinguished from true entanglements. When long threadlikemicelles (or polymers) are observed parts of film that are thinnerthan the radius of gyration of the coiling threads will be avoided,and those threads that enter the thin part will be spread mainlylaterally in the film. In the thicker parts, segments that arepointing in the direction normal to the film, and thus in thedirection parallel to the electron beam, will be more frequent,and imaged as dark spots on the micrographs.

In Figure 9A-C, the thin part of the films are at the top,where in all cases an area without any micelles is found, whereaslong threadlike micelles are found with increasing density furtherdown. In Figure 9A, atR ) 0 (pH ) 10), the micelles are muchshorter than in Figure 9B,C, where the first very long micellesbordering to the empty thin area are displayed particularly clear.It is obvious that these micelles form both branches and loops,but few loose ends. The branching is not abundant, but several100 nm separate the junctions. That the micelles are shorter inFigure 9A is seen both from the large number of open ends,and from the abundance of black dots, indicating segments

Figure 7. Effects of NaCl concentrationms on (A) the steady-stateshear complianceJe

0, (B) the relaxation timeτ, and (C) the zero shearviscosity η for C14DAO solutions (R ) 0.5) at different surfactantconcentrations.C (mol kg-1): (O) 0.05, (b) 0.10, and (4) 0.20.

τ/ηsolv ∝ exp[E/RT] (7)

Figure 8. The temperature dependence of (A) the zero shear viscosityη and (B)τΜ/ηsolv for C14DAO solutions in 0.1 M NaCl atR ) 0.5.(O) C ) 0.1 mol kg-1,(b) C ) 0.5 mol kg-1, andηsolv represents thesolvent viscosity.

Viscoelastic Properties of C14DAO Micelles J. Phys. Chem. B, Vol. 105, No. 23, 20015415

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normal to the film, found also rather close to the void area,where the film must still be quite thin.

The images thus indicate clearly a difference between themicelle structure atR ) 0 on one hand, and atR ) 0.5 and 1on the other. The micrographs in Figure 9B,C do not revealany structural difference between the half-protonated and fullyprotonated micelles, although the dynamic properties changevery substantially from the protonated to the half protonatedform. This may suggest rapid breaking of fully protonatedchains. Similar observations were made already by Clausen etal.53 for CTAC-NaSal.)

In some other images fromR ) 0.5, bilayer structuresappeared (not shown). We are not sure about the interpretationof these findings, but the fact that bilayer structures were foundonly in the samples ofR ) 0.5 (pH ) 5) indicates that thiscomposition is one where the headgroups attract each other to

make structures with little curvature possible. It should be addedthat examples of coexisting threadlike micelles and bilayers havebeen found earlier,54 and in some cases just in samplesdisplaying viscoelasticity.54

Discussion

Relaxation Mechanism.An important feature of regime Iis that the relaxation is of single-exponential type. Accordingto Cates,23,24single-exponential behavior is expected in the fast-breaking limit of the micelles and the relaxation timeτ2 is thengiven as the geometric mean of the reptation timeτrep and thebreaking timeτbreak:τ2 ) (τrepτbreak)1/2. However, this modelpredicts the relaxation time to have a concentration dependencewith a power of 1.5:τ2 ∼ C1.5. This prediction is inconsistentwith the observed independence of concentration in regime I:τM

Figure 9. Cryoscopic transmission electron micrographs of 0.1 mol kg-1 C14DAO solutions in 0.1 mol kg-1 NaCl. (A) R ) 0, (B) R ) 0.5, and(C) R ) 1.

5416 J. Phys. Chem. B, Vol. 105, No. 23, 2001 Maeda et al.

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∼ C0. We have to look for a relaxation mechanism other thanthe fast-breaking limit of the reptation mode. We tentativelyassume that the single-exponential behavior in regime I is amanifestation of a single dominating mechanism in the transientnetwork irrespective of polydispersity with respect to the micellelength. The most probable candidate for this process is achemorheological process involving the breaking/formation ofentanglement points or cross-links.5

For micelles, the entanglements or cross-links can be brokenand formed with respective rate constantsk- and k+. Thenumber of those entanglements pertaining to the residual stressn(t) decays exponentially with time,n(t) ) ⟨n⟩ exp(- k-t), sincenewly formed chains are free from strain. In this way, therelaxation timeτ1 is given byτ1 ) 1/k-. As a mechanism ofthe stress relaxation of the network, entanglements are supposedto vanish by the crossing of two chains. For this to occur, firstthe two chains should merge at the entangled point and thenthis four-way crossing should disappear leaving two chains. Thebreaking rate constant of an entanglementk- will thus be writtenas k- ) exp(∆G*/kT) in terms of the activation free energy∆G*, which is independent of the surfactant concentration C.This is consistent with the present resultτ ∼ C0 in regime I.The argument is in line with that of Shikata et al.5 Anotherpossible relaxation mechanism will be sliding of the entangle-ment point.9 This idea is in line with the observed branchesand loops in TEM picture (Figure 9B). In this case,∆G* willcorrespond the activation free energy for sliding the branchingpoint along the micelle.

In regime II, an approximate relationτ ∼ C is found. Weexpect in this concentration regime a relaxation process to holdthat is similar to that in slightly entangled semidilute solutions.We expect then,τ ∼ M2 whereM denotes the average molecularweight of micelles.55 According to the classic argument on themicelle growth,56 it is shown thatM increases withC0.5. Thissimple argument proposesτ ∼ M2 ∼ C in regime II. Theobserved exponent of unity is consistent with this expectation.On the other hand, the above assumed Rouse-type mechanismwould predict a different scaling exponent (-0.5) of Je

0. Butthis inconsistency might be compromised by taking into accountthe effect of polydispersity.

When the concentration increases, micelles grow and thenumber of micelles also increases. This will increase the numberof entanglements per micelle and hence the relaxation processthrough the diffusional motion of micelle chains becomes moreand more inefficient. Eventually, the relaxation path throughthe chain crossing becomes more effective. In this way, we canexpect a change of the relaxation mechanism with the concen-tration as observed in the present study. It is to be stated herethat our interpretation of the data in the present study in termsof the two regimes is just a possibility among others.

Conclusion

Protonation (ionization) of tetradecyldimethylamine oxide wasfound to have marked effects on the viscoelastic properties ofthe micelle solutions were found. The zero shear viscosity,theshear modulus and the relaxation time all reached the maximumvalues at the half-ionized state (the degree of ionizationR )0.5). For the half-ionized micelles (R ) 0.5) in 0.1 mol/kg NaClsolutions, the steady-state complianceJe

0 decreased withC withan exponent of 2.1( 0.2, suggesting the presence of anentangled network of flexible threadlike micelles. Two con-centration regimes were discriminated in the concentrationdependence of the relaxation time. A single Maxwell behaviorwas observed in the high concentration regime I (C > 0.1 mol/

kg) and the relaxation time was about 0.1 s and nearlyindependent ofC. At low concentrations, regime II (C < 0.09mol/kg), the relaxation time increased withC with an exponentslightly larger than 1. This change in the relaxation mechanismwith concentration can be understood from the increase of boththe number of micelles and the micelle length at low concentra-tions, resulting in that the diffusional movement of the micellesbecomes increasingly hindered, whereas at high concentrationsa relaxation mechanism involving merging and break up atmicelle crossings becomes more effective. Effects of NaClconcentrationms showed that the elastic modulus increased withms and the regime shift took place at different ratiosC/ms. Fromthe temperature dependence of the viscoelasticity atR ) 0.5 in0.1 mol/kg NaCl solutions, a value of 21.2( 2 kcal mol-1 wasobtained as the activation energy. Cryo-transmission electronmicrographs clearly showed a highly entangled network in thesolution forR ) 0.5, while much smaller micelles forR ) 0.Contrary to the expectation from the rheological results, a highlyentangled network was also observed in the solution forR ) 1.

The present results strongly suggest the short-range attractiveinteraction between the headgroups of the nonionic (deproto-nated) and the cationic (protonated) species of amine oxides.

Acknowledgment. This research is supported partly by theGrant-in-Aid for Scientific Research (B) (No. 12440200) fromMonbu-kagaku-sho, Japan

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