Worm chain

If < Iq, it becomes the case of the discrete picture and jointed-rods are applicable. If > lo, however, the elastically discrete polymer evolves into a worm chain, i.e., an elastically homogeneous chain. The orientation change can then take place over a length comparable to Iq. With this continuum of allowed orientational states, the worm chain accurately represents the angular entropy of the real polymer. 

WORM CHAIN MODEL OF LIQUID CRYSTALLINE POLYMERS... 

Figure 2.18. The mean square end-to-end distance of worm chains vs. —A2. (From Wang, 1997.)...

The worm chain in a possible polar nematic phase was discussed as well (Wang Lam, 1992). The dipolar interaction was taken into account in addition to the quadrupolar interaction. It results in the complexity of the phase diagram. 

Entropy is a measure of disorder in materials. Relaxed polymer chains with a random conformation (shape in space), like cooked spaghetti or a box of fishing worms, have a high degree of entropy, which is favored by Mother Nature. If the chains are stretched out (stressed), the number of conformations the chains can have in space is limited, and the entropy is reduced (see Figure B). The ratio of final length to initial length is denoted a. 

Semi-Flexible Chains Worm-Like Cods. 241... 

FIGURE 21.4 Nanofishing of a single polystyrene (PS) chain in cyclohexane. The solvent temperature was about 35°C (0 temperature). A cantilever with a 110 pN nm spring constant was used. The worm-like chain (WLC), solid line, and the freely jointed chain (FJC), dashed line models were used to obtain fitting curves. (From Nakajima, K., Watabe, H., and Nishi, T., Polymer, 47, 2505, 2006.)... 

As for further analysis, curve fitting against the worm-like chain (WLC) model was conducted and indicated as a solid line in Figure 21.4. The model describes single polymer chain mechanics ranging from random-coil to fully extended forms, as follows ... 

The worm like chain behaviour of the pectins is developped allowing to predict the dimensions of the chain as soon as the persistence length is known. The experimental data are compared with the theoretical prediction obtained from conformational analysis. 

As discussed in the last 3 years, polysaccharides behave in solution under a worm like chain [26] the local stiffness of the chain is characterized by a persistance length (Ip) the larger Ip is, the larger the chain deviates from the gaussian behaviour in the usual molecular weight range of these natural polymers [27], This makes difficult to use the relations given in litterature for synthetic... 

The new fibers were scientifically interesting—and they eventually laid the foundation for the synthetic textile industry—but at the time they seemed practically worthless. The first polyester fibers resembled those produced by the lowly silk worm, but Carothers did not think that the discovery would be commercially valuable. The polymer chains made in Hill s molecular still were still not long enough to make robust fibers. The filaments melted at such a low temperature and were so soluble that they could not be ironed or washed in dry cleaning fluid or hot water. Carothers knew he would have to make longer polymers if he hoped to make a marketable fiber. Instead, Carothers dramatized the romance of Hill s discovery by quoting the seventeenth-century microscopist, Robert Hooke, who had dreamed of making synthetic silk even better than that Excrement made by silk worms. 

The other limiting case concerns locally smooth chains. For the case of a Gaussian chain in a network of rods, Edwards found d (L/V) 1/2 [66] which agrees with the above discussed binary contact model. Finally, considering worm-like chain bridges the differences in the power laws between the two limiting cases and exponents between — 1 and — 1/2 may be obtained. 

The molar mass dependence of the intrinsic viscosity of rigid chain polymers cannot be described by a simple scaling relation in the form of Equation (36) with molar mass independent of K and a. over a broad molar mass range. Starting from the worm-like chain model, Bohdanecky proposed [29] the linearizing equation... 

A cardinal role for IL-4 in host protection against intestinal nematode infection was first shown in the H. polygyrus challenge model. Worm expulsion was delayed following treatment with anti-IL-4 or anti-IL-4 receptor monoclonal antibodies, while control treated animals successfully cleared infection (Urban et al., 1991b). Blockade of the IL-4 receptor effectively prevents the in vivo function of IL-4 and IL-13, as these two cytokines share the IL-4 receptor a-chain for signalling functions (Lin et al, 1995). In... 

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