Ultimate fibre length

Fibres can be processed to be finer and shorter than the figures given in Table 11.1, so as to meet end-use requirements. The ultimate fineness and length would approximate closely the cell dimensions, suitable as papermaking pulp. Thus, the average ultimate fibre length of flax would be 25 to 35 mm jute, on the other hand, would be 2 to 3 mm. 

The effect of the width of the distribution on the ultimate fibre strength, oL, is calculated for the case in which the molecular weight distribution /w(z)= z/(z)zn is a uniform distribution. The weight-average length of the distribution fw(z) is defined as... 

Before we discuss the relation between ultimate fibre strength and degree of polymerisation (zn or DP), we first show that this model in fact describes the relation between the composite strength and the aspect ratio of the rod. In the case of a monodisperse distribution, i.e. all rods or chains have the same diameter 2r and the same length a, the ultimate strength as a function of the aspect ratio fr= a(2r) 1 is given by... 

The ultimate strength of a composite of fibre and polymer is basically dependent upon the stress-strain relationship of its components. Any fibre whose strength and modulus of elasticity is greater than a polymer is capable of theoretically providing reinforcement to that polymer. Practically, however, the difference in properties has to be considerable to obtain efficient reinforcement and the effectiveness of the reinforcement is dependent upon the degree of adhesion which can be achieved. Other factors which also influence the properties of a composite are relative volumes of reinforcement and matrix, their physical and chemical properties, the temperature resistance and, of very considerable importance, the fibre length which is being used. 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

As will be shown in Sect. 3, Yoon derived the following expression for the ultimate strength of a polymer fibre with long and parallel oriented chains of finite length... 

Fig. 17 The ultimate strength of a fibre with perfectly parallel oriented chains of finite length is determined by the strength of the secondary bonding...

For the transformation of the macrocomposite model to a molecular composite model for the ultimate strength of the fibre the following assumptions are made (1) the rods in the macrocomposite are replaced by the parallel-oriented polymer chains or by larger entities like bundles of chains forming fibrils and (2) the function of the matrix in the composite, in particular the rod-matrix interface, is taken over by the intermolecular bonds between the chains or fibrils. In order to evaluate the effect of the chain length distribution on the ultimate strength the monodisperse distribution, the Flory distribution, the half-Gauss and the uniform distribution are considered. 

Fig. 45 Ultimate strength of PpPTA fibres versus the degree of polymerisation applying the Flory distribution of chain lengths for various values of the diameter 2 r calculated with Eq. 93...

The individual cells of jute are very short. Table 1.11 compares the dimension of ultimate from several sources. The cross-section of jute fibre is polygonal, usually with five or six sides. It has thick walls and a broad lumen of oval cross-section. By contrast with the regular lumen of flax, that of jute is irregular it becomes narrow in plaees quite suddenly. The lengths of various vegetable fibres varies considerably, whereas the diameter is moderately constant from fibre to fibre. 

Properties such as density, electrical resistance, ultimate tensile strength and initial modulus are related to the internal structure and chemical composition of the fibres. Properties may also vary according to variations in diameter along with the length of individual filaments, size and maturity, as well as the processing methods used for the extraction of fibres. These fibres are biodegradable and non-abrasive. However, incompatibility of the fibres and poor resistance to moisture often reduces the potential of natural fibres and these drawbacks have become a critical issue in their development." ... 

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