Modulus chains

As the chain modulus of a polymer cannot be altered in a spinning process, a larger fibre modulus can only be obtained by improving the orientation of the chains and by an increase of the shear modulus g. However, there is one exception. After dissolving native cellulose fibres with the cellulose I conformation and a chain modulus of 138 GPa into a solution, the regenerated fibres obtained by spinning of this solution and subsequent coagulation always have the cellulose II chain conformation with a chain modulus of 88 GPa [26]. 

In cellulose II with a chain modulus of 88 GPa the likely shear planes are the 110 and 020 lattice planes, both with a spacing of dc=0.41 nm [26]. The periodic spacing of the force centres in the shear direction along the chain axis is the distance between the interchain hydrogen bonds p=c/2=0.51 nm (c chain axis). There are four monomers in the unit cell with a volume Vcen=68-10-30 m3. The activation energy for creep of rayon yarns has been determined by Halsey et al. [37]. They found at a relative humidity (RH) of 57% that Wa=86.6 kj mole-1, at an RH of 4% Wa =97.5 kj mole 1 and at an RH of <0.5% Wa= 102.5 kj mole-1. Extrapolation to an RH of 65% gives Wa=86 kj mole-1 (the molar volume of cellulose taken by Halsey in his model for creep is equal to the volume of the unit cell instead of one fourth thereof). 

Figures 26 and 27 present the modulus and strength as a function of the orientation parameter sin2 for the PpPTA, PBO and PIPD-HT fibres, assuming a fibre with a single orientation angle. As the precise value of g for the PBO fibre is not known, we have taken the same value as for PpPTA. This enables us to demonstrate the effect of the chain modulus on the modulus and the strength of the fibres, in particular at medium values of the orientation parameter and for highly oriented fibres. For example, at an orientation parameter value of sin2 =0.028 the modulus and strength for a PpPTA fibre are =84 and crb=3.9 GPa, for PBO =104 and ab=5.2 GPa, and for PIPD-HT =241 and crb=8.6 GPa.

In the previous sections the theoretical relations describing the strength of a polymer fibre as a function of the intrinsic parameters, such as the chain modulus, the modulus for shear between adjacent chains, the orientation distribution and the chain length distribution, have been discussed. In this section the dependence of the strength on the time and the temperature will be investigated. 

Fig. 58 The rheological model of a polymer fibre consists of a series arrangement of an elastic tensile spring representing the chain modulus, ec, and a shear spring, g(t), with viscoelastic and plastic properties representing the intermolecular bonding...

There are two methods which have been used to date. In the first the force constants derived from IR and/or Raman data are substituted into expressions which give chain extension in terms of applied force. A chain modulus is then deduced by using an effective chain cross-sectional area. In the second method lattice dynamics is used to derive all the elastic constants for an infinite crystal. 

Shimanouchi et al.105) also derive a set of force constants from the Raman LA mode data by analysing the normal modes of vibration of the alkane chains. These constants are then used to predict the chain modulus using a simple model for the planar zigzag chain. 

If it is assumed that WF is independent of the initial modulus of the fibres made from the same polymer, then the end points are located on a hyperbola strain energy of the chain up to fracture of... 

Understanding of the mechanism of creep failure of polymeric fibres is required for the prediction of lifetimes in technical applications (Northolt et al., 2005). For describing the viscoelastic properties of a polymer fibre use is made of a rheological model as depicted in Fig. 13.103. It consists of a series arrangement of an "elastic" spring representing the chain modulus ech and a "shear" spring, yd with viscoelastic and plastic properties... 

L. M. J. Kroon-Batenburg, J. Kroon, and M. G. Nordholt, Chain modulus and intramolecular hydrogen bonding in native and regenerated eellulose fibers, Polym. Commun., 27 (1986) 290-292. 

Thermotropic polyesters are melt-spun from the nematic phase and orient easily in an elongational flow field (moderate drawdowns/forces are sufficient). In the fiber case, highly oriented fibers form easily with an initial modulus close to theory—typical values range from about 70 to 150 GPa. Ward [46] has shown that the tensile modulus may be described by an aggregate model, i.e., the modulus is a function of the inherent chain modulus, the molecular chain orientation, and the shear modulus (which described the stress transfer between chains). The tensile strength of LCP fibers follows the prediction of the lag-shear model [47]. Both the aggregate model and the lag shear model treat the LCP as though it... 

As shown by Eq. (15) and (17), the tensile elastic behaviom of fibers made from lyotropic polymers is determined by the chain modulus e the shear modulus go and the orientation parameter . As has been discussed in Sect. 2 and 3, the latter is determined by the persistence length, the molecular weight, the polymer concentration and the temperature of the liquid crystalline solution, and furthermore by the spinning and coagulation conditions. 

The elastic forces are controlled by the chain modulus ZkTE h/Na)/Na where... 

Kroonbatenburg LMJ, Kroon J, Northolt MG (1986) Chain modulus and intramolecular hydrogenbonding in native and regenerated cellulose fibres. Polym Commun 27 290-292 Kumar V (2002) Powdered/microfibrillated cellulose. WO Patent WO/2002/022172 Latarjet J (1995) A simple guide to bum treatment. Bums 21 221-225... 

Figure 7.17 show results for a plot of l/ 3 versus 1/G for hydrostatic extrusion of pressure-annealed polyethylene taken to a series of extrusion ratios (equivalent to draw ratios). It can be seen that the gradients of the fitted lines reduce with increasing extrusion ratio as the orientation parameter sirf 0 reduces, and that the lines converge to a value of E 250 GPa, in the correct range for the chain modulus of polyethylene. 

In a second version of the aggregate model Ward and co-workers assumed, on the basis of observation of the X-ray diffraction pattern, that the aggregate unit averages the deformation over a length of 8 10 monomer units. The chain modulus in this case can be determined experimentally by measuring the change in the X-ray dififaction pattern under stress, and a temperature-dependent was observed. By rearrangement of Equation (7.11) a further plot of... 

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