Double Layer Relaxation Measurements Using Atomic Force

Jun 23, 1999 - In water the measured transient forces as a function of the tip/substrate distance show a relaxation time of ∼1.1 ms when the tip is ...
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© Copyright 1999 American Chemical Society

JULY 20, 1999 VOLUME 15, NUMBER 15

Double Layer Relaxation Measurements Using Atomic Force Microscopy O. Teschke,* E. F. de Souza, and G. Ceotto Nano-structure Laboratory, Instituto de Fisica, Universidade Estadual de Campinas, 13081-970, Campinas SP, Brazil Received July 8, 1998. In Final Form: May 24, 1999 The force acting on the tip during its immersion in the double layer region was measured for various tip-approaching velocities. The double layer electric field acting on the tip results in a repulsive force component when the tip is immersed in the diffuse layer corresponding to a region far away from the liquid/solid interface (∼100 nm) and an attraction when it is immersed in the near-surface layer (∼2 nm). For higher values than 10 µm/s (in water), the transient force on the tip results from the interaction of two double layers (Si3N4 tip and mica substrate) with their charge distribution in a nonequilibrium situation. In the inner layer, the thickness of the interaction region as well as the force on the tip decrease with an increasing approaching speed while in the diffuse layer there is a force increase with an approaching velocity. Dimethyl sulfoxide shows only a repulsive force, indicating that the attraction in the near-surface layer in water is associated with a variable water dielectric constant at the liquid/solid interface. In water the measured transient forces as a function of the tip/substrate distance show a relaxation time of ∼1.1 ms when the tip is immersed in the inner layer while the diffuse layer shows a relaxation time of ∼5.6 ms. The measured diffuse layer relaxation time for dimethyl sulfoxide is ∼0.5 ms.

Double layer phenomena play a crucial role in subjects ranging from the colloidal stability to ion partitioning at biological membranes and also form the basis of electrochemical processes. The charge and potential distributions within the double layer depend on the physical and chemical interactions of the electrolyte ions with the charged solid surface.1-3 In most studies of colloidal particle interaction, the dependence of the electrical repulsion force on interparticle separation is considered to be time-invariant. However, when the time scale of the double layer relaxation is comparable to the time scale of the interaction dynamics, the electrical repulsion force acting on a particle will vary with time and the history of its encounter.4 The major source of this phenomenon is believed to stem from the redistribution of charged species within the electrical double layer.5 Thus, the (1) Bowden, J. W.; Bolland, M. D. A.; Posner, A. M.; Quick, J. P. Nature Phys. Sci. 1973, 81, 245. (2) Dugger, D. L.; Stanton, J. H.; Irby, B. N.; McConnell, B. L.; Cummings, W. W.; Maatman, R. W. J. Phys. Chem. 1964, 68, 757. (3) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480. (4) Weaver, D. W.; Feke, D. L. J. Colloid Interface Sci. 1985, 103, 267. (5) Frens, G.; Overbeek, J. T. G. J. Colloid Interface Sci. 1972, 38, 376.

interaction of the colloid particles with each other or with a substrate is a dynamic phenomenon in which charge relaxation may be important, as shown by some studies of reversible aggregation,6,7 filtration,8,9 and chromatography.10,11 Therefore, much experimental evidence indicates that the interaction potential between colloidal particles has some dynamic behavior as shown in this letter. Recently, Feke4,12 studied the effect of double layer relaxation on the interaction of colloidal particles approaching at constant speed. Although considerable advances have been made in our understanding of the influence of double layers on physical and chemical systems, direct measurements of the structure and forces residing at this interface are difficult to perform. It is inherently difficult to measure forces acting (6) Weise, G. R.; Healy, T. W. Trans. Faraday Soc. 1970, 66, 480. (7) Long, J. A.; Osmond, D. W.; Vincent, B. J. Colloid Interface Sci. 1973, 42, 545. (8) Spielman, L. A.; Friedlander, S. K. J. Colloid Interface Sci. 1974, 44, 22. (9) Prieve, D. C.; Ruckenstein, E. J. Colloid Interface Sci. 1976, 57, 547. (10) Small, H. J. Colloid Interface Sci. 1974, 48, 147. (11) DiMarzio, E. A.; Guttman, C. M. J. Polym. Sci. 1968, 137, 276. (12) Mandralis, Z. I.; Wernet, J. H.; Feke, D. L. J. Colloid Interface Sci. 1996, 182, 26.

10.1021/la980843s CCC: $18.00 © 1999 American Chemical Society Published on Web 06/23/1999

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between colloidal particles in situ, primarily because of the submicrometer size of the particles and the small magnitude of the forces.13 As a result, techniques to measure such forces directly have employed macroscopic surfaces held at nanometer separations.14 The surface force apparatus, for example, has successfully measured a variety of forces including van der Waals and double layer forces,15 solvation forces,16 steric repulsion,17 and adhesion forces.18 Although the distances between interacting surfaces are in the range typically encountered in colloidal systems, measurements are only possible for macroscopic bodies.13 Observe that the radius of curvature of the cylinders is at least 4 orders of magnitude larger than that of the typical colloidal particle. Moreover, the measurements are always performed in equilibrium conditions and the dynamic forces cannot be measured. As a result, the surface force apparatus cannot simulate the dynamic behavior of colloidal particles. In this paper, we present a simple method to study the dynamics of the electrical relaxation in a colloidal particle and a substrate interaction when they are subjected to a constant approaching velocity. More specifically, we will show that the interaction between mica surfaces and Si3N4 tips with a ∼50 Å radius at the end of a 18° half-angle cone results in a force on the tip that is a function of the approximation velocity. In our experiments, a commercial AFM instrument, TopoMetrix TMX 2000, was used where the movement of the cantilever was detected by the conventional deflection sensor using a four-quadrant detector enabling vertical as well as lateral force measurements. A special cell was built to perform observations in liquid media.19,20 The cell is made of Teflon and the sample is fixed at its bottom. It is moved in the x, y, and z directions with respect to a stationary tip. The laser beam enters and leaves the cell through a glass plate and thus does not cross the airliquid interface, which is usually curved. The top confining surface of the solution in the cell is far removed from the cantilever beam. In this geometry, the displaced liquid follows a path that is perpendicular to the cantilever beam. We have obtained the best results in these measurements with very soft cantilevers, typically ∼0.02 nN/nm (Microlever, type B, Park). The instrument was calibrated and the measured spring constant in air (0.023 nN/nm) was found to agree with that specified by the cantilever manufacturer (0.02 nN/nm). Water (Milli-Q Plus quality, resistivity ) 10 MΩ/cm) was introduced into the cell after the freshly cleaved mica was mounted on the xyz translator of the AFM. The experiments were made at a temperature of 20 °C. The measurements were performed using different scanners (1 and 7 µm range) and the results averaged. The dimethyl sulfoxide (DMSO) used in these experiments was obtained from Merck (analytical grade). When the mica basal plane is placed within the liquid, the mechanism for the formation of the double layer is (13) Flicker, S. G.; Tipa, J. L.; Bike, S. G. J. Colloid Interface Sci. 1993, 158, 317. (14) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975. (15) Israelachvili, J. N. Faraday Discuss. Chem. Soc. 1978, 65, 20. (16) Christenson, H. K. J. Chem. Soc., Faraday Trans. 1 1984, 80, 1933. (17) Israelachvili, J. N.; Tirrel, M.; Klein, J.; Almog, Y. Macromolecules 1984, 17, 204. (18) McGuiggan, P. M.; Israelachvili, J. N. J. Mater. Res. 1990, 5, 2232. (19) Teschke, O.; Douglas, R. A.; Prolla, T. A. Appl. Phys. Lett. 1997, 70, 1977. (20) Sassaki, R. M.; Douglas, R. A.; Kleinke, M. U.; Teschke, O. J. Vac. Sci. Technol. B 1996, 14, 432.

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assumed to be the dissolution of K+ ions as well as ion exchanging of K+ by H+ or H3O+ ions. It should be noted that the K+ ions initially held on the mica surface in the high-resistivity water (10 MΩ/m, ∼5 × 10-6 M 1:1 electrolyte at pH = 6) should be at least partially H3O+ ion-exchanged. Considering that the solvent volume of the cell was 300 µL and the mica-exposed area was 1.13 cm2, if all K+ ions on the mica surface were exchanged into solution, the K+ concentration would be about 8.3 × 10-8 M, almost 2 orders smaller than the calculated concentration of the H3O+ present in the solution. The charge residing within the double layer has the same net magnitude but the opposite sign of the charge present at the mica surface. The ζ potential at the macroscopic mica surface-water interface, measured using the planeinterface technique in the presence of KCl 10-3 M, was found to be ∼125 mV within the pH range from 5 to 6.21 The surface of silicon nitride tips in aqueous solution is composed of amphoteric silanol and basic silylamine [secondary (silazane, -Si2NH2) and possibly primary (silylamine, -SiNH3) amines though the latter is rapidly hydrolyzed] surface groups.22,23 At pH ∼ 6, with no added electrolyte, the silicon nitride surface is either zwitterionic (zero net charge) or slightly negatively charged;24 consequently, we assumed that the surface charge density in the tip σTip , σMica. The analysis of the force acting on the cantilever is as follows: One side of the cantilever is gold-covered; therefore, there is a charge difference between the cantilever surfaces, which may cause cantilever deformation or deflection. However, this deflection is present throughout the duration of the approach and adds to the baseline force. The influence of the cantilever charge on the measured force variation during the tip approach to the surface is negligible since the Debye’s length of mica immersed in Milli-Q water is around 100 nm and the tip height is ∼3 µm; therefore, only the tip is immersed in the mica double layer region. Supertips used in this experiments are sharpened pyramidal tips (total height ∼3 µm) with a 18° angle and ∼100 nm height apex; consequently, the main interaction region of the tip/cantilever with the mica double layer is the sharpened pyramidal region of the tip and the force variation measured by the AFM during the tip immersion in the mica surface double layer is the force experienced by the tip. The time-dependent force acting on the tip was determined by the measuring force vs tip-sample separation curves for various tip/substrate approaching speeds. When force vs tip-sample separation curves are generated, the cantilever support is maintained at a fixed position in the image scanning plane and the sample is moved along the perpendicular direction (z axis), thus moving alternately toward and away from the tip. The force vs distance curves reveal the forces on the AFM tip interacting with the sample surface in the presence of the liquid. Figure 1 shows three force vs separation curves for different approaching speeds using a Si3N4 tip and a mica surface immersed in water (only the approach to the surface is shown). A point to be observed is that there is a cantilever deflection contribution due to the surface proximity ∼100 nm before the tip touches the surface for measurements performed in Milli-Q water. This repulsive force has previously been (21) Nishimura, S.; Tateyama, H.; Tsunematsu, K.; Jinnai, K. J. Colloid Interface Sci. 1992, 152, 359. (22) Bergstrom, L.; Bostedt, E. Colloids Surf. A 1990, 49, 183. (23) Harane, D. L.; Bousse, L. J.; Shott, J. D.; Meindl, J. D. IEEE Trans. Electron Devices 1987, 34, 1700. (24) Drummond, C. J.; Senden, T. J. Colloids Surf. A 1994, 87, 217.

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Figure 1. Force vs separation curves for Si3N4 tips and mica samples immersed in water for various relative tip/substrate velocities: (a) 0.1 µm/s; (b) 5 µm/s; (c) 150 µm/s. The full line corresponds to the fitting of the data to two exponential functions Ae-2x/R - Be-2x/β corresponding to the force acting on the diffuse layer and inner layer, respectively.

Figure 2. Force vs separation curve for Si3N4 tips and mica samples immersed in DMSO for 0.1 µm/s relative tip/substrate velocity. The full line corresponds to the fitting of the data to the function Ae-2x/R and the dashed line to the region where the substrate and tip are in contact.

reported;25 however, the time-dependence component is first reported in this paper. This repulsive force component is followed by attraction when the tip is immersed in a region ∼2 nm close to the surface. The repulsive force described above, when the tip was approaching the surface was not detected for 1 M KCl or 1 M NaCl solutions (κ-1 = 0.30 nm, where the κ is the Debye-Huckel parameter), indicating that this repulsive force is not derived from thin film viscosity, neither from thin film compression effects nor from hydration forces. For 0.1 M KCl and 0.1 M NaCl solutions (κ-1 = 0.95 nm), the force acts on the tip at much smaller distances away from the mica surface than that measured within Milli-Q water (κ-1 = 134.6 nm). This indicates that the measured repulsion force is the result of the presence of a double layer. To investigate other solvent effects in the double layer region, we have also measured the force vs distance curves for DMSO, which has received considerable attention as a solvent, mainly because it is an example of a solvent with higher polarity than water. A typical force vs distance curve is shown in Figure 2; observe that there is no jump onto the surface, which is present in the water-measured curves. For Si3N4 tips, approaching mica surfaces immersed in Milli-Q water or DMSO, the forces were detected when (25) Sokolov, Y.; Henderson, G. S.; Wicks, F. J.; Ozin, G. A. Appl. Phys. Lett. 1997, 70, 844.

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the tip and mica surface diffuse layers interacted (∼100 nm in water). The charge distribution in the diffuse layers was assumed relaxed. This is correct for velocities up to 10 µm/s where a tip substrate time-independent force was measured (see Figure 3a). As the tip interacts with the substrate, the electrical fields and the diffuse layers surrounding both the tip and substrate are distorted from the equilibrium configuration they had before the encounter began. Since both the tip and the substrate are insulators and consequently have a very long charge relaxation time, charges in the solution partially neutralize the polarization charges at the tip/electrolyte/substrate interaction region; we then claim that the time constant involved in the process is the double layer relaxation time. The equilibrium electrostatic force on the tip was derived on the basis of the following principle: it is energetically favorable for a surface charge to be surrounded by a medium with a large dielectric constant like water. If the tip approaches the double layer region, it replaces the water, and since the tip material has a lower dielectric constant26,27 than water, the configuration becomes energetically unfavorable. Consequently, the tip is repelled by the double layer electric field. To estimate the size of this exchange repulsion force, we assumed for a measured double layer width that the energy change involved in the immersion of the sharpened pyramidal-shaped tip inside the double layer is given by the product of the immersed tip volume times the dielectric constant variation and times the square of the electric displacement vector (D).27,28 The energy is written as a function of D since the charge distribution is assumed constant. The displacement vector is assumed to have an exponential spatial dependence D(x) ) D0 e-κx, where κ is the Debye’s length. The change in the electric energy involved in the exchange of the dielectric constant of the double layer by that of the tip is calculated by integrating the energy expression over the tip-immersed volume in the double layer region and the force is given by the gradient of this energy as a function of the distance tip/substrate. The force has then a functional dependence on the Debye’s length (F ∝ e-2κx).27 Consequently, the repulsive and attractive force measured components as a function of the relative tip/sample approach velocity were fitted to two exponential functions Ae-2x/R - Be-2x/β. The best fitting values for the force on the tip in water as a function of approaching velocities are plotted in Figure 3. The repulsive force amplitude (A) is plotted in Figure 3a. It is possible to observe that, for scanning speeds up to 10 µm/ s, this repulsive force amplitude is constant (∼0.26 nN) and then it increases to ∼0.34 nN at 200 µm/s. This force increase is then large enough to influence AFM imaging.26 Figure 3b shows the exponential coefficient (R) which corresponds to the Debye’s length measured, for various scanning speeds. It is possible to observe that its value (∼82 nm) is unchanged with approaching velocity, within the experimental error. Figure 3c shows that the amplitude of the attractive force (B) in the inner surface region decreases as a function of the scanning speed from ∼0.18 nN at low scanning speeds down to ∼0.10 nN at ∼200 µm/s. Finally, Figure 3d shows that the screening length of the inner layer (β) increases with approaching speeds from ∼1.4 nm, at low scanning speeds, up to 7.0 nm, at high scanning speeds (∼200 µm/s). (26) Teschke, O.; Souza, E. F. Rev. Sci. Instrum. 1998, 69, 3588. (27) Teschke, O.; Souza, E. F. Appl. Phys. Lett. 1998, 71, 3588. (28) Becker, R. Electromagnetic and Interactions; Dover: New York, 1964.

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Figure 3. The parameter corresponding to the fitting of the data shown in Figure 1 to two exponential functions vs scanning speed: (a) repulsive force amplitude; (b) Debye’s length; (c) attractive force amplitude; (d) inner-layer width. The dotted line is drawn to guide the eye.

Attractive components shown near point O in Figure l for water is not present for solvents such as DMSO (see Figure 2); therefore, we assumed that the presence of the repulsive force followed by an attractive part close to the surface on the neutral tip in the double layer region is associated with the variable water dielectric constant at the liquid/solid interface. Several estimates have been given in the literature for the value of the dielectric constant as a function of the distance to the liquid/solid interface in the electric double layer. Bockris and Reddly29 suggest that, for a fully oriented primary water layer, the dielectric constant is about 6, as compared to a bulk value of 78. A decrease in the repulsion near the surface is obtained when the tip is immersed in the region of lower dielectric permittivity than the tip dielectric permittivity of the water bulk. The model of a variable dielectric constant explains the force profile measured when the tip gets close to the liquid/mica interface.27 The force transient time when the tip is immersed in the diffuse layer is calculated by means of force vs distance curves using the repulsive component. The amplitude of this force (Figure 3a) shows a region of constant value (∼0.26 nN) followed by an increase at ∼10 µm/s and then stabilization at ∼100 µm/s. The diffuse layer measured width is constant and approximately equal to 82 nm for all measured velocities, as shown in Figure 3b. If we consider the point where the force has increased to half of its maximum value, we obtain a relaxation time of ∼5.6 ms by ratio of the Debye’s length (Figure 3b) and this velocity value. Figure 4 shows a plot of the maximum repulsive force vs relative tip/substrate velocity for mica samples immersed in DMSO. Since the curve does not show a leveling (29) Bockris, J.; Reddy, A. Modern Electrochemistry; Plenum: New York, 1970.

Figure 4. The maximum repulsive force vs relative tip/ substrate velocity for Si3N4 tips and mica samples immersed in DMSO corresponding to the force amplitude A in the expression Ae-2x/R. The dotted line is drawn to guide the eye.

off of the amplitude at a high approaching speed, probably because it takes place at higher approaching speeds than our AFM can generate, we calculated the force relaxation time (τ) arbitrarily for an approaching speed of 140 µm/s and the corresponding diffuse layer width of ∼65 nm which results in a relaxation time of ∼0.5 ms. The transient time when the tip is immersed in the double layer inner region is calculated using the attractive component of the force vs distance curves for various approaching velocities. The amplitude of the force (Figure 3c) shows a region of constant value and a sharp decrease at approximately 10 µm/s. For an inner layer width of ∼2.6 nm and an approaching speed of 2.3 µm/s, which correspond to the point where the force has decreased to half of its maximum value, we obtain a relaxation time of ∼1.1 ms. The measured relaxation times for water diffuse and inner layers are in agreement with the

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previously published measurements of the low-frequency dielectric dispersion of the double layer around colloidal particles.30 The low-frequency dispersion components (corresponding to large values of τ) are generated by the polarization of the diffuse part of the double layer and the contribution of the region with bound counterions is at its maximum at higher frequencies (low values of τ). The results presented in this article show two relaxation time constants: one for the tip immersed in the diffuse double layer (∼5.6 ms) and a second when it is immersed in the inner layer (∼1.1 ms). These values tell us that the polarization that is responsible for the observed inner layer force relaxes much faster than that for the diffuse double layer. In other words, the near double layer can be viewed as being at equilibrium with its surroundings, 5 times faster than the diffuse layer, which indicates that different mechanisms are involved in these relaxations. Since the tip displacement results in a compression of the liquid in the region between the tip and substrate, the effect of the hydrodynamics of the flow has to be considered. For low tip/substrate approaching velocities, the double layer is relaxed and the hydrodynamics of the flow can be ignored.30 For high velocities, however, the diffuse double layer is not fully relaxed during the tip/substrate approach and this effect has to be considered rather than the hydrodynamic flow on the mechanism of the slipping process. The effect of the slipping process is clearly shown in the inner layer measurements where a variation of the inner layer length at high approaching speeds was registered (see Figure 3d). However, the measurements of Debye’s length as a function of the approaching tip/ substrate velocity show an invariance with approaching speed, indicating that the diffuse layer is less affected by the slipping process. The variation of the diffuse double layer relaxation time for water and DMSO is associated with their different interactions: when solutes are ionic, ion-ion interactions, both of the electrostatic and the structural types are important in the double layer region. The solvation energy

of the ion enters into consideration because the ion must shield its solvation shell on the side facing the charged surface before coming into contact with it. Therefore, the change from water to a nonaqueous solvent can affect several properties, which determine the structure of the double layer.31 DMSO ( ) 46.6) can act as an electron donor, causing strong association with cations and therefore producing lower mobilities. On the other hand, the nucleophilic property of the sulfur atom hinders any strong interaction between anions and solvent molecules, resulting in the cations being less mobile in DMSO than the anions. The values of τ measured for water (∼5.6 ms) and DMSO (∼0.5 ms), with very different solvent-ion interactions present double layer relaxation times varying by 1 order of magnitude. In conclusion, it was experimentally shown that as the tip gets close to the liquid/substrate interface, a timedependent force associated with the double layer was measured. The repulsive force component on the tip is independent of the scanning velocity, for low approaching speeds. For a higher approaching tip/substrate velocity than 10 µm/s in water, the repulsive force when the tip approaches the surface shows a relaxation time of ∼1.1 ms for the inner layer while a ∼5.6 ms repulsive force relaxation time was measured for the diffuse layer. DMSO shows a diffuse double layer relaxation time of ∼0.5 ms. Force vs distance curves measured for various approaching speeds were shown to be a method of measuring physical characteristics (double layer length, force intensity variation on an immersed tip and relaxation time) of both the inner and diffuse layers formed in mica immersed in water.

(30) Lyklema, J.; Dukhin, S. S.; Shilov, V. N. J. Electroanal. Chem. 1983, 1, 143.

(31) Popovich, O.; Tomkins, R. P. T. Nonaqueous Solution Chemistry; John Wiley: New York, 1981.

Acknowledgment. The authors thank J. R. Castro and L. O. Bonugli for technical assistance. This work was supported by the CNPq grant 523.268/95-5. E. F. Souza would like to thank FAPESP 95/9354 for support. LA980843S