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Prediction of the Adsorption of Diazepam by Activated Carbon in Aqueous Media
Prediction of the Adsorption of Diazepam by Activated Carbon in Aqueous Media DALE ERIC WURSTER,1,2 KHOULOUD A. ALKHAMIS,1 LLOYD E. MATHESON1 1
College of Pharmacy, University of Iowa, Iowa City, Iowa 52242
2
Obermann Center for Advanced Studies, University of Iowa, Iowa City, Iowa 52242
Received 30 October 2002; revised 3 March 2003; accepted 28 March 2003
ABSTRACT: Adsorption isotherms for the diazepam-activated carbon system in simulated intestinal fluid (SIF), without pancreatin, and in SIF with different percentages of ethanol were determined as were the solubilities of diazepam in SIF and in SIF with different percentages of ethanol. The surface area of the activated carbon was also evaluated. The results from the experimental work provided information on the relationship between adsorption and solubility. An excellent logarithmic relationship was observed between the adsorption affinity and the solubility of diazepam in the ethanol-SIF mixtures. This relationship was explained by a linear relationship between the differential free energy of displacement and the differential free energy of solution. Excellent correlations were also observed between the amounts of diazepam adsorbed by activated carbon and the solubilities of diazepam in the ethanol-SIF mixtures. This relationship was used to predict the complete isotherm, which was in excellent agreement with the experimental work. ß 2003 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 92:2008–2016, 2003
Keywords:
adsorption; diazepam; solubility; activated carbon; cosolvent
INTRODUCTION The ability to conduct classical adsorption experiments can be severely limited by poor solubility of a test compound. This limitation is mainly due to limitations in analytical sensitivity and to the inaccuracies in weighing and transferring very small amounts of adsorbents. Accordingly, it is desirable to develop techniques to predict the adsorption isotherms of poorly water-soluble drugs in purely aqueous systems. This goal is likely to be achieved using miscible cosolvents, because these cosolvents should affect the extent of adsorption in a systematic manner.
Khouloud A. Alkhamis’s present address is Jordan University of Science and Technology, Irbid, 22110, Jordan. Correspondence to: Dale Eric Wurster (Telephone: 319-3358825; Fax: 319-335-9349; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 92, 2008–2016 (2003) ß 2003 Wiley-Liss, Inc. and the American Pharmacists Association
2008
Diazepam was selected as a model compound in this research for the following reasons. First, the solubility of the free base form of diazepam is very low. However, diazepam’s solubility is just sufficient to allow the direct testing of the predictive method being developed. In simulated intestinal fluid (SIF) (without pancreatin), the solubility is <0.06 mg/mL at 378C. Second, diazepam is quite stable at the chosen experimental pH of 7.5.1 Third, it is a sufficiently weak base that it is unionized at a pH of 7.5. Therefore, changes in ionic strength are not likely to significantly affect the results. Finally, the carbonyl group on the seven-membered ring will likely hydrogen bond with the hydroxyl hydrogens on activated carbon. This belief is based on previous work2–5 which indicates that compounds having a carbonyl group are likely to interact with the hydroxyl groups on the activated carbon surface. Bonding specificity justifies the use of a Langmuir-like equation, which is premised on the adsorption sites being homogeneous.
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The effect of decreasing aqueous solubility on adsorption from aqueous solutions has long been known.6 Similarly, a regular increase in adsorption with increasing hydrocarbon chain length is usually observed when hydrocarbon adsorption occurs from aqueous media.6 Hansen and Craig7 observed the similarity of adsorption isotherms within a homologous series when isotherms were plotted as a function of reduced concentration (concentration at equilibrium divided by the solubility, or Ceq/solubility). Kolthoff et al.8 also noticed that the adsorption of polymers onto substrates was markedly dependent on the solvent. Rubino et al.9,10 have shown that co-solvent/water mixtures are useful for solubilizing diazepam.
Adsorption from Solution Several models have been used to characterize the process of adsorption from solution, the most frequent being the Langmuir-like equation.11,12 The original derivation of the Langmuir equation used a kinetic argument for the vapor/solid system. However, adsorption in a solution/solid system is not exactly analogous to adsorption in a vapor/solid system. The Langmuir equation has been derived for the solution/solid system using a thermodynamic (law of mass action) argument. In the current literature, the equation derived via the thermodynamic argument is usually referred to as the Langmuir-like equation. Although the Langmuir and Langmuir-like equations are identical in form, the Langmuir-like terminology alerts the reader to the potential for slight differences in the meanings of the modelistic parameters. The Langmuir-like equation is given below: ns2 K1 K2 Ceq ¼ m 1 þ K2 Ceq
ð1Þ
where ns2 is the amount of solute adsorbed, m is the mass of adsorbent, K1 is the capacity constant, K2 is the affinity constant, and Ceq is the concentration of unadsorbed solute in the bulk solution at equilibrium. The Langmuir-like equation is based on several assumptions11: there are a fixed number of sites available for adsorption, the heat of adsorption is independent of surface coverage (all of the sites available for adsorption are energetically equivalent), the adsorbed phase is confined to a monolayer, there are no lateral interactions between adsorbate molecules, the adsorbate solution is dilute, there is no mixed film formation at maximum solute adsorption,
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and molecules of solute and solvent occupy equal areas on the surface.12 The latter assumption has not been found to be critical. The Partial Molar Free Energy of Solution , of the The partial molar Gibbs free energy, G solute at activity ‘‘a’’ in solution is given by ¼G y þ RT ln a G
ð2Þ
y is the standard partial molar Gibbs where, G free energy of the solute in the solution. Butler13 defined the standard state to be the condition of unit activity of the solute in a solution having the properties of an infinitely dilute solution (a ¼ x). This standard state corresponds to the Henry’s law-based mole fraction scale, for which a ¼ g *x. This leads to ¼G y þ RT ln g x G x
ð3Þ
where gx is the activity coefficient. The partial molar Gibbs free energy of the pure solute in , relative to the Henry’s law mole solution, G fraction standard state, is given by eq. 4: y þ RT ln a ¼ G G
ð4Þ
The standard partial molar Gibbs free energy of transfer of the solute from the pure solid to the Henry’s law mole fraction standard state in y G . This is shown in the following solution is G equation: y y Diso pure G ¼ G G ¼ RT ln ax
ð5Þ
where ax* is the mole fraction solubility. Because the solubility of nonpolar solutes in water is usually very low, the free energy of solution is positive when the standard state of the solute in solution is the hypothetical ideal 1 mol dm3 solution.14
Differential Free Energy Change of Displacement The differential free energy change of displacement can be calculated from the equilibrium constant using the following relationship: DG ¼ RT ln Keq
ð6Þ
The uncertainty in application of this equation is in the selection of the standard state for Keq. Crisp15 chose, as a standard state, the solute in solution at the point in which 50% of the surface is covered by the solute. By assuming that the JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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adsorbed molecules behave ideally, the following equation can be obtained: ! 1 DG ¼ RT ln ð7Þ Ceq Ao t
either the above phosphate buffer or the above phosphate buffer and 2.4, 4.7, 7.1, 9.5, 11.9, or 14.2% ethyl alcohol (V/V). Ethanol was added as 95% ethanol (lot 94F20A; Midwest Grain Products Co., Inc., Atchison, KS).
where Ceq is the concentration of the unadsorbed solute in the bulk solution (at equilibrium) at the point of 50% of monolayer coverage, t is an assumed surface thickness across which the adsorbed molecules are free to undergo thermal ˚ ), and Ao is the limiting area movement (6.6 A occupied by an adsorbed molecule. The limiting area occupied by an adsorbed molecule can be calculated using the following equation:
Preparation of the Activated Carbon
Asp Ao ¼ ns 2 m No
ð8Þ
where, Asp is the specific surface area of s the n adsorbent obtained from a BET analysis, ð m2 Þ is the number of moles of diazepam adsorbed per gram of adsorbent at maximum surface coverage, and No is Avogadro’s number. Avogadro’s number can be omitted if the limiting area per mole of adsorbate is desired. Because the equilibrium concentration of diazepam in the liquid phase is a function of the free energy change involved in the transfer of diazepam from the liquid phase to the solid surface, the affinity of a compound for the surface can be related to the free energy change associated with that transfer.
MATERIALS AND METHODS Specific Surface Area Determination Specific surface area was determined by BET analysis of nitrogen vapor adsorption isotherms, at relative pressures of 0.025–0.20, using a Quantasorb instrument (Quantachrome Corp., Syosset, NY). Preparation of Diazepam Solutions SIF, USP (without pancreatin), was prepared according to the United States Pharmacopoeia, Volume XXIII. SIF consisted of 6.8 g of potassium phosphate monobasic (enzyme grade, lot 955698; Fisher Scientific, Fair Lawn, NJ), 190 mL of 0.2N NaOH (lot 946154; Fisher Scientific), and sufficient water to make 1000 mL (pH adjusted to 7.5 0.1 with 0.2N NaOH). Solutions of varying concentrations of diazepam were prepared using JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
A small amount of activated carbon, SuperChar1 (lot G812R; Gulf Bio-Systems, Inc., Dallas, TX), was spread evenly in a petri dish and vacuum dried using a NAPCO vacuum oven (model 5831; Precision Scientific, Chicago, IL) connected to a Welch Duo-Seal vacuum pump (model 1402; Sargent-Welch Scientific Co., Skokie, IL) and to a McLeod vacuum gauge (Kontes, Morton Grove, IL) at 1008C and 25 mmHg for 24 h before use. Upon removal from the vacuum oven, the sample was allowed to come to room temperature, while being stored in a vacuum desiccator, and was then immediately used for the experiment. Adsorption of Diazepam from Solution Diazepam (lot 227-070; Hoffmann La Roche, Inc., Basel, Switzerland) was dissolved in 500 mL of SIF, which contained the desired percentage of ethanol. Aliquots were removed from this stock solution and diluted to 100 mL using the same batch of cosolvent solution that was used to prepare the stock solution. Five-milliliter aliquots were removed from each of these latter dilutions and were then used to construct a Beer-Lambert Law plot. Ten samples of the activated carbon (approximately 5 mg each) were individually weighed in glass weighing funnels. Each sample, including the glass weighing funnel, was placed in an individual screw-top bottle, and the appropriate diazepam solution was added. Two layers of Teflon tape were placed over the top of the bottle to prevent leakage and to avoid direct contact of the suspension with the cap. The screw cap was then put on the bottle. The filled bottles were rotated in a Vanderkamp Sustained Release Apparatus (model W-115 water bath, model 103906 motor; Van-Kel Industries, Inc., Edison, NJ) with a heating circulator (model 1120; VWR Scientific, St. Paul, MN) at 25 rpm for 45 min (37.08C). Rotation of the bottles was then stopped, with the bottles in an upright position in the water bath, and the activated carbon was allowed to settle to the bottom of the bottles (2 h at 37.08C). An aliquot of the supernatant was removed for subsequent ultraviolet (230 nm) analysis. These adsorption studies were performed in triplicate.
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Ultraviolet Analysis of the Diazepam Solutions The diazepam concentrations, both before and after the attainment of equilibrium, were determined at the 230-nm absorbance maximum of unionized diazepam using a photodiode-array spectrophotometer (model 8450A; Hewlett Packard, Scientific Instrument Division, Palo Alto, CA). Quartz cuvettes with a 1-cm pathlength were used. If required, samples in SIF, or in SIF with different percentages of ethanol, were diluted with the same buffer or cosolvent. The amount of diazepam adsorbed by the activated carbon was obtained by mass balance. Both a Langmuir-like model and a model independent equation were fit to the data (Tablecurve 2D V3 software; Jandel Scientific, San Rafael, CA). Solubilities The solubilities of diazepam in SIF and in SIF with different percentages of ethanol were determined at 37.08C and at room temperature. An excess amount of diazepam was added to a 20-mL screw-top bottle containing either 10 mL of SIF or 10 mL of an SIF mixture with ethanol. Two layers of Teflon tape were placed over the top of the bottle to prevent leakage and to prevent solution contact with the cap; the screw cap was then put on the bottle. The samples were rotated in a temperature-controlled water bath for a period of time in excess of that required for equilibrium (24 h). After equilibration, the solutions were filtered rapidly through Teflon membranes with a 0.20-mm pore size. The filtered solutions were diluted with the same buffer and cosolvent system and analyzed spectrophotometrically.
Figure 1. Correlation of the solubility of diazepam to the percentage of the cosolvent.
molecule with the surface and the forces favoring interaction of the molecule with the solvent. In general, higher solubility results in lower adsorption at fixed Ceq. This generalization assumes that the adsorption mechanism remains the same. A log-linear solubility relationship was observed (Fig. 1), which clearly shows that the solubility of diazepam increases exponentially with increasing percentage of ethanol. Examples of the nonlinear equilibrium adsorption isotherms for diazepam are presented in Figures 2 and 3. The capacity and affinity constants of the Langmuir-like equation, obtained from nonlinear least-squares regression analysis, are presented in Table 1. Statistical analyses were performed to compare the parameters obtained in different cosolvent mixtures. At the 95% confidence level, the adsorption capacities are statistically equal, irrespective of
RESULTS AND DISCUSSION Surface Area of the Activated Carbon SuperChar1 was found to have a specific surface area of 3000 30 m2/g. This value is essentially the same as the value obtained by a previous investigator.2 Solubility and Adsorption The solubility of diazepam in the solution phase has an important role in the extent of its interaction with the activated carbon at fixed Ceq, because the extent of adsorption is a balance between the forces favoring interaction of the
Figure 2. Nonlinear Langmuir-like plot for diazepam adsorption by activated carbon in SIF. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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Figure 3. Nonlinear Langmuir-like plot for diazepam adsorption by activated carbon (14.2% ethanol in SIF).
the percentage of ethanol. This is important, because it indicates that the number of adsorption sites filled is independent of solvent composition. The affinity constants decreased significantly. This indicates that, when the solute-solvent interaction increases, the preference of the adsorbate for the adsorbent is diminished. An attempt was made to correlate the observed adsorption affinities to the percentages of ethanol. A significant correlation between the logarithms of the adsorption affinities and the percentages of ethanol was found (Fig. 4). This result can also be explained by the effect of solubility on the adsorption affinity. From the log-linear solubility relationship, a correlation between the logarithms of the adsorption affinities and the logarithms of the solubilities was expected. This relationship is shown in Figure 5. The plot clearly shows that the adsorption affinity of diazepam for the activated carbon surface is enhanced by decreasing the solubility in the solvent. The logarithmic relationship is likely due to a linear relationship between the partial molar free
energy change of displacement and the partial molar free energy change of solution. To confirm that speculation, the differential free energy changes of displacement and the differential free energy changes of solution were calculated. The linear relationship so obtained is shown in Figure 6. This plot clearly demonstrates that, when the positive free energy change of solution is high because of a low solute-solvent interaction, the adsorption process is more favorable. An attempt was also made to correlate the amount adsorbed to solubility. The parameters obtained previously from the Langmuir-like equation were used to predict the amounts of diazepam adsorbed at fixed Ceq, but different solvent concentrations. A significant correlation was observed between the logarithms of the amounts of diazepam adsorbed by activated carbon and the solubilities of diazepam in the ethanol-SIF mixtures (Fig. 7). This relationship was used to predict the complete adsorption isotherm for diazepam in SIF. The predicted isotherm was then compared with the experimentally determined isotherm (Fig. 8). The plot shows that the experimental data and the predicted data are almost identical, and that the relationship between the amount adsorbed and solubility is successful in predicting the adsorption isotherm in SIF. Model-Independent Approach It is conceivable that isotherm prediction might need to be made for a system that did not follow typical adsorption models. Although diazepam adsorption isotherms conform to the Langmuir-like equation, diazepam was once again used as the model drug. It was decided to find an equation that best predicted, statistically, the correlation between the amount adsorbed and Ceq. No physicochemical significance was ascribed to the relationship. Hence, the term ‘‘model independent’’ is
Table 1. Adsorption Parameters of the Nonlinear Langmuir-Like Equation Using Different Percentages of Ethanol Alcohol, % (V/V)
Capacity Constant (mg/g)
95% Confidence Limit (mg/g)
Affinity Constant (mL/mg)
95% Confidence Limit (mL/mg)
r2 (Coefficient Determination)
0.0 2.4 4.7 7.1 9.5 11.9 14.2
890 897 906 895 931 961 946
855–925 867–928 875–938 853–937 892–970 927–995 908–984
1023 844 600 439 314 194 147
897–1150 757–932 530–670 380–499 275–353 176–213 131–163
0.980 0.983 0.982 0.971 0.980 0.988 0.987
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Figure 4. Correlation of the adsorption affinity to the percentage of the cosolvent.
used to refer to an equation that has no basis in fundamental adsorption theory. An automated curve fitting program (TableCurve 2D) was used. The program offers up to 3456 linear and nonlinear equations that can be tried and then sorted according to the goodness of the fit. The fitted equations can be sorted using the coefficient of determination, degrees of freedom adjusted coefficient of determination, least squares error of fit, or F statistic. The equation that was most frequently selected by the program to fit the experimental results was the following: ðns2 =mÞ0:5 ¼ A þ B ln ðCeq =SolÞ
ð9Þ
where ns2 =m is the amount of diazepam adsorbed per mass of activated carbon, Ceq is the concentration of the unadsorbed diazepam in the
Figure 5. Correlation of the logarithm of the adsorption affinity to the logarithm of the solubility of diazepam.
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Figure 6. Correlation of the partial molar free energy of displacement to the partial molar free energy of solution.
ethanol-SIF mixture at equilibrium, Sol is the solubility of diazepam in the ethanol-SIF mixture, and A and B are constants having no particular meaning. Examples of the adsorption isotherms are presented in Figures 9 and 10. The parameters (model-independent equation) obtained for different cosolvent mixtures are presented in Table 2. A statistical analysis of the aforementioned parameters was performed. The results, at the 95% confidence level, showed that the parameters were statistically equal for adsorption experiments performed using different percentages of ethanol, and that the differences in the isotherms were due to differences in diazepam solubility. The similarity between the isotherms is demonstrated in Figure 11, where the amount adsorbed is plotted versus the reduced concentration (Ceq/solubility).
Figure 7. Correlation of the amount of diazepam adsorbed by activated carbon (Langmuir-like equation) to the solubility. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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Figure 8. Adsorption of diazepam by activated carbon (SIF only) using experimental and predicted data from the Langmuir-like equation.
An attempt to correlate the amount adsorbed to solubility was again made. The parameters obtained from the model-independent equation were used to predict the amount of diazepam adsorbed at fixed Ceq, but different solvent concentrations. A significant correlation was observed between the logarithms of the amount adsorbed and the solubilities in the ethanol-SIF mixtures (Fig. 12). This relationship was used to predict the complete isotherm. Figure 13 shows the comparison between the predicted isotherm and the isotherm obtained from direct experiment. This figure demonstrates that the predicted data from the model-independent equation and the experimental data are almost identical.
Figure 10. Model independent plot for diazepam adsorption by activated carbon (14.2% ethanol in SIF).
CONCLUSIONS Evaluation of the solvent effects indicated that increasing the solubility of diazepam decreased the adsorption affinity, whereas the capacity remained constant. An excellent logarithmic relationship was observed between the adsorption affinity and the solubility of diazepam in the ethanol-SIF mixtures. This relationship was explained by a linear relationship between the differential free energy change of displacement and the differential free energy change of solution. Excellent correlations were observed, for both the Langmuir-like equation and the model-independent equation, between the amounts of diazepam adsorbed by activated carbon and the solubilities of diazepam in the ethanol-SIF mixtures. The relationship between amount adsorbed and solubility was used to predict the complete adsorption isotherm of diazepam in SIF. This prediction was in excellent agreement with the experimental results for both equations. The experimental work and the analyses described above allow the development of the following equation: ns2 K1 K2 Ceqm =Sm ¼ m 1=Sw þ K2 Ceqm =Sm
Figure 9. Model independent plot for diazepam adsorption by activated carbon in SIF. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
ð10Þ
where Sm is the solubility of diazepam in the ethanol-SIF mixture, Sw is the solubility of diazepam in SIF, K2 is the adsorption affinity in SIF, and all of the other variables have the same
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Table 2. The Parameters of the Model Independent Equation Obtained Using Different Percentages of Ethanol Alcohol, % (V/V) 0.0 2.4 4.7 7.1 9.5 11.9 14.2
Parameter A
95% Confidence Limit
Parameter B
95% Confidence Limit
r2 Coefficient Determination
37.4 37.8 37.7 37.5 38.0 38.0 37.4
35.9–39.0 37.0–38.7 37.1–38.3 36.3–38.6 37.3–38.7 37.5–38.6 36.6–38.2
4.13 4.20 4.28 4.29 4.47 4.74 4.67
3.69–4.56 3.96–4.45 4.10–4.46 3.97–4.61 4.27–4.67 4.57–4.91 4.42–4.91
0.980 0.993 0.996 0.987 0.996 0.997 0.994
Figure 11. Adsorption of diazepam by activated carbon using different percentages of ethanol in SIF.
Figure 13. Adsorption of diazepam by activated carbon (SIF only) using experimental and predicted data from the model independent equation.
meanings as previously defined. This modified Langmuir-like equation has the same assumptions as the normal Langmuir-like equation and the additional assumptions that the adsorption capacity is not affected by the cosolvent, the adsorption mechansim remains the same, and the cosolvent can be as readily displaced from the surface by the solute (diazepam) as is water. This equation allows the capacity and affinity constants for the adsorption process in water to be obtained from a single run in another medium as long as Sm and Sw are known.
ACKNOWLEDGMENTS
Figure 12. Correlation of the amount of diazepam adsorbed by activated carbon (model independent equation) to the solubility.
The facilities provided to one of the authors (D. E. W.) by the Obermann Center for Advanced Studies contributed greatly to the completion of this work, and are gratefully acknowledged. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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REFERENCES 1. Connors KA, Amidon GL, Stella VJ. 1986. Chemical stability of pharmaceuticals. 2nd ed. New York: John Wiley & Sons, pp 412–420. 2. Wurster DE, Burke GM, Berg MJ, Veng-Pedersen P, Schottelius DD. 1988. Phenobarbital adsorption from simulated intestinal fluid, U.S.P., and simulated gastric fluid, U.S.P., by two activated charcoals. Pharm Res 5:183–186. 3. Burke GM, Wurster DE, Buraphacheep V, Berg MJ, Veng-Pedersen P, Schottelius DD. 1991. Model selection for the adsorption of phenobarbital by activated charcoal. Pharm Res 8:228–231. 4. Burke GM, Wurster DE, Berg MJ, Veng-Pedersen P, Schottelius DD. 1992. Surface characterization of activated charcoal by X-ray photoelectron spectroscopy (XPS): Correlation with phenobarbital adsorption data. Pharm Res 9:126–130. 5. Huang L-F. 1993. Determination of the heats of displacement for various barbituric acid derivatives on two activated charcoals [PhD thesis]. Iowa City, IA: University of Iowa. 6. Parfitt GD, Rochester CH. 1983. Adsorption from solution at the solid/liquid interface. New York: Academic Press, pp 23–24.
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7. Hansen RS, Craig RP. 1954. The adsorption of aliphatic alcohols and acids from aqueous solutions by non-porous carbon. J Phys Chem 59:211–215. 8. Kolthoff IM, Gutmacher RG, Kahn A. 1951. Sorption of GR-S type rubber by carbon black. II. J Phys Chem 55:1240–1246. 9. Rubino JT, Yalkowsky SH. 1985. Solubilization by cosolvents. III. Diazepam and benzocaine in binary solvents. J Parenter Sci Technol 39(3):106–111. 10. Rubino JT, Blanchard J, Yalkowsky SH. 1987. Solubilization by cosolvents. IV. Diazepam and phenytoin in aprotic cosolvent-water mixtures. J Parenter Sci Technol 41(5):172–176. 11. Kipling JJ. 1965. Adsorption from solutions of non-electrolytes. New York: Academic Press, p 93. 12. Adamson AW. 1990. Physical chemistry of surfaces. 5th ed. New York: John Wiley & Sons, pp 422–423. 13. Grant DJW, Higuchi T. 1990. Solubility behavior of organic compounds. New York: John Wiley & Sons, pp 118–120. 14. Grant DJW, Higuchi T. 1990. Solubility behavior of organic compounds. New York: John Wiley & Sons, p 356. 15. Crisp DJ. 1956. The adsorption of alcohols and phenols from nonpolar solvents onto alumina. J Colloid Sci 11:356–376.
College of Pharmacy, University of Iowa, Iowa City, Iowa 52242
2
Obermann Center for Advanced Studies, University of Iowa, Iowa City, Iowa 52242
Received 30 October 2002; revised 3 March 2003; accepted 28 March 2003
ABSTRACT: Adsorption isotherms for the diazepam-activated carbon system in simulated intestinal fluid (SIF), without pancreatin, and in SIF with different percentages of ethanol were determined as were the solubilities of diazepam in SIF and in SIF with different percentages of ethanol. The surface area of the activated carbon was also evaluated. The results from the experimental work provided information on the relationship between adsorption and solubility. An excellent logarithmic relationship was observed between the adsorption affinity and the solubility of diazepam in the ethanol-SIF mixtures. This relationship was explained by a linear relationship between the differential free energy of displacement and the differential free energy of solution. Excellent correlations were also observed between the amounts of diazepam adsorbed by activated carbon and the solubilities of diazepam in the ethanol-SIF mixtures. This relationship was used to predict the complete isotherm, which was in excellent agreement with the experimental work. ß 2003 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 92:2008–2016, 2003
Keywords:
adsorption; diazepam; solubility; activated carbon; cosolvent
INTRODUCTION The ability to conduct classical adsorption experiments can be severely limited by poor solubility of a test compound. This limitation is mainly due to limitations in analytical sensitivity and to the inaccuracies in weighing and transferring very small amounts of adsorbents. Accordingly, it is desirable to develop techniques to predict the adsorption isotherms of poorly water-soluble drugs in purely aqueous systems. This goal is likely to be achieved using miscible cosolvents, because these cosolvents should affect the extent of adsorption in a systematic manner.
Khouloud A. Alkhamis’s present address is Jordan University of Science and Technology, Irbid, 22110, Jordan. Correspondence to: Dale Eric Wurster (Telephone: 319-3358825; Fax: 319-335-9349; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 92, 2008–2016 (2003) ß 2003 Wiley-Liss, Inc. and the American Pharmacists Association
2008
Diazepam was selected as a model compound in this research for the following reasons. First, the solubility of the free base form of diazepam is very low. However, diazepam’s solubility is just sufficient to allow the direct testing of the predictive method being developed. In simulated intestinal fluid (SIF) (without pancreatin), the solubility is <0.06 mg/mL at 378C. Second, diazepam is quite stable at the chosen experimental pH of 7.5.1 Third, it is a sufficiently weak base that it is unionized at a pH of 7.5. Therefore, changes in ionic strength are not likely to significantly affect the results. Finally, the carbonyl group on the seven-membered ring will likely hydrogen bond with the hydroxyl hydrogens on activated carbon. This belief is based on previous work2–5 which indicates that compounds having a carbonyl group are likely to interact with the hydroxyl groups on the activated carbon surface. Bonding specificity justifies the use of a Langmuir-like equation, which is premised on the adsorption sites being homogeneous.
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The effect of decreasing aqueous solubility on adsorption from aqueous solutions has long been known.6 Similarly, a regular increase in adsorption with increasing hydrocarbon chain length is usually observed when hydrocarbon adsorption occurs from aqueous media.6 Hansen and Craig7 observed the similarity of adsorption isotherms within a homologous series when isotherms were plotted as a function of reduced concentration (concentration at equilibrium divided by the solubility, or Ceq/solubility). Kolthoff et al.8 also noticed that the adsorption of polymers onto substrates was markedly dependent on the solvent. Rubino et al.9,10 have shown that co-solvent/water mixtures are useful for solubilizing diazepam.
Adsorption from Solution Several models have been used to characterize the process of adsorption from solution, the most frequent being the Langmuir-like equation.11,12 The original derivation of the Langmuir equation used a kinetic argument for the vapor/solid system. However, adsorption in a solution/solid system is not exactly analogous to adsorption in a vapor/solid system. The Langmuir equation has been derived for the solution/solid system using a thermodynamic (law of mass action) argument. In the current literature, the equation derived via the thermodynamic argument is usually referred to as the Langmuir-like equation. Although the Langmuir and Langmuir-like equations are identical in form, the Langmuir-like terminology alerts the reader to the potential for slight differences in the meanings of the modelistic parameters. The Langmuir-like equation is given below: ns2 K1 K2 Ceq ¼ m 1 þ K2 Ceq
ð1Þ
where ns2 is the amount of solute adsorbed, m is the mass of adsorbent, K1 is the capacity constant, K2 is the affinity constant, and Ceq is the concentration of unadsorbed solute in the bulk solution at equilibrium. The Langmuir-like equation is based on several assumptions11: there are a fixed number of sites available for adsorption, the heat of adsorption is independent of surface coverage (all of the sites available for adsorption are energetically equivalent), the adsorbed phase is confined to a monolayer, there are no lateral interactions between adsorbate molecules, the adsorbate solution is dilute, there is no mixed film formation at maximum solute adsorption,
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and molecules of solute and solvent occupy equal areas on the surface.12 The latter assumption has not been found to be critical. The Partial Molar Free Energy of Solution , of the The partial molar Gibbs free energy, G solute at activity ‘‘a’’ in solution is given by ¼G y þ RT ln a G
ð2Þ
y is the standard partial molar Gibbs where, G free energy of the solute in the solution. Butler13 defined the standard state to be the condition of unit activity of the solute in a solution having the properties of an infinitely dilute solution (a ¼ x). This standard state corresponds to the Henry’s law-based mole fraction scale, for which a ¼ g *x. This leads to ¼G y þ RT ln g x G x
ð3Þ
where gx is the activity coefficient. The partial molar Gibbs free energy of the pure solute in , relative to the Henry’s law mole solution, G fraction standard state, is given by eq. 4: y þ RT ln a ¼ G G
ð4Þ
The standard partial molar Gibbs free energy of transfer of the solute from the pure solid to the Henry’s law mole fraction standard state in y G . This is shown in the following solution is G equation: y y Diso pure G ¼ G G ¼ RT ln ax
ð5Þ
where ax* is the mole fraction solubility. Because the solubility of nonpolar solutes in water is usually very low, the free energy of solution is positive when the standard state of the solute in solution is the hypothetical ideal 1 mol dm3 solution.14
Differential Free Energy Change of Displacement The differential free energy change of displacement can be calculated from the equilibrium constant using the following relationship: DG ¼ RT ln Keq
ð6Þ
The uncertainty in application of this equation is in the selection of the standard state for Keq. Crisp15 chose, as a standard state, the solute in solution at the point in which 50% of the surface is covered by the solute. By assuming that the JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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adsorbed molecules behave ideally, the following equation can be obtained: ! 1 DG ¼ RT ln ð7Þ Ceq Ao t
either the above phosphate buffer or the above phosphate buffer and 2.4, 4.7, 7.1, 9.5, 11.9, or 14.2% ethyl alcohol (V/V). Ethanol was added as 95% ethanol (lot 94F20A; Midwest Grain Products Co., Inc., Atchison, KS).
where Ceq is the concentration of the unadsorbed solute in the bulk solution (at equilibrium) at the point of 50% of monolayer coverage, t is an assumed surface thickness across which the adsorbed molecules are free to undergo thermal ˚ ), and Ao is the limiting area movement (6.6 A occupied by an adsorbed molecule. The limiting area occupied by an adsorbed molecule can be calculated using the following equation:
Preparation of the Activated Carbon
Asp Ao ¼ ns 2 m No
ð8Þ
where, Asp is the specific surface area of s the n adsorbent obtained from a BET analysis, ð m2 Þ is the number of moles of diazepam adsorbed per gram of adsorbent at maximum surface coverage, and No is Avogadro’s number. Avogadro’s number can be omitted if the limiting area per mole of adsorbate is desired. Because the equilibrium concentration of diazepam in the liquid phase is a function of the free energy change involved in the transfer of diazepam from the liquid phase to the solid surface, the affinity of a compound for the surface can be related to the free energy change associated with that transfer.
MATERIALS AND METHODS Specific Surface Area Determination Specific surface area was determined by BET analysis of nitrogen vapor adsorption isotherms, at relative pressures of 0.025–0.20, using a Quantasorb instrument (Quantachrome Corp., Syosset, NY). Preparation of Diazepam Solutions SIF, USP (without pancreatin), was prepared according to the United States Pharmacopoeia, Volume XXIII. SIF consisted of 6.8 g of potassium phosphate monobasic (enzyme grade, lot 955698; Fisher Scientific, Fair Lawn, NJ), 190 mL of 0.2N NaOH (lot 946154; Fisher Scientific), and sufficient water to make 1000 mL (pH adjusted to 7.5 0.1 with 0.2N NaOH). Solutions of varying concentrations of diazepam were prepared using JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
A small amount of activated carbon, SuperChar1 (lot G812R; Gulf Bio-Systems, Inc., Dallas, TX), was spread evenly in a petri dish and vacuum dried using a NAPCO vacuum oven (model 5831; Precision Scientific, Chicago, IL) connected to a Welch Duo-Seal vacuum pump (model 1402; Sargent-Welch Scientific Co., Skokie, IL) and to a McLeod vacuum gauge (Kontes, Morton Grove, IL) at 1008C and 25 mmHg for 24 h before use. Upon removal from the vacuum oven, the sample was allowed to come to room temperature, while being stored in a vacuum desiccator, and was then immediately used for the experiment. Adsorption of Diazepam from Solution Diazepam (lot 227-070; Hoffmann La Roche, Inc., Basel, Switzerland) was dissolved in 500 mL of SIF, which contained the desired percentage of ethanol. Aliquots were removed from this stock solution and diluted to 100 mL using the same batch of cosolvent solution that was used to prepare the stock solution. Five-milliliter aliquots were removed from each of these latter dilutions and were then used to construct a Beer-Lambert Law plot. Ten samples of the activated carbon (approximately 5 mg each) were individually weighed in glass weighing funnels. Each sample, including the glass weighing funnel, was placed in an individual screw-top bottle, and the appropriate diazepam solution was added. Two layers of Teflon tape were placed over the top of the bottle to prevent leakage and to avoid direct contact of the suspension with the cap. The screw cap was then put on the bottle. The filled bottles were rotated in a Vanderkamp Sustained Release Apparatus (model W-115 water bath, model 103906 motor; Van-Kel Industries, Inc., Edison, NJ) with a heating circulator (model 1120; VWR Scientific, St. Paul, MN) at 25 rpm for 45 min (37.08C). Rotation of the bottles was then stopped, with the bottles in an upright position in the water bath, and the activated carbon was allowed to settle to the bottom of the bottles (2 h at 37.08C). An aliquot of the supernatant was removed for subsequent ultraviolet (230 nm) analysis. These adsorption studies were performed in triplicate.
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Ultraviolet Analysis of the Diazepam Solutions The diazepam concentrations, both before and after the attainment of equilibrium, were determined at the 230-nm absorbance maximum of unionized diazepam using a photodiode-array spectrophotometer (model 8450A; Hewlett Packard, Scientific Instrument Division, Palo Alto, CA). Quartz cuvettes with a 1-cm pathlength were used. If required, samples in SIF, or in SIF with different percentages of ethanol, were diluted with the same buffer or cosolvent. The amount of diazepam adsorbed by the activated carbon was obtained by mass balance. Both a Langmuir-like model and a model independent equation were fit to the data (Tablecurve 2D V3 software; Jandel Scientific, San Rafael, CA). Solubilities The solubilities of diazepam in SIF and in SIF with different percentages of ethanol were determined at 37.08C and at room temperature. An excess amount of diazepam was added to a 20-mL screw-top bottle containing either 10 mL of SIF or 10 mL of an SIF mixture with ethanol. Two layers of Teflon tape were placed over the top of the bottle to prevent leakage and to prevent solution contact with the cap; the screw cap was then put on the bottle. The samples were rotated in a temperature-controlled water bath for a period of time in excess of that required for equilibrium (24 h). After equilibration, the solutions were filtered rapidly through Teflon membranes with a 0.20-mm pore size. The filtered solutions were diluted with the same buffer and cosolvent system and analyzed spectrophotometrically.
Figure 1. Correlation of the solubility of diazepam to the percentage of the cosolvent.
molecule with the surface and the forces favoring interaction of the molecule with the solvent. In general, higher solubility results in lower adsorption at fixed Ceq. This generalization assumes that the adsorption mechanism remains the same. A log-linear solubility relationship was observed (Fig. 1), which clearly shows that the solubility of diazepam increases exponentially with increasing percentage of ethanol. Examples of the nonlinear equilibrium adsorption isotherms for diazepam are presented in Figures 2 and 3. The capacity and affinity constants of the Langmuir-like equation, obtained from nonlinear least-squares regression analysis, are presented in Table 1. Statistical analyses were performed to compare the parameters obtained in different cosolvent mixtures. At the 95% confidence level, the adsorption capacities are statistically equal, irrespective of
RESULTS AND DISCUSSION Surface Area of the Activated Carbon SuperChar1 was found to have a specific surface area of 3000 30 m2/g. This value is essentially the same as the value obtained by a previous investigator.2 Solubility and Adsorption The solubility of diazepam in the solution phase has an important role in the extent of its interaction with the activated carbon at fixed Ceq, because the extent of adsorption is a balance between the forces favoring interaction of the
Figure 2. Nonlinear Langmuir-like plot for diazepam adsorption by activated carbon in SIF. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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Figure 3. Nonlinear Langmuir-like plot for diazepam adsorption by activated carbon (14.2% ethanol in SIF).
the percentage of ethanol. This is important, because it indicates that the number of adsorption sites filled is independent of solvent composition. The affinity constants decreased significantly. This indicates that, when the solute-solvent interaction increases, the preference of the adsorbate for the adsorbent is diminished. An attempt was made to correlate the observed adsorption affinities to the percentages of ethanol. A significant correlation between the logarithms of the adsorption affinities and the percentages of ethanol was found (Fig. 4). This result can also be explained by the effect of solubility on the adsorption affinity. From the log-linear solubility relationship, a correlation between the logarithms of the adsorption affinities and the logarithms of the solubilities was expected. This relationship is shown in Figure 5. The plot clearly shows that the adsorption affinity of diazepam for the activated carbon surface is enhanced by decreasing the solubility in the solvent. The logarithmic relationship is likely due to a linear relationship between the partial molar free
energy change of displacement and the partial molar free energy change of solution. To confirm that speculation, the differential free energy changes of displacement and the differential free energy changes of solution were calculated. The linear relationship so obtained is shown in Figure 6. This plot clearly demonstrates that, when the positive free energy change of solution is high because of a low solute-solvent interaction, the adsorption process is more favorable. An attempt was also made to correlate the amount adsorbed to solubility. The parameters obtained previously from the Langmuir-like equation were used to predict the amounts of diazepam adsorbed at fixed Ceq, but different solvent concentrations. A significant correlation was observed between the logarithms of the amounts of diazepam adsorbed by activated carbon and the solubilities of diazepam in the ethanol-SIF mixtures (Fig. 7). This relationship was used to predict the complete adsorption isotherm for diazepam in SIF. The predicted isotherm was then compared with the experimentally determined isotherm (Fig. 8). The plot shows that the experimental data and the predicted data are almost identical, and that the relationship between the amount adsorbed and solubility is successful in predicting the adsorption isotherm in SIF. Model-Independent Approach It is conceivable that isotherm prediction might need to be made for a system that did not follow typical adsorption models. Although diazepam adsorption isotherms conform to the Langmuir-like equation, diazepam was once again used as the model drug. It was decided to find an equation that best predicted, statistically, the correlation between the amount adsorbed and Ceq. No physicochemical significance was ascribed to the relationship. Hence, the term ‘‘model independent’’ is
Table 1. Adsorption Parameters of the Nonlinear Langmuir-Like Equation Using Different Percentages of Ethanol Alcohol, % (V/V)
Capacity Constant (mg/g)
95% Confidence Limit (mg/g)
Affinity Constant (mL/mg)
95% Confidence Limit (mL/mg)
r2 (Coefficient Determination)
0.0 2.4 4.7 7.1 9.5 11.9 14.2
890 897 906 895 931 961 946
855–925 867–928 875–938 853–937 892–970 927–995 908–984
1023 844 600 439 314 194 147
897–1150 757–932 530–670 380–499 275–353 176–213 131–163
0.980 0.983 0.982 0.971 0.980 0.988 0.987
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Figure 4. Correlation of the adsorption affinity to the percentage of the cosolvent.
used to refer to an equation that has no basis in fundamental adsorption theory. An automated curve fitting program (TableCurve 2D) was used. The program offers up to 3456 linear and nonlinear equations that can be tried and then sorted according to the goodness of the fit. The fitted equations can be sorted using the coefficient of determination, degrees of freedom adjusted coefficient of determination, least squares error of fit, or F statistic. The equation that was most frequently selected by the program to fit the experimental results was the following: ðns2 =mÞ0:5 ¼ A þ B ln ðCeq =SolÞ
ð9Þ
where ns2 =m is the amount of diazepam adsorbed per mass of activated carbon, Ceq is the concentration of the unadsorbed diazepam in the
Figure 5. Correlation of the logarithm of the adsorption affinity to the logarithm of the solubility of diazepam.
2013
Figure 6. Correlation of the partial molar free energy of displacement to the partial molar free energy of solution.
ethanol-SIF mixture at equilibrium, Sol is the solubility of diazepam in the ethanol-SIF mixture, and A and B are constants having no particular meaning. Examples of the adsorption isotherms are presented in Figures 9 and 10. The parameters (model-independent equation) obtained for different cosolvent mixtures are presented in Table 2. A statistical analysis of the aforementioned parameters was performed. The results, at the 95% confidence level, showed that the parameters were statistically equal for adsorption experiments performed using different percentages of ethanol, and that the differences in the isotherms were due to differences in diazepam solubility. The similarity between the isotherms is demonstrated in Figure 11, where the amount adsorbed is plotted versus the reduced concentration (Ceq/solubility).
Figure 7. Correlation of the amount of diazepam adsorbed by activated carbon (Langmuir-like equation) to the solubility. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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Figure 8. Adsorption of diazepam by activated carbon (SIF only) using experimental and predicted data from the Langmuir-like equation.
An attempt to correlate the amount adsorbed to solubility was again made. The parameters obtained from the model-independent equation were used to predict the amount of diazepam adsorbed at fixed Ceq, but different solvent concentrations. A significant correlation was observed between the logarithms of the amount adsorbed and the solubilities in the ethanol-SIF mixtures (Fig. 12). This relationship was used to predict the complete isotherm. Figure 13 shows the comparison between the predicted isotherm and the isotherm obtained from direct experiment. This figure demonstrates that the predicted data from the model-independent equation and the experimental data are almost identical.
Figure 10. Model independent plot for diazepam adsorption by activated carbon (14.2% ethanol in SIF).
CONCLUSIONS Evaluation of the solvent effects indicated that increasing the solubility of diazepam decreased the adsorption affinity, whereas the capacity remained constant. An excellent logarithmic relationship was observed between the adsorption affinity and the solubility of diazepam in the ethanol-SIF mixtures. This relationship was explained by a linear relationship between the differential free energy change of displacement and the differential free energy change of solution. Excellent correlations were observed, for both the Langmuir-like equation and the model-independent equation, between the amounts of diazepam adsorbed by activated carbon and the solubilities of diazepam in the ethanol-SIF mixtures. The relationship between amount adsorbed and solubility was used to predict the complete adsorption isotherm of diazepam in SIF. This prediction was in excellent agreement with the experimental results for both equations. The experimental work and the analyses described above allow the development of the following equation: ns2 K1 K2 Ceqm =Sm ¼ m 1=Sw þ K2 Ceqm =Sm
Figure 9. Model independent plot for diazepam adsorption by activated carbon in SIF. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
ð10Þ
where Sm is the solubility of diazepam in the ethanol-SIF mixture, Sw is the solubility of diazepam in SIF, K2 is the adsorption affinity in SIF, and all of the other variables have the same
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Table 2. The Parameters of the Model Independent Equation Obtained Using Different Percentages of Ethanol Alcohol, % (V/V) 0.0 2.4 4.7 7.1 9.5 11.9 14.2
Parameter A
95% Confidence Limit
Parameter B
95% Confidence Limit
r2 Coefficient Determination
37.4 37.8 37.7 37.5 38.0 38.0 37.4
35.9–39.0 37.0–38.7 37.1–38.3 36.3–38.6 37.3–38.7 37.5–38.6 36.6–38.2
4.13 4.20 4.28 4.29 4.47 4.74 4.67
3.69–4.56 3.96–4.45 4.10–4.46 3.97–4.61 4.27–4.67 4.57–4.91 4.42–4.91
0.980 0.993 0.996 0.987 0.996 0.997 0.994
Figure 11. Adsorption of diazepam by activated carbon using different percentages of ethanol in SIF.
Figure 13. Adsorption of diazepam by activated carbon (SIF only) using experimental and predicted data from the model independent equation.
meanings as previously defined. This modified Langmuir-like equation has the same assumptions as the normal Langmuir-like equation and the additional assumptions that the adsorption capacity is not affected by the cosolvent, the adsorption mechansim remains the same, and the cosolvent can be as readily displaced from the surface by the solute (diazepam) as is water. This equation allows the capacity and affinity constants for the adsorption process in water to be obtained from a single run in another medium as long as Sm and Sw are known.
ACKNOWLEDGMENTS
Figure 12. Correlation of the amount of diazepam adsorbed by activated carbon (model independent equation) to the solubility.
The facilities provided to one of the authors (D. E. W.) by the Obermann Center for Advanced Studies contributed greatly to the completion of this work, and are gratefully acknowledged. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 10, OCTOBER 2003
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