Pharmaceutical Manufacturing Handbook: Production and

of powder mixtures is usually characterized using the well - known Heckel equation
[9, 10] , which describes the relationship between the porosity of a compact and the
applied pressure and is based on the assumption that the densifi cation of the bulk
powder in the die follows fi rst - order kinetics:
1
ln
1− ρ
r
= kP + A (1)
where ρ r is the relative density of the compact at pressure σ , P is the applied pressure,
and K and A are constants. The constants A and k are determined from the
intercept and slope, respectively, of the extrapolated linear region of a plot of ln(1/1
− ρ r ) versus σ (compaction pressure). The Heckel constant k is related to the reciprocal
of the mean yield pressure, which is the minimum pressure required to cause
deformation of the material undergoing compression. The intercept obtained from
the slope of the upper portion of the curve is a refl ection of the densifi cation after
consolidation. A large value of k indicates the onset of plastic deformation at relatively
low pressure. Thus, K appears to be a material constant. The correlation
between k and the mean yield pressure P y gives Equation (2) . The constant A is
related to the densifi cation during die fi lling and particle rearrangement prior to
bonding [11] :
k =
P
1
y
A high ρ r value indicates that there will be a high volume reduction of the product
due to particle rearrangement. The constant A has been shown to be equal to the
reciprocal of the mean yield pressure required to induce plastic deformation. A
larger value for A (low yield pressure) indicates the onset of plastic deformation at
relatively low pressure, a sign that the material is more compressible.
The Heckel plot allows an interpretation of the mechanism of bonding. A nonlinear
plot with small value for its slope (a small Heckel constant) indicates that the
material undergoes fragmentation during compression. When the plot is linear, it
indicates that the material undergoes plastic deformation during compression.
In addition to the Heckel approach, other techniques may be applied to the
characterization of powder compression. One of these approaches was proposed by
Cooper and Eaton [12] :
V V
V V a
0 −
−k1
−k
= 1 exp a2
exp
−
P
P
0
s
THEORY OF PARTICLE COMPACTION 1137
( ) +
2 ( )
where V is the volume of the compact at pressure P (m 3 ), V 0 is the volume of
compact at zero pressure (m 3 ), V s is the void - free solid material volume (m 3 ), a 1 , a 2 ,
k 1 , and k 2 are the Cooper – Eaton constants.
The Kawakita equation [13] describes the relationship between volume reduction
and applied pressure according to Equation (4) , where P is the applied pressure, V 0
is the initial bulk volume, V is the volume at pressure P, a and b are the constants
characteristic of the powder under compression, and C is the degree of volume
reduction [Equation (5) ]:
(2)
(3)