Direct Measurement of Surface Forces Due to Charging of Solids

Langmuir 2002, 18, 3945-3956

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Direct Measurement of Surface Forces Due to Charging of Solids Immersed in a Nonpolar Liquid Wuge H. Briscoe† and Roger G. Horn* Ian Wark Research Institute, University of South Australia, Mawson Lakes, South Australia 5095, Australia Received November 1, 2001. In Final Form: February 20, 2002 Direct measurements of a long-range force between charged solid surfaces in a nonpolar liquid are presented for the first time. Measurements were made between mica surfaces in solutions of the anionic surfactant sodium di-2-ethylhexylsulfosuccinate (AOT) at millimolar concentrations in n-decane using a surface force apparatus which has been modified to improve its sensitivity for detecting a weak and longrange force. Modifications include a magnetic drive system, the use of a weak cantilever spring with the apparatus mounted in a vertical configuration, and a detailed consideration of the interference optics to allow accurate measurements of surface separations up to several micrometers. The results show a repulsion that is well fitted by theoretical curves based on a model in which only counterions enter the calculation, in other words, in the absence of a reservoir of ions in the solvent. Fitting the theory to the data allows an estimate of the mica surface charge density of ∼1 mC/m2. A mechanism for surface charging of mica in this solution is proposed, which includes a role for trace amounts of water that are inevitably present and adsorbed surface aggregates of AOT. The relevance of the results to previously observed charge stabilization of colloids in nonaqueous solvents is discussed.

1. Introduction The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory1,2 is widely used to explain colloidal stability and other phenomena arising from the charging of particles and surfaces in polar liquids.3,4 In general, surfaces immersed in a polar liquid such as water acquire a surface charge, due to adsorption or desorption of ions or dissociation of surface groups. Ions of opposite sign to the charged surface are dissolved and dispersed in the polar liquid, but an equal amount of charge remains in the proximity of the surface; the surface charge and the diffuse layer of counterions form an electrical double layer. Phenomena associated with the electrical double layer are fundamental to the behavior of surfaces immersed in aqueous solutions or other polar liquids in biological systems, electrochemistry, surface chemistry, and colloid science. Conventionally, the electrical double layer is not thought to be of significance in nonpolar liquids. The reason, elaborated in the next section, is that ions have very low solubility in nonpolar liquids, which means that a diffuse layer of charge cannot readily form. It is easy to follow this with the assumption that surface charging is of no significance for materials in contact with nonpolar liquids. However, the fundamental driving force for surface charging, namely, the difference in electronic properties (e.g., Fermi levels) between two dissimilar dielectric * To whom correspondence should be addressed. E-mail: [email protected]. † Current address: Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, U.K. E-mail: [email protected]. (1) Derjaguin, B. V.; Landau, L. Acta Physicochim. USSR 1941, 14, 633. (2) Verwey, E. W. J.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids: The Interactions of Sol Particles Having an Electric Double Layer; Elsevier: New York, 1948 (Dover Publications: Mineola, NY, 1999). (3) Hunter, R. J. Foundations of Colloid Science, 2nd ed.; Clarendon Press: Oxford, 1986. (4) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991.

materials,5 is still present in this situation. This suggests that in general a double layer should be established, but it is not obvious whether it should remain very thin as it would between two insulating solids6,7 or whether counterions should exist at low concentration in the nonpolar liquid, which means they would form a very thick diffuse layer. Indeed, there is ample evidence of surface charging of materials in contact with nonpolar liquids.8 This phenomenon is of importance in many practical situations including petroleum processing,9 manufacture of organic coating materials,10 various imaging process technologies,11,12 and finely controlled synthesis of particulate materials,13 to name a few. In many of these applications, the charging is facilitated by enhancing the solubility of ions in the nonpolar liquid, which can be achieved by agents such as amphiphilic molecules that can form inverse micelles or crown ethers that can form metal ion complexes.8,9,14-16 Surface charging also seems to be very sensitive to the presence of trace amounts of water in the nonpolar solvent,17-21 and it is difficult to control, or even to quantify, the small concentrations of water that are (5) Lowell, J.; Rose-Innes, A. C. Adv. Phys. 1980, 29, 947. (6) Brennan, W.; Lowell, J.; O’Neill, M. C.; Wilson, M. P. W. J. Phys. D: Appl. Phys. 1992, 25, 1513. (7) Labadz, A. F.; Lowell, J. J. Electrost. 1991, 26, 251. (8) Morrison, I. D. Colloids Surf., A 1993, 71, 1. (9) Klinkenberg, A.; van der Minne, J. L. Electrostatics in the Petroleum Industry: The Prevention of Explosion Hazards; Elsevier: Amsterdam, 1958. (10) Dowbenko, R. Fourth International Conference in Organic Coatings Science and Technology: Proceedings; Technomic: Westport, CT, 1980; p 66. (11) Jenkins, P.; Ralston, J.; Thomas, J. C.; Nicholls, S. L.; Staples, P. E. J. Colloid Interface Sci. 1999, 211, 11. (12) Pearlstine, K.; Page, L.; El-Sayed, L. J. Imaging Sci. Technol. 1991, 35, 55. (13) Arriagada, F. J.; Osseo-Asare, K. J. Colloid Interface Sci. 1995, 170, 8. (14) Lyklema, J. Adv. Colloid Interface Sci. 1968, 2, 65. (15) Parfitt, G. D.; Peacock, J. In Surface and Colloid Science; Matijevic, E., Ed.; Plenum Press: New York, 1978; Vol. 10, Chapter 4, p 163. (16) van der Hoeven, Ph. C.; Lyklema, J. Adv. Colloid Interface Sci. 1992, 42, 205.

10.1021/la015657s CCC: $22.00 © 2002 American Chemical Society Published on Web 04/06/2002

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present even in the most careful laboratory experiments. It is never possible to guarantee that the concentration of water is zero. Much of the evidence for charging of particles and surfaces in nonpolar liquids comes from electrokinetic studies.9,17,19,20,22-30 There is also evidence of colloidal stability of particle suspensions in nonpolar liquids, without the addition of polymeric steric stabilizers. This evidence points toward a stabilizing force of electrostatic or electrosteric origin between the particles which have somehow become charged, but the magnitude and range of this force are unknown. It is also unclear whether the stabilizing force includes a steric contribution from surfactants that are generally present in these systems. Electrostatic stabilization of colloidal dispersions is usually calculated using DLVO theory,1,2 but while this is appropriate for polar solvents such as water, there are serious questions about the use of this theory in nonpolar liquids. The very low concentrations of electrolytes that are possible in such solvents means that the Debye length would be very large, if indeed it makes any sense to speak of a Debye length in these systems. Furthermore, a low surface charge would mean that the total number of counterions in a considerable volume of liquid is so small that the continuum model of charge density on which part of the DLVO theory (the Poisson-Boltzmann equation) is based becomes questionable.31,32 The repulsion between charged particles in a nonpolar liquid is generally reckoned to be weak and long-ranged, but many questions about it remain unanswered. Until now, there has been no direct measurement of long-range forces between charged colloidal particles or between surfaces in nonpolar liquids, which is in contrast to the numerous studies that have been conducted in polar liquids using the surface force apparatus,33,34 atomic force microscope,35,36 and other techniques.37-40 The benefits of (17) McGown, D. N. L.; Parfitt, G. D. Kolloid Z. Z. Polym. 1967, 219, 56. (18) McGown, D. N. L.; Parfitt, G. D. Discuss. Faraday Soc. 1966, 42, 225. (19) Kitahara, A. Prog. Org. Coat. 1973, 2, 81. (20) Kitahara, A.; Karasawa, S.; Yamada, H. J. Colloid Interface Sci. 1967, 25, 490. (21) Malbrel, C. A.; Somasundaran, P. J. Colloid Interface Sci. 1989, 133, 404. (22) Kitahara, A. In Electrical Phenomena at Interfaces. Fundamentals, Measurements, and Applications; Kitahara, A., Watanabe, A., Eds.; Marcel Dekker: New York, 1984; Vol. 15, Chapter 5, p 119. (23) Kornbrekke, R. E.; Morrison, I. D.; Oja, T. Langmuir 1992, 8, 1211. (24) Morrison, I. D.; Thomas, A. G.; Tarnawskyi, C. J. Langmuir 1991, 7, 2847. (25) Tamaribuchi, K.; Smith, M. L. J. Colloid Interface Sci. 1966, 22, 404. (26) Novotny, V. Colloids Surf. 1981, 2, 373. (27) Novotny, V.; Hair, M. L. J. Colloid Interface Sci. 1979, 71, 273. (28) Lewis, K. E.; Parfitt, G. D. Trans. Faraday Soc. 1966, 62, 1652. (29) van Mil, P. J. J. M.; Crommelin, D. J. A.; Wiersema, P. H. J. Colloid Interface Sci. 1984, 98, 61. (30) Fowkes, F. M. In Surface and Interfacial Aspects of Biomedical Polymers; Andrade, J. D., Ed.; Plenum Press: New York, 1985; Vol. 1, Chapter 9, p 337. (31) Osmond, D. W. J. Discuss. Faraday Soc. 1966, 42, 247. (32) Albers, W.; Overbeek, J. Th. G. J. Colloid Sci. 1959, 14, 510. (33) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 975. (34) Pashley, R. M. J. Colloid Interface Sci. 1981, 83, 531. (35) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (36) Cappella, B.; Dietler, G. Surf. Sci. Rep. 1999, 34, 1. (37) Abrikossova, I. I.; Derjaguin, B. V. In Electrical Phenomena and Solid/Liquid Interface; Schulman, J. H., Ed.; Butterworth Scientific: London, 1957; Vol. 3, p 398. (38) Derjaguin, B. V.; Rabinovich, Y. I.; Churaev, N. V. Nature 1978, 272, 313. (39) Peschel, G.; Belouschek, P.; Mu¨ller, M. M.; Mu¨ller, M. R.; Ko¨nig, R. Colloid Polymer Sci. 1982, 260, 444.

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making direct measurements of electrostatic forces in nonpolar liquids would be as follows: (i) the existence of a force would provide further evidence that surfaces under investigation are charged; (ii) the magnitude of the force would give information about the surface charge density; (iii) measurements under different surface and solution conditions can provide valuable clues about the charging mechanisms, as they have done in aqueous systems;34 (iv) the range of force would provide information about the concentration of ionic species in the solution which is otherwise difficult to ascertain; and (v) direct quantification of the repulsive force that stabilizes colloidal dispersions in nonpolar liquids would be obtained, which would allow theoretical models to be tested. This paper reports what are believed to be the first direct measurements of electrostatic forces between surfaces immersed in a nonpolar liquid. In line with previous investigations of charging phenomena in such systems, we add an amphiphilic solute to a nonpolar solvent. Repulsive forces are detected between mica surfaces separated by ∼2 mM solutions of the anionic surfactant sodium di-2-ethylhexylsulfosuccinate (AOT) in n-decane (dielectric constant ) 2.0) with different amounts of water present. AOT is known to form inverse micelles8,41-52 with an aggregation number of 22 ( 2 in decane at concentrations exceeding ∼0.23 mM,49 which probably plays an important role in solubilizing ions in the nonpolar solvent. For reasons alluded to above and discussed further in the following section, the force is weak and long-ranged. The force has been measured with a version of the surface force apparatus (SFA) that was modified to improve its sensitivity, as described in section 3. After the results are presented in section 4, a discussion of a possible surface charging mechanism is given in section 5. 2. Theoretical Considerations A nonpolar liquid is distinguished from a polar liquid by its low dielectric constant r, for example, around 2-4. Since Coulomb attraction is inversely proportional to the dielectric constant of the medium, the electrostatic force binding a cation to an anion in an electrolyte is strengthened by a factor of 20-40 in a nonpolar liquid in comparison to that in water (r ≈ 80). Consequently, the dissociation of electrolyte, and in turn, the ionic concentration and the Debye constant, are greatly reduced, as we will now discuss. An estimate of ionic concentration resulting from electrolyte dissociation can be obtained as follows. (We stress that this calculation is only intended to be illustrative, and its results do not affect the main conclusions of our paper.) Assume that a monovalent electrolyte, A+B-, immersed in a liquid medium characterized by a dielectric constant r undergoes dissociation as described by the (40) Prieve, D. C. Adv. Colloid Interface Sci. 1999, 82, 93. (41) De, T. K.; Maitra, A. Adv. Colloid Interface Sci. 1995, 59, 95. (42) Bergenstahl, B.; Jonsson, A.; Sjoblom, J.; Stenius, P.; Warnheim, T. Prog. Colloid Polymer Sci. 1987, 74, 108. (43) Herrmann, U.; Schelly, Z. A. J. Am. Chem. Soc. 1979, 101, 2665. (44) Ueda, M.; Schelly, Z. A. Langmuir 1989, 5, 1005. (45) Sunamoto, J.; Hamada, T.; Seto, T.; Yamamoto, S. Bull. Chem. Soc. Jpn. 1980, 53, 583. (46) Mukherjee, K.; Mukherjee, D. C. Langmuir 1993, 9, 1727. (47) Valeur, B.; Keh, E. J. Phys. Chem. 1979, 83, 3305. (48) Keh, E.; Valeur, B. J. Colloid Interface Sci. 1981, 79, 465. (49) Kotlarchyk, M.; Huang, J. S.; Chen, S.-H. J. Phys. Chem. 1985, 89, 4382. (50) Assih, T.; Larche´, F.; Delord, P. J. Colloid Interface Sci. 1982, 89, 35. (51) Bergenholtz, J.; Romagnoli, A. A.; Wagner, N. J. Langmuir 1995, 11, 1559. (52) Novotny, V.; Hopper, M. A. J. Electrochem. Soc.: Electrochem. Sci. Technol. 1979, 126, 925.

Surface Forces Due to Charging of Solids

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chemical equilibrium

A+B- S A+ + B-

(1)

Then the dissociation constant KD is defined from the simple mass action law

KD )

[A+][B-] [A+B-]

)

(γ(ci)2 (γ(Rc0)2 ) c0 - ci c0(1 - R)

(2)

where c0 and ci, the electrolyte and ionic concentrations (in M), respectively, are related through the degree of dissociation R,

ci ) Rc0

(3)

which can be obtained from eq 2

KD2 + 4γ(2KDc0 - KD x R)

(4)

2γ(2c0

Here γ( is the Debye-Hu¨ckel activity coefficient53

[

γ( ) exp -

1 e2κ 2 4πr0kBT(1 + κr)

]

(5)

which takes into consideration the screening effect of the surrounding ionic ambience. In eq 5, e is the electronic charge, 0 is the permittivity of the free space, kB is the Boltzmann constant, T is the absolute temperature, r is the ionic diameter or the center-to-center distance between A+ and B-, and κ is the well-known Debye constant, which for a monovalent electrolyte is given by

κ)

x

2000NAcie2 r0kBT

(6)

in which NA is the Avogadro constant. For any given electrolyte concentration c0, ci can be obtained by solving eqs 3-6 numerically, if KD is known. To estimate KD, we turn to the theory of ion pair formation of Fuoss,53 which is a refinement of earlier developments in the theory of electrolyte dissociation54-57 and has been employed in previous studies in nonaqueous systems.8,15,16,58 Fuoss’ theory relates the dissociation constant KD to the ionic diameter r and the dielectric constant of the liquid medium r:

KD )

(

e2 1 3 1 exp 3 1000 (4πr )N 4π0kBT rr A

)

(7)

Figure 1a illustrates the effect of the dielectric constant of the medium on the ionic concentration for a number of electrolyte concentrations with an ionic diameter of 0.5 nm. The ionic concentration plunges as the dielectric constant reaches the nonpolar region, that is, ci < ∼10-9 mol/L, which is comparable to that reported in the literature.19,20,22 The dissociation becomes almost saturated as r exceeds around 13, which compares well with van der Hoeven and Lyklema’s definition16 that a polar (53) Fuoss, R. M. J. Am. Chem. Soc. 1958, 80, 5059. (54) Denison, J. T.; Ramsey, J. B. J. Am. Chem. Soc. 1955, 77, 2615. (55) Fuoss, R. M.; Kraus, C. A. J. Am. Chem. Soc. 1933, 55, 1019. (56) Gilkerson, W. R. J. Chem. Phys. 1956, 25, 1199. (57) Fuoss, R. M. J. Am. Chem. Soc. 1957, 79, 3301. (58) Green, J. H.; Parfitt, G. D. Colloids Surf. 1988, 29, 391.

Figure 1. (a) Ionic concentration and (b) Debye length as a function of the dielectric constant of the medium plotted on a log-log scale for various concentrations of a monovalent electrolyte with an ionic diameter of 0.5 nm. Symbols in (b) have the same meaning as in (a). The ionic concentration is obtained by numerically solving eqs 3-6 using KD calculated from the Fuoss theory, eq 7. As r decreases from the value for water (∼80), the ionic concentration initially stays roughly constant and the Debye length initially decreases according to eq 6. However, at low values of r (j13) ci decreases sharply and the Debye length increases enormously.

liquid has r greater than 11. In addition, as the electrolyte concentration increases, the degree of dissociation decreases although the eventual ionic concentration is higher. Equation 7 also states that the dissociation is dependent upon the size of the ions, with larger ions having reduced electrostatic energy when isolated in the solvent, so that solubility increases with ionic radius. This is the probable reason that surfactants or crown ethers, which can form large structures such as inverse micelles and chelates, have been found to be effective in solubilizing counterions. As illustrated in Figure 1a, the ionic concentration is very low in solvents of low dielectric constant, regardless of the electrolyte concentration, because the degree of dissociation is very small (R ∼ 10-10 at r ) 2). The effect on the Debye length κ-1 is a little more involved. As seen from eq 6, the Debye length is predicted to decrease as r decreases, and indeed this is the case for r > ∼13. However, for smaller dielectric constants the low dissociation becomes the predominant effect, and the consequent low ionic concentration gives rise to increasingly long Debye lengths as the dielectric constant decreases toward 2. This is illustrated in Figure 1b. Given that the ionic concentration would reach very small values, is it appropriate to use the DLVO theory, developed for aqueous media, to calculate forces between charged surfaces in nonpolar liquids? Various authors have attempted to do this, some even going to the extreme

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case of setting the Debye constant equal to zero (i.e., infinite Debye length).11,14,15,17-19,59 As a consequence, the treatment of the aqueous double-layer interaction is inherited. What is not always realized or acknowledged, however, is that setting κ ) 0 is equivalent to neglecting the presence of the ion reservoir in the bulk solution. Since the derivation of the aqueous double-layer theory is based on the assumption that counterions in the double layer are always in equilibrium with an infinite reservoir of ions which have a certain chemical potential, not allowing contact with an ion reservoir will remove the essential thermodynamic foundation of the usual DLVO theory. If the assumption of negligible ion concentration in the bulk liquid is to be followed, the proper approach is to treat the nonpolar solvent as a counterion-only system. In such a model, the only ions present are those which counterbalance the surface charge, and there is no background electrolyte. The counterion-only model has been used to describe various situations in which the concentration of counterions greatly exceeds the concentration of ions in a reservoir or where there is no solvent reservoir present. This applies for example to lamellar phases of charged lipid bilayers,60-62 clay platelets intercalated with water,4,63 and ceramic particles during liquidphase sintering at high temperature where a molten silicate phase may act as an electrolyte.64 In the case of nonpolar liquids, with no more than a miniscule concentration of ions available to form a reservoir in the solution, it also becomes reasonable to argue that a counteriononly model may be the appropriate representation. There are several difficult questions that need to be addressed in a full calculation of the effective force between particles in a colloidal suspension, but a simpler approach can be taken that is sufficient for the interpretation of our experimental data. That is to calculate the interaction free energy between flat plates and invoke the Derjaguin approximation65 to obtain the force between gently curved surfaces. It can be demonstrated that although the force in the nonpolar liquid is very long-ranged, the Derjaguin approximation remains valid for the SFA experiments that we describe below. Simple descriptions of the counterion-only model have been given previously.4,60-62,64,66 These authors have solved the Poisson-Boltzmann equation to find the pressure between flat plates whose surface charge remains constant, independent of their separation. Calculating the interaction free energy is not so straightforward. Furthermore, previous authors have not investigated plates interacting under constant potential or charge regulation conditions. Recently, one of us has, with Attard, conducted a more detailed analysis67 using a method of maximized constrained entropy to calculate interaction free energy between flat plates for different surface conditions. There is no Debye length in this system, since the average concentration of ions is equal to the surface charge per unit area divided by half the surface separation D, so it is not constant. The interaction energy decays like D-1 at large surface separation (consistent (59) Koelmans, H.; Overbeek, Th. G. Discuss. Faraday Soc. 1954, 18, 52. (60) Engstro¨m, S.; Wennerstro¨m, H. J. Phys. Chem. 1978, 82, 2711. (61) Cowley, A. C.; Fuller, N. L.; Rand, R. P.; Parsegian, V. A. Biochemistry 1978, 17, 3163. (62) Wennerstro¨m, H. Prog. Colloid Polymer Sci. 1987, 74, 31. (63) Delville, A.; Laszlo, P. Langmuir 1990, 6, 1289. (64) Clarke, D. R.; Shaw, T. M.; Philipse, A. P.; Horn, R. G. J. Am. Ceram. Soc. 1993, 76, 1201. (65) Derjaguin, B. V. Kolloid-Z. 1934, 69, 936. (66) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet, 2nd ed.; WileyVCH: New York, 1999. (67) Briscoe, W. H.; Attard, P. J. Chem. Phys., submitted.

Briscoe and Horn

Figure 2. (a) The solid curve shows a calculation of the force F between curved surfaces normalized by their radius of curvature R, based on a counterion-only model (ref 67), for a liquid of dielectric constant r ) 2.0. The surface charge density is 1 mC/m2; higher surface charge densities do not give any significant increase in the force. For comparison, the dashed curve shows the force for pure water, calculated using the normal DLVO theory with a numerical solution of the nonlinear Poisson-Boltzmann equation (ref 81), also for a constant surface charge of 1 mC/m2 (corresponding to a surface potential at infinite separation of 203 mV). This is also effectively the maximum possible force, and the ionic concentration used for the calculation, 1 × 10-7 M from the self-dissociation of water, shows the longest possible range that a double-layer force could have in an aqueous solution. (b) The same curves plotted on a log-log scale to highlight the power-law decay of the counteriononly force.

with a recent Monte Carlo study68), rather than exponentially as in the more familiar double-layer system with an ion reservoir. Reference 67 shows that the force calculated between two curved charged surfaces in a nonpolar liquid is indeed weak and long-ranged. The magnitude, as shown in Figure 2, is at least an order of magnitude weaker than the magnitude of a typical electrical double-layer force in water at separations up to 3 µm. At very large separations (>5 µm), the slow decay of the counterion-only force in a nonpolar liquid means it would be stronger than the exponentially decaying doublelayer force in water, but of course both would be extremely weak at that distance (Figure 2b). Calculations of the surface force in a counterion-only system show that the force saturates, as it does in the usual DLVO theory in aqueous liquids, for high surface potentials. There is very little difference in the force calculated for any surface potential above 150 mV. Similarly, the constant charge calculations reach a limiting (68) Meyer, S.; Levitz, P.; Delville, A. J. Phys. Chem. B 2001, 105, 10684.


force at separations greater than 10 nm when the surface charge density exceeds 1 mC/m2. The force plotted in Figure 2 is calculated for this charge density, so it shows the maximum surface force that could be expected between charged surfaces in a nonpolar liquid. Figure 2 serves to illustrate that an electrostatic force between surfaces separated by a nonpolar liquid will be very weak and long-ranged, which sets a considerable challenge for its detection. Direct measurement techniques such as atomic force microscopy (AFM) and the SFA actually measure a change in force with surface separation rather than an absolute force, and when the force is longranged its change with surface separation is small and difficult to isolate from a baseline that must be established. In the following section, we discuss modifications that we have made to an SFA to make it more sensitive to weak forces. 3. Experimental Section 3.1. Modified Surface Force Apparatus. Experiments were conducted using a version of the surface force apparatus that differs from other versions in the following respects: (1) It has a cylindrical geometry with the mechanical axis coincident with the optical axis. This simplifies the machining and reduces unwanted lever-arm motions of surfaces driven by motors that are set on a different axis. (2) The upper surface is moved by a dual motor system with a differential spring, and the lower surface is suspended on a cantilever spring whose deflection measures the surface force. (3) Two Nanomover microstepping motors (Melles Griot, USA) are used for driving the upper surface, allowing computer control and monitoring of the drive position. (4) All components of the optical system for measuring surface separation using fringes of equal chromatic order (FECO) are spatially fixed (lamp, collimating lens, filters, mirrors and prisms, microscope objective, spectrometer) while the SFA is moved bodily using an XYZ translation stage to align the contact position of the surfaces at the focal point of the microscope objective. This adjustment, which ensures correct alignment of the optical path at all times, is simpler than the usual arrangement that can require realignment of several optical components when the focus or centering has to be changed. This apparatus has been used successfully for conventional SFA measurements (for example, the distilled water data included in Figure 9 below) and for measuring forces between a mercury drop and a mica surface, in a variant in which the lower mica surface is replaced by a capillary from which a mercury drop protrudes.69 For the present purpose of measuring weak forces, two different modifications have been made. These were briefly outlined in an initial conference report on this work70 and are described more comprehensively here. To understand why the modifications were necessary, it is helpful first to consider the operation of SFAs in more detail. Force measurements in an SFA rely on detecting the deflection of a cantilever spring on which one of the mica surfaces is mounted. The deflection is found by measuring the change in position of the mica-carrying (proximal) end of the spring (using the FECO) when the other mica surface is moved with respect to the opposite (distal) end of the spring (or vice versa, in previous versions of the SFA) by a precalibrated amount using the drive mechanism. The FECO method always gives an accurate measurement of the position of the end that carries one mica surface, but uncertainties in the deflection, and hence errors in the force, arise when the position of the other (driven) end becomes uncertain. This can occur if, for example, the driving mechanism is nonlinear so that the calibration of the drive loses accuracy or if the calculated position of the driven end of the spring is rendered uncertain by stray movements arising from thermal drift. These are the two main problems which limit the accuracy of force measurement in the SFA in practice and which the present modifications are designed to minimize. (69) Connor, J. N.; Horn, R. G. Langmuir 2001, 17, 7194. (70) Briscoe, W. H.; Horn, R. G. Prog. Colloid Polymer Sci., in press.

Langmuir, Vol. 18, No. 10, 2002 3949 Considering first the effects of thermal drift, the most obvious and most common approach to reducing this problem is to maintain a constant temperature around the apparatus by (a) keeping room temperature constant and (b) enclosing the apparatus in a constant-temperature cabinet. However, since we are concerned with measuring subnanometer positions and deflections, it is not difficult to see that even a very small temperature change can cause drift that is significant on this scale, and in practice temperature changes of tenths of a degree can cause unacceptable errors. The problem is exacerbated if many data points are required so that the measurements take a long time, which will be the case when the forces must be measured over a large range in separation. A sophisticated analysis and design to minimize drift has recently been reported by Heuberger et al.71 Here we do both (a) and (b) above, keeping drift to less than 0.5 nm/min during measurement of a force curve, which typically requires 30-40 min, but we also take a significant additional measure as described below. Forces in the SFA are detected by multiplying the deflection ∆ of a spring by the spring constant k. As described above, the deflection is determined by the difference between the position of the distal end of the spring, z, and the position D of the end carrying one of the mica surfaces. Here both z and D are measured with respect to the opposing mica surface, so that D ) 0 when the two surfaces are in contact and z ) D at large separations where the force is negligible. Thus, when the surfaces are at a separation D the force is

F(D) ) k∆ ) k(D - z)

(8)

Unwanted motion due, for example, to thermal drift leads to an unknown error δz in the drive position. In this case, the force is

F(D) ) k[D - z - δz] ) Fapp(D) - k δz

(9)

where Fapp is the force that the experimenters would calculate from what they erroneously think to be the correct drive position z. Hence, the error in calculating the force from the measured data is

δF(D) ) Fapp(D) - F(D) ) k δz

(10)

In other words, the error is proportional to the spring constant, whereas the force is an inherent part of the system under investigation and is independent of k. This immediately suggests a method of making the force measurements less prone to errors caused by drift: reduce the spring stiffness. If this is done, the spring deflection for a given force will be greater, reducing the relative uncertainty arising from the error δz in the drive position. There is, however, a practical limit to how much the spring stiffness can be reduced. The reason is that in addition to serving as the force-measurement element, the cantilever spring in an SFA (or AFM) serves a second vitally important function: it provides the suspension system for one of the surfaces so that it can move with just one degree of freedom, without friction or hysteresis. Making the spring very weak will also make it too weak to support the weight of the silica disk on which the mica surface is mounted. There are also practical difficulties in handling cantilever springs that are very thin. In our modification, we have used cantilever springs that are half as thick as the usual ones, which reduces k by a factor of 8, and we have overcome the suspension problem by rotating the whole SFA to a vertical spring arrangement in which the disk mounted on the cantilever hangs downward. This is illustrated in Figure 3. In the vertical spring configuration, all optical components external to the SFA remain fixed, as described above, and the apparatus is again moved bodily to align the surfaces at the focal point of a microscope objective. The second modification is to improve the linearity of the drive mechanism controlling z, by using a magnetic drive system similar to that described by Stewart and Christenson.72 A small (71) Heuberger, M.; Zach, M.; Spencer, N. D. Rev. Sci. Instrum. 2000, 71, 4502. (72) Stewart, A. M.; Christenson, H. K. Meas. Sci. Technol. 1990, 1, 1301.

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Figure 3. A diagram of the modified surface force apparatus with the crossed cylindrical mica surfaces approaching along a horizontal axis. This arrangement allows the use of a weak double-cantilever spring (A) to suspend the right-hand surface; the deflection of this spring measures the surface force. A permanent magnet mounted in a capsule (B) close to the righthand surface is driven by passing current through an external coil (C). The left-hand surface is driven by a pair of Nanomover microstepping motors (not shown, for clarity) coupled by a differential spring mechanism to give coarse and fine motion. A container (not shown) within the SFA chamber (D) can contain P2O5 to limit moisture when required. The cradle (E) limits motion of the surface when the apparatus is rotated to the conventional orientation with the cantilever spring horizontal. White light is directed through the surfaces and focused by an objective lens (not shown) onto the entrance slit of a spectrometer; fringes of equal chromatic order measured at the exit port allow the separation between the mica surfaces to be calculated. The SFA is mounted on a base plate (F) which can be moved on three axes with respect to the fixed optical path and objective to allow appropriate centering and focusing. permanent magnet is sealed in a poly(tetrafluoroethylene) capsule and fixed close to the disk at the end of the cantilever (Figure 3). The magnet is a disk of neodymium iron boride, 4.75 mm diameter and 1.5 mm thick, with remanence approximately 1 T, supplied by Graham Handling Equipment Pty. Ltd. (Adelaide, Australia). A coil is attached to the exterior of the SFA chamber, and a dc current through the coil applies a force to the permanent magnet which, acting against the restoring force of the cantilever spring, moves it through a distance that is proportional to the current. Current is supplied by a laser diode driver (LDD5005, Newport, USA) whose range is 500 mA and maximum resolution is 7.6 µA. The coil has two windings: one with 822 turns giving relatively coarse movement and one with 57 turns for fine movement. Details of the design are given in ref 73. Calibration of the spring constants and the motion provided by the magnetic drive is achieved as follows. First, a normal pair of SFA cantilever springs is calibrated by resting the mounting block at one end of the spring on the plate of an electronic balance and attaching the other end of the spring via a rigid rod to a translation carriage driven by a Nanomover motor. Results of this procedure are shown in Figure 4a. Second, the movement in response to a current through the coil of a mica surface mounted on this spring is measured using FECO. This is repeated for the second coil winding and then for the weak spring assembly, as shown in Figure 4b. The ratios of the gradients dz/dI (where I is the current in the coil) give the ratio between the two coil windings (which is measured as 14.3 compared to a nominal 822/57 ) 14.4) and the ratio of the spring constants of the normal and weak springs (7.74 compared to a nominal 8). Results of the calibrations are summarized in Table 1. The linearity of the drive (73) Briscoe, W. H. Ph.D. Thesis, The University of South Australia, Adelaide, South Australia, Australia, 2001.

Briscoe and Horn

Figure 4. (a) Calibration of a set of “normal” (0.1 mm thick) cantilever springs to be used to calibrate the magnetic drive mechanism. The inserted picture shows schematically the experimental setup for the calibration, in which a set of normal springs are connected to a Nanomover rigidly through a rod and are mounted on a plate that is placed on a microbalance. The open symbols in the figure are from three different calibration runs, with the microbalance reading plotted as a function of the Nanomover displacement. The solid lines are the respective linear regressions. If it is assumed that the spring deflection is equivalent to the Nanomover displacement, the spring constant is given by the slope of the plot, which yields an average value of 170.7 N/m over three runs. (b) Calibrations of the spring deflections for the weak (0.05 mm thick) springs driven by the magnet coil using the coarse winding (Nc ) 822) (open symbols) and the fine winding (Nc ) 57) (filled symbols) and for the normal spring using the coarse coil (+). The solid lines are the linear regressions, and all of the runs are carried out in decane. The slopes have ratios of 7.74 between the normal and soft springs, hence giving a spring constant of 22.1 N/m for the weak spring, and a ratio of 14.3 between the coarse and fine coil windings. Calibration data, including linearity, are summarized in Table 1. (with the weak spring and coarse coil) is better than 0.15% over a range of 34 µm, and with the fine coil it is 0.3% over a range of 2.4 µm. The specified resolution in current, when applied through the fine coil, gives a resolution in the drive using the weak springs of 0.04 nm which is equivalent to a force of 0.8 nN, or F/R ) 0.4 µN/m with R ) 2 cm. In practice, however, the best resolution obtained in force measurements would still be limited by the uncertainty δz due to thermal drift as discussed above. 3.2. FECO Calculations. In making these calibrations and, more significantly, in making accurate measurements of spring deflections at large separations, it is very important to have an accurate calculation of the surface separation from the measured FECO wavelengths. This can be done using the expressions given


Langmuir, Vol. 18, No. 10, 2002 3951

Table 1. Summary of Specifications and Calibration Results for the Magnetic Drive System Employing Two Coil Windings and Two Possible Spring Stiffnesses coil winding

number of turns in coil dual cantilever spring spring thickness (mm) calibrated spring stiffness k (N/m) magnetic drive dz/dI (nm/mA) magnetic drive dF/dI (µN/mA) maximum range (500 mA) in z (µm) maximum range (500 mA) in F (µN) maximum range in F/R (mN/m) nominal resolution (7.6 µA) in z (nm) nominal resolution (7.6 µA) in F (nN)a nominal resolution in F/R (µN/m)a linearity (as % of range)

“coarse” drive

“fine” drive

822 normal weak 0.10 0.05 171 22.1 8.85 68.5 1.51 1.51 4.4 34 760 760 38 38 0.067 0.52 12 12 0.58 0.58 0.20% 0.15%

57 normal weak 0.10 0.05 171 22.1 0.617 4.79 0.105 0.105 0.31 2.4 53 53 2.6 2.6 0.0047 0.036 0.80 0.80 0.04 0.04 0.15% 0.29%

a

The range and resolution in F/R are given for a typical radius R in the SFA of 2 cm. In practice, the resolution in measuring F or F/R is limited by uncertainties in measuring spring deflection (see text).

by Horn and Smith,74 but only if the thickness of the two mica sheets is determined precisely. This requires an unequivocal determination of the harmonic order of the FECO fringe being used, which in turn requires detailed knowledge of the phase shift that occurs on reflection at a mica-silver interface. Considerable effort has gone into establishing this phase shift,75 finding the unexpected result that it must be positive, not negative as is commonly assumed. An interesting consequence of this is that the correct assignment of fringe orders differs by one from that conventionally used, so that fringes that have hitherto been designated as “odd-order” are in fact of even order, and vice versa.76 (Note however that the misassignment does not invalidate distance calculations in previous SFA experiments.) 3.3. Solution Preparation and Procedures. Measurements were conducted in solutions of AOT in decane. AOT (99%) was purchased from Sigma and used without further purification. Decane (99+%), obtained from Aldrich, was distilled under nitrogen in the presence of molecular sieves (BDH, type 4 Å, 1/16 in. pellets) immediately before use, and the distillation was carried out in a laminar flow hood. Distilled decane was directly collected into a Pyrex collecting bottle fitted with an O-ring (Teflon-coated Viton)-sealed Teflon plug, through a plumbing path consisting of Kel-F tubing and Omnifit valves. All subsequent transfer of decane and injection into the SFA chamber were undertaken with gastight Hamilton syringes, where all the necessary connections in the plumbing path were implemented with Omnifit valves and tubing. Force measurements were performed at 26 ( 0.02 °C. Mica surfaces were initially brought into contact in air, and then decane vapor was introduced into the chamber so that it condensed between the surfaces before they were separated (this was to avoid possible damage due to shearing of the surfaces during separation from strongly adhesive contact in air when using the weak springs). The 75 mL chamber was then filled with decane, and the surface force was measured to confirm cleanliness. An oscillatory force law was detected at separations less than 3 nm, in agreement with previous reports.77 An aliquot of AOT stock solution was then injected to bring the concentration in the chamber to the desired level, and force measurements were made after an equilibration time of at least 3 h. All surface separations are reported with respect to the contact position measured in air. 3.4. Water Content. Experiments were conducted at three different levels of dissolved water in the decane-AOT solution. In the first, which we call “dry”, the water level was minimized by keeping the decane as dry as possible during its distillation as described above. Karl Fischer titration measured a water (74) Horn, R. G.; Smith, D. T. Appl. Opt. 1991, 30, 59. (75) Briscoe, W. H.; Horn, R. G. In preparation. (76) Briscoe, W. H.; Horn, R. G. In preparation. (77) Christenson, H. K.; Gruen, D. W. R.; Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1987, 87, 1834.

Figure 5. Force F measured as a function of separation D between mica surfaces of mean radius R ) 1.6 cm immersed in n-decane with 2.2 mM AOT, after the solution has been exposed to ambient moisture (relative humidity 57%). Separation is measured with respect to mica-mica contact in air. The force, presented as F/R and plotted on a log scale, is very weak and long-ranged. Different symbols are from different force runs. The surfaces encounter a steep repulsion as they come to some 7 nm apart (shown in more detail in Figure 8). The solid and dotted curves are the theoretical predictions from counterion-only theory (ref 67), assuming a constant surface charge density of 1 × 10-3 C/m2 and constant potential of 100 mV, respectively. content of 32 ppm in the decane after distillation, but this measurement cannot be relied upon as an accurate figure for the water content of the solution in the SFA for two reasons: first, water would inevitably have been introduced into the chamber with the AOT, since the water content was higher in the hygroscopic AOT stock solution; and second, the Karl Fischer measurement could not be made without brief exposure to air. An open vessel of P2O5 is included in the sealed SFA chamber so that water was absorbed from the vapor space above the solution. In the second, “ambient” level, the solution was exposed to normal air throughout the experiment by leaving open an inlet hole covered by a 0.45 µm filter. The relative humidity in the laboratory was 57%, so the amount of water dissolved in the nonpolar liquid should be 57% of the saturation level of 72 ppm; that is, a water concentration of 41 ppm could be expected in the decane. However, with water likely to be found in the core of the AOT inverse micelles the overall water content would be higher than this. The third level is “wet”, in which excess water is placed in the bottom of the SFA chamber so that the liquid is saturated with water.

4. Results Initial force measurements were made in pure decane to confirm previous results of a short-range oscillatory force77 and no detectable long-range force. The oscillatory force was only measurable when the decane was dry. Following addition of 2.2 mM AOT to the decane, the force measured in ambient moisture conditions is shown in Figure 5. It is clear that there is a measurable repulsive force across the nonpolar liquid in the presence of AOT and trace water. The force is about an order of magnitude weaker than the double-layer force measured in distilled water (see Figure 9 below), and it is very long-ranged, being measurable to separations beyond 300 nm. At short range, the expected van der Waals attraction is not observed; a repulsive barrier is dominant at about 7 nm. This will be discussed shortly. Also shown in Figure 5 are two theoretical curves calculated for the counterion-only model67 under conditions of constant surface charge (1 mC/m2) and constant surface potential (100 mV). The curves fit the data well. These

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Figure 6. The force measured in 2.2 mM AOT (open symbols) and 31 mM AOT (filled squares) in decane which is kept as dry as possible, with P2O5 present in the SFA chamber throughout the measurements. The solid curves are the theoretically calculated forces from the counterion-only theory, assuming a constant charge density of 5 × 10-6 and 3 × 10-6 C/m2 for the top and the bottom curves, respectively. At separations less than about 15 nm, a repulsion due to adsorbed AOT overcomes the van der Waals attraction expected at short range.

curves are close to the theoretical maximum, and so even though they fit the data, this really only establishes a lower bound for the surface charge density. A higher value, for example, 10 mC/m2, would fit just as well. The force measured under dry conditions is shown in Figure 6. In this case, the force is even weaker (2 orders of magnitude less than a typical force in water), but despite the scatter in the data there is still clearly a repulsion present. Again the repulsion is very long-ranged, and again there is a repulsion at short range that prevents van der Waals attraction from pulling the mica surfaces into contact. The figure includes data measured at a higher AOT concentration of 31 mM. Within the experimental scatter, the long-range force does not appear to be significantly different between the two AOT concentrations. There is a difference at short range that will be discussed with Figure 8 below. The solid curves included in Figure 6 are from the counterion-only theory for surface charge values of 3 and 5 µC/m2. The fit to the data is less convincing than in Figure 5, but nevertheless the data are consistent with this model and this range of values for the surface charge density. When excess water is present, the repulsion, shown in Figure 7 (for the slightly higher AOT concentration of 2.6 mM), is comparable in magnitude to that measured in ambient moisture (Figure 5). However, close inspection of the data shows that it decays a little more quickly. In this case, the normal double-layer theory with a Debye length of 68 nm gives a better fit to the data than the counterion-only theory. This is consistent with the presence of a background 1:1 electrolyte concentration of 5 × 10-7 M in a liquid of dielectric constant 2. It is known that AOT forms inverse micelles in decane with an aggregation number of 22.49 From the concentration of AOT, we can estimate that if one micelle in every hundred carried a single anion or cation in its core, the ionic strength of the solution would be around 5 × 10-7 M, consistent with the above Debye length. The surface charge required to fit the data is 1 mC/m2, corresponding to a surface potential of 300 mV. Once again, the force is near the upper theoretical limit and so these figures are not established very precisely, but they set a reasonable lower bound. The short-range force in the presence of excess water is again repulsive, and no van der Waals attraction is

Briscoe and Horn

Figure 7. Force measured between two mica surfaces immersed in 2.6 mM AOT decane solution in the water-saturated condition, with 2.5 mL of excess water in the SFA chamber. Different symbols represent different measurements. The top dotted curve is the theoretical prediction from the counteriononly double-layer theory assuming a constant surface charge density of 1 × 10-3 C/m2. The solid curves are calculated from the normal double-layer theory using the Chan-Pashley-White algorithm (ref 81), assuming a constant surface density of 1 × 10-3 C/m2. The curve with a steeper slope has a 1:1 ionic concentration of 1 × 10-6 M, and the other, of 5 × 10-7 M, corresponding to Debye lengths of 48 and 68 nm, respectively, in the nonpolar liquid. Curves calculated for a constant surface potential of 300 mV are virtually indistinguishable from the constant-charge curves. A strong repulsion occurs at separations less than 15 nm.

seen. Figure 8 shows the short-range forces measured under all conditions on an expanded distance scale. The presence of a short-range repulsion indicates that there is a steric or electrosteric barrier that prevents van der Waals forces from pulling the mica surfaces into intimate contact. In pure decane77 and in pure water,34 there is no such repulsion at separations greater than 2 nm, so the barrier must be due to AOT that is adsorbed to the mica in some form and which is not removed by the mild pressure corresponding to the maximum force applied in these experiments. Since the length of an AOT molecule is 1.1-1.2 nm and the steric barriers are found at surface separations up to 10 nm, the adsorbate cannot be a simple monolayer, so it is presumed to be in the form of aggregates. The presence of surfactant monolayers or bilayers on mica surfaces is generally manifested as barriers occurring at specific separations corresponding to two monolayers or two bilayers that are generally the appropriate integer multiple of the molecular length.78-80 Since this is not the case here, it is more likely that the aggregates are in the form of inverse micelles or hemimicelles that are globular rather than lamellar in shape. It is also possible that the adsorbate is in the form of a monolayer of AOT atop a thin layer of water at the mica surface, although we do not favor this picture. In general, the layer thickness increases with the amount of water present, indicating that the surface aggregates include some water and that they swell in size and/or grow in number with increasing water content. At high water content in particular, the steric barrier is distinctly “soft” (decreasing in thickness by ∼50% as the force is increased from 0.06 to 1.2 mN/m), indicating that the aggregates are not completely rigid but are somewhat (78) Christenson, H. K. J. Phys. Chem. 1986, 90, 4. (79) Gee, M. L.; Israelachvili, J. N. J. Chem. Soc., Faraday Trans. 1990, 86, 4049. (80) Horn, R. G. Biochim. Biophys. Acta 1984, 778, 224.


Langmuir, Vol. 18, No. 10, 2002 3953

Figure 8. Combined data from Figure 5 ((0) 2.2 mM, ambient moisture), Figure 6 ((2) 2.2 mM, dry; (4) 31 mM, dry), and Figure 7 ((×) 2.6 mM, excess water) highlighting the repulsive forces measured at short range in AOT solutions in decane under various conditions. All separations D are measured with respect to mica-mica contact in air. The solid lines are all theoretical fits to the data sets calculated for a nonpolar liquid with r ) 2 and constant surface charge density. From the top, they are as follows: counterion-only theory, 1 × 10-3 C/m2; DLVO theory, 1 × 10-3 C/m2 and electrolyte concentration of 5 × 10-7 M; counterion-only theory, 3 × 10-6 C/m2. The presence of a repulsive force that masks the mica-mica van der Waals attraction indicates adsorption of AOT to mica, and the fact that repulsion is observed at separations larger than twice the length of an AOT molecule (∼1.1 nm) indicates that the adsorbed AOT must be in the form of multilayers or aggregates. Despite the observed repulsion, weak adhesive forces (not shown) between the adsorbed layers are measured when the surfaces are pulled apart. The adhesive forces are summarized in Table 2. Table 2. Adhesive Forces Measured for Different Solutions and Water Contents liquid and experimental conditions (symbols in Figure 8)

separation from which jump-out occurs (nm)

pull-off force F/R (mN/m)

AOT in decane; dry (4, 2) AOT in decane; ambient moisture (0) AOT in decane; excess water (b) decane water

6.7 ( 0.3 10.4 ( 0.4 9.6 ( 1.5 ∼0 0

0.36 ( 0.5 0.92 ( 0.4 2.2 ( 0.2 ∼200 ∼700

compressible. The steric barrier is thinnest at a higher AOT concentration under the dry condition. This may be explained by a competition for water between surface aggregates and inverse micelles in the bulk solution. AOT is known to be very hygroscopic, and so when present at a higher concentration it may be effective in pulling water away from the mica surface and reducing the size of the surface aggregates. While the steric barriers shown in Figure 8 prevent mica-mica contact, they do not entirely eliminate adhesion between the surfaces. There are still small but measurable pull-off forces occurring from aggregateaggregate contact that demonstrate the presence of a weak adhesion between the surfaces with the adsorbed aggregates. The values are summarized in Table 2. The adhesion could be attributed to aggregates which bridge between the surfaces or to van der Waals attraction which, because the mica surfaces remain comparably far apart, is dominated by the attraction between the aggregates themselves. We favor the latter explanation, first, due to the small magnitude of the adhesion, and second, because it increases with increasing water content in the ag-

Figure 9. Combined data from Figures 5-7 to summarize the long-range forces measured under various conditions. Symbols have the same meaning as in Figure 8. Also included are data measured in distilled water (O) to highlight the fact that the forces in AOT solutions are more than an order of magnitude weaker at separations from 20 to 200 nm. The solid lines are all theoretical fits to the data sets. Curve 1: DLVO theory for water with a constant surface potential of 155 mV and an electrolyte concentration of 1.5 × 10-5 M. Curve 2: counteriononly theory for nonpolar solvent, 1 × 10-3 C/m2. Curve 3: counterion-only theory for nonpolar solvent, 3 × 10-6 C/m2. Curve 4: DLVO theory for nonpolar solvent, 1 × 10-3 C/m2 and electrolyte concentration of 5 × 10-7 M.

gregates. This would increase the van der Waals attraction because it would increase the dielectric contrast between the aggregates and the intervening medium of decane. 5. Discussion Our results, collected together in Figure 9, clearly show the presence of a long-range repulsion between mica surfaces immersed in solutions of AOT in decane. For comparison, Figure 9 also includes the double-layer force measured in distilled water and the relevant fit to this data set using DLVO theory based on a solution of the nonlinear Poisson-Boltzmann equation.81 Experimentalists familiar with SFA or AFM measurements will know that it is not easy to obtain a good measurement of the double-layer repulsion in water, because its gentle decay out to large separations makes it difficult in practice to distinguish the force from the baseline and, in particular, to locate the separation at which this distinction is possible, that is, the separation at which a nonzero force becomes identifiable. As seen in Figure 9, the forces in the nonpolar liquid are at least an order of magnitude weaker than those in water over the range 20-200 nm, and in fact (although it is not visible in Figure 9) the decay of these forces is even slower than it is in water. Despite the experimental difficulties posed for the detection of such a weak and long-ranged force, apparent in the significant scatter in the data for F/R < 0.01 mN/m, our measurements clearly show that a repulsion is present. We ascribe the repulsion to a force of electrostatic origin between mica surfaces which have evidently become charged in the presence of the AOT-in-decane solution. Our reasons for this are twofold: first, the data fit theoretical calculations (also shown in Figure 9) of the force that would be expected in a solvent of low dielectric constant, either in the case of no background electrolyte (81) Chan, D. Y. C.; Pashley, R. M.; White, L. R. J. Colloid Interface Sci. 1980, 77, 283.

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(curves 2 and 4 for the ambient moisture and dry conditions, respectively) or in the presence of a small concentration of electrolyte (curve 3, when excess water is present). As pointed out in the preceding section, the background electrolyte concentration of some 5 × 10-7 M would be accounted for if only ∼1% of the AOT inverse micelles carried an ion, which is plausible. Pellenq et al.82 have shown that under certain conditions an attractive ion correlation force can be expected in low dielectric constant liquids, but there is no indication of this in our data, probably because the surface charge density is too small. The second reason to believe that an electrostatic force exists comes from separate measurements which give evidence that mica surfaces are charged in this solution. The evidence is from phase analysis light scattering (PALS) measurements83 of the mobility of ground mica particles of size ∼1 µm suspended in a 2 mM solution of AOT in decane, exposed to ambient moisture. Mica particles displayed a small but detectable mobility, of the order of a few times 10-10 m2/Vs, and the sign of the net charge of the particles is negative. In preparing for these measurements, it was also observed that dispersions of mica particles in distilled decane were not stable, whereas when AOT was added to the solution it was possible to obtain a dispersion that was stable for at least a few days. The short-range forces plotted in Figure 8 give evidence of adsorption of AOT to mica from a decane solution. Further evidence is obtained from Fourier transform infrared measurements showing that the AOT concentration in a supernatant solution is reduced from that in the original solution after suspension and subsequent separation by centrifugation of mica particles. While these measurements were not quantitative, they do give clear evidence of AOT adsorption to mica. (Note that adsorption occurring in the low-surface-area system of the SFA would reduce the bulk surfactant concentration by less than 1 part in 104.) Collectively, these results indicate that the mica surfaces are negatively charged, with AOT playing a role in the charging process. Furthermore, the different force curves measured at similar AOT concentrations but with differing amounts of water present (Figure 9) demonstrate that water also plays a role in determining the magnitude of the surface charge. We now offer a model for a possible charging mechanism in this system. The model is consistent with all of the above observations. AOT forms inverse micelles in decane, almost certainly with water present in the core of the micelle. As noted in the Introduction, one can never say that a nonpolar liquid is perfectly dry, and there is probably always a small amount of water present no matter what measures are taken to remove it. It is conceivable that in addition to being present in the bulk solvent, trace amounts of water accumulate at the hydrophilic mica surface84 even when the decane is “dry”. As we suggested in discussing the short-range repulsive force in the previous section, formation of surface aggregates, probably inverse micelles or hemimicelles, will occur even under dry conditions. Under ambient or higher moisture conditions, the amount of water present close to the mica surface will increase (see Figure 8). This provides an environment for the hydration of potassium ions from the mica surface. Since (82) Pellenq, R. J.-M.; Caillol, J. M.; Delville, A. J. Phys. Chem. B 1997, 101, 8584. (83) Miller, J. F.; Schatzel, K.; Vincent, B. J. Colloid Interface Sci. 1991, 143, 532. Keir, R. I.; Suparno; Thomas, J. C. Langmuir 2002, 18, 1463. (84) Christenson, H. K.; Blom, C. E. J. Chem. Phys. 1987, 86, 419.

Briscoe and Horn

water surrounding a potassium ion reduces its electrostatic attraction to the negative lattice charge of mica, the potassium ions may then be able to dissolve in the core of the surface aggregates. Micelles can exchange contents, including ions, when they collide in solution.46,85-88 It is not unreasonable to suppose that the same thing could occur if a micelle collides with a surface aggregate, allowing a potassium ion to enter the core of a bulk inverse micelle. This mechanism would result in the solubilization of potassium ions in the decane solution, leaving the mica with a net negative charge. Fowkes89-93 has previously suggested a surface charging model involving adsorption of an acidic polymeric dispersant to a basic surface site (or vice versa), followed by proton transfer and subsequent desorption of the charged species, but he did not suggest a role of aggregates, nor of aggregate collisions, in the charging mechanism. In the presence of excess water, the bulk micelles may contain a large enough aqueous core that dissociation of AOT becomes possible. Subsequent micellar collisions may result in the ions becoming separated, so that individual micelles exist with both positive and negative charges, resulting in an electrolyte solution being formed in the decane. Dissociated AOT ions would only have to exist in 1% of the micelles to account for the Debye length that is seen in Figure 7. Future force measurements with nonionic surfactants and wetting studies of water in the presence of surfactant solutions in nonpolar liquids could cast further light on the proposed charging mechanism. There is an interesting question about deciding when the background electrolyte concentration in a liquid is small enough to be neglected, so that there is no Debye length and the counterion-only model is the appropriate one to describe the force between surfaces and other colloidal behavior. In addition to solubility of ions, the question is one about the relative size of the solvent reservoir compared to the number of colloidal particles, or more precisely, the ratio of chargeable surface area to volume of solvent. The counterion-only model assumes a high area-to-volume ratio so that there is no significant reservoir of ions and the only ones present are those that have dissociated from the surface; the infinite-reservoir model used in usual DLVO calculations assumes that the number of counterions required to compensate for the total surface charge does not significantly augment or deplete the concentration of ions in the reservoir. These are limiting cases valid for a small reservoir and a large reservoir, respectively. A rule-of-thumb estimate for the crossover between counterion-only and infinite-reservoir behavior can be obtained by comparing the net concentration cQ of ions that compensate the total surface charge (i.e., the counterions) with the bulk concentration of background (85) Eicke, H.-F. Top. Curr. Chem. 1980, 87, 85. (86) Eicke, H.-F.; Shepherd, J. C. W.; Steinemann, A. J. Colloid Interface Sci. 1976, 56, 168. (87) Eicke, H.-F.; Christen, H. Helv. Chim. Acta 1974, 61, 2258. (88) Rharbi, Y.; Winnik, M. A. Adv. Colloid Interface Sci. 2001, 8990, 25. (89) Fowkes, F. M. In Solvent Properties of Surfactant Solutions; Shinoda, K., Ed.; Marcel Dekker: New York, 1967; Vol. 2, Chapter 3, p 65. (90) Fowkes, F. M.; Jinnai, H.; Mostafa, M. A.; Anderson, F. W.; Moore, R. J. Colloids and Surfaces in Reprographics Technology; American Chemical Society: Washington, DC, 1982; p 307. (91) Pugh, R. J.; Matsunaga, T.; Fowkes, F. M. Colloids Surf. 1983, 7, 183. (92) Pugh, R. J.; Fowkes, F. M. Colloids Surf. 1984, 9, 33. (93) Fowkes, F. M.; Pugh, R. J. Polymer Adsorption and Dispersion Stability; ACS Symposium Series No. 240; American Chemical Society: Washington, DC, 1984; p 331.


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electrolyte ci. The former is given by

cQ )

nQ σA ) V FV

(11)

in which nQ is the number of moles of (monovalent) counterions required to balance the total charge of an area A of surface with charge density σ, F ) NAe is the Faraday constant, and V is the volume of solvent (in liters). When cQ . ci, the counterion-only model is appropriate, and when cQ , ci the usual infinite-reservoir model is valid. The crossover regime cQ ∼ ci is a difficult one that as far as we know has not been addressed in any theoretical calculations of the osmotic pressure between plates or the force between particles. Applying eq 11 to our experiment, if we assume that for reasons of electroneutrality all the counterions stay in the region between the mica surfaces which has a volume of the order of 0.05 mL, a surface charge density of 1 mC/ m2 on the mica surfaces would give a net counterion concentration of some 4 × 10-8 M. When the ionic concentration in the remainder of the SFA is significantly less than this, then the counterion-only model should be appropriate. In our SFA experiment, it appears that when the AOT/decane solution is in contact with excess water, there is a background ionic strength of around 5 × 10-7 M, and the usual DLVO theory is appropriate, with the corresponding Debye length of 68 nm. This is consistent with the above estimate of a crossover concentration. With less water present, under the ambient condition, the counterion-only model fits the data (Figure 5), indicating that the background ionic strength of the solution in these conditions is ∼10-8 M or less. (We remark however that a DLVO fit with an ionic strength of ∼10-8 M may also be possible within the experimental scatter.) A similar question arises when considering how to evaluate the colloidal stability of a dispersion of particles in a nonpolar solvent. Our demonstration of a repulsive force in such a system is consistent with previous evidence of colloidal stability which has been inferred to arise from charge stabilization.17,18,28,91 As discussed by previous authors,8,14,15,22,94 the force in this system is expected to be long-ranged compared with typical double-layer forces in aqueous solvents, and the concentration of counterions in the solution is rather low. Such expectations are borne out by our results. This raises questions about the validity of using DLVO theory to calculate the force between particles and the stability of a colloidal dispersion.31,59 In a system in which the osmotic pressure of counterions plays a crucial role and yet there is no reservoir of electrolyte, it would be more sensible to approach the calculation of colloid stability not by considering pairwise interactions between particles but by considering an ensemble of charged particles in a liquid containing the appropriate number of counterions for overall electroneutrality. The statistical mechanics of systems such as this has been addressed by several authors in the context of concentrated aqueous colloids in which the number of counterions can be a significant fraction of the total number of ions in the solution.95-97 In this situation, the phase behavior of the system will depend on the particle concentration, in a way that the usual theory of colloid (94) van der Hoeven, Ph. C. Ph.D. Thesis, van de Landbouwuniversiteit te Wageningen, Wageningen, The Netherlands, 1991. (95) van Roij, R.; Dijkstra, M.; Hansen, J. P. Phys. Rev. Lett. 1997, 79, 3082. (96) van Roij, R.; Dijkstra, M.; Hansen, J. P. Phys. Rev. E 1999, 59, 2010. (97) Chan, D. Y. C. Phys. Rev. E 2001, 63, 061806/1.

stability does not. Calculations of the potential of mean force must presumably incorporate the dielectric constant so that the model becomes relevant to particles dispersed at a lower concentration in nonpolar liquids than in polar liquids. Finally, it is worth making a small comment on the nomenclature for the repulsive force we have reported. It is clear that the counterion-only model gives a good description of the force measured under dry and ambient moisture conditions, although the force measured in the wet condition is more consistent with the presence of background electrolyte in the decane. In the latter case (and in aqueous solutions), the force can be considered as arising from an increase in free energy when the diffuse double layers of two surfaces overlap, and so it is very reasonably called a double-layer repulsion. However, when there is no background electrolyte, the counterions from an isolated surface extend indefinitely into the solution: one cannot speak of a double layer because the diffuse region (in which the distribution of counterions is nonuniform) would have a thickness limited only by the size of the container. When there are two parallel charged plates in the counterion-only case, the counterions spread out to occupy all of the space between the plates. One cannot say that the “double layers overlap” because there are no definable double layers of the individual surfaces even at infinite separation. For this reason, we have consciously avoided using the term “double-layer force” in the title and throughout this report. The calculation of the force67 is made by working out the additional osmotic pressure due to the counterions between the plates after the counterion distribution has been optimized to minimize the total free energy for a given surface separation and boundary condition of the charged surfaces, just as it is in the usual DLVO calculation.3 But to call this an “osmotic force” would fail to capture the essential fact that it exists only because the surfaces are charged. On the other hand, as has been noted by previous authors,3,4,66 if one ignores the osmotic term and considers only the electrostatic force between charged surfaces with counterions between them, the result is actually attractive, so the observed repulsion should not be designated as “electrostatic”. It is tempting to suggest “electro-osmotic” force but there is a risk of creating confusion with the electro-osmotic effect. 6. Conclusion In this paper, we have presented the first direct measurements of repulsive forces due to the charging of solid surfaces immersed in a nonpolar liquid. The force is, as anticipated for a solvent with low dielectric constant, weak and long-ranged. This posed challenges for its measurement, which were met by making modifications to a surface force apparatus, including a detailed consideration of using FECO to allow accurate measurements of surface separations up to the micrometer range. Results measured between mica surfaces in a millimolar solution of AOT in decane that was kept as dry as experimentally possible (which we acknowledge is not perfectly dry) and also in a solution exposed to atmospheric moisture were consistent with the force calculated from a counterion-only model. In the former case, the charge density is 3-5 × 10-6 C/m2; in the latter, it is at least 1 × 10-3 C/m2. When the solution was exposed to excess water, the measured force was consistent with a normal double-layer repulsion with the same surface charge density (1 × 10-3 C/m2) and a Debye length corresponding to a low ionic strength of 5 × 10-7 M, which would be

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obtained if about 1% of the AOT inverse micelles carried a sulfosuccinate or sodium ion from dissociation of AOT. A mechanism for charging of the mica surfaces has been suggested that is consistent with all of the observations, including the presence of a short-range repulsive force due to adsorbed aggregates of AOT. It is implicitly demonstrated that force measurements in other solvents could provide a means of exploring charging mechanisms in a wider range of systems and of estimating the concentration of ions that may be present in those solvents. Detection of a long-range repulsive force is consistent with previous observations of charge stabilization of particle dispersions in nonaqueous liquids. Our measurements provide the first concrete data on which to base

Briscoe and Horn

considerations of colloidal stability and electrokinetic effects in nonpolar solvents. Acknowledgment. We acknowledge financial support from the Australian Research Council and the Ian Wark Research Institute. PALS measurements were kindly carried out by Roland Keir and Kathryn Hanton at the University of South Australia, and Jason Connor assisted with image analysis of FECO. Phil Attard is thanked for many helpful discussions, as are Fredrik Tiberg, Iain Dunlop, Simon Titmuss, Olga Vinogradova, and Lucy Wang for their comments on the manuscript. LA015657S

Direct Measurement of Surface Forces Due to Charging of Solids

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