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Dissolution Kinetics of Griseofulvin in Sodium Dodecylsulphate Solutions
Dissolution Kinetics of Griseofulvin in Sodium Dodecylsulphate Solutions JANH.
DE
SMIDT', JAAPC. A. OFFRINGA, AND DAAN J. A. CROMMELIN
Received January 5, 1987, from the Department of Pharmaceutics, Subfaculty,of Pharmacy, University of Utrecht, Accepted for publication June 18, 1987. Croesestraat 79, 3522 AD Utrecht, The Netherlands. ... .. ...
..
~
Ab~tract0 The 'rate-limitingstep in the absorption of poorly watersoluble drugs is often the dissolution process of these compounds. Surface-active agents influence the dissolution process by wetting and solubilizing. In order to study the effect of solubilization, a rotating-disk apparatus was used with griseofulvin as a model drug substance and sodium dodecylsulphate (SDS) as a model surfactant. The dissolution kinetics of griseofulvin in SDS solutions could adequately be described by the convective-diff usion model and the phase-separation model for micellar systems. The calculated micellar diffusion coefficient of SDS was in close agreement with values reported in the literature.
It is a well-established fact that poorly water-soluble drugs have a low and often varying bioavailability. Some of these drugs show higher availability when administered during a fat meal or in emulsions. These phenomena are often explained by postulating interactions of the drug substance with bile constituents like cholic acids.' There is lack of insight into the precise role of bile substances on the dissolution of poorly water-soluble drugs, and the luminal transport and the membrane penetration of drugs in solubilized form. This paper focuses on the first step in the absorption process: the dissolution phase. In order to investigate the dissolution kinetics, a system with well-defined hydrodynamic properties is required. The rotating-disk dissolution apparatus meets these demands. Griseofulvin was used as a model drug substance and sodium dodecylsulphate (SDS) as a model surfactant. Both substances have been studied extensively,* thus a validation of the equipment and the applicability of the convective-diffusion model is possible. With the phase-separation model, micellar diffusion coefficients were calculated and compared with independently obtained data and literature data.3.4 The rate-determining step in dissolution processes may be surface reaction kinetics or transport kinetics. If the dissolution process is studied in a rotating-disk apparatus, a distinction between both steps can be made by varying the speed of rotation. If the dissolution process is controlled by diffusion, the dissolution rate will be proportional to the square root of the speed of rotation. In that case, the following equation can be applied?
R
=
1.950213 p I / 6
,.JI2
ACrZ
(1)
where R is the dissolution rate, D is the diffusion coefficient, Y is the kinematic viscosity, w is the angular velocity of the disk, AC is the concentration at the surface minus the concentration in the bulk, and r is the radius of the disk. All parameters on the right-hand side of the equation can be determined by independent techniques. Dissolution rate experiments can therefore be used to determine the ratelimiting step in the dissolution process. A schematic model of a diffusion-controlled dissolution process in a micellar medium is given in Figure 1. At the surface of the dissolving disk a saturated solution of griseo0022-3549/87/0900-0711$01 .OO/O 0 1987, American Pharmaceutical Association
fulvin in the dissolution medium is maintained. Surface processes or partitioning processes over the micellar phase and water are supposed to be very fast compared with the diffusion process in the adherent diffusim layer (kl>> kz). The transport through this layer occurs for one part in the micellar phase and for the other part in the aqueous environment. Based on this model, an overall diffusion coefficient (D, ) can be calculated with eq 1.The value of this diffusion coeRcient is further proof of a diffusion-controlled dissolution process. In micellar systems, the experimentally obtained DaPpcan be analyzed with the phase-separation model. Then griseofulvin is, in this aspect, regarded as a marker molecule for the micellar diffusion of sodium dodecylsulphate micelles. The calculated apparent diffusion coefficient consists of the diffusion coefficient of a fraction of solubilized (p) and of free (1 - p) griseofulvin (eq 2),6
(2) where Dmieand Df,, are the diffusion coefficients of griseofulvin in micelles and in water, respectively. The value of p is calculated from solubility data with eq 3:
cs - c o
c,
(3)
where C , is the solubility in the dissolution medium, and C, is the solubility in the same medium without micelles (in water or 0.9% NaCl and buffer solution). It is assumed that C, is not influenced by the SDS concentration. If the partitioning of griseofulvin between the aqueous and
bulk
water
dillusion layer
Figure 1-Diffusion-controlled dissolution process in micellar medium. Key: k,, surface-effects rate constant; k2, transport rate constant. If k, >> k2, transport of the marker compound (griseofulvin) in micellar or aqueous environments will dominate the dissolution process. At the interface, a concentration equal to the Solubility of the compound in the dissolution medium will be maintained. Journal of Pharmaceutical Sciences / 711 Vol. 76, No. 9, September 1987
micellar phase is a dynamic equilibrium process, a n apparent distribution coefficient, K , can be defined by eq 4:
(4) where C ,,, is the concentration of solute in the micelles, Cfree is the aqueous concentration, V, is the volume of the water phase, and V,,, is the volume the micellar phase. If the micellar phase does not change in physical behavior by solubilization of griseofulvin, this substance can be regarded as a marker molecule for micellar diffusion of sodium dodecylsulphate. Support for the proposed dissolution model can be obtained by comparing the calculated micellar diffusion coefficient with literature data.
01
Experimental Section Materials-Griseofulvin (Aldrich, Milwaukee, WI) and sodium dodecylsulphate (Merck, Darmstadt, FRG) were used as received. Griseofulvin was stored a t 5 "C. The solutions containing 0.9% sodium chloride (Ph. Eur. grade) and 0.01 M Tris (Aldrich, Milwaukee, WI) were adjusted to pH 7.4 with hydrochloric acid. Solubility and Characterization of Griseofulvin Solutions-All experiments were carried out at 37 "C. The solubility of griseofulvin in micellar solutions was determined by shaking suspensions for 48 h. After centrifugation, aliquots were diluted and measured spectrophotometrically. However, the solubility of griseofulvin in nonmicellar solutions could not be determined unequivocally by shaking suspensions.7 Therefore, the solubility was derived from long-term dissolution rate measurements in t h e rotating-disk apparatus.8 In micellar solutions, no reproducibility problems were met in the solubility experiments. The stability of griseofulvin solutions was investigated by UV spectrophotometry and TLC.9 No changes in the spectrum or chromatogram could be detected after storage of t h e solutions for one month a t 20 "C. The UV calibration curve of griseofulvin solutions in water appeared to be nonlinear. At low concentrations (<1mg/L) a minor deviation of Beer's law was noticed, but it did not affect the results. The kinematic viscosity of the solutions was determined with Ubbelohde viscometers (Eur. Ph.). In order to investigate the effect of solubilization on micellar size, quasi elastic light scattering measurements were carried out (at t h e Van't Hoff Lab, a t Utrecht). No differences could be detected between SDS solutions (15 mM) saturated with griseofulvin and without griseofulvin (mean hydrodynamic radius of 1.7 nm). The diffusion coefficient of griseofulvin in water was measured by the capillary method.'" Capillaries of 123-mm length and inner diameter of 1.2 mm were placed in a 2.5-L water bath under constant stirring. After 165 h, a diffusion coefficient of 8 ? 1 x 10 - l o m2/s was calculated. Dissolution Rate Measurement-A rotating-disk apparatus was used as described before." The vessel was filled with 100 mL of dissolution medium. Griseofulvin concentrations were determined at 294 n m with a UV spectrophotometer (Shimadzu UV 100-02, Kyoto, Japan) every 5 s and stored in a microcomputer. Before each experiment, the extinction scale was calibrated. All experiments were carried out under sink conditions. The solubility of griseofulvin in nonmicellar solutions was determined in a 100-mL water-jacketed vessel t h a t was filled with 50 mL of dissolution medium. The experiments lasted -6 h , and every 1 0 min the concentration was determined. The solubilities measured by this method were 13.4 mg/L in water and 10.8 mg/L in the salt and buffer solution. The value obtained for t h e pure water solubility was about the same a s a n extrapolated value of Elworthy and Lipscomb7 (13.9 mg/L), measured a s a steady-state value after continuous extraction of powdered griseofulvin in a percolator. For the preparation of the pellets, -750 mg griseofulvin was compressed with a hydraulic press in a 16-mm die a t 40 kN. No differences were observed in the X-ray spectra of the griseofulvin powder taken with a Debye-Scherrer camera before and after compression. 712 / Journal of Pharmaceutical Sciences Vol. 76, No. 9, September 1987
Results and Discussion Solubility and Dissolution Rate-The solubility of griseofulvin in SDS solutions increased rapidly with the concentration of SDS above the critical micellar concentration (CMC). Figure 2 shows that the increase was linear in the concentration region studied. The increase in the sodium chloridecontaining solutions was less pronounced than in distilled water solutions. This effect has to be attributed to a different .~ aggregation number in the presence of sodium ~ h l o r i d eThe lines in Figure 2 were obtained by linear regression analysis of the solubility data. The values of the CMC (6.8 ? 0.3 mmol/L in water and 1.1 0.3 mmollL in t h e salt and buffer solution) were calculated by extrapolation of the lines to the nonmicellar solubility level. The linear increase in the solubility with the SDS concentration is a n indication that a n increase in SDS concentration leads only to a linear increase in micellar volume (i.e., increase in the number of micelles) and not to a different type of micelles (cf. eq 4). In order to avoid error accumulation for further calculations, values fitted by linear regression were used. The dissolution rate in SDS solutions increased with the concentration of SDS above the CMC and, again, this increase was greater in the solutions without sodium chloride (see Table 1). For the calculation of diffusion coefficients, the observed values of the dissolution rate were used. Dissolution and Transport of Solute-A Levich plot of the dissolution rate of griseofulvin in water and SDS solution (15 mmol/L) is given in Figure 3. In general, the linearity of a plot of the dissolution r a t e against the square root of the speed of rotation is a n indication of a diffusion-controlled dissolution process. From our results i t was concluded that surface reactions do not play a dominant role in the dissolution process of griseofulvin in SDS solutions. Further evidence was obtained by comparing the calculated micellar diffusion coefficient with known values. By applying eq 2 to the calculated dissolution rates at different SDS concentrations, the apparent diffusion coefficients were calculated; the results are given in Figure 4. As the apparent diffusion coefficients depend on the experimental conditions, a n independent or extrapolated value must be calculated. Analysis of the apparent diffusion coefficients is possible with the phase-separation model. Figure 5 shows the results of the calculation of micellar diffusion coefficients with eqs 2 and 3. The diffusion coefficientof griseofulvin in water, used in eq 2,
*
:t
Concentration SDS (rnmoVL)
Flgure 2-Solubility of griseofulvin as a function of the concentration of SDS in water ( 0 ) and in salt and buffer solutions (C). Lines were calculated by linear regression analysis.
can be corrected for the presence of other particles (micelles) in the solution.12 However, these corrections appear to have only a minor effect (<0.4%) on the values of the calculated micellar diffusion coefficient. The micellar diffusion coefficients in distilled water and in solutions containing sodium chloride are found a t the intersection of these curves with the ordinate. Hess13 derived theoretically that Dmicshould be linearly related to the square root of the micellar concentration of the surfactant (CsDs - CMC). In the equation, the influence of charge on the self-diffusion coefficient of colloidal particles is quantified. The equation predicts that the charge effects will be less pronounced under relatively high ionic strength conditions. Indeed, Figure 5 shows a smaller negative slope for the salt and buffer solutions. There is a considerable effect of concentration on the micellar diffusion coefficient, indicating that the micelle charge is fairly high. At infinite dilution ( C s ~ s= CMC), micellar diffusion coefficients of 1.7 2 0.3 x lo-'' m'ls in water and 1.3 5 0.4 x lo-'' m2/sin the salt and buffer solutions were found. There is considerable agreement with the results of the investigations of Stigter et al.3 After correction for temperature and ionic strength, values of 1.5 x lo-'' and 1.4 x lo-'' m2/s were obtained for distilled water and sodium chloride solution, respectively. Aggregation numbers for SDS micelles as a function of ionic strength are reported in the l i t e r a t ~ r e . ~
Dissolution Rate, mg/s x
4
1
lo4'
In 0.9% NaCl and Buffer Solution
In Water
-b -b
4 8 10 15 20 25 30 50 75 100
m
-;. 5 "
Table I-Dissolution Rate of Grlseofulvln In Sodium Dodecylsulphate Solutlons
Concentration of SDS, mmol/L
From the aggregation number and the (apparent) partial molar volume, the diffusion coefficients can be calculated with the Stokes-Einstein equation. The micellar diffusion coefficients for SDS calculated in this wa were 1.8 x m2/s for distilled water and 1.5 x lo-' B m2/s for the salt solution (at 25°C). These values are the same order of magnitude as the micellar diffusion coefficients calculated from our results. For the benzocaine:polysorbate 80 system, a small deviation from rotating-disk theory was observed by Singh et aL14using experimentally found apparent diffusion coefficients. This is possibly due to the use of these emperical data. A more rigorous determination of these diffusion coefficients in a membrane-diffusion cell was given by Amidon et a1.'6 The dissolution process of griseofulvin in SDS solutions, studied in a rotating-disk apparatus, was proven to be convective diffusion controlled by the observed linear relationship between the dissolution rate and the square root of
0.30 0.54 0.92 1.16 1.38
0.47 0.98 1.39 1.81 2.20 3.47 4.95 6.08
-b
"0
40
20
60
-
"Mean values of at least three determinations. SD values were typically -5%. bNot determined.
I
2
4
6
8
100
120
Figure 4-Apparent diffusion coefficient as a function of the micellar (C - CMC) concentration of SDS in water ( 0 ) and in salt and buffer Lines were calculated with eqs 2 and 3 from solubility data solutions (0). fitfed in Figure 2, and micellar diffusion coefficient data fitted in Figure 5.
0 "0
80
Micellar concentration of SDS (C CMC) in mmol/L
1.66 2.60 3.96 4.83
10
in(rad/s)lh
Figure 3-Dissolution rate of griseofulvin as a function of the square root of the speed of rotation in water ( 0 )and 0.015 M SDS (0). Lines were calculated from linear regression analysis. Each point represents the mean of at least three measurements.
2
4
-.
6
8
10
VC-CMC (rnrnol/L)'/z Flgure 5-Micellar diffusion coefficients of SDS as a function of the square root of the micellar concentration of SDS in water ( 0 )and in salt and buffer solutions (0). Lines were calculated from linear regression analysis, giving most weight to the values with the narrowest confidence limits. Journal of Pharmaceutical Sciences / 713 Vol. 76, No. 9, September 1987
the speed of rotation. The analysis of the experimental data obtained in this study also shows that the data fit well to the phase-separation model. The surface reactions involved in the dissolution process cannot be noticed as they are too fast relative to the diffusional transport process. Only for compounds that are less soluble than g r i s e ~ f u l v i n ,and ~ ~ . for ~~ cholesterol** (100 times less soluble than griseofulvinlg), solubilization is supposed to occur by direct contact of the surfactant with the solid surface and then surface-reactionscontrolled kinetics will be observed.
References and Notes
9. Townley, E. R. In Analytical Profiles o Drug Substances; Florey, K.. Ed.: Academic: New York. 1979: 01. 8. DD 217-249. 10. Stout, P. J. M.; Khoury, N.; Mauger, J.; Hoyard, S. J . Pharm. Sci, 1986,75,65-67. 11. Gri seels, H.;Van Bloois, L.; Crommelin, D. J. A.; De Blaey, C. j. Int. J . Pharm. 1983,14,299411. 12. Wang, J. H.J . A m . Chem. SOC.1954,76,4755-4763. 13. Hess, W. In Light Scattering in Liquids and Macromolecular Solutions; Degiorgio, V.; Corti, M.; Giglio, M., Eds.; Plenum: New York, 1980; 47 14. Singh, P.; Desai, J.f Flanagan, D. R.; Simonelli, A. P.; Higuchi, W. I. J . Pharm. Sci. 1968,57,959-965. 15. Amidon, G. E.;Higuchi, W. I.; Ho, N. F. H. J . Pharm. Sci. 1982, 71, 77-84. 16. Chan, A. F.;Fennel1 Evans, D.; Cussler, E. L. AIChE J . 1976, 22.. 1006-1012. 17. Carroll, B. J. J. Colloid Interface Sci. 1981, 79, 126-135. 18. Ho, N.F. H.; Gupta, S. L.; Higuchi, W. I. J. Colloid Interface Sci. 1984,101,544-553. 19. Madan, D. M.;Cadwallader, D. E. J.Pharm. Sci. 1970,59,13621363.
f
8.
~~
1. Forth, W.; Rummel, W. In International Encyclopedia of Pharmacology and Therapeutics; Pergamon: NY, 1975;Vol I, pp 215244. 2. Attwood, D.; Florence, A. T. Surfactant Systems; Chapman and Hall: London, 1983. 3. Stigter, D.; Williams, R. J.; Mysels, K. J. J . Phys. Chem. 1955, 59.330-335. 4. Kratohvil, J. P. J . Colloid Int. Sci. 1980, 75,271-275. 5. Levich, V. G. Physico-Chemical Hydrodynamics; Prentice Hall: En lewood Cliffs, N J , 1962;pp 60-72. 6. Stifbs, P. J . Coll. Int. Sci. 1982,87, 385-394. 7. Elworthy, P. H.; Lipscomb, F. J. J . Pharm. Pharmacol. 1968,20, 790-792. 8. Feld, K. M.; Higuchi, W. H.; ChingChiang, S. J . Pharm. Sci. 1982,71, 182-188.
714 / Journal of Pharmaceufical Sciences Vol. 76, No. 9, Sepfember 1987
~~~~
Acknowledgments The authors wish to thank Mr. H. Mos for performing the QELS particle size measurement.
DE
SMIDT', JAAPC. A. OFFRINGA, AND DAAN J. A. CROMMELIN
Received January 5, 1987, from the Department of Pharmaceutics, Subfaculty,of Pharmacy, University of Utrecht, Accepted for publication June 18, 1987. Croesestraat 79, 3522 AD Utrecht, The Netherlands. ... .. ...
..
~
Ab~tract0 The 'rate-limitingstep in the absorption of poorly watersoluble drugs is often the dissolution process of these compounds. Surface-active agents influence the dissolution process by wetting and solubilizing. In order to study the effect of solubilization, a rotating-disk apparatus was used with griseofulvin as a model drug substance and sodium dodecylsulphate (SDS) as a model surfactant. The dissolution kinetics of griseofulvin in SDS solutions could adequately be described by the convective-diff usion model and the phase-separation model for micellar systems. The calculated micellar diffusion coefficient of SDS was in close agreement with values reported in the literature.
It is a well-established fact that poorly water-soluble drugs have a low and often varying bioavailability. Some of these drugs show higher availability when administered during a fat meal or in emulsions. These phenomena are often explained by postulating interactions of the drug substance with bile constituents like cholic acids.' There is lack of insight into the precise role of bile substances on the dissolution of poorly water-soluble drugs, and the luminal transport and the membrane penetration of drugs in solubilized form. This paper focuses on the first step in the absorption process: the dissolution phase. In order to investigate the dissolution kinetics, a system with well-defined hydrodynamic properties is required. The rotating-disk dissolution apparatus meets these demands. Griseofulvin was used as a model drug substance and sodium dodecylsulphate (SDS) as a model surfactant. Both substances have been studied extensively,* thus a validation of the equipment and the applicability of the convective-diffusion model is possible. With the phase-separation model, micellar diffusion coefficients were calculated and compared with independently obtained data and literature data.3.4 The rate-determining step in dissolution processes may be surface reaction kinetics or transport kinetics. If the dissolution process is studied in a rotating-disk apparatus, a distinction between both steps can be made by varying the speed of rotation. If the dissolution process is controlled by diffusion, the dissolution rate will be proportional to the square root of the speed of rotation. In that case, the following equation can be applied?
R
=
1.950213 p I / 6
,.JI2
ACrZ
(1)
where R is the dissolution rate, D is the diffusion coefficient, Y is the kinematic viscosity, w is the angular velocity of the disk, AC is the concentration at the surface minus the concentration in the bulk, and r is the radius of the disk. All parameters on the right-hand side of the equation can be determined by independent techniques. Dissolution rate experiments can therefore be used to determine the ratelimiting step in the dissolution process. A schematic model of a diffusion-controlled dissolution process in a micellar medium is given in Figure 1. At the surface of the dissolving disk a saturated solution of griseo0022-3549/87/0900-0711$01 .OO/O 0 1987, American Pharmaceutical Association
fulvin in the dissolution medium is maintained. Surface processes or partitioning processes over the micellar phase and water are supposed to be very fast compared with the diffusion process in the adherent diffusim layer (kl>> kz). The transport through this layer occurs for one part in the micellar phase and for the other part in the aqueous environment. Based on this model, an overall diffusion coefficient (D, ) can be calculated with eq 1.The value of this diffusion coeRcient is further proof of a diffusion-controlled dissolution process. In micellar systems, the experimentally obtained DaPpcan be analyzed with the phase-separation model. Then griseofulvin is, in this aspect, regarded as a marker molecule for the micellar diffusion of sodium dodecylsulphate micelles. The calculated apparent diffusion coefficient consists of the diffusion coefficient of a fraction of solubilized (p) and of free (1 - p) griseofulvin (eq 2),6
(2) where Dmieand Df,, are the diffusion coefficients of griseofulvin in micelles and in water, respectively. The value of p is calculated from solubility data with eq 3:
cs - c o
c,
(3)
where C , is the solubility in the dissolution medium, and C, is the solubility in the same medium without micelles (in water or 0.9% NaCl and buffer solution). It is assumed that C, is not influenced by the SDS concentration. If the partitioning of griseofulvin between the aqueous and
bulk
water
dillusion layer
Figure 1-Diffusion-controlled dissolution process in micellar medium. Key: k,, surface-effects rate constant; k2, transport rate constant. If k, >> k2, transport of the marker compound (griseofulvin) in micellar or aqueous environments will dominate the dissolution process. At the interface, a concentration equal to the Solubility of the compound in the dissolution medium will be maintained. Journal of Pharmaceutical Sciences / 711 Vol. 76, No. 9, September 1987
micellar phase is a dynamic equilibrium process, a n apparent distribution coefficient, K , can be defined by eq 4:
(4) where C ,,, is the concentration of solute in the micelles, Cfree is the aqueous concentration, V, is the volume of the water phase, and V,,, is the volume the micellar phase. If the micellar phase does not change in physical behavior by solubilization of griseofulvin, this substance can be regarded as a marker molecule for micellar diffusion of sodium dodecylsulphate. Support for the proposed dissolution model can be obtained by comparing the calculated micellar diffusion coefficient with literature data.
01
Experimental Section Materials-Griseofulvin (Aldrich, Milwaukee, WI) and sodium dodecylsulphate (Merck, Darmstadt, FRG) were used as received. Griseofulvin was stored a t 5 "C. The solutions containing 0.9% sodium chloride (Ph. Eur. grade) and 0.01 M Tris (Aldrich, Milwaukee, WI) were adjusted to pH 7.4 with hydrochloric acid. Solubility and Characterization of Griseofulvin Solutions-All experiments were carried out at 37 "C. The solubility of griseofulvin in micellar solutions was determined by shaking suspensions for 48 h. After centrifugation, aliquots were diluted and measured spectrophotometrically. However, the solubility of griseofulvin in nonmicellar solutions could not be determined unequivocally by shaking suspensions.7 Therefore, the solubility was derived from long-term dissolution rate measurements in t h e rotating-disk apparatus.8 In micellar solutions, no reproducibility problems were met in the solubility experiments. The stability of griseofulvin solutions was investigated by UV spectrophotometry and TLC.9 No changes in the spectrum or chromatogram could be detected after storage of t h e solutions for one month a t 20 "C. The UV calibration curve of griseofulvin solutions in water appeared to be nonlinear. At low concentrations (<1mg/L) a minor deviation of Beer's law was noticed, but it did not affect the results. The kinematic viscosity of the solutions was determined with Ubbelohde viscometers (Eur. Ph.). In order to investigate the effect of solubilization on micellar size, quasi elastic light scattering measurements were carried out (at t h e Van't Hoff Lab, a t Utrecht). No differences could be detected between SDS solutions (15 mM) saturated with griseofulvin and without griseofulvin (mean hydrodynamic radius of 1.7 nm). The diffusion coefficient of griseofulvin in water was measured by the capillary method.'" Capillaries of 123-mm length and inner diameter of 1.2 mm were placed in a 2.5-L water bath under constant stirring. After 165 h, a diffusion coefficient of 8 ? 1 x 10 - l o m2/s was calculated. Dissolution Rate Measurement-A rotating-disk apparatus was used as described before." The vessel was filled with 100 mL of dissolution medium. Griseofulvin concentrations were determined at 294 n m with a UV spectrophotometer (Shimadzu UV 100-02, Kyoto, Japan) every 5 s and stored in a microcomputer. Before each experiment, the extinction scale was calibrated. All experiments were carried out under sink conditions. The solubility of griseofulvin in nonmicellar solutions was determined in a 100-mL water-jacketed vessel t h a t was filled with 50 mL of dissolution medium. The experiments lasted -6 h , and every 1 0 min the concentration was determined. The solubilities measured by this method were 13.4 mg/L in water and 10.8 mg/L in the salt and buffer solution. The value obtained for t h e pure water solubility was about the same a s a n extrapolated value of Elworthy and Lipscomb7 (13.9 mg/L), measured a s a steady-state value after continuous extraction of powdered griseofulvin in a percolator. For the preparation of the pellets, -750 mg griseofulvin was compressed with a hydraulic press in a 16-mm die a t 40 kN. No differences were observed in the X-ray spectra of the griseofulvin powder taken with a Debye-Scherrer camera before and after compression. 712 / Journal of Pharmaceutical Sciences Vol. 76, No. 9, September 1987
Results and Discussion Solubility and Dissolution Rate-The solubility of griseofulvin in SDS solutions increased rapidly with the concentration of SDS above the critical micellar concentration (CMC). Figure 2 shows that the increase was linear in the concentration region studied. The increase in the sodium chloridecontaining solutions was less pronounced than in distilled water solutions. This effect has to be attributed to a different .~ aggregation number in the presence of sodium ~ h l o r i d eThe lines in Figure 2 were obtained by linear regression analysis of the solubility data. The values of the CMC (6.8 ? 0.3 mmol/L in water and 1.1 0.3 mmollL in t h e salt and buffer solution) were calculated by extrapolation of the lines to the nonmicellar solubility level. The linear increase in the solubility with the SDS concentration is a n indication that a n increase in SDS concentration leads only to a linear increase in micellar volume (i.e., increase in the number of micelles) and not to a different type of micelles (cf. eq 4). In order to avoid error accumulation for further calculations, values fitted by linear regression were used. The dissolution rate in SDS solutions increased with the concentration of SDS above the CMC and, again, this increase was greater in the solutions without sodium chloride (see Table 1). For the calculation of diffusion coefficients, the observed values of the dissolution rate were used. Dissolution and Transport of Solute-A Levich plot of the dissolution rate of griseofulvin in water and SDS solution (15 mmol/L) is given in Figure 3. In general, the linearity of a plot of the dissolution r a t e against the square root of the speed of rotation is a n indication of a diffusion-controlled dissolution process. From our results i t was concluded that surface reactions do not play a dominant role in the dissolution process of griseofulvin in SDS solutions. Further evidence was obtained by comparing the calculated micellar diffusion coefficient with known values. By applying eq 2 to the calculated dissolution rates at different SDS concentrations, the apparent diffusion coefficients were calculated; the results are given in Figure 4. As the apparent diffusion coefficients depend on the experimental conditions, a n independent or extrapolated value must be calculated. Analysis of the apparent diffusion coefficients is possible with the phase-separation model. Figure 5 shows the results of the calculation of micellar diffusion coefficients with eqs 2 and 3. The diffusion coefficientof griseofulvin in water, used in eq 2,
*
:t
Concentration SDS (rnmoVL)
Flgure 2-Solubility of griseofulvin as a function of the concentration of SDS in water ( 0 ) and in salt and buffer solutions (C). Lines were calculated by linear regression analysis.
can be corrected for the presence of other particles (micelles) in the solution.12 However, these corrections appear to have only a minor effect (<0.4%) on the values of the calculated micellar diffusion coefficient. The micellar diffusion coefficients in distilled water and in solutions containing sodium chloride are found a t the intersection of these curves with the ordinate. Hess13 derived theoretically that Dmicshould be linearly related to the square root of the micellar concentration of the surfactant (CsDs - CMC). In the equation, the influence of charge on the self-diffusion coefficient of colloidal particles is quantified. The equation predicts that the charge effects will be less pronounced under relatively high ionic strength conditions. Indeed, Figure 5 shows a smaller negative slope for the salt and buffer solutions. There is a considerable effect of concentration on the micellar diffusion coefficient, indicating that the micelle charge is fairly high. At infinite dilution ( C s ~ s= CMC), micellar diffusion coefficients of 1.7 2 0.3 x lo-'' m'ls in water and 1.3 5 0.4 x lo-'' m2/sin the salt and buffer solutions were found. There is considerable agreement with the results of the investigations of Stigter et al.3 After correction for temperature and ionic strength, values of 1.5 x lo-'' and 1.4 x lo-'' m2/s were obtained for distilled water and sodium chloride solution, respectively. Aggregation numbers for SDS micelles as a function of ionic strength are reported in the l i t e r a t ~ r e . ~
Dissolution Rate, mg/s x
4
1
lo4'
In 0.9% NaCl and Buffer Solution
In Water
-b -b
4 8 10 15 20 25 30 50 75 100
m
-;. 5 "
Table I-Dissolution Rate of Grlseofulvln In Sodium Dodecylsulphate Solutlons
Concentration of SDS, mmol/L
From the aggregation number and the (apparent) partial molar volume, the diffusion coefficients can be calculated with the Stokes-Einstein equation. The micellar diffusion coefficients for SDS calculated in this wa were 1.8 x m2/s for distilled water and 1.5 x lo-' B m2/s for the salt solution (at 25°C). These values are the same order of magnitude as the micellar diffusion coefficients calculated from our results. For the benzocaine:polysorbate 80 system, a small deviation from rotating-disk theory was observed by Singh et aL14using experimentally found apparent diffusion coefficients. This is possibly due to the use of these emperical data. A more rigorous determination of these diffusion coefficients in a membrane-diffusion cell was given by Amidon et a1.'6 The dissolution process of griseofulvin in SDS solutions, studied in a rotating-disk apparatus, was proven to be convective diffusion controlled by the observed linear relationship between the dissolution rate and the square root of
0.30 0.54 0.92 1.16 1.38
0.47 0.98 1.39 1.81 2.20 3.47 4.95 6.08
-b
"0
40
20
60
-
"Mean values of at least three determinations. SD values were typically -5%. bNot determined.
I
2
4
6
8
100
120
Figure 4-Apparent diffusion coefficient as a function of the micellar (C - CMC) concentration of SDS in water ( 0 ) and in salt and buffer Lines were calculated with eqs 2 and 3 from solubility data solutions (0). fitfed in Figure 2, and micellar diffusion coefficient data fitted in Figure 5.
0 "0
80
Micellar concentration of SDS (C CMC) in mmol/L
1.66 2.60 3.96 4.83
10
in(rad/s)lh
Figure 3-Dissolution rate of griseofulvin as a function of the square root of the speed of rotation in water ( 0 )and 0.015 M SDS (0). Lines were calculated from linear regression analysis. Each point represents the mean of at least three measurements.
2
4
-.
6
8
10
VC-CMC (rnrnol/L)'/z Flgure 5-Micellar diffusion coefficients of SDS as a function of the square root of the micellar concentration of SDS in water ( 0 )and in salt and buffer solutions (0). Lines were calculated from linear regression analysis, giving most weight to the values with the narrowest confidence limits. Journal of Pharmaceutical Sciences / 713 Vol. 76, No. 9, September 1987
the speed of rotation. The analysis of the experimental data obtained in this study also shows that the data fit well to the phase-separation model. The surface reactions involved in the dissolution process cannot be noticed as they are too fast relative to the diffusional transport process. Only for compounds that are less soluble than g r i s e ~ f u l v i n ,and ~ ~ . for ~~ cholesterol** (100 times less soluble than griseofulvinlg), solubilization is supposed to occur by direct contact of the surfactant with the solid surface and then surface-reactionscontrolled kinetics will be observed.
References and Notes
9. Townley, E. R. In Analytical Profiles o Drug Substances; Florey, K.. Ed.: Academic: New York. 1979: 01. 8. DD 217-249. 10. Stout, P. J. M.; Khoury, N.; Mauger, J.; Hoyard, S. J . Pharm. Sci, 1986,75,65-67. 11. Gri seels, H.;Van Bloois, L.; Crommelin, D. J. A.; De Blaey, C. j. Int. J . Pharm. 1983,14,299411. 12. Wang, J. H.J . A m . Chem. SOC.1954,76,4755-4763. 13. Hess, W. In Light Scattering in Liquids and Macromolecular Solutions; Degiorgio, V.; Corti, M.; Giglio, M., Eds.; Plenum: New York, 1980; 47 14. Singh, P.; Desai, J.f Flanagan, D. R.; Simonelli, A. P.; Higuchi, W. I. J . Pharm. Sci. 1968,57,959-965. 15. Amidon, G. E.;Higuchi, W. I.; Ho, N. F. H. J . Pharm. Sci. 1982, 71, 77-84. 16. Chan, A. F.;Fennel1 Evans, D.; Cussler, E. L. AIChE J . 1976, 22.. 1006-1012. 17. Carroll, B. J. J. Colloid Interface Sci. 1981, 79, 126-135. 18. Ho, N.F. H.; Gupta, S. L.; Higuchi, W. I. J. Colloid Interface Sci. 1984,101,544-553. 19. Madan, D. M.;Cadwallader, D. E. J.Pharm. Sci. 1970,59,13621363.
f
8.
~~
1. Forth, W.; Rummel, W. In International Encyclopedia of Pharmacology and Therapeutics; Pergamon: NY, 1975;Vol I, pp 215244. 2. Attwood, D.; Florence, A. T. Surfactant Systems; Chapman and Hall: London, 1983. 3. Stigter, D.; Williams, R. J.; Mysels, K. J. J . Phys. Chem. 1955, 59.330-335. 4. Kratohvil, J. P. J . Colloid Int. Sci. 1980, 75,271-275. 5. Levich, V. G. Physico-Chemical Hydrodynamics; Prentice Hall: En lewood Cliffs, N J , 1962;pp 60-72. 6. Stifbs, P. J . Coll. Int. Sci. 1982,87, 385-394. 7. Elworthy, P. H.; Lipscomb, F. J. J . Pharm. Pharmacol. 1968,20, 790-792. 8. Feld, K. M.; Higuchi, W. H.; ChingChiang, S. J . Pharm. Sci. 1982,71, 182-188.
714 / Journal of Pharmaceufical Sciences Vol. 76, No. 9, Sepfember 1987
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Acknowledgments The authors wish to thank Mr. H. Mos for performing the QELS particle size measurement.