Langmuir 1998, 14, 7397-7402
7397
Aggregation Number of Ionic Surfactants in Complex with Polymer via Measurements of Trace Probe Electrolyte Tibor Gila´nyi* and Imre Varga Department of Colloid Chemistry, Lora´ nd Eo¨ tvo¨ s University, P.O. Box 32, Budapest 112, Hungary 1518 Received May 19, 1998. In Final Form: October 12, 1998 The distribution of ions in polymer-ionic surfactant solutions was described by the nonlinear PoissonBoltzmann (PB) theory applied for cell model. On the basis of on the PB cell model, a new trace probe electrolyte method was developed to determine the surfactant aggregation number and the osmotic pressure of the solution. Potentiometric trace probe electrolyte (NaI) measurements were performed for the PVPNaDS system, and the calculated aggregation numbers were compared to ones measured by fluorescence quenching methods. It was found that the mean aggregation number increases with the surfactant activity and that it is independent of the polymer concentration. The osmotic pressure of the PVP-NaDS system was measured by membrane osmometry.
Introduction Studies on the interactions between macromolecules and surfactants can be traced back to the early fifties. First, the protein-surfactant systems were stressed because of their biological importance. With the appearance of well-defined synthetic polymers, the research was extended to the polymer-surfactant systems, with the promise of a deeper insight into the more complex proteinsurfactant interaction. Beyond their scientific interest, the polymer-surfactant systems have received considerable attention because of the various applications in many industrial processes, for example, in pharmaceutical, biomedical, food, mineral processing, and oil recovery applications.1-3 The binding of the ionic surfactants to polymers is a cooperative process. The polymer-surfactant complex has been described as a “string of beds” or necklace structure in which the polymer chain connects micelle-like surfactant aggregates by wrapping around them.4 This illustrative picture probably well characterizes the separated individual complex molecules, for example, at a low polymer concentration of long chain polymers with a high degree of surfactant binding; otherwise, it is bewildering when the pearls are seldom in the necklace or at the semidilute polymer concentration range when the aggregates distribute statistically in the entire volume rather than along a chain. The macroscopic behavior of the ionic solutions is mainly determined by the electrostatic interactions between the ionic species. The most often used method to describe the local electric structure of the system in the case of a weak electric field, when the thermal motion of ions is important, is the application of the Poisson-Boltzmann theory, subject to boundary conditions specified by the studied system. Research in this field embraces a wide range of topics: charge distribution around a point charge (Debye(1) Li, Y.; Dubin, P. L. In Structure and Flow in Surfactant Solutions; Herb C. A., Prud’homme, R. K., Eds.; ACS Symposium Series 578; American Chemical Society: Washington, DC, 1944; Chapter 23. (2) Goddard, E. D. Colloids Surf. 1986, 19, 255. (3) Goddard, E. D., Ananthapadmanabhan, K. P., Eds. Interaction of Surfactants with Polymers and Proteins; CRC Press: Boca Raton, FL, 1992. (4) Nagarajan, R.; Kalpakci, K. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1982, 23, 41.
Hu¨ckel theory of strong electrolytes), distribution of ions around charges fixed along a chain (for example, Manning theory of polyelectrolytes), distribution of ions at interfaces or around charged macroparticles (Gouy-Chapman theory). Considering the electric structure of the polymerionic surfactant systems, all of these distribution problems are involved: the surfactant ions are distributed along the polymer chain (the polymer-surfactant complex behaves like a polyelectrolyte molecule) in the form of micelle-like aggregates (macroions), and the medium is a simple strong electrolyte (molecularly dispersed surfactant) solution. In this work the nonlinear Poisson-Boltzmann (PB) equation was applied to describe the local distribution of ions around a spherical surfactant aggregate in the complex molecule. As a first approximation the interaction among the aggregates was taken into account by means of a cell model.5,9 The presence of the macroions changes the local distribution of the small mobile ions. The activity of an electrolyte increases when we add the polymerionic surfactant complex (macroions) to the system due to the local inhomogeneities in the electric potential created by the presence of the colloid aggregates. The activity increase sensitively monitors the size and distribution of the macroions. A trace amount of NaI was used as probe electrolyte, and its activity was measured potentiometrically. The aggregation number of the surfactant in the polymer complex and the osmotic pressure of the polymersurfactant solutions were calculated from the activity measurements made on the trace electrolyte. To test the applied electric model, the aggregation numbers were compared to those calculated from time-resolved and steady-state fluorescence quenching measurements in the literature. The osmotic pressure was experimentally determined against the composition of the solutions by a specially designed osmometer and compared to the calculated values. (5) Gunnarson, G.; Jo¨nsson, B.; Wennerstro¨m, H. J. Phys. Chem. 1980, 84, 3114. (6) Vanderhoff, J. W. Pure Appl. Chem. 1980, 52, 1263. (7) Gila´nyi, T. Colloids Surf. 1988, 125, 641. (8) Vass, Sz.; To¨ro¨k, T.; Ja´kli, G.; Berecz, E. J. Phys. Chem. 1989, 93, 1758. (9) Marcus, R. A. J. Chem. Phys. 1955, 23, 1057.
10.1021/la980591v CCC: $15.00 © 1998 American Chemical Society Published on Web 12/03/1998
7398 Langmuir, Vol. 14, No. 26, 1998
Gila´ nyi and Varga indexes A and e refer to the PVP-NaDS solution in cell A and the equilibrium solution (cell B), respectively. Consequently, the emf values measured in the PVP-NaDS solution (cell A) and in its equilibrium solution (cell B) are the same:
E ) E0 -
kT 2 cNa,ecI,e] ln[γ NaI,e e
Taking into account that cNa,e ) cDS,e + cI,e and cDS,e . cI,e
E ) E0 -
Figure 1. Scheme of different osmotic and nonosmotic membrane equilibria to study the polymer-ionic surfactant solutions.
Experimental Section Materials. The investigated polymer was poly(vinyl pyrrolidone) (PVP, Fluka K-90, Mw ) 1.06 × 106 from static lightscattering measurements). The PVP solutions were purified by mixed bed anion-cation exchange, by a similar method to that which was used in the case of latex dispersions6 for the elimination of the ionic contaminants. This purification was necessary in the case of both the osmotic pressure and the potentiometric measurements to get well-reproducible results. The surfactant was sodium dodecyl sulfate (NaDS), Merk product, recrystallized twice from a 1:1 hot benzene-alcohol mixture. The critical micelle formation concentration (cmc) was found to be 8.2 mM from conductometric measurements. Potentiometric Measurements. The emf values of the following two galvanic cells were determined by means of a Radelkis research pH-meter at 25.0 ( 0.1 °C:
Cell 1: Na-glass |c NaDS, cp PVP | Au | Hg | HgIDS Cell 2: Na-glass | 10-4 M NaI, c NaDS, cp PVP | Ag | AgI The emf values were converted into mean activities (aNaDS and aNaI) using the Nernst equation. NaI was chosen as a probe electrolyte, but this choice is not exclusive. The trace electrolyte should meet the following requirements: it does not bind specifically (chemically) to the polymer or to the surfactant, and reversible electrodes are available to measure its mean activity. The binding on PVP was checked by emf measurements against the polymer concentration at a 10-4 M constant NaI concentration. The emf was constant within 0.5 mV; that is, binding of the iodide ions to PVP in the investigated concentration range cannot be detected. It was experimentally checked that the iodide ion electrode was not sensitive to the presence of the surfactant ions. In Figure 1 the scheme of different experimental arrangements for the study of the polymer-surfactant system is depicted. Any two cells are separated by membranes permeable for different components, as indicated in the figure. The condition of the thermodynamic equilibrium between any two cells is the constancy of the chemical potential (or that of the electrochemical potential in the case of ions) of the mobile components for which the membrane is permeable. Consider the PVP-NaDS solution (cell A) in equilibrium with a polymer-free NaDS solution (cell B), referred to as the equilibrium solution, at the same constant pressure and temperature. This is a nonosmotic membrane equilibrium because the pressure in the two cells is the same and the membrane is permeable for ions only. From the condition of the thermodynamic equilibrium, it follows that A aNaDS ) aNaDS,e ) γNaDS,e(cNa,ecDS,e)1/2 A aNaI ) aNaI,e ) γNaI,e(cNa,ecI,e)1/2
where γ is the corresponding mean activity coefficient and the
kT 2 cDS,ecI,e] ln[γ NaI,e e
Below a critical surfactant concentration (ccr, which is 3 mM in the case of the PVP-NaDS system), there is no interaction between the polymer and the surfactant. Above ccr, the surfactant starts to bind to the polymer. With increasing amount of bound surfactant, the equilibrium surfactant concentration increases. When it reaches the cmc, free micelles form and the equilibrium surfactant concentration becomes practically constant. The measurements on polymer-surfactant solutions were performed in the concentration range where cDS,e was smaller than the cmc and free micelles were not formed in the system. If the surfactant concentration is below ccr, the ions are in a single dispersed form and both the surfactant and the iodide ion concentrations are the same in the polymer-surfactant and in its equilibrium solution; that is, cI,e ) cI and cDS,e ) cDS. Furthermore, the equilibrium solution is a dilute electrolyte, and according to the Debye-Hu¨ckel theory at constant T and P0, its activity coefficient depends only on the ionic strength, which is cNaDS,e in cell B, since cI,e is negligible. The change of γNaI,e in the concentration range between the ccr and the cmc is only 0.6%, which can be neglected so the difference between the emf values measured at cNaDS and ccr can be given as
E(cNaDS) - E(ccr) )
kT cI,ecDS,e ln e cIccr
Following the determination of cDS,e (by means of the galvanic cell 1), the above equation was used for the calculation of the cI,e/cI quotient that can be connected to the aggregation number and the osmotic pressure of the polymer-NaDS system (see the next section). It is noted that the potentiometric method is only a tool for the rapid determination of cI,e. The measurements can be performed in a real Donnan equilibrium (between cells A and C in Figure 1) by analyzing the composition (c′DS,e and c′I,e) of the equilibrium solution and correcting the activities because of the pressure difference between the two cells. The pressure correction on the activity is usually negligible and c′I,e = cI,e. Osmotic Pressure Measurements. The pressure difference at equilibrium was measured between the polymer-surfactant solution (in cell A, P0) and the polymer-free surfactant solution (in cell C, P) separated by a membrane permeable for water and ions. The osmotic pressure is generally defined as the pressure difference between a solution and the pure solvent (e.g. between cells A and D or between cells C and D). When more than one component is passing through the membrane (here the solvent and the surfactant), the equilibrium pressure difference is called the excess osmotic pressure, which is the osmotic pressure difference between two solutions. Since this notation has not been generally accepted in practice, the pressure difference Π ) P0 - P, will be called the (excess) osmotic pressure of the polymersurfactant solution. Commercial membrane osmometers are not convenient to determine the (excess) osmotic pressure of the polymersurfactant solutions because of their low sensitivity and the extremely long equilibrium time due to the time-consuming diffusion of the surfactant. A special capillary method was developed to perform these measurements which is highly sensitive and significantly reduces the equilibrium time. Figure 2 shows the scheme of the osmotic pressure measurements. The osmometer consists of a glass capillary of 2 mm inside diameter. The capillary was immersed into the polymersurfactant solution kept at atmospheric pressure (P0). The open end of the capillary was separated from the solution by a Millipore
Ionic Surfactants in Complex with Polymer
Langmuir, Vol. 14, No. 26, 1998 7399 V - V* cI ) cI,e V
(2b)
V* may be interpreted as the “electrically excluded volume” due to the exclusion of the probe anions from the vicinity of the negatively charged macroions. (3) Instead of using a volume parameter, eq 1 can be expressed as negative adsorption of the anions onto the surfactant aggregates:
Γ- )
Figure 2. Design of the osmotic-pressure measuring equipment. membrane (with a pore size 0.025 µm). A drop of water was inserted above the membrane and then the capillary was filled up with silicon oil and connected to a piezoelectric pressure transducer. In the side of the capillary a window was cut, and it was covered with a soft rubber film. This served to eliminate the effect of fluctuations in the atmospheric pressure. The whole apparatus involving the transducer and the amplifier was temperature controlled. The sample solution and the measuring capillary were kept at 25.00 ( 0.05 °C. The recorded signal versus pressure calibration was made with water at different hydrostatic pressures. The relative position of the water meniscus and the measuring capillary was determined with a cathetometer. The calibration curve was the same within 1 Pa when it was determined at raising and at descending height of the water column, indicating that the capillary hystereses at the water/oil meniscus was negligible. The stability of the equipment was very good. During a 3-week control period the largest deviation did not exceed 10 Pa. The equilibrium time was 20-30 min for the polymersurfactant samples. The pressure was found to be constant for a 3-day checking time, indicating that the polymer did not pass the membrane. A known volume of polymer solution was titrated at constant polymer concentration (cp) with a polymer-surfactant stock solution (cp, cNaDS), and the equilibrium pressure was recorded. The surfactant concentration was calculated from the dilution. Distribution of Ions in the Polymer-Surfactant Solution. The analytical concentration of the anions of the trace (1:1) electrolyte (NaI) in the neutral polymer-anionic surfactant solution can expressed by integrating its local distribution over the whole volume of the system:
1 cI ) cI,e V
∫ exp(y) dV V
(2c)
where Γ- is the deficiency of the anions in the diffuse electrical layer of the macroions and caggr and m are the concentration in the monomer unit and the mean aggregation number of the surfactant aggregates, respectively. The interpretations of the trace electrolyte activity measurements by means of eqs 2b and 2c are equivalent. In this work the experimental data will be represented as a relative excluded volume, which may be the most expressive. To evaluate the integral in eq 1, the “chemical” structure of the system under study must be specified. It is supposed that the surfactant is in the form of monomer ions and aggregates. Groups of aggregates are interconnected by one polymer chain. The volume of the system is divided into cells (Vpol), each containing one polymer molecule. Furthermore, the volume Vpol is divided into smaller cells (cells in a cell), each containing one surfactant aggregate. If the number of the surfactant aggregates in the system is low or the polymer concentration is sufficiently high and the size of the large cell is comparable to that of the polymer coil, then the aggregate distribution can be supposed to be statistically uniform in the system. We restrict our model and measurements to this case. The intrinsic viscosity of the investigated PVP is 0.18 dm3‚g-1, and the z-average radius of gyration is 5.87 × 10-6 cm, from which it can be estimated that the condition of the statistically uniform aggregate distribution is fulfilled above 0.2% polymer concentration. This critical polymer concentration range is even smaller if we take into account that the size of the polymer coil significantly increases when the polymer interacts with the ionic surfactant. Let us divide the solution volume into electrically neutral equivalent spherical cells,5,9 each containing one surfactant aggregate of core radius a and the appropriate amount of electrolytes. Equation 1 can be expressed by means of the single cell as
∫ exp(y)r
3 cI ) cI,e 3 R - a3
R
a
2
dr
(3)
(1)
where y ) eψ/kT is the reduced electric potential with a choice ψ ) 0 in the polymer-free reference solution (cell B). The deviation between cI and cI,e can be interpreted in different ways: (1) The traditional interpretation is based on the supposition of specific counterion binding to the macroions, which can be expressed for the system concerned here as
cI(cDS + RZcM) ) cI,ecNa,e
cI - cI,e m caggr
where R is the radius of the cell. The cell radius is determined by the relation
R)
3m 4πNAcaggr
)
1/3
(4)
and the core radius of the aggregate is
a)
(2a)
where cDS refers to the concentration of the monomeric surfactant, R is the degree of counterion dissociation, and Z and cM are the total charge and concentration of the macroions (i.e. surfactant aggregates), respectively. The term (cDS + RZcM) in eq 2a is the mean counterion concentration with a contribution from the dissociation of the macroions. However, eq 2a and the physical picture attributed to it are in discrepancy with each other. If we define R as the degree of counterion dissociation from any a priori physical picture, then eq 2a is incorrect because log(c) should be averaged instead of c in the original derivation of eq 2a.7 If we accept that eq 2a is correct, then R is only a fitting parameter without the meaning of dissociation degree. (2) Solving the integral in eq 1, it can be given formally as a volume parameter, which leads to the expression
(
( ) 3mv0 4πNA
1/3
(5)
in which v0 is the molar volume of the surfactant alkyl chains in the aggregates. The y(r) function can be calculated from the PB equation for spherical symmetry and a 1:1 electrolyte as
r-2
2e2cNaDS,e d 2 dy r ) sinh(y) dr dr kT
(
)
(6)
at the boundary conditions y ) y0 at r ) a and (dy/dr)R ) 0. The electrical structure of the aggregate surface is approximated by the simplest Gouy-Chapman model. The closest distance of approach of the mobile ions to the surface is a, the core radius of the surfactant aggregate. The polymer segment density is
7400 Langmuir, Vol. 14, No. 26, 1998
Gila´ nyi and Varga
Figure 3. Relative excluded volume against the concentration of the aggregated surfactant for the PVP-NaDS system.
Figure 4. Aggregation number of NaDS in the PVP complex against the equilibrium surfactant concentration.
assumed to be small, and its effect on the ion distribution is neglected. In the close vicinity of the core, this model is probably not correct, but fortunately the integral in eq 3 is not sensitive to the inner electrical structure of the aggregate. Equation 6 was solved by means of a fourth-order RungeKutta method at a given a and R calculated from eqs 4 and 5 (v0 ) 212.4 cm3‚mol-1)8 with an arbitrary m value. Then eq 3 was solved and the calculated cI,e/cI value was checked against the measured one. The solution of eq 6 and the m value were accepted when the calculated and measured cI,e/cI values were the same within 1%. The (excess) osmotic pressure was derived from y(R) where the electric field vanishes9
π ) RTcNaDS,e(ey(R) + e-y(R) - 2)
(7)
Results and Discussion In Figure 3 the relative excluded volume V*/V is plotted against the concentration of the surfactant in its complex form (caggr ) cNaDS - ccr) at different constant polymer concentrations. V*/V depends on the number and size of the surfactant aggregates, the ionic strength of the solution, and the interaction between the aggregates. In the case of ordinary micelle formation (cp ) 0), the ionic strength is approximately constant, and for non-interacting micelles with constant size, V*/V should increase linearly with the complex concentration. In fact, the V*/V function increases linearly at low micelle concentrations but declines from linearity at higher micelle concentrations, which can be interpreted by an increase of the aggregation number and/or micelle-micelle interactions because both lead to smaller excluded volume at the same micelle concentration. In the presence of polymer the V*/V versus caggr function is a saturation-type curve. The initial slope is significantly higher than that in the case of micelle formation. This qualitatively indicates that the surfactant aggregates in the polymer complex are smaller than the free micelles. With increasing complex concentration, all the parameters affecting V*/V tend to lower the excluded volume: the ionic strength increases from 3 mM up to the cmc; the aggregation number and the interaction between the aggregates are also increasing. For the free micelle formation, the trace electrolyte activity method yields m ) 57, which is in good agreement with the aggregation number measured by static light scattering.10 In Figure 4 the aggregation numbers calculated from the trace electrolyte activity measurements are plotted against the equilibrium surfactant concentration. The reproducibility is good, and the m values fall into a narrow range (σ ) (3) in the case of every investigated polymer concentration. From these measurements the following (10) Huisman, H. F. Proc. K. Ned. Akad. Wet., Ser. B 1964, 57, 407.
Figure 5. Aggregation number of NaDS in the PVP complex against the total surfactant concentration: (4, Lissi et al.13 cp ) 1%; b, Zana et al.12 c ) 0.3-1.8%; 9, this work cp ) 0.8%).
statements can be made: (i) the aggregation numbers are significantly smaller than that of the ordinary micelles; (ii) the aggregation number increases monotonically with the equilibrium surfactant concentration; (iii) within experimental error the aggregation number is invariant with the polymer concentration and depends only on the equilibrium surfactant concentration (which is the ionic strength in these experiments performed without addition of supporting electrolyte). The number of methods available for the determination of the aggregation number of the surfactant in the polymer-surfactant complex is very limited. First, thermodynamic methods were applied to calculate the aggregation number from the dependence of ccr on the polymer concentration and from the surfactant binding isotherm.12 Recently, fluorescence probe methods are preferred for this purpose.13 In a few cases the aggregation number was also calculated from small angle neutronscattering measurements.14 In Figure 5 the aggregation numbers measured for the PVP-NaDS system are collected. At around cNaDS ) 20 mM the m values measured by the different methods fall into the same range. Zana et al.15 measured strongly increasing m with increasing surfactant concentration in fluorescence decay experiments. Lissi and Abuin16 got a constant aggregation number in steady-state fluorescence quenching measurements. They explained the discrepancy (11) Stigter, D. In Physical Chemistry: Enriching Topics from Colloid and Surface Science; van Olphen, H., Mysels, K. J., Eds.; Theorex: La Jolla, CA, 1975; p 181. (12) Gila´nyi, T.; Wolfram, E. In Microdomains in Polymer Solutions; Dubin P. L., Ed.; Plenum Press: New York, 1985; p 357. (13) Winnik, F. M.; Regismond, S. T. A. Colloids Surf., A 1996, 118, 1. (14) Cabane, B.; Duplessix, R. J. Physique 1982, 43, 1529. (15) Zana, R.; Lang, J.; Lianos P. In Microdomains in Polymer Solutions; Dubin, P. L., Ed.; Plenum Press: New York, 1985; p 357. (16) Lissi, E. A.; Abuin, E. J. Colloid Interface Sci. 1985, 105, 1.
Ionic Surfactants in Complex with Polymer
between their results and those of Zana et al. by the different investigated concentration ranges. They argued that in Zana’s measurements the saturation bound amount was exceeded and the polymer-complex and free micelles were measured together, leading to increasing “average” aggregation number. Indeed, the saturation of PVP is about 35 mM at cp ) 1%; thus, only the first point is characteristic for the complex in ref 12. However, the error of the aggregation number given by Lissi et al. is so large (σ ) (6) that it made their measurements insensitive to the changes of the aggregation number in the investigated concentration range. In the present work we measured increasing aggregation number with surfactant concentration below the concentration range investigated by Lissi et al. The increase of the complex aggregation number with the surfactant concentration is also supported by the results of fluorescence probe measurements made on other polymer-surfactant systems. These measurements give increasing aggregation numbers without exception: for example, PEO-NaDS,16-18 PEO-NaTS,18 PVA-NaDS,19 PVME-CTAB,20 PPO-CTAB,20 PPO-CTAC,21 and PVOH-Ac-CTAC.21 The dependence of the aggregation number on the equilibrium surfactant concentration can be partly explained by the well-known effect of the ionic strength on the electrical free energy of the micelle formation.11 The equilibrium surfactant concentration determines the ionic strength of the solution. cNaDS,e increases from the critical interaction concentration up to the cmc, while the amount of the polymer-bound surfactant tends to saturation. The electrical free energy of micelle formation increases with increasing aggregation number, which counteracts the growth of the micelles. At higher ionic strength the electrical free energy is smaller, leading to the formation of larger micelles. On the other hand, due to entropy reasons, the increase of the equilibrium concentration in itself leads to the shift of the distribution curve of the aggregation number to higher values, resulting in larger mean aggregates. The third effect that may affect the aggregation number is the interaction between the aggregates. The equilibrium aggregate size is determined by the free energy minimum of the system and not that of a single aggregate. This effect has not been analyzed even for the more simple ordinary micelle formation because the existing models are restricted for noninteracting dilute micellar systems. In the literature the aggregation numbers have not been studied as a function of the equilibrium surfactant concentration, and in the evaluation of the fluorescence probe measurements the equilibrium surfactant concentration has been approximated by a constant (the ccr or the cmc). As a route m has been plotted against the total surfactant concentration, which results in different curves at different polymer concentrations, showing an apparent dependence of m on the polymer concentration. Unfortunately, there are not enough published data for the PVP-NaDS system to prove by a different method that the mean aggregation number is independent from the polymer concentration. On the other hand, there are a great deal of data on the poly(ethylene oxide)-NaDS (17) Francois, J.; Dayantis, J.; Sabbadin, J. Eur. Polym. J. 1985, 21, 165. (18) van Stam, J.; Almgren, M.; Lindblad, C. Prog. Colloid Polym. Sci. 1991, 84, 13. (19) van Stam, J.; Wittouck, N.; Almgren, M.; DeSchryver, F. C.; Miguel, M. G. Can. J. Chem. 1995, 73, 1765. (20) Brackman, J. C.; Engberts, J. B. F. N. Langmuir 1991, 7, 2097. (21) Reekmans, S.; Gehlen, M.; DeSchryver, F. C.; Boe¨ns, N.; Van der Auweraer, M. Macromolecules 1993, 26, 687.
Langmuir, Vol. 14, No. 26, 1998 7401
Figure 6. Aggregation number of NaDS in the PEO complex against the equilibrium surfactant concentration: (0, Zana et al.;15 [, van Stam et al.;18 b, Francois et al.17).
Figure 7. Excess osmotic pressure of the PVP-NaDS system against the surfactant concentration (dotted line calculated from eq 7).
system, that could be used for the demonstration of the polymer concentration independence of the aggregation number. In Figure 6 we replotted the aggregation numbers against the equilibrium surfactant concentration. The equilibrium surfactant concentrations were calculated from the total concentrations using the binding isotherms of the PEO-NaDS system.12 The aggregation numbers measured in a very wide polymer and surfactant concentration range fall on the same curve especially in the case of the same author’s data. The data in Figure 6 also support the observation that in the case of the PEONaDS system the aggregation number does not depend on the polymer concentration. This work is the first in which the polymer-surfactant interaction is investigated by osmometry. In Figure 7 the measured excess osmotic pressure of the PVP-NaDS solutions is plotted against the surfactant concentration at different polymer concentrations. The osmotic pressure markedly increases when the surfactant concentration exceeds the critical interaction concentration and extremely deviates from the ideal behavior at larger polymer concentrations. The osmotic pressure calculated from the trace electrolyte activity measurements is also plotted in Figure 7. As the figure shows, the main characteristics of the measured curves are well reflected by the calculated ones. The osmotic pressure of the system can be described by the electrical interactions between the surfactant aggregates. In view of the approximations used in the derivation of the ion distribution, the underlying electrical model is acceptable. Summarizing, it can be concluded that the activity measurements on a trace electrolyte added to the system give a simple experimental method to estimate the mean aggregation number of the surfactant aggregates either in the form of a polymer-surfactant complex or in the
7402 Langmuir, Vol. 14, No. 26, 1998
form of free micelles. The important new finding of the experimental part of this work is that the aggregation number depends only on the equilibrium surfactant concentration and is independent of the polymer concentration.
Gila´ nyi and Varga
Acknowledgment. This work was supported by the Hungarian Research Fund (Grant No. T 015723). LA980591V
