J. Phys. Chem. B 2002, 106, 5035-5041
5035
Equilibrium between Poly(N,N-dimethylacrylamide) and the Lamellar Phase of Aerosol OT/Water I. E. Pacios,*,†,‡ C. S. Renamayor,† A. Horta,† B. Lindman,‡ and K. Thuresson‡ CC. y TT. Fisicoquı´micas, Facultad de Ciencias, UNED, P° Senda del Rey 9, 28040 Madrid, Spain, and Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund UniVersity, P.O. Box 124, SSE-2211 00 Lund, Sweden ReceiVed: January 25, 2002; In Final Form: March 15, 2002
A mixed amphiphilic system composed of the anionic surfactant Aerosol OT (AOT), in water forming a lamellar phase, to which is added a neutral noninteracting polymer, poly(N,N-dimethylacrylamide), is studied experimentally by SAXS, 2H NMR, and microscopy, in a range of surfactant and polymer compositions. Addition of the polymer produces a decrease in the lamellar spacing, the decrease by the polymer being almost twice that produced by an equal volume of AOT. Microscopy reveals heterogeneity, but no macroscopic phase separation occurs. 2H NMR detects that on increasing the polymer concentration some water is in an isotropic environment. It is inferred that the presence of the polymer induces a microscopic phase separation into a polymer-rich isotropic phase and a surfactant-rich lamellar phase, and this is tested theoretically by calculating the osmotic pressures in these two phases. In the lamellar phase, the effect of electrostatic, undulation, van der Waals, and hydration forces on the AOT bilayer is considered; in the isotropic phase, the osmotic contribution of the polymer is considered. These two pressures correlate well, supporting theoretically the hypothesis of the two phases in equilibrium.
Introdution The presence of macromolecules in a lyotropic mesophase with a lamellar order can induce changes in the properties of the mesophase. This influence of macromolecules has raised interest in recent years, from both industrial and fundamental research points of view, because this can bring advantages to improve the performance of products (such as aqueous liquid detergents1) or can provide simple models for the study of biomembrane processes.2 Typical lyotropic mesophases with a lamellar order are formed by amphiphilic molecules (surfactants) containing one hydrophilic (ionic) headgroup and two hydrophobic tails (hydrocarbon chains). In the lamellar phase, the surfactant molecules stack together forming bilayers. Within each bilayer, the molecules are oriented tail-to-tail. The bilayers are placed parallel to each other, separated by a layer of water molecules. For each surfactant forming a lamellar phase, the thickness of the bilayer is approximately constant, but the separation between successive bilayers is determined by the relative amount of water to surfactant. The structure is periodic (along an axis normal to the plane defined by the bilayer) with a repeat distance or a long-range periodicity equal to the sum of the thickness of one bilayer plus the separation between two successive bilayers (the thickness of the water layer). This long-range periodicity is the result of a balance of interactions (attractive and repulsive) between the bilayers themselves and of the bilayers with the water molecules. In these interactions, several contributions can be recognized, thus, the repulsive interactions of electrostatic, hydration, and steric origin and the attractive van der Waals interactions. * Author to whom correspondence should be addressed (E-mail:
[email protected]). † UNED. ‡ Lund University.
When water-soluble polymers are added, different locations for the macromolecules in the lamellae can be observed: in the water domains,3 incorporated into the surfactant bilayer,4 adsorbed onto the bilayer,5 or excluded from the lamellar phase in an isotropic phase.6 In other cases, the polymer induces a phase separation into two lamellar phases.7 The site of location of the macromolecules is determined by the polymer size8 and its interaction7 with the surfactant. The system studied in this work consists of a lamellar phase formed by an anionic surfactant, Aerosol OT (AOT), and water, in which a large nonadsorbing polymer, poly(N,N-dimethylacrylamide) (PDMAA), of high molecular weight is added. We have previously obtained evidence that the presence of this polymer induces a kind of microscopic phase separation in the AOT/H2O system.9 Here, we study the structure of the phases formed and also provide a quantitative evaluation of the equilibrium between them. From a thermodynamic point of view, several approaches can be used to evaluate the equilibrium state between the phases that are formed. (i) The free energy in the system can be calculated, accounting for the different contributions like the entropy of chain conformations, the electrostatic energy, and the van der Waals interactions.8 (ii) One could determine the Caille´ exponent, η, related with the fluctuations in the bilayers10
η)
k12kBT 8πxKB
(1)
where k1 is the position of the Bragg peak, B is the layer compression modulus at constant chemical potential related to the interactions between bilayers, and K is the curvature modulus related to the bilayer bending modulus, κ, as K ) κ/d, with d being the lamellar spacing (long-range periodicity). When a
10.1021/jp025559v CCC: $22.00 © 2002 American Chemical Society Published on Web 04/19/2002
5036 J. Phys. Chem. B, Vol. 106, No. 19, 2002
Pacios et al.
Figure 1. Micrographs from some samples showing birefringent texture.
nonadsorbing polymer is located between the bilayers, κ should not change but B changes and can be calculated, taking into account the different contributions to the layer compression, which allows us to estimate the final state of the system.3,11 (iii) In a biphasic system, the equilibrium is established when the osmotic pressures in both phases are balanced.6 This last analysis is the one that is pursued in this work. As will be shown, it provides a quantitative description of the experimental results. The starting point is a previous study of the microstructure of PDMAA/AOT/H2O mixtures in the lamellar liquid crystalline phase.9 The experimental data then showed that, although a macroscopic phase separation is not achieved, the system is biphasic at levels 24 Å. The hydration contribution increases quite fast at lower distances and is the most important term when dw e 16 Å. For the samples studied here, the lamellar distance (see Table 1) is generally greater than 36 Å (dw > 16 Å), and therefore, the magnitude of the electrostatic pressure term is, in these cases, the dominant one. Thus, it is possible to simplify eq 16 to obtain the following:
ΠElectrostatic ≈ ΠPDMAA
(17)
In the isotropic phase, the osmotic pressure is given by the equation
Figure 8. Electrostatic pressure (ΠElectrostatic) versus osmotic pressure (ΠPDMAA). Sample values are calculated theoretically (eqs 9 and 18), with dw and cPDMAA deduced from experimentation, assuming the model of two separate phases (lamellar + isotropic): s, fit to the points; ‚‚‚, equality of pressures (eq 17).
monomer unit molecular weight (99.13 × 10-3 kg/mol). From eq 19, it is estimated that A3 ) 3 × 10-5 m6‚mol/kg3. To obtain ΠPDMAA, it is necessary to know the polymer concentration in the isotropic phase, cPDMAA. This can be easily deduced from the global composition and the fraction of water that is not retained by the lamellar phase; this last portion of information was obtained from d as explained above. From this d, dw is calculated, that is, the magnitude that gives ΠElectrostatic using eq 13 with the appropriate value of S obtained from Figure 6. In Figure 8, ΠElectrostatic is plotted against ΠPDMAA. The points are values for our samples, calculated theoretically with the equations for ΠElectrostatic and ΠPDMAA using, for dw and cPDMAA, the values that are deduced from experimentation when the model of two separate phases (lamellar and isotropic) is used. The dashed line represents the equality of pressures, eq 17, that should hold in the equilibrium between the two phases. We effectively find a good correlation between the two (the slight deviation from the model in the plot can be related to an overestimation of the third virial coefficient), indicating that the proposed model is correct. Conclusions
ΠPDMAA )
(
)
1 cPDMAA + A2cPDMAA2 + A3cPDMAA3 + ... (18) RT Mn Here, R ) kBNA (NA, Avogadro’s number), cPDMAA is the PDMAA concentration (w/v) in the phase, and A2, A3, ..., are the second, third, ..., osmotic virial coefficients. Because the polymer content in the samples is relatively high, it is not possible to do the usual truncation of this series after the second term and one has to keep the third coefficient to obtain an accurate value for the osmotic polymer pressure.33 A2 is known for PDMAA (Table 2), and to obtain the third virial coefficient, the following expression can be used:34
g)
A3 n(A2Mo2)2
(19)
where g ) 0.3 when the number of structural units comprising a chain (n) is high (in our case n ≈ 3 × 104) and Mo is the
Mixing the polymer PDMAA with the lamellar system AOT/ H2O produces a decrease in the lamellar spacing, which can be explained by the polymer forming a separate phase taking some water out of the AOT/H2O lamellae. There is experimental evidence for the appearance of a second phase, which is isotropic when the polymer is added to the AOT/H2O lamellae, but this second phase does not separate macroscopically. The existence of this microscopically dispersed phase and its “equilibrium” with the lamellar phase is tested theoretically by calculating the osmotic pressures in the two phases. The calculations show that the increase of pressure in the lamellar phase, as the spacing is decreased by the addition of polymer, correlates very well with the osmotic pressure of the polymer in its isotropic phase. This validates the hypothesis and allows one to state that the addition of polymer deswells the lamellae of the surfactant by taking part of the water to form a microscopically separate isotropic polymer phase. Acknowledgment. I.E.P. aknowledges the hospitality of the Department of Physical Chemistry 1 at Lund University during
Lamellar Phase of Aerosol OT/water her stay. This work has been financed by CICYT (Spain) (Grant BQU2000-0251), UNED (Spain), and the Department of Physical Chemistry 1, Center for Chemistry and Chemical Engineering (Sweden). The NMR spectrometer was sponsored by the Natural Science Research Council (FRN) and Kjell and Ma¨rta Beijers Stiftelse. The SAXS instrument was sponsored by FRN. References and Notes (1) van de Pas, J. C.; Olsthoorn, Th. M.; Schepers, F. J.; de Vries, C. H. E.; Buytenhek, C. J. Colloids Surf. A 1994, 85, 221. (2) Petrov, A. G. The Lyotropic State of Matter, Molecular Physics and LiVing Matter Physics; Gordon and Breach Science Publishers: Amsterdam, 1999. (3) Ligoure, C.; Bouglet, G.; Porte, G.; Diat, O. J. Phys. II 1997, 7, 473. (4) Radlinska, E. Z.; Gulik-Krzywicki, T.; Lafuma, F.; Langevin, D.; Urbach, W.; Williams, C. E. J. Phys. II 1997, 10, 1393. (5) Iliopoulos, I.; Olsson, U. J. Phys. Chem. 1994, 98, 1500. (6) Deme´, B.; Dubois, M.; Zemb, T.; Cabane, B. J. Phys. Chem. 1996, 100, 3828. (7) Kosmella, S.; Ko¨tz, J.; Friberg, S. E.; Mackay, R. E. Ber. BunsenGes. Phys. Chem. 1996, 100, 1059. (8) Zhang, K.; Linse, P. J. Phys. Chem. 1995, 99, 9130. (9) Pacios, I. E.; Lindman, B.; Horta, A.; Thuresson, K.; Renamayor, C. S. Colloid Polym. Sci., in press (DOI ) 10.1007/s00396-001-0641-4). (10) Caille, M. A. C. R. Acad. Sci. (Paris) 1972, B274, 891. (11) Bouglet, G.; Ligoure, C. Eur. Phys. J. B 1999, 9, 137. (12) Porte, G.; Appel, J.; Bassereau, P.; Marignan, J. J. Phys. (Paris) 1989, 50, 1335. (13) Nallet, F.; Laversanne, R.; Roux, D. J. Phys II 1993, 3, 487. (14) Rogers, J.; Winsor, P. A. J. Colloid Interface Sci. 1969, 30, 247.
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