Intrinsic strain effect on crystal and molecular structure
of „dch32… cotton fiber
O. M. Samir and R. Somashekar
Department of Studies in Physics, University of Mysore, Manasagangothri, Mysore-570 006, India
Received 20 February 2006; accepted 27 December 2006
X-ray diffraction pattern from cotton fiber dch32 grown in the Karnataka state of India has been
recorded. Fiber was found to contain 17 Bragg reflections, of which 11 are broadened because of
crystal size and intrinsic strain influences. Contributions to integrated intensities from intrinsic strain
in the fiber have been estimated using line profile analysis. A molecular model was first constructed
with standard bond lengths and angles using helical symmetry and layer-line spacings observed in
the X-ray pattern. The model was then refined against observed X-ray data using the linked atom
least squares LALS method. The refinement has been done with and without the intrinsic strain
correction to find the extent of structural changes. These changes have been quantified in terms of
bond angles, bond lengths, and torsion angles. Young’s modulus has been estimated for these fibers
using the results of line profile analysis, and a broad agreement with the reported physical
measurements has been obtained. © 2007 International Centre for Diffraction Data.
DOI: 10.1154/1.2434790
Key words: cotton fibers, lattice strain, Young’s modulus, WAXS, LALS
I. INTRODUCTION
Cotton is cultivated in and around the southern states of
India such as Karnataka, Andrapradesh, and Maharashtra,
and is a major crop of several countries Shaw and Eckers-
ley, 1967; Hermans, 1949. It is important to understand the
relationship between the structure of this unique natural raw
fiber and its properties. Even though the crystal structure of
cotton fibers is very well reported Ellis and Warwicker,
1962; Gardener and Blackwell, 1974; Viswanathan and
Shenouda, 1971, there is continued interest in structural
studies of cotton, which is also almost pure cellulose, after
subjecting it to various physical and chemical treatments that
improve its usefulness Ford et al., 2005. Kulshreshtha and
Dweltz 1973 have reported paracrystalline lattice disorder
in cellulose.
In this study, the authors have carried out line profile
analysis of wide angle X-ray scattering WAXS data ob-
tained from dch32 raw cotton fibers employing a paracrys-
talline model to compute intrinsic strains present in these
fibers. Based on these results, our goal is to find the effect of
these parameters on the crystal and molecular structure of
dch32 raw cotton fibers. Young’s modulus, an important
mechanical property of these fibers, has been computed us-
ing the stiffness matrix.
II. LINE PROFILE ANALYSIS
The intensity profile, using the Fourier cosine series of
the Warren and Averbach method Warren, 1955; Warren
and Averbach, 1952 and Hosemman’s one-dimensional
paracrystal model Hosemman, 1982, in a direction joining
the origin to the center of the reflection, can be described as
follows:
Is =
n=-
An cos 2nds - s
o
. 1
where the An are the harmonic coefficients that can be
represented as a function of crystal size N and lattice dis-
tortion g, d is the interplanar spacing, s = sin / , s
o
is the
value of s at the peak of the reflection, is the Bragg angle,
is the wavelength of the radiation, and n is the harmonic
number. The Fourier coefficients An of the profile are ex-
pressed as the convolution of the crystal size A
s
n and lat-
tice strain A
d
n coefficients:
An = A
s
n . A
d
n . 2
The disorder component contribution is given as
A
d
n = exp -2
2
m
2
ng
2
, 3
where m is the order of reflection and the lattice disorder g
= d / d.
For a probability distribution of column length Pi, the
crystallite size contribution is
A
s
n =1-
nd
D
-
d
D
0
n
iPi di - n
0
n
Pi di
. 4
In cotton fibers, it is rare to find multiple reflections and
hence the Warren and Averbach multiple order method War-
ren and Averbach, 1952 cannot be used. Here the single
order method has been used to obtain the crystal size and
lattice strain, using an analytical function for Pi for which
an asymmetric function has been chosen exponential distri-
bution to find the finer details of the microstructure of cot-
ton fibers Hall and Somashekar, 1991. This distribution de-
pends on no columns containing fewer than p unit cells, and
those with more than p will decay exponentially. The width
of the distribution is =1/ N - p, and Pi is expressed as
Pi =
0 if p i ,
exp - n - p if p i .
5
Thus, the contribution of crystallite size to size coefficients is
given by
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