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Zero-order release from glassy hydrogels. I. Enigma of the swelling interface number
Journal of Membrane Science, 49 (1990) 207-222 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
ZERO-ORDER RELEASE FROM GLASSY HYDROGELS. ENIGMA OF THE SWELLING INTERFACE NUMBER*
207
I.
N.R. VYAVAHARE, M.G. KULKARNI and R.A. MASHELKAR** Polymer Science and Engineering Group, Chemical Engineering Division, National Chemical Laboratory, Pune 411 008 (India) (Received April 27,1988; accepted in revised form August 18,1989)
Summary In vitro release kinetics of structurally related benzoic acids and other active ingredients from glassy hydrogels are reported. It is shown that a zero-order release from swellable glassy poly (2hydroxyethyl methacrylate) (PHEMA) hydrogels can be achieved by a judicious choice of the active ingredient. The criteria for the swelling controlled zero-order release proposed in the past have been examined. The equilibrium swelling interface number (SW,) is a rather conservative criterion. It is shown that swelling controlled zero-order release can be realized for values of the swelling interface number up to 0.6. The Deborah numbers for release (DeR) for the systems which follow zero-order kinetics are in good agreement with the predictions based on the time dependent diffusion coefficient to account for the role of the molecular relaxation processes.
1. Introduction Significant advances have been made over the last two decades in the development of controlled release delivery systems. The concept has led to many pragmatic applications for the delivery of drugs, pesticides, herbicides, pheromones, etc. The merits of the controlled release methodology have been well documented [l-4]. Development of controlled release delivery systems which could release the active ingredient at a constant rate has been of considerable interest to researchers in this area. The approaches adopted in the past include the use of a rate controlling membrane [ 5-71, modification of the geometry of the release devices [ 81, and non-uniform concentration distribution of the active ingredient in the matrix [ 91. However, these modifications do not lead to strategies that will enable one to undertake mass production of such devices. *NCL Communication Nuiber 4421. **To whom all correspondence should be addressed.
0376-7388/90/$03.50
0 1990 Elsevier Science Publishers B.V.
208
2. Swelling
controlled
delivery
systems
We are concerned here with the conditions under which zero-order release could be achieved for swelling controlled delivery systems. We shall broadly review the state of present understanding on the basis of both experimental and theoretical investigations. Relaxation controlled (case II) transport of vapours and liquids in glassy polymers has been reported for a number of polymer-diluent systems [ 10-121, and a mechanistic interpretation of the phenomena has been offered [ 131. Hopfenberg and Hsu [ 141 demonstrated that the release of Sudan Red IV from polystyrene film followed zero-order kinetics as a result of constant rate of sorption of n-hexane. Hopfenberg et al. [ 151 also reported zero-order release of sodium chloride from ethylene-vinyl acetate polymer films and proposed the concept of diffusional conductance (a) as a measure of the relative magnitude of the penetrant velocity and the diffusional transport of the active ingredient. Peppas and Franson [ 161 analysed the kinetics of release of theophylline from poly (2-hydroxyethyl methacrylate-methyl methacrylate), P (HEMAMMA), copolymers, and proposed that the swelling interface number (SW) could be used to correlate the release kinetics. The swelling interface number is defined as: SW
=vd(t) R
(1)
where v denotes the velocity of the penetrating front, D, the diffusion coefficient of the active ingredient from the swollen matrix, and s(t) denotes the thickness of the swollen part of the device. In fact, SW is essentially the reciprocal of cx as defined by Hopfenberg et al. [ 151. Peppas and Franson [ 161 proposed a conservative criterion for the zero-order release in terms of the equilibrium swelling interface number (SW,) defined as:
(2) where v,,, denotes the maximum velocity of the penetration front and S,,, denotes the equilibrium thickness of the device. Based on the extrapolation of the plot of SW, vs. n, where n denotes the index of release, Peppas and Franson [ 161 postulated that zero-order release will result for SW, < 1.0. However, Davidson and Peppas [ 171 subsequently observed that the release of theophylline from these matrices approached zero order (n=0.931), even for SW,< 1.0. It was further concluded that there was no unique value for n for each value of SW,, and that the release index cannot be predicted on the basis of the equilibrium swelling interface number alone [ 171.
209
Lee [ 181 analysed the kinetics of release from swellable polymers by assuming the diffusion coefficient of the active ingredient to be a function of time: D(t)=Di+(Dm-Di)
[l-exp(-kIzt)]
(3)
where Di denotes the instantaneous component of the diffusion coefficient, D, denotes the diffusion coefficient of the active ingredient from the polymer matrix under equilibrium swelling conditions and k denotes the reciprocal of the relaxation time. The release behaviour of an active ingredient from the swellable matrix can be correlated with the Deborah number for release: (4) Although the parameter is analogous to the diffusional Deborah number (De,,) it needs to be borne in mind that, by its very definition, the Deborah number for release for a given system will vary only due to k, since D, would be constant. Thus, by analogy with the diffusional Deborah number De,,, the release kinetics would follow Fickian characteristics for: D,/kl’>>
1
or
D,/k12<<
1,
(5)
whereas the release behaviour would be anomalous, i.e. the release index would deviate from n = 0.5 for: D,/k1’81
or
D,/kl’
(6)
Zero-order release (where n = 1.0 ) would be a more specific case of anomalous behaviour. However, the parameter does not explicitly define a criterion for zero-order release. It appears from the foregoing that the criteria for zero-order release from the glassy hydrogels have not been unequivocally established. Furthermore, in the investigations undertaken so far, the influence of polymer composition and structure on the factors affecting the swelling interface number has been elucidated. However, no systematic effort seems to have been made to investigate the role of the structure of the active ingredient. Although there is an explicit statement [ 151 that, for zero-order release, the diffusion of swelling penetrant to and solute release from the advancing front should be rapid compared with the rate of swelling, it is not clear as to what are the necessary and sufficient conditions for zero-order release. As we shall show later, and as Davidson and Peppas [ 171 have realized themselves, the criterion of equilibrium swelling interface number (SW,) alone is unlikely to serve a useful purpose. The present study is aimed at this precise problem of establishing quantitative criteria for zero-order release from swellable glassy hydrogels.
210
3. Experimental 3,l Materials 2-Hydroxyethyl methacrylate monomer was obtained from Fluka AG (Switzerland), and t-butyl hydroperoxide was supplied by Wilson Laboratories. All the solutes used were obtained from the local suppliers and were purified by recrystallization before use. 3.2. Polymer synthesis 2-Hydroxyethyl methacrylate was purified according to the standard procedure reported in the literature [ 201. Bulk polymerization was carried out in test tubes using 0.6% t-butyl hydroperoxide. The use of this initiator avoided bubble formation during polymerization. The solute loading was 1% and was kept constant throughout. Polymerization was carried out at 60 ? lo C for the first 6 hr and then at 70 ? lo C for another 12 hr. The product was isolated by breaking the test tubes. The attainment of complete conversion of monomer was verified by following the UV spectrum of the monomer. No cross-linking monomers were used. Discs for the release studies were cut from the polymer cylinder, and were 1.6 cm in diameter and 0.09-0.11 cm thick. These were postpolymerized at 50’ C for 1 week and stored in a desiccator over fused calcium chloride to prevent moisture absorption during storage. 3.3 Swelling studies Dynamic swelling studies were carried out for pure poly(2-hydroxyethyl methacrylate) containing no solute [ 161. The density of the dry polymer, the equilibrium water uptake and the volume degree of swelling were measured. 3.4 In vitro release studies Discs of 1.6 cm diameter and 0.09-0.11 cm thickness were coated on one side by silicone grease so that release could take place from one side alone. The kinetics of release were followed by monitoring the absorbance of the release medium on a Hitachi 220 UV-Vis spectrophotometer at the following wavelengths: benzoic acid (228 nm), p-hydroxybenzoic acid (252 nm), p-methoxybenzoic acid (252 nm) ,p-aminobenzoic acid (268 nm), paracetamol (246 nm), aspirin (230 nm), salicylic acid (298 nm), salicylamide (237 nm), o-iodobenzoic acid (225 nm), theophylline (272 nm) and sulfamethoxazole (266 nm). 3.5 Measurement of diffusion coefficient Diffusion coefficients of the active ingredients from the swollen polymer matrices were experimentally determined according to the procedure described by Yasuda et al. [21].
211
Swelling and release studies, as well as the diffusion coefficient measurements, were made at 37” C. 4.
Results and discussion
4.1 Kinetics of release For a glassy hydrogel implant releasing active ingredient in an aqueous medium, it is obvious that the maximum thickness cannot exceed 0.1-0.15 cm. Further, the velocity of penetration of water is governed by the choice of the polymer. Hence, the only parameter which can control the value of the swelling interface number is the diffusion coefficient of the active ingredient. In this work, a wide range of solutes for which the diffusivity varied by a factor of three were chosen. Release curves for representative solutes, viz. sulfamethoxazole, p-methoxybenzoic acid and benzoic acid, are shown in Fig. 1. The index of release was determined by fitting the data into the equation:
where M, denotes the amount of active ingredient released at time t, Mm denotes the amount of active ingredient released at infinite time, K is a constant and n denotes the release index. From the data summarized in Table 1, it can be seen that the release kinetics observed experimentally yield a very wide range of values of n, viz. 0.6-1.0. In the case of benzoic acid the exponent of release is unity, which demonstrates that zero-order release can indeed be achieved from glassy hydrogel matrices by a judicious choice of the active ingredient. Further, an increase in the size of the substituent and its position relative to the carboxylic group results in a decrease in the index of release
-I *
11
0
2
4
6 RELEASE
e TIME
10
12
14
IHours)
Fig. 1. Kinetics of release of benzoic acid (0 ) ,p-methoxybenzoic (0 ) from glassy PHEMA hydrogels.
acid (0
), andsulfamethoxazole
212 TABLE 1 Summary of release kinetics data Solute
Structural formula
Release kinetic exponent
95% Confidence limits
Regression coefficient
S,,, (cm)
SW,
1.0
+ 0.0208
0.999
0.125
1.019
1.0
& 0.0520
0.999
0.115
1.987
1.0
* 0.0183
0.999
0.114
1.058
(n) M,l M,Q0.60 Benzoic acid COOH OH
Salicylic acid
p-Chlorobenzoic acid
Cl
a0
COOH
p-Methoxybenzoic acid
COOH
0.770
+ 0.0220
0.989
0.114
1.549
Paracetamol
NHCOCH3
0.723
+ 0.0069
0.999
0.112
2.080
0.791
+ 0.0196
0.990
0.126
2.221
0.708
+ 0.0055
0.998
0.117
2.396
0.690
+ 0.0053
0.999
0.112
2.108
0.760
rir0.0194
0.996
0.117
1.911
0.670
f 0.0059
0.987
0.126
2.925
0.650
t 0.0180
0.998
0.125
0.600
+ 0.022
0.997
0.120
0.880
i 0.0159
0.999
0.114
Aspirin
p-Hydroxybenzoic acid
HO
COOH
p-Aminobenzoic acid
COOH OH
Saiicylamide
CONHp
CH3
Theophylline
0 I
o-Iodobenzoic acid d
0
COOH
Sulfamethoxazole
p-Nitrobenzoic acid
COOH
-
1.180
213
from 1.0 to 0.65. In the case of theophylline, the observed index was 0.67, which compares well with the value of n= 0.71 reported by Peppas and Franson [ 161. 4.2 Penetration velocity The limiting velocity of penetration of the surrounding medium into the glassy polymer can, in principle, be calculated from knowledge of the thermophysical data according to the relationship [ 161:
1 n
V maz
=k’
$’ (Q-1)-z P
(8)
where p; and pp denote the densities of the penetrant and the polymer, respectively, Q denotes the equilibrium degree of swelling, T, is the glass transition temperature, T is the experimental temperature, af is the coefficient of expansion of free volume, p is the contribution of the diluent to the free volume of the polymer-diluent system, and k’ and m are empirical parameters. In practice, however, the estimation of the penetration velocity poses certain problems. For instance, the values of af and j3 for the polymer-diluent system are not always known, and even when available, the values are not very accurate. Secondly, the parameters 12’and m are purely empirical in nature. These have to be obtained from the knowledge of the initial velocity of the swelling front and the equilibrium concentration of the penetrating medium, which need to be experimentally determined. In addition, the same goodness of fit can result in substantial variation in m [ 221. As a result, the accuracy of m is rather uncertain. It is therefore desirable to measure the penetration velocity experimentally. The velocity of penetration of water into the glassy polymer can be measured by a variety of techniques, such as dynamic swelling measurements [ 141 and examination of photomicrographs of the cross-section of the swelling film as a function of time [ 141. Further, if it is assumed that the concentration of the active ingredient is uniform throughout the matrix and that the swollen phase contains no active ingredient, then the velocity of penetration can be calculated directly from the release data. These are valid assumptions when zero-order release is realized, as has been confirmed by independent measurements by Hopfenberg and Hsu [ 141. In this work, the velocity of the penetrating front, v,,,, was calculated from the dynamic swelling experiment (see Fig. 2 ) in two ways. In the first instance, the amount of water sorbed as a function of time was recorded for a period of 3 hr. This represents the time required for 60% of the equilibrium water uptake, since the disc is exposed to water on both sides. The penetration velocity was then calculated from the equation: V
(9)
214
0
I
I
I
I
I
I
I
4
6
12
16
20
24
26
TIME
( HOUrSl
Fig. 2. Dynamic swelling of glassy PHEMA hydrogel.
where dg,/dt represents the rate of sorption of water, pP and pi, denote the respective densities of polymer and water at 37’ C, and A, the area of the crosssection of the disc. The factor of 2 is introduced since both surfaces of the disc are exposed to the penetrant medium. The value of the penetration velocity so calculated was u,,, = 2.605 x 10e6 cm/set. This value is in good agreement with that calculated from the zero-order release data for benzoic acid, viz. 2.786~ 10W6cm/set (Fig. 3). Both these values are in fair agreement V max= with the value reported earlier, viz. umaX = 2.88 x 10e6 cm/set [ 161. Alternatively, the penetration velocity was also calculated from the equilibrium degree of swelling (Q) determined at the end of the dynamic swelling experiment. The maximum penetrant concentration cmax(x*,t) was then calculated from the equation: (Q-l)
cmax(x*,t) =$’
(10)
P
where p; and pp represent the density of the penetrant and the polymer, respectively. The penetration velocity was calculated from the equation: Umax=k’{ ]cnI,,(~*,t)
1-c*y
(11)
using the values of Fz’, m and c* reported by Peppas and Franson for the same polymer [ 161. This gave u,,, = 2.976 x 10e6 cm/set. This difference in value could be due to the uncertainties associated in the precise estimation of k’ and m, as discussed earlier. 4.3 Diffusion coefficient Diffusion coefficients of the solutes from the polymers can be estimated from
215
5s -;:
8
0.07
-
0.06
-
0.05
-
0.04
-
0.03
-
0
1
2
3
4 TIME
5
6
7
8
(Hours)
Fig. 3. Penetration velocity of water in glassy PHEMA hydrogel from the kinetics of benzoic acid release. TABLE 2 Diffusion coefficients of various active ingredients from swollen PHEMA Active ingredient
Qx 10-7 (cm”/sec)
Benzoic acid p-Methoxybenzoic acid p-Chlorobenzoic acid Paracetamol Aspirin p-Hydroxybenzoic acid p-Aminobenzoic acid Salicylamide Theophylline Salicylic acid
3.45 2.05” 3.0” 1.5 1.58 1.36 1.48 1.56 1.2 1.5
“From Ref. [ 261.
the semi-empirical approaches reported in the literature [ 21,23,24]. However, in view of the critical role played by the diffusivity in this case, it was considered more appropriate to determine the diffusivities experimentally. A number of techniques are reported in the literature for the measurement of diffusivities [21,25]. In this work, diffusivities of various solutes were determined by the method reported by Yasuda et al. [ 211. The values are summarized in Table 2. The diffusion coefficient for salicylic acid determined in this work (D,= 1.5~ 10F7 cm’/sec) compares favourably with the value (D,= 1.24~ 10d7
216 TABLE 3 Diffusivities of substituted benzoic acids from swollen PHEMA at 37°C (Ref. [ 261) Active ingredient
L&x 10-7 (cm*/sec)
Benzoic acid p-Hydroxybenzoic acid p-Iodobenzoic acid p-Fluorobenzoic acid p-Methoxybenzoic acid p-Methylbenzoic acid p-Chlorobenzoic acid p-Bromobenzoic acid
3.9
1.4 0.3 1.5 2.05 1.4 3.0 1.2
cm’/cm) reported using the double disc method [ 251. Wood et al. [ 261 investigated the release kinetics of a series of substituted benzoic acids from the swollen PHEMA implants. The values of the diffusivities were evaluated by fitting the release data in the equation for the matrix controlled release [ 261. The values are summarized in Table 3. Diffusivities of benzoic acid and phydroxybenzoic acid so calculated agree very well with the diffusivity values experimentally determined in this work. 4.4 Kinetics of release from PHEMA
hydrogels and correlation with the
swelling interface number (SW)
The experimental data obtained in this work are summarized in Table 1.It is evident that, in the case of benzoic acid, p-chlorobenzoic acid and salicylic acid, zero-order release is followed. This would appear to be the first experimental evidence to demonstrate the zero-order release of a low molecular weight solute from the PHEMA hydrogel. The experimental values of the penetration velocity and the diffusion coefficient of the active ingredients from the swollen PHEMA hydrogels enable computation of the equilibrium swelling interface numbers (SW,). These are reported in Table 1. We now examine the utility of the equilibrium swelling interface number in predicting zero-order release. Peppas and Franson [ 161 predicted that swelling controlled zero-order release would be realized from the glassy hydrogels for SW, << 1. Their prediction was arrived at by making two presumptions: (i) the diffusivity of theophylline in PHEMA can be accurately obtained by interpolating the data reported in the literature [ 231, and (ii) the extrapolation of the SW, vs. n curve from n = 0.7 to n = 1 is valid. Both these assumptions appear to be suspect. The value of diffusivity of theophylline in PHEMA (D,= 2.7 x lo-” cm’/sec) estimated by Peppas and Franson [ 161is highly overestimated. Surprisingly enough, this value is higher than that of the diffusivity of theophylline in water (D,=2.4~ lop6 cm’/sec) arrived at by Korsmeyer and Peppas
217
[27], which simply cannot be the case, since the value has to be lower in a swollen polymer [ 241. Additionally, this value differs substantially from that reported (D,= 1.7 x 10m7cm2/sec) by Davidson and Peppas subsequently [ 171. The value of the diffusivity of theophylline determined experimentally in this work is D,= 1.24 x 10e7 cm2/sec. The limiting value of the equilibrium swelling interface number (SW,) for zero-order release when corrected for the diffusivity based on our work is such that SW,-N 0.5, which is substantially different from SW,= 0.02 evaluated by Peppas and Franson [ 161. The prediction is based on the extrapolation of a semilogarithmic plot of SW, vs. n from n=0.7 to n= 1.0, which is a rather broad range for extrapolation, since one moves on the swelling number axis by almost one order of magnitude during this extrapolation, a decidedly risky endeavour. The values of the equilibrium swelling interface number as well as the index of release reported by us are based on the actual measurements where values of n= 1 have been actually realized. We conclude, therefore, that the inequality of SW, N low2as envisaged by Peppas and Franson is not a suitable criterion for predicting zeroorder release. We recall that zero-order release will be achieved from a polymer device which swells at a constant rate if the counter diffusion of the active ingredient from the swollen layer is rapid compared with the rate of swelling [ 151. This qualitative criterion can be expressed in quantitative terms by defining the rate of diffusion of the active ingredient and the velocity of the penetrating front. The value m would define a characteristic length associated with the diffusion of the active ingredient. The thickness of the swollen layer (ut) would be a function of time. The dimensionless parameter m/ut would then define the relative rates of the diffusion of the active ingredient and the penetration of the swelling front. It is obvious that, as long as the ratio is greater than unity, the release would be penetration controlled. The values of m/d are summarized in Table 4. It is clear that, for systems for which zero-order release is indeed observed, the value of the parameter is around 1.3. The value for salicylic acid is an exception. The reasons for this are not known and are currently being looked into. We have also studied the release of theophylline and benzoic acid from a series of copolymers of HEMA [ 281. The values of the parameter m/ut for theophylline increased from 0.6 to 1.5, whereas for benzoic acid these values were always greater than 1.5. The release index for theophylline varied between 0.65 and 1.0, whereas that for benzoic acid was always unity. This further supports our hypothesis. We wish to emphasize that we have established no new criterion, since the ratio ,/m is equivalent to the diffusional conductance (a) or swelling interface number (SW) defined earlier [ 15,161. We have, however, consolidated the validity of this criterion with clear experimental evidence based on a judicious choice of a number of solutes, which enables us to obtain unambiguous experimental data. The release of various active ingredients is plotted as a function of the swell-
218 TABLE 4
Diffusant -
Fraction released
Benzoic acid p-Chlorobenzoic acid p-Methoxybenzoic acid Salicylic acid Paracetamol Aspirin p-Hydroxybenzoic acid p-Aminobenzoic acid Salicylamide p-Nitrobenzoic acid Theophylline
0.7817 0.61212 0.5250 0.6131 0.6121 0.6132 0.5095 0.602 1 0.6233 0.6047 0.5983
-
De,= DJkl’ 1.242 1.3378 1.1550 0.8758 0.7722 0.8988 0.7354 0.8136 0.9660 1.1329 0.6552
8 6 5.5 7 9 7 9 8 6 7.5 10
9.580 9.375
6.406 4.838 4.380 4.000 4.625 5.380 7.0789 2.920
SW 0.8
0.4
0.8
1.2
2.0
0.6
Fig. 4. Dependence of kinetics of release (MJM,) on swelling interface number (SW); (0 ) benzoic acid, (0 ) p-chlorobenzoic acid, (A ) p-methoxybenzoic acid, ( X ) theophylline.
219
ing interface number (SW) in Fig. 4. It is evident that in all the cases a zeroorder release is observed for SW w 0.6. For instance, in the case of p-methoxybenzoic acid, the equilibrium swelling interface number is 1.55 and the release index 0.79. However, analysis of the release data for SW= 0.55 results in n = 0.93, which is close to unity. That the mechanism of release changes at this stage is also evident from Fig. 1. We therefore conclude that the release of an active ingredient from a glassy hydrogel can be realized for SW = 0.6. 4.5 Deborah number for release (De& Lee [ 181 modelled the molecular relaxation controlled diffusion of the active ingredient from the glassy hydrogels as the time dependent diffusion coefficient, and identified conditions under which zero-order release could be observed in terms of the Deborah number for release (DeR). Since the solute loadings used in this work are very low, we have assumed the relaxation constant k to be the same as that for the swollen PHEMA hydrogel. It should be noted that this would give the Deborah number for release at equilibrium swelling condition and with lower values of the Deborah number for release until the equilibrium swelling is reached. DeR provides a more conservative estimate to validate the model predictions. For DeR in the range 2-6, the release index varies in the range 0.6-0.88 as anticipated. Further, the model predicts zeroorder release for DeR = 10 and DJD, -0. For the diffusion of benzoic acid and p-chlorobenzoic acid, the Deborah number for release is close to 10. Further, it is reasonable to assume that the diffusivity of the two solutes through the equilibrium swollen polymers will be at least hundred-fold higher than that in the glassy polymer. The observed zero-order release for the two active ingredients is thus in agreement with the model predictions. In fact, a preliminary
Fig. 5. Dependence
of the release index (n) on the Deborah number for release (Dea).
220
examination of the data shows that n varies linearly with Des (Fig. 5 ) . However, the relationship needs to be verified more thoroughly. 4.6 Criteria for zero-order release from the glassy hydrogels Finally, we would like reiterate the criteria for swelling controlled zero-order release. As discussed earlier, the equilibrium swelling interface number (SLU,) is a rather conservative criterion, and it is more appropriate to consider the time dependent thickness of the swollen phase in the evaluation of SW. Further, in the evaluation of SW, it is implicit that the transport of the penetration front follows case II transport. Thus, it is necessary to ascertain that 0.1~ De, d 10.0, for which D and lzneed to be experimentally determined. Additionally, IJand D, also have to be determined. The alternative approach suggested by Lee [ 181 envisages that 0.16 De,, d 10 and De Rz 10. This requires experimental determination of D,, D and k only. Further, both DeR and DeD are independent of the thickness of the swollen layer. Hence De Rz 10 appears to be the more appropriate, necessary and sufficient condition for the zero-order release of active ingredient from the glassy hydrogels. This study has been limited to the effects of the diffusant size and structure on the release characteristics from PHEMA. The more crucial task, however, is the choice of polymer for the release of drug molecules of pragmatic interest. This is more complicated, since both the velocity of the advancing front and the diffusivity of the active ingredient are altered as the polymer is changed. Work in this direction is currently in progress and will shortly be communicated. 5. Conclusion This paper reports the in vitro release kinetics of substituted benzoic acids from glassy PHEMA. The release of benzoic acid, p-chlorobenzoic acid and salicylic acid has been shown to follow zero-order kinetics. Diffusional conductance (a) and/or swelling interface number (SW) are more relevant criteria than the equilibrium swelling interface number (SW,), which is a more conservative criterion. Alternatively, 0.1 d De,, < 10 and DeR z 10 have been shown to be necessary and sufficient conditions for zero-order release from glassy hydrogels. Acknowledgement One of us (N.R.V. ) would like to acknowledge the support received from the Council of Scientific and Industrial Research for the award of a research fellowship.
221
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19 20 21 22
J. Robinson (Ed. ) , Sustained and Controlled Release Drug Delivery Systems, Marcel Dekker, New York, NY, 1978. A.F. Kydonieus (Ed. ) , Controlled Release Technologies: Method, Theory and Applications, CRC Press, Boca Raton, FL, 1980. D.H. Lewis (Ed.), Controlled Release of Pesticides and Pharmaceuticals, Plenum Press, New York, NY, 1981. E.J. Ariens (Ed.), Drug Design, Vol. 10, Academic Press, New York, NY, 1980. S. Borodkin and F.E. Tucker, Linear drug release from laminated hydroxypropyl cellulosepolyvinyl acetate films, J. Pharm. Sci., 64 (1975) 1289. I. Olanoff, T. Koinis and J.M. Anderson, Controlled release of tetracycline. I. In vitro studies with trilaminated 2-hydroxyethyl methacrylate systems, J. Pharm. Sci., 68 (1979) 1147. A.S. Obermeyer and L.D. Nichols, Controlled release from ultramicroporous cellulose triacetate, in: D.R. Paul and F.W. Harris (Eds.), Controlled Release Polymeric Formulations, ACS Symp. Ser., No. 33, American Chemical Society, Washington, DC, 1976, p. 303. W.D. Rhine, V. Sukhatme, D.S.T. Hsieh and R.S. Langer, A new approach to achieve zeroorder release kinetics from diffusion controlled polymer matrix systems, in: R.W. Baker (Ed.), Controlled Release of Bioactive Materials, Academic Press, New York, NY, 1980, p. 77. P.I. Lee, Drug release from glassy hydrogel beads, in: Proc. 10th Int. Symp. Controlled Release of Bioactive Materials, San Francisco, CA, 1983, p. 136. T.K. Kwei and H.M. Zupko, Diffusion in glassy polymers. I., J. Polym. Sci., Part A-2, 7 (1969) 867. H.B. Hopfenberg, L. Nicolais and E. Drioli, Relaxation controlled (case II) transport of lower alcohols in poly(methy1 methacrylate), Polymer, 17 (1976) 195. N.L. Thomas and A.H. Windle, Diffusion mechanics of the system PMMA-methanol, Polymer, 22 (1981) 627. A.H. Windle, Case II sorption, in: J. Kronyn (Ed.), Polymer Permeability, Academic Press, New York, 1985. H.B. Hopfenberg and K.C. Hsu, Swelling controlled constant rate delivery systems, Polym. Eng. Sci., 18 (1978) 1186. H.B. Hopfenberg, A. Apicella and D.E. Saleeby, Factors affecting water sorption in and solute release from glassy ethylene-vinyl alcohol copolymers, J. Membrane Sci., 8 (1981) 273. N.A. Peppas and N.M. Franson, The swelling interface number as a criterion for prediction of diffusional solute release mechanisms in swellable polymers, J. Polym. Sci., Polym. Phys. Ed., 21 (1983) 983. C.W.R. Davidson and N.A. Peppas, Solute and penetrant diffusion in swellable polymers. VI. The Deborah number and swelling interface number as indicators of the order of bimolecular release, J. Controlled Release, 3 (1986) 259. P.I. Lee, Interpretation of drug release kinetics from hydrogel matrices in terms of time dependent diffusion coefficients, in: PI. Lee and W.R. Good (Eds.), Controlled Release Technology, Pharmaceutical Applications, ACS Symp. Ser., No. 348, American Chemical Society, Washington, DC, 1987, p. 71. J.S. Vrentas, C.M. Jarzebski and J.L. Duda, A Deborah number for diffusion in polymersolvent systems, AIChE J., 21 (1975) 894. D.D. Perrin, W.L.F. Armarego and D.R. Perrin, Purification of Laboratory Chemicals, 2nd edn., Pergamon Press, London, 1980. H. Yasuda, C.E. Lamaze and L.D. Ikenberry, Permeability of solute through hydrated polymer membranes. Part I. Diffusion of sodium chloride, Makromol. Chem., 118 (1968) 19. S. Joshi, Ph.D. Thesis, University of Delaware, 1981.
222 23
24 25 26
27 28
H. Yasuda, L.D. Ikenberry and C.E. Lamaze, Permeability of solutes through hydrated polymer membranes. Part II. Permeability of water soluble organic solutes, Makromol. Chem., 125 (1969) 108. M.G. Kulkarni and R.A. Mashelkar, A unified approach to transport phenomena in polymeric media: diffusion in structured solid polymers, Chem. Eng. Sci., 38 (1983) 921. J.M. Wood, D. Attwood and J.H. Collett, The influence of gel formulation on the diffusion of salicylic acid in poly (HEMA) hydrogels, J. Pharm. Pharmacol., 34 (1982 ) 1. J.M. Wood, D. Attwood and J.H. Collett, Influence of gel and solute structure on in uitro and in uiuo release kinetics from hydrogels, in: S.W. Shalaby, A.S. Hoffman, B.D. Ratner and T.A. Horbett (Eds.), Polymers as Biomaterials, Plenum Press, New York, NY, 1984,347. R.W. Korsmeyer and N.A. Peppas, Effect of the morphology of hydrophilic polymeric matrices on the diffusion and release of water soluble drugs, J. Membrane Sci., 9 (1981) 211. N.R. Vyavahare, M.G. Kulkarni and R.A. Mashelkar, Zero order release from glassy hydrogels. II. Matrix effects, J. Membrane Sci., submitted.
ZERO-ORDER RELEASE FROM GLASSY HYDROGELS. ENIGMA OF THE SWELLING INTERFACE NUMBER*
207
I.
N.R. VYAVAHARE, M.G. KULKARNI and R.A. MASHELKAR** Polymer Science and Engineering Group, Chemical Engineering Division, National Chemical Laboratory, Pune 411 008 (India) (Received April 27,1988; accepted in revised form August 18,1989)
Summary In vitro release kinetics of structurally related benzoic acids and other active ingredients from glassy hydrogels are reported. It is shown that a zero-order release from swellable glassy poly (2hydroxyethyl methacrylate) (PHEMA) hydrogels can be achieved by a judicious choice of the active ingredient. The criteria for the swelling controlled zero-order release proposed in the past have been examined. The equilibrium swelling interface number (SW,) is a rather conservative criterion. It is shown that swelling controlled zero-order release can be realized for values of the swelling interface number up to 0.6. The Deborah numbers for release (DeR) for the systems which follow zero-order kinetics are in good agreement with the predictions based on the time dependent diffusion coefficient to account for the role of the molecular relaxation processes.
1. Introduction Significant advances have been made over the last two decades in the development of controlled release delivery systems. The concept has led to many pragmatic applications for the delivery of drugs, pesticides, herbicides, pheromones, etc. The merits of the controlled release methodology have been well documented [l-4]. Development of controlled release delivery systems which could release the active ingredient at a constant rate has been of considerable interest to researchers in this area. The approaches adopted in the past include the use of a rate controlling membrane [ 5-71, modification of the geometry of the release devices [ 81, and non-uniform concentration distribution of the active ingredient in the matrix [ 91. However, these modifications do not lead to strategies that will enable one to undertake mass production of such devices. *NCL Communication Nuiber 4421. **To whom all correspondence should be addressed.
0376-7388/90/$03.50
0 1990 Elsevier Science Publishers B.V.
208
2. Swelling
controlled
delivery
systems
We are concerned here with the conditions under which zero-order release could be achieved for swelling controlled delivery systems. We shall broadly review the state of present understanding on the basis of both experimental and theoretical investigations. Relaxation controlled (case II) transport of vapours and liquids in glassy polymers has been reported for a number of polymer-diluent systems [ 10-121, and a mechanistic interpretation of the phenomena has been offered [ 131. Hopfenberg and Hsu [ 141 demonstrated that the release of Sudan Red IV from polystyrene film followed zero-order kinetics as a result of constant rate of sorption of n-hexane. Hopfenberg et al. [ 151 also reported zero-order release of sodium chloride from ethylene-vinyl acetate polymer films and proposed the concept of diffusional conductance (a) as a measure of the relative magnitude of the penetrant velocity and the diffusional transport of the active ingredient. Peppas and Franson [ 161 analysed the kinetics of release of theophylline from poly (2-hydroxyethyl methacrylate-methyl methacrylate), P (HEMAMMA), copolymers, and proposed that the swelling interface number (SW) could be used to correlate the release kinetics. The swelling interface number is defined as: SW
=vd(t) R
(1)
where v denotes the velocity of the penetrating front, D, the diffusion coefficient of the active ingredient from the swollen matrix, and s(t) denotes the thickness of the swollen part of the device. In fact, SW is essentially the reciprocal of cx as defined by Hopfenberg et al. [ 151. Peppas and Franson [ 161 proposed a conservative criterion for the zero-order release in terms of the equilibrium swelling interface number (SW,) defined as:
(2) where v,,, denotes the maximum velocity of the penetration front and S,,, denotes the equilibrium thickness of the device. Based on the extrapolation of the plot of SW, vs. n, where n denotes the index of release, Peppas and Franson [ 161 postulated that zero-order release will result for SW, < 1.0. However, Davidson and Peppas [ 171 subsequently observed that the release of theophylline from these matrices approached zero order (n=0.931), even for SW,< 1.0. It was further concluded that there was no unique value for n for each value of SW,, and that the release index cannot be predicted on the basis of the equilibrium swelling interface number alone [ 171.
209
Lee [ 181 analysed the kinetics of release from swellable polymers by assuming the diffusion coefficient of the active ingredient to be a function of time: D(t)=Di+(Dm-Di)
[l-exp(-kIzt)]
(3)
where Di denotes the instantaneous component of the diffusion coefficient, D, denotes the diffusion coefficient of the active ingredient from the polymer matrix under equilibrium swelling conditions and k denotes the reciprocal of the relaxation time. The release behaviour of an active ingredient from the swellable matrix can be correlated with the Deborah number for release: (4) Although the parameter is analogous to the diffusional Deborah number (De,,) it needs to be borne in mind that, by its very definition, the Deborah number for release for a given system will vary only due to k, since D, would be constant. Thus, by analogy with the diffusional Deborah number De,,, the release kinetics would follow Fickian characteristics for: D,/kl’>>
1
or
D,/k12<<
1,
(5)
whereas the release behaviour would be anomalous, i.e. the release index would deviate from n = 0.5 for: D,/k1’81
or
D,/kl’
(6)
Zero-order release (where n = 1.0 ) would be a more specific case of anomalous behaviour. However, the parameter does not explicitly define a criterion for zero-order release. It appears from the foregoing that the criteria for zero-order release from the glassy hydrogels have not been unequivocally established. Furthermore, in the investigations undertaken so far, the influence of polymer composition and structure on the factors affecting the swelling interface number has been elucidated. However, no systematic effort seems to have been made to investigate the role of the structure of the active ingredient. Although there is an explicit statement [ 151 that, for zero-order release, the diffusion of swelling penetrant to and solute release from the advancing front should be rapid compared with the rate of swelling, it is not clear as to what are the necessary and sufficient conditions for zero-order release. As we shall show later, and as Davidson and Peppas [ 171 have realized themselves, the criterion of equilibrium swelling interface number (SW,) alone is unlikely to serve a useful purpose. The present study is aimed at this precise problem of establishing quantitative criteria for zero-order release from swellable glassy hydrogels.
210
3. Experimental 3,l Materials 2-Hydroxyethyl methacrylate monomer was obtained from Fluka AG (Switzerland), and t-butyl hydroperoxide was supplied by Wilson Laboratories. All the solutes used were obtained from the local suppliers and were purified by recrystallization before use. 3.2. Polymer synthesis 2-Hydroxyethyl methacrylate was purified according to the standard procedure reported in the literature [ 201. Bulk polymerization was carried out in test tubes using 0.6% t-butyl hydroperoxide. The use of this initiator avoided bubble formation during polymerization. The solute loading was 1% and was kept constant throughout. Polymerization was carried out at 60 ? lo C for the first 6 hr and then at 70 ? lo C for another 12 hr. The product was isolated by breaking the test tubes. The attainment of complete conversion of monomer was verified by following the UV spectrum of the monomer. No cross-linking monomers were used. Discs for the release studies were cut from the polymer cylinder, and were 1.6 cm in diameter and 0.09-0.11 cm thick. These were postpolymerized at 50’ C for 1 week and stored in a desiccator over fused calcium chloride to prevent moisture absorption during storage. 3.3 Swelling studies Dynamic swelling studies were carried out for pure poly(2-hydroxyethyl methacrylate) containing no solute [ 161. The density of the dry polymer, the equilibrium water uptake and the volume degree of swelling were measured. 3.4 In vitro release studies Discs of 1.6 cm diameter and 0.09-0.11 cm thickness were coated on one side by silicone grease so that release could take place from one side alone. The kinetics of release were followed by monitoring the absorbance of the release medium on a Hitachi 220 UV-Vis spectrophotometer at the following wavelengths: benzoic acid (228 nm), p-hydroxybenzoic acid (252 nm), p-methoxybenzoic acid (252 nm) ,p-aminobenzoic acid (268 nm), paracetamol (246 nm), aspirin (230 nm), salicylic acid (298 nm), salicylamide (237 nm), o-iodobenzoic acid (225 nm), theophylline (272 nm) and sulfamethoxazole (266 nm). 3.5 Measurement of diffusion coefficient Diffusion coefficients of the active ingredients from the swollen polymer matrices were experimentally determined according to the procedure described by Yasuda et al. [21].
211
Swelling and release studies, as well as the diffusion coefficient measurements, were made at 37” C. 4.
Results and discussion
4.1 Kinetics of release For a glassy hydrogel implant releasing active ingredient in an aqueous medium, it is obvious that the maximum thickness cannot exceed 0.1-0.15 cm. Further, the velocity of penetration of water is governed by the choice of the polymer. Hence, the only parameter which can control the value of the swelling interface number is the diffusion coefficient of the active ingredient. In this work, a wide range of solutes for which the diffusivity varied by a factor of three were chosen. Release curves for representative solutes, viz. sulfamethoxazole, p-methoxybenzoic acid and benzoic acid, are shown in Fig. 1. The index of release was determined by fitting the data into the equation:
where M, denotes the amount of active ingredient released at time t, Mm denotes the amount of active ingredient released at infinite time, K is a constant and n denotes the release index. From the data summarized in Table 1, it can be seen that the release kinetics observed experimentally yield a very wide range of values of n, viz. 0.6-1.0. In the case of benzoic acid the exponent of release is unity, which demonstrates that zero-order release can indeed be achieved from glassy hydrogel matrices by a judicious choice of the active ingredient. Further, an increase in the size of the substituent and its position relative to the carboxylic group results in a decrease in the index of release
-I *
11
0
2
4
6 RELEASE
e TIME
10
12
14
IHours)
Fig. 1. Kinetics of release of benzoic acid (0 ) ,p-methoxybenzoic (0 ) from glassy PHEMA hydrogels.
acid (0
), andsulfamethoxazole
212 TABLE 1 Summary of release kinetics data Solute
Structural formula
Release kinetic exponent
95% Confidence limits
Regression coefficient
S,,, (cm)
SW,
1.0
+ 0.0208
0.999
0.125
1.019
1.0
& 0.0520
0.999
0.115
1.987
1.0
* 0.0183
0.999
0.114
1.058
(n) M,l M,Q0.60 Benzoic acid COOH OH
Salicylic acid
p-Chlorobenzoic acid
Cl
a0
COOH
p-Methoxybenzoic acid
COOH
0.770
+ 0.0220
0.989
0.114
1.549
Paracetamol
NHCOCH3
0.723
+ 0.0069
0.999
0.112
2.080
0.791
+ 0.0196
0.990
0.126
2.221
0.708
+ 0.0055
0.998
0.117
2.396
0.690
+ 0.0053
0.999
0.112
2.108
0.760
rir0.0194
0.996
0.117
1.911
0.670
f 0.0059
0.987
0.126
2.925
0.650
t 0.0180
0.998
0.125
0.600
+ 0.022
0.997
0.120
0.880
i 0.0159
0.999
0.114
Aspirin
p-Hydroxybenzoic acid
HO
COOH
p-Aminobenzoic acid
COOH OH
Saiicylamide
CONHp
CH3
Theophylline
0 I
o-Iodobenzoic acid d
0
COOH
Sulfamethoxazole
p-Nitrobenzoic acid
COOH
-
1.180
213
from 1.0 to 0.65. In the case of theophylline, the observed index was 0.67, which compares well with the value of n= 0.71 reported by Peppas and Franson [ 161. 4.2 Penetration velocity The limiting velocity of penetration of the surrounding medium into the glassy polymer can, in principle, be calculated from knowledge of the thermophysical data according to the relationship [ 161:
1 n
V maz
=k’
$’ (Q-1)-z P
(8)
where p; and pp denote the densities of the penetrant and the polymer, respectively, Q denotes the equilibrium degree of swelling, T, is the glass transition temperature, T is the experimental temperature, af is the coefficient of expansion of free volume, p is the contribution of the diluent to the free volume of the polymer-diluent system, and k’ and m are empirical parameters. In practice, however, the estimation of the penetration velocity poses certain problems. For instance, the values of af and j3 for the polymer-diluent system are not always known, and even when available, the values are not very accurate. Secondly, the parameters 12’and m are purely empirical in nature. These have to be obtained from the knowledge of the initial velocity of the swelling front and the equilibrium concentration of the penetrating medium, which need to be experimentally determined. In addition, the same goodness of fit can result in substantial variation in m [ 221. As a result, the accuracy of m is rather uncertain. It is therefore desirable to measure the penetration velocity experimentally. The velocity of penetration of water into the glassy polymer can be measured by a variety of techniques, such as dynamic swelling measurements [ 141 and examination of photomicrographs of the cross-section of the swelling film as a function of time [ 141. Further, if it is assumed that the concentration of the active ingredient is uniform throughout the matrix and that the swollen phase contains no active ingredient, then the velocity of penetration can be calculated directly from the release data. These are valid assumptions when zero-order release is realized, as has been confirmed by independent measurements by Hopfenberg and Hsu [ 141. In this work, the velocity of the penetrating front, v,,,, was calculated from the dynamic swelling experiment (see Fig. 2 ) in two ways. In the first instance, the amount of water sorbed as a function of time was recorded for a period of 3 hr. This represents the time required for 60% of the equilibrium water uptake, since the disc is exposed to water on both sides. The penetration velocity was then calculated from the equation: V
(9)
214
0
I
I
I
I
I
I
I
4
6
12
16
20
24
26
TIME
( HOUrSl
Fig. 2. Dynamic swelling of glassy PHEMA hydrogel.
where dg,/dt represents the rate of sorption of water, pP and pi, denote the respective densities of polymer and water at 37’ C, and A, the area of the crosssection of the disc. The factor of 2 is introduced since both surfaces of the disc are exposed to the penetrant medium. The value of the penetration velocity so calculated was u,,, = 2.605 x 10e6 cm/set. This value is in good agreement with that calculated from the zero-order release data for benzoic acid, viz. 2.786~ 10W6cm/set (Fig. 3). Both these values are in fair agreement V max= with the value reported earlier, viz. umaX = 2.88 x 10e6 cm/set [ 161. Alternatively, the penetration velocity was also calculated from the equilibrium degree of swelling (Q) determined at the end of the dynamic swelling experiment. The maximum penetrant concentration cmax(x*,t) was then calculated from the equation: (Q-l)
cmax(x*,t) =$’
(10)
P
where p; and pp represent the density of the penetrant and the polymer, respectively. The penetration velocity was calculated from the equation: Umax=k’{ ]cnI,,(~*,t)
1-c*y
(11)
using the values of Fz’, m and c* reported by Peppas and Franson for the same polymer [ 161. This gave u,,, = 2.976 x 10e6 cm/set. This difference in value could be due to the uncertainties associated in the precise estimation of k’ and m, as discussed earlier. 4.3 Diffusion coefficient Diffusion coefficients of the solutes from the polymers can be estimated from
215
5s -;:
8
0.07
-
0.06
-
0.05
-
0.04
-
0.03
-
0
1
2
3
4 TIME
5
6
7
8
(Hours)
Fig. 3. Penetration velocity of water in glassy PHEMA hydrogel from the kinetics of benzoic acid release. TABLE 2 Diffusion coefficients of various active ingredients from swollen PHEMA Active ingredient
Qx 10-7 (cm”/sec)
Benzoic acid p-Methoxybenzoic acid p-Chlorobenzoic acid Paracetamol Aspirin p-Hydroxybenzoic acid p-Aminobenzoic acid Salicylamide Theophylline Salicylic acid
3.45 2.05” 3.0” 1.5 1.58 1.36 1.48 1.56 1.2 1.5
“From Ref. [ 261.
the semi-empirical approaches reported in the literature [ 21,23,24]. However, in view of the critical role played by the diffusivity in this case, it was considered more appropriate to determine the diffusivities experimentally. A number of techniques are reported in the literature for the measurement of diffusivities [21,25]. In this work, diffusivities of various solutes were determined by the method reported by Yasuda et al. [ 211. The values are summarized in Table 2. The diffusion coefficient for salicylic acid determined in this work (D,= 1.5~ 10F7 cm’/sec) compares favourably with the value (D,= 1.24~ 10d7
216 TABLE 3 Diffusivities of substituted benzoic acids from swollen PHEMA at 37°C (Ref. [ 261) Active ingredient
L&x 10-7 (cm*/sec)
Benzoic acid p-Hydroxybenzoic acid p-Iodobenzoic acid p-Fluorobenzoic acid p-Methoxybenzoic acid p-Methylbenzoic acid p-Chlorobenzoic acid p-Bromobenzoic acid
3.9
1.4 0.3 1.5 2.05 1.4 3.0 1.2
cm’/cm) reported using the double disc method [ 251. Wood et al. [ 261 investigated the release kinetics of a series of substituted benzoic acids from the swollen PHEMA implants. The values of the diffusivities were evaluated by fitting the release data in the equation for the matrix controlled release [ 261. The values are summarized in Table 3. Diffusivities of benzoic acid and phydroxybenzoic acid so calculated agree very well with the diffusivity values experimentally determined in this work. 4.4 Kinetics of release from PHEMA
hydrogels and correlation with the
swelling interface number (SW)
The experimental data obtained in this work are summarized in Table 1.It is evident that, in the case of benzoic acid, p-chlorobenzoic acid and salicylic acid, zero-order release is followed. This would appear to be the first experimental evidence to demonstrate the zero-order release of a low molecular weight solute from the PHEMA hydrogel. The experimental values of the penetration velocity and the diffusion coefficient of the active ingredients from the swollen PHEMA hydrogels enable computation of the equilibrium swelling interface numbers (SW,). These are reported in Table 1. We now examine the utility of the equilibrium swelling interface number in predicting zero-order release. Peppas and Franson [ 161 predicted that swelling controlled zero-order release would be realized from the glassy hydrogels for SW, << 1. Their prediction was arrived at by making two presumptions: (i) the diffusivity of theophylline in PHEMA can be accurately obtained by interpolating the data reported in the literature [ 231, and (ii) the extrapolation of the SW, vs. n curve from n = 0.7 to n = 1 is valid. Both these assumptions appear to be suspect. The value of diffusivity of theophylline in PHEMA (D,= 2.7 x lo-” cm’/sec) estimated by Peppas and Franson [ 161is highly overestimated. Surprisingly enough, this value is higher than that of the diffusivity of theophylline in water (D,=2.4~ lop6 cm’/sec) arrived at by Korsmeyer and Peppas
217
[27], which simply cannot be the case, since the value has to be lower in a swollen polymer [ 241. Additionally, this value differs substantially from that reported (D,= 1.7 x 10m7cm2/sec) by Davidson and Peppas subsequently [ 171. The value of the diffusivity of theophylline determined experimentally in this work is D,= 1.24 x 10e7 cm2/sec. The limiting value of the equilibrium swelling interface number (SW,) for zero-order release when corrected for the diffusivity based on our work is such that SW,-N 0.5, which is substantially different from SW,= 0.02 evaluated by Peppas and Franson [ 161. The prediction is based on the extrapolation of a semilogarithmic plot of SW, vs. n from n=0.7 to n= 1.0, which is a rather broad range for extrapolation, since one moves on the swelling number axis by almost one order of magnitude during this extrapolation, a decidedly risky endeavour. The values of the equilibrium swelling interface number as well as the index of release reported by us are based on the actual measurements where values of n= 1 have been actually realized. We conclude, therefore, that the inequality of SW, N low2as envisaged by Peppas and Franson is not a suitable criterion for predicting zeroorder release. We recall that zero-order release will be achieved from a polymer device which swells at a constant rate if the counter diffusion of the active ingredient from the swollen layer is rapid compared with the rate of swelling [ 151. This qualitative criterion can be expressed in quantitative terms by defining the rate of diffusion of the active ingredient and the velocity of the penetrating front. The value m would define a characteristic length associated with the diffusion of the active ingredient. The thickness of the swollen layer (ut) would be a function of time. The dimensionless parameter m/ut would then define the relative rates of the diffusion of the active ingredient and the penetration of the swelling front. It is obvious that, as long as the ratio is greater than unity, the release would be penetration controlled. The values of m/d are summarized in Table 4. It is clear that, for systems for which zero-order release is indeed observed, the value of the parameter is around 1.3. The value for salicylic acid is an exception. The reasons for this are not known and are currently being looked into. We have also studied the release of theophylline and benzoic acid from a series of copolymers of HEMA [ 281. The values of the parameter m/ut for theophylline increased from 0.6 to 1.5, whereas for benzoic acid these values were always greater than 1.5. The release index for theophylline varied between 0.65 and 1.0, whereas that for benzoic acid was always unity. This further supports our hypothesis. We wish to emphasize that we have established no new criterion, since the ratio ,/m is equivalent to the diffusional conductance (a) or swelling interface number (SW) defined earlier [ 15,161. We have, however, consolidated the validity of this criterion with clear experimental evidence based on a judicious choice of a number of solutes, which enables us to obtain unambiguous experimental data. The release of various active ingredients is plotted as a function of the swell-
218 TABLE 4
Diffusant -
Fraction released
Benzoic acid p-Chlorobenzoic acid p-Methoxybenzoic acid Salicylic acid Paracetamol Aspirin p-Hydroxybenzoic acid p-Aminobenzoic acid Salicylamide p-Nitrobenzoic acid Theophylline
0.7817 0.61212 0.5250 0.6131 0.6121 0.6132 0.5095 0.602 1 0.6233 0.6047 0.5983
-
De,= DJkl’ 1.242 1.3378 1.1550 0.8758 0.7722 0.8988 0.7354 0.8136 0.9660 1.1329 0.6552
8 6 5.5 7 9 7 9 8 6 7.5 10
9.580 9.375
6.406 4.838 4.380 4.000 4.625 5.380 7.0789 2.920
SW 0.8
0.4
0.8
1.2
2.0
0.6
Fig. 4. Dependence of kinetics of release (MJM,) on swelling interface number (SW); (0 ) benzoic acid, (0 ) p-chlorobenzoic acid, (A ) p-methoxybenzoic acid, ( X ) theophylline.
219
ing interface number (SW) in Fig. 4. It is evident that in all the cases a zeroorder release is observed for SW w 0.6. For instance, in the case of p-methoxybenzoic acid, the equilibrium swelling interface number is 1.55 and the release index 0.79. However, analysis of the release data for SW= 0.55 results in n = 0.93, which is close to unity. That the mechanism of release changes at this stage is also evident from Fig. 1. We therefore conclude that the release of an active ingredient from a glassy hydrogel can be realized for SW = 0.6. 4.5 Deborah number for release (De& Lee [ 181 modelled the molecular relaxation controlled diffusion of the active ingredient from the glassy hydrogels as the time dependent diffusion coefficient, and identified conditions under which zero-order release could be observed in terms of the Deborah number for release (DeR). Since the solute loadings used in this work are very low, we have assumed the relaxation constant k to be the same as that for the swollen PHEMA hydrogel. It should be noted that this would give the Deborah number for release at equilibrium swelling condition and with lower values of the Deborah number for release until the equilibrium swelling is reached. DeR provides a more conservative estimate to validate the model predictions. For DeR in the range 2-6, the release index varies in the range 0.6-0.88 as anticipated. Further, the model predicts zeroorder release for DeR = 10 and DJD, -0. For the diffusion of benzoic acid and p-chlorobenzoic acid, the Deborah number for release is close to 10. Further, it is reasonable to assume that the diffusivity of the two solutes through the equilibrium swollen polymers will be at least hundred-fold higher than that in the glassy polymer. The observed zero-order release for the two active ingredients is thus in agreement with the model predictions. In fact, a preliminary
Fig. 5. Dependence
of the release index (n) on the Deborah number for release (Dea).
220
examination of the data shows that n varies linearly with Des (Fig. 5 ) . However, the relationship needs to be verified more thoroughly. 4.6 Criteria for zero-order release from the glassy hydrogels Finally, we would like reiterate the criteria for swelling controlled zero-order release. As discussed earlier, the equilibrium swelling interface number (SLU,) is a rather conservative criterion, and it is more appropriate to consider the time dependent thickness of the swollen phase in the evaluation of SW. Further, in the evaluation of SW, it is implicit that the transport of the penetration front follows case II transport. Thus, it is necessary to ascertain that 0.1~ De, d 10.0, for which D and lzneed to be experimentally determined. Additionally, IJand D, also have to be determined. The alternative approach suggested by Lee [ 181 envisages that 0.16 De,, d 10 and De Rz 10. This requires experimental determination of D,, D and k only. Further, both DeR and DeD are independent of the thickness of the swollen layer. Hence De Rz 10 appears to be the more appropriate, necessary and sufficient condition for the zero-order release of active ingredient from the glassy hydrogels. This study has been limited to the effects of the diffusant size and structure on the release characteristics from PHEMA. The more crucial task, however, is the choice of polymer for the release of drug molecules of pragmatic interest. This is more complicated, since both the velocity of the advancing front and the diffusivity of the active ingredient are altered as the polymer is changed. Work in this direction is currently in progress and will shortly be communicated. 5. Conclusion This paper reports the in vitro release kinetics of substituted benzoic acids from glassy PHEMA. The release of benzoic acid, p-chlorobenzoic acid and salicylic acid has been shown to follow zero-order kinetics. Diffusional conductance (a) and/or swelling interface number (SW) are more relevant criteria than the equilibrium swelling interface number (SW,), which is a more conservative criterion. Alternatively, 0.1 d De,, < 10 and DeR z 10 have been shown to be necessary and sufficient conditions for zero-order release from glassy hydrogels. Acknowledgement One of us (N.R.V. ) would like to acknowledge the support received from the Council of Scientific and Industrial Research for the award of a research fellowship.
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