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A Hydrodynamic Atomic Force Microscopy Flow Cell for the Quantitative Measurement of Interfacial Kinetics: The Aqueous Dissolution of Salicylic Acid and Calcium Carbonate Barry A. Coles,* Richard G. Compton, Marco Sua´rez, Jonathan Booth, Qi Hong, and Giles H. W. Sanders Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QZ U.K. Received July 29, 1997. In Final Form: October 27, 1997X A novel liquid flow cell allows atomic force microscopy (AFM) images to be obtained under defined hydrodynamic flow conditions, enabling reaction fluxes calculated from proposed heterogeneous reaction mechanisms to be compared with those determined experimentally. The cell employs an inclined jet to direct a fluid flow at the sample surface to cover the area under investigation including the AFM scanning cantilever tip. The flow pattern and velocity were calculated by using the finite element fluid dynamics program FIDAP and confirmed by placing an electrode at the sample position and measuring the limiting current for the one-electron oxidation of potassium hexacyanoferrate(II) in water as a function of flow rate. The operation of the cell has been further confirmed by the direct measurement of the dissolution rate of calcite exposed to a flow of 0.98 mM aqueous HCl by deducing the rate of removal of the surface from the change of the z-piezo voltage. The rate constant k1 ) 0.035 cm s-1 obtained for the dissolution step was in excellent agreement with the value (0.043 ( 0.015) cm s-1 found from independent channel flow cell experiments. The dissolution of the (1 h 10) and (110) faces of salicylic acid (SA) single crystals in water and in solutions of salicylic acid was studied as a function of flow rate and was found to be consistent with a model combining a constant rate of dissolution with a simultaneous reprecipitation having a first-order dependence on [SA]0, with the flux J ) kd - kp[SA]0 where the parameters are k1dh 10 ) 3 × 10-9 mol cm-2 s-1 and k1ph 10 ) 1.74 × 10-4 cm s-1 for the (1h 10) face and k110 ) 1.5 × 10-8 mol cm-2 s-1 and k110 ) 1.06 d p × 10-3 cm s-1 for the (110) face.
Introduction Reacting surfaces have been studied by atomic force microscopy (AFM), for example by Hansma et al.1 who observed that steps on a calcite surface moved laterally as dissolution proceeded under an aqueous solution. While this approach can identify features such as steps or etch pits which contribute to the dissolution process, it remains essentially qualitative since the transport conditions are not defined. No attempts have been reported in which a chemical model of a complex interfacial reaction has been related to a quantitative measurement of the reaction flux; this would require defined hydrodynamics and mass transport so that the space and time variations of concentrations close to the surface can be modeled. Defined hydrodynamic conditions allow more information to be obtained, as has been demonstrated by measurements in channel flow cells2,3 in which solution passed along a rectangular channel and a solid substrate formed part of one wall, with laminar flow conditions applying. An electrode flush with the wall and immediately downstream of the solid surface monitored the reaction electrochemically. The flow pattern in a channel is known, and this enabled it to be shown, for example, that the reaction between H+ and calcite2 was a first-order Abstract published in Advance ACS Abstracts, December 15, 1997. X
(1) Hillner, P. E.; Manne, S.; Gratz, A. J.; Hansma, P. K. Ultramicroscopy 1992, 42, 1387. (2) Compton, R. G.; Unwin, P. R. Philos. Trans. R. Soc. London 1990, A330, 1. (3) Tam, K. Y.; Compton, R. G.; Atherton, J. H.; Brennan, C. M.; Docherty, R. J. Am. Chem. Soc. 1996, 118, 4419.
heterogeneous reaction of H+. However, insertion of a scanning probe into a channel in order to make a simultaneous observation of the changes in surface topography or a direct physical measurement of the rate of surface dissolution would invalidate the analytic expression for flow velocities, and therefore, the particular advantage of using a channel geometry would be lost. In this paper4 we report the development of a novel flow cell, which allows AFM images to be obtained in the presence of a flowing liquid and allows the flow pattern to be calculated, and the application of the flow cell to the study of the dissolution processes of salicylic acid and calcite. It is of importance both to the manufacturer and to the administrator of pharmaceutical products to understand the fundamental factors which influence the rate of dissolution of drugs. Most researchers have satisfactorily explained their data on the basis of the Nernst-Brunner two-film model of diffusion-controlled kinetics.5 It is assumed that an effective liquid film exists between the surface of the solid and the stirred bulk solution. At the solid-film interface, the film is saturated with the compound. The diffusion of the compound through this film is solely responsible for the rate of dissolution. Linear concentration gradients are assumed to exist for all species (4) A preliminary account of some of this work was published in: Coles, B. A.; Compton, R. G.; Booth, J.; Hong, Q.; Sanders, G. H. W. J. Chem. Soc., Chem. Commun. 1997, 619. (5) Higuchi, W. I.; Parrott, E. L.; Wurster, D. E.; Higuchi, T. J. Am. Pharm. Assoc., Sci. Ed. 1958, 47, 376. (6) Hamlin, W. E.; Northam, J. I.; Wagner, J. G. J. Pharm. Sci. 1965, 54, 1651. (7) Collett, J. H.; Rees J. A.; Dickinson, N. A. J. Pharm. Pharmacol. 1972, 24, 724. (8) Vinograd, J. R.; McBain, J. M. J. Am. Chem. Soc. 1941, 63, 2008.
S0743-7463(97)00843-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/06/1998
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in the film. It is clear that this picture neglects the effects of the ion and base strength of the medium, the diffusivities of the reaction products, and the properties of surfaces. In the Noyes-Whitney model9 the relationship between the dissolution flux J mol cm-2 s-1 and the saturation solubility CS of a compound is expressed by the equation
J ) KA(CS - C)
(1)
where K is a constant, A is the surface area of the dissolving solid, and C is the concentration of the dissolution medium. According to the Nernst-Brunner diffusion layer model, the outermost layer of the solid dissolves instantaneously into a thin layer of solvent to form a saturated solution, and the transfer of the dissolved compound to the bulk solution occurs by the diffusion of the molecules through this layer. If h is the diffusion layer thickness and D is the diffusion coefficient of the solute in this layer, then K ) D/h, and therefore eq 1 may be rewritten
J ) (DA/h)(CS - C)
(2)
Under sink conditions where CS . C and if A is kept constant, eq 2 reduces to
J/ACS ) D/h
(3)
This equation is obeyed well6 in a nonreactive medium where the diffusion coefficient of the compound remains relatively constant and the compound does not undergo any chemical change such as ionization, complexation, or degradation. Collet and co-workers7 suggested, on the basis of a study of the dissolution rate of salicylic acid, that the change in the diffusion coefficient with respect to the pH is responsible for deviation from the NoyesWhitney equation. The two primary factors affecting the diffusion of the strong and weak electrolytes over this wide range of concentrations are the mobilities of the ions and the extent of dissociation, the latter modified by the activity coefficient and other secondary factors.8 Moreover, the diffusion of a given ion may depart from its true value depending upon the electrical gradient produced by the buffers or other ions. On the other hand, several authors5 have postulated that the self-buffering action and the pH in the diffusion layer formed in the dissolution process of organic salts and acids are more important factors than the pH of the bulk solution and the diffusion coefficient variation,9 and therefore, the dissolution rates of organic acids should remain unchanged or only change slightly when the pH of the bulk solution changes. With the AFM flow cell, we can study the dissolution process directly on the crystal surface and deduce the kinetics and mechanism of this process. Cell Design Initial designs tested were aimed at retaining a channel geometry which was modified to allow a probe to be inserted with a minimal and calculable perturbation of the flow pattern. In practice these proved difficult to set up and use, so an alternative approach of development from a standard liquid cell accessory was chosen. The Topometrix10 Discoverer liquid immersion cell meets the requirement of being a fully enclosed cell, but the inlet and outlet ports are positioned tangentially at the sides of an irregular volume so that the flow in the vicinity of the scanning cantilever is unpredictable. Our design is (9) Serajuddin, A. T. M.; Jarowski, C. I. J. Pharm. Sci. 1985, 74, 148. (10) Topometrix Corporation, Santa Clara, CA.
Figure 1. (a) Top view of the Topometrix sample cell showing the new inlet duct. (b) Perspective view of the jet and AFM cantilever (not to scale).
based on the standard cell which we have extended by the addition of a new inlet port so that solution can be delivered through a small 1/2 mm square stainless steel duct directly to the front of the cantilever chip. The liquid jet is aligned parallel to the front of the cantilever support chip and transverse to the cantilever (Figure 1a) and inclined down toward the surface (Figure 1b). At the end of the duct, the underside is cut back and polished flat, and this surface is positioned so as to be 20 µm above the sample surface when sample contact with the AFM scanning tip is established. After leaving the duct, the flow is not confined except by the sample below and the cantilever chip to one side, giving a complex flow pattern which is not amenable to an analytic solution. Such flows can, however, be simulated using computational fluid dynamics programs. The flow field was calculated by two-dimensional simulations, and experimental data was obtained to demonstrate the validity of this design. Initial studies using the FLOTRAN11 and subsequently FIDAP12 simulation programs showed that a satisfactory flow field could be set up using an inclined jet. For the duct geometry employed, it was confirmed that over the full range of flow rates a stagnation point would exist below the jet, with a small fraction of the solution flowing backward under the lower edge of the duct. All of the solution reaching the scanned area of the sample will therefore be fresh solution originating from the jet, which is an essential requirement for full characterization; there will be no (11) FLOTRAN, Ansys Inc., Houston, PA, 1992. (12) FIDAP, FDI Inc., Evanston, IL, 1995.
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Figure 2. The element mesh used for the calcite dissolution simulation.
mixture or entrainment of the surrounding bulk solution. Tests of the cell under flow conditions using a calibration microgrid confirmed that AFM images could be obtained without detectable deterioration of image quality up to the highest flow rates used, which corresponded to peak flow velocities at the exit of the jet of 20 cm s-1, with a Reynolds number Re ≈ 40 in the jet tube. Theory Flow Simulation. FIDAP is a proprietary fluid dynamics program which uses the finite element method to simulate fluid flows in steady-state or transient conditions, including the effects of temperature and the presence of chemical species. In the finite element method, the flow region is divided into elements connected to each other at nodes. The equations of conservation of momentum, mass, and energy are solved for each element, and the values of velocity, temperature, pressure, and concentration at each node are obtained. The flow cell simulation was based on a two-dimensional finite element model of a section of fluid 5.86 × 3.06 mm, which included the vertical cross section of the jet tube and which was bounded below by the sample surface. The y-axis was perpendicular to the sample surface; the x-axis was parallel to the sample and to the front of the AFM cantilever support chip (Figures 1b and 3a). The models comprised from 4373 to 6564 elements and employed graded meshes as shown in Figure 2 for efficient use of computer resources, with a fine element mesh being used in regions of high gradients of velocity or of concentration. Thus, for the simulation incorporating the electrode, the element size at the leading edge was 0.6 (x) × 0.1 (y) µm, ensuring that the diffusion layer extended across several elements, whereas at the upper boundary of the model where velocities were low, the elements could be much larger with dimensions on the order of 0.4 mm. The mesh size was progressively reduced and the grading adjusted until optimum convergence was obtained (e.g.
