# Characterization of celluloses by means of viscoelastic parameters

Authors:
M. Řehula; R. Adámek

Authors‘ workplace:
Charles University in Prague, Faculty of Pharmacy in Hradec Králové, Department of Pharmaceutical Technology
^{}

Published in:
Čes. slov. Farm., 2008; 57, 215-220

Category:
Original Articles

## Overview

In tablet formulation it is necessary to start from viscoelastic parameters of the excipients employed. Plasticity and elasticity of excipients are influenced by the type of bonds which are being formed in the course of the compaction process. The present paper evaluates the viscoelastic properties of selected fillers intended for direct compaction of tablets. The determinations included cellulose powder, microcrystalline celluloses Avicel PH 101, Avicel PH 102, Avicel PH 103, Avicel PH 200, Avicel PH 301, and Ceolus KG 802. Elasticity of the excipients was evaluated by means of Young’s modulus of elasticity and differential elastic potential energy. Plasticity was evaluated by means of the stress relaxation test using the three-exponential equation following Maxwell’s model. The method was supplemented with a novel original parameter, total plasticity PT. The study examined the effect of particle size of fillers, density, moisture content, and molecular weight on elasticity and plasticity of celluloses. The results of the paper revealed that particle size of celluloses did not influence elasticity and plasticity of excipients. With increasing density of celluloses, elasticity was increased and at the same time plasticity was decreased. The above-mentioned viscoelastic parameters were influenced by the content of moisture in fillers. With increasing amount of moisture in fillers, elasticity was decreased and plasticity increased. With increasing molecular weight of cellulose, elasticity was decreased and plasticity increased.

**Key words:**

Young’s modulus of elasticity – differential elastic potential energy – three-exponential equation of plasticity – residual and total plasticity – celluloses

## Introduction

Elasticity and plasticity are usually considered to be
the principal viscoelastic properties. Elastic deformation can be
defined as a reversible change in the shape or volume of
material resulting from force, when after the action of force is
completed, material returns to its original shape ^{1)}.Elastic deformation is time-independent and
fully restorable.

Plastic deformation can be defined as a permanent
change in the shape of material resulting from applied tension ^{1)}.
The same author further points out that viscoelasticity reflect the
time-dependent character of deformation.

In the evaluation of viscoelastic properties of fillers,
four groups of methods are employed; the method based on the
“force-route” record ^{2, 3)},
elastic recovery ^{4)},
creep test ^{5)}, and
stress relaxation ^{6)}.

The present study evaluated plasticity of fillers by
means of the stress relaxation test. If during compaction after
reaching the maximal compaction force the upper punch is stopped and
the volume of the tablet is left constant for a certain period
of time, we can observe an exponential decrease in the strength in
the tablet. Stress relaxation can thus be defined as a decrease
in compaction force in time while keeping a constant volume of
the material under compaction ^{7)}.
The extent of relaxation depends on the amount of energy stored in
the tablet during compaction and also on bond formation ^{8)}.

For the evaluation of the decrease in strength during
the test, one- to four-exponential equations are used ^{9)}.
The authors studied the behaviour of relaxation to 360 s and
found that the graph of the decrease in strength in dependence on
time corresponded to Maxwell’s body 30 s after achieving the
maximal strength. This model is composed of a spring and piston
arranged in a series. The spring represents the elastic
properties and the piston the plastic ones. The following equation
corresponds to such a model:

F(t) = F_{MAX }exp(t/T)

where F(t) is
strength in time t and F_{MAX }themaximal strength in time 0, T is the time constant.

Other authors ^{10) }in
their book present a simplified variant of the equation (E_{1–3}
– modulus of elasticity):

F(t) = E_{1}^{-t/T}_{1}
+ E_{2}^{-t/T}_{2}
+ E_{3}^{-t/T}_{3}

This study used the stress relaxation method to evaluate the viscoelastic characteristics of the fillers cellulose powder, and microcrystalline celluloses Avicel PH 101, Avicel PH 102, Avicel PH 103, Avicel PH 200, Avicel PH 301, and Ceolus 802.

## Experimental part

### Raw materials used

The model pharmaceutical fillers for direct compression were the microcrystalline celluloses Avicel PH 101 (lot 6902C), Avicel PH 103 (lot Z726C), Avicel 301 (lot P926C), all manufactured by the firm FMC Corporation, Belgium; cellulose powder Vitacel A 300 (lot 0708050429), J. Rettenmaier, Germany, Ceolus KG-802 (lot K3B1), Asahi Kasei Chemicals Corporation, Japan. All materials comply with the European Pharmacopoeia and were used without any adjustments.

### Preparation of tablets

Tablets of a diameter of 13 mm and weight of 500 mg were compacted in a compaction preparation (Adamus HT, Machine Factory Group, Szczecin, Poland) in a device for testing the strength of materials under tension and pressure T1-FRO 50 (Zwick GmbH, Ulm, Germany). Adjustment of the device: distance of jaws, 117 mm, rate of the cycle, 2 mm/s, pre-load, 2 N, compaction forces, 250 N, 500 N, 1000 N, 2000 N, 3000 N, 4000 N, 5000 N, 7500 N, 10000 N, 12500 N, and 15000 N. For the determination of Young’s modulus of elasticity and elastic potential energy, tablets were compacted without a pause; for the determination of stress relaxation, tablets were compacted with a pause of 180 s. During the pause, the upper punch was stopped at the point where it reached the maximal strength, and the decrease in strength in the punch in dependence on time was recorded. In each compaction force, six tablets were evaluated.

When compaction was finished, the height of each tablet was measured (a digital micrometric screw Mitotuyo, Japan).

### Calculation of Young’s modulus of elasticity

Young‘s modulus of elasticity was calculated according to the equation:

CP = E_{Y}
*Δl/l
,

where CP is compaction pressure, E_{Y}
Young’s modulus of elasticity, and Δl/ldeformation expressed as the ratio of the
change in the length of the body to the original height. The term Δl
is the difference of heights of the tablets 5 s after completion
of compaction and the height at the maximal pressure, l
is the height of the tablet at the maximal pressure. In the graphic
representation of the dependence of CP on l/l,
the gradient of the developed line is the Young’s modulus of
elasticity which is searched for.

### Calculation of elastic potential energy

The following equation served to calculate elastic
potential energy, which causes the increase in height of the tablet
after the completion of compaction ^{11)}:

where
A is the area of the tablet (m^{2}),
other terms are explained above.

The differences in elastic potential energy of the tablets compacted without a pause and those with a pause yielded differential elastic potential energy (J).

### Calculation of stress relaxation parameters

To calculate the parameters of the decrease in strength in the tablet at 180 s with a pause, the following three-exponential equation is employed:

CP = E_{1}e^{-t/T}_{1}
+ E_{2}e^{-t/T}_{2}
+ E_{3}e^{-t/T}_{3}
[MPa]

Parameters of the above-mentioned equation were
calculated using the programme OriginPro 7.5 by means of the
function ExpDec3. The parameter CP (MPa) is the compaction pressure
at a given moment in time t (s), E_{1 3}
(N) is the amount of strength which was decreased in the given
process, T_{1-3} is
the relaxation constant which states the rate and the steep gradient
of the process. The residual plasticity P_{R}
(MPas) is calculated from the following equation ^{10)}:

P_{Ri} =
E_{i} * T_{i
} [MPas]

for
each compaction pressure. The total plasticity P_{T}
(MPas) is then equal to the area under the curve of the graph of the
dependence of P_{R}/CP
on CP.

## Results and discussion

The stress relaxation test was employed to evaluate
plasticity. The results obtained in this test expressing the decrease
in compaction pressure in dependence on time were evaluated by means
of a three-exponential equation. This equation corresponds to
three Maxwell’s models arranged in parallel^{10)}.
The springs E_{1–3}
represent the elastic modulus, the pistons P_{R1–3},
the plastic modulus. After compaction of the material by a certain
pressure, a certain value of the spring E and the zero value of
P_{R} are achieved.

The given relation divides the whole process of decrease
in compaction pressure in dependence on time into three processes.
According to the present authors’ idea, in the first process a high
decrease in the modulus E_{1}
is due to the extension of the spring in order to achieve greater
mutual approximation of the surfaces of the particles. The given
approximation does not result in the development of new bonds yet.
That is why the increase in the value of the modulus of the residual
plasticity P_{R1} is
minimal. In the second process it can be assumed that by the action
of smaller released elastic energy further approximation of the
surfaces of the particles occurs and conditions are produced for the
development of bonds. In the third process, the elastic modulus E_{3}
possesses approximately the same value as the parameter E_{2}
and at the same time a high value of the modulus of the residual
plasticity P_{R3}.
This process is called the plastic process, in which deformation is
not restorable and the process is time-dependent ^{12–14)}.
In the third process, only a small amount of elastic energy
suffices for further approximation of the surfaces of the particles
and development of bonds.

Viscoelastic properties were studied in cellulose powder and in microcrystalline celluloses, which possess substantially smaller molecular weights than cellulose powder. The microcrystalline celluloses employed differ in the sizes of particles, densities, and moisture content.

The obtained results are shown in Tables 1 and 2 and in Figures 1–6. In the graphs there are obviously great standard deviations in some parameters. They are caused by close affinities of the excipients tested and further by the use of original methodologies producing greater variability of results.

The first marker under evaluation was molecular weight
of the celluloses. Cellulose powder possesses the molecular weight of
about 243000, microcrystalline celluloses only about 36000 ^{15)}.
For the evaluation of viscoelastic parameters, a comparison was
made of the properties of cellulose powder and the microcrystalline
cellulose Avicel PH 102. Young’s modulus of elasticity in cellulose
powder in comparison with Avicel PH102 was higher by 10 MPa and
differential elastic potential energy was higher by 0.51 J. The
higher values in both cases mean lower elasticity. On the other hand,
the values of plasticity in all three processes were higher in
cellulose powder. The parameter P_{T1}
was higher by 0.73 MPas, the parameter P_{T2
}higher by 8.33 MPas, and the parameter P_{T3
}higher by 146.32 MPas. Cellulose powder in
contrast to Avicel PH 102 thus showed lower elastic properties and at
the same time higher plasticity. These regularities are caused by the
type and number of bonds which are being formed during compaction
process. Cellulose powder, in contrast to Avicel PH 102, possesses
a low crystalline share and at the same time a larger
amorphous share, which on compaction readily forms hydrogen bonds.
Also in cellulose powder, in contrast to Avicel PH 102, the principle
of mechanical interlocking plays its role^{
16)}.

Another marker under evaluation is particle size. In
this part of the study, Avicel PH 101 with a particle size of 50
μm,
Avicel PH 102 with a particle size of 100 μm,
and Avicel PH 200 with a particle size of 180 μm
were compared. The values of Young’s modulus of elasticity ranged
from 522 to 524 MPa, the values of differential elastic potential
energy from 1.72 to 1.99 J, and the values of plasticity P_{T1}
from 3.25 to 3.36 MPas, P_{T2}
from 25.01 to 25.41 MPas, and P_{T3}
from 408.10 to 411.65 MPas. The results cannot clearly demonstrate
the effect of particle size on viscoelastic properties of
microcrystalline celluloses. It is due to the method of production,
when the primary needle-shaped objects of the size of about 20 μm
granulate into the objects of varying particle sizes. The
microcrystalline celluloses under study of varying sizes therefore
possess the same compaction properties.

Another important factor is the density of
microcrystalline celluloses. The comparison included Ceolus KG
802 with a density of 0.2 g/cm^{2},
Avicel PH 101 with a density of 0.3 g/cm^{2},
and Avicel PH 301 with a density of 0.4 g/cm^{215)}. Young’s
modulus decreased with increasing density from 529 to 506 MPa
and differential elastic potential energy decreased from 1.99 to 1.50
J. With a decrease in the values of the above-mentioned
parameters, elasticity of microcrystalline celluloses was increased.
The parameter of plasticity P_{T1}
ranged from 0.44 to 3.32 MPas. With low values it is not possible to
assume a significant influence of the factor under studies. The
parameter P_{T2}
decreased from the value of 26.25 MPas to the value of 24.66 MPas and
the parameter P_{T3}
also decreased from the value of 406.65 MPas to the value of 400.56
MPas. Plasticity of microcrystalline celluloses generally decreased
with increasing density.

The final parameter under evaluation was the declared moisture content of microcrystalline celluloses, comparing Avicel PH101 with a moisture content of 5% and Avicel PH 103 with a moisture content of 3%.

Young’s modulus of elasticity in Avicel PH 101
was 524 MPa and in Avicel PH 103 496 MPa. Differential elastic
potential energy in Avicel PH 101 was 1.99 J and in Avicel PH 103,
1.79 J. With a decreasing moisture content in the particles of
microcrystalline cellulose, elasticity was increased. When comparing
plasticities, with an increasing moisture content the parameter P_{T1
}ranged insignificantly from 3.32 MPas to
3.55 MPas, the parameter P_{T2}
ranged insignificantly from 25.41 MPas to 26.25 MPas. On the other
hand, the principal parameter necessary for the formation of bonds
P_{T3} decreased with
decreasing moisture from 409.35 MPas to 389.70 MPas. A decreasing
moisture content in microcrystalline celluloses decreases
plasticity by decreasing the number of hydrogen bonds, which are
being formed during compaction process.

An important characteristic of fillers is their plasticity. The present paper has demonstrated that cellulose powder possesses higher plasticity than other microcrystalline celluloses. Furthermore, it has been demonstrated that plasticity is not influenced by particle size of microcrystalline celluloses. Plasticity is further increased with decreasing density of microcrystalline celluloses and increasing moisture in the particles of microcrystalline celluloses.

The paper was supported by the Research Project MSM 0021620822.

Received 11 August 2008 / Accepted 20 August 2008

**Address
for correspondence:**

Assoc. prof. RNDr. Milan Řehula, CSc.

Univerzita Karlova v Praze, Farmaceutická fakulta v Hradci Králové, Katedra farmaceutické technologie

Heyrovského 1203, 500 05 Hradec Králové

e-mail: milan.rehula@faf.cuni.cz

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