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Influence of loading rate and packing fraction on visco-elastic behaviour of powder compacts
231
Powder Technology, 69 (1992) 231-238
Influence of loading rate and packing fraction on visco-elastic behaviour of powder compacts S. Malamataris”, J. E. Rees and J. P. Hart School of Pharmacy and Pharmacology, Universrty of Bath, Claverton Down, Bath BA2 7AY (UK) (Received
January
17, 1991; in revised form September
26, 1991)
Abstract The visco-elastic characteristics of compacts of Starch 1500, Emcompress and paracetamol powders were studied at different loading rates and values of packing fraction. Creep experiments were performed using a tensile tester fitted with a compression cage, operated at selected platten rates to achieve specific mean rates of load application to constant load. Derived measurements included the instantaneous and retarded elastic compliance, the retardation of elastic compliance and the apparent viscosity. An improved method is proposed to calculate the ratio of elastic to plastic deformation for particulate solids during compaction, and to characterize their rheological behaviour. The time at which total creep compliance is equal to the equilibrium value of elastic compliance at infinite time is shown to be a possible parameter for quantifying the retardation of elastic compliance.
Introduction
The ability to form powdered materials into tablets depends, among other factors, on the plastic deformation and elastic recovery during compression and ejection from the die. For the assessment of the visco-elasticity** of powders, several ‘indirect’ methods have been described [l-4]. These methods have been based on measurements of changes in tablet thickness that occur during loading and after ejection, but they cannot be considered fundamental, since the loading and ejection conditions are arbitrarily chosen. Therefore, they are applicable only for comparative evaluations. Attempts to characterize the visco-elasticity from stress relaxation studies, by maintaining constant strain and determining the force decay with time, have shown that the results depend on the initial rate of strain application, as this cannot be applied instantaneously [5,6]. Other investigators have studied creep behaviour of particulate solids by applying constant stress to a powder sample and monitoring the strain or the compliance (strain/constant stress) with time [7-91. The creep curves obtained show three distinct regions, corresponding to different types of rheological behaviour: elastic, visco-elastic and plastic deformation [8, 91. The *Author to whom correspondence should be addressed at: Department of Pharmacy, University of Salonika, Salonika 54006 (Greece). **V&o-elasticity is considered here to be identical with plastoelasticity.
0032-5910/92/$5.00
suitability of the ratio of elastic (reversible) to plastic (irreversible) deformation has been considered with a view to predicting the compactibility of powders [9, lo]. Alternatively, analysis of the creep compliance curves can quantify the plastic and retarded elastic deformation, and describe the retardation of the elastic deformation by a parameter having dimensions of time
WI* However, in all compaction studies, including those involving creep analysis, a finite time elapses before a selected applied load or stress is achieved. During this time, the particulate solid consolidates by various mechanisms, such as rearrangement, deformation and fragmentation. Interparticle bonding will also occur. Such effects will influence the response of a partly consolidated powder bed to subsequent load, whether this is constant in a creep experiment, increasing with time during further compaction, or decreasing with time under stress relaxation conditions. The ranking of powdered materials in terms of the ratio of reversible (elastic) to irreversible (plastic) deformation is therefore difficult, even on the basis of creep analysis, since the relative contribution of different consolidation mechanisms is unknown and because it is unclear which specific time in the compliance profile is relevant for this ranking. In the present work, we have attempted to quantify the effects of the loading rate, and the consolidation during preloading, on the v&o-elastic parameters measured in creep experiments. Several pharmaceutical
0 1992 - Elsevier Sequoia. Ah rights reserved
232
powders were used which consolidate by different mechanisms. We have also attempted to identity a specific time of creep for the optimal comparison of the elastic and plastic deformation. Such information is intended to provide a better quantification of the visco-elastic behaviour during tableting and to allow eventual correlation with the properties of the resulting tablets.
Experimental Materials and methodr The following materials which differ in their compres-
sion behaviour were used; a modified starch (Starch 1500, Colorcon Ltd, Orpington, UK), a direct-compression form of dicalcium phosphate dihydrate (Emcompress, E. Mendell Co, Carmel, NY, USA) and paracetamol powder (Cambrian Chemicals, UK). The paracetamol powder was classified using a zig-zag classifier (Multiplex - Alpine, Augsburg, Germany) to give three particle size fractions: less than 15 pm, 1545 pm and larger than 45 pm. Starch 1500 and Emcompress were used as received from the suppliers. Accurately weighed powder samples, sufficient to produce tablets 2.21 mm thick at zero theoretical porosity, were stored for 7 days at 25 “C and 53% relative humidity. Plots of creep compliance 21s. time were obtained using a mechanical testing machine (T22K, J. J. Lloyd Instruments, Southampton, UK) fitted with a compression cage, constant stress module, two linear displacement transducers and a 12.7 mm flat-faced punch and die set. Using a graphics dump routine, the plot was transferred onto a dot matrix printer. The visco-elastic parameters were obtained by regression analysis. Details of the equipment and procedure have been described elsewhere [ 131. A range of constant loads was applied up to 18 kN and the platten rate was adjusted to achieve controlled mean rates of load application of 4, 8, 16, 32 and 64 kN min-‘. For selected materials (Starch 1500 and Emcompress) the creep testing was repeated on the formed compacts by applying a second and higher constant load at the same mean loading rate, in order to investigate the combined effect on the visco-elastic parameters of loading rate and of consolidation that occurred during preloading.
Results and discussion Typical.curves of total compliance (A) and compliance due to elastic deformation (B) with respect to time for the three materials investigated, are shown in Fig. 1 (i-iv). Curve (B) is derived from (A) by subtracting the plastic component of compliance determined as
the product of the slope of the linear region (k,) and time (t). For Starch 1500 and Emcompress, the effect of loading rate on the equilibrium value of elastic compliance, J,, is illustrated in Fig. 2. The term J, is the total of elastic and visco-elastic compliance. For the three size fractions of paracetamol, the elastic compliance results are given in Table 1. From Fig. 2, it can be seen that for Starch 1500 there are separate linear relationships between the elastic compliance and the logarithm of the initial packing fraction, pa at each of the different loading rates employed. The initial packing fraction refers to the value at zero creep time when constant load was first reached and creep monitoring began. For Emcompress, (Fig. 2) and paracetamol (Table l), elastic compliance is smaller than that for Starch 1500 by as much as one or two orders of magnitude. There is apparently no systematic or major effect of varying the loading rate for Emcompress or paracetamol, partly because the elastic compliance in each case is low, but also because the standard deviations of J, and kl values are relatively large compared with those for Starch 1500. Table 1 shows that, for the different size fractions of paracetamol powder, the elastic compliance increases with a reduction in particle size. This increase in elastic compliance may be attributed to the increased void space (i.e. lower pf values), in the compacts formed from paracetamol of smaller particle size, facilitating more extensive particle deformation, both elastic and plastic. The apparent viscosity of each material in the compacted state is given by the reciprocal slope for the linear region of the compliance curves (l/k,). Values of this parameter at different packing fractions are shown in Fig. 3. for Starch 1500 and Emcompress. For paracetamol, the results are given in Table 1. Starch 1500 showed much lower apparent viscosity values than Emcompress or paracetamol. The values for starch seem to increase exponentially with packing fraction, and also show a dependence on the loading rate, especially at higher packing fractions (Fig. 3). Absence of such a clear trend for Emcompress may be attributed to the low k, values and also to the relatively large standard deviations, as in the case of elastic compliance. The apparent viscosity results for paracetamol were of the same orders of magnitude as those for Emcompress, ranging from 4X 10’ to 4X 10” MPa s; the values increased with particle size and also with the level of applied load and the rate of loading. From the results in Table 1, particles of paracetamol smaller than 15 pm clearly are capable of more extensive plastic deformation than those of larger size. Furthermore, the particle size of paracetamol is a more important factor than load or loading rate.
233
3 E-7
(ii)
32E-8.
(Ill)
(IV)
6E-8
t P al 0
;
3 E-8
15E-8
i
Y
"I.
Y 45
I
90
45
Time
Fig. 1. Creep compliance curves for (i) Starch 1500, (ii) Emcompress, (A) = total compliance and (B) = elastic compliance.
As reported for previous creep studies [ll], the apparent viscosity values were inversely related to the elastic compliance values; they should also reflect the extent of elastic retardation. The elastic retardation has been expressed by Tsardaka and Rees [ll] using a parameter, k2, which relates exponentially the extent of elastic compliance to reciprocal time. The parameter k,, which has dimensions of time, should indicate the time at which the ratio of elastic compliance to plastic compliance [(Jet,- k,t)/(k,t)] is maximized; Tsardaka and Rees found the values for Starch 1500, Avicel and Emcompress to be 1.75, 1.52 and 0.82 s respectively [ll]. Bangudu and Pilpel, on the other hand, have measured the ratio of elastic recovery (ER) to stress relaxation or plastic compression (PC) by varying the duration of the separate phases of the compression cycle (i.e. loading, holding and unloading); in that case, PC is a combination of elastic and plastic deformation. They found that for Avicel, the ER/PC ratio reached a minimum (i.e. the actual elastic/plastic ratio reached a maximum) at a selected compression cycle lasting for 90 s, which corresponded to holding under load for 30 s [12]. A similar time of 30 s has been reported by Rees and Rue [6] for the semi-logarithmic plots of force remaining VS. time for Avicel and Starch 1500
(iii) paracetamol
90
IS)
>45 pm and (iv) paracetamol
<15 pm.
to become linear in stress relaxation tests. This time of 30 s shows no agreement with the k2 values of 1.52 s and 1.75 s quoted above. It is, however, remarkably close to the time t, for the Starch 1500 creep curves, when the total compliance, Jet,, becomes equal to the elastic compliance at infinite time,J,, that is the intercept at zero creep time of the extrapolated terminal linear region of the creep curve. Consequently, this time value, t,, may be suitable for quantifying the elastic retardation. The results obtained for the powders tested under different loading conditions are given in Table 2. For several reasons, time tl may provide optimal conditions at which to quantify the ratio of reversible (elastic) to irreversible (plastic) compliance. Firstly, t, can be identified experimentally. Secondly, it does not seem to be affected by the loading rate (Table 2) but only by the nature and the particle size of the particulate solid material. Furthermore, the ratio [(J(,,, - k,ti)/(k,ti)] takes into account each of the main v&o-elastic parameters, i.e. the elastic compliance, the apparent viscosity and the compliance retardation which reflects deviation from ideal visco-elastic behaviour. Staniforth and Pate1 [9] have suggested that the ratio ER/PC is a poor method for predicting the compaction behaviour of powders, but that the data from creep
234
14
-Y
2
1
J:
05
1
07
I
1
0 75
08
Pack1
ng
Fig. 2. Effect of initial packing fraction (logarithmic (open
symbols),
at various mean
loading rates:
(V)
I
,
0 a5
09
I
0 95
fraction scale) on the elastic 4; (B)
8; (0)
analysis could predict the compactibility of powders within acceptable limits, except in certain cases when particle size changes are involved 19, lo]. However, they did not take into account the packing fraction or the consolidation state of the powders, and the ratio of elastic/plastic deformation was calculated at an arbitrarily chosen time of creep. Table 3 shows our results for the ratio of elastic to plastic compliance of each test material, obtained at different packing fractions, loading rates and times held under load. Values are quoted at 90 s and at the creep retardation time t, of the material concerned, namely 27, 7, 4.5, 5 and 18 s respectively for Starch 1500, Emcompress and the three size fractions of paracetamol
comphance of Starch 1500 (solid symbols) and Emcompress 32 and (A) 64 kN min-‘.
16; (+)
(> 45 pm, 1545 pm and < 15 pm). At the retardation time t,, the ratio is relatively high for the coarsest paracetamol (> 45 pm), low for Starch 1500 and tends to decrease with the particle size of paracetamol. The effects of loading rate and packing fraction on the elastic/plastic ratio differ for the various materials tested and, in general, they are less important than the effects of creep time. The combined effect of loading rate and amount of preloading on creep behaviour of preformed compacts has been analysed on the basis of the results for elastic compliance, apparent viscosity and compliance retardation. Figure 4 shows plots of the elastic compliance obtained for preformed compacts of Starch 1500 and
235
TABLE 1. Elastic compliance and apparent under different compression conditions
viscosity for different
Paracetamol size (pm)
load (kN)
Loading rate (kN min-‘)
>45
Constant 8
4 16 4 16 4 16
1545 < 15
particle
size fractions
of paracetamol
12
powder
in creep testing
16
Pr”
J,
1lk,’
Pf
Jd
l/k,
Pf
Jl
l/k1
0.84 0.84 0.82 0.82 0.79 0.78
2.3 1.4 0.8 2.2 3.8 2.9
17.2 30.5 13.0 16.0 4.0 5.6
0.88 0.88 0.88 0.85 0.83 0.83
1.0 0.4 1.1 0.8 2.6 2.8
26.5 27.9 15.1 22.3 6.8 7.1
0.90 0.90 0.87 0.86 0.84 0.83
0.5 0.4 0.9 1.2 2.1 3.0
30.0 41.0 16.8 24.6 8.7 9.0
“Packing fraction. bElastic compliance (MPa-’ X lo-*). ‘Apparent viscosity (MPa s X 109).
200
140
80 m 0 x
12
VI p" zz
J \8
4
I
I
I
k
085
075
Pack! Fig. 3. Effect of initial packing fraction
“CJ
1
I
095
fraction
on the apparent
viscosity of Starch 1500 and Emcompress
(key as in Fig. 2).
236 TABLE 2. Compliance retardation different compression conditions
for powders
tested
under
Starch 1500
0.75 0.80 0.75 0.80
27 27 90 90
6.5 6.5 2.3 2.3
10.8 10.6 3.6 3.5
Emcompress
0.75 0.80 0.75 0.80
7 7 90 90
41.8 33.3 4.9 2.7
38.3 34.7 3.0 2.8
into a compact. Clearly, for Starch 1500 the elastic compliance decreases when the load applied to form the initial compact is above 6 kN (pi> 0.7). In contrast, for Emcompress the elastic compliance increases slightly when the precompaction load exceeds 8 kN &>0.7). These contrasting effects seen in Fig. 4 are due to the different consolidation mechanisms of Starch 1500 and Emcompress. In a brittle material such as Emcompress, the compacts preformed at low loads are still capable of extensive fracture on a second loading, to a constant load of 12 kN. Thus much of the elastic deformation is relieved by brittle fracture. Conversely, in compacts preformed at 12 kN, fracture will be virtually complete, so that, on repeat loading to 12 kN, there will be minimal fragmentation but extensive elastic deformation. Compacts of a brittle material, at high loads, retain a considerable volume of residual void space (cf Fig. 3); the voids can therefore accommodate extensive deformation, in this case elastic deformation, commensurate with the high load applied. Conversely, in a material like Starch 1500, which is capable of relieving elastic strain by undergoing plastic deformation, a high preload will cause extensive plastic consolidation, thus considerably reducing the voidage. This effect is most marked at a low rate of loading since more time is available for plastic flow. Since a constant second load of 12 kN was applied, the Ji values at each condition were constant until the limitation in residual void space at higher preloads restricted the amount of elastic deformation which could occur. The apparent viscosity results on the preformed compacts were found to be consistent with those of elastic compliance, the usual inverse relationship between apparent viscosity and elastic compliance being observed. However, the retardation time, t,, was independent of both the loading rate and the consolidation state of the preformed compacts.
Paracetamol (>45 pm)
0.80 0.85 0.80 0.85
4.5 4.5 90 90
56.8 82.1 2.9 4.2
54.6 55.0 2.8 2.8
Conclusions
Paracetamol (15-45 pm)
0.80 0.85 0.80 0.85
5 5 90 90
35.0 25.6 2.0 1.5
47.0 68.0 2.7 3.8
Paracetamol (x15 pm)
0.80 0.85 0.80 0.85
18 18 90 90
8.7 9.0 1.9 2.0
8.7 15.6 1.9 3.3
Material
Loading rate (kN min-‘)
Compliance retardation constant load @IV) of 4
6
8
10
12
16
18
24 26 27 28 29
-
-
Starch 1500
4 8 16 32 64
28 27 25 27 27
26 26 25 26 28
28 27 27 28 26
26 26 25 27 28
Emcompress
4 8 16 32
6 7 6 8
7 6 7 6
6 7 7 7
6 8 8 7
Paracetamol (>45 pm) Paracetamol (1545 pm) Paracetamol (<15 pm)
4 16 4 16 4 16
4 5 5 6 18 17
4 5 5 5 19 19
-
-
TABLE 3. Ratio of elastic/plastic deformation fractions, loading rates and creep time Material
Packing fraction
(s) at
Creep time (s)
777B4 4 4 6 20 18
4 5 5 5 17 16
4 5 5 5 20 18
at different packing
Ratio of elastic/ plastic deformation at loading rate (kN min-‘) of 16
4
Emcompress prepared by applying loads of 0, 4, 6, 8, 10 and 12 kN and then loading again at various rates to 12 kN constant load. The results quoted for zero ‘load applied’ are for powder samples not preformed
From the above, it is concluded that the loading rate employed during creep analysis affects the elastic compliance more than the apparent viscosity. For materials which consolidate by fragmentation, no obvious effect of loading rate was observed. The time, t,, when the total compliance is equal to the equilibrium value of elastic compliance at infinite time, is proposed as a suitable parameter to quantify elastic compliance retardation. This time t, is also an appropriate time at which to calculate the ratio of elastic/plastic deformation. When quoting this ratio, the packing fraction and the loading rate also need to be defined in order
237
2
b b x 7
m k
1
7
0.3
0.2
01
I
I
I
0
I
I
Load
to preform
I
8
4
compacts
I 12
(kN)
Fig. 4. Effect of the compaction load used to preform compacts of Starch 1500 and Emcompress compliance when loaded at different rates and held at 12 kN constant load (key as in Fig. 2).
to characterize the rheological pactibility of a given powder.
behaviour
List of symbols
ER J
Jw
elastic recovery creep compliance (MPa-‘) total creep compliance at time, t
and corn-
J,
k, kz
on their subsequent
elastic creep
intercept at zero time of the extrapolated linear region of the total compliance curve, i.e. compliance due to elastic and visco-elastic deformation at infinite time (MPa-‘) slope of the linear region of the total compliance curve (MPa-’ s-l) parameter (s) relating exponentially the fraction of retarded elastic compliance with reciprocal time: (J,,,--k,t)=J, exp-k,h ln[A/(J,, -k&l = kd
238
PC Pi t
4
plastic compression packing fraction time (s) time (s) when total compliance .JcI, equals J,
References N. A. Armstrong and R. F. Hames-Nutt,.Z. Pharm. PharmacoZ., 24 (1972) 135 P. J. Okada and Y. Fukumori, Chem. Pharm. Bull., 22 (1974) 493. I. Krycer, D. G. Pope and J. A. Hersey,.Z. Pharm. PharmacoZ., 34 (1982) 802. S. Malamataris, S. Bin-Baie and N. Pdpel, J. Pharm Pharmacol, 36 (1984) 616.
10 11 12 13
S. T. David and L. L. Augsburger, J. Pharm. Sci., 66 (1977) 155. J. E. Rees and P. J. Rue, Z. Pharm. PharmacoZ., 30 (1978) 601. M. Morii, N. Takeguchi and I. Horikoshi, Chem. Pharm. BUZZ., 21 (1973) 589. J. E. Rees, A. B. Mashadt and J. P. Hart, unpublished results (1984). J. N. Staniforth and C. I. Pate], Powder TechnoZ., 57 (1989) 83. J. N. Stamforth, A. R. Baichwal and J. P. Hart, Znt. .Z.Phamz., 40 (1987) 267. K. D. Tsardaka and J. E. Rees, .Z. Pharm. Pharmacol, 41 (1989) 28 P. A. B. Bangudu and N. Pilpel, J. Pharm. PharmacoZ., 37 (1985) 289. K. D. Tsardaka, Ph.D. Thesis, University of Bath, UK, 1990.
Powder Technology, 69 (1992) 231-238
Influence of loading rate and packing fraction on visco-elastic behaviour of powder compacts S. Malamataris”, J. E. Rees and J. P. Hart School of Pharmacy and Pharmacology, Universrty of Bath, Claverton Down, Bath BA2 7AY (UK) (Received
January
17, 1991; in revised form September
26, 1991)
Abstract The visco-elastic characteristics of compacts of Starch 1500, Emcompress and paracetamol powders were studied at different loading rates and values of packing fraction. Creep experiments were performed using a tensile tester fitted with a compression cage, operated at selected platten rates to achieve specific mean rates of load application to constant load. Derived measurements included the instantaneous and retarded elastic compliance, the retardation of elastic compliance and the apparent viscosity. An improved method is proposed to calculate the ratio of elastic to plastic deformation for particulate solids during compaction, and to characterize their rheological behaviour. The time at which total creep compliance is equal to the equilibrium value of elastic compliance at infinite time is shown to be a possible parameter for quantifying the retardation of elastic compliance.
Introduction
The ability to form powdered materials into tablets depends, among other factors, on the plastic deformation and elastic recovery during compression and ejection from the die. For the assessment of the visco-elasticity** of powders, several ‘indirect’ methods have been described [l-4]. These methods have been based on measurements of changes in tablet thickness that occur during loading and after ejection, but they cannot be considered fundamental, since the loading and ejection conditions are arbitrarily chosen. Therefore, they are applicable only for comparative evaluations. Attempts to characterize the visco-elasticity from stress relaxation studies, by maintaining constant strain and determining the force decay with time, have shown that the results depend on the initial rate of strain application, as this cannot be applied instantaneously [5,6]. Other investigators have studied creep behaviour of particulate solids by applying constant stress to a powder sample and monitoring the strain or the compliance (strain/constant stress) with time [7-91. The creep curves obtained show three distinct regions, corresponding to different types of rheological behaviour: elastic, visco-elastic and plastic deformation [8, 91. The *Author to whom correspondence should be addressed at: Department of Pharmacy, University of Salonika, Salonika 54006 (Greece). **V&o-elasticity is considered here to be identical with plastoelasticity.
0032-5910/92/$5.00
suitability of the ratio of elastic (reversible) to plastic (irreversible) deformation has been considered with a view to predicting the compactibility of powders [9, lo]. Alternatively, analysis of the creep compliance curves can quantify the plastic and retarded elastic deformation, and describe the retardation of the elastic deformation by a parameter having dimensions of time
WI* However, in all compaction studies, including those involving creep analysis, a finite time elapses before a selected applied load or stress is achieved. During this time, the particulate solid consolidates by various mechanisms, such as rearrangement, deformation and fragmentation. Interparticle bonding will also occur. Such effects will influence the response of a partly consolidated powder bed to subsequent load, whether this is constant in a creep experiment, increasing with time during further compaction, or decreasing with time under stress relaxation conditions. The ranking of powdered materials in terms of the ratio of reversible (elastic) to irreversible (plastic) deformation is therefore difficult, even on the basis of creep analysis, since the relative contribution of different consolidation mechanisms is unknown and because it is unclear which specific time in the compliance profile is relevant for this ranking. In the present work, we have attempted to quantify the effects of the loading rate, and the consolidation during preloading, on the v&o-elastic parameters measured in creep experiments. Several pharmaceutical
0 1992 - Elsevier Sequoia. Ah rights reserved
232
powders were used which consolidate by different mechanisms. We have also attempted to identity a specific time of creep for the optimal comparison of the elastic and plastic deformation. Such information is intended to provide a better quantification of the visco-elastic behaviour during tableting and to allow eventual correlation with the properties of the resulting tablets.
Experimental Materials and methodr The following materials which differ in their compres-
sion behaviour were used; a modified starch (Starch 1500, Colorcon Ltd, Orpington, UK), a direct-compression form of dicalcium phosphate dihydrate (Emcompress, E. Mendell Co, Carmel, NY, USA) and paracetamol powder (Cambrian Chemicals, UK). The paracetamol powder was classified using a zig-zag classifier (Multiplex - Alpine, Augsburg, Germany) to give three particle size fractions: less than 15 pm, 1545 pm and larger than 45 pm. Starch 1500 and Emcompress were used as received from the suppliers. Accurately weighed powder samples, sufficient to produce tablets 2.21 mm thick at zero theoretical porosity, were stored for 7 days at 25 “C and 53% relative humidity. Plots of creep compliance 21s. time were obtained using a mechanical testing machine (T22K, J. J. Lloyd Instruments, Southampton, UK) fitted with a compression cage, constant stress module, two linear displacement transducers and a 12.7 mm flat-faced punch and die set. Using a graphics dump routine, the plot was transferred onto a dot matrix printer. The visco-elastic parameters were obtained by regression analysis. Details of the equipment and procedure have been described elsewhere [ 131. A range of constant loads was applied up to 18 kN and the platten rate was adjusted to achieve controlled mean rates of load application of 4, 8, 16, 32 and 64 kN min-‘. For selected materials (Starch 1500 and Emcompress) the creep testing was repeated on the formed compacts by applying a second and higher constant load at the same mean loading rate, in order to investigate the combined effect on the visco-elastic parameters of loading rate and of consolidation that occurred during preloading.
Results and discussion Typical.curves of total compliance (A) and compliance due to elastic deformation (B) with respect to time for the three materials investigated, are shown in Fig. 1 (i-iv). Curve (B) is derived from (A) by subtracting the plastic component of compliance determined as
the product of the slope of the linear region (k,) and time (t). For Starch 1500 and Emcompress, the effect of loading rate on the equilibrium value of elastic compliance, J,, is illustrated in Fig. 2. The term J, is the total of elastic and visco-elastic compliance. For the three size fractions of paracetamol, the elastic compliance results are given in Table 1. From Fig. 2, it can be seen that for Starch 1500 there are separate linear relationships between the elastic compliance and the logarithm of the initial packing fraction, pa at each of the different loading rates employed. The initial packing fraction refers to the value at zero creep time when constant load was first reached and creep monitoring began. For Emcompress, (Fig. 2) and paracetamol (Table l), elastic compliance is smaller than that for Starch 1500 by as much as one or two orders of magnitude. There is apparently no systematic or major effect of varying the loading rate for Emcompress or paracetamol, partly because the elastic compliance in each case is low, but also because the standard deviations of J, and kl values are relatively large compared with those for Starch 1500. Table 1 shows that, for the different size fractions of paracetamol powder, the elastic compliance increases with a reduction in particle size. This increase in elastic compliance may be attributed to the increased void space (i.e. lower pf values), in the compacts formed from paracetamol of smaller particle size, facilitating more extensive particle deformation, both elastic and plastic. The apparent viscosity of each material in the compacted state is given by the reciprocal slope for the linear region of the compliance curves (l/k,). Values of this parameter at different packing fractions are shown in Fig. 3. for Starch 1500 and Emcompress. For paracetamol, the results are given in Table 1. Starch 1500 showed much lower apparent viscosity values than Emcompress or paracetamol. The values for starch seem to increase exponentially with packing fraction, and also show a dependence on the loading rate, especially at higher packing fractions (Fig. 3). Absence of such a clear trend for Emcompress may be attributed to the low k, values and also to the relatively large standard deviations, as in the case of elastic compliance. The apparent viscosity results for paracetamol were of the same orders of magnitude as those for Emcompress, ranging from 4X 10’ to 4X 10” MPa s; the values increased with particle size and also with the level of applied load and the rate of loading. From the results in Table 1, particles of paracetamol smaller than 15 pm clearly are capable of more extensive plastic deformation than those of larger size. Furthermore, the particle size of paracetamol is a more important factor than load or loading rate.
233
3 E-7
(ii)
32E-8.
(Ill)
(IV)
6E-8
t P al 0
;
3 E-8
15E-8
i
Y
"I.
Y 45
I
90
45
Time
Fig. 1. Creep compliance curves for (i) Starch 1500, (ii) Emcompress, (A) = total compliance and (B) = elastic compliance.
As reported for previous creep studies [ll], the apparent viscosity values were inversely related to the elastic compliance values; they should also reflect the extent of elastic retardation. The elastic retardation has been expressed by Tsardaka and Rees [ll] using a parameter, k2, which relates exponentially the extent of elastic compliance to reciprocal time. The parameter k,, which has dimensions of time, should indicate the time at which the ratio of elastic compliance to plastic compliance [(Jet,- k,t)/(k,t)] is maximized; Tsardaka and Rees found the values for Starch 1500, Avicel and Emcompress to be 1.75, 1.52 and 0.82 s respectively [ll]. Bangudu and Pilpel, on the other hand, have measured the ratio of elastic recovery (ER) to stress relaxation or plastic compression (PC) by varying the duration of the separate phases of the compression cycle (i.e. loading, holding and unloading); in that case, PC is a combination of elastic and plastic deformation. They found that for Avicel, the ER/PC ratio reached a minimum (i.e. the actual elastic/plastic ratio reached a maximum) at a selected compression cycle lasting for 90 s, which corresponded to holding under load for 30 s [12]. A similar time of 30 s has been reported by Rees and Rue [6] for the semi-logarithmic plots of force remaining VS. time for Avicel and Starch 1500
(iii) paracetamol
90
IS)
>45 pm and (iv) paracetamol
<15 pm.
to become linear in stress relaxation tests. This time of 30 s shows no agreement with the k2 values of 1.52 s and 1.75 s quoted above. It is, however, remarkably close to the time t, for the Starch 1500 creep curves, when the total compliance, Jet,, becomes equal to the elastic compliance at infinite time,J,, that is the intercept at zero creep time of the extrapolated terminal linear region of the creep curve. Consequently, this time value, t,, may be suitable for quantifying the elastic retardation. The results obtained for the powders tested under different loading conditions are given in Table 2. For several reasons, time tl may provide optimal conditions at which to quantify the ratio of reversible (elastic) to irreversible (plastic) compliance. Firstly, t, can be identified experimentally. Secondly, it does not seem to be affected by the loading rate (Table 2) but only by the nature and the particle size of the particulate solid material. Furthermore, the ratio [(J(,,, - k,ti)/(k,ti)] takes into account each of the main v&o-elastic parameters, i.e. the elastic compliance, the apparent viscosity and the compliance retardation which reflects deviation from ideal visco-elastic behaviour. Staniforth and Pate1 [9] have suggested that the ratio ER/PC is a poor method for predicting the compaction behaviour of powders, but that the data from creep
234
14
-Y
2
1
J:
05
1
07
I
1
0 75
08
Pack1
ng
Fig. 2. Effect of initial packing fraction (logarithmic (open
symbols),
at various mean
loading rates:
(V)
I
,
0 a5
09
I
0 95
fraction scale) on the elastic 4; (B)
8; (0)
analysis could predict the compactibility of powders within acceptable limits, except in certain cases when particle size changes are involved 19, lo]. However, they did not take into account the packing fraction or the consolidation state of the powders, and the ratio of elastic/plastic deformation was calculated at an arbitrarily chosen time of creep. Table 3 shows our results for the ratio of elastic to plastic compliance of each test material, obtained at different packing fractions, loading rates and times held under load. Values are quoted at 90 s and at the creep retardation time t, of the material concerned, namely 27, 7, 4.5, 5 and 18 s respectively for Starch 1500, Emcompress and the three size fractions of paracetamol
comphance of Starch 1500 (solid symbols) and Emcompress 32 and (A) 64 kN min-‘.
16; (+)
(> 45 pm, 1545 pm and < 15 pm). At the retardation time t,, the ratio is relatively high for the coarsest paracetamol (> 45 pm), low for Starch 1500 and tends to decrease with the particle size of paracetamol. The effects of loading rate and packing fraction on the elastic/plastic ratio differ for the various materials tested and, in general, they are less important than the effects of creep time. The combined effect of loading rate and amount of preloading on creep behaviour of preformed compacts has been analysed on the basis of the results for elastic compliance, apparent viscosity and compliance retardation. Figure 4 shows plots of the elastic compliance obtained for preformed compacts of Starch 1500 and
235
TABLE 1. Elastic compliance and apparent under different compression conditions
viscosity for different
Paracetamol size (pm)
load (kN)
Loading rate (kN min-‘)
>45
Constant 8
4 16 4 16 4 16
1545 < 15
particle
size fractions
of paracetamol
12
powder
in creep testing
16
Pr”
J,
1lk,’
Pf
Jd
l/k,
Pf
Jl
l/k1
0.84 0.84 0.82 0.82 0.79 0.78
2.3 1.4 0.8 2.2 3.8 2.9
17.2 30.5 13.0 16.0 4.0 5.6
0.88 0.88 0.88 0.85 0.83 0.83
1.0 0.4 1.1 0.8 2.6 2.8
26.5 27.9 15.1 22.3 6.8 7.1
0.90 0.90 0.87 0.86 0.84 0.83
0.5 0.4 0.9 1.2 2.1 3.0
30.0 41.0 16.8 24.6 8.7 9.0
“Packing fraction. bElastic compliance (MPa-’ X lo-*). ‘Apparent viscosity (MPa s X 109).
200
140
80 m 0 x
12
VI p" zz
J \8
4
I
I
I
k
085
075
Pack! Fig. 3. Effect of initial packing fraction
“CJ
1
I
095
fraction
on the apparent
viscosity of Starch 1500 and Emcompress
(key as in Fig. 2).
236 TABLE 2. Compliance retardation different compression conditions
for powders
tested
under
Starch 1500
0.75 0.80 0.75 0.80
27 27 90 90
6.5 6.5 2.3 2.3
10.8 10.6 3.6 3.5
Emcompress
0.75 0.80 0.75 0.80
7 7 90 90
41.8 33.3 4.9 2.7
38.3 34.7 3.0 2.8
into a compact. Clearly, for Starch 1500 the elastic compliance decreases when the load applied to form the initial compact is above 6 kN (pi> 0.7). In contrast, for Emcompress the elastic compliance increases slightly when the precompaction load exceeds 8 kN &>0.7). These contrasting effects seen in Fig. 4 are due to the different consolidation mechanisms of Starch 1500 and Emcompress. In a brittle material such as Emcompress, the compacts preformed at low loads are still capable of extensive fracture on a second loading, to a constant load of 12 kN. Thus much of the elastic deformation is relieved by brittle fracture. Conversely, in compacts preformed at 12 kN, fracture will be virtually complete, so that, on repeat loading to 12 kN, there will be minimal fragmentation but extensive elastic deformation. Compacts of a brittle material, at high loads, retain a considerable volume of residual void space (cf Fig. 3); the voids can therefore accommodate extensive deformation, in this case elastic deformation, commensurate with the high load applied. Conversely, in a material like Starch 1500, which is capable of relieving elastic strain by undergoing plastic deformation, a high preload will cause extensive plastic consolidation, thus considerably reducing the voidage. This effect is most marked at a low rate of loading since more time is available for plastic flow. Since a constant second load of 12 kN was applied, the Ji values at each condition were constant until the limitation in residual void space at higher preloads restricted the amount of elastic deformation which could occur. The apparent viscosity results on the preformed compacts were found to be consistent with those of elastic compliance, the usual inverse relationship between apparent viscosity and elastic compliance being observed. However, the retardation time, t,, was independent of both the loading rate and the consolidation state of the preformed compacts.
Paracetamol (>45 pm)
0.80 0.85 0.80 0.85
4.5 4.5 90 90
56.8 82.1 2.9 4.2
54.6 55.0 2.8 2.8
Conclusions
Paracetamol (15-45 pm)
0.80 0.85 0.80 0.85
5 5 90 90
35.0 25.6 2.0 1.5
47.0 68.0 2.7 3.8
Paracetamol (x15 pm)
0.80 0.85 0.80 0.85
18 18 90 90
8.7 9.0 1.9 2.0
8.7 15.6 1.9 3.3
Material
Loading rate (kN min-‘)
Compliance retardation constant load @IV) of 4
6
8
10
12
16
18
24 26 27 28 29
-
-
Starch 1500
4 8 16 32 64
28 27 25 27 27
26 26 25 26 28
28 27 27 28 26
26 26 25 27 28
Emcompress
4 8 16 32
6 7 6 8
7 6 7 6
6 7 7 7
6 8 8 7
Paracetamol (>45 pm) Paracetamol (1545 pm) Paracetamol (<15 pm)
4 16 4 16 4 16
4 5 5 6 18 17
4 5 5 5 19 19
-
-
TABLE 3. Ratio of elastic/plastic deformation fractions, loading rates and creep time Material
Packing fraction
(s) at
Creep time (s)
777B4 4 4 6 20 18
4 5 5 5 17 16
4 5 5 5 20 18
at different packing
Ratio of elastic/ plastic deformation at loading rate (kN min-‘) of 16
4
Emcompress prepared by applying loads of 0, 4, 6, 8, 10 and 12 kN and then loading again at various rates to 12 kN constant load. The results quoted for zero ‘load applied’ are for powder samples not preformed
From the above, it is concluded that the loading rate employed during creep analysis affects the elastic compliance more than the apparent viscosity. For materials which consolidate by fragmentation, no obvious effect of loading rate was observed. The time, t,, when the total compliance is equal to the equilibrium value of elastic compliance at infinite time, is proposed as a suitable parameter to quantify elastic compliance retardation. This time t, is also an appropriate time at which to calculate the ratio of elastic/plastic deformation. When quoting this ratio, the packing fraction and the loading rate also need to be defined in order
237
2
b b x 7
m k
1
7
0.3
0.2
01
I
I
I
0
I
I
Load
to preform
I
8
4
compacts
I 12
(kN)
Fig. 4. Effect of the compaction load used to preform compacts of Starch 1500 and Emcompress compliance when loaded at different rates and held at 12 kN constant load (key as in Fig. 2).
to characterize the rheological pactibility of a given powder.
behaviour
List of symbols
ER J
Jw
elastic recovery creep compliance (MPa-‘) total creep compliance at time, t
and corn-
J,
k, kz
on their subsequent
elastic creep
intercept at zero time of the extrapolated linear region of the total compliance curve, i.e. compliance due to elastic and visco-elastic deformation at infinite time (MPa-‘) slope of the linear region of the total compliance curve (MPa-’ s-l) parameter (s) relating exponentially the fraction of retarded elastic compliance with reciprocal time: (J,,,--k,t)=J, exp-k,h ln[A/(J,, -k&l = kd
238
PC Pi t
4
plastic compression packing fraction time (s) time (s) when total compliance .JcI, equals J,
References N. A. Armstrong and R. F. Hames-Nutt,.Z. Pharm. PharmacoZ., 24 (1972) 135 P. J. Okada and Y. Fukumori, Chem. Pharm. Bull., 22 (1974) 493. I. Krycer, D. G. Pope and J. A. Hersey,.Z. Pharm. PharmacoZ., 34 (1982) 802. S. Malamataris, S. Bin-Baie and N. Pdpel, J. Pharm Pharmacol, 36 (1984) 616.
10 11 12 13
S. T. David and L. L. Augsburger, J. Pharm. Sci., 66 (1977) 155. J. E. Rees and P. J. Rue, Z. Pharm. PharmacoZ., 30 (1978) 601. M. Morii, N. Takeguchi and I. Horikoshi, Chem. Pharm. BUZZ., 21 (1973) 589. J. E. Rees, A. B. Mashadt and J. P. Hart, unpublished results (1984). J. N. Staniforth and C. I. Pate], Powder TechnoZ., 57 (1989) 83. J. N. Stamforth, A. R. Baichwal and J. P. Hart, Znt. .Z.Phamz., 40 (1987) 267. K. D. Tsardaka and J. E. Rees, .Z. Pharm. Pharmacol, 41 (1989) 28 P. A. B. Bangudu and N. Pilpel, J. Pharm. PharmacoZ., 37 (1985) 289. K. D. Tsardaka, Ph.D. Thesis, University of Bath, UK, 1990.