Study of Interaction of Poly(ethylene imine) with ... - ACS Publications

Langmuir 2000, 16, 4495-4510

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Study of Interaction of Poly(ethylene imine) with Sodium Dodecyl Sulfate in Aqueous Solution by Light Scattering, Conductometry, NMR, and Microcalorimetry Mitchell A. Winnik,* Simon M. Bystryak,† and Christophe Chassenieux‡ Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6

Vladimir Strashko and Peter M. Macdonald Department of Chemistry and Erindale College, University of Toronto, 3359 Mississauga Road North, Mississauga, Ontario, Canada L5L 1C6

Junaid Siddiqui Dupont Films, PO Box 411, Hopewell Virginia 23860 Received November 30, 1999. In Final Form: February 17, 2000

Light scattering studies show that in aqueous solution poly(ethylene imine) (PEI) exists largely in the form of individual macromolecules plus a small fraction of aggregates. The aggregates make a large contribution to the scattering signal but only a very small contribution to the solution viscosity. Addition of sodium dodecyl sulfate (SDS) to the solution has a number of interesting consequences. Microcalorimetry experiments show that well below the critical micelle concentration of SDS, individual SDS molecules add to the PEI through an exothermic process. At higher SDS concentrations, there is a noncooperative adsorption, which is endothermic in nature, of SDS micelles onto the polymer chains. The surfactant-polymer complex likely contains several polymer molecules. These solutions are characterized by a higher specific conductivity than can be explained by the sum of the conductivities of all the individual ions in solution, even if the Na+ and DS- ions were free in solution and not bound to the polymer. Pulsed-gradient NMR measurements were carried out to examine the Na+ and DS- ion mobility in the solutions. These measurements showed that surfactant binding to the polymer released sodium ions from the SDS micelles. The increase in pH showed that this binding also releases a small amount of OH- into the solution. These two effects by themselves are not large enough to account for the measured conductivity of the solutions. We speculate that there is high ionic mobility inside the polymer-surfactant complex that adds to the overall conductivity of the solution.

Introduction Water-soluble polymer-surfactant systems have been intensively studied over the past 2 decades.1-3 A steadily growing interest in these systems is driven by their wide range of technical applications. For example, water-soluble polymer-surfactant mixtures are used in various technological formulations, such as paints, coating fluids, inks, drug delivery systems, and foodstuffs. The properties of the polymer-surfactant combinations are also appreciated in formulations for cosmetic products and laundry detergents and in tertiary oil recovery. The polymer* To whom correspondence should be addressed: e-mail, [email protected]. † Permanent address: Skye PharmaTech, 6354 Viscount Rd., Mississauga, Ontario L4V 1H3, Canada. ‡ Permanent address: Laboratoire de Physico-chimie Macromole´culaire, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France. (1) Water-soluble Polymers: Synthesis, Solution Properties, and Applications; Shalaby, S. W., McCormick, C. L., Butler, G. B., Eds.; ACS Symposium Series No. 467; American Chemical Society: Washington, DC, 1991. (2) Hydrophilic Polymers, Performance with Environmental Acceptance; Glass, J. E., Ed.; Advances in Chemistry Series No. 258; American Chemical Society: Washington, DC, 1996. (3) Interaction of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993.

surfactant association depends on many factors including Coulombic interactions, the hydrophobicity of the polymer-surfactant pair, and conformational features of the polymer.4 The current view that has emerged from these studies of polymer-surfactant complexes is that surfactants often interact cooperatively with polymers at a critical aggregation concentration, cac, forming micelle-like aggregates along the polymer (“necklace of beads” model).5 This is the case for almost all systems consisting of uncharged polymers and ionic surfactants.6,7 For polyelectrolytes interacting with oppositely charged surfactants,4,8 the situation is more complex. Polymer-bound micelles form, and the cac values are often several orders of magnitude smaller than the critical micelle concentration (cmc) of the surfactant.4 In these systems, at even lower concentration, individual surfactant molecules can bind to the polymer through ion-pairing interactions. (4) Hayakawa, K.; Kwak, J. C. T. In Cationic Surfactants; Rubingh, D. N., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; p 189. (5) Cabane, B.; Duplessix, R. J. Phys. (Paris) 1982, 43, 1529. (6) Saito, S. In Nonionic Surfactants: Physical Chemistry; Schick, M. J., Ed.; Surfactant Sci. Ser.; Marcel Dekker: New York, 1987; Chapter 15. (7) Brackman, J. C.; Engberts, J. B. F. N. Chem. Soc. Rev. 1993, 85. (8) Wei, Y.-C.; Hudson, S. M. J. Macromol. Sci. Rev. Macromol. Chem. Phys. 1995, C35, 15.

10.1021/la991553u CCC: $19.00 © 2000 American Chemical Society Published on Web 04/12/2000

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Systems in which polyelectrolyte binds to the oppositely charged micelles are usually biphasic, but a number of polyelectrolyte-micelle complexes constitute reversible aggregates. Different structures of polyelectrolytesurfactant complexes have been reported. The structure of the complex depends on the different types of interactions that play a role. These include pure electrostatic forces, structural features of the different types of charged groups, and other factors such as the presence of hydrophobic moieties on the polyelectrolyte, the flexibility of the polymer backbone and its architecture, and the type of the counterions present. The structure of polyelectrolyte-surfactant complexes may be referred to as “intrapolymeric”, if each aggregate in solution contains only one polymer molecule, or “interpolymeric”, if the complex contains several polymer molecules. Many investigators have suggested that polyelectrolyte-surfactant complex formation is accompanied by conformational changes of polymer chains.8 Several experimental techniques have been used to monitor these polymer-surfactant structure changes, including fluorescence, light scattering, and viscosity.3 The general picture that has emerged from these studies is that micellelike surfactant aggregates may contribute to conformational change through hydrophobic interactions as well as through partial neutralization of the polymer charge. Fluorescence spectroscopy is often particularly useful for elucidation of detailed structural aspects of the process of polymer-surfactant interaction.9 Features of the interaction of polyelectrolytes with oppositely charged surfactants revealed by fluorescence spectroscopy have been described in a number of publications.10-13 Guillemet and Piculell10 investigated the interaction between sodium dodecyl sulfate (SDS) and a hydrophobically modified polyelectrolyte, a cellulose derivative substituted with cationic hydrophobic side chains. Chandar et al.11 found that binding of dodecyltrimethylammonium bromide to poly(acrylic acid) leads to increased excimer formation as a result of polymer coiling. Chu and Thomas12 studied the effects of surfactant chain length and polymer concentration on the cac by a fluorescence probe technique and found that coiling of the polymer occurs upon its interaction with the surfactant. Recently, Fundin et al.13 showed through time-resolved fluorescence quenching experiments in the poly(acrylic acid) (PAA)-cetyltrimethylammonium bromide (C16TAB) system that the mean aggregation number of the polymer-bound micelles is much smaller than that of normal C16TAB micelles. Light scattering measurements allow one to follow changes in the hydrodynamic radius or the radius of gyration of the polymer that reflect the conformational transitions of the polymer upon its interaction with surfactant.14 For example, Xia et al.15 studied the interaction between poly(dimethyldiallyammonium chloride) and mixed micelles of sodium dodecyl sulfate (SDS) plus Triton X-100 in aqueous solution by light scattering. They found that intrapolymer complex formation occurs at low polymer concentrations, and in the limit of excess surfactant, the intense binding of the micelles to the polymer (9) Winnik, F.; Regismond, S. Colloids Surf., A 1996, 118, 1. (10) Guillemet, F.; Piculell, L. J. Phys. Chem. 1995, 99, 9201. (11) Chandar, P.; Somasundaran, P.; Turro, N. J. Macromolecules 1988, 21, 950. (12) Chu, D. Y.; Thomas, J. K. J. Am. Chem. Soc. 1986, 108, 6270. (13) Fundin, J.; Hansson, P.; Brown, W.; Lidegran, I. Macromolecules 1997, 30, 1118. (14) Herslof, A.; Sundelof, L. O. J. Phys. Chem. 1992, 96, 2345. (15) Xia, J.; Zhang, H.; Rigsbee, D. R.; Dubin, P. L.; Shaikh, T. Macromolecules 1993, 26, 2759.

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produces a strong chain expansion and a near doubling of the radius of gyration. Although a large number of studies have examined linear polymers, much less attention has been paid to branched and hyperbranched polymers. Interesting but as yet unanswered questions include what kind of conformational changes are characteristic for globular, highly branched polymers and whether intrapolymer and interpolymer complexes, resembling those proposed for linear polymers, also exist for hyperbranched polymers. It is in this context that we report a study by a variety techniques of the interaction between SDS and the highly branched polymer poly(ethylene imine) (PEI). Commercial PEI is a hyperbranched polymer containing three different types of amino groups: secondary and tertiary amino groups in the main chain and secondary and primary amino groups in the side chain.16 The ratio of primary-to-secondary-to-tertiary amino groups is 1:2: 1.17 It is a polybase with a weak polyelectrolyte character in unbuffered water18 and behaves as a strong polyelectrolyte upon protonation with acid. This polymer was recently characterized by laser light scattering and viscometry measurements by Park and Choi.19 They fractionated the polymer to obtain samples of different molecular weight. All of the solution properties they determined at 35 °C were characteristic of a branched polymer. Viscometry measurements gave [η] ) 0.513Mw0.31(0.01, where [η] is the intrinsic viscosity. The normal exponent of the Mark-Houwink relation for flexible linear polymer system is usually 0.7 in a good solvent and 0.5 under theta conditions. The exponents of scaling relationships between Mw and the z-average radius of gyration, RG, the hydrodynamic radius RH, the viscometric radius, RV, and the thermodynamic radius, RT, were lower than those for a linear polymer in a good solvent. These low exponents were attributed to the compact structure of a highly branched polymer. We recently reported the synthesis and fluorescent properties of pyrene-labeled poly(ethylene imine) (PEIPy)20 and used this fluorescence to examine its interaction with SDS in aqueous solution.21 In these studies, we showed that in the absence of SDS, the pyrene monomer intensity is substantially reduced due to quenching of Py fluorescence by secondary and tertiary amines, whereas the excimer emission is less affected. The fluorescence properties of the PEI-Py changed upon association with SDS. The increase in monomer fluorescence intensity with increasing SDS concentration indicates that SDS molecules protect Py from quenching, through formation of polymer-bound micelles. We examine here the interaction between PEI and SDS in aqueous solution using viscometry, light scattering, pulsed field gradient NMR, and microcalorimetry. We undertook these experiments with the hope that viscometry and light scattering measurements could shed more light on the PEI conformational changes that occur upon its interaction with SDS. In a preliminary report of our study of PEI-SDS interactions,22 we described an unusual behavior of conductivity vs [SDS] plots in the presence of (16) Rivas, B. L.; Geckeler, K. E. Adv. Polym. Sci. 1992, 102, 171. (17) Dick, R. C.; Ham, G. E. J. Macromol. Sci., Part A 1970, 1301. (18) Mark, H. F., et al., Eds. Encyclopedia of Polymer Science and Technology, 2nd ed.; Wiley: New York, 1985; Vol. 1, pp 680-723. (19) Park, I.-H.; Choi, E.-J. Polymer 1996, 37, 313. (20) Winnik, M. A.; Bystryak, S. M.; Liu, Z.; Siddiqui, J. Macromolecules 1998, 31, 6855. (21) Winnik, M. A.; Bystryak, S. M.; Siddiqui, J. Macromolecules 1999, 32, 624. (22) Bystryak, S. M.; Winnik, M. A.; Siddiqui, J. Langmuir 1999, 15, 3748.

Water-Soluble Polymer-Surfactant Systems

PEI. SDS solutions, in the presence of all other nonionic water-soluble polymers that have been examined, have a conductivity that is less than or equal to that of the SDS solution itself. SDS solutions in the presence of PEI have an enhanced conductivity. To examine the possible origins of this effect, we report pulsed-gradient NMR experiments, which examine the mobility in the solution of the water molecules, the sodium ions, and the dodecyl sulfate (DS-) ions. Microcalorimetry is a valuable technique that often allows one to elucidate the mechanism of the polymersurfactant interactions.23 In particular, microcalorimetric measurements of the heat adsorbed or evolved upon interaction between polymer and surfactant can give detailed information about the nature of that interaction. The evaluation of the enthalpy of adsorption (integrated or differential) enables one to determine the contribution of hydrophobic interactions and entropy effects in the process. Therefore, we examine the interaction between PEI and SDS using isothermal titration microcalorimetry (ITC). The results obtained using these different techniques lead to a clearer picture of the mechanism of PEI-SDS interactions and the structure of the polymer-surfactant complex. Experimental Section (A) Materials. Hyperbranched poly(ethylene imine) (PEI), with a nominal molecular weight 75 000 (manufacturer’s specification; Mw calculated from light scattering is approximately 10 times higher, see below) was purchased from Aldrich, but manufactured by BASF. The polymer was used as received, although the purity, especially of PEI, was checked by careful 1H measurements and by atomic absorption spectroscopy for the presence of inorganic impurities. SDS was obtained from Fisher Scientific. Its purity was assessed by determination of its cmc (see below), and it was used without further purification. Aqueous solutions were made up using distilled water, which was deionized in a Millipore Milli-Q water system. The solution concentrations of PEI are given as weight percents (grams per 100 mL) or as the molar concentration on a monomer basis (moles of monomer per liter of solution). SDS concentrations are given in moles per liter. We use the notation CPEI to refer to concentrations in g/L and [SDS] to refer to molar concentrations. (B) Viscometry Measurements. Viscosities of aqueous solutions were measured at 20.0 ( 0.2 °C using a Ubbelohde suspended level viscometer. The intrinsic viscosity [η] was obtained by extrapolation of the reduced ηred ) (1/CPEI)((η/η0) 1) and inherent ηin ) (1/CPEI) ln((η/η0)) viscosities to zero PEI concentration, where CPEI is the concentration of PEI, η is the viscosity of a solution at a concentration CPEI, and η0 is the viscosity of the solvent. All solutions were filtered through 0.2 µm Anotop filters. (C) Light Scattering. Static (SLS) and dynamic light scattering (DLS) measurements were performed using a digital correlator with 136 channels (Brookhaven BI-2030AT) in combination with an argon-ion laser (Excel 3000) emitting vertically polarized light with a wavelength (λ) of 514.5 nm. The “multiple sample time” procedure allowed the intensity autocorrelation function (g2(t)) to be determined along a time scale ranging from 10 µs to 1 s. The angular range investigated was comprised between 30° and 130°. All measurements were carried out at 20.0 ( 0.2 °C. Toluene was used as the reference in the SLS measurements with a value of 3.1 × 10-5 cm-1 for the Rayleigh ratio, Rtol.24 The solutions were filtered through 0.2 µm Anotop filters prior to the measurements. (1) Dynamic Light Scattering. The autocorrelation functions g2(t) were analyzed in terms of a continuous distribution of relaxation times τ (23) Wang, G.; Olofsson, G. J. Phys. Chem. B 1998, 102, 9276. (24) Moreels, E.; de Ceuninik, W.; Finsy, J. J. Chem. Phys. 1987, 86, 618.

Langmuir, Vol. 16, No. 10, 2000 4497 g1(t) )

∫ A(τ) exp(- τt) dτ ∞

(1)

0

where g1(t) is the normalized electric field autocorrelation function, which is related to g2(t) through the Siegert relation.25 A(τ) was obtained by regularized inverse Laplace transform (RILT) of the experimental data using a constrained regularization calculation algorithm called REPES without assuming a specific shape.26 An apparent diffusion coefficient D for a given PEI concentration was calculated from the average relaxation times 〈τ〉 using D ) (q2〈τ〉)-1, where q is the scattering vector defined as q ) (4πn/λ sin(θ/2)), with n the refractive index of the solvent, λ the wavelength of the radiation, and θ the scattering angle. An apparent hydrodynamic radius (RH) can be calculated using the Stokes-Einstein relation: RH ) kBT/(6πη0D), with kB the Boltzmann constant, T the absolute temperature, and η0 the viscosity of the solvent. (2) Static Light Scattering. As detailed in the results section, the distributions of relaxation times obtained from DLS are bimodal. The amplitudes of the slow As(q) and fast Af(q) components represent the relative contribution of each mode of relaxation to the total scattered intensity, I. The light intensity scattered by the fast mode of relaxation is given by

If(q) )

Af(q) Af(q) + As(q)

(I(q) - Isol(q))

(2)

where Isol(q) represents the intensity scattered by the solvent. For weakly interacting systems, the excess scattering intensity for the fast mode of relaxation If(q) is related to the weight average molar mass of the particles (Mw,f) according to classical Zimm equation:27

(

1 + 2A2C Mw,f KC 1 ) ) Rθ,f Mapp,fP(q) P(q)

)

(3)

K is a contrast factor, which depends on the refractive index increment of the PEI macromolecules in water [(dn/dc)λ ) 0.21 mL/g].19,28 Rθ,f ) Rtol(If/Itol)q is the Rayleigh ratio at wave vector q using toluene as a reference. A2 is the second virial coefficient, and P(q) is the particle form factor. If q-1 is much larger than the overall size of the particles, P(q) is close to unity. (D) Conductivity Measurements. Conductivity titration measurements were carried out at 20° C using a Fisher Scientific conductometer. Simultaneous with the conductivity, the pH of the solutions was measured using a pH-meter purchased from EXTECH Instruments (Waltham, MA). All experiments were carried out with aqueous solutions in the cell under constant stirring. To avoid disturbance of the conductivity and pH measurements, the titrations never lasted longer than 30 min, and after each run, the electrodes were rinsed with water and calibrated using standard calibration solutions. (E) Pulsed Field Gradient NMR. Proton NMR self-diffusion measurements were performed using an MRI (magnetic resonance imaging) probe with actively shielded gradient coils (Doty Scientific, Columbia, SC) installed in a Chemagnetics CMX300 NMR spectrometer operating at 299.5 MHz for protons. Diffusion coefficients of water, polymer, and surfactant were determined using the PGSE (pulsed-gradient spin-echo) technique29 with the following typical parameters as indicated in parentheses: sweep width (10 kHz), number of data points (512), 90 pulse length (22.5 µs), interpulse delay (50 ms), and recycle delay (5 s). The gradient pulse was applied along the z-direction for durations varying between 2 and 32 ms. Two different gradient (25) Berne, B.; Pecora, R. Dynamic Light Scattering; Wiley: New York, 1976. (26) Stepanek, P. In Dynamic Light Scattering; Brown, W., Ed.; Oxford University Press: Oxford, 1993; Chapter 4. (27) Huglin, M. B., Ed. Light scattering from polymer solutions; Academic Press: London and New York, 1972. (28) Van Den Berg, J. W. A.; Bloys Van Treslong, C. J.; Polderman, A. Recl. Trav. Chim. 1973, 92, 3. (29) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 45, 288.

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amplitudes were employed: a lower amplitude of 35 G cm-1 for faster diffusion and a higher amplitude of 200 G cm-1 for slower diffusion. The lower gradient amplitude was calibrated using the known diffusion coefficient of 2 vol % water in deuterium oxide (D0 ) 1.9 × 10-9 m2 s-1)30 while the higher gradient amplitude was calibrated using a 9.5 wt % PEO (Mw ) 6000) in water solution in which the diffusion coefficient could be measured at either gradient strength. No echo distortion or drift due to eddy currents was observed under these conditions. Although the number of transients varied depending on concentration, typically at least 512 transients were signal averaged for any one value of the gradient pulse length. The data were processed with an exponential line broadening corresponding to 10 Hz and zero filled to 2048 points prior to Fourier transformation. The sample temperature was controlled to 25 °C. Sodium NMR self-diffusion measurements were performed with the same MRI probe installed in the same NMR spectrometer, but operating at 79.23 MHz for 23Na. The PGSE technique was again used, with typical parameters as indicated in parentheses: sweep width (50 kHz), number of data points (2k), 90° pulse length (13.5 µs), interpulse delay (10 ms), and recycle delay (0.5 s). The gradient pulse of amplitude ∼35 G cm-1 (calibrated as above) was applied along the z direction for durations varying between 1 and 5 ms. The data were processed with an exponential line broadening corresponding to 10 Hz prior to Fourier transformation. The sample temperature was controlled to 25 °C. (F) Isothermal Calorimetry Titrations. Isothermal titration calorimetry (ITC) experiments were carried out using an Omega isothermal titration microcalorimeter (MicroCal, Northampton, MA). In the ITC experiment on the study of polymer-surfactant interactions the enthalpy changes measured at constant temperature upon addition of small amounts of concentrated surfactant solution to the sample cell containing the polymer solution are compared to those in the reference cell (containing pure water). Five experiments were carried out. In each, 7 µL aliquots (except the first one which was 2 µL) of 130 mM SDS water solution were injected into the 1.3337 mL sample cell containing either (i) pure water or (ii) aqueous 0.5 wt % PEI solution at pH 10.6, (iii) 0.083 wt % PEI solutions at pH 10.2, or (iv) and (v) the same PEI solutions at an initial pH of 5.8. All experiments were performed at 30° C. Samples were stirred at 400 rpm and auto-degassed. The time between injections was 3.5 min. The plot of enthalpy change per injection vs time was first constructed and treated as raw data. For each injection, the experimental heat (enthalpy) change hi (in calories) resulting from injection i was obtained by the raw data peak integration. The values of integrated molar enthalpy change for injection i ∆Hi (in calories per mole) were obtained by dividing hi by number of moles of surfactant added ni; hence ∆Hi ) hi/ni. Then, plots of ∆Hi against the total surfactant concentration added were prepared and are referred to as enthalpy curves.

Results and Discussion (A) Viscometry. The plots of inherent viscosity ηin and reduced viscosity ηred vs PEI concentration in aqueous solution are shown in Figure 1. The intrinsic viscosity of PEI in pure water, obtained by extrapolation of the ηred and ηin values to zero PEI concentration, is equal to 32.4 ( 0.3 mL/g. The same sample (BASF is the only manufacturer) of hyperbranched PEI with nominal molecular weight 75 000 (manufacturer’s specification) was recently characterized by laser light scattering and viscometry measurements by Park and Choi.19 They fractionated the polymer to obtain samples of different molecular weight. All of the solution properties they determined at 35 °C were characteristic of a branched polymer. Viscometry measurements gave [η] ) 0.513Mw0.31(0.01, where [η] is the intrinsic viscosity. The value of the exponent is much smaller than that expected for a flexible linear polymer in a good solvent (0.7) and in a theta solvent (0.5). The (30) Mills, R. J. Phys. Chem. 1973, 77, 685.

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Figure 1. Variation of the reduced viscosity (closed circles) and inherent viscosity (open circles) for different concentrations of PEI in water.

Figure 2. Distributions of relaxation times obtained at θ ) 90° for PEI solutions at 0.2 wt %. From bottom to top: in pure water, with 1 M NaCl, and at pH ) 11.2.

exponents of the scaling relationships for PEI found by Park and Choi for Mw and the z-averaged radius of gyration, RG, the hydrodynamic radius RH, the viscometric radius, RV, and the thermodynamic radius, RT, were lower than those of a linear polymer in a good solvent. These low exponents were attributed to the compact structure of a highly branched polymer. Using the scaling laws for fractionated PEI samples determined by Park and Choi,19 we can estimate the molecular weight for our sample to be Mw ) (6.4 ( 0.2) × 105 g/mol. One should note that the manufacturer’s nominal M is almost an order of magnitude lower than the value of Mw estimated from viscosity measurements. (B) Dynamic Light Scattering. (1) DLS of PEI Solutions. In Figure 2 we plot typical distributions of relaxation times obtained by Laplace inversion of the DLS signal for 0.5 wt % PEI aqueous solutions. The three curves refer to the polymer in pure water (pH 9.9), to the polymer in water with the pH adjusted to 11.2 with NaOH, and the polymer in the presence of 1 M NaCl. The polymer


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solution is characterized by two q2-dependent relaxation processes over the whole concentration range investigated (from 0.1 to 1 wt %). The fast mode of relaxation, after extrapolation to zero PEI concentration, corresponds to an RH value of 16.0 ( 0.8 nm, which in turn corresponds to a molecular weight Mw ) (5.6 ( 0.6) × 105 g/mol. This value was calculated using the scaling law RH ) (7.53 × 10-2)Mw0.43(0.01 obtained by Park and Choi.19 By comparison with the value of Mw obtained from viscometry, the fast mode of relaxation is attributed to the diffusion of individual PEI macromolecules. The slow mode of relaxation (RH(Cf0) ) 60 nm) is attributed to the diffusion of PEI aggregates in the solution. This tendency for aggregation of PEI has already been described for linear31 and hyperbranched samples.32,33 In the latter case, Park33 has informed us that the addition of salt (1 M NaCl) or an increase in the pH of the solution (to pH ) 11) can prevent the formation of such aggregates at low polymer concentrations (c < 0.4 wt %). When we carried out our measurements using the same procedures, we still found evidence for the presence of aggregates (see Figure 2). According to Smits et al.,31 complete removal of the slow mode of relaxation is possible after filtration of the solutions through low-porosity filters. Our experiments show that the slow mode of relaxation of the PEI samples did not disappear after filtration of our samples through 0.1 µm Anotop filters. Thus, we imagine that the aggregates re-form immediately and spontaneously after disruption by filtration. We also found that dialysis and sonication of the PEI samples did not eliminate the PEI aggregates. This situation is reminiscent of the case of poly(ethylene oxide) (PEO), where the purity of water turned out to be a key factor in the formation of PEO aggregates.34 Moreover, the weak polyelectrolyte nature of PEI should be taken into account in this phenomenon.31 It should be noted that the fraction of the PEI molecules involved in the formation of aggregates is small. The intensity of scattered light Ii for fast and slow modes of relaxation is proportional to the term Ai(I(q) - Isol(q)), where Ai is the amplitude of either the slow (As(q)) or the fast Af(q)) components. On the other hand, Ii is proportional to Mwi × Ci for the aggregates as well as for free PEI. Thus the concentration of aggregates Cag can be estimated from the expression

As(qf0) Cag Mf ) CPEI - Cag Ms Af(qf0)

(4)

where Ms and Mf represent the molecular weights of the aggregates and of the PEI macromolecules, respectively. Assuming that the scaling law for PEI macromolecules19 (see above) also holds for the aggregates (this is equivalent to assuming a fractal dimension of 2.2 for the aggregates), we obtain Ms ≈ 106 g/mol. Using this value, we estimate that only 1% of the total concentration of the solution is involved in these aggregates for a solution at CPEI ) 0.5 wt %, whereas the relative amplitude of the slow relaxation process As(qf0) is equal to 60%. (2) DLS of PEI + SDS Solutions. The DLS experiments for the PEI aqueous solutions in the presence of different concentrations of SDS were performed at CPEI ) 0.5 wt %. In this case, the distributions of relaxation times display the same fast and slow modes of relaxation as (31) Smits, R. G.; Kuil, M. E.; Mandel, M. Macromolecules 1994, 27, 5599. (32) Budzynski, D. M. Ph. D Thesis, University of Illinois 1996. (33) Park, I. H. Private communication. (34) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 5943.

Figure 3. Variation of the apparent diffusion coefficients for the fast (circles) and the slow (squares) modes of relaxation with the concentration of SDS.

those for PEI solutions in the absence of SDS. The presence of the PEI aggregates affects the analysis dramatically. Both modes of relaxation are relatively broad and characterized by close average relaxation times, and consequently, it is very difficult to discriminate between them. Therefore, the parameters such as the apparent diffusion coefficient D and the hydrodynamic radius RH for the PEI + SDS system obtained from the DLS data are characterized by large error bars (Figures 3, 5, and 6). Nevertheless, we are convinced that the observed changes in the aforementioned parameters are significant. Figure 3 describes the variation of the apparent diffusion coefficients for PEI aqueous solutions with the concentration of SDS for both modes of relaxation. In both cases, an increase of SDS concentration from 0 to 25 mM leads to a decrease in D. In Figure 3, we also show values of the ratio of SDS molecules to EI monomer units in the solution by defining β ) [SDS]/[EI]. Above 25 mM SDS, D values level off with increasing SDS concentration. As can be seen in Figure 3, the initial decrease in D is much less pronounced for the aggregates than for the PEI macromolecules. To obtain an estimate of the hydrodynamic radius of the equivalent hard sphere whose diffusion coefficient is equal to the one measured from the fast relaxation process, the Stokes-Einstein relation is used RH ) kBT/(6πη0D). Here η0 is the viscosity felt locally by the equivalent hard spheres and is commonly assumed to be equal to the viscosity of the solvent. Nevertheless the macroscopic viscosity η of the PEI solution is clearly affected upon addition of SDS. To obtain η values, we measured the viscosities of 0.5 wt % % PEI solutions in the presence of the various SDS concentrations corresponding to those examined in the light scattering experiments. These results are plotted in Figure 4. One sees that below 8 mM the presence of SDS has little effect on the solution viscosity, whereas above 8 mM, the viscosity η of the PEI

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Figure 4. SDS concentration dependence of the reduced viscosity for solutions at 0.5 wt % PEI.

Figure 5. SDS concentration dependence of the apparent hydrodynamic radius (triangles) and of the apparent molecular weight (squares) calculated with the refractive index increment for PEI in water for the fast mode of relaxation (CPEI ) 0.5 wt %).

solutions increases steadily with increasing [SDS]. Figure 5 presents the variation of the hydrodynamic radius RH,f calculated for the fast mode of relaxation with increasing SDS concentration. One can see that RH,f increases by a factor of 2 when [SDS] increases from 8 to 18 mM. Above 18 mM, added SDS leads to a constant value for RH. A somewhat different behavior is inferred if one uses η

Winnik et al.

instead of η0 for the calculation of RH from D. Under these circumstances the RH,f values peak at 20 mM SDS and then decrease to ca. 20 nm at 100 mM SDS. In fact, as shown in the section describing PFG NMR results, the mobility of water in PEI solutions is affected upon the addition of SDS. For [SDS] ) 100 mM, the mobility of water decreases by a factor 20-25% compared to its value in PEI solution. This means that the local viscosity felt by the complex is higher than the viscosity of water especially at the highest SDS concentration. If this fact is taken into account in the calculation of RH for the fast mode of relaxation, it should lead to a small decrease in the hydrodynamic radius of the complex at the highest SDS concentrations. As mentioned in the Introduction, both intrapolymerand interpolymer-surfactant complexes may occur upon interaction between a polymer and surfactant in water. Viscosity and light scattering techniques are especially useful for determining the hydrodynamic volume of the polymer-surfactant complexes.14,15 In the sodium hyaluronate-tetradecyltrimethylammonium bromidesodium chloride-water system, for example, the viscosity was found to decrease with addition of surfactant and to pass through a marked minimum value as an indication of coil contraction and the aggregation of polymer chain.14 At higher surfactant concentrations, the binding of surfactant to the polymer leads to an expanded polymer chain. Our data in Figure 5 exhibit the type of behavior that has been observed for a number of different polymerand protein-surfactant systems.35,36 For example, Gimel and Brown35 studied the properties of lysozyme solutions at 25 °C in the presence of different SDS concentrations using dynamic and static light scattering measurements. They found that the hydrodynamic radius of lysozyme increases with increasing SDS concentration up to 9 mM and then decreases when the amount SDS added was above 9 mM. The authors of ref 35 interpreted these results in terms of the formation of a lysozyme-surfactant complex. In addition, they proposed that two lysozyme molecules are present in the protein-surfactant complex. The interaction between the cationic polymer poly(dimethyldiallylammonium chloride) (PDMDAAC) and anionic/nonionic (SDS plus Triton X-100) mixed micelles has been studied by DLS by Dubin et al.36 In this case, the polymer-surfactant interaction is primarily influenced by the composition of the mixed micelle (i.e., the mole fraction of anionic surfactant, Y). For example, the hydrodynamic diameter Ds of the polymer-micelle complex increased with increasing Y up to Y ) 0.26 and then decreased with further increasing Y. The authors of ref 36 interpreted these striking results in terms of complexes that formed initially at low Y, with dimensions not much larger than those of the uncomplexed polymer. The mixture formed higher order aggregates with increasing Y. In the presence of a large fraction of anionic surfactant, the aggregates at least partially redisperse. To interpret our light scattering results, we have to take into account the hyperbranched structure of the PEI macromolecules and the rather large polydispersity of the polymer. We suggest the following qualitative model to explain the variation of RH for the fast mode of the PEISDS system: In the presence of low concentrations of SDS ([SDS] < 18 mM), individual surfactant molecules bind to the polymer chains forming micelle-like aggregates. (35) Gimel, J. C.; Brown, W. J. Chem. Phys. 1996, 104, 8112. (36) Dubin, P. L.; Vea, M. E. Y.; Fallon, M. A.; The, S. S.; Rigsbee, D. R.; Gan, L. M. Langmuir 1990, 6, 1422.


Figure 6. Variation of the ratio KC/Rθ with the square of the wave vector for a solution at CPEI ) 0.5 wt % and [SDS] ) 100 mM. Calculations are made with the total scattered intensity (circles) and the calculated intensity scattered by the fast (triangles) or the slow (squares) modes of relaxation.

This process may be accompanied by the formation of interpolymer complexes, where the micelle-like aggregates play the role of bridges between two or more PEI macromolecules. These multipolymer PEI complexes may consist of PEI macromolecules of different sizes. Thus, the average hydrodynamic radius for the fast mode of the relaxation time increases from approximately 18 nm without surfactant to 32 nm at 18 mM SDS. As the concentration of SDS is increased further, the average fast mode hydrodynamic radius of the PEI macromolecules does not change substantially. SDS concentrations above 20 mM do lead to a significant increase in the bulk solution viscosity η. Depending upon whether one employs η or the pure solvent viscosity ηo to calculate RH,f from measured values of D, one reaches different conclusions about the dependence of the magnitude of RH,f on SDS concentration for [SDS] > 20 mM. When RH,f values are calculated from ηo, these values remain constant for [SDS] up to 100 mM. When RH,f values are calculated from η, these values decrease to 18 nm for [SDS] ) 100 mM. As we will see in the following section, the apparent molecular weight (Mapp,f) of the fast component decreases as the concentration of SDS in the solution is increased. This result suggests that the amount of SDS in the solution becomes enough to “solubilize” PEI molecules; that is, the PEI interpolymer complexes may partially redisperse. (3) Static Light Scattering. (a) Data Treatment. The angular dependence of the ratio KC/Rθ for the 0.5 wt % PEI aqueous solution in the presence of 100 mM SDS is shown in Figure 6. The ratio KC/Rθ has been plotted versus the square of the wave vector using the total scattered intensity (a) as well as the intensities calculated for the fast (b) and the slow (c) modes of relaxation. In all three cases, the calculations were made using the value of the refractive index increment of PEI in water and a total PEI concentration of 0.5 wt %. Straight lines correspond to least-squares fits of the data. The intercept is equal to the inverse of the weight average molecular weight and the slope is proportional to the z-average radius of gyration Rg.

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As can be seen in Figure 6, for the fast mode of relaxation (case b), there is no systematic angular dependence of the ratio KC/Rθ. Thus the particle form factor is close to unity over the whole angular range investigated. The radius of gyration can therefore be estimated to be below 20 nm, which is consistent with a value of 18 nm for the hydrodynamic radius. Note that in the range of SDS concentrations between 12.5 and 25 mM, the angular dependence of the ratio KC/Rθ appears for the fast mode of relaxation; however, the error bars are very large (around 40%). The data for the slow mode of relaxation (case c) are less noisy, and accurate values for the radius of gyration are obtained (Rg,s(CPEIf0) ) 70 ( 10 nm). To obtain the molecular weight of the aggregates, one should know the refractive index increment of the aggregates in water and their concentration in the solution (which is very low according to the calculation described above). The total scattered intensity, case a, represents an average of the signals contributing to cases b and c. The angular dependence of the total intensity is due mainly to the species which exhibits the slow mode of relaxation. Since Rg,f contributes to the z-average value of Rg,t, the latter is smaller than Rg,s. Without the special analysis of the data to separate these contributions, we would obtain for the polymer in solution a value of Mw four times higher than that of Mw,f. To conclude, we can say that our analysis of the SLS data is based on a single assumption: the concentration of the species responsible for the fast mode of relaxation is essentially equal to the total concentration of polymer in the solution. This assumption seems to be reasonable, since the Mw values calculated for the polymer (see below) are consistent with the value inferred from the DLS measurements in which the fast and slow modes are clearly separated. (b) PEI Solutions. For the 0.5 wt % PEI, the apparent molecular weight of the particles (Mapp,f) corresponding to the fast mode of relaxation obtained from SLS is equal to (3.5 ( 0.1) × 105 g/mol. Using scaling laws obtained by Park19 for A2, the true molecular weight of the PEI macromolecule (Mw,f) is estimated to be 5.9 ( 0.2 × 105 g/mol.37 Thus both DLS and SLS give similar values for Mw,f: (5.9 ( 0.2) × 105 g/mol and (5.6 ( 0.6) × 105 g/mol, respectively. The slightly overestimated value of the PEI molecular weight calculated from viscometry measurements (Mw ) (6.4 ( 0.2) × 105 g/mol) could be due to the contribution of the aggregates to the viscosity of the solution. The contribution of the aggregates cannot be resolved from that of the individual PEI macromolecules. (c) PEI/SDS Solutions. The apparent molecular weight extrapolated to zero angle for the fast mode of relaxation (eq 3) along with hydrodynamic radius RH,f has been plotted versus the concentration of SDS in Figure 5. Thus it is possible to compare the changes of parameters Mapp,f and RH,f for the PEI-SDS complex with increasing SDS concentration. Mapp,f values were calculated using the value of the refractive index increment for PEI in water (dn/dc ) 0.21 mL/g), because the corresponding value for the PEI-SDS complex in water is unknown. This is equivalent to assuming that the scattering by the PEISDS complex is caused primarily by the PEI macromolecules. Since SDS micelles have a much lower molecular weight and a much lower refractive index increment (dn/ dc ) 0.11 mL/g),27 the above assumption is, presumably, (37) The weight averaged molar mass of the fast component is calculated with the expression (1/Mapp,f) ) ((1/Mw,f) + 2A2C) with Mapp,f ) 3.5 × 105 g/mol, C ) 0.5 wt %, and A2 ) 0.135Mw-0.53, one evaluates Mw - 472.5Mw-0.47 - 3.5 × 105 ) 0; a graphical solution to this equation leads to Mw ) 5.9 × 105 g/mol.

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Figure 8. Specific conductivity and the pH of SDS solutions in the absence and in the presence of 0.5 wt % PEI, plotted against the total concentration of SDS: pH in the presence of 0.5 wt % PEI (0); measured conductivities (4); conductivities corrected for the contribution of OH- ions (2).

Figure 7. Variation of the apparent molar mass of the system with the concentration of SDS at CPEI ) 0.5 wt %. Calculations were made using the intensity scattered by the fast mode of relaxation and the refractive index increment of PEI in water (circles) or the refractive index increment of SDS in water (triangles).

acceptable. In general, however, the values of the apparent molecular weight Mapp,f obtained in this way are underestimated especially at high SDS concentrations. This factor could partly explain why, at high concentrations of SDS (above 40 mM), the value of Mapp,f is smaller than the apparent molecular weight of the PEI macromolecules with no SDS added. The “true” values of Mapp,f are, therefore, between the Mapp,f values obtained for two extreme cases when calculations are made using the refractive index increments for PEI and SDS in water (both cases are plotted in Figure 7). Returning to Figure 5, we see that the variation in the size of the PEI-SDS complex correlates with the variation in apparent molecular weight for [SDS] e 20 mM. At higher SDS concentrations, the apparent molecular weight of the fast component decreases substantially, whereas the changes in RH,f are more modest. (C) Conductivity and Ion Mobility. (1) Conductivity and pH Measurements. In a previous report,22 we described conductivity and pH measurements of the interaction of SDS with aqueous solutions of two polyamines, PEI and linear poly(vinylamine) (PVAm). In unbuffered water, the solution pH is high, and these polymers are protonated to only a very small degree. As very weak polyelectrolytes, these polymers should behave in manner similar to that of other nonionic water-soluble polymers. Surprisingly, however, we found enhanced conductivity for the solutions in which both polyamine and SDS were present. The changes in the specific conductivity (k) of unbuffered SDS solutions in the absence and in the presence of 0.5 wt % PEI are presented in Figure 8 along with the changes in pH of the 0.5 wt % PEI solution. The k vs [SDS] plot for SDS alone is typical of anionic and

cationic surfactants in aqueous solutions.38-40 At low concentrations, below the critical micelle concentration (cmc), the conductivity is due to the sum of the contributions of the free Na+ and dodecyl sulfate (DS-) ions. Above the cmc, the increase in k is smaller because the micelles have lower mobility than the free DS- ions, and a fraction of the sodium ions are ion-paired with the micelles. For SDS in the presence of other nonionic polymers (such as PEO), a somewhat modified response is found. At very low SDS concentrations, the conductivity initially increases almost linearly as SDS is added to the solution. Then the k vs [SDS] plot deviates from a straight line but at higher SDS concentrations merges with the conductivity curve for pure SDS. This type of plot for PEO + SDS is well documented.38,41 The first break occurs at a concentrations below the normal cmc of SDS. This critical aggregation concentration (cac) is due to the formation of polymer-bound micelles. The second break point, the polymer saturation point (PSP), represents the surfactant concentrations beyond which all further surfactant added forms free SDS micelles. The common feature of the k vs [SDS] plots for nonionic polymers such as PEO and poly(vinylpyrollidone) is that the absolute values of the specific conductivity of the solutions in the presence of the polymer is always found to be less than or equal to the specific conductivity in its absence. As can be seen in Figure 8, the change in the solution conductivity for the PEI-SDS system is completely different than that for PEO-SDS. The distinguishing feature of the k vs [SDS] plot for the PEI-SDS system is that the absolute values of the specific conductivity of the SDS solutions in the presence of PEI are higher than that in their absence over the whole range of SDS concentrations. Thus, the fundamental difference between the conductivity changes for the PEI- and PEO-SDS systems is that for PEI + SDS the conductivity of the solution increases upon binding of the SDS to the polymer (38) Jones, M. N. J. Colloid Interface Sci. 1967, 23, 36. (39) Schwuger, M. J. J. Colloid Interface Sci. 1973, 43, 491. (40) Moroi, Y.; Matsuoka, K. Bull. Chem. Soc. Jpn. 1994, 67, 2057. (41) Minatti, E.; Zanette, D. Colloids Surf. A 1996, 113, 237.


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macromolecules. The same trend was observed also for PVAm + SDS. Potentiometric measurements (see Figure 8) showed that binding of SDS to the PEI is accompanied by the consumption of protons and, as a consequence, by an increase in the pH of the solutions. We assumed22 that one or both of the following reactions between the PEI and the SDS occur

PEI + H+ + DS- h PEIH+/DS-

(5a)

or

PEI-H+/OH- + DS- h PEI-H+/DS- + OH-

(5b)

Under these conditions, the contribution of OH- to the cumulative conductivity of the solution in the presence of the PEI is significant. The conductivity changes, corrected for the OH- contribution as described in ref 22 for SDS solutions in the presence of 0.5 wt % PEI, are also shown in Figure 8. As can be seen in this figure, the absolute values of the specific conductivity, corrected for OHconductivity are still significantly higher than those obtained in the absence of the polymer over the whole range of SDS concentrations. (2) Pulsed-Gradient NMR. To understand the mechanism of this unusual behavior, we have to identify which ionic species have enhanced mobility in the presence of PEI. The main candidates for contributors to the enhanced conductivity are Na+, OH-, DS-, and possibly low concentrations of protonated polymer. To measure the mobility of these species in the solution, we used pulsed-fieldgradient NMR (PFG NMR) to examine the self-diffusion of water molecules and Na+, and DS- ions in the absence and presence of 0.5 wt % PEI. The PFG NMR experiments were carried out on solutions with the same range of concentrations as those for the conductivity measurements. In a PFG NMR experiment, under fast exchange, the measured self-diffusion coefficient of a given component i of the system is a population-weighted average of the self-diffusion coefficients of this species in its different states in the solution. These states include free ion and ions bound to micelles or to the polymer. The measured self-diffusion coefficient of the component i (i ) Na+, DS-, H2O) corresponds to the weighted average 42

Di ) pif Dif + pib Dib

(6)

where the superscripts f and b refer to the free and bound states, pif and pib are the free and bound fractions of component i, respectively, and Dif and Dib are the selfdiffusion coefficients of species i in the free and bound states, respectively. It should be emphasized that we determined the Di at SDS concentrations above its normal cmc. Therefore the fraction of free ions is the fraction not bound to either polymer or free micelles. In this case, Dib is the weighted average of the self-diffusion coefficients for the polymer-bound state and the micelle-bound state. Without additional information, one cannot separate these contributions. In Figure 9, we plot values of the self-diffusion coefficient for the DS- ion in aqueous solution for SDS concentrations up to 200 mM. The upper curve refers to SDS in water and the lower curve to SDS + 0.5 wt % PEI in water. In the upper curve, the lowest concentration point is for a solution just above the surfactant cmc; thus the high (42) Kamenka, N.; Burgaud, I.; Zana, R.; Lindman, B. J. Phys. Chem. 1994, 98, 6785.

Figure 9. Plot of the mean self-diffusion coefficient of DS, measured by PG-NMR, against total SDS concentration, in the absence and in the presence of 0.5 wt % PEI.

Figure 10. Plot of the mean self-diffusion coefficient of Na+, measured by PG-NMR, as a function of the total SDS concentration, in the absence and in the presence of 0.5 wt % PEI.

mobility contains a large contribution of free ions to the signal. In the presence of polymer, this same SDS concentration is now well above the cac of the solution. Thus the free DS- ion concentration is smaller, and the ion mobility is smaller by a factor of 2. As the SDS concentration is increased, the mean diffusion coefficient decreases and appears to level off at the highest concentration (200 mM). It is likely that at this surfactant concentration, the DS- ion signal is dominated by the mobility of free SDS micelles. The sodium ion mobility vs SDS concentration is plotted in Figure 10. At the lowest SDS concentration (10 mM), in the absence of PEI, Di for Na+ is about a factor of 4 larger (1.2 × 10-9 m2 s-1) than that (3.1 × 10-10 m2 s-1) of the bulkier DS- ion. For this solution, the Na+ mobility drops substantially for SDS concentrations up to 50 mM but then increases slightly. In the presence of polymer, the Na+ mean diffusion coefficient is higher than that in the absence of polymer.

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mobility. Thus the DS- ion makes little contribution to the enhanced conductivity of the SDS + PEI solutions. The data in Figure 10 indicate that the sodium ion is one reasonable candidate for the enhanced conductivity. These data show that Na+ of SDS has a higher diffusivity in the presence of PEI than in the absence of polymer. One can explain the influence of the polymer on sodium ion mobility in terms of the influence of the polymer on SDS micelles in solution. The reaction shown in eq 5b can be rewritten (5c) to emphasize that above the cmc of SDS, a significant fraction of the Na+ are ion-paired with the micelles. The formation of polymer-bound micelles increases the amount of free Na+ in the solution.

PEI-H+/OH- + DS-/Na+ h PEI-H+/DS- + OH- + Na+ (5c)

Figure 11. Plot of the mean self-diffusion coefficient of H2O, measured by PG-NMR, as a function of the total SDS concentration, in the absence and in the presence of 0.5 wt % PEI.

One of the difficulties in interpreting the changes in the measured diffusion coefficients is that both the SDS and polymer present affect the solution viscosity. In Figure 4, we showed that the addition of small amounts of SDS ( cmc are certainly in error. Values of the net enthalpy calculated in this way are plotted in Figure 13b. One can see in both parts a and b of Figure 13 that the first aliquots of SDS added to the PEI solutions lead to an exothermic effect. We conclude that in this concentration range SDS monomers bind to the PEI macromolecule, and this interaction is exothermic. At [SDS] < cmc, the exothermic effect for the 0.5 wt % PEI solution is more pronounced than that for 0.083 wt % PEI. The higher concentration PEI solution has a larger number of binding sites for monomeric SDS. With increasing SDS concentration, the net enthalpies of the interaction between SDS and the PEI, at both PEI concentrations, become less exothermic. This change is likely due to the contribution of endothermic ion-ion repulsive interactions between SDS molecules or aggregates bound to the PEI. At approximately 5 mM SDS, the enthalpy curves in Figure 13 for the 0.083 wt % PEI approach a maximum and, above this concentration, decrease with increasing [SDS]. Since micellization of SDS is known to be exothermic (see above), we assume that in this region the formation of SDS-PEI micelle-like aggregates may occur. The SDS concentration corresponding to the enthalpy maximum in Figure 13b can be considered to be a critical aggregation concentration (cac) for the formation of mixed aggregates. Above 10 mM SDS concentration, the net enthalpy increases, passes through a second small maximum, and again decreases. Above 16 mM SDS the net enthalpy levels off and is practically equal to 0. For [SDS] between 8 and 16 mM, the use of eq 8b to calculate (∆Hai)net values is not valid. We can say, however, that since the dilution and the net enthalpy curves merge above approximately 16 mM SDS, the polymer is saturated. SDS micelles added to the calorimetry cell are only diluted, and eq 8b again becomes approximately correct. The most interesting insight from this analysis is that the polymer becomes saturated with SDS at an SDS/EI ratio of 1.0. For addition of SDS to the 0.5 wt % PEI solution, similar processes are assumed to occur. Above approximately 5 mM SDS, the endothermic effect caused by interaction between the bound SDS monomers or aggregates becomes smaller, and the net enthalpy curve approaches a plateau (Figure 13b). We suppose that in this region micelle-like aggregates are formed in the same way as with the 0.083 wt % PEI solution. The difference between the net enthalpy curves for the two PEI concentrations is a consequence of the different ratio of bound and free SDS molecules and aggregates in the solution. Above approximately 15 mM SDS, the formation of both free SDS micelles as well as bound micelle-like aggregates takes place. The shapes of the enthalpy curve (Figure 13a) and the net enthalpy curve (Figure 13b) indicate that noncooperative binding occurs. Our interpretation of these data is that the equilibrium between bound and free micelles is shifted to free micelles

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Figure 14. A plot of the molar enthalpy vs PEI concentration, expressed in terms of monomer units, for addition of aliquots of a 10 wt % PEI solution to water and to 32 mM SDS solution in water.

with increasing SDS concentration. Because of the larger number of binding sites, this region spans a much larger range of SDS concentrations at 0.5 wt % PEI than that at 0.083 wt % PEI, and the polymer does not become saturated with surfactant. In Figures 12 and 13, ∆H values are obtained for the addition of SDS to solutions of the polymer in the calorimetry cell. In Figure 14, we show the results of the inverse experiment, addition of a 10 wt % PEI solution to the calorimetry cell. The open points show that the dilution of the PEI solution with water leads to almost no change in enthalpy. When PEI is injected into 32 mM SDS, the first two aliquots have a strong exothermic effect. Further addition of PEI to the SDS solution is increasingly endothermic until the system passes through a broad maximum, followed by a decrease ultimately reaching ∆H ) 0. These results can be explained as follows. First additions of PEI to the SDS micelle solution lead to binding to the PEI of individual SDS molecules, which are in dynamic equilibrium with SDS micelles. As was shown above, this PEI-SDS interaction is exothermic. Further addition of PEI to SDS likely involves endothermic binding of free micelles to the PEI macromolecules. The enthalpy curve for this PEI + SDS system reaches its maximum at approximately 100 mM PEI monomer unit concentration. Above this point, only parts of the PEI macromolecules are able to bind to the SDS micelles, and the endothermic enthalpy change (∆Hi) is smaller than that in the region when [EI] is below 100 mM. (3) Comparison with Other Studies. Over the past decade, various groups have used microcalorimetry to examine polymer-surfactant interactions. Bloor et al.45 studied the interaction of SDS with poly(N-vinylpyrrolidone) (PVP) by isothermal titration calorimetry and potentiometric (emf) measurements. They showed that in the presence of 1 wt % PVP, the enthalpy of SDS addition was positive. Values of ∆Hai at first increase, then pass through a maximum, then decrease sharply to an exothermic minimum, and finally increase again, converging

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to the titration curve of the SDS in the absence of the PVP. The value of the maximum was higher (more endothermic) than that of the SDS alone. Bloor et al.45 related the maximum Cmin and minimum Cmax of the enthalpy curve to the cac and polymer saturation point (PSP) values, which coincided with those obtained by potentiometric measurements. The enthalpy profile between Cmin and Cmax shows that the binding of SDS to PVP is a cooperative process, and that above Cmax the polymer is fully saturated with bound surfactant. When more surfactant is added, only free micelles form. Wang and Olofsson49 carried out an in-depth calorimetric study of the interaction between two ethyl(hydroxyethyl)cellulose (EHEC) polymer samples of different hydrophobicity (different degrees of ethyl substitution) with a series of ionic surfactants such as SDS, alkyltrimethylammonium halides (RTAX with R ) C12, C14, and C16, and X ) Br or Cl) and dodecylammonium chloride. The results were compared with those obtained for PEO solutions. The plots of ∆Hai for PEO and the two hydrophobically modified EHEC samples had very similar features and were similar to the titration curve for the PVP-SDS system described above. In all of these systems, with increasing SDS concentration, the enthalpy curves in the presence of the polymers start to deviate from the SDS dilution curve above a certain SDS concentration. The ∆Hai vs [SDS] plots give a pronounced endothermic peak followed by a broad exothermic peak. Then the curves joined the SDS dilution curve. Wang and Olofsson49 related the onset of the deviation and the converging point of the enthalpy curves in the presence of polymers to the cac and the PSP, respectively. Three features distinguish the enthalpy curve for the more hydrophobic EHEC sample. First, the cac was significantly lower than that of the less hydrophobic polymer. Second, the heights of the endothermic and exothermic peaks were significantly increased, whereas the PSP values were the same. Cationic alkyltrimethylammonium surfactants have a much weaker interaction with the less hydrophobic EHEC sample than SDS. However, a strong interaction was observed for the more hydrophobic EHEC sample with SDS and with the cationic surfactants. Wang and Olofsson49 also mention that a broad exothermic peak seen in the SDS curve was lacking in the RTAX curves, and that for all of the surfactants, the curves in the presence of the polymers approach the surfactant dilution curve in water from above. The cationic surfactant with much smaller NH3+ headgroup, dodecylammonium chloride, had an interaction with these polymers that was much stronger than that of the trimethylammonium surfactants. For this surfactant, moreover, the enthalpic curve for the more hydrophobic EHEC showed a broad exothermic minimum following the endothermic peak, of the sort found for SDS. The similarity of the enthalpic curves for the above systems to those for the mixture of SDS with pentanol-1 allowed Wang and Olofsson to interpret their results in terms of the solubilization of polymer segments and/or substituents in surfactant aggregates in the form of mixed micelles. They consider that the first endothermic increase in ∆H is caused by the weak endothermic interaction between the monomer SDS and the PEO backbone. When the cac region is reached, aggregates begin to form, incorporating EO segments into mixed micelles. The exothermic peak could arise from the rehydration of EO segments that are expelled from the hydrophobic core in the process of the reorganization of the mixed micelles. (49) Wang, G.; Olofsson. G. J. Phys. Chem. 1995, 99, 5588.

Winnik et al.

Finally, at the saturation concentration (PSP), free SDS micelles begin to form. Similar events occur for the two EHEC samples. The more pronounced endothermic effect of the more hydrophobic EHEC can be explained in terms of the larger number of substituents with ethyl end groups that can be solubilized in the hydrocarbon surfactant core. The weak interaction revealed by microcalorimetry of cationic surfactants with PEO and with the less hydrophobic EHEC confirmed the well-known fact that cationic surfactants have much weaker interactions with nonionic polymers than SDS. A common explanation for this effect is that the trimethylammonium headgroup has a hydrophobic character. The hydration of micelles of the cationic surfactants with trimethylammonium headgroups is less favorable than that for SDS micelles,50-52 and EO groups do not have a water shielding effect for alkyltrimethylammonium micelles. Dodecylammonium micelles are more hydrated than alkyltrimethylammonium surfactants since the NH3+ headgroup is much smaller. Here the EO water-shielding effect would be significant. Wang and Olofsson conclude that SDS can interact with both the ethyl end groups and the EO groups of the polymer, while the trimethylammonium surfactants are indifferent to the EO groups and only interact with the hydrophobic ethyl substituents. Therefore, the more hydrophobic EHEC showed a stronger interaction with the trimethylammonium surfactants. An increase in temperature causes EO groups in water to become more hydrophobic, and as a consequence, the cationic surfactants interact more strongly with the PEO than at room temperature. A recent paper53 described the interaction between SDS and an oligomeric poly(ethylene glycol) (PEG 1000), investigated through density and heat capacity measurements at 298.15 K. These experiments showed that a stoichiometric complex is formed between surfactant micelles and the polymer, with approximately 2.3 EO units of the polymer per SDS molecule. The authors discovered that the polymer had an interesting effect on the sphereto-rod micellar transition at high concentrations of the SDS (approximately 20 mM). When the polymer concentration was low, normal free SDS micelles coexist with polymer-bound micelles. The free micelles were able to undergo the shape transition. However, when the polymer concentration was large enough to bind all surfactant molecules, the sphere-to-rod transition was completely suppressed. Faes et al.54 studied the self-association of copolymers of N-isopropylacrylamide and N-n-octadecylacrylamide (Pnipam-C18) in aqueous solutions by time-resolved fluorescence quenching and examined the polymer interaction with N-cetylpyridinium chloride (C16PyCl) and cetyltrimethylammonium bromide (CTAB) by titration microcalorimetry. The polymer has a cloud point near room temperature and phase separates when the solution is heated to 30 °C. In ITC experiments performed at 30 °C, the addition of C16PyCl to the two-phase system resulted in an initial exothermic interaction followed by an endothermic interaction between the polymer and the surfactant. The authors assume that the first aliquots of surfactant added to the solution dissociate to form (50) Mukerjee, P. J. Colloid Sci. 1964, 19, 722. (51) Tabony, J. Mol. Phys. 1984, 51, 975. (52) Finney, J. L.; Soper, A. K.; Turner, J. Z. Pure Appl. Chem. 1993, 65, 2521. (53) Ballerat-Busserolles, K.; Roux-Desgranges, G.; Roux, A. H. Langmuir 1997, 13, 1946. (54) Faes, H.; De Schryver, F. C.; Sein, A.; Bijma, K.; Kevelam, J.; Engberts, J. B. F. N. Macromolecules 1996, 29, 3875.


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monomers, which interact with the collapsed multipolymeric demixed phase, and this interaction resulted in the exothermic part of the enthalpy curve. A further increase of the surfactant monomer concentration led to an endothermic interaction due to ion-ion interactions. The peak in the enthalpy curve is taken to signal the onset of mixed-micelle formation. Above this surfactant concentration, the shape of the enthalpic curve suggests a noncooperative type of binding, with an equilibrium between adsorbed micelles and free micelles. We note that the profile of the enthalpy curve for the Pnipam-C18/H2OC16PyCl system is similar to that which we obtained from our experiments on SDS + PEI-SDS at high pH. The major difference between the two experiments is that the enthalpy curve for the Pnipam-C18/H2O-C16PyCl system has a more pronounced endothermic peak. Despite the fact that the enthalpy vs surfactant plot profiles are similar, the mechanisms of the polymer-surfactant interactions in these systems are likely to be different (see below). Brackman et al. 55 studied the interaction of poly(propylene oxide) (PPO) with the nonionic surfactant n-octylthioglucoside (OTG) by microcalorimetry. The enthalpy curve for OTG also consists of three regions such as that for the SDS and for some cationic surfactants. However, the enthalpy of micellization, calculated as the difference in dilution enthalpy between regions I and III, is endothermic (+4.5 kJ mol-1). Brackman et al.55 have shown (1) that PPO has a small endothermic effect on the premicellar enthalpy of dilution, (2) that the transition region was located in the same concentration range with and without polymer, indicating that there is no cmc change, and (3) that there is a strong endothermic effect (+4.3 kJ mol-1) in the postmicellar region in the presence of the PPO. The authors contend that this is the enthalpy of interaction between PPO and OTG micelles. Since ∆H is endothermic, it must be compensated by a positive entropy change originating from the release of water molecules from the hydrophobic hydration shell of the polymer upon interaction with the micelles. The authors also suggest that PPO may bind in more hydrophobic regions of the micellar core. Wang and Olofsson49 proposed a similar mechanism of surfactant binding for PEO and for HM-EHEC binding to SDS systems in the concentration region where micelle-like aggregates start to form. The interaction of polyelectrolytes with ionic surfactants has also been studied by microcalorimetry.56-59 We will not review this substantial literature but will instead provide a few comments to indicate how the presence of ions on the PEI, even in unbuffered solution, could affect the enthalpy of interaction with SDS. Most of the key features can be seen in the paper of Skerjanc et al.,56 who investigated the binding of cationic surfactants to sodium poly(styrene sulfonate) (NaPSS). They found exothermic binding of the surfactants to the polymer, which increased sharply at a critical surfactant concentration several orders of magnitude lower than the surfactant cmc. This phenomenon was expected because it is well-known that the cac value for polyelectrolyte-ionic surfactant systems is much lower than the cmc. The authors calculated that at these bulk concentrations of surfactant, the local

surfactant concentration around the polyion at a distance equal to the length of the surfactant hydrocarbon tail ranges from about 2 × 10-2 to 1 × 10-3 M. These concentrations are comparable to, or higher than, the cmc of C12PyCl and C16PyCl. From this point of view, micellization close to the polyion may occur at low total concentrations of surfactant in the solution because Coulombic attraction increases the local concentration of surfactant. The observed overall enthalpy of binding was assumed to contain the following contributions: (1) the enthalpy change due to electrostatic binding of cations to the polyelectrolyte; (2) the heat effect accompanying the aggregation of the bound detergent molecules into minimicelles; (3) the enthalpy change ensuing from the interaction of the minimicelles with the polyion. The authors concluded that the enthalpy change was mainly caused by the aggregation process (2) assuming that the contributions from electrostatic interactions in processes 1 and 3 should be small. As can be seen from the above considerations, the energetics of polymer-surfactant interactions is different for the different classes of polymers and surfactants and depends on the mechanisms of their interaction. PEI in aqueous solution at high pH is known to have a small fraction of charged amino groups, approximately 1 per 100 monomer units. These solutions should have some properties of a polyelectrolyte. However, the ethylene groups of the polymer give the polymer some hydrophobic character. In this regard, electrostatic as well as hydrophobic interactions of the PEI with the SDS may take place. Comparison of the microcalorimetric data for nonionic polymers with SDS (considered above) and the PEI-SDS systems shows that in the PEI-SDS system, the character of the polymer-surfactant interactions is different. For PEI-SDS, there is an initial exothermic effect, which may have two contributions. First, the monomeric dodecyl sulfate anion can interact electrostatically with the positive charged amino groups. In addition, it may bind to the hydrophobic regions of the PEI macromolecules. From our potentiometric titration data (Figure 8), we know that the interaction between SDS and PEI is accompanied by a consumption of protons. This result is strong evidence for an electrostatic interaction between DS- and cationic sites on the PEI. As was shown in the work cited above, the initial exothermic effect can also be caused by the binding of ionic surfactants to the polymer hydrophobic microdomains. A Russian group60-62 showed that the electrostatic interaction between SDS and linear PEI63 leads to an increase in the hydrophobic character of the linear PEI macromolecules. They infer that SDS binds to linear PEI through both electrostatic and hydrophobic interactions. The authors infer that the number of SDS molecules bound to the linear PEI due to hydrophobic interactions is much larger than those bound electrostatically. Something similar may occur in the hyperbranched PEI-SDS system. However, further information is required to sort out the contribution of hydrophobic interactions of DS- with branched PEI to the exotherm observed during the initial binding of SDS to the PEI solutions.

(55) Brackman, J. C.; van Os, N. M.; Engberts, J. B. F. N. Langmuir 1988, 4, 1266. (56) Skerjanc. J.; Kogej, K.; Vesnaver, G. J. Phys. Chem. 1988, 92, 6382. (57) Rigsbee, D. R.; Dubin, P. L. Langmuir. 1996, 12, 1928. (58) Bronich, T. K.; Kabanov, A. V.; Kabanov, V. A.; Yu, K.; Eisenberg, A. Macromolecules 1997, 30, 3519. (59) Kevelam, J.; van Breemen, J. F. L.; Blokzijl, W.; Engberts, J. B. F. N. Langmuir 1996, 12, 4709.

(60) Yui, T. S. T. I.; Abilov, Zh. A.; Pal’mer, V. G.; Musabekov, K. B. Issled. Ravnovesnych Sist. 1982, 78. (61) Yui, T. S. T. I.; PalÅmer, V. G.; Musabekov, K. B. Izv. Akad. Nauk, Kaz. SSR Ser. Khim. 1984, 19. (62) Abilov, Zh. A.; Beisebekov, M.; K.; Musabekov, K. B. In Reakzii v zhidkoi faze; Izd. KazGU: Alma-Ata, 1979; p 134. (63) Linear PEI is crystalline, with only limited solubility in water. One can study its aqueous solutions only at low concentrations or at low pH.

4510


The decrease in ∆Hai in the titration PEI with SDS is similar to that found for the other systems and is most likely caused by electrostatic repulsion between bound surfactant ions. Above the cac, the exothermic process of SDS micellization within the PEI coil and the endothermic electrostatic repulsion between DS- anions compete with each other. As a consequence, the net enthalpy curves for the PEI-SDS system exhibit either the small minimum seen with the 0.083 wt % PEI solution or the plateau at 0.5 wt % PEI. With further increase in the SDS concentration, the endothermic contribution from electrostatic repulsion interactions dominates, and the binding of SDS to the PEI is driven only by an increase in the entropy of the system. This effect is particularly well developed in the presence of the 0.5 wt % PEI. Thus, it is possible to propose that the formation of the PEI-SDS mixed aggregates might proceed in different ways at different SDS concentrations and different ratios of SDS/EI. At higher SDS concentrations PEI-SDS mixed aggregates are formed through noncooperative binding of free micelles to the polymer. This process is characterized by an overall increase in the entropy of the system. Rigsbee and Dubin57 attribute the entropy increase to the release of small ions. Another possible contribution to an increase in ∆S is the release of water molecules from the hydrophobic hydration shells of the polymer.64 As was shown in refs 54 and 55, an endothermic noncooperative interaction also occurs for nonionic polymer-nonionic surfactant and nonionic polymer-ionic surfactant interactions. If we suppose that PEI has hydrophobic interactions with SDS at high pH, then the release of water molecules may play an important role in the increase of entropy upon interaction of PEI with SDS. Overview Light scattering studies show that in aqueous solution, PEI exists largely in the form of individual macromolecules plus a small fraction of aggregates. The aggregates make a large contribution to the scattering signal but only a very small contribution to the solution viscosity. In all other respects, the aggregates make a negligible contribution to the polymer interaction with SDS. Through these experiments, we find for our polymer Mw ≈ 6 × 105, with a broad polydispersity, and a mutual diffusion coefficient of 1.2 × 10-11 m2 s-1. This corresponds to RH ) 18 nm. When SDS is added to the 0.5 wt % PEI solution, this diffusion coefficient drops by a factor of 2 for SDS concentrations of 40-60 mM, but a significant portion of this decrease is due to an increase in the bulk solution viscosity. Values of RH,f calculated using the bulk solution viscosity as a measure of the local friction pass through a sharp maximum at a ratio of about 1.7 SDS molecules per 10 EI monomer units (where [SDS] ) 20 mM and RH ) 30 nm) and then slowly decrease with increasing SDS concentration. We infer that SDS binds to the polymer and promotes the formation of mixed aggregates containing more than one polymer molecule. ITC experiments show that when SDS is added to a 0.5 wt % PEI solution, (64) Jolicoeur, C.; Philip, P. R. Can. J. Chem. 1974, 52, 1834.

Winnik et al.

the first aliquots provoke an exothermic interaction, which is attributed to the binding of individual SDS molecules to the polymer. Later additions become increasingly endothermic and pass through a maximum at an SDS to EI ratio of 0.1. The change in the sign of ∆Hai is likely due to the endothermic repulsion between DS- ions bound to the polymer. Once the cell contains 10 mM SDS, subsequent addition of SDS to the solution results in noncooperative binding of micelles to the polymer. Solutions containing 10-30 mM SDS in the presence 0.5 wt % PEI have a conductivity that is substantially larger than the sum of the conductivities of the free ions in solution. Most of the experiments described in this paper were carried out in the hopes of explaining this increase. The conductivity depends on the mobility of the various ions present in the solution. To examine these mobilities directly, pulsed-gradient NMR measurements were carried out to determine the self-diffusion coefficients Di of DS- anions and Na+ cations in the presence and absence of PEI. At 10 mM SDS, the Di of DS- decreases as the SDS concentration is increased, consistent with an increased fraction of the ions bound to the less mobile micelles. Its mobility decreases even further in the presence of PEI. The sodium ion mobility also decreases with increasing surfactant concentration, but at any given SDS concentration in the presence of PEI, the mobility was found to increase. One concludes that binding of SDS micelles to the PEI leads to release of sodium ions into the solution. All of these solutions, however, exhibit mean sodium ion mobilities less than that of free sodium ions in water. To get a sense of the mobilities of the various species in the solution at 0.5 wt % PEI + 50 mM SDS, it is instructive to examine the magnitude of the various diffusion coefficients in the system. From the fast component of the DLS signal, we find a mutual diffusion coefficient of 1.2 × 10-11 m2 s-1 for the PEI. From PG-NMR measurements, we find Di values of 1.0 × 10-10 m2 s-1 for DS-, 1.0 × 10-9 m2 s-1 for Na+, and 1.9 × 10-9 m2 s-1 for water molecules. Water mobility is similar in magnitude to that in the absence of polymer and surfactant, although this statement masks more subtle features of the interaction seen in Figure 11. To explain the enhanced conductivity of the solutions, we imagine that ion transport within the polymersurfactant complex is much more rapid than free ion mobility in water. The complex acts as a sodium ion or proton “channel”. As suggested in Chart 1, the primary carrier of ion current in the water phase is the sodium ion. Once the ion encounters a polymer-surfactant complex, a different sodium ion exits elsewhere in the complex. This admittedly speculative suggestion, unfortunately, does not tell us anything about the structure of the complex that promotes this rapid ion mobility in its interior. Acknowledgment. The authors thank NSERC Canada, ICI, and ICI Canada for their support of this research. LA991553U

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