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Research Article
Pore Direction in Relation to Anisotropy of Mechanical Strength in a Cubic
Starch Compact
Yu San Wu,
1,5,6
Lucas J. van Vliet,
2
Henderik W. Frijlink,
1
Ietse Stokroos,
3
and Kees van der Voort Maarschalk
1,4
Received 3 November 2007; accepted 20 February 2008; published online 9 April 2008
Abstract. The purpose of this research was to evaluate the relation between preferential direction of
pores and mechanical strength of cubic starch compacts. The preferential pore direction was quantified in
SEM images of cross sections of starch compacts using a previously described algorithm for
determination of the quotient of transitions (Q). This parameter and the mechanical strength were
evaluated in compacts of different porosities. Starch was chosen as a model compound for materials with
ductile behaviour of which tablets with low porosities can be made and which shows some elastic
recovery after compaction. At medium and high porosity Q was significantly higher in the images
providing a side view of the compact than in the images providing a top view (0.973 vs. 0.927 and 0.958
vs. 0.874 at 0 mm from the side of the compact and 0.956 vs. 0.854 and 0.951 vs. 0.862 at 3.5 mm),
indicating that the pores were mainly oriented in the direction perpendicular to the direction of
compression. This was accompanied by a lower crushing force in this direction. This could be explained
by considering the pores as cracks which propagate through the sample during crushing. For both
directions the crushing force decreased with increasing porosity. The yield strength of the compacts also
decreased with increasing porosity, but this parameter was not dependent on the direction of crushing
when the porosity was below 10%. The results show that pore direction significantly influences the
crushing force but does not influence the yield strength, at porosities below 10%.
KEY WORDS: anisotropy; compact; fracture; mechanical strength; pore direction.
INTRODUCTION
It is well known that porosity influences the mechanical
strength of compacts (1–6) and that the mechanical strength
of tablets compressed with uni-axial compression is an
anisotropic property, i.e. the mechanical strength depends
on the direction of measurement (7–17). In earlier research
Ando et al (9) and Galen and Zavaliangos (16) determined
the mechanical strength and took SEM images of cross
sections of the tablets. There was no parameter to quantify
the directions of the pores; the human observer determined
the orientation of the pores and particles. This suggested
that the (anisotropy in) pore structure is the cause of the
anisotropy in mechanical strength. In the present paper
attention will be paid to both the quantification of the
preferential pore direction and the anisotropy in mechanical
strength in a cubic starch compact to better understand the
correlation between these two parameters. Starch was chosen
as a model compound for materials with ductile behavior of
which tablets with extremely low porosities can be made and
which show some elastic recovery after compaction. It was
believed that studying the fracture behavior of compacts with
an extremely low porosity would make it easier to evaluate
the influence of the pore structure.
MATERIALS AND METHODS
Materials
To obtain bodies with a low porosity we chose to use
pregelatinized starch, a visco-elastic material. By using a slow
compression rate, a slow decompression rate, and a powder
with a relatively high moisture content the powder shows
plastic deformation with little relaxation. The 106–150 μm
fraction of pregelatinized potato starch (Prejel JF, Avebe,
Foxhol, The Netherlands) was obtained by 30 min. vibratory
sieving (Fritsch analysette 3, Germany) followed by 12 min
air jet sieving over a sieve of 106 μm (Alpine A200,
Augsburg, Germany), to remove the fines. Before use the
powder was stored at least three days at a relative humidity of
1530-9932/08/0200-0528/0 #2008 American Association of Pharmaceutical Scientists 528
AAPS PharmSciTech, Vol. 9, No. 2, June 2008 ( #2008)
DOI: 10.1208/s12249-008-9074-4
1
Department of Pharmaceutical Technology and Biopharmacy,
University of Groningen, Groningen, The Netherlands.
2
Quantitative Imaging Group, Department of Imaging Science &
Technology, Faculty of Applied Sciences, Delft University of
Technology, Delft, The Netherlands.
3
Laboratory for Cell Biology and Electron Microscopy, University of
Groningen, Groningen, The Netherlands.
4
Department of Pharmaceutics, NV Organon, part of Schering-Plough,
Oss, The Netherlands.
5
Solvay Pharmaceuticals, Building WNH, C.J. van Houtenlaan 36,
1381 CP Weesp, The Netherlands.
6
To whom correspondence should be addressed. (e-mail: Yu-San.
Wu@solvay.com)
70%. The apparent particle density was measured with
helium pycnometry (Quantachrome, Syosset, New York,
USA). Corrected for the moisture content at a relative
humidity of 70%, measured with a moisture analyzer
(Sartorius MA40, Göttingen, Germany), this was found to
be 1439 kg/m
3
.
Tablet Compaction
A hydraulic press (ESH compaction apparatus, Hydro
Mooi, Appingedam, The Netherlands) was used to compress
the starch in a square shaped die with sides of 7 mm. Before
compaction, the die was lubricated with magnesium stearate
using a brush. Varying quantities of powder were used to
obtain cubic shaped compacts with different porosities. The
rate of compression was 0.1 kN/s and the rate of decompres-
sion varied between 0.001 kN/s for the compacts with low
porosity and 0.1 kN/s for the compacts with higher porosities.
Compact thickness was measured immediately after compres-
sion, further all compact dimensions were measured after
24 h with an electronic micrometer (Mitutoyo, Tokyo, Japan)
and the weight of the compacts was measured with an
analytical balance (Mettler-Toledo, Greifensee, Switzerland).
The porosity of the compacts was calculated from these data
and the true density. The porosity calculated in this way will
be referred to as ‘porosity’while the porosity calculated with
image analysis will be referred to as ‘local porosity’.
Determination of Mechanical Properties
For the assessment of the mechanical strength a cubic
compact was used. The cubic shape makes it possible to
compare the properties in the horizontal direction with the
properties in the vertical direction, since the outside dimen-
sions of the compact are the same in all directions. The
consequence of this methodology is that the tensile strength
of the specimen can not be measured, as is done when a
cylindrical body is subjected to the diametric compression test
(18). However, if the fracture shows ductile behaviour (i.e.
the fracture has been preceded by considerable plastic
deformation (19)), it does provide an opportunity to measure
the yield strength, which can also be used to describe the
mechanical strength.
The mechanical properties of the cubes were determined
by compressing these between the punches of a compaction
simulator (ESH, Brierley Hill, UK) while registering the
force–displacement curve on an X–Y recorder (Kipp &
Zonen, Delft, The Netherlands). The upper punch moved
downwards with a linear speed of 0.75 mm/s. The strength in
the x-direction was determined by placing the cube between
the upper punch and the lower punch in such a way that the
direction of the original compression was perpendicular to the
direction of crushing. The strength in the z-direction was
determined by placing the compact in such a way that the
direction of the compression was parallel to the direction of
crushing. In this way the force at which fracture occurred
(crushing force) was registered. The yield point was defined
as the maximum in the stress–strain curve or as the
intersection of the two tangents of the initial and final parts
of the stress strain curve (20). By dividing the force at which
yielding occurred by the area of a side of the cube (49 mm
2
)
the yield strength was calculated.
Imaging of Planes in the Compact
Compacts were embedded with glycolmethacrylate resin.
After hardening of the resin, several planes in the compact
were smoothed using a microtome as described earlier (21).
The planes in the compact that have been imaged are
depicted in Fig. 1. Two sets of images were defined, plan
and elevation images. Plan images provide a top view and
elevation images provide a side view. Of each plane nine
images were taken. Figure 1also clarifies the nomenclature of
the different directions. The z-direction is the direction of
compression and the x- and y-direction lie perpendicular to
this direction.
Fig. 1. The locations of the plan images (left) and of the elevation images (right) in the cubic compact. Per plane nine images were taken in a
3× 3 pattern
529Pore Direction in Relation to Anisotropy of Mechanical Strength
SEM BEI (Backscattered Electron Imaging) images
were taken using a JEOL scanning electron microscope
(JEOL, type JSM-6301F with standard paired semiconductor
element detector, Japan) operated at an accelerating voltage
of 10 kV. The diaphragm was 50 μm and the working distance
was 15 mm. The magnification was 60×. Before taking SEM
images, the compacts were stored overnight in a closed
container with a few osmium tetroxide crystals for evapora-
tion to obtain a better contrast between the resin and the
starch in the images.
Fig. 2. Force displacement curves of crushing in the x-direction (above) and in the z-direction (below) of cubes with a different porosity.
Arrows indicate yield points and the ‘x’indicates where fracture occurred. The images depict cubes after crushing
530 Wu et al.
Image Analysis
Matlab 7.0.232 R2006a (The MathWorks Inc, Natick,
USA) and the DIPimage toolbox version 1.5.3 (Quantitative
Imaging Group, Faculty of Applies Sciences, Delft University
of Technology, The Netherlands) (22) were used for the
image analysis. A previously described method was used to
detect a preferential pore direction (21). This method was
applied to a cubic NaCl compact with a high porosity. In the
present paper we modified this technique to make it suitable
for the analysis of starch compacts with low porosities.
The first step in image analysis was the removal of small
irregularities in the starch grains so that the borders between
the grains and the pores would be clearly defined, while small
artefacts caused by the use of the microtome were removed.
This was done by using a separable bilateral filter (23). The
bilateral filter replaces each pixel value by a weighted sum of
its neighbours. The weighting depends on the product of a
proximity measure in space (x,ydistance) and intensity (pixel
value). Both proximities use a Gaussian weighting that decay
from the current pixel. The scales (standard deviations) of the
two Gaussians were set to respectively 3 pixels and 0.7 times
the full-width at half its maximum (FWHM) of the distribu-
tion of the pixel values. The FWHM was measured in the
grey-value histogram of the image. The histogram shows one
great Gaussian shaped peak, with tails to the left and right
representing respectively the dark (empty) and white (filled)
pore space. The tails have no effect on the measured peak
width. The filter’s spatial scale is set just large enough to
cover the scratches and the intensity scale is set such to
encompass noise and scratches in the grains, but to exclude
pixel values from across the grain boundary. Hence, the noise
is suppressed, but the transitions between grain and pores are
preserved (unaltered).
Secondly, the local porosity of the images was deter-
mined by counting the white pixels and the black pixels. The
segmentation relies on the histogram of the bilateral filtered
image. We again measured the position of the peak and its
FWHM. We then labelled all pixels that were respectively
lower or higher than 1.25 times the FWHM of the peak as
black (empty pores) or white (filled pores).
In the images of the compacts with a low porosity (i.e.
values approaching 0%) it could be seen that the resin had
not penetrated the pores of the compacts. Therefore, the local
porosity in these compacts was calculated as the percentage
of black pixels only. In the compacts with the intermediate
porosity (approx. 13%) and high porosity (approx. 22%), the
resin had penetrated the pores, at least partly. Therefore,
the local porosity in these compacts was calculated as the
percentage black and white pixels of the total number of
pixels in the image.
The principle of the quotient of the number of transitions
(Q) was described earlier (21). In the present research we
made use of the same principle. However, the number of
transitions was calculated in the filtered gray-scale image. By
doing so, the pores with a higher contrast between the pore
and the grain are more important for the calculation of Q
than the pores with only a small contrast between the pore
and the grain. This method was chosen since it was believed
that pores with a higher contrast between the pore phase and
the grains, were deeper pores i.e. larger in the third
dimension and are considered to have a more pronounced
effect on the mechanical strength. The number of transitions
was calculated as the sum of the (absolute) change in pixels
value between all adjacent pixels in one direction (either y
and xor zand x). The quotient number of transitions was
then calculated according to the following equations. For the
plan images:
QP¼NTy
NTx
ð1Þ
And for the elevation images:
QE¼NTz
NTx
ð2Þ
In which:
Nomenclature
Q
P
or Q
E
quotient of the number of transitions in
[Plan or Elevation] image(s)
N
Ty
sum of the absolute change in pixel value
between all adjacent pixels in the y-direction
N
Tx
sum of the absolute change in pixel value
between all adjacent pixels in the x-direction
N
Tz
sum of the absolute change in pixel value
between all adjacent pixels in the z-direction
Fig. 3. Crushing force versus porosity (above) and yield strength
versus porosity (below), in the x-direction and the z-direction. The
porosity was calculated out of weight and volume
531Pore Direction in Relation to Anisotropy of Mechanical Strength
RESULTS AND DISCUSSION
Mechanical Strength
Figure 2shows some force–displacement curves of the
crushing of starch cubes with different porosities. Some
images of the fractured cubes are also shown to illustrate
the result of the different behaviour during fracture. The
upper part of Fig. 2shows the curves for crushing in the x-
direction and the lower part of Fig. 2shows the crushing in
the z-direction. Arrows indicate the points defined as yield
point (the first maximum or the intersection of the regression
lines of the first and the second linear part of the curve)
whereas the points where fracture occurred are indicated with
an “x”. The shapes of the curves change dependent on the
porosity. With increasing porosity, the yield point becomes
less and less pronounced and fracture occurs at lower forces.
Figure 3shows the crushing force and the yield strength in the
x-direction and the z-direction at different porosities. The
crushing force decreases with increasing porosity. However,
at all porosities the crushing force was higher when the tablets
were crushed in the z-direction. For both directions the
relation between crushing force (F) and porosity (ε) showed
an exponential relation with an R-squared value of 0.99 (F=
5176.e
−0.063ε
for the crushing force in the z-direction and F=
2854.e
−0.058ε
for the crushing force in the x-direction).
The yield strength of the specimen also decreases with
increasing porosity. At porosities below 10% there is no
difference in the yield strength measured in the x-orz-
direction as can be seen in Fig. 3. However, at porosities
higher than 10%, the yield strengths start to deviate from
each other. This is indicated by a trend line of the values for
the yield strength of compacts with a porosity higher than
10%. The equation for the trend line for the yield strength in
the z-direction (yield strength
z
=−37.1ε+1851 [R
2
=0.925]) is
different from the one describing the yield strength in the x-
direction, (yield strength
x
=−57.5ε+2014 [R
2
=0.973]). The
95% confidence intervals of the intercept of the trend lines
show some overlap, but this is not the case for the 95%
confidence interval of the slope of the lines. Below a certain
porosity the compacts do not break anymore, but only yield.
Image Analysis
Figure 4shows some original plan and elevation images
from compacts with low, intermediate and high porosity.
All images are taken from the 0 mm plane. Pores that are
filled with resin are white, unfilled pores are black, and the
starch grains have an intermediate gray intensity. Resin has
not penetrated all the pores, especially in the compacts
with the lowest porosity. The local porosity determined
with image analysis was slightly higher than the porosity
Fig. 4. Original plan and elevation images of starch cubes with a porosity of 0% (left), 13% (middle), and 24% (right). All images are taken
from the 0 mm plane
532 Wu et al.
determined out of weight and volume (Fig. 5). Due to a
lower surface roughness on the 3.5 mm plane, the local
porosity was lower than at the 0 mm plane (note that the
3.5 mm plane was made visible by removal of material and
subsequently polished, whereas for the 0 mm plane only the
microtome was used). Tablets with a porosity of 0% as
calculated out of volume and weight of the tablet were not
completely transparent indicating that the actual porosity was
not zero. This is in agreement with the results found with
image analysis that also indicate that the porosity of the
densest compacts is somewhat above 0%.
It can also be seen in Fig. 4that there is no orientation in
the plan images, while the pores in the elevation images seem
to be mainly oriented along the x-direction. For the plan
images no preferential direction of the pores was expected
since the direction in which the image was taken was the same
as the direction of compression. Visual inspection of the
images confirmed that there was no preferential direction of
the pores. This would mean that the quotient of transitions
equals unity. However, this is not the case as can be seen in
Fig. 6which shows the quotient number of transitions for the
plan and the elevation images. This can be caused by the fact
that the images are taken with a scanning electron micro-
scope. The transitions in the scanning direction could be less
sharp than the transitions perpendicular to this direction. This
could mean that even in images of an isotropic structure a
quotient of transitions lower than unity is found.
There is a significant difference in the quotient of
transitions between the plan and the elevation images (p<
0.01, Mann–Whitney test, SPSS 12.0.1). This applies to all
porosities and at both locations in the tablet except for 0% at
the 3.5 mm plane (from this plane, only three elevation
images could be used because of technical problems with the
other six images). A higher quotient in the elevation images
than in the plan images means that the elevation images have
relatively more transitions in the z-direction (see Eqs. 1and
2). This means that the pores are preferentially oriented in
the x-direction (perpendicular to the direction of compres-
sion) which can also be seen with the naked eye in the images
in Fig. 4.
Pore Direction
The observation that the pores are mainly oriented in the
x-direction is probably caused by the combination of particle
deformation and stress relaxation. Pregelatinized starch is a
ductile material which shows visco-elastic deformation during
compaction and always some elastic recovery afterwards (24).
The high moisture (16.7%) content facilitates deformation of
the material (25,26). This deformation behaviour combined
with uni-axial compression will result in pancake like shaped
particles. When the decompression speed is extremely low
(0.001 kN/s), the compact shows only a minor porosity
expansion. This can be deducted from the increase in
compact thickness calculated out of the thickness immediately
after compression and after 24 h (0.9% sd. 0.2%). After this
small expansion the pancake like stacking stays intact. In
images of tablets with a low porosity a large number of
transitions in the z-direction (direction of compression) can
therefore be seen, corresponding to a large difference in
quotient of transitions between the plan and the elevation
images. For the compacts with higher porosities, having been
subjected to a faster decompression rate, the increase in
compact thickness is 2.8% sd. 0.4%. The structure is less
dense, resulting in a lower number of transitions in the z-
direction and consequently a smaller difference in quotient of
transitions between the plan and the elevation images.
Crushing Force
When a body containing fine cracks is subjected to
compressive stress, the fine cracks extend parallel to the
Fig. 5. Local porosity as calculated with image analysis in the images
taken from 0 mm from the side and from images taken from 3.5 mm
from the side
Fig. 6. Quotient of the number of transitions in the plan and
elevation images of the compacts of low, intermediate, and high
porosity from the plane at 0 mm from the side of the cube (above)
and from the plane at 3.5 mm from the side (below)
533Pore Direction in Relation to Anisotropy of Mechanical Strength
compression axis causing failure planes parallel to the
compressive stress (27). If the cracks are slightly off with
respect to the direction of the applied load, wing cracks
appear along the loading direction, splitting the material into
slender columns which then fail (27,28). It is therefore not
difficult to imagine that the larger the dimensions of the
cracks along the compaction direction, the lower the crushing
force will be when crushed in compression. This is why the
crushing force of the starch cubes in the x-direction is much
lower than the crushing force in the z-direction (see Fig. 3).
Apparently, the pores in the cubes (which are mainly oriented
in the x-direction) act as some sort of quasi cracks.
Another observation supporting this hypothesis is that
the fracture of the starch cubes when crushed in the x-
direction showed failure planes parallel to the compressive
stress especially at the highest porosity (see Fig. 2). These are
probably caused by the opening of the pores in the x-
direction. When the cubes were crushed in the z-direction
the fragments of the cube after fracture more looked like
slender columns after failure (Fig. 2). This could indicate wing
crack development during crushing in the z-direction.
Porosity is a property without direction. This paper
shows that direction of pore structure plays a significant role
as can be deducted from Fig. 3where it is shown that at a
similar porosity the crushing force in the x-direction is
significantly different from that in the z-direction (7–17).
Formulation approaches that minimize the anisotropy in pore
structure, possibly by reducing wall effects by focussing on
lubrication, will help to control this effect.
Yield Strength
There was no difference in yield strength between the x-
direction and the z-direction of the cube at porosities lower
than 10%. Furthermore, there was no difference in porosity
measured in the plan images and in the elevation images
(Fig. 5). Since yielding is a material property, yielding does
not depend on the direction of the pores, but on the pore
fraction (porosity) in the cross section. Because the porosity
in the plan images is similar to the porosity measured in the
elevation images, it is not surprising that there was no
difference in yield strength between the x-direction and the
z-direction. The explanation for the observation that the yield
strength decreases with increasing porosity is the same. With
increasing porosity, the cube consists of less material resulting
in a lower yield strength of the cube.
At porosities higher than 10% the values for the yield
strength in the x-direction and z-direction deviate more from
each other, but it is questionable whether at these high
porosities a yield strength is present at all, because the
fracture shows more brittle behaviour with increasing poros-
ity. In case of brittle fracture no plastic deformation takes
place and thus no yielding point can be defined.
CONCLUSION
The anisotropy in pore structure in a cubic starch compact
could be detected with image analysis. The different compres-
sive forces at which fracture occurred in the x-direction and in
the z-direction could be explained with these results. The yield
strength of the cube was not dependent on the pore direction
at porosities lower than 10%, showing that the pore direction
influences the force at which fracture occurs, but does not
influence the yield strength of the compact.
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