Microfibrillar angle

The cell wall of any cellulose fiber is built of external shell and inner secondary S-wall. The S-wall is 3-6 gm thick and composed of three layers. The dominating S2-layer contains nanofibrillar bundles, i.e., microfibrils (MF], orientated under microfibrillar angle (MFA] toward the fiber axis (Fig. 7.12]. Such orientation of the microfibrils affects the mechanical properties of cellulose fibers. When the MFA declines, an increase of tensile strength and modulus of the fibers is observed. Thus, measurement of MFA is important since it allows to detail the structure of the fiber cell wall and to predict its mechanical properties. 

Measurement techniques for MFA are divided into microscopy and X-ray diffraction. Microscopy methods can include polarization microscopy, confocal reflectance microscopy, fluorescence microscopy, as well as electron microscopy in combination with preparation of thin sections and dyeing [Donaldson, 1991 Donaldson et al., 2004 Martz, 1955]. For instance, the technique of polarization microscopy involves rotating the plane of fibers until the bright cell wall becomes dark, the so-called maximum extinction 

X-ray diffraction is currently perhaps the most popular method for measuring MFA (Cave, 1966 Eichhorn et al., 2001], 

Typical methods obtain the MFA by measuring the azimuthal distribution of intensity of the [200] equatorial reflection. The sample is oriented so that the axis of the fiber was in a vertical direction and then the azimuthal position is changed until the intensity of the peak reaches minimal value. The sample can be located under angle 45° or 90° to a beam of X-ray, while azimuthal distribution of intensity of the [200] reflection is photographed on a photo-film. If the sample is under 45° to beam, the MFA can be calculated by the equation of Eichhorn et al. [2001]  

X-ray determination of MFA using the photo-films is a complicated and long process. If the X-ray diffractometer is used for this purpose, the procedure will be carried out much easier and faster (Andersson et al., 2000]. However, calculations of MFA from diffractograms are more complex therefore, preliminary calibration of obtained azimuthal angles is required using independent methods, e.g., microscopy. 

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The middle layer (S2) forms the main portion of the cell wall. Its thickness in softwood tracheids varies between 1 (earlywood) and 5 (latewood) jiim and it may thus contain 30-40 lamellae or more than 150 lamellae. The thickness naturally varies with the cell types. The microfibrillar angle (Fig. 1 -16) varies between 10° (earlywood) and 20-30° (latewood). It decreases in a regular fashion with increasing fiber length. The characteristics of the S2 layer (thickness, microfibrillar angle, etc.) have a decisive influence on the fiber stiffness as well as on other papermaking properties. 

Figure 4 Effects of chemical treatments on relationships between logarithm of E l 7 and logarithm of tan 6. Dotted lines represent experimental correlations for untreated specimens. Various values of relative increase of matrix rigidity (/ ) and mobility factor (jx) were simulated. (A, A) Experimental values of untreated and treated specimens. (O, ) Theoretical plots for zero mean microfibrillar angle and theoretical plots assuming swelling effect only. See legend to Fig. 2 for treatment abbreviations.

GPa and 2 GPa are reasonable estimates of the cellulose and matrix Young s modulus, respectively. The calculated value of E /y was 46.9 GPa, which was a value compatible with measurements at various mean microfibrillar angles, prolonged to 0° [4]. The value of was adjusted to yield the estimate of tan 8 = 0.0046 deduced from measurements [4]. These two values correspond to a point shown by an open circle placed at an extreme position down and right on the regression line in the log E /y - log tan 8 graph. 

These are covered with a sheath of para-crystaUine polyglucosan material surrounded by hemicellulose [29]. In most natural fibers, these micro-fibrils orient themselves at an angle to the fiber axis called the micro-fibril angle. The ultimate mechanical properties of natural fibers are found to be dependent on the microfibrillar angle. Gassan et al. have performed calculations on the elastic properties of natural fibers [30]. 

The relationship between the strength of the biofibers with the microfibrillar angle and cellulose content is given in the following equation ... 

Furthermore, the elongation at break can be correlated with the microfibrillar angle 0 based on the equation shown below ... 

The cell walls differ among themselves in their composition and orientation of the cellulose microfibrils. In most plant fibres, these microfibrils are oriented at an angle to the normal axis called the microfibrillar angle (Fig. 19.2). The characteristic value for this structural parameter varies from one plant fibre to another. 

Fibre Density (gcm"3) Young s modulus (GPa) Tensile strength (MPa) Elongation (%) Microfibrillar angle (°)... 

The structure, microfibrillar angle, cell dimensions, defects, and the chemical composition of fibers are the most important variables that determine the overall... 

It is important to mention that the chemical composition of each type of fibers and the orientation of microfibrils about the fiber axis, called microfibrillar angle (Table 8.1), may significantly differ. Similarly, depending on the cellulose and lignin contents, crystallinity index of each type of fiber differs. In view of these, when lignocellulosic fibers are tested for their tensile properties, their fracture mode differs, which may be intercellular or intracellular or mixed modes of fracture. Accordingly, the tensile properties and fractographs are different for each type of fiber. These are also listed for some fibers in Table 8.1 and Fig. 8.3, respectively. 

Theoretical Prediction of Microfibrillar Angle and Strength of the Fibre... 

Strength properties of the fibre are dependent mainly on the fibrillar structure, microfibrillar angle, and the cellulose content. There is a correlation between percentage elongation and microfibrillar angle d as follows ... 

Table 9.7 Chemical compositions and microfibrillar angles of some natural fibers...

Fiber Cellulose (wt %) Hemicellulose (wt %) Lignin (wt %) Pectin (wt %) Microfibrillar angle ( )... 

The right column displays the USAXS patterns of the two materials after relaxation (x = 3°). Obviously, in the twisted-bimdle sample the microfibrillar angle has recovered to a considerable extent. It is interesting to note that the overall elastic recovery of the material with twisted bundles is better than that of the straight-bundle material. 

Each fibril has a complex, layered structure consisting of a thin primary wall that is the first layer, deposited during cell growth and encircling a secondary wall. The secondary wall is made up of three layers and the thick middle layer determines the mechanical properties of the fibers. The middle layer consists of a series of helically wound cellular microfibrils formed from long chain cellulose molecules the angle between the fiber axis and the microfibrils is called the microfibrillar angle. The characteristic value for this parameter varies from one fiber to another [10]. 

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