Snake like motion

Extension of this theory can also be used for treating concentrated polymer solution response. In this case, the motion of, and drag on, a single bead is determined by the mean intermolecular force field. In either the dilute or concentrated solution cases, orientation distribution functions can be obtained that allow for the specification of the stress tensor field involved. For the concentrated spring-bead model, Bird et al. (46) point out that because of the proximity of the surrounding molecules (i.e., spring-beads), it is easier for the model molecule to move in the direction of the polymer chain backbone rather than perpendicular to it. In other words, the polymer finds itself executing a sort of a snake-like motion, called reptation (47), as shown in Fig. 3.8(b). 

My mental eye, rendered more acute by the repeated visions of the same dream, could now distinguish larger structures of manifold conformations long rows sometimes fitted together all twining and twisting in snake-like motion. 

FIGURE 13-67 Schematic diagram illustrating a snake-like motion among a set of obstacles. 

Much effort has gone in trying to predict melt rheological response from the molecular structure. Physical chemists have considered the modes of vibration of short-chain molecules (to explain the low molecular weight shear viscosity data in Fig. 3.10), applied mathematicians have attempted to explain the non-Newtonian and elastic properties of melts from the lifetimes of temporary entanglements between molecules, while physicists have used the snake-like motions of sections of polymer chains (reptation) for the same purpose. None of these approaches has been completely successful. 

An alternative interpretation of the entanglement phenomenon is to consider that a large MW polymer flows by a series of snake-like motions called reptation (De Gennes 1971). The concept of entanglements will be adopted in this text because it has been commonly used in polymer science and may be more intuitively understood by cereal chemists who are new to the area. 

In the liquid the whole polymer chain undergoes vigorous Brownian motion the molecules move as a whole by snake-like motions, as envisaged in the theory of rubber elasticity. In the glass it is clear that although the chain is essentially immobile, Umlted Brownian motion is possible before the onset of the liquid-like Brownian motion at the glass transition. 

The basic idea, proposed by de Gennes [23], is that relaxation mechanism of linear pendant chains is governed by the reptation or snake-like motion of the chains retracting along their primitive path from the free end to the fixed one. This model proposed that the relaxation time of pendant chains should increase exponentially with the number of entanglements in which it is involved. Pendant chains must then contribute to viscoelastic properties for frequencies greater than the inverse of reptation times. Tsenoglou [26], Curro and Pincus [27], Pearson and Helfand [24] and Curro et al. [25] developed models for the relaxation of pendant chains in random cross-linked networks. 

Nakabo et al. [14] developed a snake-like swimming robot with a patterned-electrode IPMC. The aim is that a snake-like motion sweeps a smaller area than simple bending swimming. Thus, it is suitable for future swimming robots in thin tubes, such as blood vessels, as shown in Figure 6.16. 

On the other hand, the reptation theory proposed by de Gennes<4) assumes that a flexible chain is diffusing in a fixed three-dimensional mesh of obstacles that the chain cannot cross (Figure 2). Thus, the chain would be topologically constrained to move by a curvilinear, or snake-like, motion alone. This motion has been termed reptation (from reptile ). One can visualize that the flexible chain is reptating by a Brownian diffusion within a tube surrounded by obstacles, but motions proceed perpendicular to the axis if the tube is blocked. For a chain made from N monomers of size a, the coefficient of the curvilinear diffusion, along the tube is... 

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