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Moisture Sorption Kinetics for Water-Soluble Substances IV: Studies with Mixtures of Solids
Moisture Sorption Kinetics for Water-Soluble Substances IV: Studies with Mixtures of Solids MARK J. KONTNY A N D GEORGEZ O G R A F I ~ Received March 5, 1984, from the School of Pharmacy, University of Wisconsin-Madison,Madison, WI 53706. 1984. Abstract 0 This paper extends earlier work from this laboratory concerning the sorption kinetics of water vapor on deliquescent watersoluble substances to mixtures of these solids. A theoretical model, based on heat transport control, excellently predicted a priori the rate of water uptake by a variety of binary mixtures of alkali halides and sugars. The rates for mixtures containing highly water-soluble quaternary ammonium salts, as either one or both of the components, were less successfully predicted as the combined water solubilities of the two components increased. It is concluded that water-soluble deliquescent substances,normally encountered in pharmaceutical dosage forms, rapidly form saturated aqueous solutions in the aqueous film formed as water vapor uptake proceeds, and that the water uptake rate can be predicted a priori from known and experimentally determinable parameters using the heat transport model.
Accepted for publication July 27,
I1 of ref. 1.) Since all of these parameters are either available in the literature or experimentally determinable, it was possible to use eq. 1 to predict, a priori, the value of W' for various values of RHi with solids of varying Fit to eq. 1 was excellent for a variety of alkali halides, sugars, and quaternary ammonium salts. In the present study, the heat transport model was extended to systems containing more than one water-soluble substance. The general aim was to see if the model would be useful when parameters determined for single component systems were appropriately combined for any mixture of solids. It was experimentally tested under vacuum conditions using various mixtures of some of the substances previously studied.2
Experimental Section This paper extends earlier work reported from this lab~ratoryl-~ concerning the sorption kinetics of water vapor on deliquescent water-soluble substances. Models were developed previously to describe the rate of sorption on a solid substance as a function of the relative humidity, RHi, of the environment surrounding the sample. In this model it is assumed that water sorbed on a solid surface dissolves some of the solid to form a saturated solution with a relative humidity, RHO.Further water vapor will continue to condense on this liquid film in accord with the model predictions as long as RHO is less than RH, and a saturated solution is maintained. The most general model developed3accounts for water uptake in the presence of air by assuming that both diffusion of water vapor to and heat transport away from the surface limit the rate of water uptake. The heat change results from the condensation of water vapor and other processes such as solution and hydration. The net heat generated maintains the liquid-vapor interface at temperature T,, elevated above that of the atmosphere maintained at T, by external means. The water vapor pressure over the saturated film, therefore, rises with temperature until the pressure difference between the surface and the atmosphere becomes infinitesimal and remains so during steady-state uptake. In an environment consisting of pure water vapor (initial vacuum conditions), vapor diffusion need not be considered. For this special case, only the rate at which heat is transported away from the surface is assumed to limit the sorption rate, W '. The mathematical expression derived' to express this rate as a function of RHi and RHOis:
(The various symbols represent parameters listed in Appendix 124
I Journal of Pharmaceutical Sciences Vol. 74, No. 2, February 1985
Materials-The materials used in this study and their sources have all been reported with the exception of tetraethylammonium bromide (Aldrich Chemical Co.), which was used as received.2 Equipment a n d Procedures-The apparatus, consisting of an electrobalance within a vacuum system, and the general procedures used to measure sorption kinetics have been described in considerable detail elsewhere? All studies were carried out using disks prepared by compressing mixtures of solids, previously mixed to various proportions. All samples were ground to a fine powder before compression. The relative humidity over a saturated solution of each mixture used, at 25"C, was measured directly by dissolving an excess of each of the materials in water, freezing this mixture by immersing the sample cell in a dry ice:methanol bath, evacuating the volume above the frozen sample, and melting the sample at 2 5 T , allowing liquid-vapor reequilibration in the closed system. This freeze-evacuate-equilibrate cycle was repeated twice before the vapor pressure above the saturated solution was measured using an oil manometer, as described elsewhere.2
Results Studies With Single Component Systems-In the previous study,2 the only solid showing very poor fit to eq. 1 was tetrabutylammonium bromide, the only substance exhibiting an exothermic heat of solution. It was suggested2that this lack of fit might be the result of the very unusual hydration properties of this omp pound.^ It has since been observed that the tetrabutylammonium ion, because of this hydration, exhibits a significant heat of dilution amounting to -8 kcal/mol for a saturated ~ o l u t i o n .~ Since the value for the heat of solution used in the earlier report' was taken at infinite dilution, and since it appears that a saturated solution actually exists in the aqueous film, a correction for AH in eq. 1 was made using the heat of dilution. Figure 1 shows the marked improvement in results when the heat of dilution is taken into account. Also shown in Fig. 1 are the results with tetraethylammonium bro0022-3549/85/0200-0124$01 .OO/O 0 1985, American Pharmaceutical Association
mide,6 which exhibits an exothermic heat of solution, comparable with tetrabutylammonium bromide, but only a negligible heat of d i l ~ t i o n .The ~ fit of experiment to theory is again excellent, confirming that the model adequately describes the kinetics of water vapor sorption onto the tetraalkylammonium salts. Studies With Mixtures-In order to use eq. 1 to obtain the theoretical description of sorption rate versus relative humidity for mixtures of the various solids, it was necessary to determine RHOfor the mixture, as well as to account for the heat changes occurring when more than one solid dissolves. Table I lists the RHOvalues experimentally determined for each mixture. The value of AH. used for mixtures in eq. 1 was determined by summing the heat contributions of each component:
AH = AH,
where AH, is the heat of condensation of water, Csat,"is the solubility of each individual component alone in water (expressed as molality), and AH, is the heat of solution for each component in water (see Table I of ref. 2 for individual values of Cmtand AH,). The heat of dilution was also included when tetrabutylammonium bromide was used. It is thus assumed in eq. 2 that any effect of a heat of mixing of two or more components is negligible. Figures 2-6 depict typical results
obtained with a variety of mixtures of alkali halides, sucrose, and quaternary ammonium salts. The theoretical plots in each case were obtained from eq. 1, as described above. Fit of theory and experiment for selected mixtures of alkali halides and sucrose, shown in Figs. 2-4 is excellent, while the combinations of quaternary ammonium salts and potassium bromide, depicted in Fig. 5, show a slightly less satisfactory fit. Figure 6 shows that the combination of two quaternary ammonium salts deviates significantly from the theoretical model. As noted in Fig. 5 for tetrabutylammonium bromide-potassium bromide mixture^,^ the composition of the mixture had no effect on RHO or the kinetics of water vapor uptake. This was confirmed with some of the other systems as well and is consistent with the theoretical model. To more conveniently illustrate the fit of data from all mixtures to eq. 1, extrapolated values of RHOare presented in Table I and compared with experimental values obtained from direct measurements of mixed saturated solutions. These extrapolated values were obtained by assuming the heat transport model to be correct (using appropriate values of C,,, and AH, obtained from eq. 1 in ref. 2) and regression of actual sorption data points to obtain the best fitting RHOvalue. As seen in Table I, the fit gave RHOvalues which are in excellent agreement with actual RHOmeasurements. The mixture of choline bromide and tetrabutylammonium bromide is not included in this comparison because, as shown in Fig. 6, it did not come close to satisfactorily fitting the theoretical model. 0.r
0.6 h
.-c
0
E 3
E
3 E
Y
Y
W
!-
<
1.0
-
0.8
-
0.6
-
0.4
-
U
y
2 5
W
I-
< U
0.4
W
Y
4. 0.3
U
k 4.
0.5
E
1.21
3
U
W
3 0.2 0 40
50
60
70
00
90
Table I-Comparison
L
100
RELATIVE HUMIDITY Figure 1-Water uptake rate versus relative humidity for tetraethylammonium bromide (0)and tetrabutylammonium bromide (0).The lines are theoretical/y derived from eq. 7: (-) tetraethylammonium bromide; (-) tetrabutylammonium bromide, no correction for heat of dilution; (- - - -) tetrabutylammonium bromide, corrected for heat of dilution.
60 65
70
75 80 85
SO 95
100
RELATIVE HUMIDITY Figure 2-Water
uptake rate versus relative humidity for sodium chloride-potassium bromide. The solid line is the theoretical plot obtained from eq. 7.
of Experimental RHOValues with Those Extrapolatedfrom Kinetic Experiments
Mixture
Sodium chloride-potassium bromide Potassium chloride-sodium chloride Potassium chloride-potassium bromide Sucrose-potassium bromide Sucrose-dextrose monohydrate Sucrose-sodium chloride-potassium bromide Choline bromide-potassium bromide Tetrabutylammoniumbromide-potassium bromide Tetrabutvlammoniurnbromide-choline bromide
RHOValues
Experimental 64 67 73 66 68 57 40 57 34
Extrapolated 63 74 81 68 71 53 42 64
Journal of Pharmaceutical Sciences / 125 Vol. 74, No. 2, February 1985
Table I1 lists, along w i t h experimentally determined RHO values for saturated solutions of mixtures, values of RHOcalculated from a theoretical expression derived by Ross:'
(3)
. . . (a:)"
a,., = (a:)l(a:)z(a:)s
the individual saturated solutions of each ith component, also expressed as a decimal. T h e equation was derived assuming a dilute solution, ideal conditions, and independent contributions of each component. It is included here only t o show t h a t those
'"I
where a,., is the water activity of the mixture, defined as equal t o (RHO/lOO),and (a:), represents t h e relative humidities of
1.6
0.7.
0
0.6
h
/
0.5
. C
E
0,
0.4
W
2 a 0.3-
W
Y
2 0.84
5I- 0.6 a
-
0.4
Y
a
li
=
0.2-
a 3
0.1-
L
8 l-
o.2 0.030
40
50
60
70
80
100
90
RELATIVE HUMIDITY d 5
60
O
7'0
_I
60
90
100
RELATIVE HUMIDITY
Figure 5- Water uptake rate versus relativehumidity for various mixtures (rnol%: mol%) of tetrabutylammonium bromide-potassium bromide. Key: (0)50:50; (0)75:25; (0)25:75;0choline bromide-potassium bromide. The solid line is the theoreticalplot obtained from eq. 1.
Figure 3-Water uptake rate versus relative humidity for sucrose-potassium bromide. The solid line is the theoreticalplot obtained from eq. 1.
1816
-
1
.-C
14-
F
1
0
0
12 -
0
W
b
I-
a
.
0
10-
[r
W
0
Y 0%-
30
06-
8
04-
3
0
I-
E
02-
30
Figure 4-Water uptake rate versus relative humidity for sodium chloride-sucrose-potassium bromide. The solid line is the theoretical plot obtained from eq. 1.
40
50
80
70
80
90
100
RELATIVE HUMIDITY
RELATIVE HUMIDITY
Figure 6-Water uptake rate versus relative humidity for tetrabutylammonium bromide-choline bromide. The solid line is the theoretical plot obtained from eq. 7.
Table Il-Comparison of Calculated' and Experimentally Determined Values of RHOfor Mixtures of Substances RHOValues Mixture Calculated Experimental
Sodium chloride-potassium bromide Potassium chloride-sodium chloride Potassium chloride-potassium bromide Sucrose-potassium bromide Sucrose-dextrose monohydrate Sucrose-sodium chloride-potassium bromide Choline bromide-potassium bromide Tetrabutylammonium bromide-potassium bromide Tetrabutylammonium bromide-choline bromide a Calculated from eq. 3.
126 J Journal of Pharmaceutical Sciences Vol. 74, No. 2,February 7985
61 64 68 68 69 51 33 49
25
64 67 73 66 68
57 40
57 34
mixtures which best fit eq. 1 are also those which behave most ideally as saturated solutions, i.e., solute-solute interactions appear to play a negligible role. On the other hand, those systems showing significant deviation from eq. 3, presumably because of large nonidealities caused, in part, by the much higher mole fractions in solution, also show a greater tendency to not fit the heat transport-controlled model for water vapor uptake kinetics.
Discussion In addition to generally confirming the validity of the heat transport model for water vapor uptake by mixtures of deliquescent solids, this study provides excellent evidence that an important assumption of the model, i.e., that close to a saturated solution is present at the onset of deliquescence, appears to be well supported for all systems studied. This includes choline bromide-potassium bromide and tetrabutylammonium bromide-potassium bromide, where the combined solubilities are -30 molal, and even tetrabutylammonium bromide-choline bromide, where the combined solubility exceeds 50 molal. On the other hand, whereas the rates of water vapor uptake a t higher relative humidities are well predicted for mixtures of alkali halides and sugars, the predicted values for systems containing quaternary ammonium salts are generally greater than the actual values. Since such systems have aqueous films containing in excess of 30 molal of dissolved materials, it would not be surprising if the kinetics of mass transport in such mixtures, not presumed theoretically to play a role in determining water uptake rates, would now have some effect. This would be particularly true when one reached a combined solubility in excess of 50 molal, as in the case of choline bromide-tetrabutylammonium bromide. For example, in previous studies it was shown that saturated solutions of single component systems, including tetrabutylammonium bromide, with viscosities as high as 200 times that of water, fit the theoretical model well. The viscosity of a saturated solution of the mixture of choline bromide and tetrabutylammonium bromide, however, is -500 times that of water. It is also possible that additional heat changes are occurring with these systems and that not including these in eq. 3 results in the poorer fit seen in Figs. 5 and 6. Miyajima et al.," for example, have reported that mixing dextrose and tetrabutylammonium bromide in water at 25°C can result in a significant endothermic heat of mixing due, presumably, to an interference with the structuring of water molecules. If such a heat change was occurring during water sorption studies involving tetrabutylammonium bromide, it would tend to produce greater rates of sorption than predicted by eq. 1. In all cases where quaternary ammonium salts are used in mixtures (Figs. 5 and 6), however, the observed rates are lower than predicted. Such
endothermic heats of mixing could be great enough to negate the predominant effect of the heat transport model kinetically, thus allowing mass transport in the aqueous film, as described above, to predominate. From a pharmaceutical point of view, most salts, sugars, and other water-soluble substances used in solid dosage forms should have properties in the range of those seen with the alkali halides and sugars used in this study. Hence, the general model developed from this theory of water vapor uptake (see eq. 1) should be applicable to most pharmaceutical systems containing mixtures of water-soluble substances.
Conclusions The rate of water vapor uptake by mixtures of deliquescent solids has been experimentally determined as a function of relative humidity. A theoretical model, previously developed for a single component system has been used to predict a priori the kinetics of water vapor uptake by various mixtures. Good agreement between theory and experiment for various solid pairs and one ternary system indicates the general validity of the model when applied to mixtures of pharmaceutical interest and strongly suggests that all components maintain a saturated aqueous solution during the entire process of water vapor uptake. This may have important implications for modeling situations where water vapor uptake and chemical degradation of drugs are occurring simultaneously.
References and Notes 1. Van Campen, L.; Amidon, G. L.; Zografi, G . J. Pharm. Sci. 1 9 8 3 , 72, 1381. 2. Van Campen, L.; Amidon, G . L.; Zografi, G . J. Pharm. Sci. 1 9 8 3 , 72,1388. 3. Van Campen, L.; Amidon, G. L.; Zografi, G . J. Pharm. Sci. 1 9 8 3 , 72,1394. 4. Frank, H. S.;Wen, W. Y. Disc.Faraday SOC.1957,24,133. 5. Wen, W. Y. in "Water and Aqueous Solutions"; Horne, R. A., Ed.; Wiley-Interscience: New York, 1972; p 613. 6. Properties of tetraethylammonium bromide: RHO= 44; C,,(25"C) = 12.65 m;' = -1.79 kcal/mol? 7. The authors thank Dr. Lynn Van Campen for permission to use
unpublished data obtained with this system (Van Campen, L., PbD. Thesis, University of Wisconsin-Madison, 1981). 8. Ross, K. D. Food Technol. 1 9 7 5 , 2 9 , 26. 9. Krishnan, C. V.; Friedman, H. L. J. Phys. Chem. 1 9 6 9 , 73,3934. 10. Miyajima, K.; Sawada, M.; Nakagaki, M. Bull. Chem. SOC.Jpn. 1983,56,2905.
Acknowledgments Mark J. Kontny expresses appreciation to the United States Pharmacoepial Convention, Inc. for awarding him a USP Fellowship during 1983-1985. Additional research support from W. H. Rorer, Inc. is also gratefullyacknowledged. The authors also wish to thank Mr. Lawrence Ennett and Mr. Kevin Bjerke for their technical assistance and insights provided throughout the course of this study.
Journal of Pharmaceutical Sciences Vol. 74, No. 2, February 1985
1
127
Accepted for publication July 27,
I1 of ref. 1.) Since all of these parameters are either available in the literature or experimentally determinable, it was possible to use eq. 1 to predict, a priori, the value of W' for various values of RHi with solids of varying Fit to eq. 1 was excellent for a variety of alkali halides, sugars, and quaternary ammonium salts. In the present study, the heat transport model was extended to systems containing more than one water-soluble substance. The general aim was to see if the model would be useful when parameters determined for single component systems were appropriately combined for any mixture of solids. It was experimentally tested under vacuum conditions using various mixtures of some of the substances previously studied.2
Experimental Section This paper extends earlier work reported from this lab~ratoryl-~ concerning the sorption kinetics of water vapor on deliquescent water-soluble substances. Models were developed previously to describe the rate of sorption on a solid substance as a function of the relative humidity, RHi, of the environment surrounding the sample. In this model it is assumed that water sorbed on a solid surface dissolves some of the solid to form a saturated solution with a relative humidity, RHO.Further water vapor will continue to condense on this liquid film in accord with the model predictions as long as RHO is less than RH, and a saturated solution is maintained. The most general model developed3accounts for water uptake in the presence of air by assuming that both diffusion of water vapor to and heat transport away from the surface limit the rate of water uptake. The heat change results from the condensation of water vapor and other processes such as solution and hydration. The net heat generated maintains the liquid-vapor interface at temperature T,, elevated above that of the atmosphere maintained at T, by external means. The water vapor pressure over the saturated film, therefore, rises with temperature until the pressure difference between the surface and the atmosphere becomes infinitesimal and remains so during steady-state uptake. In an environment consisting of pure water vapor (initial vacuum conditions), vapor diffusion need not be considered. For this special case, only the rate at which heat is transported away from the surface is assumed to limit the sorption rate, W '. The mathematical expression derived' to express this rate as a function of RHi and RHOis:
(The various symbols represent parameters listed in Appendix 124
I Journal of Pharmaceutical Sciences Vol. 74, No. 2, February 1985
Materials-The materials used in this study and their sources have all been reported with the exception of tetraethylammonium bromide (Aldrich Chemical Co.), which was used as received.2 Equipment a n d Procedures-The apparatus, consisting of an electrobalance within a vacuum system, and the general procedures used to measure sorption kinetics have been described in considerable detail elsewhere? All studies were carried out using disks prepared by compressing mixtures of solids, previously mixed to various proportions. All samples were ground to a fine powder before compression. The relative humidity over a saturated solution of each mixture used, at 25"C, was measured directly by dissolving an excess of each of the materials in water, freezing this mixture by immersing the sample cell in a dry ice:methanol bath, evacuating the volume above the frozen sample, and melting the sample at 2 5 T , allowing liquid-vapor reequilibration in the closed system. This freeze-evacuate-equilibrate cycle was repeated twice before the vapor pressure above the saturated solution was measured using an oil manometer, as described elsewhere.2
Results Studies With Single Component Systems-In the previous study,2 the only solid showing very poor fit to eq. 1 was tetrabutylammonium bromide, the only substance exhibiting an exothermic heat of solution. It was suggested2that this lack of fit might be the result of the very unusual hydration properties of this omp pound.^ It has since been observed that the tetrabutylammonium ion, because of this hydration, exhibits a significant heat of dilution amounting to -8 kcal/mol for a saturated ~ o l u t i o n .~ Since the value for the heat of solution used in the earlier report' was taken at infinite dilution, and since it appears that a saturated solution actually exists in the aqueous film, a correction for AH in eq. 1 was made using the heat of dilution. Figure 1 shows the marked improvement in results when the heat of dilution is taken into account. Also shown in Fig. 1 are the results with tetraethylammonium bro0022-3549/85/0200-0124$01 .OO/O 0 1985, American Pharmaceutical Association
mide,6 which exhibits an exothermic heat of solution, comparable with tetrabutylammonium bromide, but only a negligible heat of d i l ~ t i o n .The ~ fit of experiment to theory is again excellent, confirming that the model adequately describes the kinetics of water vapor sorption onto the tetraalkylammonium salts. Studies With Mixtures-In order to use eq. 1 to obtain the theoretical description of sorption rate versus relative humidity for mixtures of the various solids, it was necessary to determine RHOfor the mixture, as well as to account for the heat changes occurring when more than one solid dissolves. Table I lists the RHOvalues experimentally determined for each mixture. The value of AH. used for mixtures in eq. 1 was determined by summing the heat contributions of each component:
AH = AH,
where AH, is the heat of condensation of water, Csat,"is the solubility of each individual component alone in water (expressed as molality), and AH, is the heat of solution for each component in water (see Table I of ref. 2 for individual values of Cmtand AH,). The heat of dilution was also included when tetrabutylammonium bromide was used. It is thus assumed in eq. 2 that any effect of a heat of mixing of two or more components is negligible. Figures 2-6 depict typical results
obtained with a variety of mixtures of alkali halides, sucrose, and quaternary ammonium salts. The theoretical plots in each case were obtained from eq. 1, as described above. Fit of theory and experiment for selected mixtures of alkali halides and sucrose, shown in Figs. 2-4 is excellent, while the combinations of quaternary ammonium salts and potassium bromide, depicted in Fig. 5, show a slightly less satisfactory fit. Figure 6 shows that the combination of two quaternary ammonium salts deviates significantly from the theoretical model. As noted in Fig. 5 for tetrabutylammonium bromide-potassium bromide mixture^,^ the composition of the mixture had no effect on RHO or the kinetics of water vapor uptake. This was confirmed with some of the other systems as well and is consistent with the theoretical model. To more conveniently illustrate the fit of data from all mixtures to eq. 1, extrapolated values of RHOare presented in Table I and compared with experimental values obtained from direct measurements of mixed saturated solutions. These extrapolated values were obtained by assuming the heat transport model to be correct (using appropriate values of C,,, and AH, obtained from eq. 1 in ref. 2) and regression of actual sorption data points to obtain the best fitting RHOvalue. As seen in Table I, the fit gave RHOvalues which are in excellent agreement with actual RHOmeasurements. The mixture of choline bromide and tetrabutylammonium bromide is not included in this comparison because, as shown in Fig. 6, it did not come close to satisfactorily fitting the theoretical model. 0.r
0.6 h
.-c
0
E 3
E
3 E
Y
Y
W
!-
<
1.0
-
0.8
-
0.6
-
0.4
-
U
y
2 5
W
I-
< U
0.4
W
Y
4. 0.3
U
k 4.
0.5
E
1.21
3
U
W
3 0.2 0 40
50
60
70
00
90
Table I-Comparison
L
100
RELATIVE HUMIDITY Figure 1-Water uptake rate versus relative humidity for tetraethylammonium bromide (0)and tetrabutylammonium bromide (0).The lines are theoretical/y derived from eq. 7: (-) tetraethylammonium bromide; (-) tetrabutylammonium bromide, no correction for heat of dilution; (- - - -) tetrabutylammonium bromide, corrected for heat of dilution.
60 65
70
75 80 85
SO 95
100
RELATIVE HUMIDITY Figure 2-Water
uptake rate versus relative humidity for sodium chloride-potassium bromide. The solid line is the theoretical plot obtained from eq. 7.
of Experimental RHOValues with Those Extrapolatedfrom Kinetic Experiments
Mixture
Sodium chloride-potassium bromide Potassium chloride-sodium chloride Potassium chloride-potassium bromide Sucrose-potassium bromide Sucrose-dextrose monohydrate Sucrose-sodium chloride-potassium bromide Choline bromide-potassium bromide Tetrabutylammoniumbromide-potassium bromide Tetrabutvlammoniurnbromide-choline bromide
RHOValues
Experimental 64 67 73 66 68 57 40 57 34
Extrapolated 63 74 81 68 71 53 42 64
Journal of Pharmaceutical Sciences / 125 Vol. 74, No. 2, February 1985
Table I1 lists, along w i t h experimentally determined RHO values for saturated solutions of mixtures, values of RHOcalculated from a theoretical expression derived by Ross:'
(3)
. . . (a:)"
a,., = (a:)l(a:)z(a:)s
the individual saturated solutions of each ith component, also expressed as a decimal. T h e equation was derived assuming a dilute solution, ideal conditions, and independent contributions of each component. It is included here only t o show t h a t those
'"I
where a,., is the water activity of the mixture, defined as equal t o (RHO/lOO),and (a:), represents t h e relative humidities of
1.6
0.7.
0
0.6
h
/
0.5
. C
E
0,
0.4
W
2 a 0.3-
W
Y
2 0.84
5I- 0.6 a
-
0.4
Y
a
li
=
0.2-
a 3
0.1-
L
8 l-
o.2 0.030
40
50
60
70
80
100
90
RELATIVE HUMIDITY d 5
60
O
7'0
_I
60
90
100
RELATIVE HUMIDITY
Figure 5- Water uptake rate versus relativehumidity for various mixtures (rnol%: mol%) of tetrabutylammonium bromide-potassium bromide. Key: (0)50:50; (0)75:25; (0)25:75;0choline bromide-potassium bromide. The solid line is the theoreticalplot obtained from eq. 1.
Figure 3-Water uptake rate versus relative humidity for sucrose-potassium bromide. The solid line is the theoreticalplot obtained from eq. 1.
1816
-
1
.-C
14-
F
1
0
0
12 -
0
W
b
I-
a
.
0
10-
[r
W
0
Y 0%-
30
06-
8
04-
3
0
I-
E
02-
30
Figure 4-Water uptake rate versus relative humidity for sodium chloride-sucrose-potassium bromide. The solid line is the theoretical plot obtained from eq. 1.
40
50
80
70
80
90
100
RELATIVE HUMIDITY
RELATIVE HUMIDITY
Figure 6-Water uptake rate versus relative humidity for tetrabutylammonium bromide-choline bromide. The solid line is the theoretical plot obtained from eq. 7.
Table Il-Comparison of Calculated' and Experimentally Determined Values of RHOfor Mixtures of Substances RHOValues Mixture Calculated Experimental
Sodium chloride-potassium bromide Potassium chloride-sodium chloride Potassium chloride-potassium bromide Sucrose-potassium bromide Sucrose-dextrose monohydrate Sucrose-sodium chloride-potassium bromide Choline bromide-potassium bromide Tetrabutylammonium bromide-potassium bromide Tetrabutylammonium bromide-choline bromide a Calculated from eq. 3.
126 J Journal of Pharmaceutical Sciences Vol. 74, No. 2,February 7985
61 64 68 68 69 51 33 49
25
64 67 73 66 68
57 40
57 34
mixtures which best fit eq. 1 are also those which behave most ideally as saturated solutions, i.e., solute-solute interactions appear to play a negligible role. On the other hand, those systems showing significant deviation from eq. 3, presumably because of large nonidealities caused, in part, by the much higher mole fractions in solution, also show a greater tendency to not fit the heat transport-controlled model for water vapor uptake kinetics.
Discussion In addition to generally confirming the validity of the heat transport model for water vapor uptake by mixtures of deliquescent solids, this study provides excellent evidence that an important assumption of the model, i.e., that close to a saturated solution is present at the onset of deliquescence, appears to be well supported for all systems studied. This includes choline bromide-potassium bromide and tetrabutylammonium bromide-potassium bromide, where the combined solubilities are -30 molal, and even tetrabutylammonium bromide-choline bromide, where the combined solubility exceeds 50 molal. On the other hand, whereas the rates of water vapor uptake a t higher relative humidities are well predicted for mixtures of alkali halides and sugars, the predicted values for systems containing quaternary ammonium salts are generally greater than the actual values. Since such systems have aqueous films containing in excess of 30 molal of dissolved materials, it would not be surprising if the kinetics of mass transport in such mixtures, not presumed theoretically to play a role in determining water uptake rates, would now have some effect. This would be particularly true when one reached a combined solubility in excess of 50 molal, as in the case of choline bromide-tetrabutylammonium bromide. For example, in previous studies it was shown that saturated solutions of single component systems, including tetrabutylammonium bromide, with viscosities as high as 200 times that of water, fit the theoretical model well. The viscosity of a saturated solution of the mixture of choline bromide and tetrabutylammonium bromide, however, is -500 times that of water. It is also possible that additional heat changes are occurring with these systems and that not including these in eq. 3 results in the poorer fit seen in Figs. 5 and 6. Miyajima et al.," for example, have reported that mixing dextrose and tetrabutylammonium bromide in water at 25°C can result in a significant endothermic heat of mixing due, presumably, to an interference with the structuring of water molecules. If such a heat change was occurring during water sorption studies involving tetrabutylammonium bromide, it would tend to produce greater rates of sorption than predicted by eq. 1. In all cases where quaternary ammonium salts are used in mixtures (Figs. 5 and 6), however, the observed rates are lower than predicted. Such
endothermic heats of mixing could be great enough to negate the predominant effect of the heat transport model kinetically, thus allowing mass transport in the aqueous film, as described above, to predominate. From a pharmaceutical point of view, most salts, sugars, and other water-soluble substances used in solid dosage forms should have properties in the range of those seen with the alkali halides and sugars used in this study. Hence, the general model developed from this theory of water vapor uptake (see eq. 1) should be applicable to most pharmaceutical systems containing mixtures of water-soluble substances.
Conclusions The rate of water vapor uptake by mixtures of deliquescent solids has been experimentally determined as a function of relative humidity. A theoretical model, previously developed for a single component system has been used to predict a priori the kinetics of water vapor uptake by various mixtures. Good agreement between theory and experiment for various solid pairs and one ternary system indicates the general validity of the model when applied to mixtures of pharmaceutical interest and strongly suggests that all components maintain a saturated aqueous solution during the entire process of water vapor uptake. This may have important implications for modeling situations where water vapor uptake and chemical degradation of drugs are occurring simultaneously.
References and Notes 1. Van Campen, L.; Amidon, G. L.; Zografi, G . J. Pharm. Sci. 1 9 8 3 , 72, 1381. 2. Van Campen, L.; Amidon, G . L.; Zografi, G . J. Pharm. Sci. 1 9 8 3 , 72,1388. 3. Van Campen, L.; Amidon, G. L.; Zografi, G . J. Pharm. Sci. 1 9 8 3 , 72,1394. 4. Frank, H. S.;Wen, W. Y. Disc.Faraday SOC.1957,24,133. 5. Wen, W. Y. in "Water and Aqueous Solutions"; Horne, R. A., Ed.; Wiley-Interscience: New York, 1972; p 613. 6. Properties of tetraethylammonium bromide: RHO= 44; C,,(25"C) = 12.65 m;' = -1.79 kcal/mol? 7. The authors thank Dr. Lynn Van Campen for permission to use
unpublished data obtained with this system (Van Campen, L., PbD. Thesis, University of Wisconsin-Madison, 1981). 8. Ross, K. D. Food Technol. 1 9 7 5 , 2 9 , 26. 9. Krishnan, C. V.; Friedman, H. L. J. Phys. Chem. 1 9 6 9 , 73,3934. 10. Miyajima, K.; Sawada, M.; Nakagaki, M. Bull. Chem. SOC.Jpn. 1983,56,2905.
Acknowledgments Mark J. Kontny expresses appreciation to the United States Pharmacoepial Convention, Inc. for awarding him a USP Fellowship during 1983-1985. Additional research support from W. H. Rorer, Inc. is also gratefullyacknowledged. The authors also wish to thank Mr. Lawrence Ennett and Mr. Kevin Bjerke for their technical assistance and insights provided throughout the course of this study.
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