Langmuir 2007, 23, 10053-10062
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Aggregate Formation in Aqueous Solutions of Carboxymethylcellulose and Cationic Surfactants Siwar Trabelsi, Eric Raspaud, and Dominique Langevin* Laboratoire de Physique des Solides, UniVersite´ Paris-Sud, Baˆ timent 510, 91405 Orsay Cedex, France ReceiVed June 5, 2007. In Final Form: July 13, 2007 The addition of cationic surfactants to an aqueous solution of an anionic polymer, carboxymethylcellulose (carboxyMC), causes the spontaneous formation of aggregates in a certain range of concentrations. Here we studied two surfactants, dodecyl and hexadecyl trimethylammonium bromide (DTAB and CTAB, respectively). Using different techniques (light scattering, potentiometry, viscosimetry, and zetametry), we found that a simple lengthening of the surfactant tail length by four CH2 groups drastically changes the aggregate morphology, size, and charge. We explored in detail how the surfactant and polymer concentrations act on these systems.
1. Introduction The interactions between oppositely charged polymers and surfactants in aqueous solutions have attracted a growing interest in colloidal science.1,2 These mixtures are frequently used in many industrial applications such as food, cosmetics, detergents, paints, and so forth. The association between oppositely charged polymers and surfactants is driven by both electrostatic and hydrophobic interactions. Many factors can influence the phase behavior of theses mixtures such as polymer charge density, backbone rigidity, and concentration Cp, as well as surfactant chain length and concentration Cs. Cooperative binding of surfactant to polyions occurs above a surfactant critical aggregation concentration (cac) lower than the critical micelle concentration (cmc) of the pure surfactant solution. The determination of the cac is usually made with surfactant-selective electrodes, which measure the number of surfactant molecules bound per polymer charged group (binding isotherm). The number of bound surfactants increases with Cs and eventually saturates. At high enough Cs, surfactant binding renders the aggregates hydrophobic, and phase separation with precipitation of a concentrated phase may occur. Static (SLS) and dynamic light scattering (DLS) allow one to determine the molecular weight and the gyration and hydrodynamic radii of the aggregates. The combination of SLS and DLS therefore provides information on their shape and conformation. However, in most studies, only DLS is used, and few detailed studies attempting to characterize the structure of polymersurfactant aggregates can be found in the literature.3-19 In general, * Corresponding author. (1) Goddard, E. D.; Ananthapadmanabhan, K. P. Interaction of Surfactants With Polymers and Proteins; CRC Press: Boca Raton, FL, 1993. (2) Kwak, J. C. T. Polymer-Surfactant Systems; Surfactant Science Series; Marcel Dekker: New York, 1998; Vol. 77. (3) Xia, J.; Zhang, H.; Rigsbee, D. R.; Dubin, P. L.; Shaikh, T. Macromolecules 1993, 26, 2759. Li, Y.; Xia, J.; Dubin, P. L. Macromolecules 1994, 27, 7049. (4) Fundin, J.; Brown, W. Macromolecules 1994, 27, 5024. (5) Berret, J. F.; Cristobal, G.; Herve´, P.; Oberdisse, J.; Grillo, I. Eur. Phys. J. 2002, 9, 301. Berret, J. F.; Vigolo, B.; Eng, R.; Herve´, P.; Grillo, I.; Yang L. Macromolecules 2005, 37, 4922. Berret, J. F. J. Chem. Phys. 2005, 123, 164703. (6) Voisin, D.; Vincent, B. AdV. Colloid Interface Sci. 2003, 106, 1. (7) Guillot, S.; Delsanti, M.; Langevin, D. Langmuir 2003, 19, 230. Trabelsi, S.; Guillot, S.; Raspaud, E.; Delsanti, M.; Langevin, D.; Boue´, F. AdV. Mater. 2006, 18, 2403. (8) Wang, C.; Tam, K. C.; Jenkins, R. D.; Tan, C. B. J. Phys.Chem. B 2003, 107, 4667. Wang, C.; Tam, K. C. J. Phys.Chem. B 2004, 108, 8976. (9) Cardenas, M.; Schillen, K.; Nylander, T.; Jansson, J.; Lindman, B. Phys. Chem. Chem. Phys. 2004, 6, 1603. Dias, R.; Pais, A. C. C.; Miguel, M. C.; Lindman, B. Colloids Surf., A 2004, 250, 115.
the addition of surfactants to polyelectrolyte solutions leads to a partial collapse of the polyelectrolyte chains, and the average hydrodynamic radius decreases. When the precipitation threshold is approached, the formation of multichain aggregates is sometimes reported. In other cases, precipitation does not occur, and the aggregate size goes through a maximum. Interestingly, the positions of the maximum or the precipitation threshold do not always correspond to situations where the ionic concentrations of the polymer and the surfactant are equal (neutralization), suggesting that electrostatic forces are not the only ones acting in these processes. The solubility of the aggregates is less for linear polymers than for polymers with non-ionic water-soluble side branches; for this reason, branched polyelectrolytes are widely used in the applications.1 The size of the aggregates decreases when the length of the side branches increases.11,16,17 In general, the aggregates are quite polydisperse, although relatively monodisperse aggregates are found in some cases.5,7,9,11,14 Zhou et al.11 argue that, at low surfactant concentrations, the polymer chains form open network structures with the surfactant acting as cross-linking sites, whereas, at high surfactant concentrations, they are more collapsed, and relatively monodisperse aggregates can form. These studies deal mostly with synthetic flexible polymers, but a few studies deal with semiflexible polymers such as polysaccharides7,11,13,18 and, with DNA,9,14 a polymer with a more rigid backbone. In the case of DNA, the collapse process is actively studied in view of applications in gene therapy. Understanding the level of compaction of the polymer chains and its relation to solubility and decompaction is therefore important. The investigations remain scarce, and more work is needed to understand the details of these processes. (10) Nizri, G.; Magadassi, S.; Schmidt, J.; Cohen, Y.; Talmon, Y. Langmuir 2004, 20, 4380. (11) Zhou, S.; Xu, C.; Wang, J.; Golas, P.; Batteas, J. Langmuir 2004, 20, 8482. (12) Yoshimura, T.; Nagata, Y.; Esumi, K. J. Colloid Interface Sci. 2004, 275, 618. (13) Villeti, M. A.; Borsali, R.; Crespo, J. S.; Soldi, V.; Fukada, K. Macromol. Chem. Phys. 2004, 205, 907. (14) McLoughlin, D.; Delsanti, M.; Tribet, C.; Langevin, D. Europhys. Lett. 2005, 69, 461. (15) Naderi, A.; Claesson, P. M.; Bergstro¨m, M.; Dedinaite, A. Colloids Surf., A 2005, 253, 83. (16) Kizhakkedathu, J.; Nisha, C. K.; Manorama, S. V.; Maiti, S. Macromol. Biosci. 2005, 5, 549. (17) Balomenou, I.; Bokias, G. Langmuir 2005, 21, 9038. (18) Mata, J.; Patel, J.; Jain, N.; Ghosh, G.; Bahadur, P. J. Colloid Interface Sci. 2006, 297, 797. (19) Yan, Y.; Li, L.; Hoffmann, H. J. Phys. Chem. B. 2006, 110, 1949.
10.1021/la7016177 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/23/2007
10054 Langmuir, Vol. 23, No. 20, 2007
In this paper, we report a study of a polysaccharide, carboxymethylcellulose (carboxyMC), a polymer of intermediate flexibility (intrinsic persistence length comparable to a micellar diameter), in aqueous solutions with cationic surfactants. In a former work on carboxyMC and dodecyl trimethylammonium bromide (DTAB), combined SLS and DLS showed that the aggregates formed at high surfactant concentrations are monodisperse, spherical, and grow continuously with increasing DTAB concentrations.7 This polymer has a very low cac with cationic surfactants, and the partial collapse of the polymer chains occurs before the formation of multichain aggregates, facilitating the analysis of the binding processes. Note that, in the case of DNA, chain collapse and the formation of multichain aggregates occurs simultaneously, and the latter phenomenon had to be studied with small DNA fragments.14 We have extended the work on carboxyMC by varying the chain length of the surfactant. We also investigated the influence of polymer concentration Cp on the aggregate behavior. We used different techniques, namely, DLS, SLS, and viscosimetry, as well as electrophoretic mobility and binding isotherm measurements. 2. Experimental Section 2.1. Materials. DTAB and hexadecyl trimethylammonium bromide (CTAB) were obtained from Aldrich (purity 99%) and recrystallized three times before use in acetone-ethanol (24:1) solutions. CarboxyMC is an anionic water-soluble polymer derived from cellulose. Cellulose itself is a polymer with anhydroglucose units that contains three hydroxyl groups that can be substituted with sodium-carboxyl groups: sodium carboxyMC is then obtained. The average number of hydroxyl groups substituted per monomer anhydroglucose unit is known as the degree of substitution (DS). In this work, we have used three types of sodium carboxyMC (blanose 12m31P, 9M31F, 7M31CF) supplied by Aqualon Hercules, with a minimum purity of 99.5%. These three polymers differ in their degrees of substitution (DS ) 1.23, 0.9, and 0.7, respectively). With the monomer length of cellulose being approximately b ∼ 5 Å, and the Bjerrum length in aqueous solution being lb ) 7 Å, one can calculate the Manning ratio A/lb, with A being the average distance between charged groups along the polymer chain: A ) b/DS. In the case of carboxyMC with DS ) 1.23 and 0.9, A/lb < 1, which means that the Manning condensation along the polymer chain occurs in dilute solutions without surfactant. In the case of DS ) 0.7, A/lb > 1, indicating that there is no Manning condensation along the polymer chains, again in dilute solutions. The molecular weight, Mw, of the different carboxyMCs was measured by light scattering of dilute solutions in 0.1 M sodium chloride without any surfactant. Polymer concentrations ranged from 2.6 to 28 mg/L. The solvent was previously intensively filtered using 0.22 µm syringe filters (cellulose ester, Millipore) to eliminate dust particles; after this treatment, the intensity scattered by the solvent was about 10 times less than the intensity scattered by toluene. This low level allowed us to detect the weak signal due to the polymers and to determine their molecular weights, which were close to 2 × 105 g/mol (Mw ) 2.05 × 105 for DS ) 0.7, 1.63 × 105 for DS ) 0.9, and 1.71 × 105 for DS ) 1.23). All the mixed solutions studied here were prepared by mixing equal volumes of polymer and surfactant solutions, except those described in section 3.3.3. The solutions with scattering less than 10 times that of toluene were centrifuged (1500 rpm for 30 min in the scattering cell) in order to eliminate the contribution of the dust particles to the light scattering signal. 2.2. Methods. 2.2.1. Potentiometry. We used surfactant-selective solid membrane electrodes. The experimental set up used in the electromagnetic field measurements20 and the results for carboxyMC (20) Turmine, M.; Mayaffre, A.; Letellier, P. J. Colloid Interface Sci. 2003, 264, 7.
Trabelsi et al. (DS ) 1.23) have been described previously.21 The electrodes are sensitive to free surfactant (not bound to polymer) in the solution; the binding isotherms are obtained by plotting the degree of binding β as a function of free surfactant concentration Cf: β ) Cb/[Cp] and Cb ) Cs - Cf, where Cb is the (molar) concentration of the surfactant bound to the polymer, Cs is the total surfactant concentration, and [Cp] is the polymer concentration in terms of charge molarity: [Cp] )
Cp DS 162 + 80DS
with Cp being expressed in grams per liter (for instance, 1 g/L is equivalent to 3.21 mM polymer charges for DS ) 0.7). 2.2.2. Viscosimetry. Relative viscosities were measured using capillary glass tubes (Cannon-Fenske routine glass viscometers from Ever Ready Thermometer Co). We used two different tubes: type 50 for solutions containing 127 mg/L polymer, and type 100 for solutions containing 1000 mg/L polymer. A fixed amount of solution was poured into the tube and placed in a thermal bath at 25 °C. The relative viscosity is the ratio of flow times for the solution and for water: ηrel ) ηs/η0 ) t/t0. The relative viscosities were measured three times for each sample, and average values were taken. 2.2.3. Static and Dynamic Light Scattering. We used a homebuilt light scattering setup, of classical design, operating with a He-Ne laser (Melles Griot 75 mW, wavelength λ ) 632.8 nm). The detector was a Hamamatsu photon counting head H7421-40, connected to a universal counter (Racal-Dana 1991). The correlator was a Flex2k-12x2 from correlator.com. The scattering angle range is 20° < θ < 140°, corresponding to a wave vector range of 0.45 × 10-7< q < 2.5 × 10-7 m-1 (q ) 4πn sin(θ/2)/λ, with n being the solution refractive index). The intensity of the light scattered by solutions of particles of weight Mw and sufficiently diluted so that interactions between them are negligible can be expressed through the Rayleigh ratio, Rsample, as Rsample(q) ) MwP(q) KIC
(1)
P(q) denotes the particle form factor, and C denotes their concentration. The constant KI is given by KI ) 4π2n2(dn/dC)2/(Naλ4), where dn/dC is the refractive index increment, and Na is Avogadro’s number.22 When the radius R of the particles is small, qR , 1 and P(q) ∼ 1. Toluene of Rayleigh ratio Rtoluene ) 1.406 × 10-5 cm-1 was used for calibration. Then one has Rsample(q) ) Rtoluene(n/ntoluene)2Isample(q)/Itoluene, where ntoluene and Itoluene correspond to the toluene sample. The refractive indices of pure carboxyMC and DTAB are similar, and we have taken dn/dC ) 0.144 cm3/g as in ref 7. Because the solutions are very dilute, we used n ) 1.33. In dynamic or quasi-elastic light scattering experiments, the normalized intensity correlation function g(2)(q,t) is measured. It is related to the normalized electric field correlation function g(1)(q,t) through the Siegert relation:22 g(2)(q,t) ) 1 + B|g(1)(q,t)|2
(2)
where B is an instrumental parameter, taking into account deviations from ideal correlations. In the most simple case, for monodisperse particles, the correlation function is given by g(1)(q,t) ) exp[-t/τ(q)]
(3)
where the characteristic decay time τ is related to the diffusion coefficient: (21) Jain, N.; Trabelsi, S.; Guillot, S.; McLoughlin, D.; Langevin, D.; Letellier, P.; Turmine, M. Langmuir 2004, 20, 8496. (22) Pecora, R. Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy; Plenum Press: New York, 1985.
Aggregate Formation in CarboxyMC-Surfactant D(q) ) 1/[τ(q)q2]
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Using the Stokes-Einstein equation, the hydrodynamic radius can be deduced from the diffusion coefficient D(q), extrapolated to q ) 0: D0 )
kT 6πηsRh
Table 1. Values of the cac, u, Cturb, and Cprec for the Mixed Solutions
surfactant
carboxyMC concentration (mg/L)
DTAB
127
(5) 1000
where D0 ) limqf0 D(q), k is the Boltzmann constant, T is the absolute temperature, and ηs is the solvent viscosity.22 When the radius R of the particles is small, qR,1 and D(q) are constant and equal to D0. If the spheres are polydisperse, g(1)(τ) is no longer exponential, but can be fitted by a stretched exponential:23 g(1)(q,t) ) exp -{[t/τ(q)]a}
(6)
The average diffusion coefficient is still given by eq 4, and it is the equivalent of a first “cumulant” and the average hydrodynamic radius by eq 5. 2.2.4. Zetameter. We used a Zetasizer (Nano Series Malvern Instruments). The instrument measures the electrophoretic mobility µ by performing an electrophoresis experiment and measuring the velocity of the particles using laser doppler velocimetry (LDV). The zeta potential ζ is then obtained from the Henry equation:24 µ)
2ζ f(κR) 3ηs
(7)
where is the dielectric constant, κ-1 is the Debye length, and f(κR) is the Henry function (correction factor that takes into account the shape of particles).
3. Experimental Results 3.1. Potentiometry. The cac was measured with surfactantselective electrodes on the various samples. The measured values are reported in Table 1. We also give in the table the values of the cooperativity parameter u, defined as
u)
[SS][OO] [OS]2
where O represents a charged monomer, and S represents a monomer bound to surfactant; OO denotes two adjacent charged monomers, OS denotes a charged monomer adjacent to a bound monomer, and SS denotes two adjacent monomers bound to surfactant; SS, OO, and OS evolve according to K
OO + S+ 798OS Ku
OS + S+ 798SS Ku is linked to the probability of surfactant binding to a monomer adjacent to a monomer already bound, whereas K is linked to the probability of binding to a monomer surrounded by unbound monomers; u, the ratio of the two probabilities, characterizes the cooperativity of binding. In order to obtain the values of u, the curves β(Cs) were fitted by a theoretical form currently used to analyze this type of data: β ) 0.5{1 - (1 - s)/[(1 - s)2 + 4s/u]0.5}, with s ) KuCf.21 Other expressions can be used, but with the aim here being to compare the different systems, we chose the simplest one. (23) Brown, J. C.; Pusey, P. N. J. Chem. Phys. 1975, 62, 1136. (24) Evans, D. E.; Wennerstrom, H. The Colloidal Domain; Wiley: New York, 1999.
CTAB
127 1000
DS
u
cac (mM)
Cturba (mM)
Cprecb (mM)
0.7 0.9 1.23c 0.7 0.9 1.23c 1.23c 1.23c
10 13 11 7 13 170 8 96
0.2 0.1 0.1 0.2 0.1 1 0.02 0.08
5 5 4 5 5 5 0.3 1
9 10 10 5 8 7 no 5
a Cturb ) surfactant concentrations at which the solutions become turbid. b Cprec ) surfactant concentration at which solutions precipitate. c Data for carboxyMC DS ) 1.23 were taken from ref 21.
The cooperativity parameter u was small for DS ) 0.7 and 0.9, probably because the distance A between adjacent charges is large (A ) 7 and 5.6 Å, respectively). For DS ) 1.23 and Cp ) 1000 mg/L, the cooperativity was larger, the charges being closer (A ) 4 Å). However, for Cp ) 127 mg/L, the values of u were small and not very different from those of the other DS. It is indeed known that cooperativity increases with polymer concentration by the self-screening of electrical charges (or, equivalently, with added salt).25 Although the cac was much lower for CTAB than for DTAB (Table 1), the cooperativity parameter u was only slightly larger for DTAB than for CTAB, showing that the length of the hydrophobic tail does not significantly affect the cooperativity in the solution. Figure 1 shows the evolution of β as a function of polymer concentration Cp for 5 mM DTAB. At low Cp, β increased when the polymer concentration increased, reached a maximum at approximately 100 mg/L, then decreased tending toward 1. The degree of binding here took values larger than 1, meaning that the aggregates are not stoichiometric. At large enough polymer concentrations (Cp > 100 mg/L), β decreased, probably because of the self-screening effect mentioned earlier. Non-stoichiometric aggregates have also been found in other similar systems, with β being calculated directly from the aggregate composition as determined by neutron scattering (assuming Cf ) 0).5 3.2. Viscosimetry. Viscosity is very sensitive to any change in polymer conformation (extension or collapse). Factors that influence the conformation are mainly the DS, the molecular weight, the concentration, and the flexibility of polymer chains. Figure 2 shows an example of viscosity variation as a function of surfactant concentration for various degrees of substitution. Below the cac, the polymer chains are extended, and they overlap forming networks (semidilute regime). The viscosity was larger for the larger DS: large charge density means more repulsive interactions between charged sites of polymer and more extended polymer chains. In this region, the relative viscosity decreased slightly with increasing Cs. The decrease is similar to the addition of salt and is induced by the screening of repulsive interactions between charged monomers. Above the cac, the viscosity decreased sharply toward the viscosity of water. This decrease is attributed to the binding of surfactant molecules onto the polymer chain; since the polymer chains are less charged, they are less extended and cannot overlap, therefore the solutions are no longer in the semidilute regime. 3.3. Dynamic and Static Light Scattering. The increase in Cs leads to a partial collapse of polymer chains as indicated by the viscosity measurements. The light scattering experiments were essentially performed above a surfactant concentration where (25) Hansson, P.; Almgren, M. J. Phys. Chem. 1996, 100, 9038.
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Figure 1. Variation of the degree of binding β as a function of Cp (DS ) 0.7) for 5 mM DTAB.
Figure 2. Relative viscosity of mixed solutions as a function of Cs with Cp ) 1000 mg/L: triangles: DS ) 0.7; squares: DS ) 0.9; circles: DS ) 1.23.
the chains are collapsed (viscosity of the solutions equal to that of water). They were stopped at concentrations close to the precipitation limit, where the samples become too turbid. We will first discuss the DTAB results. 3.3.1. CarboxyMC-DTAB. The light scattering measurements were performed in a wide range of polymer concentrations (from 5 to 1000 mg/L) and for different degrees of substitution (mostly DS ) 0.7). Surfactant concentrations were varied between 3 and 7 mM. (a) Hydrodynamic Radius. We found earlier that, at low polymer concentrations (∼100 mg/L), the autocorrelation function g(1)(q,t) was a simple exponential function, and the diffusion coefficient D was independent of q.7 This indicates that the DTAB-carboxyMC aggregates are compact and monodisperse. Complementary X-ray and neutron scattering experiments suggested that they were made of spherical surfactant micelles wrapped by polymer chains. Their hydrodynamic radius Rh, as deduced from the Stokes-Einstein equation (eq 5), is plotted as a function of Cs in Figure 3. The hydrodynamic radius increased exponentially with the surfactant concentration and linearly with DS.
Figure 3. Hydrodynamic radius of aggregates with Cp ) 127 mg/L as a function of Cs: triangles: DS ) 0.7; squares: DS ) 0.9; circles: DS ) 1.23. Data taken from ref 7.
The aggregate size was also measured at different polymer concentrations, keeping the surfactant concentration constant: Cs ) 3, 5, and 7 mM (Figure 4). Below 500 mg/L, the hydrodynamic radius was independent of Cp. For 7 mM, there is no data beyond 300 mg/L because precipitation occurred. For Cs ) 3 mM or 5 mM and above 400 mg/L, the aggregates grew until precipitation occurred. Simultaneously, the autocorrelation function g(1)(q,t) transformed into a stretched exponential (eq 6), with R ∼ 0.8 for the five points of Figure 4, for which Cp g 500 mg/L, and the average diffusion coefficient D ) 1/[q2τ(q)] became q-dependent. This suggests that the aggregates become large (qR ∼ 1) and polydisperse. The hydrodynamic radius was deduced from an extrapolation of D to q ) 0, as explained in section 2.2.3 (value plotted in Figure 4). For 3 mM, there is no point above 500 mg/L in Figure 4, but not because of precipitation. The autocorrelation function could still be fitted by a stretched exponential with R ∼ 0.67. The extrapolation to q ) 0 of the diffusion coefficient is very small, meaning that Rh is too large to be determined. Here, τ(q) ∼ 1/q3,
Aggregate Formation in CarboxyMC-Surfactant
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Figure 4. Hydrodynamic radius Rh of the aggregates as a function of Cp: circles: Cs ) 3 mM; squares: Cs ) 5 mM; triangles: Cs ) 7 mM.
which, together with R ∼ 0.67, is the signature of internal modes such as those found in solutions of long flexible polymers26,27 or microgels.28 This suggests that the aggregates are now very large and loose, and that only the interior is seen with light scattering. Note that this behavior was also observed without added surfactant at very high polymer concentrations (above 1000 mg/L), where the polymer network begins to be entangled (the chains are only overlapping at smaller polymer concentrations7). Indeed, we noticed that the internal slow modes disappeared once solutions were diluted (still without added surfactant) below 1000 mg/L. With 3 mM DTAB, the polymer network is partially collapsed and therefore denser, perhaps stabilizing a structure similar to that seen at larger polymer concentrations without surfactant. At higher Cs, the internal modes definitely disappeared, and the small aggregates described earlier are formed. This behavior is similar to that observed by Zhou et al. with cationic hydroxyethylcellulose,11 although they did not analyze their data in terms of stretched exponentials. (b) Gyration Radius. Other properties of the aggregates were also determined by analyzing the static scattering intensity at different scattering angles by using eq 1. For most samples, the form factor P(q) was approximated using the Guinier law in order to determine the gyration radius Rg:
( ) 2
-q2Rg I(q) P(q) ) exp 3 I(0)
qRg < 1
(8)
where I(0) denotes the scattered intensity extrapolated to zero q. We have done this analysis for four solutions with Cs ranging from 4 to 7 mM (Cp ) 127 mg/L and DS ) 0.7), for which the aggregates were large enough to lead to an observable q variation in the intensity. The values of the gyration radius are given in Table 2. For all samples, the ratio Rh/Rg was close to 1.29. This is as expected for spheres of radius R ∼ Rh: Rh2 ) (5/3)Rg2. This suggests that the DTAB/carboxyMC aggregates are spherical, as found earlier for DTAB and carboxyMC with DS ) 1.23. (c) Molecular Weight. Let us now discuss the variation of I(0) with polymer concentration. As shown by eq 1, I(0)/C is directly proportional to the molecular weight Mw, provided the aggregates (26) Adam, M.; Delsanti, M. J. Phys. Lett. 1977, 38, L-271. (27) Dubois-Violette, E.; de Gennes P. G. J. Phys. (France) 1967, 3, 181. (28) Raspaud, E.; Lairez, D.; Adam, M. Macromolecules 1994, 27, 2956.
Figure 5. Variation of normalized I(Cp)/Cp with polymer concentrations for q ) 0 and three DTAB concentrations: circles: 3 mM DTAB; squares: 5 mM DTAB; triangles: 7 mM DTAB. The curves have been normalized by I(Cp ) 50 mg/L). Table 2. Values of Rh, Rg, and of the Ratio Rh/Rg for the Mixed Solutions of DTAB and 127 mg/L CarboxyMC (DS ) 0.7) CDTAB (mM)
Rh(nm)
Rg(nm)
Rh/Rg
4 5 6 7
34.5 ( 2.7 41.5 ( 3 73 ( 2.7 93 ( 0.07
30 ( 1.4 31 ( 1.4 50 ( 1.4 74 ( 1.8
1.15 ( 0.125 1.34 ( 0.12 1.53 ( 0.06 1.26 ( 0.03
are diluted enough and the interactions between them are negligible. If we assume that the aggregate concentration C is proportional to the polymer concentration Cp, then I(0)/Cp is also proportional to Mw. The values of I(0) determined at three different surfactant concentrations Cs ) 3, 5, and 7 mM are reported in Figure 5. Because I(0) is strongly dependent on Cs (for Cp ) 50 mg/L, it increased by a factor of 100 between Cs ) 3 mM and 7 mM), the data of Figure 5 are normalized by the value measured at 50 mg/L for each surfactant concentration in order to facilitate comparisons. When Cp increased, I(0)/Cp first decreased slightly below 50 mg/L and then increased above 100 mg/L. Note that all these variations, which will be discussed in detail in section 4, are seen for aggregates having the same hydrodynamic radius (Figure 4). At larger polymer concentrations (Cp > 500 mg/L) and in the case of 5 mM DTAB, the solutions became turbid and I(0)/Cp increased again. In this range, Rh increased sharply from 40 to 120 nm with further addition of polymer until the precipitation threshold was reached (Figure 4). 3.3.2. CarboxyMC-CTAB. In the case of carboxyMC-CTAB, the solutions became rapidly turbid in a broad range of polymer and surfactant concentrations, making light scattering measurements difficult to interpret. For that reason, experiments have been done either at low polymer concentration (10 mg/L) or at low surfactant concentration (0.1 mM). (a) Quasi-elastic Scattering. Let us first discuss the quasielastic scattering measurements performed at several surfactant concentrations, with the polymer concentration Cp being constant and equal to 10 mg/L. The correlation function g(1)(q,t) was either a single exponential or a stretched exponential depending on q and Cs. Figure 6 displays the variation of the diffusion coefficients as a function of the scattering wave vector q. For Cs e 1 mM, the correlation function g(1)(q,t) was a single exponential in the whole explored q range. The diffusion
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Figure 6. Diffusion coefficient for CTAB and 10 mg/L carboxyMC (DS ) 0.7) as a function of scattering wave vector at different CTAB concentrations.
coefficient weakly depended on q and approached 3.5 × 10-12 m2/s in the limit q ) 0, with the corresponding hydrodynamic radius Rh being equal to 61 nm. This weak variation of D(q) with q may be understood in terms of polydispersity.29 For Cs g 2 mM and q g 0.015 nm-1, g(1)(q,t) could be fitted by a simple exponential, and the diffusion coefficient is independent of q and Cs: D ) (6.5 ( 0.3) × 10-12 m2/s, leading to a hydrodynamic radius Rh ) (33 ( 2) nm. At lower q, g(1)(q,t) was a stretched exponential with an exponent R decreasing progressively from 1 to 0.67 for decreasing q values. The corresponding effective diffusion coefficient varied linearly with q (τ(q) ∼ q3), suggesting that the scattering came from internal modes. This behavior points toward the existence of large aggregates with a complex architecture that changes with the observation scale 1/q. The aggregates are larger than the largest length scale explored here (qmin ∼ 5 × 106 m-1 corresponding to a length scale of 1/q ∼ 200 nm) and exhibit a broad distribution of internal modes as in microgels. They are made of subunits of size 33 nm (seen at q > 0.015 nm-1). (b) Elastic Scattering. The static scattered intensity by these solutions has been measured as a function of q. The intensities, normalized by the toluene intensity, are plotted in Figure 7 for different surfactant concentrations. As for DTAB, I(q) depends on both q and Cs. For 0.1 mM e Cs e 1 mM, the intensity shows a steep decrease at small q, followed by a smooth one at high q. In the latter part, the intensity could be fitted to Guinier’s law (eq 8), with gyration radii varying between 40 and 55 nm, that is, close to the hydrodynamic radius of 61 nm measured in the same conditions. It can also be noted in Figure 7 that lower Cs leads to larger intensities. This variation is quite puzzling because the subunits have the same diffusion coefficient in this concentration range (Figure 6). This is possibly due to a variation of the composition of the aggregates, with the amount of water increasing with increasing surfactant concentration. Since it was not possible to measure the intensity scattered by all of the aggregates as a whole (this would require very low q values), these variations remain difficult to interpret. Because we were not able to extrapolate the scattered intensity to zero q, we could not estimate the molecular weight of the aggregates and follow their variation as a function of the polymer concentration. The intensity scattered at 90° (corresponding to q ) 0.015 nm-1) by the internal subunits was analyzed instead. Results are plotted in Figure 8, where the intensity divided by
Figure 7. Scattered intensity versus scattering wave vector at a fixed carboxyMC concentration (10 mg/L) and different CTAB concentrations.
Figure 8. Variation of I(Cp)/(Cp*Itol) as a function of polymer concentration for two CTAB concentrations: circles: 0.1 mM CTAB; squares: 0.2 mM CTAB.
Cp and measured at Cs ) 0.1 and 0.2 mM is plotted versus Cp. Several remarks can be made in comparison with the DTABcarboxyMC system: (i) On the magnitude: Unlike in the DTAB case for which an increase of Cs by a factor of 2-3 (from 3 to 7 mM) raised the intensity by a factor of 100, here the effect of Cs on the intensity was weak. Also here the intensity depended much more on Cp than in the DTAB case. (ii) On the Variation: The shape of the curves determined for the two systems was surprisingly similar. Both I/Cp curves reached a maximum at an intermediate polymer concentration, which was larger for Cs ) 0.2 mM than for Cs ) 0.1 mM. For Cs g 2 mM, all the data fall onto the same curve, which may be also divided into two parts: at low q, a steep decrease in I(q) (like I(q) ∼ q-1.7), followed by a smooth one at high q. In the latter part, the intensity level was quite small (about 4 times larger than the toluene intensity) and could be fitted to Guinier’s law (eq 8) with Rg ∼ 40 nm. Let us recall that, in this q range, inelastic scattering evidenced subunits with Rh ∼ 33
Aggregate Formation in CarboxyMC-Surfactant
Figure 9. Effect of sample preparation: SP ) equal volumes of surfactant and polymer solutions, surfactant added first. PS ) equal volumes of surfactant and polymer solutions, polymer added first. Dilution: SP sample with 7 mM surfactant diluted with water. SP dilute: SP samples prepared with the same amount of polymer as that in the dilution series. V different: samples prepared with a 20 mM surfactant solution.
nm. This leads to Rh/Rg ∼ 0.8-0.9, suggesting that the subunits are either elongated or less dense than a compact sphere. Note that a similar ratio (equal to 0.81) is expected for a random polymer chain.30 3.3.3. Influence of the Order of Mixing: Case of Small Aggregates. We have used different mixing procedures in order to obtain samples containing 127 mg/L (or less) carboxyMC (DS ) 0.7) and 4, 5, 6, and 7 mM DTAB. The samples were characterized by their hydrodynamic radii Rh. These procedures were (a) mixing equal volumes of surfactant and polymer solutions, adding either the surfactant solution to the polymer solution or the polymer solution to the surfactant solution. For these two procedures, the diffusion coefficients were independent of q, and the measured Rh were equal. (b) mixing different volumes of a dilute polymer solution and a concentrated surfactant solution (20 mM DTAB). In this case, the diffusion coefficients were slightly q-dependent (the variation of D increased with decreasing Cs, from about 10% for 7 mM to 30% for 4 mM), indicating a larger polydispersity than that in procedure a. The values of Rh here were independent of Cs and remained close to 150 nm. (c) dilution of a solution containing 7 mM DTAB and 127 mg/L CarboxyMC. Here too, the values of Rh were independent of Cs and close to 150 nm. The measured Rh values are shown on Figure 9, evidencing the important influence of the order of mixing. These results will be discussed in section 4.1. 3.4. Zeta Potential. The aggregates are expected to have either positive or negative surface potential depending on the surfactantto-polymer ratio. Figure 10 shows the evolution of the zeta potential versus surfactant concentration for DTAB and CTAB aggregates with carboxyMC (DS ) 0.7). In the case of DTAB, the zeta potential was close to -60 mV at low surfactant concentrations and started to increase above the cac. Whatever the surfactant concentration, the zeta potential (29) Koppel, D. E. J. Chem. Phys. 1972, 57, 4814.
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Figure 10. Zeta potential of DTAB and CTAB aggregates with carboxyMC (DS ) 0.7) as a function of surfactant concentration: squares: CTAB and Cp ) 127 mg/L; triangles: CTAB and Cp ) 10 mg/L; circles: DTAB and Cp ) 127 mg/L; down triangles: DTAB and Cp ) 1000 mg/L. The arrow indicates the concentrations of electroneutralization.
always remained negative, and charge reversal was not observed. The behavior was similar for Cp ) 127 and 1000 mg/L, but, at a given surfactant concentration, the zeta potential was smaller for Cp ) 1000 mg/L than for Cp ) 127 mg/L, possibly because the polymer brings more negative charges. In the case of CTAB, two polymer concentrations, 10 and 127 mg/L, were used. At low CTAB concentrations, the zeta potential was negative and smaller for 127 mg/L than for 10 mg/L. When Cs increased, the zeta potential increases and reaches zero when Cs ) [Cp] (in mole charges, neutralization concentration). When Cs increased further, the zeta potential became positive and seemed to saturate at a value close to +35 mV above 2 mM.
4. Discussion Although DTAB and CTAB binding to carboxyMC are similar (the binding cooperativity is similar), the multichain aggregates formed with the two surfactants are extremely different. 4.1. DTAB-CarboxyMC Aggregates. At low polymer concentrations, the DTAB-carboxyMC aggregates were found to be monodisperse, spherical, and always negatively charged. An increase in the surfactant concentration led to a reduction in their zeta potential and to their exponential growth. The effect of the polymer concentration on the aggregates was, however, quite puzzling: while at low Cp their size remained constant, a change was observed in the zeta potential together with the magnitude of the scattered intensity. At large Cp, the aggregates became large, polydisperse, and loosely packed (internal modes were seen). The different regions of the phase diagram are schematized in Figure 11. The origin of the variation of the scattered intensity at low Cp is attributed to a variation in the amount of water in the aggregates, as discussed in detail in the Appendix. Table 3 gives the values of the ratio of the volume fraction of the aggregates φ to the volume fraction of polymer and surfactant φdry. 4.1.1. Size of the Small Aggregates. We have previously proposed7 the following simple model. If we assume that, once neutralized by the charges of the surfactant, the charged monomers are insoluble in water, the chain will collapse and form hydrophobic particles, leaving its remaining charged monomers at the surface of the particles. The area Σ occupied by the charged monomers will be determined by a balance between surface energy and electrostatic energy, as in surfactant micelles; this
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Figure 11. Scheme of the phase diagram indicating the different regions with dense aggregates, loose aggregates, and precipitates in the case of DTAB-carboxyMC mixed solutions. Table 3. Values of R, Rh, O, and Odry for the Mixed Solutions of 5 mM DTAB with Different Cp (DS ) 0.7) Cp (mg/l) 10 30 60 127 300 400 500
R (nm) 35.6 40.7 37.2 30.4 29.6 28.3 28.3
Rh(nm)
φdry
φ
φ/φdry
42.3 43.8 40.8 41.5 41.4 42.7 49.4
2.5 × 3.9 × 10-5 1 × 10-4 3.6 × 10-4 7.3 × 10-4 9 × 10-4 10-3
6.9 × 4.9 × 10-5 1.4 × 10-4 9 × 10-4 2 × 10-4 3 × 10-4 6 × 10-4
2.8 1.3 1.4 2.5 2.7 3 6
10-5
10-5
area is therefore expected to be comparable: Σ ∼ 0.5 nm2. The radius of the aggregates will then be given by Rth ) 3φ/(c-Σ), where φ is the volume fraction of the particles and c- is the number of charged monomers per unit volume: c- ) c* - cs, where cs is the number density of surfactant ions, and c* is the number density such as c- is zero at the precipitation boundary. This expression is found easily by writing the volume/surface ratio of the spherical particles. The values of the calculated radii are in reasonable agreement with the measured ones.7 This model presupposes that the particles are negatively charged, and this is indeed the case, with the zeta potential of the particle being negative, despite Cs > C0, and β > 1. This is by itself a puzzling result, and suggests that the internal positive charges of the aggregates are compensated by bromide counterions. The reason for this is unclear at the moment. Note that Mata et al. studied the same system and found that the aggregates radius depended on the type of surfactant counterions.18 The zeta potential varies continuously over up to two decades of surfactant concentration. Such a continuous and smooth variation is unusual. In general, charge reversal occurs in a narrow range, and the zeta potential rapidly saturates.31 The data for 127 mg/L follow rather well a logarithmic variation (Figure 10), suggesting a screening of the charge of the aggregates by condensed counterions.32 In most other studied systems, the surfactant chain length is larger, the cac is smaller, and the amount of free surfactant and free counterions is smaller, and this is perhaps why screening is not seen there. The above model will become really predictive when the value of c* and the amount of water in the particle could be predicted. Why the particle size increases exponentially with surfactant concentration and linearly with the polymer degree of charge, and why it is independent of polymer concentration indeed remains to be explained. A recent model attempts to predict the size of domains formed by partially collapsed polyelectrolyte chains by a Rayleigh-type instability, and addresses both the (30) Oono, Y. J. Chem. Phys. 1983, 79, 4629. (31) Koltover, I.; Salditt, T.; Safinya, R. Biophys. J. 1999, 77, 915. (32) Alexander, S.; Chaikin, P. M.; Grant, P.; Morales, G. J.; Pincus, P. J. Chem. Phys. 1984, 80, 57766.
problems of screening and inclusions of counterions in the collapsed globules.33 Since the size of the globule is very small, a uniform bulk charge density is assumed. The model predicts that the size of the domains decreases when the polymer charge density increases, a result opposite to what is seen here. Note that, here also, one expects that the bulk charge density is zero, thus there are only surface charges. Let us note that the above models rely on the fact that these particles are at thermodynamic equilibrium, although it seems that this is not the case here. The size of the particles remains unchanged for months, but they might be trapped in metastable states. We have shown in section 3.3.3 that the size of the aggregates depends on the way in which the polymer and the surfactant were mixed. This is as reported recently for similar particles.5,15,34 Methods to produce well-defined particles using trapping methods have even been devised.34 When polymers and surfactants self-assemble, the primary steps are therefore crucial in determining the aggregate structure. Indeed, once formed, the structures seem trapped, even when the aggregates are immersed in a solution that contains a large amount of mobile (free). surfactant molecules. It was claimed recently19 that phase separation in oppositely charged polyelectrolytesurfactant systems is similar to the clouding phenomena in nonionic surfactant or polymer solutions.35 When the temperature increases, these surfactants or polymers are less soluble in water, and phase separation occurs. Here, when Cs is increased, surfactant binding renders the aggregates hydrophobic and also less watersoluble. In polymer solutions undergoing clouding phenomena, aggregates containing several polymer chains start forming before phase separation and are also surprisingly monodisperse.19,36 4.1.2. Size of Large Aggregates. X-ray and neutron scattering experiments suggested that the small carboxyMC-DTAB aggregates are made of spherical surfactant micelles wrapped by polymer chains.7 At larger polymer concentrations, the micelles could still be present, and because all the polymer cannot wrap the micelles, these micelles could be surrounded by polymer chain loops and free ends. When the ratio Cs/Cp decreases, more water is incorporated, and the aggregates become larger, polydisperse, and softer, until they behave as microgels. Their size increases above the resolution limit of the light scattering setup (∼200 nm) and can no longer be determined. However, the viscosity of the solutions is comparable to that of water, meaning that the aggregates are not touching and that the surfactant-free polymer network has disappeared. Attempts to visualize the aggregates with an optical microscope failed, either because the aggregates were too small or because they contained too much water and the contrast was too poor. 4.2. CTAB-CarboxyMC Aggregates. At small Cs, the aggregates with CTAB have an hydrodynamic radius of about 60 nm, which is rather constant, despite the large variation in scattered intensity, likely due to a variation in the water content. As for the DTAB-carboxyMC aggregates with Cp less than 50 mg/L, the amount of water in the aggregates increases with decreasing Cp and probably has the same origin. The intensity increase seen at low q reveals a clustering of the aggregates. The aggregates are considerably modified in the surfactant concentration range of 1-2 mM. Above 1 mM, the aggregates are loose at high length scale and exhibit a broad distribution of internal modes. Similar variation has already been observed and (33) Deserno, M. Eur. Phys. J. E 2001, 6, 163. (34) Lapitsky, Y.; Kaler, E. W. Colloids Surf., A 2004, 250, 179. (35) Nicholson, L. K.; Higgins, J. S.; Hayter, J. B. Macromolecules 1981, 14, 836. (36) Dawson, K. A.; Gorelov, A. V.; Timoshenko, E. G.; Kuznetsov, Y. A.; Du Chesne, A. Physica A 1997, 244, 68.
Aggregate Formation in CarboxyMC-Surfactant
predicted in flexible polymers with quasi-elastic neutron scattering.37,38 At a length scale of 1/q between the polymer and the monomer sizes, internal modes reflected by a stretched exponential and by a proportionality between D and q are observed. Outside of this range, a diffusive mode is seen with a singleexponential decay and a diffusion coefficient independent of q, which corresponds to the diffusion of either monomers (large q) or polymers (small q). The situation seen with CTABcarboxyMC aggregates could be similar, with the “monomers” being subunits of size 33 nm. At low q, the intensity varies as q1.6, suggesting fractal-like arrangements of subunits, similar to what was seen by Voisin and Vincent with a cationic polyelectrolyte.6 Most of the measurements have been done in a surfactant concentration range where the aggregates are positively charged, contrary to the DTAB-carboxyMC aggregates. The zeta potential measured at 10 mg/L also varies continuously over up to two decades of surfactant concentration. Note that the broad variation could be due in part to the progressive internal reorganization of the aggregates suggested by the light scattering results. Figure 10 shows that the zeta potential saturates above 2 mM, where the aggregates are made of subunits with radius 30 nm, whereas, below 1 mM, the aggregates are much smaller, with a radius of about 60 nm.
5. Conclusion The strong interactions between DTAB and carboxyMC lead to the formation of multichain aggregates well above the cac. At low polymer concentrations, the aggregates are spherical, rigid, and monodisperse, and their size increases exponentially with Cs. At high polymer concentrations, the aggregates become larger, polydisperse, and softer. X-ray and neutron scattering experiments suggest that the small carboxyMC-DTAB aggregates are made of spherical surfactant micelles wrapped by polymer chains.7 At larger polymer concentrations, the micelles could still be present, and because all the polymer cannot wrap the micelles, these micelles could be surrounded by polymer chain loops and free ends. These multichain aggregates remain negatively charged, even above the surfactant concentration at which the surfactant brings the same amount of charges as the polymer in the solution (electroneutrality). This is because bromide counterions remain trapped in the aggregates. The volume fraction of the aggregates φ is significantly larger than that of the polymer and surfactant φdry, indicating that the aggregates contain an appreciable amount of water. When the polymer concentration increases, the amount of water increases, because when the relative amount of surfactant decreases, the collapse is less effective and more water should be present in the aggregate. A different behavior is seen at very low polymer concentrations, however, in a region where binding is weak. The size of the aggregates depending on the mixing procedure and thermodynamic theories cannot be used to explain these features, but similarities with mesoglobules formed close to a cloud point were stressed. The increase of surfactant tail length dramatically changes the behavior of aggregates. The CTAB-carboxyMC aggregates are much larger than DTAB-carboxyMC ones and therefore still contain much more water. At large Cs, they exhibit an internal structure and are made of large subunits. Their charge vanishes (37) Chen, H.; Zhang, Q.; Li, J.; Ding, Y.; Zhang, G.; Wu, C. Macromolecules 2005, 38, 8045. (38) Schaefer, D. W.; Han, C. C. Quasielastic light scattering from dilute and semidilute polymer solutions. In Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy; Plenum Press: New York, 1985; pp 181-243.
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at the surfactant concentration at which the surfactant brings the same amount of charges as the polymer in the solution (electroneutrality), a situation found for many other polymersurfactant systems, but not for DTAB-carboxyMC. The interpretation of these differences remains to be clarified. Acknowledgment. We thank M. Turmine for allowing us to use her electrodes to perform the binding isotherms measurements in her laboratory. We also thank J.F. Argillier for making available to us a Zetasizer.
Appendix Let us discuss the possible origin of the variation of the scattered intensity at low Cp. 1. First Hypothesis: The Aggregates Do Not Contain Water. The variation of I(Cp)/Cp is shown for small Cp (below 500 mg/L) in Figure 5. One could first assume that this variation is due to the interactions between aggregates. Let us use a virial expression for the osmotic pressure in this dilute regime:
KIC 1 ) [1 + 2M0A2C + ....] I M0
(9)
with A2 being the second virial coefficient and M0 being the true molecular weight. Assuming that the aggregates do no contain water and that all the polymer chains are in the aggregates, we have C ) Cp + Cb, with Cb being the bound surfactant concentration (Cb ) β[Cp]). For hard spheres, A2 ) 4V, with V being the volume of the aggregates; we calculated V by assuming that the aggregates were spherical (although this is not strictosensu valid, since Rh and Rg were calculated assuming that interactions were negligible) and by using hydrodynamic radii obtained from DLS. The values found for A2exp/ASD 2 in the range 50 mg/L < Cp < 500 mg/L were positive and about 200 for 3 mM DTAB and 100 for 5 mM. This means that the interactions should be much more repulsive than hard spheres. Now in order to be valid, this interpretation has to be corroborated by DLS results. The expansion of the diffusion coefficient with the polymer concentration can be written as D ) D0(1 + kDφ), where φ is the volume fraction of the particles (φ ∝ C), and kD is another coefficient coupling thermodynamic and hydrodynamic effects. In the case of hard spheres, kD ) 1.56, while Figure 4 suggests that kD ∼ 0, meaning that the particles cannot be more repulsive than hard spheres; they are rather more attractive. Similar estimations show that the intensity variation with Cp seen below 50 mg/L cannot be attributed to interactions between aggregates either. 2. Second Hypothesis: No Interaction between Aggregates. One alternative explanation is that the aggregates contain water and that the amount of water varies with polymer concentration. We have calculated the volume fraction φ) φdry(Rh/R)3, with φdry being the volume fraction occupied by surfactant and polymer in the particle, and R being the dry radius: V ) 4πR3/3; V ∼ Mw is obtained from I(q ) 0), as the polymer and surfactant densities are close to 1. The values of φ and φdry were calculated for 5 mM DTAB, the concentration at which β was measured at different Cp: φ ∼ Cp + Cb (concentrations taken here in g/g). Theses values are reported in Table 3. One sees that φ is significantly larger than φdry, indicating that the aggregates contain an appreciable amount of water. When the polymer concentration increases, the amount of water first decreases (below 50 mg/L) and increases afterwards. The latter increase is understandable, because when the amount of polymer increases at constant surface concentration, the relative amount of surfactant decreases, the collapse is less effective, and more water should be present in
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the aggregate. At the lowest polymer concentrations, we find again a large amount of water in the aggregate, but at these low concentrations, β is very small, possibly accounting for the change in behavior. The picture is now consistent with the lack of variation of the hydrodynamic radius with polymer concentration. Indeed, assuming hard sphere-like particles, the calculated values of kDφ are less than 1 for Cp < 500 mg/L, meaning that the effect of
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interactions is indeed negligible at these low volume fractions. The fact that the overall size does not change is of course surprising and cannot be explained at the present time. The aggregate size is determined by a balance between electrostatic and hydrophobic interactions, but with the last interactions still being poorly understood, it is not easy to go further with the discussion. LA7016177
