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Langmuir 1996, 12, 4628-4637
Articles Interaction between an Anionic Polysaccharide and an Oppositely Charged Surfactant. Quasi Elastic Light Scattering, Size Exclusion Chromatography, and Capillary Electrophoresis Study of the Sodium Hyaluronate/ Tetradecyltrimethylammonium Bromide/Sodium Chloride/ Water System A° sa Herslo¨f-Bjo¨rling* and Lars-Olof Sundelo¨f Physical Pharmaceutical Chemistry, Uppsala University, Biomedical Center, P.O. Box 574, S-751 23 Uppsala, Sweden
Bedrˇich Porsch Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, 162 06 Prague 6, Czech Republic
Ludmila Valtcheva and Stellan Hjerte´n Department of Biochemistry, Uppsala University, Biomedical Center, P.O. Box 576, S-751 23 Uppsala, Sweden Received March 21, 1995. In Final Form: May 15, 1996X The interaction between the anionic polysaccharide sodium hyaluronate (NaHy) and the positively charged surfactant tetradecyltrimethylammonium bromide (TTAB) in water leads to phase separation if an insufficient amount of salt (NaCl in this study) is added. With increasing TTAB concentration a pronounced interaction remains even under single-phase conditions. This is experimentally supported by a lowered relative viscosity, a decreased electrophoretic mobility as determined by high performance capillary electrophoresis (HPCE) approaching zero mobility at infinite TTAB concentrations, and changes in hydrodynamic size as well as an increased relative scattered intensity as determined by quasi elastic light scattering (QELS). The extent of this interaction is controlled mainly by the ionic strength of the solution and by the concentration of surfactant. The data obtained are reasonably explained by the model developed in interaction studies of a positively charged polymer with a negatively charged surfactant.
Introduction Polysaccharides constitute a class of polymers with extremely varied properties depending upon the structure of the repeating unit, the number of substituents and the substituent distribution, the nature of ionizable groups, the degree of branching, and other structural features.1-5 Even the molecular weight has a substantial influence on the properties, especially in biological systems. Polysaccharides often have structures composed of both hydrophobic and hydrophilic parts, a feature which contributes to the intricate balance between solubility and insolubility in water. In some cases the solubility in water is predominantly governed by ionizable groups. The degree of ionization of these groups will then affect the solubility and also the conformational properties of the polysaccharide. The criteria for solubility are rather * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, August 1, 1996. (1) The Polysaccharides. Molecular Biology; Aspinall, G. O., Ed.; Academic Press: London, 1982; Vol. 1. (2) The Polysaccharides. Molecular Biology; Aspinall, G. O., Ed.; Academic Press: London, 1983; Vol. 2. (3) The Polysaccharides. Molecular Biology; Aspinall, G. O., Ed.; Academic Press: London, 1985; Vol. 3. (4) Rees, D. A. Biochem. J. 1972, 126, 257. (5) Crescenzi, V.; Dentini, M.; Coviello, T. Biophys. Chem. 1991, 41, 61.
S0743-7463(95)00222-8 CCC: $12.00
complex, however, especially if the solution contains additional components. The interaction between water soluble polymers and low molecular weight amphiphilic substances has been studied intensely during the last two decades. A special class of such studies have dealt with the interaction between polyelectrolytes and oppositely charged amphiphiles.6 In such systems the interaction is normally strong due to the Coulombic attraction. In composition regions where the amphiphile forms micelles, phase separation frequently occurs.7-10 The system can be made to return to single phase conditions if a sufficient amount of supporting electrolyte is added.6-8,11-15 In the case of (6) Lindman, B.; Thalberg, K. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993; p 203. (7) Thalberg, K.; Lindman, B.; Karlstro¨m, G. J. Phys. Chem. 1990, 94, 4289. (8) Thalberg, K.; Lindman, B.; Karlstro¨m, G. J. Phys. Chem. 1991, 95, 3370. (9) Leung, P. S.; Goddard, E. D. Colloids Surf. 1985, 13, 47. (10) Dubin, P. L.; Oteri, R. J. Colloid Interface Sci. 1983, 95, 453. (11) Thalberg, K.; Lindman, B. J. Phys. Chem. 1989, 93, 1478. (12) Thalberg, K.; Lindman, B. Langmuir 1991, 7, 277. (13) Thalberg, K.; Lindman, B.; Karlstro¨m, G. J. Phys. Chem. 1991, 95, 6004. (14) Thalberg, K.; van Stam, J.; Lindblad, C.; Almgren, M.; Lindman, B. J. Phys. Chem. 1991, 95, 8975.
© 1996 American Chemical Society
Anionic Polysaccharide and an Oppositely Charged Surfactant
mixed micelles (composed of both charged and noncharged amphiphiles) the intensity of this type of interaction has been found to depend upon the surface charge density of the micelles.16 Certainly also the linear charge density of the polymer should play a substantial role. For the case of polyelectrolytes with a positive backbone charge the interaction with negatively charged mixed micelles has been studied in a number of papers, of which many have been published by Dubin and co-workers. As pointed out by Thalberg et al.,7,8,12 the association of sodium hyaluronate with cationic surfactants is essentially purely electrostatic in nature. Hence, especially studies of the polymer poly(dimethyldiallylammonium chloride) (PDMDAAC) interacting with the ionic/nonionic micelles with the composition SDS/Triton-100 have produced results of relevance10,16-28 also for our studies of a biologically important charged polysaccharide. The results of Dubin et al. have especially been related to coil size, micellar dimensions, and surface charge of the micelles. The ionic strength has been kept rather high (approximately 0.4 M) to avoid complications from the Donnan effect. Similar studies will be reported here for a different system composed of a nonbranched negatively charged polysaccharidessodium hyaluronate (NaHy)swith a moderate linear charge density (one negative unit charge per disaccharide unit) and having a fairly stiff chain.29,30 The amphiphile chosenstetradecyltrimethylammonium bromide (TTAB)sforms micelles of a linear dimension only about one fourth of that of the SDS/Triton-100 mixed micelles also having a higher surface charge density. The hydrodynamic volume per mass for NaHy at an ionic strength between 0.2 and 0.4 is estimated here to be approximately 1.5 times that of PDMDAAC for identical molecular weights.27 In order to establish single-phase conditions in our case the ionic strength had to be increased by addition of NaCl to a concentration of at least 200 mM. The type of electrolyte added and the corresponding phase diagrams will be the subject of a special study.31 The present paper is a continuation of a previous study where mainly hydrodynamic aspects were treated.32 In agreement with other investigations it was concluded that a strong interaction between NaHy and TTAB still prevailed after single-phase conditions had been restored (15) Thalberg, K.; Lindman, B. Colloids Surf., A: Physicochem. Eng. Aspects 1993, 76, 283. (16) Dubin, P. L.; Rigsbee, D. L.; Gan, L.-M.; Fallon, M. A. Macromolecules 1988, 21, 2555. (17) Dubin, P. L.; Davis, D. Colloids Surf. 1985, 13, 113. (18) Dubin, P. L.; Rigsbee, D. R.; McQuigg, D. W. J. Colloid Interface Sci. 1985, 105, 509. (19) Dubin, P. L.; Chew, C. H.; Gan, L. M. J. Colloid Interface Sci. 1989, 128, 566. (20) Dubin, P. L.; The, S. S.; McQuigg, D. W.; Chew, C. H.; Gan, L. M. Langmuir 1989, 5, 89. (21) Dubin, P. L.; The, S. S.; Gan, L. M.; Chew, C. H. Macromolecules 1990, 23, 2500. (22) Dubin, P. L.; Vea, Y. M. E.; Fallon, M. A.; The, S. S.; Rigsbee, D. R.; Gan, L. M. Langmuir 1990, 6, 1422. (23) Dubin, P. L.; Davis, D. D. Macromolecules 1984, 17, 1294. (24) Dubin, P. L.; Oteri, R. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1982, 23, 45. (25) Sudbeck, E. A.; Dubin, P. L.; Curran, M. E.; Skelton, E. A. J. Colloid Interface Sci. 1991, 142, 512. (26) Xia, J.; Zhang, H.; Rigsbee, D. R.; Dubin, P. L.; Shaikh, T. Macromolecules 1993, 26, 2759. (27) Li, Y.; Xia, J.; Dubin, P. L. Macromolecules 1994, 27, 7049. (28) Li, Y.; Dubin, P. L.; Havel, H. A.; Edwards, S.L.; Dautzenberg, H. Macromolecules 1995, 28, 3098. (29) The Biology of Hyaluronan; Evered, D., Whelan, J., Eds.; John Wiley & Sons: Chichester, 1989; pp 298. (30) Laurent, T. C.; Fraser, J. R. E. FASEB J. 1992, 6, 2397. (31) Herslo¨f, A° .; Bjo¨rling, M.; Sundelo¨f, L.-O. Macromolecules, in press. (32) Herslo¨f, A° .; Sundelo¨f, L.-O.; Edsman, K. J. Phys. Chem. 1992, 96, 2345-2348.
Langmuir, Vol. 12, No. 20, 1996 4629
by addition of electrolyte. The results were compatible with a model of complexation between NaHy and TTAB micelles in similarity with results published by others.6-8,11-15 Against this background and in order to try to resolve what type of complex formed, it was found of primary importance to study the particle size distributions in a composition region close to phase separation conditions. Quasi elastic light scattering (QELS) was selected for this purpose due to its capacity to resolve the simultaneous presence of both small and large particles as well as their relative amounts. However, due to the broad molecular weight distribution of the NaHy sample, it was found convenient to perform complementary measurements also by means of size exclusion chromatography (SEC). Combining the size distribution analysis from QELS and SEC then allowed a more detailed size analysis. Since the complexation between the micelles and the polymer is expected to lead to changes in the overall charge of the polymer as well as to conformational changes, the electrophoretic mobility as a function of TTAB concentration was determined by means of high-performance capillary electrophoresis (HPCE). Experimental Section Materials. NaHy was kindly supplied by Pharmacia AB, Uppsala, Sweden, and a set of samples were used ranging in molecular weight from 185 000 to 2 400 000. The lower molecular weights were prepared from high molecular weight samples by acidic hydrolysis. HPCE and most of the QELS measurements were performed on NaHy with MW 740 000. For the SEC studies and the intrinsic viscosity determinations, NaHy of MW’s 185 000, 440 000, 560 000, 740 000, 770 000, 960 000, and 2 400 000 was used. The numbers given are the supplier’s weight-average molecular weights, determined by low-angle laser light scattering. TTAB was obtained from Sigma Chemical Co., St. Louis, MO. Pullulan standards were obtained from Polymer Laboratories, Shropshire, U.K. NaCl and sodium phosphate (Na2HPO4‚2H2O and NaH2PO4‚H2O, respectively) were of analytical grade and purchased from Merck, Darmstadt, Germany. Oil Orange SS ((o-tolylazo)naphthol) was obtained from Tokyo Kasei Inc., Japan. Fused silica tubing with i.d. ) 75 µm and o.d. ) 150 µm for the HPCE experiments was bought from MicroQuartz, Munich, Germany. Acrylamide, ammonium persulfate, and N,N,N′,N′tetramethylethylenediamine (TEMED) used for capillary coating were of electrophoresis purity grade and obtained from Bio-Rad Laboratories, Richmond, CA. Bind silane ((γ-(methacryloxy)propyl)trimethoxysilane) was purchased from Pharmacia AB, Uppsala, Sweden. All chemicals were used without further purification. Water from a Millipore ultrapure water purification unit Milli-Q was used. Solutions were prepared by weight from individual stock solutions of polyelectrolyte, surfactant, and salt in water. Once prepared, the solutions were allowed to stand with magnetic stirring overnight or longer to ensure homogeneity. The hyaluronate concentration in the stock solutions was determined by optical rotation measurements. Methods. HPCE is a rather new analytical technique based on the principles of electrophoresis but instrumentally designed similarly to high-performance liquid chromatography (HPLC). Two of the advantages with HPCE are that mobilities can be determined rapidly and that an extremely small sample volume is needed (a few nanoliters is sufficient for one measurement). The principle scheme of an HPCE instrument is presented in Figure 1. The electrophoresis experiments were performed using a laboratory-assembled HPCE system consisting of a 10 kV power supply (constructed by P. A. Lidstro¨m, Department of Biochemistry, Uppsala University, Uppsala, Sweden), a W + W 1100 recorder (LKB, Bromma, Sweden), and a Linear 206 PHD variable-wavelength UV monitor (a gift from Linear Instruments, Reno, NV) used as stationary detector. The narrow-bore electrophoresis capillary had the following dimensions: total length, 16.3 cm; length from application to detection point, 13.0 cm; i.d., 75 µm; o.d., 150 µm. The interior surface of the capillary was
4630 Langmuir, Vol. 12, No. 20, 1996
Herslo¨ f-Bjo¨ rling et al.
Figure 1. Schematic diagram of a capillary electrophoresis instrument: (1) capillary; (2) capillary inlet; (3) capillary outlet; (4) electrolyte buffer; (5) power supply; (6) data acquisition; (7) UV detector. coated with non-cross-linked acrylamide, as described elsewhere.33 The coating is necessary in order to prevent electroendosmosis and electrostatic interaction between the negatively charged silica wall and the positively charged TTAB. The samples consisted of 0.1% (w/w) NaHy dissolved in 5 mM sodium phosphate buffer (pH 7), 205 mM NaCl, and TTAB varying in concentration from zero to 50 mM. The corresponding NaHyfree solution was used as a background electrolyte. The voltage applied was 1000 V, and the detection of NaHy was performed at a wavelength of 205 nm. In capillary electrophoresis the parameter measured is the migration time, i.e. the time it takes for a sample zone to migrate from application to detection point. On the basis of the measured migration times, electrophoretic mobilities were calculated by the following relation
u ) lL/(tV)
(1)
where u is the electrophoretic mobility, l is the migration distance (the distance from the application to the detection point), L is the total capillary length, t is the migration time, and V is the voltage applied. Since the electrophoretic mobility is dependent on the net surface charge density of the particles, the change of the mobility can be used as a measure of the change of this parameter provided all other factors like viscosity, pH, ionic strength, conductivity, and temperature are constant. Conductivity measurements of the solutions used as background electrolytes for the HPCE measurements were performed with a Metrohm 660 Conductometer (Metrohm AG Herisau, Switzerland). The SEC equipment consisted of a VCR 40 HPLC pump (Academy Development Works, Prague, Czech Republic), an injection valve Rheodyne 7125 (Rheodyne Inc., Cotati, CA) with a 200 µL loop, and an R 401 differential refractometer (Waters Assoc., Milford, MA) connected through a Black Star 2308 A/D converter (Black Star Ltd., Huntingdon, U.K.) to an IBMcompatible computer. The software (Copyright J. Horsky, Institute of Macromolecular Chemistry, Prague) uses a broad standard calibration procedure and allows calculations of molecular weight distributions and averages. Three stainless steel columns in series (250 mm × 8 mm i.d., supplied by Tessek Ltd., Prague) were packed with diol-modified Lichrospher 300, 1000, and 4000 packing (particle size 10 µm), prepared according to a recently described procedure34 (a slurry technique at 30 MPa with methanol/dioxane, volume ratio 1:1, as the slurry liquid). All three columns exhibited good efficiency around 6000 theoretical plates (testing substance, mannitol). SEC sample solutions in the mobile phase (100, 200, and 400 mM NaCl in water) had concentrations e0.05% (w/w) to avoid viscous fingering effects.35 (33) Hjerte´n, S. J. Chromatogr. 1985, 347, 191. (34) Porsch, B. J. Chromatogr. 1993, 653, 1. (35) Yau, W. W.; Kirkland, J. J.; Bly, D. D. Modern Size-Exclusion Liquid Chromatography. Practice of Gel Permeation and Gel Filtration Chromatography; John Wiley & Sons: New York, 1979.
All QELS measurements were performed at room temperature and at a fixed angle of 90°. High-quality 10 × 10 mm2 cells (Hellma G.m.b.H., Mullheim Baden, BRD) were used. An argon ion laser (Coherent Innova 70-2, Coherent Laser Division, Palo Alto, CA) with a nominal maximum power output of 2 W and tuned to 514.5 nm served as a coherent light source. The laser beam was spatially filtered before being focused into the solution. A set of field and aperture stops together with a lens defined the scattering characteristics into a photomultiplier unit (Brookhaven Instruments Corporation, NY). High voltage was provided from an Ortec aggregate. The photon-counting signals were processed in a digital correlator (BI 8000AT, Brookhaven Instruments Corporation). The Brookhaven particle size distribution software package contains five of the most common distribution analytical procedures; mainly CONTIN36 was used here. All optical components were mounted on a high-quality optical table (Newport Research Corporation, CA) with vibration damped supports. The polymer solutions contained 0.1% (w/w) NaHy and were filtered directly into sample cells through a filter of pore size 0.8 µm (Millex-AA, SLAA 025 BS, Millipore). To reveal any time dependent effects, like slow aggregation, each sample was measured three times: immediately, one day, and finally one week after filtration. No time dependent effects could be detected. The measured intensity autocorrelation function G(2)(τ) is related to the electric field autocorrelation function g(1)(τ) by36
G(2)(τ) ) A[1 + β|g(1)(τ)|2]
(2)
where A is the baseline constant, β is an equipment-related constant, τ is the correlation time, and the equation applies for the case of a continuous distribution of decay rates Γ.
g(1)(τ) ) Ψ(Γ) exp(-Γτ) dΓ
(3)
The decay rate is related to the diffusion coefficient, D, by the relation Γ ) q2D, where the scattering vector q is defined as q ) (4πn/λ) sin(ϑ/2), n is the refractive index of the medium, λ is the wavelength of the light used in vacuum, and ϑ is the scattering angle. The normalized distribution is defined so that Ψ(Γ) dΓ equals the fraction of the total intensity scattered by molecules having a decay rate within the interval (Γ, Γ + dΓ).36 In the case of a monodisperse solute, g(1)(τ) reduces to a single exponential which decays asymptotically to the baseline value A. In the case of a polydisperse solute, the distribution of diffusion coefficients is in principle obtained from g(1)(τ) by inverse Laplace transformation and converted to a particle size distribution in terms of the equivalent sphere radius, r, via the Einstein-Stokes formula
D ) kT/(6πηr)
(4)
where η is the viscosity of solvent and k is Boltzmann’s constant. This is achieved by the CONTIN software. The average diameter calculated is defined as the inverse z-average dH ) 〈1/dh〉z-1, where dh is the hydrodynamic diameter.37 The BI-8000 correlator calculates a statistical baseline from the average photon-counting rate and determines the measured baseline from six successive channels delayed by 1024 sampling times when the linear mode (uniform channel spacing) is used. Even minute amounts of dust give rise to awkward components of the correlation function, both through heterodyning and long correlation times resulting in large baseline differences. In the present study, the difference between a calculated and a measured baseline was very small, from 0.01 to 0.1% for all samples. The CONTIN algorithm could therefore be used with confidence. For the solutions free of surfactant, cumulant analysis was also performed. All measurements were performed using 64 channels with a linear mode setting. The size distributions of both micelles and polymer were calculated by CONTIN starting with channel 2. Alternatively, the CONTIN procedure was applied starting from channel 32 to exclude the signal due to free micelles (i.e. micelles not contained in the polyelectrolyte-micelle complex), (36) Stock, R. S.; Ray, W. H. J. Polym. Sci., Polym. Phys. Ed. 1985, 23, 1393. (37) Pusey, P. N. In Industrial Polymers: Characterization by Molecular Weight; Transcripta Books: London, 1973; pp 26.
Anionic Polysaccharide and an Oppositely Charged Surfactant
Figure 2. Relative viscosity at 25 °C as a function of TTAB concentration for solutions of the same NaHy concentration (0.1% (w/w)) but with different NaCl concentrations: [NaCl] ) 200 (0), 230 (9), 250 (O), and 400 mM (b). Relative viscosity is here taken as the viscosity of the solution relatively to the viscosity of a similar solution but without TTAB. The molecular weight of NaHy was 560 000. and the polymer size distributions (or the polyelectrolyte-micelle complex size distributions) were evaluated. The correct viscosity to be inserted in eq 4 should be, somewhat vaguely stated, the viscosity experienced by the polyelectrolytesurfactant complex and should, for dilute solutions, have a value somewhere between the value for the pure salt solution and the value for the solution containing both salt and surfactant. In cases when no complexation occurs between polyelectrolyte and surfactant, the correct value should be the latter one. In the case of complexation, the viscosity may approach the viscosity of the pure salt solution, since the contribution from surfactant gradually decreases depending on the degree of complexation. The change in solvent viscosity due to the presence of NaCl and TTAB is not too large (η ) 1.021 and 1.0735 cP for 200 mM NaCl and for 400 mM NaCl + 50 mM TTAB, respectively, as compared to 1.000 cP for pure water). Nevertheless, in order to be more precise in the data treatment, the following values for the solvnt viscosity were chosen: For solutions containing NaHy/TTAB/ NaCl/water, the viscosity of a TTAB/NaCl/water solution with the same concentrations as in the NaHy solution was used. For solutions with NaHy/NaCl/water and with TTAB/NaCl/water, the viscosity value used was the viscosity for the corresponding NaCl/water solution. With these “solvent” viscosity values the complexation between NaHy and TTAB was probably somewhat underestimated. In more concentrated polymer solutions the particles may experience a considerable interaction (both thermodynamic and hydrodynamic) and the simple relation (eq 4) no longer applies. Hence all QELS experiments were performed at a NaHy concentration of 0.1% (w/w) to obtain unbiased particle sizes. Refractive indices were measured with an Abbe refractometer (ATAGO type 1T, from Itema, Japan). Viscosity measurements were carried out in a thermostated (25 ( 0.1 °C) home-built automatic low-shear capillary viscometer designed in the laboratory of Pharmacia AB. Readings of flow times were made automatically by a photosensor and sent to a computer for data processing. To determine the NaHy concentration, optical rotation was measured at 436 nm (mercury lamp) with a Perkin-Elmer 241 polarimeter. Solubilization studies of the hydrophobic dye Oil Orange SS ((o-tolylazo)naphthol) were performed simply by mixing the actual components and visually observing the color “reaction”. When the dye is solubilized in a hydrophobic environment, it gives a strong orange color. All measurements, if not otherwise stated, were performed at room temperature.
Results and Discussion It was shown in a previous paper32 that, at single-phase conditions but close to the phase separation limit (200 mM NaCl), there is still a strong interaction between NaHy and TTAB. This interaction reveals itself as a decrease in relative viscosity, ηrel, when [TTAB] is increased from 0 to 50 mM. Figure 2 shows how ηrel (i.e., the viscosity
Langmuir, Vol. 12, No. 20, 1996 4631
for an aqueous solution of NaHy, TTAB, and NaCl divided by the viscosity for the corresponding solution without TTAB) decreases upon increasing TTAB addition until a minimum value is obtained. The ordinate in Figure 2 represents the effect of successive additions of the surfactant to a solution at a fixed concentration of NaHy and NaCl relative to the same solution free of surfactant. Its advantage is that it does not contain an unknown concentration of the complex in the interacting case. The magnitude of the decrease in ηrel, for a solution with 200 mM NaCl, is about 18% when [TTAB] is increased from 0 to 30 mM. When a sufficient amount of TTAB has been added, the relative viscosity increases again, still being lower than the viscosity at [TTAB] ) 0. These viscosity changes are most pronounced for NaCl concentrations close to phase separation and decrease with increasing NaCl concentration. The viscosity measurements indicate that the interaction still exists up to approximately 250 mM NaCl. In the case of no interaction at 400 mM NaCl, the increase of ηrel corresponding to the dissolution of TTAB in water should be observed if the system would be described by the Einstein viscosity equation for noninteracting spheres, as it is approximately seen in Figure 2. On the other hand, the hydrodynamic interaction dissipation tensor in the interacting system would be extremely complex and, hence, even the equivalent sphere picture in terms of Flory-Fox38 should be used with caution. Especially, the assumption of additivity of component contributions to relative viscosity might be greatly misleading. It has been shown16,23-27 that the composition of the complex is mainly determined by the specific charge of the micelle and the ionic strength of the solution. The shallow minima located in Figure 2 between 20 and 30 mM and 10 and 20 mM and near 10 mM TTAB at 200, 230, and 250 mM NaCl, respectively, may be related to the point where the complex has reached equilibrium saturation at a given ionic strength. When the amount of micelles is low, only intramolecular association takes place and the mass/volume ratio of the complex increases26 upon addition of micelles until the complex becomes saturated. When more micelles are added, the observed increase of ηrel probably simultaneously reflects the addition of micelles and the onset of interparticle equilibrium association that is likely to occur here, as the selected polymer concentration is slightly above the coil overlap concentration c* ) 0.08% (defined as 1/[η]). The binding of TTAB onto NaHy as micelles may occur before the bulk cmc is reached (cf. phase separation below the cmc11,32). It was shown in the previous paper that the cmc of TTAB is decreased from about 3 to 0.5 mM when the NaCl concentration is increased from zero to 200 mM. However, the lower cmc at 200 mM NaCl was unchanged by the presence of NaHy.32 Consequently, the measurements were here made above the cmc, and the observed effects are most likely due to micelle adsorption. It is also believed that the interaction in the homogeneous region reflects the situation in the two-phase region and vice versa. The solubilization studies support micelle adsorption to the polyelectrolyte chain. The hydrophobic substance Oil Orange SS ((o-tolylazo)napthol) is dissolved into the concentrated “gel” phase resulting from phase separation even when the TTAB concentration is below the cmc, indicating the presence of hydrophobic micellar cores. Oil Orange SS is solubilized neither in a pure NaHy solution nor in a NaHy solution containing NaCl, whereas it is dissolved in a TTAB solution, where [TTAB] ≈ the (38) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953.
4632 Langmuir, Vol. 12, No. 20, 1996
Figure 3. Electrophoretic mobility as a function of TTAB concentration of NaHy (MW ) 740 000 and c ) 0.1% (w/w)) in 205 mM NaCl.
cmc. The micelle adsorption is further supported by the absence of phase separation for alkyltrimethylammonium bromides with less than ten carbons in the hydrocarbon tail.17 For these surfactants the cmc is very high. Nonadecyltrimethylammonium bromide (NoTAB), with nine carbons in the hydrocarbon tail, has a cmc about 140 mM39 and does not cause phase separation in the NaHy system. When this high cmc is reached, the electrolyte concentration from the monomer surfactant itself is high enough to considerably decrease the electrostatic interaction between the polyelectrolyte and the micelles. From an electrostatic viewpoint, a surfactant monomer with its counterion is simply an univalent salt. Any preferential exchange of the Na+ counterions of NaHy to TTA+ counterions must therefore be of nonelectrostatic origin. The TTAB micelles, on the other hand, can be regarded as multivalent counterions. The main reason for the formation of the polymer-micelle complex is the entropy gain due to release of the univalent counterions.8,40 The micelles may exhibit multisite interactions with NaHy, and a corresponding number of counterions are released from both polyelectrolyte and micelle. This gain decreases and polymer-micelle interactions are increasingly screened when the ionic strength of the univalent salt increases and a redissolution of the precipitate formed at low salt concentration is observed at high surfactant and/ or salt concentration.11,32 NaHy exhibits a fairly high chain stiffness, its persistence length being around 5 nm.41,42 Comparing this value with the micelle diameter43 of ca. 5 nm, the complete wrapping of a NaHY chain around the micelle seems impossible (cf. ref 44). Some more Cl- or Br- ions must therefore participate in the interaction to keep the electroneutrality of the system. The interaction between the negatively charged polymer chain and the positively charged TTAB micelles should lead to a change in electrophoretic mobility. Since it was believed that this change could be related to the degree of adsorption of micelles, capillary electrophoresis measurements were performed at constant polymer and NaCl concentration but for varying [TTAB]. The results are shown in Figure 3. The distinct decrease of the mobility of NaHy with increasing TTAB concentration in the single-phase solution containing 205 mM NaCl (Figure 3) indicates a strong polyelectrolyte-micelle interaction. Although an in(39) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentration of Aqueous Surfactant Systems; National Bureau of Standards: Washington, DC, 1971. (40) Carnali, J. O. Langmuir 1993, 9, 2933. (41) Cleland, R. L. Arch. Biochem. Biophys. 1977, 180, 57. (42) Cleland, R. L. Biopolymers 1984, 23, 647. (43) Nicoli, D. F.; Ciccolello, R.; Briggs, J.; Dawson, D. R.; Offen, H. W.; Romsted, L.; Bunton, C. A. NATO ASI Ser., Ser. B. 1981, 73, 363. (44) McQuigg, D. W.; Kaplan, J. I.; Dubin, P. L. J. Phys. Chem. 1992, 96, 1973.
Herslo¨ f-Bjo¨ rling et al.
Figure 4. Plot of the electrophoresis data according to eq 6. Unfilled circles correspond to Cmu/∆u plotted versus ∆u/u0. The filled circle indicates the extrapolated value, i.e. ξnP0 ) 38.1 mM, and the slope is -31.8 mM. Squares correspond to mobilities, u, plotted versus 1/Cm, both quantities being expressed in relative numbers. The dashed line indicates that the mobility extrapolates to 0 when Cm becomes large.
creased TTAB concentration in the background electrolyte results in an increased conductivity, the increase is too small to explain the decreased mobility. The conductivity of 205 mM NaCl was measured to be 17.88 mS as compared to 18.99 mS for the similar NaCl solution also containing 50 mM TTAB. Expressed in percent, the difference is 6.2%. The NaHy mobility in the presence of 50 mM TTAB was only 23% of the mobility in the absence of TTAB; i.e., the mobility was reduced more than four times. The contribution of TTAB to the viscosity of the electrophoresis buffer was negligible and consequently could not significantly affect the mobility of NaHy. Considering those results, one can assume that the decreased mobility of NaHy is due to complexation between NaHy and TTAB, which results in a lower net charge density for the complex as compared to single-chain NaHy. When the measured mobilities are plotted versus 1/[TTAB] (see Figure 4), one finds that the mobility tends to zero when [TTAB] tends to infinity. This indicates that for large values of [TTAB] the polymer charge is entirely balanced by the charge of interacting micelles. Even if the mobility, u, can formally be written as the quotient between an effective charge, qeff, and an effective friction coefficient, feff; i.e., u ) qeff/feff, it will be difficult to develop proper separate expressions for qeff and feff and their variation with composition. Dubin and co-workers28 have recently published an attempt to treat electrophoresis data in terms of separate expressions for the charge and the friction. Their theory was tried but does not seem to fit our data. Nor does the model of Kuhn et al.45 seem to apply directly. Building upon the fact that the experimental mobility retains its sign for the entire composition range of [TTAB] and furthermore tends to 0 when [TTAB] f ∞, a modified equilibrium approach was tried. In this treatment46 the polymer is assumed to have a given number of adsorption sites per molecule with which the free micelles set up an equilibrium. Since the mobility apparently goes to zero for a large excess of TTAB, the fraction of sites occupied by micelles, R, is taken to be proportional to the relative decrease in mobility with a proportionality factor ξ; i.e.
R ) ξ[u0 - u]/u0 ) ξ∆u/u0
(5)
where u0 is the mobility of the polymer in the absence of TTAB and u is the mobility for a given concentration [TTAB]. This is similar to the Kuhn approach for the (45) Kuhn, R.; Frei, R.; Christen, M. Anal. Biochem. 1994, 218, 131. (46) Sundelo¨f, L.-O.; Porsch, B.; Holmberg, C. Work in progress.
Anionic Polysaccharide and an Oppositely Charged Surfactant
Langmuir, Vol. 12, No. 20, 1996 4633
Table 1. Intrinsic Viscosity Values for NaHy with MW 185 000 and 560 000 for Different NaCl Concentrations [η] (g mg-1) [NaCl] (mM)
MW ) 185 000
MW ) 560 000
200 250 400
0.383
0.837 0.808 0.823
0.371
case that the saturated complex has zero mobility with an exception for the proportionality factor ξ. This factor takes into account the change in ζ-potential as the polymer is decharged due to adsorption of micelles but also the change in friction caused by the adsorbed micelles. If the saturation level of the total amount of polymer sites expressed as molarity is denoted P0 (at a given polymer concentration; P0 should be proportional to the polymer concentration) and if K is the equilibrium constant for the interaction between the surfactant monomer and the polymer, one can show that the following expression holds
Cmu/∆u ) ξnP0 - ξ2(1/K - nP0)∆u/u0
(6)
Here Cm denotes the total concentration of TTAB expressed as monomer and n is the aggregation number of the micelles adsorbed. In Figure 4 the measurable quantity Cmu/∆u has been plotted versus the quantity ∆u/u0 for [NaCl] ) 205 mM. A good straight line relationship is obtained, indicating consistency of the data. The slope of this line gives ξ2(1/K - nP0) ) 34.3 mM, and from the intercept one gets ξnP0 ) 39.1 mM. Since the total molarity of polymer charge (one per disaccharide) is of the order of 2-3 mM for the polymer concentration in question, P0 can at most have a similar value; i.e., P0 e 3 mM, say. For micelles the number of available sites would be much smaller, possibly of the order of P0 ≈ 0.03 mM. For an aggregation number n ) 30 one then finds ξ ≈ 40. Taking into consideration that the ζ-potential for this type of polymer has a tendency to compensate for the changes in nominal charge, this value of ξ does not seem too unlikely. If a value of ξ ) 40 is inserted into the expression for the slope, one may calculate an approximate value of K and one finds K ≈ 1. This means that the adsorption equilibrium is pushed very far toward the adsorbed state already if Cm is greater than say 5 mM. This analysis of the electrophoresis data indicates that an equilibrium model combined with a correction for changes in both the ζ-potential and the friction will provide consistency within the data. Furthermore, the numerical values of the parameters calculated agree fairly well with what could be expected if other information on the system is taken into account. The goal of the QELS measurements was to determine the particle size distribution as a function of system composition. Since the QELS measurements were performed at selected concentrations of 200 mM NaCl, where the system just reaches single-phase behavior, and of 400 mM NaCl, where the ionic strength prevents complex formation, and since the concentration of TTAB was varied from 0 to 50 mM, the total ionic strength at both NaCl concentrations varied in these experiments. To interpret the QELS particle size distributions as a result of interaction with micelles unambiguously, the knowledge of (i) NaHy coil size as a function of ionic strength of the solution and of (ii) particle size and/or molecular weight distribution of the NaHy sample itself was highly desirable. SEC experiments in a mobile phase containing 100, 200, and 400 mM NaCl on diol silica-based rigid packing were performed on all NaHy samples available. The NaHy
Figure 5. (a, top) Molecular weight distribution by weight for NaHy with a nominal MW ) 740 000 as determined by SEC. (b, bottom) Hydrodynamic size distribution by weight for NaHy with a nominal MW ) 740 000 as determined by SEC.
peaks normalized to unit area were compared at all three NaCl concentrations for every molecular weight and were found undistinguishable within the experimental error. SEC separates macromolecules according to hydrodynamic volume47 and may therefore be compared with intrinsic viscosity, which is a sensitive probe of the polyelectrolyte coil expansion.48 The intrinsic viscosities of NaHy for two different molecular weights at different NaCl concentrations (summarized in Table 1) are constant within the error of determination in the NaCl concentration interval used. Both intrinsic viscosity and SEC thus confirm an invariability of the NaHy coil size resulting from its chain stiffness49,50 with respect to the ionic strength of the solution within the concentration range selected for QELS measurements. The molecular weight distribution of NaHy with nominal MW ) 740 000 (the sample used for QELS) as obtained from SEC is shown in Figure 5A. The distribution is seen to be very broad but unimodal. Molecular weights covering the interval from approximately 1 × 104 to 3.8 × 106 are seen to be present. The weight average MW (Mw), number average MW (Mn), and polydispersity index (Mw/Mn) were calculated to be 741 000, 169 000, and 4.4, respectively. The reliability of the broad standard calibration procedure (47) Potschka, M. J. Anal. Biochem. 1987, 162, 47. (48) Morawetz, H. In Macromolecules in Solution; Wiley: New York, 1975. (49) Fouissac, E.; Milas, M.; Rinaudo, M.; Borsali, R. Macromolecules 1992, 25, 5613. (50) Rinaudo, M. J. Appl. Polym. Sci.: Appl. Polym. Symp. 1993, 52, 11.
4634 Langmuir, Vol. 12, No. 20, 1996
Herslo¨ f-Bjo¨ rling et al.
Table 2. QELS Particle Size Diameters in Terms of Inverse z-Averages, dH, for Pullulan Standards
a
MWa
dH (nm)
48 000 100 000 186 000 380 000 853 000
11.9 16.5 23.8 34.4 49.9
Supplier’s data.
Figure 6. Coil size calibration curve. Hydrodynamic sizes in terms of inverse z-averages, dH, from QELS for pullulan standards versus their elution volume, Ve, from SEC.
has previously been verified using broad dextran standards.51 NaHy samples with nominal weight average molecular weights 185 000, 440 000, 560 000, and 960 000 were used as calibrants here. The rigid silica matrix of the SEC columns allows their calibration in terms of QELS particle size diameters dH (inverse z-averages) and hence a comparison between SEC and QELS may be done. Narrow pullulan standards were used, and Table 2 contains the results from QELS experiments of these calibrants. Aqueous NaCl (10 mM) was here used as a SEC mobile phase as well as solvent for the QELS experiments, and the pullulan concentrations were low enough for the concentration dependence of the diffusion coefficient to be neglected. The software handled size data in the same way as Mw values. The resulting calibration curve log dH (from QELS) versus elution volume Ve (from SEC) is presented in Figure 6. This calibration was then used to determine the massdefined size distribution of NaHy from a SEC experiment in 0.1 M NaCl as mobile phase. The mass-defined size distribution (presented in Figure 5b) and the weight average of hydrodynamic sizes, 〈1/dh〉w ) 54 nm, are correctly calculated. The lowest nonzero value of this NaHy size distribution is observed at about 12.5 nm, which corresponds to a Mw ca. 104 (Figure 4a), confirming a larger coil size as compared to pullulan (Table 2) at the same molecular weight. The distributions of dh of TTAB and NaHy in the absence of TTAB as obtained from QELS at both NaCl concentrations used are shown in Figure 7. The inverse z-average dH of TTAB micelles is 5 nm at both NaCl concentrations, and for NaHy dH ) 58 and 60 nm in 400 and 200 mM NaCl, respectively. The observed difference simply reflects the experimental and CONTIN procedure errors. A good agreement between SEC and QELS size distributions for NaHy is obtained. As expected, the z-defined QELS distributions extend to larger sizes as compared to SEC experiments.52 The weight average size obtained from SEC is accordingly lower (54 nm). (51) Porsch, B.; Sundelo¨f, L.-O. J. Chromatogr. 1994, 669, 21. (52) Mrkvickova, L.; Porsch, B.; Sundelo¨f, L. O. J. Appl. Polym. Sci., in press.
Figure 7. QELS size distributions for (A) TTAB in 200 mM NaCl, (B) TTAB in 400 mM NaCl, (C) NaHy in 200 mM, and (D) NaHy in 400 mM NaCl. [TTAB] ) 50 mM, [NaHy] ) 0.1% (w/w), and the molecular weight of NaHy is 740 000. The CONTIN analysis was started from channel 2.
As follows from Figures 5b and 7, the lowest particle sizes found in the NaHy sample do not differ too much from the average micelle size. This implies rather highresolution requirements when both micelles and NaHy are present in the solution. The resolution of exponentials in a bimodal system like ours has been shown to be not very high.53 The Laplace inversion performed by CONTIN is an ill-defined procedure.54 The CONTIN analysis of such systems may be biased due to both an overcompensation of dust36 and a baseline error,55 a narrowing and a shift of peaks are frequently observed. The information concerning both NaHy and micelles should be obtained only in low number channels; the rest of the channels should contain only a signal from the complex. As the molecular weight distribution of the NaHy sample was proved to be unimodal, the complex should be unimodal as well. The CONTIN procedure should then be free of any bias due to bimodal fitting. Extensive tests were performed concerning the parameter setting of the QELS experiments as well as the CONTIN range and the first channel that was used in the calculations. It was found that the effect of micelles disappears completely when the CONTIN calculation is performed starting from channel 32. The reliability of the procedure may be estimated to be confident to within (2 nm by comparing the calculated sizes starting from channels 2 and 32 in the absence of TTAB at both NaCl concentrations (see Figures 8A and E and 9A and E and Table 3). This approach allows an elucidation of the possible bias of distributions in the case of a bimodal CONTIN analysis of TTAB-containing solutions when all channels (channel 1 is always excluded due to hardware disturbancies) are used. The plot of residuals in Figure 10 illustrates the quality of fits generally obtained (all channels used, corresponds to the distribution in Figure 8D). The calculated size distribution in the presence of TTAB, when all channels were used, is shown in Figures 8A-D (400 mM NaCl) and 9A-D (200 mM NaCl). The TTAB (53) Pike, E. R.; Watsom, D.; MacNeil Watson, F. In Measurement of Suspended Particles by Quasi-Elastic Light Scattering; Dahneke, B., Ed.; Wiley: New York, 1983. (54) Bott, S. In Measurement of Suspended Particles by Quasi-Elastic Light Scattering; Dahneke, B., Ed.; Wiley: New York, 1983. (55) Ruf, H.; Haase, W. Q.; Wang, E.; Grell, P.; Ga¨rtner, H.; Michel, H.; Dufour, J. P. Prog. Colloid Polym. Sci. 1993, 159.
Anionic Polysaccharide and an Oppositely Charged Surfactant
Figure 8. QELS-size distributions for NaHy with MW ) 740 000 (0.1% (w/w)) in 400 mM NaCl and with TTAB concentrations ranging from 0 to 50 mM in parts A-D and E-H, respectively. In parts A-D the CONTIN analysis is started from channel 2, and in parts E-H, it is started from channel 32.
concentration increases from 0 (top) to 5, 25, and 50 mM (bottom). The CONTIN procedure resolved the free micellar peak from the polymer peak, and the micellar size obtained is in good agreement with previous studies (5 nm).43 Apart from an increase of the relative scattering amplitude of the micellar peak at the expense of that of the polymer peak observed as the TTAB concentration was increased, some narrowing and shifting of peaks was seen. This problem was most pronounced in the case of no interaction between TTAB and NaHy, i.e., at the high NaCl concentration (400 mM). The disturbance of the polymer peak could be avoided when CONTIN was applied starting from channel 32. The resulting distributions are presented in Figures 8E-H (400 mM NaCl) and 9E-H (200 mM NaCl). The TTAB concentration increases from 0 (top) to 5, 25, and 50 mM (bottom). The inverse z-averages, dH, of NaHy obtained from QELS experiments in 400 mM NaCl corresponding to the particle size distributions in Figure 8 are summarized in Table 3. When CONTIN was applied from channel 2, an increase of the dhpeak (the maximum of the CONTIN size distribution of the NaHy peak) from 47 to 80 nm is observed when the TTAB concentration is increased. In spite of a good fit of data (see residuals in Figure 10 indicating a high-quality correlation function), these changes clearly
Langmuir, Vol. 12, No. 20, 1996 4635
Figure 9. QELS-size distributions for NaHy with MW ) 740 000 (0.1% (w/w)) in 200 mM NaCl and with TTAB concentrations ranging from 0 to 50 mM in parts A-D and E-H, respectively. In parts A-D the CONTIN analysis is started from channel 2, and in parts E-H, it is started from channel 32. Table 3. QELS Hydrodynamic Diameters in Terms of Peak Values, dhpeak, and Inverse z-Averages, dH, for NaHy (MW ) 740 000 and 0.1% (w/w)) in 400 mM NaCl for Various TTAB Concentrations for CONTIN Analysis Started from Channels 2 and 32, Respectively a ) 2a [TTAB] (mM) 0 5 25 50 a
dh
peak
(nm)
47 51 71 80
a ) 32a
dH (nm) 58 47 33 32
dh
peak
(nm)
53 55 54 50
dH (nm) 64 67 67 60
a ) first channel used in the CONTIN analysis.
relate to the above-mentioned artifacts of the CONTIN procedure. At 400 mM NaCl we know NaHy to be unperturbed by TTAB (Figure 11). Accordingly, when CONTIN was applied starting from channel 32, the free micellar peak has disappeared and the polymer size distributions (Fib. 8E-H) as well as dH and the dh peak values (Table 3) do not change within the experimental error. The removal of the bias by starting CONTIN from channel 32 is thus reconfirmed. This latter procedure allows an unambiguous interpretation of QELS results at 200 mM NaCl, where NaHy
4636 Langmuir, Vol. 12, No. 20, 1996
Herslo¨ f-Bjo¨ rling et al.
Figure 10. Plot of residuals. Here [NaHy] ) 0.1% (w/w), [NaCl] ) 400 mM, and [TTAB] ) 50 mM. The CONTIN analysis was started from channel 2. The corresponding bimodal distribution is presented in figure 8D.
Figure 11. Relative scattered intensities in terms of photon count rate for NaHy (MW ) 740 000 and 0.1% (w/w)) as a function of TTAB concentration for 200 and 400 mM NaCl and for two different laser outputs: 200 mM NaCl and 1.6 W (0), 200 mM NaCl and 0.6 W (b), 400 mM and 1.6 W (O), and 400 mM and 0.6 W (9). Table 4. QELS Hydrodynamic Diameters in Terms of Peak Values, dhpeak, and Inverse z-Averages, dH, for NaHy (MW ) 740 000 and 0.1% (w/w)) in 200 mM NaCl for Various TTAB Concentrations for CONTIN Analysis Started from Channels 2 and 32, Respectively a ) 2a
a ) 32a
[TTAB] (mM)
dhpeak (nm)
dH (nm)
dhpeak (nm)
dH (nm)
0 5 25 50
49 42 75 87
60 56 83 81
50 42 74 91
59 55 87 98
a
a ) first channel used in the CONTIN analysis.
and TTAB interact strongly. The particle size distributions using both calculation procedures are displayed in Figure 9A-H. The calculations starting with channel 2 are found in parts A-D, and the calculation starting with channel 32 is found in parts E-H. The TTAB concentration increases from 0 (top) to 5, 25, and 50 mM (bottom). Some free micelles are present at all TTAB concentrations for the calculations starting with channel 2 although no resolution is seen at 5 mM TTAB. The micellar peak is relatively small (as compared to the 400 mM NaCl case), which implies a relatively seen smaller contribution of free micelles (due to complexation) to the total scattered intensity at all TTAB concentrations. The calculated inverse z-averages from Figure 9A-H are summarized in Table 4. No pronounced change in the polymer size distribution is seen as the TTAB concentration is increased from 0 to 5 mM, but a consistent increase of the apparent polymer size at 25 and 50 mM TTAB and a decrease of the width of the distribution are observed in both bimodal and unimodal CONTIN analysis. In terms of average sizes the increase is definitely beyond the experimental error and both calculation variants of the CONTIN procedure agree quite well in terms of dH and dhpeak. The dH value (CONTIN from channel 32) decreases slightly at 5 mM TTAB and then increases up to 100 nm, and the
dhpeak increases up to 90 nm. The effect of averaging of dH (1/z average of both micelles and NaHy) when CONTIN was applied starting from channel 2 is quite small as compared to the 400 mM case due to a relatively low contribution of micelles to the total scattered intensity. The “narrowing” of the NaHy size distribution should be accepted with caution: biased results of bimodal analysis are easy to find (see above); on the other hand, distributions obtained starting from channel 32 should be real. The QELS data seem to agree quite well with the picture proposed by the Dubin group26,27 for the case of PDMDAAC. When the amount of micelles is low (5 mM TTAB), an intrapolymer complex is formed that contracts due to more effective polyion charge neutralization by micelles as compared to univalent counterions. When more micelles are available, the complex continues to accumulate them. If a sufficient number of micelles is trapped, their repulsive interaction becomes operative and the size of the complex begins to increase (25 mM TTAB). Until this point where the complex approximately reaches equilibrium saturation by micelles, its mass to volume ratio might continually increase and the decrease of the relative viscosity (Figure 2) is seen.26 Above the TTAB concentration needed to form the saturated complex at the given salt concentration, both the relative viscosity and the size of the complex increase. When a sufficient excess of micelles is present in the solution, the onset of dynamic association of these equilibrium intraparticle complexes is probably seen (50 mM TTAB). Additional support for the complexation at 200 mM NaCl is given by the increase in relative scattered intensities in terms of photon count rate as given in Figure 11. The relative scattered intensity is taken to be the scattered intensity of the solution minus the scattered intensity of the solvent, where the corresponding NaHy-free solution is taken as the solvent. At a laser power of 0.6 W, an increase in intensity by more than a factor of ten is observed, when the TTAB concentration increases from zero to 50 mM. The increase at the high laser power is smaller due to the fact that the photomultiplier is probably saturated for the strongly scattering solutions. Anyhow both laser powers were needed to cover the range of solutions measured. The steepest increase of the scattered intensity is seen up to 25 mM of TTAB, again indicating the concentration of TTAB where the complex is saturated by micelles in the presence of 200 mM NaCl. It also follows from Figure 11 that the relative scattered intensity of NaHy in 400 mM NaCl is constant at all concentrations of TTAB for both laser powers used, confirming the absence of interaction at this salt content. The good behavior of QELS experiments themselves (excellent baseline agreement) confirms that there is no onset of phase separation on the microscale (no formation of large fractal aggregates); i.e., the solution exhibits true single-phase behavior on the long time scale. The total QELS scattered intensity, I, of micelles and NaHy coils should be the sum of their relative contributions in the noninteracting case, i.e., in terms of number of particles
∑iNiP′MiP′2Pi(Θ)
I ≡ KmNmMm2 + KP′
(7)
where the subscript m denotes micelles and the subscript P′ corresponds to NaHY. K, N, and M correspond respectively to an optical constant, the number of particles, and the molecular weight of the particles. Pi(Θ) is the Debye scattering function. For the noninteracting case (400 mM NaCl) the first term describes the increase in the scattered intensity of the solvent and the second one should be a constant. The relative scattered intensity is then a constant, as observed in Figure 11. In the
Anionic Polysaccharide and an Oppositely Charged Surfactant
interacting case the observed increase of the scattered intensity is due to an increase of the apparent molecular weight of the complex. Assuming only intramolecular complex formation, the NiP′ is a constant, and a transfer of micelles inside of the polymer results in the increase of the complex molecular weight, which greatly increases the second term in eq 7. The corresponding decrease of the first term in eq 7 should be much smaller. Unfortunately, the optical constant in the second term of eq 7 cannot be assumed to remain unchanged; intuitively, its increase should be expected, as polymer-micelle complexes have been shown to be very dense.26 This would then introduce an additional increase of the second term in eq 7. Hence, the unknown value of the optical constant of the complex makes detailed analysis impossible. Only a rough estimate could be done. The molecular weight of the micelle is estimated to be 25 000 using an aggregation number of 75.56,57 As the molecular weight of our sample is 740 000, only 30 micelles within an intramolecular complex would increase the scattered intensity as compared to a noninteracting case by a factor of three. Assuming an increase of the optical constant in the second term by a factor of two (which does not seem impossible), an increase of the scattered intensity by a factor of six is obtained, as seen in Figure 11 at 25 mM TTAB, where the complex is probably already saturated. (56) Armstrong, D. W. Sep. Purif. Methods 1985, 14, 213. (57) Ikeda, S. Colloid Polym. Sci. 1991, 269, 49.
Langmuir, Vol. 12, No. 20, 1996 4637
Conclusions The results presented here are in line with the results from the previous paper.32 There seems to be no interaction between NaHy and TTAB when the NaCl concentration is as high as 400 mM. Neither the hydrodynamic size nor the relative intensities (from QELS) are changed with increasing TTAB concentrations, and the relative viscosity increases only slightly due to increasing concentration of free micelles. A strong interaction is observed in 200 mM NaCl, where the system is close to phase separation, as evidenced by the distinct increase of electrophoretic migration time, the decrease in relative viscosity, and the changes of the hydrodynamic size and the relative scattering intensity (from QELS) with TTAB concentration. The extent of the interaction is controlled mainly by the ionic strength of the solution and the concentration of the surfactant. As the interaction is essentially electrostatic in nature, it is not surprising that the model developed in interaction studies of a positively charged polymer with a negatively charged surfactant applies well here. Acknowledgment. Financial support from the Swedish Natural Science Research Council and from the Swedish Council for the Engineering Sciences is gratefully acknowledged. B.P. also wishes to thank the Faculty of Pharmacy, Uppsala University, for a research grant supporting “bilateral research cooperation with Central and Eastern Europe”. LA950222O
