Polymer in a lyotropic lamellar system: an experimental study

Apr 5, 1993 - Collige de France, 11 place Marcellin Berthelot, 75232 Paris Cedex 5, France ... as e-"*, with 1 /*, the Debye length, about 7.6 A for a...
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J . Phys. Chem. 1993, 97, 11108-1 1114

11108

Polymer in a Lyotropic Lamellar System: An Experimental Study M. Singh,'J R. Ober,* and M. Klemant Laboratoire de Physique des Solides. Bat. 51 0, UniversitC de Paris-Sud, 91405 Orsay Cedex. France; Laboratoire de MinCralogie-Cristallographie,UniversitCs Pierre et Marie Curie (Paris VI) et Paris VII, 4 place Jussieu,case 1 1 5. 75252 Paris Cedex 5, France; and Physique de la Mati2re CondensCe, CollPge de France, I 1 place Marcellin Berthelot. 75232 Paris Cedex 5, France Received: April 5, 1993; In Final Form: June 28, 1993'

We have used a dilute solution in brine of a neutral, flexible polymer, polyacrylamide (nonhydrolyzed), as the solvent of a quasi-ternary system containing CPCl (cetylpyridinium chloride), and hexanol. The phase diagram is not fundamentally modified by the addition of the polymer, but the polymer manifests its presence, specially in the more dilute samples (i-e., samples with higher volume fraction of the solvent), by a strong decrease of the interlamellar spacing of the Laphase, as is seen by small-angle X-ray scattering experiments. Microscopic studies of the textures show oily streaks whose typical mode of splitting does not display well-defined elliptical focal domains and also shows an increase in the number of focal conic domains of the second kind, i.e., typical defects with a positive gaussian curvature; both of these facts suggest that the modulus of compressibility, B, and the saddle-splay rigidity, E, are smaller than in samples without polymer. We present qualitative arguments attributing some of these effects and the decrease of the periodicity, to the osmotic pressure gradient introduced by the presence of the polymer molecules which enter the layers in the form of a 2D solution, which causes the membranes to be drawn together. We have no clear understanding up to now of the behavior of K and

K. I. Introduction Recently there have been some speculations on the effect that the introduction of a neutral, flexible polymer (forming a semidilute solution with the solvent) would have on a layered system.'-3 While some studies on the system of bilayers predict an increase in the rigidity2 or in the elastic modulus of bending, K,some other theoretical studies3 predict K to decrease and the Gaussian rigidity, K,to increase. These studies assume that the polymer stays entirely in between two bilayers in the solvent and that adsorption on the bilayer is weak. A prerequisite in this direction is of course to see if a solution of polymer can actually be confined and stabilized within a lamellar system. There have been indeed very few results up to now: since the dynamical process of introducing polymer chains between the bilayels (into a region where they should loose entropy with respect to the bulk solution) is not necessarily easy. This was however not the case in our system, which is made of a dilute solution of polyacrylamidein brine as the solvent in the lamellar system. The phase diagram has been checked by making (polarized light) microscopic studies and small-angle X-ray measurements on the lamellar samples. We use cetylpyridiniumchloride as the surfactant and hexanol as the cosurfactant. When diluted with 0.16 M NaCl in water as the solvent (with no polymer), this system has already been studied extensively by Porte and co-workerss7(establishment of the phase diagram) and by our group*-lO (relation between defect textures and the elastic moduli in the L, phase), in the absence of polymer. The surfactant molecules self-assemble in a way, such that their polar heads are toward water, and the hydrophobic tails are away from it, thereby forming a bilayer. The rigidity K of such assemblies of bilayers versus bending can be easily changedll-12by varying the amount of cosurfactant, shorter-tailed molecules which find a place somewhere inside the bilayers. At the same time, this induces changes on the Gaussian rigidity K. The presence of NaCl screens any long-ranged electrostatic t Laboratorie de Physique des Solides and Laboratoire de MinkralogieCristallographie. t Physique de la Matibre Condensb. *Abstract published in Aduonce ACS Abstracts, September 1, 1993.

interactionsthat are present.13 The electrostatic interactionsdrop as e-xd, with 1/K, the Debye length, about 1.6 A for a 0.16 M NaCl aqueous solution. The La system that we have studied is made of stacks of bilayers, with the bilayer thickness being about 25 A, and the interlamellar thicknesses ranging from 100 to 300 A. Apart from the short-ranged hydrophilic and hydrophobic interactions, there are basically two long-rangedinteractions that compete with each other to keep the system of bilayers stable: the steric-repulsive interaction^,'^ which arise due to the confinement of the layers within each other; and the long-rangedvan der Waals attractiveinteractions. These have thefollowingforms:

Fvdw/A= -C/12?rd2 where bilayers are separated by a distance d; C, the Hamaker constant,l3 lying in the range (3-9) X J for interactions between bilayers (chains of hydrocarbon present in the bilayers) across the solvent, and is a constant until about 30 A, beyond which it diminishesdue to retardation effects, becoming less than half its value at around 100 A. So the van der Waals become quite weak having an effective range of up to perhaps 150 A. We give the experimental details in section 11. The first step in this study was to sketch the phase diagram of the system and see how it differs from the system with no polymer in it. In section I11 we describe the phase diagram. In sections IV and V we give the details of the polarized microscopic analysis and small-angle X-ray scatteringrespectively. Section VI summarizes our conclusions, in which we show that the above results arenot incontradiction with a possible structural model of dilute chains in between the bilayers, with no interactions existing in between the bilayers and the polymer chains. A detailed account of our model will be given elsewhere.

11. Experimental Methods Preparation and Characterization of the Polymer. The polymer used in the system was polyacrylamide (PAM),lSfabricated and

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11109

Polymer in a Lyotropic Lamellar System

P .

h

// 2*5{

F

-c

v

1

0

~=0.3%

x=2.1

1.21

~=0.89

-1

-6

-5

-4

4 C CPCI ( % b y w e i g h t )

In c

Figure 1. ln(q/qo) vs In c. q is the measured viscosity of the solution in m Pa s measured at room temperature (22 "C); 10is the viscosity of the solvent (1% brine), measured to be 0.85 m Pa s; c is the concentration of the polymer in weight (g/cm'). We find that x = 0.9 for $I I0.7%. For the region beyond this concentration, till around $I = 8 8 , x varies from 1.2 to 3, after which the solution shows aggregation effects; x = 6 here. purified at the Laboratoire de Physique et Chimie Macromo16culaire, ESPCI, Paris.16 It was prepared by redox-initiated polymerization in water, with ammonium persulfate as the initiator. Acetone molecules left as residue were removed by the method of freeze-drying. By viscometry in pure water at 25 OC, the polymer was characterized as having a molecular weight of 220 000, and intrinsic viscosity of 107.5 cm3/g. From these measurements we find that the hydrodynamic radius of the coils of polymer in the solvent radius of gyration is 150 A. Exhaustive experimental studies made on nonhydrolyzed polya~rylamidel~ show that aqueous solutions of polyacrylamide show a deviation from the Flory power law and obey R, = 0.075 MO.64 A. This gives the radius of gyration for our polymer to be around 200 A. From the viscosity measurements, it is possible to determine the crossover concentration, 4* (the concentration at which one crosses over from the dilute regime of polymer solution to the semi-dilute regime). Newtonian viscosity of polymer solutions as a function of their concentrations, obeys a universal law:18

where x = 4-5, for 4

> 4*,

= 1, for 4 < 4*,

when solution is semidilute when solution is dilute

Using a rotating viscometer at FAST19 and measuring viscosity by varying the shear rate and taking the values a t low (going to zero) shear rates, we found that 4* = 7 X 10-3. There was a wide crossover region till polymer concentrations of 8 X lo-*, after which the polymer started showing aggregation effects (Figure 1). Sample Preparation and Observation. 200 samples were made with cetylpyridinium chloride as the surfactant and hexanol as the cosurfactant. The weight fraction of the solvent was within the range 75-95%. Three sets of samples were made: (i) with simply 1% brine (by weight) as the solvent; (ii) with 0.1% PAM in 1% brine (both by weight) as the solvent; (iii) with 0.3% PAM in 1% brine as the solvent. These were kept in closed tubes at room temperature and observed over long durations (6-8 weeks). It was seen that the samples containing polymer were turbid. However we can be sure about the homogeneity of our samples with polymer because, apart from the fact that they appeared

-----

denotes the phase boundary when the polymer I S present

Figure 2. Brine-rich side of the phase-diagram of the system cctylpyridinium chloride/hexanol/O. 16 M brine: continuous lines show phase boundaries when there is no polyacrylamide in the samples; dashed lines show changes in the phase boundary due to the presence of the polymer. homogeneous for a long duration (roughly 2 months), we prepared most of our measurements, particularly the small-angle X-ray, and obtained the same results (same periodicity of the lamellae in the case of SAXS). Furthermore, it must be noted that such a turbidity is observed in samples with no polymer in them, although not to such degree and also only in those samples which had significant number of spherolitesas defects, the sizes of these defects being of the order of 50 pm or more. It has been advanced by Porte et a1.6 that it is precisely the presence of these defects in nonpolymeric samples which is the origin of turbidity. As stated below in more details, we are in presence of a particularly large number of spherolites in our samples. Light-scattering studies would shed more light on this point. Observations were made by polarizing microscopy and smallangle X-ray scattering. Samples for microscopic observation were prepared between glass slide and cover-slip, thickened with spacers (10 and 50 Mm) and sealed with a fast-setting two-part epoxy resin. Some samples were also introduced in thin rectangular capillaries (2 mm X 100 pm, 2 mm X 50 pm, and 2 mm X 30 pm) by capillarity. The L, phase was characterized by its textures (focal domains, dislocation lines, etc.). X-ray scattering experiments helped further characterising the system. Samples showing the lamellar phase were filled in Lindenmann capillaries 1 mm in diameter. The X-ray generator is a copper rotating anode machine operating at 40 kV and 25 mA. The X-ray apparent source has dimensions of 0.1 mm X 0.1 mm. A vertical mirror (acts as a total reflector for the K, (= 1.54 A) wavelength and eliminates the shorter wavelengths of the beam) reflects and directs the X-ray on the positive sensitive proportional counter. A nickel filter attenuates the KBwaves. The dimensions of the beam on the counter are 3 mm vertically and0.3 mm horizontally. Thecounter has a window with a height of 3 mm, a 50-mm useful length and a 200-pm spatial resolution. Distance between the sample and the counter is 802 mm. 111. The Phase Diagram

The sequence of phases that follows when the cosurfactant/ surfactant ratio (hlc) is increased remains the same in samples containing the polymer as in the samples containing no polymer in the solvent, namely: the isotropic micellar phase LI, the biphase L1+ L,, the lamellar phase L,, the biphase L, + Lj, the anomalous isotropic L3 phase, and finally a multiphasic region. Thedifference arises (Figure 2) (i) at the ratio at which the various phase

11110 The Journal of Physical Chemistry, Vol. 97,No. 42, 1993

Singh et al.

(3)

layers belonging to a FCD is positive, the singularity set reduces to the hyperbola, and the layers are parallel “rugby balls”-like, in the degenerate case already mentioned. We shall refer to the two types of FCDs which differ by their Gaussian curvature as FCD-I (G < 0) and FCD-I1 (G > 0), where G = qu2. The correlation between A and the sign of G has been stressed8 in relationship with the structure of the phases neighboring the lamellar Laphase; it appears experimentally that in the swollen surfactant we have studied, the lamellar L, phase displays at least two types of FCDs, differing by the nature of their singularities, and consequently by their Gaussian curvature G. The A = 0 boundary passes inside the domain of existenceof the Laphase.lO Samples with a larger hexanol content, Le., close to the L3phase (also called the sponge phase; it is a random G < 0 phase) display FCD-I’s, assembled in oily streaks (G < 0); those with a smaller hexanol content, close to the micellar L1 phase (G > 0), display FCD-11’s. FCD-11’s do not assemble, generically, and carry a large compressibility energy W,. Also, they always anneal to spherolites (smaller W,than rugby balls, for the same volume of defect), at constant layers number. These defects are found embedded in a birefringent, grainy medium, which might probably be made of even smaller spherolites or of parabolic focal domains formed to relax the stress (Figures 4a-c shows these regions clearly). This grainy medium does not seem to fill the entire volume and seem to be confined as areas parallel to the plane of observation. The two types of FCDs coexist in the intermediate region of the L, phase on the phase diagram (Figure 3). Their different stabilities is related to values of the K constant differing in magnitude and also in sign.6 As we dilute our samples in the region of coexistence more, the number density of the spherolites (and the area of the grainy medium) increases, with oily streaks becoming less in number and shorter in length. Thus the region favoringdefects of positive curvature dominates. On further dilution, samples show only spherolitesand focal conic domainsof the second kind irrespective of the value of h/c. The density of the spherolites decreases as we increase the ratio h/c. So far, all that we have said holds for both kinds of samples, with or without polymer. Samples with polymer show an increased presence of objects (FCD-11) which are more elongated than the spherolites and whose density increases as we dilute the sample. There is also an increaseddensity of spherolites. Also the region of coexistence extends over a slightly larger area on the phase diagram. In the region of coexistence of the two kinds of defects, the oily streaks are seen very often to either end abruptly on the grainy regions, suggesting that instead of traversing this region that favors negative A, they go underneath it, or close on themselves (see Figure 4a). This is seen when there is no polymer in the system. In samples with polymer, the oily-streaks are seen to traverse the medium as finely divided branches (Figure 4d,e), particularly in regions where the ratio h/cis small. This indicates their lack of stability in this region, preferring to transform into edge dislocations of small Burgers’ vector.

More specifically, in lyotropics, the FCDs belonging to the same chain originate in an instability of a large Burgers’ vector dislocation. The analysis of this shows the importance of the Gaussian curvature driven term Kqu2 in the nucleation process, and in particular stresses the necessity of a positive A = K + 2K term, which can be estimated from the measurements of some invariants belonging to the FCDs in the chain. In all the experimental examples alluded to, the Gaussian curvature of the layers belonging to a FCD is negative, and the singularity set consists of two conjugate conics. A degenerate case is when the ellipse is degenerate to a circle and the hyperbola to a straight line, in which case the layers fold into half tori. On the other hand, if A is negative, the Gaussian curvature of the

V. X-ray Scattering Small-angle X-ray experiments made on the samples showed the following: (i) appearanceof the first order quasi-Braggpeakin both kinds of samples, with and without the polymer, with the higher order peaks absent (Figures 5a,b). For a sample with the polymer present in it, this peak appears at a higher q value than for the sample of the same composition (fph = 4i,4, = fp;, 4b = 4 i + 4”). but withno polymer in it, so that theinterlamellar periodicity becomes smaller when the polymer is present. This reduction in the periodicity is much more evident in diluter samples. The more concentrated they are, the less is the decrease in the periodicity.

h/c

La 0 751

75

80

85

90

dilution(% by weight)

Figure 3. h / c vs &;, phase diagram, showing the dependence on dilution in both kind of systems; with and without the polymer.

transitions take place, and (ii) the radial nature of the boundaries on the phase diagram. The boundaries of the monophasic regions namely the L1,the L,, and the L3,were seen to shrink in samples with polymer: the more the polymer, the smaller the monophasic area. The area of the L3 phase which occupies a very narrow region in the phase diagram, when there is no polymer in the system, seems either to shrink even further or not exist at all in the presence of the polymer. We say this because we were not able to prepare monophasic L3 samples. Next, the L, phase with no polymer in it is unstable in the dilute regions (with samples being unstable for fpb 2 0.85, fpb being the volume fraction of the solvent, at the lower and the higher h / c regions of L,). With the polymer it is even more so, with the boundaries of the lamellar phase going more inward (in the phase diagram), in the dilute part of the diagram. Drawing the phase diagram (Figure 3) with h/c as they axis and fpb as the independent x axis, we show qualitatively this dependenceon dilution. It is this expression of the phase diagram we shall refer to in the sequel.

IV. Optical Microscopy Analysis Focal conic domains (FCDs) are the defects which keep the layers thickness constant in lamellar systems. They are by far the most conspicuous imperfections in such systems. They have been thoroughfullystudied in thermotropics,where they associate according to Friedel’s laws20 and in lyotropics, where it has been shown that they often assemble into chains of domains (Friedel’s oily streaks, see ref 7). In both cases, these assemblies bring the compressibilityenergy W, = Jfc dVto a minimum, compared to the curvature energy W,= Jf, dV, wheref, and fc are as follows:

f, = ‘/zK(ul + u2)’ + k l u z

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11111

Polymer in a Lyotropic Lamellar System

a

d

b

P

'

i

. i

Figure 4. Networkof oily streaks,coexisting with spherolytesembedded in a grainy medium,which can possiblybe smaller sizedspherolytes. Composition of the samples: (a) h / c = 0.75; f$b = 0.75; P = 0; (b) h / c = 0.65; f$b = 0.8; P = 0.3%; here one can also see parabolic focal domains. (c) oily streaks are seen to end abruptly on the grainy medium, probably traversing under it. h / c = 0.6; f$b = 0.75; P = 0. (d) Oily streaks are seen to traverse the grainy medium, dividing into finer oily streaks. h / c = 0.6; f$b = 0.8; P = 0.3%. (e) h / c = 0.75; f$b = 0.8; P = 0.3%.

(ii) It is well-known that the shape of the Bragg peak of SmA's is controlled by the elastic constants of the system.21 From

-

I (4 - q&-x; qo = 2 r / d Le., q at the first Bragg peak, one expects: (4)

wherex = 2-q, Bis the compression modulus at constant chemical potential, d is the interlamellar periodicity. It has already been claimed22 that for this system (CPCl hexanol + brine), molecular interactions play sufficient role, so

+

that a universal value of the exponent cannot be pulled out. But although this exponent is here system dependent (also the apparatus gives a significant contribution to the width, at least 0.003 A-l), it nevertheless can give a qualitative idea of the effect the polymer has on the system. We find that the value of x is consistentlyreduced in systems with polymer in them as compared to the systems with no polymer (Table I). (iii) In addition to the Bragg peak, there also appears a strong small angle signal, again in both types of samples. As the system is made more diluted, this signal becomes more intense. In fact, in extremely diluted samples, this signal completely overwhelms the Bragg peak (Figure 6). It is suggested by some authors23~2~ that this might be due to surfactant concentration fluctuations owing to the membrane undulations. This signal is even more

Singh et al.

11112 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 1500

I

0

0

1 0

0

* 1s

Figure 5. Intensity vs q (A-I) curves showing the shift of Bragg peak toward higher q for samples with polymer and also showing a pronounced central peak (at small q) when polymer is present: (a, top) h / c = 0.75, t$b = 0.75, P = 046,0.3%. (b, bottom) h / c = 0.75, Ob = 0.85, P = os%,0.3%.

pronounced in sampleswith polymer, where it appears at a higher qvalue. Further detailed study was not possible with the apparatus we used (for which q C 0.01 A-1 cannot be reached).

VI. Discussion At this stageof our research, it appears difficult to draw definite conclusions regarding the conformation of the polymer in this system. We can, however, try to build a preliminary picture of this conformation on the basis of our results. We think that even if it turns out to be not entirely true, it captures some part of the reality and holds some interest on its own. Some conclusions that we can draw straightforwardly from the examination of the phase diagram are as follows:

(a) we already know that, in the dilute part of the phase diagram (see Figure 2), the radial nature of the phase boundaries is lost (ref 5 , for example) because of B (the modulus of compressibility of the membranes) being small; this effect is more pronounced in the preaenceofthepolymer,seemingtoindicate that theaddition of the polymer decreases B we give other arguements below, pointing to the same effect. (b) The quasi-disappearance of the L, phase indicates that is pushed toward negative values (this is perhaps also related to the nonappearance of the oily streaks which split into focal domains). The samples with polymer show up, for the same values of &, &, and f$br a periodicity which is much smaller (from 5% to 30%

Polymer in a Lyotropic Lamellar System

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11113

TABLE I: Values of Interlamellar Periodicities, d (A), for Different Dilutions and Different Rigidities W c ) of the Membrane,

As Obtained from SAXS.

4b d p'

hlc 0.6 0.65 0.75 0.85

0.85

0.8

0.75

d

X

0%

p'

0.3%

p'

p'

0%

0.3%

101.4 99.3 101.4 102.5

96.3 96.3 94.4 96.3

0.73 0.74 0.73 0.78

0.72 0.71 0.73 0.77

'P

0%

129.5 127.8 130.4

d

X

'P

0.3%

110.8 116.8 120.2

'P

0%

0.9

'P

0.87 0.86 0.88

0.3% 0.79 0.82 0.83

-

'P

0%

179 174.2 187.9

d

X

'P

0.3%

146.3 149.7 153.3

P=

X

0%

P=

0.3%

p" 0%

0.3%

1.08 1.03 1.11

0.93 0.97 0.97

290.6

190.5

p'

p'

0%

p'

0.3%

a Also are tabulated the values of the exponent, x ; scattered intensity I la - &. A significant amount of contribution to the width of the peak is due to the apparatus, approximately 0.003 A-l. This gives an uncertainty in x to be 0.01. Whereas in the concentrated region of the phase diagram, this error is significant, in the dilute part of the diagram, where thermal fluctuations are dominant and are the main origin of the width of the peak, this error is not so important.

900

I

0

Figure 6. Intensity vs q (A-*) curves. Bragg peak being overwhelmed by the central peak at high dilutions; h / c = 0.85; &, = 0.9; P = 0.3%. less) than without polymer, the relative differencebecoming bigger as the dilution is increased. It is not possible to attribute this difference to the effect of osmotic pressure due to the solvent (with polymer) coexisting with the lamellar phase, because (i) we do not observe such a situation at all and (ii) such a situation, if otherwise possible, should give much bigger variations of the periodicity, from 40% in the most concentrated samples that we have studied, to 60% in our most dilute samples( Y .Nastishin, privatecommunication). The lamellar phase occupies a monophasic region in the phase diagram and in a biphase coexists either with the micellar L1 phase, or a sponge LJ phase. It would be of course of great interest to measure the weight fration $b in the two phases in the biphasicsamples,as well as the polymer content in the solvent, but it can be reasonably expected that the polymer concentration is the same in the two phases in equilibrium and that the brine content I$b is not significantly different, since the extent of the biphasic domain is so small. Similarly we have no reason to believe that the polymer enters the bilayers, although its affinity with the aliphatic chains is great (L. Lbger, private communication). Neutron scattering (to be published) has indeed shown that the change in the bilayer thickness is not enough for this to be true. It is therefore reasonableto infer that for the same compositions &, $E, and I$b, the lamellae are more stretched and with less

fluctuations, in the presence of the polymer than without. We believe the polymer coils to be lying between the bilayers, having no particular interactions with the nearby layers, thus avoiding them, in order to have more configurations available (in the manner of ref 25, where one talks of the confinement energy of the polymer). The system in this way has a higher potential energy due to the confinementof the macromoleculeswithin, and also due to the additional elastic energy required to deform the bilayers to accommodate the coils, but a model which is to be published elsewhere indicates that this new potential energy gives a stable situation. In this model, we treat each coil as a statistical medium of total free energy:

U,, = ~ , T N ( u / D ) + ~ /2K ~ N (the number of monomers each of length a in a coil) being large, and D being the distance between the bilayerswhich confine the polymer coil. The coils are uniformly separated in between the two bilayers, forming bumps at regular intervals on the bilayers (Figure 7a). We estimate this interval to be of the same order of magnitude as the wavelength of light (for the concentration of polymer that we use). This might provide an explanation for the turbidity that we observe in our samples.

Singh et al.

11114 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

results from a competition between curvature elasticity(governed by K ) and layer elasticity (governed by B), when B is large. Conversely,if B is too small, the oily streaks split to focal domains of large eccentricity or do not split at all, showing at most a series of transversal striations as in the model of Schneider and Webb.27 Likewise, we see an increase in the number of focal conic domains of the second kind, in samples with polymer. Since these defects deform the surrounding region, costing energy of compression given by

-

+

W, BR;X(Rl/R, R,/R1) (5) it gives a further indication that B decreases. Notice that increased number of spherolites may also be the origin of increased turbidity in our system. Figure 7. (a, top) Polymer coils are spread in between two bilayers, deforming them to form bumps. The separation between two bumps 1, should depend on the concentrationof the polymer used can be estimated as I where n, is the number of coils/area, = Nu3/&, lo5 A. (b, bottom) Polymer coil when confined between two solid plates which are separated by a distance D < Rn (the Flory radius of the coil in the bulk) is deformed into a disklike shape. The dimension of the coil in the plane parallel to the plane of the bilayers, R, should scale as the Flory radius of a polymer in two dimensions, Le., R Nl4, and should also depend on the length D . Thus R u N / ~ ( u / D ) * cd / ~ is . the mean distance between the layersthat is measured by the X-rays. The presence of the polymer deforms the membranes, stretching the membrane. Here, thedistancebetween the bilayers is D . Between two bumps, the separation between the layers is D’.

-

-

-

-

Also, in such an arrangement, osmotic pressure gradient is built up on a local scale, which will force the bilayers to come closer in between the bumps (Le., to “flocculate”).26 It is the balance between this local osmotic pressure

(which is comparable in magnitude to the Flory-Huggins osmotic pressure and which scales are N - l l Z ( ~ z / D ) l and ~ / ~ )the elastic energieswe mentioned earlier that fixes the interbilayer distance, d. The presence of the polymer coils in between the membranes will have an effect of attenuating the Helfrich repulsive interactions of the membranes, thereby decreasing B. In effect, a decrease in the exponent of the structure factor of samples which have polymer in them, as measured from the SAXS, suggests a decrease in either the modulus of rigidity, K,or in the modulus of compressibility, B, or both. At this stage, not much comments can be made on the nature of K,but the fact that B might be decreasing is also reflected in the small-angle scattered peak observed in SAXS which has been attributed in other lamellar systems23.24 to concentration fluctuations in the bilayer and hence to small B. Also, we were not able to observe, in the textual studies of our samples, oily streakswith well-defined focal domains alongthem. Oilystreaks,whichareedgedislocations withspecial features, exists only in a certain domain of composition of the swollen lamellar system in systems which have no polymer in them. Their splitting into focal domains of small eccentricity

Acknowledgment. We would like to thank Y.Nastishin for interesting discussions on the subject. References and Notes (1) Ji, H.; Hone, D. Macromolecules 1988, 21, 2600. (2) De Gennes, P.-G. J. Phys. Chem. 1990,94,8407. (3) Brooks, J. T.; Marques,C. M.;Cates, M. E.J.Phys. II(Paris) 1991, I, 673. (4) Klkicheff, P.; Cabane, B.; Rawiso, M. J. Colloid Interface Science 1984, 102, 51. (5) Porte, G.; Gomati, R.; El Haitamy, 0.;Appel, J.; Marignan, J. J. Phys. Chem. 1986, 90, 5746. (6) Gomati, R.; Appel, J.; Bassereau,P.; Marignan, J.; Porte G. J . Phys. Chem. 1987, 91, 6203. (7) Porte, G.; Appel, J.; Bassereau, P.; Marignan, J. J . Phys. (Fr) 1989, 50, 1335. (8) Boltenhagen, P.; Lavrentovich, 0.;Kleman, M. J . Phys. II(Fr) 1991, 1, 1233. Kleman, M. Phys. Rev. A 1992, (9) Boltenhagen, P.; Lavrentovich,0.; 46, R1743. (10) Boltenhagen, P.; Kleman, M.; Lavrentovich, 0. C.R . Acad. Sci. Paris II 1992, 315, 921. (1 1) The moduli K and K have been experimentallymeasured by many groups: Farago, B.; Richeter, D.; Huang, J, S.; Safran, S. A.; Milner, S . T. Phys. Rev. Lett. 1990,65, 1930 measured K/K in the system decanbD20AOT and butanol. Meunier, J.; Lee, L. T.; Lungmuir 1989,5,415measured K/K in the system heptane-HZO-AOT. Boltenhagen et a1.* measured the system CPCI-hexanol-brine. (12) Szleifer, I.; Kramer, D.; Ben-Shaul,A.; Roux, D.; Gelbart, W. Phys. Rev. Leu. 1988, 60, 1966. (13) Israelachvili, J. N. Intermolecular and surface forces; Academic Press: New York. (14) Helfrich, W. 2.Naturforsch. 1978, 3317,305. (15) Formula of polyacrylamide: (-CH2CH2CONHr).. (16) We are grateful to Dr. I. Iliopoulos,Laboratoirede Physique-Chimie Macromoleculaire,ESPCI, Paris, for providing the polymer. (17) J. Francois; D. Sarazin; T. Schwartz; Weill, G. Polymer 1979, 20, 969. (18) DeGennes, P. G. Scaling conceprs ofpolymer, 1979, Cornel1 U.P. (19) We thank Dr. C. Allain, FAST, University of Paris-Sud, Paris, for the use of her rheometer facilities. (20) Friedel, G. Ann. Phys. France 1922 18,273. (21) Caille, A. C. R . Acad. Sci. Paris B 1972, 275, 891. (22) Bassereau, P.; Marignan, J.; Porte, G. J. Phys. (Fr) 1987, 48, 673. (23) Porte, G.; Bassereau, P.; Marignan, J.; May, R. Europhysics Lerr. 1988, 7, 713. (24) Nallet, F.; Roux, D.; Milner, S. T. J. Phys. (Fr) 1990, 51, 2333. (25) Daoud, M.; DeGennes, P. G. J . Phys. France 1977, 38, 85. (26) Asakura, S.; Oosawa, F. J . Chem. Phys. 1954, 22, 1255. (27) Schneider, M. B.; Webb, W. W. J. Phys. France 1984, 45, 273.