Effect Of Particle Size Brittleductile Transitions

It has been known for many years that if Heckel plots were constructed for a material of varying particle size the reciprocal of the gradient over the central linear portion of the graph (now defined as the deformation stress, ad) varied either remaining constant or increasing as particle size decreased (Hersey and Rees, 1970; York, 1978). An extensive study (Roberts and Rowe, 1986, 1987b; Roberts etal., 1989a) showed that the effect of particle size was even more complex, depending on the material under test (Fig. 20). For a material known to undergo plastic deformation (e.g. microcrystalline cellulose) no effect of particle size could be seen; for a material known to undergo brittle fracture (e.g. dolomite), the deformation stress increased with decreasing particle size and for materials known to undergo a combination of brittle fracture and plastic deformation (e.g. a-lactose monohydrate) the deformation stress increased with decreasing particle size to a plateau value.

A comparison of the shapes of the curves with that predicted schematically in Fig. 1 shows that the point of change is indicative of a brittle-ductile transition equivalent to the critical particle size dcrjt predicted from theory. This has been confirmed for sodium chloride using independent measurements of yield stress and critical stress intensity factor (Roberts etal., 1989a).

Calculated critical sizes (equation 4) for a variety of excipients and drugs using yield stress data and critical stress intensity factors given in previous tables are shown in Table 18. It can be seen that critical particle sizes can vary over several orders of magnitude. The values appear reasonable in the

1000 900 800 700 600

A-jfc-A

10 100 Median particle size (ym)

fig. 20 The effect of particle size on the deformation stress as measured using Heckel plots for: dolomite; a lactose monohydrate; microcrystalline cellulose (adapted from Roberts and Rowe, 1987b).

light of experimental findings for microcrystalline cellulose and a-lactose monohydrate in Fig. 20. The value for microcrystalline cellulose is similar to that determined for other polymeric materials (Kendall, 1978). The differences in the two values for the two lactoses are consistent with the findings of workers describing their compaction properties (Vromans etal., 1986). Of the three drugs paracetamol has the lowest critical particle size, which is consistent with it being very brittle. However, the addition of a polymeric binder to paracetamol (i.e. paracetamol DC) increases its critical particle size by an order of magnitude causing it to become plastic in nature.

60 40 20

Table 18 Critical particle size for some excipients and drugs

H

Kico

dent

Material

(MPa)

(MPam172)

(p-m)

Microcrystalline cellulose

168"

0.7569

1949

Lactose 0 anhydrous

251*

0.7597

873

Ibuprofen

35"

0.1044

854

Aspirin

87°

0.1561

309

Paracetamol DC

265"

0.2463

83

a-Lactose monohydrate

515*

0.3540

45

Sucrose

645d

0.2239

12

Paracetamol

A2ld

0.1153

7

" Jetzer et al. (1983a) b Leuenberger (1982) c Ridgway et al. (1969a) d Duncan-Hewitt and Weatherly (1989b)

" Jetzer et al. (1983a) b Leuenberger (1982) c Ridgway et al. (1969a) d Duncan-Hewitt and Weatherly (1989b)

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