pubs.acs.org/Langmuir © 2010 American Chemical Society
Direct Measurement of Double-Layer, van der Waals, and Polymer Depletion Attraction Forces between Supported Cationic Bilayers Travers H. Anderson,† Stephen H. Donaldson,† Hongbo Zeng,‡ and Jacob N. Israelachvili*,† †
Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106-5080, and ‡Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2 V4, Canada Received May 21, 2010. Revised Manuscript Received July 15, 2010 The interactions of supported cationic surfactant bilayers and the effects of nonadsorbing cationic polyelectrolytes on these interactions were studied using the surface forces apparatus (SFA) technique. Bilayers of the cationic surfactant di(tallow ethyl ester) dimethyl ammonium chloride (DEEDMAC) were deposited on mica surfaces using the Langmuir-Blodgett technique, and the interactions between the bilayers were measured in various salt, nonionic polymer (PEG), and cationic polyelectrolyte solutions at different polymer molecular weights and concentrations. The forces between the bilayers in CaCl2 solution are purely repulsive and follow the DLVO theory quantitatively down to bilayer separations of ∼2 nm. Addition of nonadsorbing polymer or polyelectrolyte has a number of effects on the interactions including the induction of a depletion-attraction between the bilayers and screening of the double-layer repulsion due to the added ions in the solution from the polyelectrolyte. The experimental results are shown to agree well with standard theories of depletion attraction and double-layer screening associated with dissolved polyelectrolyte. We also observed significant time and rate effects on measuring the equilibrium bilayer-bilayer interactions possibly due to the unexpectedly long times (>1 min) associated with the charge regulation of the bilayer surfaces. Implications for the interactions and stability of vesicle dispersions, i.e., of free rather than supported bilayers, in polymer solutions are discussed.
Introduction Colloidal vesicle dispersions are widely used in a variety of industries including the medical, food, cosmetic, paint, plastic, and consumer product industries. Applications of vesicle dispersions generally require control of their colloidal properties, most importantly the stability of the dispersions. Furthermore, many consumer products contain additives such as polymer, perfumes, and dyes and are increasingly moving toward highly concentrated dispersions in order to reduce their carbon footprint. Unfortunately, the stability behavior of vesicle dispersions often becomes difficult to control for these types of complex multicomponent and highly concentrated mixtures. Kinetic stability models, such as those postulated by Smoluchowski,1,2 and computer simulations3-8 are commonly used to predict and understand stability behavior. These methods require detailed knowledge of the interparticle (e.g., vesicle-vesicle) interactions within the dispersion. Theories for the interbilayer forces are described well in the *To whom correspondence should be addressed. E-mail: jacob@ engineering.ucsb.edu. (1) Nir, S.; Bentz, J. J. Colloid Interface Sci. 1978, 65(3), 399–414. (2) Krivitsky, D. S. J. Phys. A 1995, 28(7), 2025–2039. (3) Linse, P.; Lobaskin, V. J. Chem. Phys. 2000, 112(8), 3917–3927. (4) Broukhno, A.; Jonsson, B.; Akesson, T.; Vorontsov-Velyaminov, P. N. J. Chem. Phys. 2000, 113(13), 5493–5501. (5) Brukhno, A. V.; Akesson, T.; Jonsson, B. J. Phys. Chem. B 2009, 113, 6766– 6774. (6) Ilett, S. M.; Orrock, A.; Poon, W. C. K.; Pusey, P. N. Phys. Rev. E 1995, 51(2), 1344–1352. (7) Semenov, A. N. Macromolecules 2008, 41, 2243–2249. (8) Lekkerkerker, H. N. W.; Poon, W. C. K.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20(6), 559–564. (9) Cowley, A. C.; Fuller, N. L.; Rand, R. P.; Parsegian, V. A. Biochemistry 1978, 17(15), 3163–3168. (10) Horn, R. G. Biochim. Biophys. Acta 1984, 778(1), 224–228. (11) Marra, J.; Israelachvili, J. N. Biochemistry 1985, 24(17), 4608–4618. (12) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Brady, J.; Evans, D. F. J. Phys. Chem. 1986, 90(8), 1637–1642.
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literature and have been measured for many bilayer systems.9-15 However, detailed knowledge of the interactions between charged bilayers in complex solutions of polyelectrolytes is still incomplete. Generally, vesicle dispersions become unstable when the vesicles are sufficiently attracted to one other to begin forming aggregates. Attractive van der Waals (VDW) forces are commonly the cause and are unfortunately unavoidable. A common method of overcoming the attractive van der Waals force is to make vesicles out of surfactants with charged headgroups so that a strong electrostatic repulsive force exists between the surfaces of the vesicles. Together, the van der Waals and electrostatic interactions make up the so-called Derjaguin-Landau-VerweyOverbeek (DLVO) interaction which, for simple vesicle dispersions, may be sufficient to accurately determine the vesiclevesicle interaction and predict the stability behavior of the dispersion.1,16 However, due to cost and environmental pressures, many products are tending toward highly concentrated vesicle dispersions that force the vesicles to pack in close contact thereby increasing the likelihood of vesicle deformation, fusion, and engulfing (forming multiwalled liposomes). Additionally, additives such as polymers, perfumes, and dyes are commonly added to the dispersions to give desirable consumer properties, but they also affect the vesicle-vesicle interactions, as well as the behavior of the surfactants within the bilayers (intravesicle interactions). In these types of complex vesicle dispersions, the DLVO theory may (13) Horn, R. G.; Israelachvili, J. N.; Marra, J.; Parsegian, V. A.; Rand, R. P. Biophys. J. 1988, 54(6), 1185–1186. (14) McGuiggan, P. M.; Pashley, R. M. J. Colloid Interface Sci. 1988, 124(2), 560–569. (15) Pashley, R. M.; McGuiggan, P. M.; Horn, R. G.; Ninham, B. W. J. Colloid Interface Sci. 1988, 126(2), 569–578. (16) Nir, S.; Bentz, J. J. Colloid Interface Sci. 1980, 74(1), 295–296.
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not be sufficient to describe the complete intervesicle interaction. In such complex systems, depletion-attraction, polymer-induced steric stabilization (repulsion), hydration repulsion, bilayer undulation, modified electrostatic, deformation stresses, and hydrophobic interactions can become important and add to the standard DLVO forces that govern the fundamental bilayer-bilayer interaction between vesicles. Fundamental bilayer-bilayer interactions have been measured directly in aqueous conditions for zwitterionic bilayers11,13 and charged bilayers12,14 and have been shown to follow DLVO theory quite well. It is also well-known that the addition of nonadsorbing, uncharged polymer to the aqueous phase may cause vesicle aggregation17-20 due to a depletion-attraction force, first proposed by Asakura and Oosawa.21,22 The interaction is entropic in nature due to the loss of conformational entropy of the dissolved polymer within the depletion gap distance, Δ ∼ Rg, between the vesicle surfaces. As the vesicle surfaces come within a distance Δ of one another, the dissolved polymer is entropically excluded from the gap between the vesicles setting up an (attractive) osmotic pressure which acts to drive the water in the depletion zone into the bulk and pull the vesicles together. Attractive depletion forces have been directly measured between hard surfaces23,24 and between uncharged bilayers.25,26 The bilayer-bilayer interaction is complicated further if the dissolved polymer is charged, which is usually necessary to (i) keep the polymer from adsorbing to the vesicle surfaces and bridging multiple vesicles together or (ii) create a desired (e.g., rheological) property or performance of the dispersion. In addition to the depletion attraction, polyelectrolytes add more charge to the aqueous phase and have been shown to effectively screen out the electrostatic repulsive forces between surfaces,27 much like additional salt, and cause instabilities in vesicle dispersions.28 A full description of the vesicle-vesicle interaction must also include the deformation of the vesicles which may be caused by the interaction forces between them or by external forces such as crowding. Unlike most colloidal particles, vesicles are composed of essentially only surfaces, or 2D membranes (the bilayer), and hence do not have bulk elastic properties, but rather surface (thin film) properties such as area expansion and bending moduli. Additionally, the surfactant bilayers that form the vesicle surface may be soft or fluid-like (above the Kraft temperature) or stiff and rigid (below the Kraft temperature) and are selectively permeable, allowing water to pass through relatively easily while acting as an impermeable wall to ions. For this reason, the standard contact mechanics theories such as the Johnson-Kendall-Roberts (JKR) theory29 do not apply to adhering vesicles, regardless of (17) Joanny, J. F.; Leibler, L.; DeGennes, P. G. J. Polym. Sci., Part B: Polym. Phys. 1979, 17(6), 1073–1084. (18) Prestidge, C.; Tadros, T. F. Colloids Surf. 1988, 31, 325–346. (19) Liang, W.; Tadros, T. F.; Luckham, P. F. J. Colloid Interface Sci. 1993, 158(1), 152–158. (20) Ogden, A. L.; Lewis, J. A. Langmuir 1996, 12(14), 3413–3424. (21) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22(7), 1255–1256. (22) Asakura, S.; Oosawa, F. J. Polym. Sci. 1958, 33(126), 183–192. (23) Ruths, M.; Yoshizawa, H.; Fetters, L. J.; Israelachvili, J. N. Macromolecules 1996, 29(22), 7193–7203. (24) Kleshchanok, D.; Tuinier, R.; Lang, P. R. Direct measurements of polymer-induced forces. J. Phys.: Condens. Matter 2008, 20, (7). (25) Kuhl, T.; Guo, Y. Q.; Alderfer, J. L.; Berman, A. D.; Leckband, D.; Israelachvili, J.; Hui, S. W. Langmuir 1996, 12(12), 3003–3014. (26) Kuhl, T. L.; Berman, A. D.; Hui, S. W.; Israelachvili, J. N. Macromolecules 1998, 31(23), 8250–8257. (27) Tadmor, R.; Hernandez-Zapata, E.; Chen, N. H.; Pincus, P.; Israelachvili, J. N. Macromolecules 2002, 35(6), 2380–2388. (28) Huh, J. Y.; Lynch, M. L.; Furst, E. M. Microscopic structure and collapse of depletion-induced gels in vesicle-polymer mixtures. Phys. Rev. E 2007, 76, (5). (29) Israelachvili, J. N. Intermolecular and Suface Forces, 2nd ed.; Academic Press: London, 1992.
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Figure 1. Top: The cationic surfactant DEEDMAC used to make the supported bilayers in the SFA studies. Middle: The polymers PEG, polyDADMAC, and poly(allyl)amine used to study the repulsive electrostatic and attractive depletion forces between DEEDMAC bilayers. Bottom: Schematic of the supported bilayers and surface geometry in the SFA experiments.
the rigidity of the bilayers. Theoretical modelings of vesicle contact mechanics have been done,30-32 but most put unnecessary emphasis on the bending energies of the bilayers and ignore the stretching energies and differential osmotic pressures built up by the semipermeable bilayers of the vesicle.33 In this paper, we present direct measurements of the bilayerbilayer interactions between two supported cationic surfactant bilayers in various aqueous solutions and consider in detail the DLVO, modified electrostatic, and depletion-attraction interactions induced by polyelectrolytes. We show that the addition of cationic polyelectrolyte has at least two major effects: (i) it screens (reduces) the repulsive electrostatic forces, and (ii) it induces a depletion attraction. Both of these effects act to push the vesicle dispersion toward an unstable state. We compare our results with current theories. To our knowledge, these are the first direct measurements of the interactions between highly charged bilayers in the presence of polyelectrolytes. In an accompanying paper,34 we address the contact mechanics of adhesive vesicles, accounting for the inevitable stretching of, and the differential osmotic pressure generated across, the bilayers of the vesicles. Together, these papers address the interactions involved in determining the interactions and stability of vesicle dispersions.
Materials and Methods The cationic surfactant di(tallow ethyl ester) dimethyl ammonium chloride (DEEDMAC, see Figure 1) was provided by Procter & Gamble Co. (Cincinnati, OH). The cationic polymers (30) Evans, E. A. Biophys. J. 1985, 48(1), 175–183. (31) Evans, E. A. Biophys. J. 1985, 48(1), 185–192. (32) Foo, J. J.; Chan, V.; Liu, K. K. Ann. Biomed. Eng. 2003, 31(10), 1279–1286. (33) Bailey, S. M.; Chiruvolu, S.; Israelachvili, J. N.; Zasadzinski, J. A. N. Langmuir 1990, 6(7), 1326–1329. (34) Ramachandran, A.; Anderson, T. H.; Zeng, H.; Leal, L. G.; Israelachvili, J. N. Using SFA measurements to predict the adhesive interactions between vesicles. Langmuir Submitted.
DOI: 10.1021/la1020687
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Article poly(diallyldimethyl)ammonium chloride (polyDADMAC) at low molecular weight (∼50 000) and high molecular weight (∼400 000) and poly(allyl)amine (polyAA) with a molecular weight of ∼16 000 were purchased from Sigma-Aldrich. All chemicals were used without further purification. All solutions were prepared using Milli-Q water, and unless otherwise noted, the SFA experiments were performed in a solution of 4.5 mM CaCl2 at pH 4.0 ( 0.2 adjusted with a small amount of HCl and allowed to equilibrate overnight with a small amount of DEEDMAC in order to saturate the solution with surfactant. All solutions used in SFA experiments were deaerated prior to use to prevent bubble nucleation during the experiments. All experiments were carried out at room temperature (23 °C). Cationic bilayers used in the SFA were made by LangmuirBlodgett (LB) deposition of DEEDMAC on mica SFA surfaces. Bilayers were deposited on the mica surfaces in a subphase of 4.5 mM CaCl2 at pH 4. The DEEMAC was spread on the airwater interface of the LB trough and compressed to a surface pressure of 42 mN/m, which corresponds to an area per headgroup of ∼50 A˚2. The mica surfaces were then pulled up through the DEEDMAC film (from the water phase to the air phase) to deposit the inner monolayer and then down (from the air phase to the water phase) to deposit the outer monolayer of the bilayer. The headgroups of DEEDMAC adhere strongly to mica through strong electrostatic interactions (mica has a negative surface charge). The supported bilayers were then transferred underwater into and mounted in the SFA (Figure 1), which was already filled with the solution in which the forces were measured. Care was taken during the transfer of the bilayers from the LB trough to the SFA to prevent them from being exposed to air. The bilayers were allowed to equilibrate in the SFA for 1-2 h to reach thermal equilibrium and allow the DEEDMAC surfactants to adopt an equilibrium area per headgroup (∼55 A˚2). The SFA chamber was prepared for mounting of the surfaces by first passivating the internal stainless steel surfaces with 30% nitric acid solution, then cleaning with chloroform and ethanol before filling with the desired aqueous solution. The force between the bilayers was measured in an SFA 2000 which has been described in detail elsewhere.35,36 Briefly, the technique directly measures the force F, attractive or repulsive, between surfaces with a crossed-cylinder geometry (locally identical to a sphere-sphere or sphere-flat geometry) as a function of the distance D between the surfaces. Mica SFA surfaces are made with uniformly thick mica sheets of approximately 2 cm2, backsilvered with 55 nm of silver, then glued onto cylindrical silica disks with a radius of curvature R ≈ 2 cm. The distance between the surfaces D is measured with an optical technique based on multiple beam interference fringes (fringes of equal chromatic order, FECO) where D is determined from measurements of the wavelength of the FECO fringes in a spectrometer with a resolution of (1 A˚. The distance between the surfaces is controlled with a series of coarse and fine micrometers and piezoelectric crystals. The force between the surfaces is determined by the deflection of a double cantilever spring of stiffness K supporting the lower surface. The force between two cylindrical surfaces as measured in the SFA is directly proportional to the energy between two flat surfaces by the Derjaguin approximation,29 E(D) = F(D)/2πR. Throughout this paper, the distance D = 0 will refer to the distance measured when two bilayer surfaces are pressed together under pressure high enough to cause the surfaces to flatten in contact and will be referred to as bilayer-bilayer contact. Unless otherwise mentioned, the forces were measured using a “quasi-static” technique. The equilibrium forces between the bilayers are measured at any distance after the surfaces have been (35) Israelachvili, J. N.; Adams, G. E. Measurement of Forces between 2 Mica Surfaces in Aqueous-Electrolyte Solutions in Range 0-100 Nm. J. Chem. Soc., Faraday Trans. I 1978, 74, 975-1001. (36) Israelachvili, J.; Min, Y.; Akbulut, M.; Alig, A.; Carver, G.; Greene, G. W.; Kristiansen, K.; Meyer, E.; Pesika, N.; Rosenburg, K.; Zeng, H. Recent advances in the surface forces apparatus (SFA) technique. Rep. Prog. Phys. 2009, 72.
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Figure 2. Measured forces between DEEDMAC bilayers in various CaCl2 solutions at pH 4. Solid lines are DLVO fits using the parameters given in Table 1. given at least 30 s to reach equilibrium at that distance. The surfaces are then quickly moved to a new distance and allowed to equilibrate again for 30 s before the force is measured again. This technique takes longer but gives the most accurate force-distance profile. A “dynamic” technique was used to study the rate effects on the bilayer forces. In these experiments, the surfaces are brought together at a constant velocity, usually between 2 and 20 nm/s, and the force is measured instantaneously at each data point.
Results and Discussion Interactions between Cationic Bilayers in CaCl2 (No Added Polymer). The interaction between DEEDMAC bilayers in salt solutions of 4.5, 9.0, and 27.0 mM CaCl2 are shown in Figure 2. The measured interaction is monotonically repulsive (positive forces or energies) at all distances under these conditions. The forces have been plotted on a semilog scale to emphasize the exponential nature of the repulsive forces, consistent with an electrostatic double-layer repulsion between the cationic bilayers. Strong steric repulsive forces were measured starting at a distance of approximately 2 nm in all experiments, likely due to undulation, protrusion, and/or steric-hydration forces.37,38 The surfaces were pressed together to very high pressures (>100 MPa); however, hemifusion of the bilayers was not observed. The chain melting temperature of DEEDMAC is >50 °C, and so, the bilayers were in the frozen state during these experiments, explaining why hemifusion did not occur even at very high pressures.10 The thickness of the compressed bilayers was determined to be 3.0 ( 0.5 nm by first measuring mica-mica contact before depositing the bilayers, then measuring bilayerbilayer contact after LB deposition of the bilayers. Note that this measurement includes any associated hydration layers at the headgroups of the surfactants, which would be expected at the bilayer-mica interfaces and at the bilayer-bilayer interface. However, under the compressive pressure of the >100 MPa, the thickness of each bilayer would be less than that of the free, unstressed bilayer. A brief description of the specific electrostatic and van der Waals theories for this system will be useful for discussing and interpreting these results, as well as the results of the more complicated systems. The electrostatic interactions for cationic (37) Israelachvili, J. N.; Pashley, R. M. Nature 1983, 306(5940), 249–250. (38) Safinya, C. R.; Roux, D.; Smith, G. S.; Sinha, S. K.; Dimon, P.; Clark, N. A.; Bellocq, A. M. Phys. Rev. Lett. 1986, 57(21), 2718–2721.
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Table 1. Fitting Parameters Used in DLVO Fits to SFA Data in Figures 2 and 3 solution
Debye length, κ-1 fitted surface properties
polyDADMAC [CaCl2] conc. MW measured theoretical potential, (mM) (wt%) (kDa) (nm) (nm) ψ0 (mV) 4.5 0 NA 2.76 2.64 142 9 0 NA 1.91 1.87 120 27 0 NA 1.01 1.08 83 a a 1.82 123 4.5 0.5 50 1.75 a a 1.57 115 4.5 1 50 1.62 a a 1.35 107 4.5 2 50 1.30 a a 1.82 123 4.5 0.5 400 1.75 a Designates κeff-1, ψeff, and σeff as given by eqs 4-6.
charge density, σ (C/m2) 0.088 0.057 0.027 a 0.060 a 0.052 a 0.044 a 0.060
surfaces such as these bilayers in a CaCl2 solution are determined by solving the Poisson-Boltzmann equation.29 For a crossed cylinder geometry as in the SFA (locally identical to a spheresphere or sphere-flat geometry), the interaction is given by FðDÞ kB T 2 zeψ0 expð- KDÞ ð1Þ tanh2 ¼ 128πKεε0 R e 4kB T where κ -1 is the Debye length given by 1=2 εε0 kB T 0:176 -1 K ¼ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nm 6NA ½CaCl2 e2 ½CaCl2
ð2Þ
where ψ0 is the surface potential of the bilayers, R the radius of curvature of the SFA surfaces, z the valence of the counterions, ε0 the permittivity of free space, ε the dielectric constant of water, and [CaCl2] the concentration in mol/L. Note that in this case the Debye length must take into account the divalent Ca2þ ions in solution, but the equation for the force is the standard equation for monovalent electrolyte, since the counterion to the cationic bilayer surfaces is the monovalent anion Cl-. The other half of the DLVO theory is the van der Waals interaction, which is given by the following equation for the interaction between two thin films (bilayers in this case) ! FðDÞ A 1 2 1 ¼ ð3Þ þ R 6 D2 ðD þ HÞ2 ðD þ 2HÞ2 where A is the Hamaker constant, taken to be 8 10-21 J for this system, and H is the thickness of the bilayers. The forces between DEEDMAC bilayers in CaCl2 were fitted with the DLVO interaction (the sum of eqs 1 and 2) shown by the solid lines in Figure 2. The two parameters used to fit the electrostatic part of the DLVO theory are the Debye length, κ-1, and the surface potential ψ0, and the values used for these parameters are given in the first three lines of Table 1. As expected for such a simple system, the DLVO theory fits the experimental data very well. In the conditions of these experiments, the repulsive electrostatic forces dominate the attractive van der Waals forces at distances larger than ∼0.5 nm. Below 0.5 nm, the van der Waals interaction wins out over the double-layer force due to its inverse squared dependence on D as compared to the exponential dependence of the double-layer force. The ζ potentials for DEEDMAC vesicles were measured by Lynch et al.39 at similar salt concentrations; these were smaller than the values obtained for ψ0. The discrepancy is likely due to (39) Lynch, M. L.; Kodger, T.; Weaver, M. R. J. Colloid Interface Sci. 2006, 296(2), 599–607.
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ψ0 appearing in the electrostatic equation in a hyperbolic tangent squared term which is robust over large changes in the value of ψ0, hence contributing large errors to the fits of ψ0, listed in Table 1. Additionally, inherent differences between the definitions and ways of measuring the ζ potential and surface potential ψ0 could add to the discrepancy.40-42 Effect of Cationic Polyelectrolytes on the Electrostatic Interaction. The addition of polyelectrolytes to the solution has a number of effects on the bilayer-bilayer interaction, the most important of which are the effects on electrostatic interactions between the bilayers and the induction of an attractive depletion interaction. We will first consider the effect on the electrostatic interaction. The charges associated with added polyelectrolyte screen the electrostatic force in the same manner as standard electrolytes (e.g., NaCl, CaCl2). Tadmor et al.27 have shown that the electrostatic equations still apply, but take into account the polyelectrolyte by using an effective Debye length and surface potential given by !1=4 Fs -1 K-1 ð4Þ Keff ¼ Fs þ zp Fp and ψeff
!1=2 kB T Fs ln ¼ ψ0 e Fs - zp Fp
ð5Þ
where Fs is the number density of ions in solution excluding polymer counterions, Fp is the number density of polymer in solution, and zp is the number of elementary charges (valence) per polyelectrolyte chain. Similarly, the effective surface charge density can be calculated using a modified Grahame equation given by 1=4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi eψ0 Fs Fs þ zp Fp ð6Þ σeff ¼ 8εε0 kB T sinh 2kB T This type of electrostatic screening is due to the counterions associated with the dissolved polyelectrolyte.27 In this case, the counterions are negative and will be prevalent in the space between the cationic surfaces even if the gap between the surfaces is small enough to exclude the polymer, and hence the theory is valid down to very small distances (
