Rigidity, fiber

The standard gel-forming reaction is shown in Figure 8.2. Acrylamide and the cross-linker N, A-methylenebisacrylamide (bis) are mixed in aqueous solution and then copolymerized by means of a vinyl addition reaction initiated by free radicals.1317 Gel formation occurs as acrylamide monomer polymerizes into long chains cross-linked by bis molecules. The resultant interconnected meshwork of fiberlike structures has both solid and liquid components. It can be thought of as a mass of relatively rigid fibers that create a network of open spaces (the pores) all immersed in liquid (the buffer). The liquid in a gel maintains the gel s three-dimensional shape. Without the liquid, the gel would dry to a thin film. At the same time, the gel fibers retain the liquid and prevent it from flowing away. 

In terms of copolymerization, the addition of a comonomer to a crystalline polymer usually causes a marked loss in crystallinity, unless the second monomer crystallizes isomorphously with the first. Crystallinity typically decreases very rapidly, accompanied by reductions in stiffness, hardness, and softening point, as relatively small amounts (10-20 mol%) of the second monomer are added. In many cases, a rigid, fiber-forming polymer is converted to a highly elastic, rubbery product by such minor... 

For materials with a strong bond between the matrix and the fiber, models for steady transverse creep are available. The case of a linear matrix is represented exactly by the effect of rigid fibers in an incompressible linear elastic matrix and is covered in texts on elastic materials.7,11,12 For example, the transverse shear modulus, and therefore the shear viscosity, of a material containing up to about 60% rigid fibers in a square array is approximated well... 

Since Brownian motion can be neglected, the stress tensor for a suspension of rigid fibers can be obtained from Eq. (6-36) simply by dropping the Brownian term ... 

Sintered porous-metal-powder filters Sintered, stainless steel, semi rigid fiber filters... 

The proportionality between N and y has been observed at low deformation rates for concentrated LCP solutions in cresol [Kiss and Porter, 1980 Moldenaers and Mewis, 1992], for colloidal and noncolloidal suspensions, and fiber suspensions in a Newtonian matrix [Zirnsak et al., 1994], as well as for block copolymers and multibranched star polymers [Brady and Bossis, 1985 Kotaka and Watanabe, 1987 Masuda et al., 1987 English et al., 1997]. For LCP this behavior was considered originating in polydomain flow [Larson and Doi, 1991], while for rigid fiber suspensions in interparticle interactions [Zirnsak et al., 1994]. It is tempting to postulate that the clay platelet orientation is the origin of the difference. Evidently, the scan direction and the pre-shearing time between data points affect the orientation, but the proportionality Ni =ay and complexity of the ) = f(y) dependence remain. The Larson-Doi [1991] theory of polydomain flow leads to... 

Figure 21.2 Interaction of textile technology and composite engineering to form rigid fiber assemblies. Source Reprinted with permission from Hearle JWS, Du GW, J Text Inst, 81(4), 1980. (a) Knitted stmchire with repeated reversal of yam directions, (b) Simple plain weave fabric with threads continuous in X and Y directions, (c) Triaxial weave fabric, (d) Braid with yams at 9 to axis, (e) Triaxial braid. Copyright 1980, The Textile Institute.

Flexural Rigidity (Fibers). A measure of the rigidity of individual strands or fibers the force couple required to bend a specimen to unit radius of curvature. 

Garg and Kenig 23 HBA/HNA HNA/TA/AA Theoretical treatment of the development of orientation in simple molded parts, based on the flow of a dilute suspension of rigid fibers. Demonstrated variations in cross-sectional mechanical properties by successively removing surface layers. 

Chaouche, M. Koch, D.L. 2001. Rheology of non-Brownian Rigid Fiber Suspensions with Adhesive Contacts. J. Rheol. 45 (2) 369-382... 

Another special case is the fiber optic-coupled thermometer, which allows inaccessible targets to be measured by replacing the optic with a flexible or rigid fiber optic bundle. This, of course, limits the spectral performance, and hence the temperature range, to the higher values, but it has allowed temperature measurements to be made when previously none were possible. 

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