Thixotropy of Different Concentrations of Microcrystalline Cellu1ose:Sodium Carboxymethyl Cellulose Gels M. DOU-PLANAS’”,C. ROLDAN-GARCIA~, J. V. HERRAEZ-DOMINGUEZ‘, AND R. BELDA-MAXIMINO‘ Received May 15: 1989, fro,m the ‘Department of Toerrnod namics, Faculty of Pharmacy, and the *Department of Physiology, faculty of lccepted for publication February 15, 1990. Medicine, Va encia University, Valenoa 46010, Spain. .
.
-
-
-
-
. . ~ ..
_
is made of the rheologic behavior of microcrystalline ce1lulose:sodiurn carboxymethyl cellulose gels at six different concentrations (between 1 and 2.5% by weight).The thixotropy of these gels was analyzed in terms of agitation time, the duration of storage, concentration. and temperature; a semiempirical function was thus obtained providing thixotropic area as a function of these variables. The instantaneous variation rate in thixotropic area was defined, providing a better understanding of the rate of structural breakdown. Also, it is shown that after 5 min of agitation, the variation rate becomes negligible (-0.7% of the initial value);this result is practically independent of the remaining variables. Abstract 2 An extensive study
A great number of dispersed systems, (i.e., suspensions, gels, etc.) used in the pharmaceutical industry present thixotropic behavior which consists of the reversible, isothermic decrease in the viscosity of a fluid when the latter is agitated. This property is due to the structural breakdown of such substances on being subjected to shearing stress ( 7 ) for a n interval of time; i t manifests particularly during preparation procedures, storage, and use. The study of thixotropyl-4 is generally carried out by obtaining the rheograms corresponding to the “up” curve ID = f i r ) ) for increasing T values, and different “down” curves for decreasing T values after subjecting the fluid to different periods of agitation,s where D is shear rate. Studies on this subject69 usually obtain thixotropic area and its variation with factors such as agitation time, storage time, temperature, concentration, and so on. In this work, we analyze the thixotropic behavior of microcrystalline cellu1ose:sodium carboxymethyl cellulose gels at concentrations of 1, 1.5, 1.75, 2, 2.25, and 2.5% by weight. A semiempirical equation is obtained, relating thixotropic area and concentration and agitation time and storage time, that is applicable to temperatures between 22 and 35°C. In addition, instantaneous thixotropic rate is defined as obtained by derivation of the aforementioned equation. In our opinion, the latter provides a clear idea of the rate at which gel structural breakdown occurs. Finally, a comparison is made of the results obtained with those reported in an earlier studylo where mean thixotropic rate was defined as the ratio between thixotropic area increments and agitation time.
Experimental Section The experimental measurements in determining the thixotropic behavior of a gel were made with a Brookfield Digital DV I1 rotary cylinder viscometer, using an interval of eight angular velocities between 0.3 and 60 rpm. The viscometer was connected to a Macintosh Plus computer equipped with a data-input Link program. A number of complementary calculations were made with a HewlettPackard HP 9826 computer. The experiments were made at 22,25,28,30, and 35 “C, introducing the containers with the gel into a thermostatic bath and directly measuring from them to avoid prior decantation of the fluid. 0022-3549/91/0100-0075$01 .OO/O C:, 1991, American Pharmaceufical Association
The microcrystalline cellu1ose:sodium carboxymethyl cellulose gels (MCC:NaCMC;Avicel RC-581; American Viscose Division, FMC Corporation, Philadelphia, PA) were prepared at 20 “C. The product was slowly dispersed in deionized water, vigorously agitated for 10 min, left to rest for 5 min, and again agitated for another 10 min to create a homogeneous mix and facilitate gel formation while avoiding the internal creation of bubbles. Nipagin was used in the usual proportion as a preservative agent against fungi and bacterial contamination. In this way, 150 flasks (300 mL each) were prepared. Of these, 30 flasks, one for every concentration and temperature value, were determined after 1 day of storage, the next 30 flasks after 8 days, and so on after 15, 22, and 29 days of storage at rest. The aim was to establish possible modifications in the thixotropic behavior of the gels with varying times ofstorage at rest. The fact that the measurements were made with the actual storage flasks prevented prior fluid decantation and represents an additional advantage of the viscometer employed.5
The experimental measurements were made as follows. At constant temperature and with the viscometer rotary cylinder immersed in the fluid, shear angular velocity was increased from 0.3 to 0.6, 1.5,3, 6, 12, 30, and 60 rpm. The mean viscosity value (7)was calculated in centipoise (cP),corresponding to three measurements made at each rotary speed. Once transformed to shear stress (7)and shear rate (D), these values made it possible to construct the rheogram D = /IT), corresponding to the “up” curve. The “down” curve was then obtained following 1 min of agitation at 60 rpm, reducing angular velocity progressively from 60 to 0.3 rpm. This procedure was repeated for 2, 3, 4, and 5 min of agitation, providing a total of five “down” curves for each flask. This was considered to be sufficient, as in an earlier studylo it was found that the greatest thixotropic decrease occurs during this time interval. In this way, a total of >7200 T values were gathered in terms of variables such as shear rate (D) agitation time ( t ” ) ,storage time (fs), and temperature (7’).
Results and Discussion Rheological Behavior of Gels in Terms of Concentration and Agitation Time-The thixotropic behavior of the gels is expressed by their rheograms, D = /IT), corresponding to the “up” curve and the different “down” curves obtained after varying agitation times. Figure 1 (A and B) shows the rheograms for the 1.5 and 2.5% MCC:NaCMC gels after 8 days of storage at rest and a temperature of 28°C. The corresponding separation between the “up” and “down” curves is appreciable, demonstrating the thixotropic behavior of the test substance. The comparative study of >900 rheograms obtained for different concentrations, temperatures, and storage times made it possible to show that T decreases when D tends towards zero, reflecting t h e pseudoplastic or nonlinear slightly plastic character of these gels. A further point worth noting is that with the lesser D used in our experiments, the rheogram gradients are noticeably smaller than those obtained with D = 1.267 s - ’ , where the curve rise becomes steadily faster. This implies a considerable decrease in fluid Journal of Pharmaceutical Sciences I 75 Vol. 80, No. 1, January 1997
a
0
2
4
(2.25%)
K,= 8 4 . 6
(2%)
K,- 6 3 . 4
(1.75%)
K,
10
6
K,- 92.6
-
98.1
(1.5%)
(1.11-2)
6
20
K,= 18.0
Figure 2-Variation in thixotropic area for different gel concentrations, subjected to constant agitation at 60 rpm, as a function of time. Both concentrations and K, values were obtained by fitting to S,= qt) by eq 3. The graph corresponds to a storage time at rest of 1 day.
0
5
10
15
20
25
120
t (n.m-2) Figure 1-Rheograms corresponding to the “up” and “down” curves after 1, 2,3,4, and 5 min of agitation at 60 rpm and corresponding to a temperature of 28 “C for the following MCC:NaCMC concentrations and storage times: (A) 1.5% and 8 days; (B) 2.5% and 8 days.
1 1 L
100
Concentration(c)
K,=
viscosity as T increases; this fact is all the more apparent in the rheograms corresponding to the “up” curve, and less so for the “down” curves corresponding to the same concentration and storage time. It was also found that the shear stress of the “up” curve ( T ~ ) and that corresponding to the same D for the “down” curve ( T ~obtained ) after 5 min of agitation approximately satisfy the equation TD = 0 . 6 0 ~ (SD ~ = 0.061,regardless of concentration, storage time, and D within the limits imposed for the different variables involved in the study. In principle, these results indicate that the T required in certain industrial processes may be reduced 40%, provided the MCC:NaCMC gels are previously subjected to constant agitation at 60 rpm for 5 min. Another result that should be pointed out is the effect of concentration on 7.The increase in viscosity with increasing concentration was disproportionate. As an example, on comparing Figures 1A and 1 B, a concentration increase from 1.5 to 2.5% corresponds to an approximately threefold increase in viscosity from 8 to 25. Variation in Thixotropic Area as a Function of Concentration, Agitation, and Storage Time-The determination of thixotropic area (the area between the ccupO curve, each of the “down” curves and, in our case, the ordinates D, = 0.063s-l and D, = 12.673 s-’) was carried out by numerical integration11 applied to the experimental data of the rheograms obtained. For example, Figures 2 and 3 provide the thixotro76 I Journal of Pharmaceutical Sciences Vol. 80, No. 7 , January 7997
20
86.7
(2.5%)
K,- 81.4
(2.25%)
K,-
74.0
(2%)
K,-
513.4
( 1.75%)
K,-
45.6
(1.5%)
K,-
20.8
t (min) a Figure &Variation in thixotropic area for different gel concentrations, subjected to cohstant agitation at 60 rpm, as a function of time. Both concentrations and K, values were obtained by fitting to S, = It)by eq 3. The graph corresponds to a storage time at rest of 15 days.
pic areas (in Nm-* s-’) as a function of agitation time (ta;in min) for all the concentrations studied, and for 1and 15 days of storage, respectively. By comparing the results obtained, we found that for a given agitation time, the absolute thixotropic area of the gel increases with MCC:NaCMC
concentration. On the other hand, this area increases with agitation time (particularly during the first 3 min), and tends to reach a maximum constant value on increasing t,. To gain further insight to this subject, the thixotropic areas (S,) obtained for the different concentrations and storage times were fitted using functions of the following type:
These functions satisfy the theoretical frontier conditions; with t = 0, the thixotropic area must be zero, and with t + 00, STtends towards a finite value ( K l ) ,corresponding to maximum gel structural breakdown. The fittings made with these functions offered estimation errors of 4%. On the other hand, the maximum thixotropic areas (K,) as a function of gel concentration ( C ) for the different storage times are given in Figures 4A-4E. The distribution of experimental points obtained (K,, C ) was in turn fitted by singleparameter empirical functions (for greater simplicity) of the following type, whose correlation coefficients are provided in each of the graphs shown in Figure 4:
K1 = K2C3I2
(2)
Moreover, these functions satisfy the requirement that for zero concentration, thixotropic area is also zero (i.e., thixotropic behavior is not observed). Thus, the semiempirical equation obtained that provides MCC:NaCMC gel thixotropic area as a function of gel con-
I20
centration and constant 60 rpm agitation time is of the following type:
ST= K
~ (1C-e-?~
~
~
(3)
where S , is given in N * rn-, * s-l, concentration is in % by weight, and agitation time is in min; K , is a parameter whose decrease with increased storage time implies a decrease in thixotropic area (this indicates a more stable gel formation). The experimental values ofK, for storage times (t,) of 1,8,15, 22, and 29 days are 28.7, 28.3, 23.8, 21.5, and 19.8 N m-' * s-', respectively. Comparison of the experimental results with those obtained on applying eq 3 is given in Figure 5. The fitted equation of the straight line is as follows:
-
ST(theor) = (0.997 2 0.005)S~(exp)
(4)
This equation provides a correlation coefficient (r)of 0.99 and error of estimate of 3.9. This therefore shows that eq 3 is useful over the entire values interval of the variables studied, and for a temperature range of 22 to 35 "C. Thixotropic Rate-In our opinion, a knowledge of the rate at which gel structural breakdown occurs provides a better understanding of the rheologic behavior of the gel when subjected to agitation in production and packaging processes. The knowledge of this rate is useful in comparing structural breakdowns that may be identical but occur over different time intervals-an aspect that cannot be analyzed by the simple study of thixotropic area. In an earlier paper10 we suggested defining this rate as follows:
I00 80 7vl n
where uT represents mean rate of variation in thixotropic area (AS,) for an agitation time of At,. The values obtained for uT
60
'E
z 40 ~
J
120 1
/
2e 0
I00
-
C ( % Weight)
80 -
60 100 80 60
I-
I
m
'v)
% z
- 40
J 20 0
C(%
Weight)
0
20
40
60
80
100
120
Figure &Maximum thixotropic area (K,) as a function of concentration for the following storage times: (A) 1 day; (B) 8 days; (C)15 days; (D) 22 Figure SThixotropic area values obtained on applying eq 3 in relation days; (E)29 days. The correlation coefficients of the fitting made via functions of the type represented by eq 2 are 0.985,0.996,0.984,0.990,to the experimental values obtained by numerical integration. The straight line shown is that obtained by minimum square fitting. and 0.982,respectively. Journal of Pharmaceutical Sciences / 77 Vol. 80,No. 1, January 1991
were fitted as a function of agitation time (t,) by the following hyperbolic empirical equation:
where the parameters A (0.24 & 0.03) and B (0.78 ? 0.06) provided a good reproduction of the values corresponding to the experiments performed. However, much more precise information may be obtained in relation to this variation if At, is made to approach zero, whereby instantaneous thixotropic rate (or instantaneous thixotropic area variation per unit time) may be defined as proposed in this study; that is:
-
N
l Y) N*
60
I€
z V
’
I-
> 40 This makes it possible to determine how fast structural breakdown occurs a t any given instant. Calculation of the corresponding value is very simple, due to eq 3, as its derivation in terms of t provides instantaneous thixotropic rate as a function of concentration, agitation time, and K , (which is, in turn, dependent on storage time); that is:
20
0
The results obtained by applying eq 8 to the experiments performed made it possible to obtain graphic representations of uT as a function o f t for the different concentrations and storage times involved (two examples are given in Figures 6 and 7). The exponential decrease with time means that the instantaneous thixotropic rate tends towards zero when t approaches infinity; although, in practice and for 5-min agitations, this rate (i.e., structural breakdown speed) is already negligible (-0.7% of the value initially obtained for t = 0):
t (min) Figure 7-Thixotropic rate as a function of time, for different gel concentrations subjected to constant agitation at 60 rprn, after 29 days storage at rest. uT(5) =
UT(0)/e5= 0.007~~(0)
(9)
This again shows that -5 min are sufficient to secure the almost entire structural breakdown of the gel. A further advantage of eq 8 in relation to eq 6 is that the latter was limited to agitation times in excess of 0.78 min, below which S , proved negative. Thus, the field of application of the equation as proposed in this study is more general in context. In addition, its great simplicity should be stressed; that is, it depends on a single parameter (a function of storage time) and still includes both gel concentration value and agitation time.
Conclusions
80
60 ”
‘E 40
z v
+
>
20
0 t
(min)
Figure GThixotropic rate as a function of time, for different gel concentrations subjected to constant agitation at 60 rprn, after 1 day storage at rest.
78 i Journal of Pharmaceutical Sciences Vol. 80, No. 1, January 1991
A description has been given of the thixotropic behavior of MCC:NaCMC gels at six different concentrations (between 1 and 2.5% by weight) and for different agitation and storage times a t temperatures spanning 22 to 35 “C.In order to carry out the study, >7200 experimental measurements of T were made as a function of the different D values provided by the rotary viscometer employed. The following results should be pointed out. Shear stress ( T ) tends to be neutralized on reducing D, whereas a t the same time viscosity decreases considerably on increasing this rate. Both observations point to the nonlinear, pseudoplastic or slightly plastic nature of the gels studied. The results provided by the comparison of the shear efforts obtained for the “up” curve and corresponding “down”curve after 5 min of agitation show that the shear effort required in certain industrial processes may be reduced 40%, provided that prior to manipulation, the gels are subjected to agitation for 5 min a t 60 rpm. This result is independent of concentration, storage time, and D. It has also been found that the gel evolves in relation to concentration so that an increase of up to 800%in is produced for a concentration of 2.5%compared with the 1%MCC:NaCMC preparation.
As to thixotropic area, it has been shown to increase both with gel concentration and agitation time. The quantification of these areas provided a semiempirical function that satisfies the theoretical limiting conditions and provides the value of area in terms of the aforementioned variables and storage time. This function has been found to respond to experimental values with estimation errors of
.
-
-
-
-
. . ~ ..
_
is made of the rheologic behavior of microcrystalline ce1lulose:sodiurn carboxymethyl cellulose gels at six different concentrations (between 1 and 2.5% by weight).The thixotropy of these gels was analyzed in terms of agitation time, the duration of storage, concentration. and temperature; a semiempirical function was thus obtained providing thixotropic area as a function of these variables. The instantaneous variation rate in thixotropic area was defined, providing a better understanding of the rate of structural breakdown. Also, it is shown that after 5 min of agitation, the variation rate becomes negligible (-0.7% of the initial value);this result is practically independent of the remaining variables. Abstract 2 An extensive study
A great number of dispersed systems, (i.e., suspensions, gels, etc.) used in the pharmaceutical industry present thixotropic behavior which consists of the reversible, isothermic decrease in the viscosity of a fluid when the latter is agitated. This property is due to the structural breakdown of such substances on being subjected to shearing stress ( 7 ) for a n interval of time; i t manifests particularly during preparation procedures, storage, and use. The study of thixotropyl-4 is generally carried out by obtaining the rheograms corresponding to the “up” curve ID = f i r ) ) for increasing T values, and different “down” curves for decreasing T values after subjecting the fluid to different periods of agitation,s where D is shear rate. Studies on this subject69 usually obtain thixotropic area and its variation with factors such as agitation time, storage time, temperature, concentration, and so on. In this work, we analyze the thixotropic behavior of microcrystalline cellu1ose:sodium carboxymethyl cellulose gels at concentrations of 1, 1.5, 1.75, 2, 2.25, and 2.5% by weight. A semiempirical equation is obtained, relating thixotropic area and concentration and agitation time and storage time, that is applicable to temperatures between 22 and 35°C. In addition, instantaneous thixotropic rate is defined as obtained by derivation of the aforementioned equation. In our opinion, the latter provides a clear idea of the rate at which gel structural breakdown occurs. Finally, a comparison is made of the results obtained with those reported in an earlier studylo where mean thixotropic rate was defined as the ratio between thixotropic area increments and agitation time.
Experimental Section The experimental measurements in determining the thixotropic behavior of a gel were made with a Brookfield Digital DV I1 rotary cylinder viscometer, using an interval of eight angular velocities between 0.3 and 60 rpm. The viscometer was connected to a Macintosh Plus computer equipped with a data-input Link program. A number of complementary calculations were made with a HewlettPackard HP 9826 computer. The experiments were made at 22,25,28,30, and 35 “C, introducing the containers with the gel into a thermostatic bath and directly measuring from them to avoid prior decantation of the fluid. 0022-3549/91/0100-0075$01 .OO/O C:, 1991, American Pharmaceufical Association
The microcrystalline cellu1ose:sodium carboxymethyl cellulose gels (MCC:NaCMC;Avicel RC-581; American Viscose Division, FMC Corporation, Philadelphia, PA) were prepared at 20 “C. The product was slowly dispersed in deionized water, vigorously agitated for 10 min, left to rest for 5 min, and again agitated for another 10 min to create a homogeneous mix and facilitate gel formation while avoiding the internal creation of bubbles. Nipagin was used in the usual proportion as a preservative agent against fungi and bacterial contamination. In this way, 150 flasks (300 mL each) were prepared. Of these, 30 flasks, one for every concentration and temperature value, were determined after 1 day of storage, the next 30 flasks after 8 days, and so on after 15, 22, and 29 days of storage at rest. The aim was to establish possible modifications in the thixotropic behavior of the gels with varying times ofstorage at rest. The fact that the measurements were made with the actual storage flasks prevented prior fluid decantation and represents an additional advantage of the viscometer employed.5
The experimental measurements were made as follows. At constant temperature and with the viscometer rotary cylinder immersed in the fluid, shear angular velocity was increased from 0.3 to 0.6, 1.5,3, 6, 12, 30, and 60 rpm. The mean viscosity value (7)was calculated in centipoise (cP),corresponding to three measurements made at each rotary speed. Once transformed to shear stress (7)and shear rate (D), these values made it possible to construct the rheogram D = /IT), corresponding to the “up” curve. The “down” curve was then obtained following 1 min of agitation at 60 rpm, reducing angular velocity progressively from 60 to 0.3 rpm. This procedure was repeated for 2, 3, 4, and 5 min of agitation, providing a total of five “down” curves for each flask. This was considered to be sufficient, as in an earlier studylo it was found that the greatest thixotropic decrease occurs during this time interval. In this way, a total of >7200 T values were gathered in terms of variables such as shear rate (D) agitation time ( t ” ) ,storage time (fs), and temperature (7’).
Results and Discussion Rheological Behavior of Gels in Terms of Concentration and Agitation Time-The thixotropic behavior of the gels is expressed by their rheograms, D = /IT), corresponding to the “up” curve and the different “down” curves obtained after varying agitation times. Figure 1 (A and B) shows the rheograms for the 1.5 and 2.5% MCC:NaCMC gels after 8 days of storage at rest and a temperature of 28°C. The corresponding separation between the “up” and “down” curves is appreciable, demonstrating the thixotropic behavior of the test substance. The comparative study of >900 rheograms obtained for different concentrations, temperatures, and storage times made it possible to show that T decreases when D tends towards zero, reflecting t h e pseudoplastic or nonlinear slightly plastic character of these gels. A further point worth noting is that with the lesser D used in our experiments, the rheogram gradients are noticeably smaller than those obtained with D = 1.267 s - ’ , where the curve rise becomes steadily faster. This implies a considerable decrease in fluid Journal of Pharmaceutical Sciences I 75 Vol. 80, No. 1, January 1997
a
0
2
4
(2.25%)
K,= 8 4 . 6
(2%)
K,- 6 3 . 4
(1.75%)
K,
10
6
K,- 92.6
-
98.1
(1.5%)
(1.11-2)
6
20
K,= 18.0
Figure 2-Variation in thixotropic area for different gel concentrations, subjected to constant agitation at 60 rpm, as a function of time. Both concentrations and K, values were obtained by fitting to S,= qt) by eq 3. The graph corresponds to a storage time at rest of 1 day.
0
5
10
15
20
25
120
t (n.m-2) Figure 1-Rheograms corresponding to the “up” and “down” curves after 1, 2,3,4, and 5 min of agitation at 60 rpm and corresponding to a temperature of 28 “C for the following MCC:NaCMC concentrations and storage times: (A) 1.5% and 8 days; (B) 2.5% and 8 days.
1 1 L
100
Concentration(c)
K,=
viscosity as T increases; this fact is all the more apparent in the rheograms corresponding to the “up” curve, and less so for the “down” curves corresponding to the same concentration and storage time. It was also found that the shear stress of the “up” curve ( T ~ ) and that corresponding to the same D for the “down” curve ( T ~obtained ) after 5 min of agitation approximately satisfy the equation TD = 0 . 6 0 ~ (SD ~ = 0.061,regardless of concentration, storage time, and D within the limits imposed for the different variables involved in the study. In principle, these results indicate that the T required in certain industrial processes may be reduced 40%, provided the MCC:NaCMC gels are previously subjected to constant agitation at 60 rpm for 5 min. Another result that should be pointed out is the effect of concentration on 7.The increase in viscosity with increasing concentration was disproportionate. As an example, on comparing Figures 1A and 1 B, a concentration increase from 1.5 to 2.5% corresponds to an approximately threefold increase in viscosity from 8 to 25. Variation in Thixotropic Area as a Function of Concentration, Agitation, and Storage Time-The determination of thixotropic area (the area between the ccupO curve, each of the “down” curves and, in our case, the ordinates D, = 0.063s-l and D, = 12.673 s-’) was carried out by numerical integration11 applied to the experimental data of the rheograms obtained. For example, Figures 2 and 3 provide the thixotro76 I Journal of Pharmaceutical Sciences Vol. 80, No. 7 , January 7997
20
86.7
(2.5%)
K,- 81.4
(2.25%)
K,-
74.0
(2%)
K,-
513.4
( 1.75%)
K,-
45.6
(1.5%)
K,-
20.8
t (min) a Figure &Variation in thixotropic area for different gel concentrations, subjected to cohstant agitation at 60 rpm, as a function of time. Both concentrations and K, values were obtained by fitting to S, = It)by eq 3. The graph corresponds to a storage time at rest of 15 days.
pic areas (in Nm-* s-’) as a function of agitation time (ta;in min) for all the concentrations studied, and for 1and 15 days of storage, respectively. By comparing the results obtained, we found that for a given agitation time, the absolute thixotropic area of the gel increases with MCC:NaCMC
concentration. On the other hand, this area increases with agitation time (particularly during the first 3 min), and tends to reach a maximum constant value on increasing t,. To gain further insight to this subject, the thixotropic areas (S,) obtained for the different concentrations and storage times were fitted using functions of the following type:
These functions satisfy the theoretical frontier conditions; with t = 0, the thixotropic area must be zero, and with t + 00, STtends towards a finite value ( K l ) ,corresponding to maximum gel structural breakdown. The fittings made with these functions offered estimation errors of 4%. On the other hand, the maximum thixotropic areas (K,) as a function of gel concentration ( C ) for the different storage times are given in Figures 4A-4E. The distribution of experimental points obtained (K,, C ) was in turn fitted by singleparameter empirical functions (for greater simplicity) of the following type, whose correlation coefficients are provided in each of the graphs shown in Figure 4:
K1 = K2C3I2
(2)
Moreover, these functions satisfy the requirement that for zero concentration, thixotropic area is also zero (i.e., thixotropic behavior is not observed). Thus, the semiempirical equation obtained that provides MCC:NaCMC gel thixotropic area as a function of gel con-
I20
centration and constant 60 rpm agitation time is of the following type:
ST= K
~ (1C-e-?~
~
~
(3)
where S , is given in N * rn-, * s-l, concentration is in % by weight, and agitation time is in min; K , is a parameter whose decrease with increased storage time implies a decrease in thixotropic area (this indicates a more stable gel formation). The experimental values ofK, for storage times (t,) of 1,8,15, 22, and 29 days are 28.7, 28.3, 23.8, 21.5, and 19.8 N m-' * s-', respectively. Comparison of the experimental results with those obtained on applying eq 3 is given in Figure 5. The fitted equation of the straight line is as follows:
-
ST(theor) = (0.997 2 0.005)S~(exp)
(4)
This equation provides a correlation coefficient (r)of 0.99 and error of estimate of 3.9. This therefore shows that eq 3 is useful over the entire values interval of the variables studied, and for a temperature range of 22 to 35 "C. Thixotropic Rate-In our opinion, a knowledge of the rate at which gel structural breakdown occurs provides a better understanding of the rheologic behavior of the gel when subjected to agitation in production and packaging processes. The knowledge of this rate is useful in comparing structural breakdowns that may be identical but occur over different time intervals-an aspect that cannot be analyzed by the simple study of thixotropic area. In an earlier paper10 we suggested defining this rate as follows:
I00 80 7vl n
where uT represents mean rate of variation in thixotropic area (AS,) for an agitation time of At,. The values obtained for uT
60
'E
z 40 ~
J
120 1
/
2e 0
I00
-
C ( % Weight)
80 -
60 100 80 60
I-
I
m
'v)
% z
- 40
J 20 0
C(%
Weight)
0
20
40
60
80
100
120
Figure &Maximum thixotropic area (K,) as a function of concentration for the following storage times: (A) 1 day; (B) 8 days; (C)15 days; (D) 22 Figure SThixotropic area values obtained on applying eq 3 in relation days; (E)29 days. The correlation coefficients of the fitting made via functions of the type represented by eq 2 are 0.985,0.996,0.984,0.990,to the experimental values obtained by numerical integration. The straight line shown is that obtained by minimum square fitting. and 0.982,respectively. Journal of Pharmaceutical Sciences / 77 Vol. 80,No. 1, January 1991
were fitted as a function of agitation time (t,) by the following hyperbolic empirical equation:
where the parameters A (0.24 & 0.03) and B (0.78 ? 0.06) provided a good reproduction of the values corresponding to the experiments performed. However, much more precise information may be obtained in relation to this variation if At, is made to approach zero, whereby instantaneous thixotropic rate (or instantaneous thixotropic area variation per unit time) may be defined as proposed in this study; that is:
-
N
l Y) N*
60
I€
z V
’
I-
> 40 This makes it possible to determine how fast structural breakdown occurs a t any given instant. Calculation of the corresponding value is very simple, due to eq 3, as its derivation in terms of t provides instantaneous thixotropic rate as a function of concentration, agitation time, and K , (which is, in turn, dependent on storage time); that is:
20
0
The results obtained by applying eq 8 to the experiments performed made it possible to obtain graphic representations of uT as a function o f t for the different concentrations and storage times involved (two examples are given in Figures 6 and 7). The exponential decrease with time means that the instantaneous thixotropic rate tends towards zero when t approaches infinity; although, in practice and for 5-min agitations, this rate (i.e., structural breakdown speed) is already negligible (-0.7% of the value initially obtained for t = 0):
t (min) Figure 7-Thixotropic rate as a function of time, for different gel concentrations subjected to constant agitation at 60 rprn, after 29 days storage at rest. uT(5) =
UT(0)/e5= 0.007~~(0)
(9)
This again shows that -5 min are sufficient to secure the almost entire structural breakdown of the gel. A further advantage of eq 8 in relation to eq 6 is that the latter was limited to agitation times in excess of 0.78 min, below which S , proved negative. Thus, the field of application of the equation as proposed in this study is more general in context. In addition, its great simplicity should be stressed; that is, it depends on a single parameter (a function of storage time) and still includes both gel concentration value and agitation time.
Conclusions
80
60 ”
‘E 40
z v
+
>
20
0 t
(min)
Figure GThixotropic rate as a function of time, for different gel concentrations subjected to constant agitation at 60 rprn, after 1 day storage at rest.
78 i Journal of Pharmaceutical Sciences Vol. 80, No. 1, January 1991
A description has been given of the thixotropic behavior of MCC:NaCMC gels at six different concentrations (between 1 and 2.5% by weight) and for different agitation and storage times a t temperatures spanning 22 to 35 “C.In order to carry out the study, >7200 experimental measurements of T were made as a function of the different D values provided by the rotary viscometer employed. The following results should be pointed out. Shear stress ( T ) tends to be neutralized on reducing D, whereas a t the same time viscosity decreases considerably on increasing this rate. Both observations point to the nonlinear, pseudoplastic or slightly plastic nature of the gels studied. The results provided by the comparison of the shear efforts obtained for the “up” curve and corresponding “down”curve after 5 min of agitation show that the shear effort required in certain industrial processes may be reduced 40%, provided that prior to manipulation, the gels are subjected to agitation for 5 min a t 60 rpm. This result is independent of concentration, storage time, and D. It has also been found that the gel evolves in relation to concentration so that an increase of up to 800%in is produced for a concentration of 2.5%compared with the 1%MCC:NaCMC preparation.
As to thixotropic area, it has been shown to increase both with gel concentration and agitation time. The quantification of these areas provided a semiempirical function that satisfies the theoretical limiting conditions and provides the value of area in terms of the aforementioned variables and storage time. This function has been found to respond to experimental values with estimation errors of
