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## A statistical design to evaluate the influence of manufacturing factors

## and material properties on the mechanical performances of

## microcrystalline cellulose

### Jen-Sen Wu, Hsiu-O Ho, Ming-Thau Sheu

)*Graduate Institute of Pharmaceutical Sciences, Taipei Medical College, 250 Wu-Hsing Street, Taipei 110, Taiwan*
Received 10 April 2000; received in revised form 26 June 2000; accepted 11 September 2000

**Abstract**

In this study, a statistical experimental design was used to evaluate the effects of manufacturing factors and material properties on the

Ž .

mechanical performances of microcrystalline cellulose MCC products for the purpose of optimizing mechanical performances and reducing source variations affecting tablet strength of MCC. Results demonstrated that only fracture toughness and sensitivity to compaction speed among mechanical performances were affected by the manufacturing factors; however, the use of manufacturing factors to predict the mechanical performances was poor. On the other hand, the critical stress intensity factor, fracture toughness, and sensitivity to compaction speed can be quantitatively predicted by material properties examined in this study. Meanwhile, the cohesive energy

Ž .

density CED , degree of crystallinity, crystallinity index, and shape index may serve as important material properties for controlling the mechanical performances of MCC. In conclusion, although the MCC products with high fracture toughness and low sensitivity to compaction speed could be optimally obtained, it was not possible to manipulate manufacturing factors to directly control the exact mechanical performances of MCC products. Instead, material properties of MCC products might potentially be used to precisely predict their mechanical performances. The influence of source variations of MCC products on the strength of tablets might be reduced by regulation of their CED, degree of crystallinity, crystallinity index, and shape index. q 2001 Elsevier Science B.V. All rights reserved.

*Keywords: Microcrystalline cellulose; Molecular-related property; Particle morphology; Mechanical parameter; Compactibility; Compressibility*

**1. Introduction**

Ž .

Microcrystalline cellulose MCC is a widely used ex-cipient in direct compression formulations. Source and batch variations have been reported to affect the material

w x

properties and tablet strength of MCC 1,2 . Reduction in the influence of source variation of MCC on tablet strength has been attempted by the process of harmonization. For excipients used in direct compression, both compactibility and compressibility determine the strength of tablets. The compactibility of tablets originates from the intermolecular attraction between particles. The attractive forces of a material can be represented by its cohesive energy density

ŽCED . The CED has been used to estimate Young’s. w x

modulus of a variety of pharmaceutical powders 3 . Mean-while, several mechanical parameters, including Young’s

)

Corresponding author. Tel.: q886-2-23771942; fax: q 886-2-23771942.

Ž .

*E-mail address: mingsheu@tmc.edu.tw M.-T. Sheu .*

Ž . Ž .

modulus *E , critical stress intensity factor* *K*_{IC} , and

Ž .

fracture toughness FT , have been successfully used to probe the mechanical properties and fracture mechanics of

w x

pharmaceutical powders 4 . As a result, the tensile strength of compacts was reported to represent the synergism of

w x

these mechanical parameters 5 .

The compressibility describes the deformability of ma-terials. For polymer excipients, compressibility is related to the aggregation state of the polymer chains. A polymer solid with disordered polymer chains is mechanically weak

w x

and has a higher tendency to deform plastically 6 . Since the plastic deformation process is a function of time, the compressibility of a material deformed plastically is

influ-w x

enced by the speed of compaction 7 . The sensitivity of changing compressibility to compaction speed might pro-duce the problem of the deterioration in strength of tablets when the formulation designer switches from a low-speed formulation phase to high-speed large-scale production. In summary, the influence of source variation on tablet strength of an excipient deformed plastically is closely 0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.

Ž .

Ž

linked to its mechanical performances mechanical

param-.

eters and sensitivity to compaction speed .

Industrially, MCC is generally manufactured by mineral acid hydrolysis. The hydrolysis conditions have been re-ported to affect the particle shape, the crystallinity, and the

w x

molecular weight of MCC 8 . It has been proposed that the irregular shapes of particles provide mechanical

inter-w x

locking to strengthen MCC compacts 9 . On the other hand, the aggregation state of a polymer chain and the molecular weight remarkably influence the viscoelasticity

w x

of semicrystalline polymers 10,11 . Further, changes of the aggregation state of a polymer chain might alter the

w x

molar volume and result in a change of its CED 12 , thus changing the intermolecular attraction between particles. Meanwhile, being a semicrystalline polymer, the viscoelas-tic behavior of the amorphous portion of MCC molecules might be responsive to the sensitivity of changing

com-w x

pressibility to compaction speed as well 13 . Therefore, it

Ž

is interesting to explore how the material properties

par-.

ticle morphology and molecular-related properties of MCC affect its mechanical performances. Furthermore, the corre-lation constructed between manufacturing factors and me-chanical performances is useful for manufacturers to opti-mize the mechanical performances of MCC products. It is also desirable to find the key material properties that control the mechanical performances of individual excipi-ents. Only then, can reduction in source variations affect-ing the strength of tablets be made by the control of manufacturing factors and regulation of key material prop-erties. However, no work has been detail reported on these matters.

In this study, the main object is to statistically evaluate the effects of manufacturing factors and material properties on the mechanical performances of MCC products. Manu-facturing conditions could then be optimized to engineer MCC products with desired mechanical performances. On the other hand, the key material properties that control the mechanical performances of MCC products were possibly deduced as a practical way to regulate the qualities of MCC products for minimizing the source variation.

**2. Experimental design**

A three-factor, five-level central composite design was used. This design is useful for exploring quadratic re-sponse surfaces and constructing a second-order polyno-mial model, thus helping to optimize a process using a small number of experimental runs. The design consists of replicated center points and the set of points lying at each edge of the multidimensional cube that defines the region of interest. A central composite design is made rotatable by the choice of f. The value of f for a design with three factors is 1.68179. The independent variables and their corresponding real and orthogonal values in the central composite design are listed in Table 1. The model

con-Table 1

Independent variables and their corresponding real and orthogonal values in the central composite design

Independent variable Level

y1.68179 y1 0 1 1.68179
Ž*X*1.Concentration 2.16 2.50 3.00 3.50 3.84
Ž .
of HCl N
Ž*X*2.Temperature 8CŽ . 73 77 83 89 93
Ž*X*3.Duration of 43.2 50.0 60.0 70.0 76.8
Ž .
hydrolysis min
*structed is as follows: Y s b q b X q b X q b X q*_{0} _{1} _{1} _{2} _{2} _{3} _{3}
*b X X q b X X q b X X q b X*2_{q}* _{b X}*2

_{q}

*2*

_{b X}_{q}4 1 2 5 2 3 6 1 3 7 1 8 2 9 3

*E, where b to b are the regression coefficients; X , X ,*0 9 1 2

*and X*3 *are the factors studied; Y is the measured *
*re-sponse; and E is the error term. The stepwise multiple*
regression method is a combination of forward and
back-ward regressions and is used to eliminate non-significant
terms from polynomial equations. In this study, the
a-val-ues for both forward and backward regression processes
are designated as 0.1. The polynomial equations and
re-sponse surface plots were obtained with the statistical

Ž .

package, Design-Expert 5 State-Ease, USA .

**3. Materials and methods**

*3.1. Materials and sample preparations*

Ž .

Wood pulp, Temalfa 94 lot no. 61398 , was obtained

Ž .

from Tembec Canada . In preliminary studies, the ex-treme values assigned to the independent variables were first checked to establish that MCC could be prepared under these conditions. The 20 experiments designed to test the effect of three hydrolysis factors are shown in Table 2. A total of 300 g of wood pulp was used for each experiment. After hydrolysis, the hydrolyzed product was washed with distilled water until the pH value of the washing solution was near neutral, and no white precipita-tion appeared with the addiprecipita-tion of a 0.1 N AgNO solu-3

tion. Next, the hydrolyzed product was centrifuged to eliminate water. The wet mass was then forced through a 1.19-mm sieve and oven-dried for 12 h at 60 " 18C. The dried granules were milled and screened through a series

Ž

of sieves with different-sized openings 355, 150, 125, 88,

.

75, 60, and 25 mm to control the particle size distribution of the MCC products to the same range as Avicel PH 102

Žthe mean particle size lying at 10% of normal distribution

w_{d10 is not more than 45 mm, the mean particle size lying}x
w x

at 50% of normal distribution d50 is in the range of 75–95 mm; and the mean particle size lying at 90% of

w x _{.}

normal distribution d90 is not less than 140 mm . The obtained MCC products were stored for at least 7 days at a relative humidity of 40% before any test. The water

con-Ž .

Table 2

Three-factor central composite design: variables, their levels, and matrix and data of the response

Ž .

Run Independent variable Response mechanical performances

a 1r2 a y1 a

Ž . Ž . Ž .

*X*1 *X*2 *X*3 *E GPa* *K*IC MPa m FT N m Sensitivity to compaction

b y3
Ž .
speed =10
1 y1 y1 y1 10.87 " 0.99 0.860 " 0.024 151.5 " 3.2 3.37 " 1.17
2 y1 1 1 12.43 " 1.31 0.750 " 0.063 105.9 " 13.9 2.81 " 0.50
3 1 y1 1 8.77 " 1.17 0.613 " 0.049 83.4 " 12.8 2.06 " 0.17
4 1 1 y1 8.95 " 0.89 0.853 " 0.081 119.8 " 21.9 2.87 " 0.58
5 0 0 0 9.57 " 0.76 0.604 " 0.019 112.4 " 19.7 2.68 " 0.95
6 0 0 0 8.79 " 0.79 0.829 " 0.119 114.7 " 23.8 2.62 " 0.45
7 y1 y1 1 7.70 " 0.15 0.685 " 0.043 130.7 " 19.4 2.45 " 0.14
8 y1 1 y1 8.51 " 0.60 0.927 " 0.137 179.3 " 44.7 2.03 " 0.11
9 1 y1 y1 9.63 " 0.82 0.645 " 0.064 89.1 " 10.5 3.02 " 1.16
10 1 1 1 6.37 " 0.47 0.477 " 0.018 58.5 " 6.5 2.19 " 1.07
11 0 0 0 10.43 " 0.51 0.781 " 0.178 165.4 " 54.0 2.79 " 0.24
12 0 0 0 7.85 " 0.54 0.572 " 0.028 95.6 " 14.3 2.23 " 0.53
13 1.68179 0 0 8.24 " 0.26 0.629 " 0.068 93.8 " 19.0 2.24 " 0.78
14 y_{1.68179} _{0} _{0} _{8.61 " 0.27} _{0.574 " 0.027} _{99.0 " 12.4} _{2.09 " 0.54}
15 0 1.68179 0 8.98 " 0.64 0.445 " 0.029 63.7 " 11.0 2.73 " 0.46
16 0 y_{1.68179} _{0} _{10.44 " 1.15} _{0.620 " 0.019} _{115.7 " 16.5} _{2.43 " 0.51}
17 0 0 1.68179 8.21 " 0.39 0.532 " 0.036 67.5 " 7.7 3.00 " 0.14
18 0 0 y1.68179 11.34 " 0.84 0.558 " 0.060 96.7 " 11.2 2.62 " 0.29
19 0 0 0 9.36 " 0.30 0.487 " 0.054 82.5 " 8.8 2.54 " 0.71
20 0 0 0 8.49 " 0.20 0.584 " 0.072 97.1 " 7.7 3.26 " 1.18
a

Variation is indicated as "S.E.

b

All values are the mean " S.D. of three determinations.

Ž

OHAUS moisture determination balance Model MB200,

.

OHAUS, USA .

*3.2. Measurement of molecular-related properties*
*(* *)*

*3.2.1. Degree of polymerization DP*

The DP was determined according to National Formu-lary XVIII. The kinematic viscosities of the MCC solution

Ž

and solvent 1.0 M cupriethylenediamine hydroxide

solu-.

tion were measured with a Wells-Brookfield plate

vis-Ž .

cometer Model DV-II q , USA .

*3.2.2. Degree of crystallinity*

Powder X-ray diffraction measurements were carried out at room temperature on a Shimadzu X-ray

diffractome-Ž .

ter Model XD-5, Japan using monochromatic CuK a radiation and a scan rate of 48r2u per minute over the range of 4–508r2u. According to Nelson and O’Connor

w_{14 , the degree of crystallinity was calculated as follows:}x

*% Degree of crystallinitys I*

### Ž

002y*am*

_{I}### .

r*002= 100;*

_{I}### Ž .

1*where I*

_{002}s

_{the diffractogram height at the position of the}

Ž .

*002 peak 2u s 22.68 ; and I*am is the height of amorphous

Ž .

background 2u s 198 .

*3.2.3. Crystallinity index*

The crystallinity index was determined from the solid-state 13C CPrMAS nuclear magnetic resonance spectra

w x

and was calculated as described by Ek et al. 15 . The measurements were performed on a Bruker MXL 300 spectrometer operating at 75.47 MHz with spinning at 4.5 kHz using a double air-bearing probe and ZrO rotors. The2

instrumental parameters were: 3 ms contact time, and 2048 data points filled to 4096 K. The chemical shift scale was referenced to the methyl group in adamantane located at 14.0396 ppm. The number of scans on each spectrum was 10,000.

*(* *)*
*3.2.4. True density and cohesiÕe energy density CED*

The true density was measured using a nitrogen-air

Ž .

pycnometer Model PYC-G100A-1, PMI, USA . The CED of MCC products was calculated from true density as

w x

described by Roberts and Rowe 12 . The average of three determinations was reported.

*3.3. Measurement of particle morphology*

The image of particles was collected using an image

Ž .

analyzer Microtek, Model MRS-600ZS, Taiwan . The

Ž

software package, Image-Pro Plus 1.0 Media Cybernetics,

.

USA , was used to obtain all dimensions of particles. The shape index and the surface roughness were calculated as

w x w x

described by Iida et al. 8 and Podczeck and Newton 16 .
At least 150 particles were analyzed for each MCC
prod-uct. The surface roughness was calculated as follows:
*Surface roughness s 2p r r P f ;*

### Ž

e### .

### Ž

m### .

### Ž .

2*where r s arithmetic mean of the distances between the*e

center of gravity and the perimeter for an angle of 58
*between the measurements; P s perimeter of the particle*m

*outline; and f is a correction factor to minimize the effect*

w

of ellipticity on the surface roughness *f s 1.008 y 0.231*

Ž Ž ..x

= 1 y breadth of the particlerlength of the particle
w_{16 . A perfect sphere has a surface roughness value of}x

1.00, and increasing surface roughness leads to values smaller than 1.00. The shape index was calculated as follows:

*Shape index s 4p A rP*2_{;} _{3}

### Ž

### .

m### Ž .

*where A is the projected area of a particle. Theoretically,*
only a circle can have a shape index of 1.00. For other
irregular figures, the value is smaller than 1.00.

*3.4. Measurement of mechanical performances*

All mechanical properties and sensitivity to compaction speed were determined using a three-point beam bending

Ž

test on a dynamic mechanical analyzer Perkin Elmer,

.

Model DMA 7e, USA . Beams were prepared by compact-ing the powders in a rectangular die, 25 mm in length and 5 mm in breadth. The thickness of the beams was con-trolled at 2 mm by the design of the depth of the upper punch. Since all beams were compressed to a constant thickness of 2 mm, porosity could be varied by changing the weight of powder placed in the die cavity.

*3.4.1. Mechanical properties*

All mechanical properties are influenced by the solid

w x

fraction of beams. By using Spriggs equation 17 , they were compared at zero porosity by extrapolating the plot of measured mechanical strength vs. porosity to zero. In order to cover a range of porosities, 18 beams of each

Ž .

MCC product were tested. Young’s modulus *E* was
obtained by stressing beams to fracture at a frequency of 1
Hz. The maximum Young’s modulus was recorded. The

Ž .

critical stress intensity factor *K*_{IC} was determined and

w x

calculated as described by Roberts et al. 18 . Fracture

Ž .

toughness FT was determined and calculated as

de-w x

scribed by Mashadi and Newton 4 .

*3.4.2. SensitiÕity to compaction speed*

Beams with a porosity of 0.21 were prepared. The damping of beams was measured using a frequency scan on a dynamic mechanical analyzer beginning at a fre-quency of 1 Hz and ending at 16 Hz. The graphs of damping vs. frequency were plotted, and the sensitivity to compaction speed was defined as the slope multiplied by

y_{1. The average of three beams was reported.}

*3.5. Statistical methods*

*3.5.1. Pearson correlation analysis*

Pearson correlation measures the closeness of a linear relationship between two variables. If one variable can be

expressed exactly as a linear function of another variable, then the correlation is 1 or y1, depending on whether the two variables are directly or inversely related. A correla-tion of zero means that each variable has no linear predic-tive ability for the other.

*3.5.2. Canonical correlation analysis*

Canonical correlation analysis is used to examine the linear relationships between a set of independent variables

Ž*X*. *and a set of more than one dependent variable Y*Ž .
w_{19 . It is especially useful when the dependent or criterion}x

variables are moderately intercorrelated. The technique
*consists of finding one linear combination of the X *
vari-ables, say

*U s a X q a X q a X q PPP*1 1 2 2 3 3

### Ž .

4*and one linear combinations of the Y variables, say*

*V s b Y q b Y q b Y q PPP*1 1 2 2 3 3

### Ž .

5*U and V are called the canonical variables of the X ’s and*
*Y ’s, respectively. For any particular choice of coefficients,*

*the a’s and the b’s, the values of U and V can be*

Ž

computed for each individual in the sample 20 runs for

.

*this study . The resulting correlation between U and V is*
called the first canonical correlation and is dependent on
*the choice of the a’s and the b’s. In canonical correlation*
analysis, the values of the a and b coefficients are selected
*to express the best correlations between U and V. *
*Multi-variate tests based on several approximate F statistics*
including Wilks’ Lambda test, Hotelling–Lawley Trace
test, and Roy’s Greatest Root test, are used to determine
whether the first canonical correlation is significant.

Ž

The SAS System for Windows 6.12 edition SAS

Insti-.

tute, USA was used to carry out all statistical tests in this
*study, and P - 0.05 was considered to be statistically*
significant for all statistical tests.

**4. Results and discussion**

Measurements of mechanical performances of MCC products manufactured according to this statistical experi-mental design were conducted, and results are shown in

Ž .

*Table 2. Young’s modulus E describes the stiffness of a*
material and originates from the dependence of the energy
of interaction between molecules and their distance of

Ž .

separation. The critical stress intensity factor *K*_{IC}
de-scribes the state of stress around an unstable crack or flaw
in a material and is an indication of the stress required to
produce propagation of a crack. Thus, it is a measure of
the brittleness of materials as reflected by the resistance of
a material to cracking via tensile stresses acting normal to

Ž .

the crack wall. Fracture toughness FT is an estimate of the energy necessary for crack propagation.

For amorphous materials, the extent of deformation is sensitive to compaction speed. Compaction at low speed

Ž

Fig. 1. Damping of beams produced from MCC vs. the frequency of deformation numbers refer to MCC products obtained from runs 1 to 5 of

.

experimental design as listed in Table 2 .

results in the formation of tablets with low porosity, since deformation is dominated by the viscous component, which is irreversible. Compaction at high speed produces tablets with higher porosity and lower strength, because of an

w x

increase of elasticity of materials 13 . MCC is a semicrys-talline polymer, therefore, the amorphous portion of the MCC molecule might possess viscoelasticity and be sensi-tive to tableting speed. Damping has been used to measure

Ž . Ž .

w x

the viscoelasticity of a material 20 . The lower the damp-ing value, the less of a tendency there is for a material to deform irreversibly. Therefore, damping of beams pro-duced from MCC decreases with an increase of deforma-tion frequency as shown in Fig. 1. Meanwhile, at a definite frequency of deformation, damping remains constant as the

w x

porosity of MCC compacts falls below 0.4 21 . Thus,

sensitivity of changing compressibility to compaction speed of MCC products is simulated by the sensitivity of chang-ing dampchang-ing values to deformation frequency of the beams with a porosity of 0.21.

The stepwise multiple regression of these mechanical

Ž

performances with respect to hydrolysis factors *X , X ,*_{1} _{2}

.

*and X*_{3} based on a central composite design of 20

experi-Ž . Ž .

*Fig. 3. Response surface plot showing the effect of temperature X*2 *and duration of hydrolysis X*3 on the sensitivity to compaction speed of MCC

Ž . Ž . Ž .

mental sets was only able to generate two second-order

Ž .

polynomial equations for fracture toughness FT and sen-sitivity to compaction speed.

*FT s 106.11 y 16.51 X y 15.39 X ,* R2_{s}_{0.3598 ;}

### Ž

### .

1 3

6

### Ž .

Sensitivity to compaction speeds_{0.002717 y 0.0001679 X}_{1}2

q_{0.0002457X X ,}

_{Ž}

*2s*

_{R}_{0.3091 .}

_{.}

_{Ž .}

_{7}2 3

The results show that FT and sensitivity to compaction speed are significantly affected by the hydrolysis factors

Ž*P - 0.05 . According to Eq. 6 , FT was independent of*. Ž .
Ž .

*temperature X . Fig. 2 shows the effect of HCl concen-*2

Ž . Ž .

tration *X*1 and duration of hydrolysis *X*3 on FT at a

Ž .

fixed temperature 838C . The fracture toughness de-creased with increasing HCl concentration and duration of hydrolysis. On the other hand, Fig. 3 shows the effect of

Ž . Ž .

*temperature X*_{2} *and duration of hydrolysis X*_{3} on
sensi-tivity to compaction speed at low, medium, and high

Ž

concentrations of HCl 2.50, 3.00, and 3.50 N,

respec-.

tively . Either increasing temperature for a short duration or lowering temperature with prolonged hydrolysis would result in a decrease of sensitivity to compaction speed of MCC products irregardless of what level of HCl concentra-tion was used. Based on these two quantitative equaconcentra-tions, a MCC product with high fracture toughness and low sensi-tivity to compaction speed could be optimally obtained by

Ž . Ž

hydrolysis at high temperature 898C , short duration 50

. Ž . 2

*min , and low level of HCl 2.50 N . However, the R*

values of these two polynomial equations are quite low,
which means that the predicted precision of FT and
sensi-tivity to compaction speed by these hydrolysis factors are
*poor. Results also demonstrate that E and K*IC depend on
none of the selected variables. This means that neither the
stiffness nor brittleness of MCC products are affected by
these hydrolysis factors.

Since the use of manufacturing factors to predict the mechanical performances was poor, it was thought that material properties of MCC instead might possibly be correlated with mechanical performances to some extent and might be useful to predict the mechanical perfor-mances of MCC products. Material properties of MCC are divided into molecular-related properties and particle mor-phology. Table 3 shows the average experimental results of these material properties of MCC products. The degree

Ž .

of polymerization DP of MCC is the average number of glucose units in a molecule, which is proportional to the molecular mass. The degree of crystallinity was calculated from the X-ray diffractogram. This parameter describes the regularity of the arrangement of polymer chains. The crystallinity index was calculated from NMR spectra by

Ž .

dividing the intensity of the crystalline C4 peak 89 ppm

Ž .

by the sum of the crystalline and amorphous C4 84 ppm intensities. This index indicates the extent of hydrogen bonding between glucose units of the MCC molecule,

` X

since the O_{3} H PPP O intramolecular hydrogen bonding_{5}
makes the C4 carbon peaks shift toward a lower magnetic

w x

field 22 . The CED was calculated from the true density. Denser molecules of the same chemical structure of MCCs result in a higher value of CED, thus indicating higher

Table 3

Molecular-related properties and particle morphology of MCC products

Run Degree of Degree of Crystallinity Cohesive energy Surface Shape

a a b b

Ž . Ž . Ž . Ž .

polymerization DP crystallinity % index % density CED, MPa roughness index

1 241.02 " 0.78 67.8 56.9 926.36 " 3.68 0.86 " 0.12 0.59 " 0.19 2 191.18 " 0.92 74.2 57.8 928.79 " 4.95 0.90 " 0.09 0.73 " 0.14 3 206.54 " 0.81 79.3 61.2 921.32 " 2.77 0.88 " 0.06 0.69 " 0.11 4 187.75 " 1.73 74.8 59.4 934.96 " 10.28 0.88 " 0.06 0.68 " 0.11 5 195.78 " 1.67 73.2 70.8 917.36 " 6.43 0.89 " 0.07 0.70 " 0.14 6 206.92 " 0.63 74.1 64.0 925.88 " 11.12 0.88 " 0.08 0.69 " 0.15 7 236.17 " 1.27 77.5 58.5 910.14 " 1.22 0.83 " 0.09 0.59 " 0.14 8 200.56 " 0.06 77.9 64.7 924.80 " 2.61 0.87 " 0.06 0.68 " 0.12 9 205.43 " 0.90 79.1 64.3 928.40 " 9.34 0.88 " 0.08 0.69 " 0.14 10 188.21 " 0.94 77.1 65.3 925.82 " 2.45 1.01 " 0.10 0.90 " 0.17 11 207.44 " 0.90 75.4 65.6 933.59 " 2.13 0.88 " 0.07 0.69 " 0.13 12 199.16 " 0.86 75.0 67.8 910.82 " 3.95 0.88 " 0.09 0.67 " 0.15 13 193.71 " 0.04 78.3 67.0 917.55 " 7.87 0.88 " 0.07 0.70 " 0.13 14 229.47 " 0.67 76.7 65.0 907.71 " 5.59 0.87 " 0.07 0.65 " 0.14 15 189.57 " 0.95 76.7 62.7 917.11 " 4.83 0.87 " 0.06 0.70 " 0.10 16 247.31 " 1.17 79.2 65.8 922.36 " 10.04 0.85 " 0.10 0.59 " 0.17 17 195.37 " 1.59 77.1 64.2 921.84 " 6.56 0.88 " 0.11 0.70 " 0.17 18 206.14 " 1.41 75.9 66.0 922.79 " 6.15 0.87 " 0.09 0.65 " 0.13 19 197.90 " 2.49 71.7 68.5 925.19 " 6.27 0.88 " 0.09 0.69 " 0.13 20 199.14 " 0.03 76.3 71.2 920.37 " 1.79 0.88 " 0.10 0.68 " 0.14 a

All values are the mean " S.D. of three determinations.

b

*()*
*J.-S.*
*Wu*
*et*
*al.*
r
*Powder*
*Technology*
*118*
*2001*
*219*
*–*
*228*
Table 4

Correlation matrix of material properties and mechanical performances of MCC products

Variable DP Crystallinity Degree of CED Surface Shape *E* KIC FT Sensitivity to

index crystallinity roughness index compaction

speed
) )
DP 1 y_{0.27035} y_{0.0628} y_{0.2783} y_{0.5511} y_{0.7162} _{0.2068} _{0.2063} _{0.4026} _{0.0087}
Ž0.2490. Ž0.7924. Ž0.2349. Ž0.0118. Ž0.0004. Ž0.3817. Ž0.3828. Ž0.0784. Ž0.9709.
)
Crystallinity 1 0.1584 y_{0.2348} _{0.1898} _{0.2053} y_{0.2558} y_{0.4683} y_{0.2236} y_{0.1542}
Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .
index 0.5048 0.3190 0.4228 0.3852 0.2763 0.0373 0.3433 0.5162
)
Degree of 1 y0.2120 0.0128 0.1352 y0.3617 y0.2585 y0.2546 y0.4839
Ž . Ž . Ž . Ž . Ž . Ž . Ž .
crystallinity 0.3696 0.9573 0.5698 0.1171 0.2712 0.2787 0.0306
)
CED 1 0.2739 0.2689 0.4062 0.4683 0.2570 0.4263
Ž0.2426. Ž0.2517. Ž0.0756. Ž0.0373. Ž0.2741. Ž0.0609.
)
Surface 1 0.9531 y0.3234 y0.3043 y0.4357 y0.1252
Ž . Ž . Ž . Ž . Ž .
roughness 0.0001 0.1643 0.1921 0.0549 0.5989
)
Shape 1 y0.3705 y0.3019 y0.4606 y0.2106
Ž . Ž . Ž . Ž .
index 0.1078 0.1957 0.0410 0.3728
*E* 1 0.2917 0.3143 0.4240
Ž0.2121. Ž0.1772. Ž0.0625.
)
*K*IC 1 0.8518 0.1571
Ž0.0001. Ž0.5084.
FT 1 0.0620
Ž0.7950.
Sensitivity to 1
compaction
speed

*Figures in parentheses indicate P values.*

)

w x

attractive forces between molecules 12 . On the other hand, particle morphology was described by the shape index and surface roughness. The shape index represents the regularity of particle shape, and the parameter of surface roughness describes the degree of roughness of particle surfaces.

The relationships between these molecular or particle features and mechanical performances were deduced by Pearson correlation analysis. Further, the canonical correla-tion analysis was employed to examine the key material properties for controlling mechanical performances of MCC

w x

products as described by Bohidar and Bohidar 23 . The
correlation matrix for the Pearson correlation analysis is
*shown in Table 4. K*IC shows a moderate correlation to

Ž .

*CED 0.4683, P s 0.0373 . As expected, an increase in*
intermolecular attraction enhances resistance of MCCs to
*cracking. Further, K*IC also shows a moderate correlation

Ž .

*to the crystallinity index y0.4683, P s 0.0373 . When*
the extent of intramolecular hydrogen bonding increases,

*K*IC of MCC decreases. This might be explained by the
intramolecular hydrogen bonding confining the polymer
chains to a specified aggregation state, thus reducing the
free polymer chains able to participate in the
intermolecu-lar hydrogen bonding between particles. Since hydrogen
bonding is the strongest attractive force among the
inter-molecular forces, the decrease in interinter-molecular hydrogen
bonding between particles is accompanied by a decrease in
mechanical strength of beams. FT displays a moderate

Ž .

*correlation to shape index y0.4606, P s 0.0410 . When*
particles of MCC become irregular, FT increases. This
might be explained by the irregular particles providing a
greater extent of mechanical interlocking, and the energy
necessary for crack propagation being larger than that in
symmetrical ones. The sensitivity to compaction speed has
a moderate correlation with degree of crystallinity

Žy* _{0.4839, P s 0.0306 . This result demonstrates that an}*.

increase in the amorphous portion of MCC molecules is accompanied by increasing sensitivity of changing com-pressibility to compaction speed of these polymer solids.

The key material properties of MCC products were evaluated by canonical correlation analysis. The

indepen-Ž . Ž

*dent variables X are material properties degree of *

crys-.

tallinity, crystallinity index, CED, and shape index . Since the DP and surface roughness correlated to none of the

Ž .

mechanical performances as shown in Table 4 , these two material properties were excluded from the canonical

cor-Ž .

*relation analysis. The dependent variables Y are *
mechan-ical performances. The first canonmechan-ical correlation is 0.8917,
*which is statistically significant based on approximate F*

Ž .

*statistics of Wilks’ Lambda test P s 0.0132 , Hotelling–*

Ž .

*Lawley Trace test P s 0.0020 , and Roy’s Greatest Root*

Ž .

*test P s 0.0001 . Standardized coefficients and the *
corre-lation of the canonical variables with the original variables
for the first canonical correlation are shown in Table 5.
*Considering the coefficients of X-set variables, the CED is*
*the highest contributor to the X ’s canonical variable. This*

Table 5

Canonical correlation analysis of material properties and mechanical performances of MCC products

Variable Standardized Correlation

coefficients

*(* *)*

*Material property X Õariable*

Degree of crystallinity y_{0.2958} y_{0.5540}

Crystallinity index y_{0.1370} y_{0.4786}

Cohesive energy density 0.7389 0.6750

Shape index y_{0.5907} y_{0.4601}

*(* *)*

*Mechanical property Y Õariable*

Young’s modulus 0.3965 0.7413

Critical stress intensity factor 0.5458 0.7458

Fracture toughness 0.0212 0.6369

Sensitivity to compaction speed 0.4218 0.6770

shows that the attractive force between molecules is the most important material property controlling the mechani-cal performances of MCC products. The correlation

be-Ž .

tween CED and its canonical variable is moderate 0.6750 . At the same time, the degree of crystallinity, crystallinity index, and shape index also present a moderate correlation

Ž

to their canonical variables y_{0.5540, y0.4786, and}
.

y_{0.4601, respectively . This means that the degree of}

crystallinity, crystallinity index, and shape index also serve as important material properties controlling the mechanical performances of MCC. All mechanical performances show a moderate correlation to their respective canonical vari-ables. This means that all mechanical performances are well controlled by these material properties of MCC prod-ucts examined.

**5. Conclusions**

Among the mechanical performances of MCC products, only fracture toughness and sensitivity to compaction speed were affected by the manufacturing factors. However, the manufacturing factors cannot be used to precisely predict mechanical performances. Nevertheless, a MCC product with high fracture toughness and low sensitivity to com-paction speed could be optimally obtained by hydrolysis at

Ž . Ž .

high temperature 898C , of short duration 50 min , and

Ž .

with a low level of HCl 2.50 N . Pearson correlation analysis revealed that the critical stress intensity factor, fracture toughness, and sensitivity to compaction speed of MCC products can be quantitatively predicted by material properties examined in this study. Thus, MCC products with optimized mechanical performances might be ob-tained by the selection of adequate material properties. The CED, representing the attractive forces between molecules, was found to be the key material property of MCC prod-ucts controlling their mechanical performances. In

addi-tion, the degree of crystallinity, crystallinity index, and shape index may also serve as important properties for controlling the mechanical performances of MCC. There-fore, the influence of source variations of MCC products on the strength of tablets might be reduced by regulation of their CED, degree of crystallinity, crystallinity index, and shape index.

*List of symbols*

*A* projected area of a particle
CED cohesive energy density
DP degree of polymerization

*E* Young’s modulus

*F* Fisher’s F distribution

*f* a correction factor defined in Eq. 2Ž .

FT fracture toughness

*I*002 the X-ray diffractogram height at the position of

the 002 peak of MCC products

*I*am the X-ray diffractogram height of amorphous

background of MCC products

*K*_{IC} critical stress intensity factor

*P* probability

*P*_{m} perimeter of a particle outline

*R*2 _{squared multiple correlation coefficient}

*r*_{e} arithmetic mean of the distances between the
center of gravity and the perimeter of a particle

*U* canonical variable of the independent variables

*V* canonical variable of the dependent variables

*X* independent variable

*Y* dependent variable

*Greek letters*

a _{critical value of probability used in the stepwise}

multiple regression

f _{value for rotatability of the central composite}

design

**Acknowledgements**

We would like to express our sincere thanks for the financial support of the National Science Council of the

Ž .

Republic of China NSC 89-2320-B038-065 .

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