Langmuir 1996, 12, 3031-3037
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Interactions between Polymer-Grafted Membranes in Concentrated Solutions of Free Polymer E. Evans,*,† D. J. Klingenberg,‡ W. Rawicz,† and F. Szoka§ Departments of Physics and Pathology, University of British Columbia, Vancouver, British Columbia, Canada V6T 1W5, Department of Chemical Engineering and Rheology Research Center, University of Wisconsin, Madison, Wisconsin 53706, and School of Pharmacy, University of California, San Francisco, California 94143-0446 Received October 30, 1995. In Final Form: March 7, 1996X Polymers grafted or otherwise immobilized at surfaces are often used to stabilize particle suspensions in situations where nonspecific colloidal forces or specific chemical bonds act to coagulate the particles. Although the motivation is clear, criteria for steric stabilization are not well established for environments that contain large amounts of free polymer which can induce strong attraction through depletion forces. To examine these criteria, we have performed micromechanical tests of adhesion between pairs of large vesicles with membranes made from mixtures of phospholipids and phospholipids grafted with poly(ethylene oxide) PEO chains in aqueous solutions of free (nonadsorbing) PEO chains. Solutions were made with two free polymer fractions (Np ≈ 114 and 444 monomers in average length) over a large range of volume fractions between 0.01 and 0.2. Three graft chain lengths (Ng ≈ 45, 114, and 273 monomers) and several surface densities were used to extend the scale of surface roughness from ∼0.5 nm for smooth bilayers to nearly 16 nm for the most prominent graft. On the basis of established theory, the grafted polymers were expected to form structures that varied from dilute noninteracting chains to semidilute marginal brushes with mean volume fractions of up to 0.06. Surprisingly, we found a consistent pattern of interaction for all graft lengths and surface densities; i.e., there was no adhesion below a threshold level of free polymer concentration and adhesion energy increased strongly with free polymer concentration above the threshold. Moreover, there was no tendency toward stabilization even at the highest volume fractions of 0.15-0.2. When both surfaces carried grafts (symmetric interactions), the stabilization threshold was proportionally higher than when one of the two surfaces was bare (asymmetric interactions). Significantly, these features were independent of free and graft polymer molecular weights. Correlation of the energy scale for free polymer depletion at the threshold to the graft surface density and symmetry of the steric interaction implies a simple criterion for stabilization of surfaces grafted with homopolymers in semidilute solutions of nonadsorbing free polymer and good solvent.
Introduction Steric stabilization underlies many technological processes (e.g., in paper pulp manufacture and oil recovery).1 On an even grander scale, this approach (aided slightly by electrostatic repulsion) is used universally in nature to prevent untargeted adhesion of suspended cells in the circulations of biological organisms.2 Guided by nature’s success, polymers have recently been grafted to liposome capsules in the design of drug delivery systems for use in humans.3 However, particles in these technological and medical applications are often suspended in relatively concentrated solutions of macromolecules that are excluded or repelled from the interfaces. Thus, depletion forces arise that can destabilize the suspension and cause particle aggregation. Several experimental studies have examined destabilization of polymer-grafted colloids4,5 and rough biological cells6-8 by depletion forces. Even so, the results have not led to well-defined criteria for stabiliza* Address correspondence to this author. † University of British Columbia. ‡ University of Wisconsin. § University of California. X Abstract published in Advance ACS Abstracts, May 15, 1996. (1) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (2) Evans, E. In Handbook of Biological Physics Vol. 1; Lipowsky, R., Sackmann, E., Eds.; Elsevier Science: Amsterdam, 1995; p 723. (3) Woodle, M. C.; Newman, M. S.; Cohen, J. A. J. Drug Targeting 1994, 2, 397. (4) Vincent, B.; Luckham, P. F.; Waite, F. A. J. Colloid Interface Sci. 1980, 73, 508. (5) Vincent, B.; Edwards, J.; Emmet, S.; Jones, A. Colloids Surf. 1986, 18, 261. (6) Brooks, D. E. J. Colloid Interface Sci. 1973, 43, 687 and 714. Chien, S. Adv. Chem. Ser. 1980, No. 188, 1.
S0743-7463(95)00955-3 CCC: $12.00
tion. Hence, we have measured interaction potentials (adhesion energies) between macroscopic vesicles with membranes made of lipid and polymer lipid surfactants in aqueous (good solvent environment) solutions of nonadsorbing free polymer chains. The vesicles were decorated with polymer chains of various lengths and surface densities so as to produce graft structures from dilute mushrooms to semidilute brushes. As macrocolloids, lipid bilayer membranes attract one another through long-range van der Waals forces but the free energy of adhesion per unit area (wa) for neutral phospholipids is extremely small. The reason is that shortrange hydration forces stabilize the surfaces at separations of 2-3 nm.9-11 By comparison, addition of poly(ethylene oxide) PEO (glycol) or dextran (polyglucose) polymers to the aqueous environment increases the adhesion energy by 1 to 2 orders of magnitude when volume fractions reach 0.1-0.2.12 From X-ray diffraction studies,13 it is known that multilamellar dispersions of phospholipid bilayers exclude large PEO and dextran polymers from the interbilayer space when the lipid is swollen in semidilute solutions of these polymers. Consistent with free polymer exclusion and the good solvent conditions in water at room (7) Buxbaum, K.; Evans, E.; Brooks, D. E. Biochemistry 1982, 21, 3235. (8) Evans, E.; Kukan, B. Biophys. J. 1983, 44, 255. (9) Rand, R. P.; Parsegian, V. A. Biochim. Biophys. Acta 1989, 988, 351. (10) McIntosh, T. J.; Simon, S. A. Biochemistry 1986, 25, 4058. (11) Evans, E.; Needham, D. J. Phys. Chem. 1987, 91, 4219. (12) Evans, E.; Needham, D. Macromolecules 1988, 21, 1822. (13) Parsegian, V. A.; Rand, R. P.; Fuller, N. L.; Rau, D. C. Methods Enzymol. 1986, 127, 400. Burgess, S. W.; McIntosh, T. J.; Lentz, B. R. Biochemistry 1992, 31, 2653.
© 1996 American Chemical Society
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temperature,14 the adhesion energy rises progressively with no dependence on molecular weight of the polymer. As predicted by self-consistent mean field theory SCMF,15 these attributes are signatures of nonspecific depletion forces in good solvents. In the semidilute regime, inhomogeneities in the polymer solution are characterized by a single correlation length ξp that depends only on concentration and excluded volume properties of the polymer. Although depletion fields diminish exponentially with distance from nonadsorbing surfaces, the polymer concentration is reduced midway between the surfaces to create a long-range osmotic force that pulls the surfaces together.16 Thus, at contact where the polymer is excluded, the scale of adhesion energy is given simply by the product of osmotic pressure Πp and correlation length of free polymer in solution, i.e., Πpξp. This energy scale for depletion-driven attraction between smooth surfaces increases strongly with volume fraction φp of free polymer in good solvents but is indifferent to polymer molecular weight in the semidilute regime. In contrast to smooth surfaces, theoretical predictions for interactions in free polymer solutions are less well established when the surfaces are decorated with endgrafted polymers that project a large, compressible roughness. Early analyses of steric stabilization were based on intuitive geometrical models.5,17 More recently, Gast and Leibler18 used the SCMF method to determine the free polymer concentration profile assuming that the graft is a region of uniform concentration. For free polymer concentrations less than the graft concentration, the authors concluded that the free polymer is excluded from the graft to promote weak adhesion. However, for free polymer concentrations comparable tosor abovesthe graft concentration, they expected the free polymer to penetrate the graft, mask depletion, and cause stabilization. In another SCMF approach, van Lent et al.19 employed a lattice version of the theory to determine concentration profiles of both free and graft polymer chains for closelyopposed surfaces. These authors also predicted that surfaces should adhere at low free polymer concentrations but with adhesion energy increasing more strongly to a maximum value at volume fractions comparable to the graft volume fraction. As predicted in earlier geometric theories,17 van Lent et al.19 concluded that the interaction potential in the regime of attraction diminishes as the length of free polymer chains approaches the length of graft polymer chains. In marked contrast with these conclusions, we will show in the sections to follow that measurements of adhesion energies between polymergrafted membranes in solutions of free polymer chains do not agree with these models. Specifically, we find steric stabilization against adhesion at low free polymer concentrations up to a threshold level, above which, adhesion strengthens progressively with no indication of restabilization at volume fractions reaching ∼0.2. Furthermore, the adhesion energies are indifferent to sizes of the graft and free polymer chains throughout the semidilute regime. Experimental Methods and Procedures Polymer Grafted Membranes. Micromechanical manipulation of two large (∼20 µm size) membrane vesicles in aqueous polymer solutions was used to test adhesion of surfaces with (14) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 5943. (15) Joanny, J. F.; Leibler, L.; de Gennes, P. G. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1073. (16) Evans, E. Macromolecules 1989, 22, 2277. (17) Jones, A.; Vincent, B. Colloids Surf. 1989, 42, 113. (18) Gast, A. P.; Leibler, L. Macromolecules 1986, 19, 686. (19) van Lent, B.; Israels, R.; Scheutjens, J. M. H. M.; Fleer, G. J. J. Colloid Interface Sci. 1990, 137, 380.
Evans et al. well-defined polymer structures. The vesicle membranes were made from mixtures of 1-stearoyl-2-oleoyl phosphatidylcholine (SOPC) (Avanti Biochemicals, AL) and a specially synthesized phospholipid with a poly(ethylene oxide) (PEO) chain covalently attached at one end to the water soluble head group (also, now available from Avanti Biochemicals). The mole fractions xg of PEO lipid in the surfaces ranged from 0.01 to 0.06. Using an area A1 ≈ 68 Å2 per SOPC lipid, the surface density Fg/am2 of grafted chains was calculated from the relation Fg/am2 ≈ xg/A1. The value for statistical segment length am (≈4.3 Å) was derived from measurements of adhesion energy between smooth surfaces in PEO solutions as will be described in Results. Three molecular weight fractions were chosen for the grafted PEO chains: Mw 2000, 5000, and 12000 (i.e., Ng ≈ 45, 114, and 273 monomers respectively). On the basis of theoretical estimates described below, the grafted polymers were expected to form structures from dilute noninteracting chains to semidilute marginal brushes with average volume fractions φg in the semidilute range 0.020.06 (see Table 1 below). The conventional criterion for a brush is that the end-to-end length of a dilute chain must exceed the distance between grafted chains, i.e., Ng6/5 > 1/Fg in good solvents, which was achieved only with the two longest chains. Needed for calculation of graft and free polymer properties, virial coefficients of PEO in aqueous solution were measured using both freezing point depression and vapor pressure osmometers. Solutions of free polymer were made with two different molecular weight fractions, Mw 5000 or 20 000 (i.e., Np ≈ 114 or 456 monomers, respectively). In the semidilute regime (>0.01 volume fraction for chain lengths >100 monomers), the osmotic pressures Πp were essentially independent of molecular weight and described well by a Taylor (virial) expression to cubic order in volume fraction given by
Πp ≈ (kBT/vm)(νeφp2/2 + βeφp3/3) where kBT/vm is thermal energy per volume vm of a monomer of the polymer in aqueous solution, νe is the excluded volume parameter from Flory theory, and (kBTβe/vm) is the third virial coefficient. Although scaling theory20 predicts that the osmotic pressure should increase as φp9/4, the values of osmotic pressure measured for φp > 0.08 rise much more strongly. Thus, we have used the Taylor expansion given above with second and third virial coefficients to describe the osmotic pressure data. The measurements yielded values of νe ≈ 0.51 and βe ≈ 5.0 based on kBT/vm ≈ 668 atm. With these colligative properties, the mean volume fraction φg of monomers and thickness hg for the brushlike grafts were estimated from the theoretical relations of Milner et al.,21 i.e.
φg ≈ (vm/am3) Fg2/3/νe1/3 and hg ≈ Ng(νeFg)1/3am As listed in Table 1 below, these estimates indicated that the experimental range of PEO lipid fractions and graft chain lengths yielded a wide range of surface concentrations and thicknesses for the layers. Bare SOPC vesicles were effectively smooth with a head group roughness not much greater than the size of a monomeric segment of the polymer. By comparison, the polymergrafted surfaces were expected to project steric layers that varied from 40 to 160 Å. X-ray diffraction studies on multibilayer arrays made with the same molecular weight PEO lipids have yielded graft thicknesses similar to values in Table 1 at comparable surface densities.22 Adhesion Tests. Large vesicles were formed by hydration of mixtures of the diacyl lipid surfactants (dried from chloroformmethanol solution) in a nonelectrolyte buffer (∼0.1 M sucrose). Diacyl lipids are insoluble in an aqueous environment and form cohesive fluid membrane capsules with negligible permeability to osmotic solutes like sugar or salts.11 For each adhesion test, two vesicles were selected from the initial suspension in a chamber (20) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1985. (21) Milner, S. T.; Witten, T. A.; Cates, M. E. Macromolecules 1988, 21, 2610. (22) Kenworthy, A. K.; Simon, S. A.; McIntosh, T. J. Biophys. J. 1995, 68, 1903. Kenworthy, A. K.; Hristova, K.; Needham, D.; McIntosh, T. J. Biophys. J. 1995, 68, 1921.
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Table 1. Peo-Lipid Grafts Used in Adhesion Tests Mw φg xg Fg hg mol wt surface surface mean thickness (PEO) mole fraction density × am2 volume fraction (nm) 2 000 5 000 5 000 5 000 12 000 12 000 a
0.010 0.012 0.023 0.057 0.010 0.020
0.0027 0.0032 0.0062 0.0155 0.0027 0.0054
0.021 0.032 0.059 0.019 0.030
4.2a 5.8 7.2 9.7 13.0 16.4
Estimate of the end-to-end length in dilute suspension.
Figure 2. (a) Video micrograph of fluorescence emitted from PEO 2000-lipids (1 mol %) in the membranes of an adherentsymmetric pair of vesicles. The adhesion was driven by depletion forces in a semidilute solution of unlabeled PEO 20000 chains (6% by volume). No adhesion was observed in the absence of free polymer when the polymer-grafted lipids were present in the membranes. The terminus of one alkyl chain of the polymer-grafted diacyl lipid was labeled by the fluorophore BODIPY. (b) Photometric measurements of fluorescence intensity in single bilayer regions and in the center of the doublebilayer contact are listed by the observation windows sketched on the traced outline of the adherent vesicles. As seen, the intensity level in the contact region was twice that observed in single membrane regions outside the contact. These tests demonstrated that even low surface concentrations of polymergrafted lipids were not driven out of the contact by strong adhesion in the free polymer solution.
Figure 1. Video micrographs of two large lipid bilayer vesicles (∼20 µm diameters) manipulated by micropipets to test adhesion in a semidilute solution of free PEO polymer. The vesicle on the right was aspirated with large suction pressure so that the vesicle behaved as a rigid test surface. The vesicle on the left was aspirated with low-variable suction controlled to regulate adhesive spreading on the test surface. In (a), the vesicles were maneuvered into close proximity and left stationary. As the suction applied to the vesicle on the left was lowered, the membrane spread on the stiff pressurized vesicle surface to reach an equilibrium contact in (b) set by the pressure level. When released from the pipet in (c), the adherent vesicle membrane covered the stiff vesicle to an extent limited by its surface area to volume ratio. on the microscope stage and transferred to an adjacent chamber that contained a slightly more concentrated buffer with 20 mM NaCl, glucose, plus free polymer. In the test chamber, a small difference in index of refraction between the interior and exterior of the vesicle greatly enhanced the optical image as shown in Figure 1. After transfer, the vesicles dehydrated rapidly to equilibrium volumes set by the osmotic strength of the new environment. In each test, one vesicle was aspirated and held
by a micropipet with high suction to create a rigid spherical segment outside of the pipet. This vesicle became the test surface for adhesion. The other vesicle was aspirated by a second pipet with low suction controlled to regulate the adhesion process. The second vesicle was maneuvered into close proximity of the test vesicle surface (Figure 1a) and adhesion was allowed to proceed in discrete (equilibrium) steps by incremental reductions in pipet suction (Figure 1b,c). To verify that the PEO lipids were not squeezed out of the contact region in situations of strong adhesion, we examined fluorescence images of strongly adherent vesicle pairs where the bilayers were made with SOPC and a PEO lipid labeled by a fluorescent group on one of its hydrocarbon chains. As shown by the images in Figure 2, the fluorescence intensity emitted from the adhesion zone was twice the level of that emitted from single bilayer regions outside the contact. This observation confirmed that the PEO-grafted lipid was uniform over the entire surface of each vesicle. In the adhesion tests, the slightly dehydrated vesicles deformed as liquid-filled bags with constant surface area and volume. (By comparison, spherical vesicles are essentially rigid and oppose adhesion.) The bilayer bending stiffness is so small that macroscopic-size vesicles offer negligible resistance to deformation until the surfaces reach pressurized contours as shown in Figure 1.23 Thus, the membrane tension (set by pipet suction) limited the extent of spreading on the test vesicle surface (cf. Figure 1b). Reductions in pipet pressure were monitored over the forward process of adhesion followed by increases throughout the reverse process of separation to verify reversibility. Because of the large osmotic strength of the impermeable solutes trapped inside the vesicles, the small suction pressures did not alter vesicle volumes during adhesion tests. These kinematic and mechanical (23) Evans, E. Adv. Colloid Interface Sci. 1992, 39, 103. Evans, E. Colloids Surf. 1990, 43, 327.
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features enabled sensitive measurements of adhesion energy between the membrane surfaces. Analysis of Adhesion. In the absence of electrostatic forces and neglecting subtle fluctuation effects, interactions between vesicle surfaces in solutions of free polymer can be viewed as a superposition of van der Waals attraction, osmotic attraction due to free polymer depletion, and steric repulsion from elastic compression of the polymer brush.23 Although conservative potentials underlie interactions in reversible adhesion, the effective range from the membrane surface is much smaller than the macroscopic dimensions observable in mechanical experiments. Hence, measurements of adhesion energy embody the cumulation of all interactions (defined as total force per unit area σn normal to the surface) into an integral over distance from large (∼infinite) separation to nanoscale contact, i.e.
∫
wa ) - σn dz
(1)
Stationary geometries of adherent vesicles can be predicted from a variational analysis where the energy gained by formation of an infinitesimal area of contact is balanced by the mechanical work required to displace the membrane.23 This leads to an equation analogous to the Young-Dupre relation for liquid drop adhesion to solid surfaces
wa ) Tm (1 - cos θc)
(2)
In this equation, wa is the free energy reduction per unit area of contact (adhesion energy) defined by eq 1. The angle θc is the apparent contact angle at the contact perimeter (sketched in Figure 1b), which establishes the mechanical leverage factor (1 - cos θc). (The submicroscopic contact angle is effectively zero since the membrane of the adherent vesicle bends sharply to parallel the membrane of the test vesicle inside the contact.) The bilayer tension Tm is specified by the pipet suction pressure P through the following mechanical prescription23
Tm ) PRp/(2 - Rpc)
(3)
where Rp is the inner pipet radius and c is the constant mean curvature (i.e., sum of principal curvatures) that defines the shape of the unsupported bilayer of the adherent vesicle. Because the area and volume of the adherent vesicle remained fixed throughout contact formation, both the constant mean curvature c and the apparent contact angle θc are uniquely defined by the extent of spreading on the spherical test surface and were calculated with a computational algorithm.23 In experiments, the extent of spreading on the test vesicle is best quantitated by measuring the polar height zc of the adhesion cap and dividing by the diameter 2Rs of the spherical test surface (i.e., xc ) zc/2Rs). Sample data in Figure 3 demonstrate results for reciprocal tension versus apparent contact angle derived from measurements of pipet pressure and extent of adhesion in all of the tests. As shown in Figure 3, the adhesion tests were fully reversible and the results were accurately described by eq 2 with fixed values of adhesion energy.
Results Using the methods just described, adhesion between pairs of vesicles was tested in solutions of free PEO polymer up to 0.2 volume fraction. Three distinct sets of experiments were performed, i.e., (i) symmetric interactions between two smooth, bare bilayers of SOPC, (ii) asymmetric interactions between smooth, bare bilayers and polymer-grafted bilayers, and (iii) symmetric interactions between two polymer-grafted bilayers. Beginning with adhesion of bare lipid bilayers, we will show that attraction driven by van der Waals forces was extremely weak by comparison to attraction induced by free polymer depletion. Then, we will show that addition of grafted polymer chains to one or both of the bilayer surfaces suppressed adhesion by van der Waals attraction to an undetectable level and prevented adhesion over a range of low free polymer concentrations. However, adhesion appeared
Figure 3. Results from tests of adhesion between bare lipid vesicle pairs demonstrate the relation between apparent contact angle θc and reciprocal tension 1/Tm in the adherent vesicle bilayer as derived from measurements of the extent of spreading and pipet suction pressure. Coincidence of the closed and open data symbols for contact formation and separation show that the adhesion processes were reversible. The curves superposed on the data are the behavior predicted for the uniform values of adhesion energy listed in the figure. The lower value for adhesion energy demonstrates weak van der Waals attraction in the absence of free polymer whereas the upper value shows the marked increase in strength of adhesion in solutions of 3% free PEO polymer by volume.
above a threshold and continued to strengthen with added concentration of free polymer. Notably, in all cases, there was no detectable dependence on molecular weights of the graft or free polymer chains. Interaction between Bare Membranes. Results of adhesion tests with bare, smooth surfaces are plotted in Figure 4 as a function of volume fraction φp of free polymer in the bulk solution. To demonstrate that adhesion energy depended only upon the chemical nature of the free polymer (i.e., excluded volume properties and statistical segment length), two sets of measurements are shown: (1) data for adhesion of SOPC bilayer vesicles obtained here in solutions of two PEO molecular weight fractions; (2) data obtained previously12 by the same method in solutions of three molecular weight dextran polymers. For both types of polymer, the adhesion energy was found to increase rapidly with polymer concentration from the small level (∼0.01 mJ/m2) produced by van de Waals attraction between the uncharged bilayers but was independent of molecular weight. Using the colligative properties of each polymer measured by osmometry, the solid curves superposed on the data in Figure 4 were predicted by SCMF analysis as described previously.12,16 For smooth, hard surfaces, the adhesion energy at contact is given by ∼5Πpξp.16 In the semidilute regime and good solvent conditions, a single correlation length ξp (that depends only on volume fraction and solvent quality) is sufficient to describe variations in the spatial distribution of monomer segments for free polymer chains. For a Flory mean field expansion of the free energy,15 the correlation length is specified by ξp ) am/(6νeφp)1/2, whereas the correlation length predicted by scaling theory20 follows ξp ∼ 1/φp3/4. However, both mean field and scaling theories predict the same dependence of depletion-driven adhesion energy on volume fraction over the initial range of the semidilute regime, i.e., Πpξp ∼ φp3/2. Because of the shortrange hydration barrier, the adhesion energy profiles for bare SOPC bilayers lie slightly below the ideal analysis for hard walls.12 The statistical segment length am was the only unknown parameter needed to fit the theory to the adhesion energy measurements, which had to be accurate to (5% to match the data. The profiles plotted
Polymer Membrane Interactions
Figure 4. Adhesion energies wa measured between symmetric pairs of bare lipid vesicles in solutions of PEO and dextran polymers as functions of volume fraction φp. The data for dextran solutions of three separate weight fractions Mw ≈ 147 500 (asterisks), 36 500 (open squares), and 11 200 (open triangles) were plotted from ref 12. In this study, two sets of PEO solutions were used with nominal weight fractions of Mw ≈ 20 000 (closed circles) and 5000 (open circles). As expected for semidilute solutions in good solvents, the adhesion energies were found to depend on the chemical nature of the free polymer in solution but not on free polymer length. The curves superposed on the data are adhesion energies predicted from self-consistent mean field theory using the excluded volume parameters measured separately for each polymer by osmometry. The only unknown parameter in these fits was the statistical segment length for each type of polymer, which were restricted to ∼4.3 Å for PEO and ∼6.2 Å for dextran within (5%.
in Figure 4 were predicted using segments lengths of ∼6.2 Å for dextran and ∼4.3 Å for PEO, which slightly exceed the cube root of monomer volumes in aqueous solution (i.e., 5.5 and 3.9 Å, respectively). (Note: the osmotic pressure measurements for dextran yielded a second virial coefficient kBTνe/vm of ≈190 atm as compared to 340 atm for PEO.) Clearly, SCMF theory correlates extremely well with the measured energies for adhesion of bare SOPC bilayers and the segment lengths are well within the range of values deduced from measurements of radius of gyration in dilute solutions. Interactions between Polymer-Grafted Membranes. With PEO chains attached to lipid head groups in the membranes, the adhesion response of vesicles in free polymer solutions was altered significantly but in an unexpectedly simple way. First, in the absence of free polymer, no adhesion was detected between vesicle pairs with any of the grafted chain lengths and surface concentrations. (Note: the detection limit for adhesion energy in these experiments was ∼1 µJ/m2, which is 2 orders of magnitude lower than the scale shown in Figure 4.) Next, stabilization of the membrane surfaces persisted when free polymer was added up to a threshold concentration φp* above which strong adhesion occurred. The features are demonstrated clearly in Figure 5 by results from tests of adhesion between asymmetric bare and PEO 5000-lipid vesicle pairs in solutions of free PEO 20000; the vesicles were prepared with three surface concentrations of PEO 5000-lipid in the bilayer. As seen in Figure 5, the presence of a polymer layer on one surface merely shifted the adhesion profiles to larger free polymer concentrations. It is important to recognize that the threshold concentration φp* could not be found precisely
Langmuir, Vol. 12, No. 12, 1996 3035
Figure 5. Adhesion energies wa measured between asymmetric pairs of bare lipid and PEO 5000-lipid vesicles in solutions of free PEO 20000 polymer as functions of volume fraction φp. The surface densities of the graft layers are given as mol % of the total lipid mixture. The results demonstrate the increase in stabilization associated with increase in graft density. (For reference, the adhesion energy profile for bare lipid membranes is given by the solid curve. The dashed curves through the data were hand-drawn to guide the eye.)
because in the vicinity of eφp*, it was necessary to wait long periods of time and even to push the vesicles into contact to assay for adhesion. Hence, values for the threshold concentration were deduced from extrapolation of the adhesion energy profile to zero. For φp < φp*, no measurable adhesion was observed and the threshold concentration shifted upward with increases in graft surface density Fg. Above the threshold concentration (φp > φp*), the adhesion energy strengthened with free polymer concentration as for bare surfaces but we saw no hint of restabilization at large volume fractions in the range of φp ∼ 0.15-0.2. The same behavior was observed for adhesion of symmetric PEO 5000-lipid vesicle pairs, but the threshold for adhesion was shifted to even higher free polymer concentrations at each graft surface density as seen in Figure 6. Again, the adhesion energy profiles above φp* paralleled that measured for interactions between bare surfaces. This response was also observed for the shortest (PEO 2000-lipid) and the longest (PEO 12000-lipid) grafts in free PEO 20000 solutions as seen in Figure 7. Surprisingly, when the molecular weight of the free polymer in solution was lowered from 20 000 to 5000, the threshold concentration and adhesion energy profile remained the same for PEO 12000-lipid grafts even though the free chains were much shorter than the graft chains (cf. Figure 7). In Table 2, we have summarized the threshold concentrations in relation to the graft composition and a symmetry index ng, which identifies the steric configurations in these tests, i.e., ng ) 1 for bare versus graft and ng ) 2 for graft versus graft. As a final note, in tests of symmetric polymer grafts at high free polymer concentrations, long waiting periods were also needed for adhesion to develop probably due to slow migration of trapped free PEO chains out of the gap. Similarly, leaving the vesicle pair adherent for long periods always resulted in extremely strong attachment, perhaps due to kinetic restrictions of interpenetrated chains from opposing grafts since this was not observed for asymmetric interactions.
3036 Langmuir, Vol. 12, No. 12, 1996
Figure 6. Adhesion energies wa measured between symmetric pairs of PEO 5000-lipid vesicles in solutions of free PEO 20000 polymer as functions of volume fraction φp. The graft compositions (surface densities given as mol % of the total lipid mixture) are the same as for the asymmetric tests plotted in Figure 5; comparison shows the increase in stabilization associated with increase in number of intervening graft layers (i.e., from ng ) 1 to 2). (For reference, the adhesion energy profile for bare lipid membranes is given by the solid curve. The dashed curves through the data were hand-drawn to guide the eye.)
Figure 7. Adhesion energies wa measured between symmetric pairs of PEO-lipid vesicles of two chain lengths (Mw ≈ 2000 and 12 000) in solutions of free PEO 20000 polymer (open symbols) as functions of volume fraction φp. The surface densities of the graft layers are given as mol % of the total lipid mixture. Also, another set of adhesion energies is plotted for PEO 12000-lipid vesicles in solutions of free PEO 5000 polymer (closed circles)swhere the free chains were much shorter than the graft chains. As for adhesion between pairs of bare lipid vesicles, the energies above the stability limit were indifferent to chain length of the free polymer in solution. (For reference, the adhesion energy profile for bare lipid membranes is given by the solid curve. The dashed curves through the data were hand-drawn to guide the eye.)
Energy Scale for Depletion at the Adhesion Threshold vis-a-vis Graft Properties As implied by adhesion energies plotted in Figures 5-7, destabilization and adhesion occurred when depletion in the free polymer solution increased sufficiently to overcome an energy barrier. Once this barrier had been surpassed,
Evans et al.
Figure 8. Correlation of the apparent barrier energies at the stability boundary to properties of the steric layers (ng, Ng, Fg). The apparent barrier energies were calculated from the energy scale Πpξp* for depletion at the threshold concentrations φp* (Table 2). The result is that demarcation between stabilization and adhesion can be represented by a simple-unifying relation over the range of free polymer volume fractions from 0.01 to 0.2, i.e., ngFg3/2 ∼ Πpξp/(kBT/am2), with no dependence on graft or free polymer chain lengths. Table 2. Adhesion Threshold and Stability Boundary Ng PEO lipid index (Mw/44)
Fg surface density × am2
ng symmetry index
φp* free polymer threshold
45 114 114 114 114 114 114 273 273
0.0027 0.0032 0.0032 0.0064 0.0064 0.0155 0.0155 0.0027 0.0054
2 1 2 1 2 1 2 2 2
0.010 0.017 0.026 0.033 0.050 0.068 0.095 0.024 0.042
the adhesion energy strengthened progressively as if the depletion emanated from impenetrable walls moved outward by an extended short-range repulsion. Significantly, the steric stabilization depended on graft surface density Fg and the symmetry index ng (1 or 2) but not on the molecular weight of free polymer chains in solution. Dependence on symmetry of the steric interaction clearly rules out intensive stabilization criteria that are based solely on osmotic pressure or volume fraction. The criteria must depend on an extensive parameter like the elastic energy for deformation of the graft layer(s). Assuming superposition of steric repulsion and depletion forces, we have chosen the energy scale for free polymer depletion evaluated at the adhesion threshold to provide an apparent scale for the steric energy barrier. From the observed threshold concentrations and properties of the grafts (ng, Ng, Fg) listed in Table 2, we calculated the threshold energy scale (Πpξp)* at φp* and correlated the values with graft surface density Fg for the two longest graft chain lengths (Ng ) 114, 273) and for each interaction symmetry (ng ) 1 or 2). Plotted on a log-log scale, we found that the threshold energy increased as Fg3/2 in all three cases. Furthermore, with Ng ) 114 and 273, the correlations for symmetric interactions (ng ) 2) were superimposable, i.e., no dependence on graft chain length. On the other hand, the correlations for asymmetric and symmetric interactions (ng ) 1 and 2) with Ng ) 114 were displaced by a factor of log (2) on the log-log plot, which showed that the dependence on ng was linear. Therefore, we have combined all of the results derived from the data in Table 2 into one log-log plot in Figure 8, which shows that the threshold
Polymer Membrane Interactions
energy scale (Πpξp)* at φp* increases as ngFg3/2. This correlation implies a parsimonius criterion for stabilization of surfaces grafted with homopolymers in semidilute solutions of the same free polymer and good solvent. Discussion The experiments described here provide the first direct measurements of energetics for depletion-driven attraction between polymer-grafted surfaces. In all of the tests, the adhesion response was the same: i.e., the surfaces were stabilized by the graft layer(s) with no detectable attraction below a threshold level of free polymer in solution; for concentrations above the threshold, adhesion increased in strength progressively with no indication of weakening even at volume fractions of ∼0.2. Importantly, the threshold concentration φp* was found to depend only on graft surface density and symmetry of the steric interaction but not on molecular weights of the graft or free polymer chains. The lack of dependence on molecular weights demonstrates that long range correlations in both the graft and free polymer chains are screened by excluded volume interactions when the free polymer is present in solution at semidilute concentrations. As discussed in the Introduction, previous predictions17-19 are inconsistent
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with our results in the following ways: Specifically, in ref 19, no energy barrier to adhesion was anticipated at low free polymer concentrations and the adhesion energy was expected to diminish significantly if the length of the free polymer chains was less the length of the graft chains. In ref 17, restabilization was expected at large concentrations. Similarly, in ref 18, restabilization was expected when the free polymer concentration reached the monomer concentration in the graft, which would not depend on whether one or both surfaces bear grafted chains. On the basis of the simple behavior observed in our experiments, a useful guide for future models would be to treat the graft polymer-free polymer interface similar to the SCMF treatment of a phase-separated or immiscible mixture of two polymers in semidilute conditions where correlations are fully screened by excluded volume effects.24 Acknowledgment. This work was supported by Medical Research Council of Canada Grant MT 7477 to E.E. and USPHS NIH Grant GM30163 to F.S. LA9509559 (24) Hong, K. M.; Noolandi, J. Macromolecules 1981, 14, 727.
