632
Langmuir 2004, 20, 632-636
NMR Investigation of the Short-chain Ionic Surfactant-Water Systems M. V. Popova,*,† Y. S. Tchernyshev,† and D. Michel‡ Department of Quantum-magnetic Phenomena, Physical Institute, St. Petersburg State University, St. Petersburg 198504, Russia, and Faculty of Physics and Geosciences, University of Leipzig 04103 Leipzig, Germany Received August 11, 2003. In Final Form: November 7, 2003 The structure and dynamics of surfactant molecules [CH3(CH2)7COOK] in heavy water solutions were investigated by 1H and 2H NMR. A double-exponential attenuation of the spin-echo amplitude in a CarrPurcell-Meiboom-Gill experiment was found. We expect correspondence to both bounded and monomeric states. At high concentrations in the NMR self-diffusion measurements also a double-exponential decay of the spin-echo signal versus the square of the dc magnetic gradient was observed. The slow component of the diffusion process is caused by micellar aggregates, while the fast component is the result of the self-diffusion of the monomers through the micelles. The self-diffusion studies indicate that the form of micelles changes with increasing total surfactant concentration. The critical temperature range for selfassociation is reflected in the 1H transverse relaxation.
Introduction The self-association process of surfactants in water solutions has been the subject of many theoretical and experimental investigations (see for example refs 1-8). Different experimental techniques have been employed for these studies.9 It is known that the process of selfassociation, caused by hydrophobic interaction, occurs in a certain concentration range referred to as the critical micelle concentration (cmc). The value of the cmc depends on many factors, primarily on the length of the hydrophobic part of the molecule. Up to now many papers were published (see for example ref 9) in which self-organizing processes of amphiphilic molecules with long hydrophobic chains were studied by various experimental methods. However, to achieve a deeper understanding of the role of the hydrophobic chains in the self-association process, it is important to investigate short-chain ionic surfactants. Moreover, as the authors of ref 10 point out, an adequate physical explanation of the existence of the narrow concentration range for cmc in which there is a transition to the micellar state does not exist. At least for shortchain surfactants, with a methyl group number in the range of 6-7, the micelle formation is spread out on a wider range of concentration and is accompanied by the formation of premicellar aggregates. The existence of * Author to whom correspondence should be addressed at 198540 Ulianovskaja 1, Petrodvoretz, Saint-Petersburg, Russia. Telephone +7 812 4284362; fax +7 812 4287240; e-mail
[email protected]. spbu.ru. † St. Petersburg State University. ‡ University of Leipzig. (1) Grebenkov, D. S. J. Colloid Interface Sci. 2002, 249, 162. (2) Alonso, B.; Harrris, R.; Kenwright, A. J. Colloid Interface Sci. 2002, 251, 366. (3) Sterpone, F.; Briganti, G.; Pierleoni, C. Langmuir 2001, 17, 5103. (4) Gorski, N.; Kalus, J. Langmuir 2001, 17, 4211. (5) Dvinskikh, S. V.; Furo, I. Langmuir 2000, 16, 2962. (6) Bandyopadhyay, S.; Tarek, M.; Lynch, M. L.; Klein M. L. Langmuir 2000, 16, 942. (7) Edlund, H.; Sadaghiani, A.; Khan, A. Langmuir 1997, 13, 4953. (8) Schoot, P.; Cates, M. E. Langmuir 1994, 10, 670. (9) Jo¨nsson, J.; Lindman, B.; Holmbarg, K.; Kronberg, B. Surfactants and polymers in aqueous solution; J. Wiley and Sons: New York, 1999. (10) Kevelam, J. Polymer-Surfactant Interactions. Aqueous Chemistry of Laundry Detergent; Internet resources: 1998.
premicelles in the form of dimers of amphiphilic molecules for derivatives of strong acids was shown in papers by Mukerjee and Mysels and co-workers.11,12 Later the presence of larger premicellar formations was proven for sodium octanoate solutions on a basis of potentiometric measurements and light scattering by Friman et al.13 and also by Persson et al.14 on the basis of 13C NMR chemical shift measurements. Apparently, the existence of such self-associates in the self-association process of surfactants still remains an open problem and, thus, is not mentioned in some monographs devoted to this field. Even the existence of self-associates in a concentration range lower than the cmc is not considered.15,16 There are no data on the temperature stability of such formations. NMR methods seem to be particularly suitable for the investigation of micellar solutions (see, e.g., the review in ref 17). On the basis of measurements of the self-diffusion coefficients D, it is possible to estimate the micellar size and shape, the degree of counterion binding, and the hydration numbers for micelles.18 Measurements of the longitudinal relaxation times T1 for separate groups in a hydrophobic chain allow the study of conformation changes in the monomeric and micellar state.19 In addition, transverse relaxation times T2 should be used in order to investigate micellar sizes and, in particular, the degree of molecules packing in a micelle. This is caused by their particular sensitivity to slow motions. However, experimental data about direct measurements of T2 by pulse methods is still absent, and in some works only estimations of spin relaxation times derived from line width measure(11) Mukerjee, P.; Mysels, K. J.; Dulin, C. I. J. Phys. Chem. 1957, 62, 1390. (12) Mukerjee, P. J. Phys. Chem. 1965, 69, 2821. (13) Friman, R.; Pettersson, K.; Stenius, P. J. Colloid Interface Sci. 1975, 53, 90. (14) Persson, B. O.; Drakenberg, T.; Lindman, B. J. Phys. Chem. 1979, 83, 3011. (15) Moroi, Y. Micelles. In Theoretical and Applied Aspects; Plenum Press: New York, 1992. (16) Clint, J. H. Surfactant Aggregation; Blackie and Son: 1992. (17) So¨derman, O.; Stilbs, P. Prog. NMR Spectrosc. 1994, 26, 445. (18) Stilbs, P.; Lindman, B. J. Phys. Chem. 1981, 85, 2587. (19) Zana, R. Surfactant Solution. New Method of Investigation; Marcel Dekker: New York and Basel, Switzerland, 1987.
10.1021/la035465s CCC: $27.50 © 2004 American Chemical Society Published on Web 12/12/2003
NMR of Short-Chain Ionic Surfactant-Water Systems
Langmuir, Vol. 20, No. 3, 2004 633
Figure 1. Dependence of the relative monomeric pa and micellar pb fractions in the transversal relaxation function on the surfactant concentration at T ) 293 K. (In this and the following figures, the lines drawn are only a guide for the eye).
ments may be found.20,21 Hence, there are almost no reliable data from NMR studies concerned with surfactant solutions in a wide range of temperatures and concentrations. This situation stimulated us to present results of selfdiffusion and NMR relaxation time measurements for short-chain surfactant molecules in a wide temperature and concentration range in order to derive more detailed conclusions on the sizes and shapes of self-associates and also on their hydration degree. Materials and Methods The surfactant (potassium nonanoate) was dissolved in heavy water. Surfactant concentrations were varied from 0.125 to 1.5 mol/L, corresponding to 2.5-30 wt %. The content of residual H2O was not larger than 2 wt %. Before the measurements, all solutions were kept at 293 K for 2-3 days to achieve thermodynamic equilibrium. The surfactant solutions were investigated at temperatures between 275 and 353 K. The initial measurements were carried out at 293 K, and then the samples were gradually heated or cooled in steps smaller than about 2 K. Finally, the samples were kept for 20-30 min at the set temperature before measurement. Measurements of the self-diffusion coefficients D of protons were made from the attenuation of the Hahn spin-echo in a constant field gradient and applying a home-built spin-echo spectrometer operating at 20 MHz. Self-diffusion coefficient measurements of deuterons were carried out with a Bruker spectrometer (at 13.8 MHz). Proton spin relaxation times T2 (with the CPMG pulse group) were run at 20 MHz, also on a Bruker spectrometer. The accuracy in the temperature-dependent measurements was (0.5 K.
Results and Discussion Transverse Relaxation. The decay of the spin-echo amplitude A(t) for the CPMG pulse sequence 90°-(180°)n is characterized by a biexponential function at all concentrations:
( )
A(t) ) pa exp -
( )
t t + pb exp T2a T2b
(1)
Here pa and pb are the relative fractions of the relaxation components T2a and T2b, respectively. The relaxation times T2a and T2b assume values from 1.2 to 2.5 s and from 0.1 to 0.4 s, respectively. The relative fraction pb increases with rising total concentration from 6% (at c ) 2.5%) to 92% (at c ) 30%) as can be seen in Figure 1. The double-exponential relaxation function can be caused by two factors. The first is a double-exponential behavior due to differences in the T2 values for various groups within the same molecule. The long component probably arises from the CH3 group, from residual water (H2O), and from CH2 groups, which are very close to the (20) To¨rnblom, M.; Henriksson, U.; Ginley, M. J. Phys. Chem. 1994, 98, 7041. (21) Stubenrauch, C.; Nyde´n, M.; Findenegg, G. H.; Lindman, B. J. Phys. Chem. 1996, 100, 17028.
Figure 2. Concentration of micellized (1) and free (2) surfactant vs total surfactant concentrations c at T ) 293 K.
Figure 3. Dependence of the relaxation rates T2a-1 and T2b-1 on the total concentration of surfactant c at T ) 293 K. The relaxation rates T2a-1 and T2b-1 are ascribed to the monomeric and micellar states, respectively.
methyl group. The short relaxation time may be related to the residual groups’ proximity to the polar groups. If we were to take into account a fast exchange between bonded and free surfactants, then we would expect the relative fractions to be independent of the concentration. This is in contradiction to our observations (Figure 1). Moreover, a fast exchange does not explain the temperature dependence of the relative fractions of the T2a and T2b relaxation components, as will be seen below. An alternative explanation for the observed doublecomponent relaxation attenuation is distinction in molecular mobility in the monomer and aggregate states. Additionally, in the aggregates the increase of the relaxation rate due to intermolecular dipole interactions is probable, while for monomers in the D2O solution these interactions are small. With slow exchange, when the lifetime of a molecule in each of these states is not less than the appropriate relaxation time, the T2a and T2b times and the relative fractions pa and pb may be derived from the experimental values directly. These correspond to the monomeric and aggregated states of the surfactant molecules, respectively. Starting with this assumption, based on the experimentally obtained values pa and pb, it is possible to obtain the dependence of the micellar and monomeric concentrations in a solution, cmic and cmon, on the total surfactant concentration c (Figure 2). It is apparent from Figure 2 that the common character of the dependencies is in good agreement with those obtained earlier for the ionic surfactants from the measurement of self-diffusion by the method of radioactive labels22 and also from NMR measurements with pulsed field gradients.18 According to ref 23, the cmc value for potassium nonanoate is 0.34 mol/L, which corresponds in Figure 2 to the beginning of the appreciable increase in the micellar concentration. The monomeric concentration, however, reaches a maximum value at only c = 0.5 mol/L (∼10%). In Figure 3 the dependencies of relaxation rates T2a-1 and T2b-1 are shown as functions of the total concentration. A concentration range less than 10% corresponds to a gradual transition from the monomeric to the aggregated state. The relative fraction of the monomeric phase decreases from 90% to 70% in this range, and the (22) Lindman, B.; Kamenka, N.; Puyal, M.; Brun, B.; Jo¨nsson, B. J. Phys. Chem. 1984, 88, 53. (23) Wennerstro¨m, H.; Lindman, B. Phys. Rev. 1979, 52, 1.
634
Langmuir, Vol. 20, No. 3, 2004
Figure 4. Temperature dependence of the fraction p of premicellar aggregates obtained from the transversal relaxation function at c ) 2.5%.
relaxation rate (∼0.4 s-1) in this phase practically does not change at all. This demonstrates the insignificant role of the exchange process between monomers and aggregated phases. Unexpectedly, a phase existed with a relative fraction of about 10% (at a minimum total concentration of 2.5%). The relaxation rate of this phase is large (∼5 s-1). The presence of this phase is caused by the existence of premicellar aggregates consisting of a small amount of the amphiphilic molecules. The presence in a solution of such aggregates for short-chain ionic surfactants was discussed in other papers.13,14 The relatively small relaxation time of this phase (200 ms at c ) 2.5%) indicates a sufficiently dense packing of the molecules in the aggregates. The temperature stability of these formations is insignificant. If the temperature increases up to 313 K, the experimentally observable relaxation is given by a single-exponential function with a relaxation time corresponding to those of monomeric states. This is consistent with the disappearance of aggregates. A decrease of the temperature to 275 K results in an essential increase of the fraction of the aggregated state (see Figure 4) and an increase in the relaxation rate in these formations. With the increase of the total concentration from 2.5% to 10%, a reduction of the relaxation rate T2b-1 from 5 to 2.5 s-1 was found to be a consequence of the structural reorganization inside these aggregates. This may be caused by the gradual increase of the aggregation number and the larger mobility of the hydrophobic tails inside the micelles. Moreover, the shape of the aggregates may become more spherical, leading to smaller packing densities. In the concentration range from 10% to 30%, two phases, monomeric and micellar, may exist simultaneously. The relative fraction of the monomeric phase decreases from 70% down to 10% with increasing concentration, resulting in an appropriate growth of the fraction of the aggregated state. The increase of the relaxation rate T2b-1 of the micellar phase in this concentration range occurs owing to the partial transformation of the micelles from a spherical shape to a nonspherical one. It is known that these micellar shapes have a larger density of amphiphilic molecules packing than spherical ones.24 Hence, for such micellar shapes we may expect an increase of the intermolecular contribution to the observable relaxation rate and also an increasing local order Sloc which can be seen in the broadening of the 1H NMR line. A small change in the slope of the plot of T2b-1 versus the concentration occurs at c ) 20%. This may be caused by an increasing molecular packing density as opposed to a change in the micellar size or shape. As will be shown below, this assumption is supported by self-diffusion experiments on surfactants. The increase in the relaxation rate T2a-1 of the monomeric component at a concentration more than 10% is (24) Missel, P.; Maser, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1983, 87, 1264.
Popova et al.
Figure 5. Temperature dependence of transversal relaxation rate T2b-1 (for the micellar state) at c ) 30%.
apparently caused by the influence of exchange processes between micelles and monomers, which is appreciable at large concentrations. The existence of such an exchange follows also from the self-diffusion data (see below). The temperature stability of the nonspherical micelles at large concentrations (20-30%) also appears to be insignificant. In Figure 5 the dependence of the relaxation rate in aggregated phases in the temperature range of 293-343 K is given. It can be seen that at 320 K the slope of the dependency changes. This can be related to the transformation to spherical formations at higher temperatures. Self-Diffusion of Surfactant. The surfactant selfdiffusion coefficient D was measured by the attenuation of a spin-echo signal amplitude A(G0) in the two-pulse sequence 90°-τ-180° as a function of the square of the dc magnetic field gradient G0 according to
A(G0) ) A(0) exp(-2/3Dγ2G02τ3)
(2)
Here A(0) is the initial amplitude of an echo signal at G0 ) 0, γ is the gyromagnetic ratio of the protons, and τ is the interval between the two pulses. It is supposed that, during self-diffusion, a particle undergoing Brownian motion can move through an average distance satisfying the Einstein relation 〈r2〉1/2 ) x6Dτ. The typical interval τ between the two pulses in an NMR experiment lies between 10 and 100 ms, corresponding to an average diffusion length 〈r2〉1/2 of a particle about (2-5) × 104 Å for the micelles and (6-30) × 104 Å for the monomers. In the micellar surfactant solutions we have to allocate at least two range scales on which the molecules may move. Aside from the average distance given above, we also have to consider the motion of a particle through a distance of about 20-30 Å, the size of a micellar aggregate. But, as is well-known, the latter motion cannot be resolved in a spin-echo signal attenuation measurement for reasonable gradient values G0, as discussed above. In the following, we begin with a situation where the exchange process between molecular monomers and micelles or aggregates is so fast that we observe an effective self-diffusion coefficient Dexp according to
Dexp ) pmicDmic + pmonDmon
(3)
Here pmic and pmon are the relative fractions of the micellar and monomeric fractions, respectively, with pmic + pmon ) 1, and Dmic and Dmon are the surfactant self-diffusion coefficients in these states. As may be seen from Figure 6, for concentrations of 2.5-10%, the change of ln [A(G0)] as a function of the square of the magnetic field gradient has a linear character at all temperatures. The self-diffusion coefficient Dexp calculated from these dependencies in the concentration range, corresponding to the premicellar state (2.5-5%), remains constant. It follows from the relaxation data that the fraction of self-associates is small at these concentra-
NMR of Short-Chain Ionic Surfactant-Water Systems
Langmuir, Vol. 20, No. 3, 2004 635
Figure 6. Plot of the amplitude of the echo signal versus the square of the dc magnetic field gradient G0 at c ) 10% at different temperatures. (The lines drawn show the results of calculations).
Figure 7. Dependence of the surfactant self-diffusion coefficient on the total surfactant concentration c.
tions and the aggregation number of these associates is insignificant. So the experimental self-diffusion coefficient basically corresponds to the monomeric self-diffusion at this concentration range. At a temperature of 293 K, the value Dexp ) 4.4 × 10-10 m2 s-1 extrapolated to zero concentration is close to the self-diffusion value received for sodium octanoate monomers in ref 22. With concentrations higher than 5% (Figure 7) an essential reduction of the coefficient Dexp is observed. That is caused by both an increase of the micellar state fraction and an increase of the obstacle fraction, resulting in hindered diffusion. The problem of the obstruction effect for the diffusion of Brownian particles in a solution has often been considered (see, for example, refs 25-29), also including charged particles. The reduction of the experimentally observable self-diffusion coefficient can be expressed by
Dexp ) D0(1 - kΦ)
(4)
Here Dexp is the experimentally obtained self-diffusion coefficient, D0 is the micellar self-diffusion coefficient at infinite dilution, Φ is the micellar volume fraction in a solution, and k is a coefficient between 1.7 and 2.1. Using the values for the micellar and monomer fractions received from the relaxation data, we obtain the value (1 - kΦ) = 0.42 at c ) 30%, in contrast to the experimental ratio Dexp/D0 ≈ 0.075 measured under the same conditions. This large divergence is caused by the increase in the micellar sizes with increasing concentration and by the increase of their aggregation number. The hydrodynamic micellar radius Rh is usually estimated on the basis of the Stokes-Einstein formula:
kBT Rh ) 6πηDm
(5)
Here T is the temperature, η is the viscosity of the solvent, kB is Boltzmann’s constant, and Dm is the micellar selfdiffusion coefficient, with the obstruction effect taken into account. (25) Wang, J. J. Am. Chem. Soc. 1954, 76, 4755. (26) Mazo, R. J. Chem. Phys. 1965, 43, 2873. (27) Otsuki, T.; Okano, K. J. Chem. Phys. 1982, 77, 1443. (28) Bezrukov, O. F.; Lukianov, A.; Pozdishev, V. Mol. Phys. Biophys. Aq. Syst. L 1986, 6, 90. (29) Bell, G. Trans. Faraday Soc. 1964, 60, 1754.
Figure 8. Plot of the amplitude of the echo signal versus the square of the dc magnetic field gradient G0 at c ) 30% at different temperatures.
We estimate the value of Rh in the concentration range close to the cmc value. Using the experimental selfdiffusion Dexp ) 3.4 × 10-10 m2 s-1 at =10% and the fractions of the monomeric (pmon) and micellar (pmic) states (see Figure 1), and also the value of the obstacle coefficient (1-2Φ) for this concentration, we obtain a value for Rh of 14 Å. This slightly exceeds the radius of the “dry” micelle (Rh0 = 12 Å), calculated with Tanford’s formula,30 using the length lc of an extended alkyl chain, lc ) 1.5 + 1.265nc. Here nc is the number of alkyl groups in a molecule. If we additionally consider the micellar hydration sphere, this value will be a reasonable approximation. The resulting error in the size Rh can have a 10-20% effect owing to the small difference between the values Dmon and Dexp in this concentration range and the error in the Dexp value of about 5-7% in our experiments. At concentrations of 15% and higher, the attenuation of the spin-echo amplitude as a function of G02 is described by the superposition of two exponents (Figure 8) according to
A(G0) )
∑i A0i exp(-2/3Diγ2G02τ3)
(6)
Here A0i are the initial amplitudes of the echo signal and Di are coefficients reflecting a fast and a slow surfactant self-diffusion. We begin with a discussion of the slow diffusion. In the concentration range between 20% and 30%, the Rh value calculated on the basis of eq 5 exceeds the value Rh0. This can be related to a further micelle transformation. The alternative forms can thus be prolate or oblate ellipsoids for which the self-diffusion coefficient is expressed by a modified equation:31
Dm )
kBT F 6πηb
(7)
Here F is a function that depends on the ratio x of the long (a) and short (b) axes of the ellipsoid:
F)
ln [x + (x2 - 1)1/2]
F)
(x2 - 1)1/2 arctan(x2 - 1)1/2 (x2 - 1)1/2
x>1
(8)
x
