J . Phys. Chem. 1990, 94, 8407-8413
8407
FEATURE ARTICLE Interactions between Polymers and Surfactants P. G. de Gennes CollPge de France, 75231 Paris Cedex 05, France (Received: April 5, 1990)
A surfactant film (at the water/air interface, or in a bilayer) is exposed to a solution of a neutral, flexible, polymer. Depending on the interactions, and on the Langmuir pressure ll of the pure surfactant film, we expect to find three types of behavior: ( I ) The polymer does not absorb. (11) The polymer absorbs and mixes with the surfactant. (111) The polymer absorbs but segregates from the surfactant. Our interest here is in case 11. We predict that (a) bilayers become rigid; (b) bilayers, exposed to polymer on one side only, tend to bend strongly; (c) the surface viscosity of monolayers or bilayers is considerably increased; soap films or foams, which usually drain by turbulent (two-dimensional) flows, may be stabilized in case 11.
1. Introduction A vast number of industrial products (paints, foods, lubricants, etc.) are based on emulsions or dispersions and require the simultaneous presence of surfactants and polymers; in the simplest cases the surfactants provide stability while the polymer solute gives special rheological features. However, our fundamental knowledge on the interactions, the structures, and the practical properties of mixed polymer/surfactant systems is still rather restricted. Poly(oxyethy1ene) (a typical water-soluble polymer) gives remarkable associated structures when it interacts with surfactant micelles in water.' Also, when it is trapped in lamellar phases of soap plus water, it strongly distorts the overall smectic arrangement.2 Our aim here is to discuss (theoretically) a different family of cases where the surfactant and the polymer compete for one same interface, for instance, an air-water, or oil-water interface. When no polymer is present, the surfactant builds up a monolayer with I's molecules per unit area; if the surfactant is slightly soluble in water, we monitor I's via the bulk concentration of surfactant (or equivalently by a choice of the corresponding chemical potential
When adsorption occurs, two scenarios may follow: (i) homogeneous mixing of polymer and surfactant inside the layer, and (ii) segregated patches of polymer and surfactant. In section I1 we discuss the thermodynamic factors which impose one scenario. In section 111 we focus our attention on the mixing case and explore some mechanical properties of bilayers covered with polymer. In section IV we discuss surface viscosities. A final remark: most of our discussion also applies to polymer adsorption on bilayers. A vesicle, made with an insoluble lipid, optimizes its free energy at constant lipid number, thus achieving a situation of zero surface tension; in this case, the polymer is injected at fixed total surface pressure II = 0. 11. The Three Regimes 1 . Free Energy. Let us call rs the number of surfactant molecules per unit area, and rpthe corresponding number of monomers that are in direct contact with the surfactant (we come back to this point in section 11.4). Our aim is to construct a free energy F (r,,r,) (per unit area) with special emphasis on the 0). situations of small polymer content (I',
-
P A*
If the surfactant is practically insoluble, we put it at the free surface of a Langmuir trough3 and monitor rsvia the surface pressure II. What happens if we now add a soluble polymer in the water phase? Sometimes the polymer will simply avoid the surface. Let us quote two examples of this attitude: (a) If the surfactant is nonionic, with a hydrophilic part which is identical with the polymer units, there will be a strong repulsion between the hydrophilic "brush" and the polymer (water being a good solvent for both). (b) If the polymer is electrically charged, while the surfactant and the interface are uncharged (Le., a negligible f potential), then the polymer will be repelled by the (oil or air) region of low dielectric constant; the long-range image forces will suppress adsorption. In the present paper, we restrict our attention to polymers that are neutral, and also flexible (thus ruling out certain polysaccharides). We are interested mostly in situations where the polymer does absorb; this often occurs with poly(oxyethy1ene) (which may have a certain affinity toward polar heads). Adsorption should also be found with polymers which carry both hydrophilic functions and short hydrophobic groups4 (Figure I ) . ( 1 ) Cabane, B.;Duplessix, R. J . Phys. 1982, 43, 1529-1542; Colloids Sur/ 1985, 13, 19-33; J . Phys. 1987, 48, 651-662. (2) Kekicheff, P.; Cabane, B.; Rawiso, M . J . Colloid Interface Sci. 1984, 102, 51-70. (3) Gaines, G. Insoluble Monolayers at LiquidlGas Interfaces; Wiley: New York, 1956.
The first term F, corresponds to a simple surfactant film. We know F, from the measured Langmuir isotherm II, (r,)
Equation 1 assumes that F(rs,rp) may be expanded in powers of rp.Strictly speaking this is not true, because the entropy of mixing gives a term kTN-'rp In rp(where N is the degree of polymerization). But we focus on the limit of large N , where this term is negligible. (In polymer language, our approximation amounts to saying that the surfactant/polymer consolute point is identical with the 8 point.) 2. Adsorption Criterion. The function WI(r,)defined in eq 1 tells us how much we gain by transferring one monomer from the bulk solution to the interface. It is helpful to write w,(r,) = up+ c l r , + ... (3)
If U p < 0, the polymer tends to absorb on a pure water surface (as is the case with POE). If Up > 0, it does not. When the coefficient Cl is negative (positive), the monomers are attracted (repelled) by the surfactant. (4) If the hydrophobic groups are long, the polymer becomes a polysoap and is associated inside the bulk water phase; we do not consider these cases here.
0022-3654/90/2094-8407$02.50/0 0 1990 American Chemical Society
8408 The Journal of Physical Chemistry, Vol. 94, No. 22, 1990
de Gennes
AIR
El
c
rs
AIR
0
r
Figure 3. Distortions in the surfactant concentration r,(r) at a distance r from an adsorbed monomer. In case a, the surfactant avoids the monomer. A second monomer hitting the interface at point r will have its energy lowered by the depletion. The net result is an attraction between monomers. In case b, the surfactant is attracted by the monomer. This again leads to an attraction between monomers. Figure 1. Modes of adsorption of a polymer (P) on a surfactant layer (S),at an air/water interface: (a) attractive interactions between polymer and polar heads; (b) some small hydrophobic parts (a)of the polymer chain enter the aliphatic region of (S). Both processes probably contribute for poly(oxyethy1ene) or sodium dodecyl sulfate.
w
P
Conversely, we may think of (more exotic) cases where U > 0 (no absorption on the free surface of water), but C, C 0. ?phis may lead to an “inverted” special transition, with adsorption occurring for II, > II*(T). 3. Mixing versus Segregation. Let us now consider the terms in the free energy;, they represent the pairwise inof order rS2 teractions between monomers. Here, it is important to realize that besides the direct interaction described by W,, we have an indirect attraction, mediated by the fluctuations of r,. Assume that we have fixed one monomer at point 0 on the interface. Then the surfactant concentration r,(2)at some distance r from 0 will be modified. A second monomer will be attracted toward this modified region (Figure 3). Similar effects are known in various subsectors of polymer physics: (a) in a polymer solvent system, the monomers alter the surrounding density, and this generates an attractive interaction which is important at high temperatures (where the solvent is close to its liquid-gas critical point and thus highly compressible). This is the basis of Flory’s explanation for inverse consolute systems;’ (b) when a polymer is dissolved in a mixture of two good solvents A and B, the indirect attraction between monomers, mediated by the local A/B composition, may induce precipitation, especially in the vicinity of an AB consolute point.* From the point of view of the free energy,’ the indirect interaction may be analyzed as follows. Consider for instance the case of soluble surfactants, where we impose the chemical potential F , = wr,) + wlr(rs)rp + o(r;) (4) (where the prime denotes differentiation). At fixed F , and rP = 0, we had a certain surfactant Concentration rSo such that pee, = F’(I’@). When we impose rp# 0, the surfactant concentration I’, is modified: rs = rs0 A ..., where A is linear in rp; expanding eq 4, we get
+ +
Figure 2. A bilayer B adsorbing a flexible polymer P. In case a, only the outer surface has been exposed to P, and the bilayer is assumed impermeable to P. I n case b, both sides have been exposed.
If Up < 0 and C, > 0, it may happen that W , ( r , )changes sign at one particular concentration r,*(T), or equivalently at a certain surface pressure n,(r,*)= II*. In the language of statistical physics, the line rs= r*(r ) corresponds to a “special transition” (from adsorbing at I’, < r*to nonadsorbing at rs> r*. There exists abundant theoretical literatures and also a few experimental studies6 on this transition. ( 5 ) (a) Eisenrieglcr, E.;Kremer, K;Binder, K. J . Chem. Phys. 1982, 77, 6296. (b) Eisenreiglcr, E. J . Chem. Phys. 1983, 79, 1052. (c) de Gennes, P. G.; Pincus, P. J . Phys. Lett. (Paris) 1983, 44, 241.
Inserting ( 5 ) back into the free energy ( I ) , we find
(7) The last term (always negative) in eq 7 describes the indirect (6) di Meglio, J. M.; Taupin, C. Macromolecules 1989, 22, 2388. (7) A good experimental study of an inverse consolute point is by: Wolf, B.; Adam, H. J. Chem. Phys. 1981, 75,4121. (8) de Gennes, P. G.J . Phys. Lett. 1976, 37 L, 59. (9) Brochard, F.; de Gennes, P. G. Ferroelectrics 1980, 30, 3 3 .
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The Journal of Physical Chemistry, Vol. 94, No. 22, 1990 8409
Feature Article
@HOMOGENEOUS
I NO ADSORPTION
\O
Tt
I\
II
-
I +GAS
\ =
‘t
Figure 4. Various regimes expected for polymer adsorption on a surfactant film, as a function of the surface concentration rsof surfactant, and of the temperature T. The regions marked L + G correspond to a two-phase surfactant system (liquid + gas). In all the cases represented, the special transition (at r = r*(T))separates an adsorbing region (at low r,) from a nonadsorbing region at high rS.This would probably occur when the adsorption is of the type described in Figure I b.
attraction. It is important when F”= (I/I’,)(dIIs/dI’,) is small (e.g., near a liquid gas critical point of the surfactant monolayer). It can be checked that eqs 6 and 7 also hold if we deal with an insoluble surfactant, Le., if we fix the total surface pressure I’I (eq 2), rather than ps. What is the range of this indirect interaction? This question can be answered if we add suitable gradient terms to the free energy ( I ) , of the form
Then, at the mean-field level, the correlation length [r for the fluctuations of r is given by
and the range of the monomer-monomer interaction is Er; it is small an comparable to the size of the polar heads (except in the vicinity of a two-dimensional critical point of the-surfactant). Having now defined the renormalized interaction W,, we predict that a goo! admixture of polymer and surfactant-will occur whenever W, is positive. On the other hand, when W 2< 0, the polymer will segregate inside the absorbed layer. The_re may exist one particular line in the (r,,, T) plane on which W, = 0. We call this the 8 line for the adsorbed polymer. A 8 line will show up if the indi_rect attractions are strong enough (F” small) to compensate W2.
T C
I
I
I
Figure 5. Regimes in the (r,,T ) plane for “inverted”special transitions: when adsorption occurs only at high FS(rs> r*(T).This might occur if the adsorption process is of the type shown on Figure la.
On the whole, we can summarize the thermodynamics of a given polymer/surfactant system at one given interface in terms of a (rS,T) diagram, with two major dividing lines: the special transition ( W , = 0) and the 8 line. Of course, for certain simple systems, we may find no dividing lines at all, for instance, if the polymer adsorbs at all rsand never demixes. But we expect many more possibilities. In Figures 4 and 5 we have focused on cases where the surfactant monolayer has a phase change (such as two-dimensional liquid/gas) allowing for a critical point (at which F”vanishes). A few conjectured shapes are represented: in Figure 4 for “direct” special transitions (adsorption below r*)and in Figure 5 for “inverse” transitions (adsorption beyond r*). 4. Role of the Adsorption Cloud. It is important to realize that I’ as defined in eq 1, is the number of monomers per unit area t r a t are in direct contact with the surfactant. The total number of monomers adsorbed rPis larger. We know that, in adsorption of polymers from good solvents, there is a diffuse cloud which extends very far from the adsorbing plane; for a simple discussion of the diffuse layer, see ref 10. (a) Most of the equilibrium adsorption cloud is self-similar, with a mesh size 5 = z, at any distance z > D from the adsorbing surface. Since the concentration c ( z ) of monomers is related to the mesh size F by a classical scaling lawlo F = a(ca3)-3/4 (where a is a monomer size), we can write c(z)
= a-3(a/z)4/3
(D < z
< RF)
(8)
The profile c ( z ) is ultimately cut off at very large distances z = (IO) de Gennes, P. G.Adu. Colloid Interface Sei. 1987, 27, 189-209.
8410 The Journal of Physical Chemistry, Vol. 94, No. 22, 1990 c a3
de Gennes 'C
f
~
\
polymer
heads
I
'
O
a
D
*f
1
Figure 6. Qualitative concentration profile in weak adsorption (after ref 5 ) . There is a large self-similar region (D < z < RF)and a smaller "proximal region" ( z < D).The scaling exponents quoted are approxi-
mate, but numerically good.
-
RF, where RFis the size of a single coil in bulk solvent.I0 (From N31Sa.) the Flory analysis," we know that RF (b) The lower cutoff ( D ) is usually comparable to the monomer size (a). In such a case, the total coverage rpdiffers from rponly through a numerical coefficient. However, the situation is more complex if we focus our attention on regimes where rpa2> a, and we are then dealing with the vicinity of the special transition. Let us measure the distance to the special transition by a dimensionless parameter 6
