Mechanism and Kinetics of Salicylic Acid Dissolution in Aqueous

J. Phys. Chem. B 2002, 106, 4763-4774

4763

Mechanism and Kinetics of Salicylic Acid Dissolution in Aqueous Solution under Defined Hydrodynamic Conditions via Atomic Force Microscopy: The Effects of the Ionic Additives NaCl, LiCl and MgCl2, the Organic Additives 1-Propanol, 2-Propanol, and the Surfactant Sodium Dodecyl Sulfate Shelley J. Wilkins, Barry A. Coles, and Richard G. Compton* Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, United Kingdom

Andrew Cowley Chemical Crystallography Department, Oxford UniVersity, Parks Road, Oxford, United Kingdom ReceiVed: October 25, 2001; In Final Form: January 30, 2002

The kinetics and mechanism controlling the aqueous dissolution from the (110) plane of salicylic acid (SA) in the presence of the solution phase ionic additives sodium chloride, lithium chloride, and magnesium chloride; the organic additives 1-propanol and 2-propanol; and the surfactant sodium dodecyl sulfate (SDS) have been investigated using a hydrodynamic atomic force microscope flow cell. Topographical images reveal that the surface dissolves via the retreat of macrosteps across the surface in the presence of the ionic additives at low concentrations (0.1 M). The rate of step retreat is dependent on the step height and the presence of hillocks on steps and planes. As the concentration of NaCl and LiCl is increased to ca. 1.0 M the height of the macrosteps decreases. For MgCl2, in contrast, dissolution at high concentrations is inhibited, and after a transient dissolution, the surface features then remain intact. In the presence of the aqueous organic additives and the surfactant, the surface morphology differs from that after exposure to the ionic additives in that the (110) face is less rough with considerably smaller macrosteps. The flow pattern in the hydrodynamic AFM flow cell is well established, allowing the deduction of dissolution rate. The dissolution flux has been studied as a function of flow rate and quantitatively interpreted using a model combining dissolution with the possibility of partial reprecipitation, the latter having a first order dependence on the surface concentration [SA]0: J ) kf - kb [SA]0. In the modeling, the ratio kf /kb is constrained to be equal to the measured solubility of SA in the medium concerned. This simple equation was found to give a good fit to the kinetic data obtained in the presence of the ionic additives only. However, satisfactory parametrization of the data was possible if kf and kb were optimized independently of the solubility constraint. The parameters for kf are found to be 1.7 × 10-8, 1.5 × 10-8, and 8.9 × 10-9 mol cm-2 s-1 for dissolution in 0.1 M, 0.5 M, and 1 M NaCl or LiCl, and 1.5 × 10-8 for dissolution in 0.1 M MgCl2. For 1 M MgCl2, the rate was too small to measure. For the organic additives and surfactant, the rate constants are different for each additive but independent of additive concentration. Values for kf and kb are found to be 1.4 × 10-8 mol cm-2 s-1 and 2.0 × 10-3 cm s-1 for dissolution in 0.5 and 1.0 M 1-propanol; 1.8 × 10-8 mol cm-2 s-1 and 2.0 × 10-3 cm s-1 in 0.5 and 1.0 M 2-propanol and 2.2 × 10-8 mol cm-2 s-1 and 3.0 × 10-3 cm s-1 in 0.126 mM, 0.252 mM, 1.26 mM, and 2.52 mM SDS.

Introduction The significance of crystallization mechanisms and kinetics in directing crystallization pathways of pharmaceutical solids and the factors affecting their formation have been reviewed.1,2 Over the past several years theoretical and experimental studies of nucleation phenomena, growth dynamics, and mechanisms of defect formation and impurity defects were performed using light scattering techniques,3 interferometry,4 X-ray topography,5 and atomic force microscopy.6-11 Despite progress in understanding the phenomena provided by these efforts, further work is required to achieve a comprehensive appreciation and to be able to rigorously control macromolecular crystallization for practical applications. * To whom correspondence should be addressed. E-mail: richard. [email protected].

The principles underlying crystal growth are poorly understood in general. The use of additives to control or inhibit the growth of organic crystals is of vital importance in the chemical and pharmaceutical industries.12,13 In this work, the impact of additives on crystals of salicylic acid during in-situ dissolution is studied using atomic force microscopy in a flow cell.8-11,14 The principle of the method is outlined in the next section. The flow cell consists of a commercial fluid AFM cell with an inlet port added in the form of a precisely shaped and positioned stainless steel jet so that solution can be delivered directly in front of the cantilever chip. The jet is inclined to the crystal surface and parallel to the front of the cantilever chip. The flow is thus confined by the crystal surface and the cantilever support chip giving a complex flow pattern that has been simulated using computational fluid dynamics programs. The flow pattern was initially solved using

10.1021/jp0139585 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/17/2002

4764 J. Phys. Chem. B, Vol. 106, No. 18, 2002

Wilkins et al. TABLE 1: Total Solubility of Salicylic Acid in Water and in the Presence of Additives at 21°C additive

concentration (M)

total solubility of salicylic acid (mM ( 0.5mM)

water NaCl NaCl NaCl LiCl LiCl LiCl MgCl2 MgCl2 MgCl2 1-propanol 1-propanol 2-propanol 2-propanol SDS SDS SDS SDS

n/a 0.1 0.5 1.0 0.1 0.5 1.0 0.1 0.5 1.0 0.5 1.0 0.5 1.0 1.26 × 10-4 2.52 × 10-4 1.26 × 10-3 2.52 × 10-3

16.5 14.9 13.2 11.7 14.6 13.0 8.0 11.7 8.0 6.8 17.1 19.5 16.3 17.8 14.4 14.5 16.2 16.5

TABLE 2: Viscosity and Density Values of Aqueous Solutions Containing Additive at 21°C Figure 1. Unit Cell of salicylic acid. Cell coordinates taken from ref 15, structure drawn using ref 16.

additive

concentration (M)

viscosity, η cP

density, F g cm-3

ref

NaCl NaCl NaCl LiCl LiCl LiCl MgCl2 MgCl2 MgCl2 1-propanol 1-propanol 2-propanol 2-propanol SDS SDS SDS SDS

0.1 0.5 1.0 0.1 0.5 1.0 0.1 0.5 1.0 0.5 1.0 0.5 1.0 1.26 × 10-4 2.52 × 10-4 1.26 × 10-3 2.52 × 10-3

0.995 1.035 1.083 1.014 1.072 1.146 0.965 1.165 1.418 1.064 1.197 1.106 1.279 0.978 0.978 0.978 0.978

1.003 1.018 1.036 0.999 1.009 1.021 1.007 1.037 1.074 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998

17 17 17 18 18 18 19 19 19 20 20 20 20 21 21 21 21

subsequently completed and applied to the dissolution of salicylic acid exposed to pure aqueous solutions.9 The dissolution of salicylic acid was studied as a function of flow rate based upon a model assuming a constant rate of dissolution with simultaneous precipitation having a first order dependence on [SA]0 with time Figure 2. Crystal structure of the salicylic acid unit cell.

an approximate two-dimensional simulation with a finite element fluid dynamics program.8 Three-dimensional simulations were

Figure 3. Schematic representation of a typical crystal surface.

J mol cm-2 s-1 ) DSA

(∂[SA] ∂y )

y)0

) kf - kb[SA]y)0 (1)

The relationship between the rate constants and the solubility

Mechanism and Kinetics of Salicylic Acid Dissolution

J. Phys. Chem. B, Vol. 106, No. 18, 2002 4765

Figure 4. (a) In situ images of the (110) surface of salicylic acid during the dissolution process in 0.1 M sodium chloride flowing at a rate of 2.19 × 10-2 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s. (b) In situ images of the (110) surface of salicylic acid during the dissolution process in 1 M sodium chloride flowing at a rate of 1.74 × 10-2 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s.

is shown in eq 2.

[SA]sol )

kf kb

(2)

If the solubility is measured, the relationship between the flux and flow rate is only dependent on one of the heterogeneous rate constants and can be determined by the best fit of the experimental curves by the model described. It must be emphasized that the constants kf and kb are surface aVeraged values. In the work reported in the present paper, ionic additives NaCl, LiCl, and MgCl2, the organic additives 1-propanol and 2-propanol, and the surfactant SDS are added to the hydrodynamic flow cell in varying concentrations. The effects are assessed through investigation of surface morphology together with dissolution kinetics as reflected in the parameters kf and kb.

Figure 5. Plot of dissolution rate vs flow rate of the (110) face of salicylic acid in (() 0.1 M NaCl, (2) 0.5 M NaCl, and (b) 1 M NaCl showing the theoretical curve using the model compared to the experimental data.


Wilkins et al.

Figure 6. (a) In situ images of the (110) surface of salicylic acid during the dissolution process in 0.1M lithium chloride flowing at a rate of 8.26 × 10-2 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s. (b) In situ images of the (110) surface of salicylic acid during the dissolution process in 0.5 M lithium chloride flowing at a rate of 5.61 × 10-2 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s.

This generic methodology in which the use of the liquid flow cell permits interpretation of the dissolution rate in terms of an interfacial reaction mechanism, gives the possibility to design and screen additive candidates for crystalline materials to improve their quality through additive interaction possibly leading to morphology control. Method Salicylic acid crystals of 0.5-8 mm were grown over 200 h from a saturated solution in ethanol by gradually decreasing the temperature from 30 to 25 °C. Salicylic acid crystals were indexed using standard methods with a NONIUS KCCD

diffractometer using MoKR radiation (0.71073 A). In our experiments, X-ray diffraction analysis revealed the salicylic acid crystals were monoclinic with space group P21/a with a ) 11.43, b ) 11.19, and c ) 4.91. The largest face in the elongated direction is the 110 can be seen in Figure 1. These are in good agreement with published values of a ) 11.52, b ) 11.21, c ) 4.92, and β) 90.83.15 A Topometrix TMX 2010 atomic force microscope operating in contact mode with SFM probes type 1520-00 and a 75 µm scanner type 5590-00 was used to obtain the images. The hydrodynamic flow cell used for in-situ AFM imaging has been described in detail elsewhere.8


Figure 7. Plot of dissolution rate vs flow rate of the (110) face of salicylic acid in (() 0.1 M LiCl, (2) 0.5 M LiCl, and (b) 1 M LiCl showing the theoretical curve using the model compared to the experimental data.

For dissolution measurements, a crystal of salicylic acid typically 3 × 1 × 1 mm in size exposing the 110 face was mounted on a latex substrate. A new crystal was used for each experiment. The latex mount was sealed inside the flow cell and solution passed through at rates ranging from 0.0025 to 0.0174 cm3 s-1. The crystals were allowed to dissolve in the additive environment by flowing the additive solution over the crystal for 20 min before recording image sequences. Images

J. Phys. Chem. B, Vol. 106, No. 18, 2002 4767 of area 20 × 20 µm were recorded in a continuous sequence at approximately 60 s intervals at each of the flow rates. The average piezo voltage was calculated for each scan and hence the change in height of the mean surface level was derived using the calibration factor of 0.333 V µm-1 determined for the scanner. The flow system was gravity fed from a reservoir; the flow rates were varied by adjusting the height difference between the reservoir and capillary outlet. Measurements were taken at a temperature of 21 °C. The total solubilitites of salicylic acid at 21 °C were determined by UV spectrophotometric analysis. An excess of salicylic acid was added to 10 mL flasks of each of the solutions of NaCl, LiCl, and MgCl2 in each of the concentrations 0.1, 0.5, and 1 M, 1-propanol and 2-propanol in the concentrations 0.5 and 1 M and SDS in concentrations 1.26 × 10-4, 2.52 × 10-4, 1.26 × 10-3, and 2.52 × 10-3M and left to equilibrate for 24 h. A small aliquot was removed from each of the flasks and centrifuged to separate the excess salicylic acid from the saturated solution. The solutions were diluted 100 fold with phosphate buffer of pH 7.429 and the solubilities calculated from the UV absorption spectra. The solubilities found are listed in Table 1. Modeling of the kinetic data was performed using FIDAP a fluid dynamics program which employs finite element methods to solve flow cell problems. A three-dimensional flow simulation of the cell has been described fully previously.9 The flow region

Figure 8. (a) In situ images of the (110) surface of salicylic acid during the dissolution process in 0.1 M magnesium chloride flowing at a rate of 8.4 × 10-3 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s. (b) In situ images of the (110) surface of salicylic acid during the dissolution process in 1 M lithium chloride flowing at a rate of 1.65 × 10-2 L s-1. Sequence after (a) 0, (b) 59, and (c) 118 s.


Wilkins et al. Results

Figure 9. Plot of dissolution rate vs flow rate of the (110) face of salicylic acid in (() 0.1 M MgCl2, (2) 0.5 M MgCl2, and (b) 1 M MgCl2 showing the theoretical curve using the model compared to the experimental data on 0.1 M MgCl2 only.

is divided into elements connected together at nodes, appropriate boundary conditions are applied based on the boundaries and surfaces exposed in the flow cell. The equations of momentum, mass and energy are solved for each element and the values for velocities, pressure, temperature and concentrations at each node are obtained. In this simulation, data files were prepared containing x, y, and z components of velocity at 35 769 points in the smaller volume starting at the mouth of the jet and enclosing the scanning cantilevers, for 14 flow rates encompassing the practical range of the cell. These data files may be freely downloaded from the worldwide web.22 The grid files can be adjusted for temperature and fluid variations by use of the Reynolds number, as shown in eq 3

Vf )

Re × d × η F

(3)

where Vf is the flow rate, Re is the Reynolds number, d is the hydraulic diameter of the jet at 0.054 cm, η is the absolute viscosity, and F is the fluid density. The viscosity and density values used in our simulations for each of the solutions were calculated from published data as shown in Table 2. Simulations of chemical processes within the cell were carried out by finite difference methods in two dimensions as described fully elsewhere.9 Two FORTRAN 77 programs were prepared. The first of these finds the solution flow path which passes over the scanning tip position and generates a 2D grid file of velocities in a surface which follows the flow path. The second program performs a bicubic spline interpolation from this 2D grid to provide the velocity components in a user specified grid, further details may be obtained from our webpage.22 The value of [SA]y)0 is handled implicitly and is deduced by equating the hypothesized dissolution flux (eq 1) with the known rate of transport of SA in solution. The images presented in this work are shaded topographical images acquired using the known calibration coefficient to obtain height information from the z-piezo voltages. Materials Solutions were made up using triply distilled deionized water of resistivity greater than 107 Ω cm (Elgastat, High Wycombe, UK). The chemicals used were salicylic acid 99+% and SDS (Aldrich, Gillingham, Dorset, UK); sodium chloride 99.9%, magnesium chloride hexahydrate 99% and lithium chloride 99% (BDH Ltd., Poole, Dorset, UK). The buffer solution for solubility measurements contained 0.0303 M Na2HPO4 and 0.0068 M KH2PO4 (BDH Ltd., Poole, Dorset).

The crystal structure of salicylic acid is monoclinic with four molecules contained within the unit cell as shown in Figure 2. The slowest growing and hence the largest surface is the (110) face thus easily distinguishable for imaging purposes. Images of the (110) surface ex-situ prior to dissolution experiments typically showed the surface to be flat with a few minor defects. Incomplete layers on the surface resulted in macrosteps typically no more than 100 nm in height. The morphology of the (110) plane exposed to water has been described previously.8,9 The surface is very rough with hillocks and large macrosteps typically 3 µm high. The rate constant kf for the dissolution of the (110) face in water in these experiments was found to be 2.0 × 10-8 mol cm-2 s-1, at 21 °C, with solubility (kf /kb) of 16.5 mM. This single parameter was capable of quantifying the net dissolution rates across the full range of flow rates studied in pure water. A schematic diagram of a typical surface is shown in Figure 3. The surface shows a series of macrosteps with growth hillocks at ledges and on flat terraces. The step movement retreats across the surface in the direction of flow moving to areas of lower surface under-saturation. The step height and size of growth hillocks vary with additive species and concentration of additive as described below. Exposure of the salicylic acid (110) plane to aqueous 0.1 M NaCl after approximately 20 min results in the appearance of many small hillocks which are formed at macrosteps across the surface, as shown in the sequence of images in Figure 4a. At flow rates of 0.004 cm3 s-1 these hillocks appear to grow as evidenced by the increase in z-piezo voltage at these points. The surfaces become very rough as a result of these growths. The step heights of the macrosteps are typically around 300 nm and the hillocks are typically 400-600 nm high for the sequence shown in Figure 4a. The steps can be seen to translate across the surface in the direction of flow. The steps are not uniform but zigzagged at kinks. The rate of movement of each step is determined by the step height and is influenced by the presence of growths on ledges and at kinks. The larger the step height, the slower the step retreat. Terraces between the steps constitute regular molecular planes. Dissolution from kinks occurs more rapidly than from the step edge because the energy barrier for dissolution is likely to be higher from a ledge than from a kink. At the higher flow rate of 0.02 cm3 s-1 the morphology is similar. However there is less reprecipitation consistent with convection “dilution” of the surface concentration and the surface appears less rough. The best fit of the theoretical model with the experimental data across all the flow rates measured gives a rate constant kf of 1.65 × 10-8 mol cm-2 s-1 when combined with the measured solubility of 14.9 mM, as shown in Figure 5. Again, a good agreement within experimental error is seen across the entire flow rate range using a single kinetic parameter. The dissolution of salicylic acid in 0.5 M NaCl gives similar topographical images to those obtained for 0.1 M NaCl although the density of kinks across the surface is marginally reduced. The surface is still quite rough with growths on steps across the surface. A good correlation between experimental data and theory gave a rate constant of 1.5 × 10-8 mol cm-2 s-1 based on the measured solubility of 13.2 mM (Table 1), shown in Figure 5. Over the full flow rate range explored the “back” reaction term, kb[SA]y)0, in eq 1 was found to be kinetically significant. The success of the kinetic modeling thus suggests the viability of the simple rate equation proposed given that the dissolution


J. Phys. Chem. B, Vol. 106, No. 18, 2002 4769

Figure 10. (a) In situ images of the (110) surface of salicylic acid during the dissolution process in 0.5 M 1-propanol flowing at a rate of 2.86 × 10-3 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s. (b) In situ images of the (110) surface of salicylic acid during the dissolution process in 1 M 1-propanol flowing at a rate of 5.61 × 10-3 L s-1. Sequence after (a) 0, (b) 59, (c) 118, (d) 177, (e) 236, and (f) 295 s.

dependence of the flow rate is modelable with the single kinetic parameter kf once the solubility has been measured and used to relate kb to kf. The fact that as the solubility changes, the same form of equation is applicable supports the basis of the kinetic modeling, albeit simplistic. As the concentration of NaCl is increased to 1 M, the topography of the (110) surface changes. A typical sequence of images is shown in Figure 4b. The surface roughness decreases with fewer hillocks of typical size 2-4µm. The steps are less defined with irregular undulating planes rather than clear edges with flat terraces as seen at lower concentrations. A step edge can be seen to form in the bottom left of the images in the sequence in the direction of flow, the step forms defined kinks which start to dissolve into a regular step by the last image in

the sequence. Analysis of a typical image shows the step heights vary considerably between 200 nm and 2500 nm. The presence of the additive in high concentration considerably diminishes the dissolution flux of the plane giving a best fit with a rate constant kf of 8.9 × 10-9 mol cm-2 s-1 based on the measured solubility of 11.7 mM as shown in Figure 5. Again this single rate constant fits the dissolution/reprecipitation data across the full flow rate range. Dissolution of salicylic acid in 0.1 M LiCl gives a similar topographical appearance to that seen in images obtained with 0.1 M NaCl. The surface appears relatively rough with small growth hillocks

Mechanism and Kinetics of Salicylic Acid Dissolution in Aqueous

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