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Interaction between Gelatin and Anionic Surfactants P. C. Griffiths,*,† P. Stilbs,‡ A. M. Howe,§ and T. H. Whitesides| Department of Chemistry, University of Wales Cardiff, P.O. Box 912, Cardiff CF1 3TB, U.K., Physical Chemistry, Royal Institute of Technology, Stockholm, S100 44, Sweden, Kodak European Research, Headstone Drive, Harrow, Middlesex HA1 4TY, England, and Imaging Research and Advanced Development, Eastman Kodak Company, Rochester, New York 14650-2109 Received April 1, 1996. In Final Form: July 23, 1996X The effects of alkyl chain length of homologous alkyl sulfate surfactants ranging from C8 to C14 on the diffusion behavior of both the surfactant and gelatin have been investigated by pulsed-gradient spin-echo NMR spectroscopy. Changes in the diffusivity of the surfactant can be rationalized in terms of a two-state model consisting of gelatin-bound micelles in equilibrium with freely diffusing unimeric surfactant. A minimum in the diffusivity of gelatin is observed when the binding of surfactant amounts to about 1 micelle/strand. The depth of this minimum increases with the chain length of the surfactant. These effects are explained in terms of micelle-mediated transient cross-links as proposed by Greener et al. (Macromolecules 1987, 20, 2490). The effective strength of the cross-links is a decreasing function of the number of micelles/strand because of the electrostatic repulsion between the micelles; the strength increases with an increase in the size of the micelles.
Introduction The interactions between synthetic homopolymers and selected surfactants have been studied extensively.1-10 Most of the available evidence supports a picture of the complex consisting of spherical, monodisperse micelles adsorbed onto the polymer coil in a “bead-and-necklace” arrangement.11 In the presence of the polymer, adsorbed micelles form at a critical aggregation concentration (cac), well below the conventional critical micelle concentration (cmc) observed in the absence of polymer. Recent theoretical modeling10 of this system suggests that the polymer segments bind in the micelle palisade layer and shield a fraction of the hydrophobic core from contact with water, resulting in a decrease in the interfacial free energy. Several other classes of polymers interact strongly with surfactants. In particular, surfactants bind to hydrophobically modified polymers, such as water-soluble polymers with hydrophobic end caps or polymers with hydrophobic side chains.8,12-21 Ionic surfactants bind
strongly to polyelectrolytes of opposite charge.22-24 Weaklycharged polyampholytes like proteins are well-known to complex with anionic surfactants; the interaction has both charge and hydrophobic contributions and is sufficiently strong to destroy the tertiary structure of the protein. This phenomenon is the basis for the molecular weight determination of polypeptides by means of sodium dodecyl sulfate (SDS) polyacrylamide gel electrophoresis. This paper is concerned with the complexes formed from a particular polypeptide polyampholyte (gelatin) and anionic surfactants. Gelatin is a denatured polypeptide derived from collagen and is widely used in the food and photographic industries. The formation of gelatinsurfactant complexes is particularly relevant in the latter application since surfactants are commonly incorporated into gelatin containing solutions to promote emulsification and to control surface tension during coating operations. The formation of complexes of gelatin and anionic surfactants has been studied by precipitate formation below the isoelectric point,25,26 rheology,27,28 surface tension,29-31 equilibrium dialysis,32,33 ion-selective electrode studies,34
†
University of Wales Cardiff. Royal Institute of Technology. § Kodak European Research. | Eastman Kodak Company. X Abstract published in Advance ACS Abstracts, October 1, 1996. ‡
(1) Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294. (2) Goddard, E. D. J. Am. Oil Chem. Soc. 1994, 71 (1), 1. (3) Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Anathapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL 1993; p 1. (4) Goddard, E. D. Polymer-surfactant interaction. Part II. Polymer and surfactant of opposite charge. Interactions of surfactants with polymers and proteins; Goddard, E. D. Anathapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL 1993; p 171. (5) Lin, M. Y.; Sinha, S. K.; Chari, K. J. Phys. IV 1993, 3, 153. (6) Cabane, B.; Duplessix, R. J. Phys. (Paris) 1987, 48, 651. (7) Cabane, B. Colloids Surf. 1985, 13, 19. (8) Francois, J.; Dayantis, J.; Sabbadin, J. Eur. Polym. J. 1985, 21, 165. (9) Cabane, B. J. Phys. (Paris) 1981, 42, 847. (10) Nikas, Y. J.; Blankschtein, D. Langmuir 1994, 10, 3512. (11) Whitesides, T. H.; Miller, D. D. Langmuir 1994, 10, 2899. (12) Gelman, R. A.; Barth, H. G. Adv. Chem. Ser. 1986, 213. (WaterSoluble Polymers), 101. (13) Gelman, R. A.; Barth, H. G. Polym. Mater. Sci. Eng. 1984, 51, 556. (14) Varelas, C. G.; Dualeh, A. J.; Steiner, C. A. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1991, 32 (1), 583. (15) Wu, S.; Steiner, C. A. Mater. Res. Soc. Symp. Proc. 1994, 331 (Biomaterials for Drugs), 205.
S0743-7463(96)00314-9 CCC: $12.00
(16) Dualeh, A. J.; Steiner, C. A. ACS Symp. Ser. 1992, 480 (Polyelectrolyte Gels), 42. (17) Dualeh, A. J.; Steiner, C. A. Macromolecules 1990, 23 (1), 251. (18) Loyen, K.; Iliopoulos, I.; Audebert, R.; Olsson, U. Langmuir 1995, 11 (4), 1053. (19) Magny, B.; Iliopoulos, I.; Audbert, R.; Piculell, L.; Lindman, B. Prog. Colloid Polym. Sci. 1992, 89, 118. (20) Magny, B.; Iliopoulos, I.; Zana, R.; Audebert, R. Langmuir 1994, 10, 3180. (21) Sarrazin-Cartalas, A.; Iliopoulos, I.; Audebert, R.; Olsson, U. Langmuir 1994, 10, 1421. (22) Li, Y. J.; Dubin, P. L.; Havel, H. A.; Edwards, S. L.; Dautzenberg, H. Macromolecules 1995, 28 (9), 3098. (23) Guillemet, F.; Piculell, L. J. Phys. Chem. 1995, 99(22), 9201. (24) Guillemet, F.; Piculell, L.; Nilsson, S.; Djabourov, M.; Lindman, B. Prog. Colloid Polym. Sci. 1995, 98, 47. (25) Pankhurst, K. G. A.; Smith, R. C. M. Trans. Faraday Soc. 1944, 40, 465. (26) Knox, W. J.; Wright, J. F. J. Colloid Interface Sci. 1965, 20, 177. (27) Greener, J; Constestable, B. A.; Bale, M. D. Macromolecules 1987, 20, 2490. (28) Howe, A. M.; Wilkins, A. G.; Goodwin, J. W. J. Photogr. Sci. 1992, 40, 234. (29) Kragh, A. M. Trans. Faraday Soc. 1964, 60, 225. (30) Knox, W. J.; Parshall, T. O. J. Colloid Sci. 1970, 33, 16. (31) Wustneck, R.; Hernel, H.; Kretzschmar, G. J. Colloid Interface Sci. 1983, 93, 419. (32) Isemura, T.; Tokiwa, F.; Ikeda, S. Bull. Chem. Soc. Jpn. 1962, 35, 240. (33) Arora, J. P. S.; Soam, D.; Singh, S. P.; Kumar, R. Tenside Deterg. 1984, 21, 2.
© 1996 American Chemical Society
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film thickness,35 and 13C NMR spectroscopy.36 Whitesides and Miller11 proposed a structure for the SDS/gelatin complex analogous to the “bead-and-necklace” model and showed that SDS micelles adsorbed on gelatin have a similar size and shape to those formed in the absence of the polymer. However, unlike the neutral homopolymer cases, the binding between gelatin and SDS is a result of both electrostatic and hydrophobic interactions, a conclusion supported by 13C NMR studies.36 These workers also pointed out the strong electrostatic interactions between adjacent micelles attached to a single polymer strand. Manifestations of this interaction are the stepwise binding of micelles and a monotonic increase in surfactant monomer (unimer) activity throughout the binding regime. This electrostatic repulsion also provides a natural explanation for the “saturation” of the polymer by micelles. This model has been quantitatively modeled and extended by Nikas and Blankschtein.10 Mixtures of gelatin with anionic surfactants show large increases in viscosity, a phenomenon investigated by Greener et al.27 These workers studied the effect of alkyl chain length on the viscosity of 5% (w/w) gelatin solutions at 41 °C for a homologous series of simple alkyl sulfate surfactants. An increase in the alkyl chain length resulted in a lowering of the onset of thickening and a considerable enhancement in the degree of thickening. The onset of thickening occurred at the cac. A maximum in the viscosity was observed at a surfactant concentration somewhat above the cac, which was suggested to be the result of the formation of transient cross-links between gelatin strands mediated by micelles bound to more than one polymer strand. Similar viscosity increases are also observed for the two most commonly studied homopolymer systems, poly(vinylpyrrolidone) or poly(ethylene oxide) (PEO) with sodium dodecyl sulfate. Here again, a maximum viscosity is found at a characteristic value of the surfactant concentration. The position of this maximum is independent of the polymer molecular weight but linearly dependent on the polymer concentration.1,5 The viscosity at the maximum is more strongly dependent on the polymer molecular weight than is the viscosity of the polymer alone. Chari1,5,37 proposes that the maximum in the viscosity corresponds to the saturation of the polymer with surfactant. In contrast to Greener et al.,27 Chari proposes that the increased viscosity is due to the expansion of the polymer as the result of charge repulsion between adsorbed micellessi.e., no transient cross-links are formed. These two apparently diametric opinions can be rationalized by considering the polymer concentrationsthe data of Chari et al. are for low-concentration systems, mostly below C*, the polymer overlap concentration, whereas the data of Greener et al.27 correspond to systems above C*. Indeed, the increase in the viscosities for the low molecular weight systems presented by Chari et al.1 are considerably smaller than those for the Greener et al.27 data. It is interesting to note, however, that the highest molecular weight system studied by Chari et al.1 (0.5% PEO 885K) must be above C*, and this system does exhibit a similar viscosity enhancement as that seen in the data of Greener et al.27 Miller et al.36 and Griffiths et al.38 have used the pulsed(34) Fruhner, H.; Kretzschmar, G. Colloid Polym. Sci. 1992, 270, 177. (35) Wustneck, R.; Miller, H.-J. Colloid Polym. Sci. 1986, 264, 97. (36) Miller, D. D.; Lenhart, W.; Antalek, B. J.; Williams, A. J.; Hewitt, J. M. Langmuir 1994, 10, 68. (37) Chari, K.; Antalek, B.; Minter, J. Phys. Rev. Lett. 1995, 74 (18), 3624. (38) Griffiths, P. C.; Stilbs, P.; Cosgrove, T.; Howe, A. M. Langmuir 1996, 12, 2884.
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gradient spin-echo NMR (PGSE-NMR) technique to study the diffusion of SDS and gelatin in their mixtures. On addition of SDS, both the gelatin and SDS self-diffusion coefficients decreased. At 40 mM SDS, the gelatin diffusivity exhibits a minimum which is over an order of magnitude lower than the surfactant-free value. The maximum in the solution viscosity observed by Greener et al. occurs at essentially the same value of surfactant concentration, so that the diffusion behavior mirrors the viscosity. The purpose of this paper is to study the effect of alkyl chain length on the interaction between gelatin and a homologous series of alkyl sulfates. A particular aim will be to shed light on the mechanism by which surfactants control the mobility of the polymer and increase the viscosity of gelatin solutions. Experimental Section Materials. The sodium dodecyl sulfate was obtained from BDH Laboratory Supplies and recrystallized from ethanol before use. The other alkyl sulphates were obtained from Lancaster Synthesis, Ltd., and used as received. The fractionated gelatin used in this study was derived from an alkali-processed type IV photographic gelatin by fractional precipitation from water with methanol and NaNO3. In contrast to the starting, nonfractionated gelatin, which is distinctly bimodal, gel-permeation chromatography shows the fractionated material to be monomodal with 80% R chains and 19% low molecular weight material (Mw ) 95 400; Mn ) 68 100; Mw/Mn ) 1.4). The following abbreviations are used: SOS, sodium octyl sulfate; SDecS, sodium decyl sulfate; SDS, sodium dodecyl sulfate; and STS, sodium tetradecyl sulfate. In order to minimize sample-to-sample variations, all samples were prepared from a stock gelatin solution made up at twice the final concentration. The gelatin stock solution was prepared by warming the required amount of gelatin and solvent (D2O) to 45 °C with occasional shaking. The solution was maintained at that temperature for 2 h. To an aliquot of this stock gelatin solution were added varying volumes of stock surfactant solution and pure D2O. All of the samples were equilibrated at 44 °C for at least 6 h prior to measurements being taken. All of the PGSENMR solutions were made up in D2O (Isotech, Ltd.). Throughout this paper the surfactant concentration is expressed in mM units. Gelatin concentrations, expressed as percent (w/w) in D2O, are about 10% more concentrated than those in a similar solution in water at the same nominal concentration because of the density difference between H2O and D2O. NMR Experiments. The self-diffusion measurements,39 using the Fourier transform PGSE-NMR technique, were performed on a Bruker MSL200 spectrometer employing the longitudinal eddy current delay sequence.40 The attenuation of the spin-echo amplitude after Fourier transformation was sampled as a function of the duration, δ, of the applied gradient pulses (0.2 e δ e 6.5 ms). The first radiofrequency pulse interval, τ, was fixed at 10 ms during the experiments in order to keep the spin-spin relaxation effects on the echo amplitude to a minimum. The gradient pulse interval, ∆, was kept constant at 140 ms. The magnitude of the field gradient pulses, G, can also be varied during the experiment; values of 0.087 < G < 1.6 T m-1 were used. The use of large pulsed gradients often produces eddy currents in the metallic material that comprises the probe and its assembly which changes the resistance of the coils. These factors result in a mismatch between successive pairs of gradient pulses and has a serious effect on signal intensity and stability. To eliminate these problems, the spectrometer is equipped with a Woodward gradient amplifier41 which delivers pairs of read and write gradients matched to better than 10 ppm. Furthermore, in all of the diffusion sequences employed, three field gradient prepulses were applied before every scan to bring the effects of coil heating and eddy currents to near steady-state conditions. Field gradient (39) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (40) Gibbs, S. J.; Johnson, C. S., Jr. J. Magn. Reson. 1991, 93, 391. (41) Boener, R. M.; Woodward, W. S. J. Magn. Reson., Ser. A 1994, 106, 195.
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Figure 2. Viscosity of surfactant containing gelatin solutions for the surfactants of Figure 1. Conditions and symbols are as in Figure 1. Figure 1. Self-diffusion coefficients of fractionated gelatin from PGSE-NMR as a function of surfactant concentration: Filled circles, SOS; open circles, SDecS; filled triangles, SDS; open triangles, STS. Conditions were 5% (w/w) gelatin in D2O at 44 °C. calibration was carried out by the use of known self-diffusion standards (H2O/D2O mixtures). A constant temperature of 44 ((1) °C was used. For molecules undergoing unhindered Brownian motion, the decay of the echo amplitude A(δ) obeys39
A(δ) ) A(o) exp(-τ/T2) exp(-kDS)
(1)
where τ is the time over which spin-spin relaxation (defined by the time constant T2) operates, k ) (γGδ)2(∆ - δ/3), where γ is the magnetogyric ratio of the nucleus under observation and DS represents the self-diffusion coefficient.
Results Gelatin. The effect of the concentration of the surfactant and the alkyl group chain length on the selfdiffusion coefficient of the gelatin is shown in Figure 1. The longer the alkyl chain, the more the diffusion of gelatin is slowed by the addition of surfactant; the diffusivity of gelatin is almost 2 orders of magnitude less in the presence of 50 mM STS than in its absence. For each of the surfactants, other than SOS, the gelatin self-diffusion coefficient decreases to a local minimum and then rises to a plateau before finally decreasing again at higher surfactant concentrations. Interestingly, the initial slope appears to be the same for all of the alkyl chain lengths. The STS data do not show the second decrease because the solubility limit of the surfactant is exceeded under our conditions at around 100 mM. For SOS, much less dramatic changes in diffusivity are seen, and Dsgelatin changes only slowly with concentration. Figure 2 shows the effect of the various surfactants on the viscosity of 5 wt % gelatin solutions. The trends in the viscosity observed on changing surfactant structure are similar to those reported by Greener et al.27 with two exceptions. For the fractionated gelatin, the magnitude of the viscosity increase is lower and there is a plateau in the viscosity rather than the maximum observed by Greener et al.27 The reason for the absence of the maximum in the viscosity for the fractionated gelatin system is as yet unknown. The value of the viscosity at
Figure 3. Self-diffusion coefficients of surfactant in gelatin solution for the surfactants of Figure 1. Conditions and symbols are as in Figure 1.
the plateau increases with alkyl chain length, as does Greener’s maximum. Inspection of Figures 1 and 2 indicates that, on increasing surfactant concentration, the trends in the bulk viscosity of the solution mirror those of the self-diffusion coefficient of the gelatin. For homologues greater than octyl, both the magnitude and position of the minimum in the self-diffusion coefficient show a good correlation with those at the onset of the plateau of the viscosity. For the octyl sulfate there are no extrema. Hence, as expected, the viscosity and diffusion measurements probe the same structural properties of the system. Surfactant. Figure 3 shows the surfactant selfdiffusion coefficients as a function of surfactant concentration. The most striking observation is the large decrease in the surfactant mobility with an increase in chain length; with the addition of two methylene groups, the mobility decreases about 5-fold. This decrease is much larger than that expected on the basis of the surfactant unimer size alone. Except for SOS, the general shapes of the curves are similar. As the surfactant concentration increases, there is an initial, rapid decrease in the value
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of the self-diffusion coefficient, followed by a plateau. For SDecS and SDS, there is a further decrease in the selfdiffusion coefficient at the higher surfactant concentrations.
Table 1. Summary of cmc and cac Data for the Surfactants Used in This Study
surfactant
Discussion
SOS SdecS SDS
STS
134 mM (25 °C) 138 mM (45 °C) 102 mM (21 °C, 0.1 M NaCl) 33-34 mM (25 °C) 34-35 mM (45 °C) 15.1 mM (25 °C, 0.1 M NaCl) 8.1-8.3 mM (25 °C) 8.1 mM (45 °C) 1.5 mM (25 °C, 0.1 M NaCl) 2.1 mM (25 °C) 2.3 mM (45 °C)
70 mM (pH ∼ 6)b 6 mM (pH ∼ 6)b 0.3 mM (pH ) 5.7)c 1.0 mM (pH ) 6.0)c 1.7 mM (pH ) 6.8)c 0.3 mM (pH ) 5.7, 0.1 M NaClc ∼0.15 (pH ∼ 6)b
a Mukerjee, P. Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; National Standards Reference Data; US National Bureau of Standards: Washington, DC, 1971; p 36. b This work. c Whitesdies and Miller, ref 11.
Dsobs )
DsuCu + DsmCm Ct
(2)
(
)
On the basis of the previous work that has been reported,38 the simplest reasonable model to use as a basis for understanding the surfactant diffusion data is a twostate model in which unimer is in equilibrium with gelatinbound micelles (and possibly a small amount of bound unimeric material). The uncomplexed unimer diffuses at a rate that is expected to be very similar to that in water, modified by a small obstruction effect due to the presence of the gelatin. Since the molecular size of the unimer is small, the gelatin matrix is not expected to offer serious hindrance to its passage. The micellar species, on the other hand, are bound to the gelatin strands and therefore move with them. The possibility exists that the micelles could diffuse at a somewhat greater rate than the gelatin if creeping motions along the strands are allowed, but this possibility is ignored in our discussion. Under these conditions, the observed surfactant selfdiffusion coefficient, Dsobs, is the concentration-weighted average of unimer and micellar diffusion; that is, the selfdiffusion coefficient is given by eq 2.
critical micelle concentration cmca
critical aggregation concentration cac in 5% (w/w) gelatin at 44 °C
In this equation, Dsu and Dsm are the diffusion coefficients of unimer (superscript u) and micelle (superscript m), respectively, and Cu, Cm, and Ct are the concentrations of surfactant in unimer form (u), micellar form (m), and total (t). Since the micelles are assumed to move with the gelatin, Dsm ) Dsgelatin, where Dsgelatin is the self-diffusion coefficient of the gelatin. PGSE-NMR studies of probe molecules located in the core of micelles in these systems support this equivalence.36,38 Using this approach, we can estimate the unimer concentration from eq 3:
Dsobs - Dsgelatin Ct Cu ) Dsu - Dsgelatin
(3)
Figure 4. Binding isotherms derived by application of eq 3 to the self-diffusion data (see text).
Except for SOS, direct measurement of the diffusion of the unimer form in noninteracting gelatin-containing solutions was impossible because the cac’s for the more hydrophobic surfactants were too low (the cmc’s and cac’s in gelatin solution for these surfactants are summarized in Table 1). However, in water, direct measurement below the cmc gave the following values: SOS (10.5 ( 0.5) × 10-10 m2 s-1; SDecS, (9.1 ( 0.5) × 10-10 m2 s-1; SDS, (8.15 ( 0.5) × 10-10 m2 s-1. A value for the STS unimer could not be determined because of the very low cmc. These values decrease by about 15% for each pair of methylene groups in the tail. The diffusivity of the STS unimer in water can therefore be estimated to be about 7.2 × 10-10 m2 s-1. For SOS in gelatin, measurements of the selfdiffusion coefficients below the cac (70 mM) are possible and give an average value of 6.9 × 10-10 m2 s-1. It is reasonable to assume therefore that the presence of 5% gelatin decreases the diffusivity of the surfactant by a factor of approximately 0.66. We assume that this same retardation applies to all of the unimers. Thus, the unimer diffusivities in 5% gelatin can be estimated to be: SOS, 6.9 × 10-10 m2 s-1 (measured); SDecS, 6.0 × 10-10 m2 s-1; SDS, 5.3 × 10-10 m2 s-1; and STS, 4.7 × 10-10 m2 s-1. Using these values, eq 3 was used to calculate the
concentration of unimer necessary to produce the observed surfactant diffusivities of Figure 3, given the gelatin diffusivities of Figure 1. For surfactant concentrations above the cac and below the point at which free micelles are formed (taken to be the concentration of the surfactant at the end of the plateau in Figure 3), it is assumed that all of the surfactant that is not unimer is in the form of bound micelles. The binding isotherms thus calculated are displayed in Figure 4. All of the binding isotherms have a similar shape, displaced as expected to lower surfactant concentrations for more hydrophobic surfactants. As discussed previously for the particular case of SDS,11,38 the activity of the unimer increases monotonically above the cac, though in the semilog display of Figure 4 this increase is not dramatic. The most striking feature of the curves describing gelatin diffusivity in Figure 1 is the deep minimum in the diffusivity displayed by each of the more hydrophobic surfactants. Since the favored mechanism for the viscosity plateau/maximum involves cross-linking of the gelatin by means of bound micelles, it is natural to seek an explanation for this minimum in terms of the number of micelles in the system. We have reported11 that the aggregation number (60) for SDS bound to gelatin is essential the same as that for free micelles under otherwise
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Figure 5. Self-diffusion coefficients of fractionated gelatin plotted as a function of the calculated micelle concentration (in mM micelle/L). Note the common minimum in the diffusivities of the three more hydrophobic surfactants at around 0.6 mM, corresponding to approximately 1 micelle/gelatin strand.
similar conditions of pH and ionic strength. Similar measurements42 of SDecS/gelatin yield the same result: nagg ) 41 in water and 39 in gelatin. For SOS and STS, aggregation numbers in water of 27 and 80 have been reported; it is assumed that these values apply to gelatinbound micelles of these surfactants as well. With these values of the aggregation number, together with the calculated concentration of bound surfactant, the data in Figure 1 can be recast as a plot of gelatin diffusivity as a function of the concentration of micelles in the system; this value is given by Cm/nagg. The gelatin self-diffusion data are plotted against the micellar concentration in Figure 5. In this plot, the minimum in diffusivity for all three hydrophobic surfactants occurs at the same concentration of micelles, Cm/nagg ∼ 0.6-0.8 mM. With a gelatin concentration of 5% (w/w), this value corresponds to an average of 0.8-1.1 micelles/gelatin strand (assuming Mn and Mw averages, respectively). It is concluded that maximal cross-linking of the gelatin occurs when there is about 1 micelle/strand. When a larger number of micelles are present in the system, cross-linking is less efficient because either (i) fewer cross-links are formed or (ii) they are each weaker, probably as a reflection of increased electrostatic repulsion among the chains. It is worth pointing out that this result does not support the interpretation that the increased viscosity observed in (42) Zana, R.; Lang, J.; Lianos, P. Polym. Sci. Technol. (Plenum) 1985, 30 (Microdomains Polym.), 357. (43) Preliminary PGSE-NMR data indicate that Ds increases for gelatin in the presence of SDS at polymer concentrations below C*.
Griffiths et al.
these systems is solely due to the result of chain expansion. If that were the case, the viscosity would continue to rise to the saturation level as the greater number of bound micelles increased the average charge density on the chains. In fact, with only 1 micelle/strand, the viscosity would probably be expected to fall in the absence of crosslinking since the attraction of the chain for the micelle should cause a decrease in the overall chain dimensions. This was found for gelatin concentrations below C*.27,43 The question remains why the depth of the minimum depends on the surfactant structure. Examination of Figure 1 or Figure 5 shows that SOS gives no indication of a minimum, while for the series SDecS, SDS, and STS, the depth of the minimum increases by about a factor of 5. A possible explanation for this difference is the increasing size of the bound micelles, in particular, their increasing surface area. Apparently, the micelles formed by SOS are so small that little or no cross-linking can occur. With an aggregation number of 27 and a relatively short hydrophobic tail, these micelles have a hydrophobic core area44 of about 1.1 × 10-17 m2. Similar calculations for SDecS, SDS, and STS give surface areas of 1.7 × 10-17 m2, 2.5 × 10-17 m2, and 3.4 × 10-17 m2, respectively. In this interpretation, SOS micelles can interact with only one chain at time; SDecS micelles, with 1.5 times the surface area, can bind two strands of gelatin relatively weakly; and the larger surfactants, with 2.2 and 3.0 times the surface area, interact with two strands with increasing strength. Conclusions The diffusion rate studies reported in this paper are readily interpretable in terms of the standard picture of polymer-surfactant interaction: free surfactant unimer in equilibrium with bound micellar structures, the number of which increase with an increase in the activity of unimer. The gelatin diffusion minimum can be explained most conveniently by the formation of micelle-mediated transient cross-links between strands, which have optimal strength when approximately one micelle is bound per gelatin strand. It is suggested that the cross-link density or strength/cross-link diminishes as the result of the increased electrostatic repulsion between micelles as their number increases. The surface area of the micelles, to which the gelatin is bound, increases with surfactant chain length; the greater strength of interaction is reflected in a deeper minimum diffusivity with more hydrophobic surfactants. Acknowledgment. This work has been supported by the Swedish Natural Sciences Research Council (NFR). We thank Andrew Cox for technical assistance and Ste´phane Pe´lissier for the viscosity measurements. LA960314T (44) Nagarajan, R.; Ruckenstein, E. Langmuir 1991, 7, 2934.
