Crankshaft model

FIG. 13.31 Crankshaft models of ratability of main chain according to (a) the Schatzki model with rotation around the first and seventh bond (b) the Boyer model with rotation around the first and fifth bond (c) the Wunderlich helix model with rotation around the first and sixth bond. From Haward (1973). Courtesy Chapmann Hall. 

The crankshaft model treats the molecule as a collection of mobile segments that have some degree of free movement. This is a very simplistic approach, yet very useful for explaining behavior (Fig. 2). As the free volume of the chain segment increases, its ability to move in various directions also increases. This increased mobility in either side chains or small groups of adjacent backbone atoms results in a greater compliance (lower modulus) of the molecule. These movements have been studied, and Heijboer classified p and y transitions by their type of motions. The specific temperature and frequency of this softening help drive the end use of the material. 

Fig. 1 Free volume, v, in polymers (A) the relationship of free volume to transitions, and (B) a schematic example of free volume and the crankshaft model. Below the Tg in (A) various paths with different free volumes exist depending on heat history and processing of the polymer, where the path with the least free volume is the most relaxed. (B) shows the various motions of a polymer chain. Unless enough free volume exists, the motions cannot occur. (From Menard K. Dynamic Mechanical Analysis A Practical Introduction, CRC Press Boca Raton, 1999).

Other cooperative transition models, crankshaft models being an example, have been suggested. These, too, can give rise to diffusion of conformational states, and hence to functional forms similar to eq. 3.6 and especially the asymptotic behavior of eq. 3.8. Monnerie will discuss these models elsewhere in this volume. ... 

Following the above conclusion it is clear that the rather bizarre spectra of these polymers derive from the special features of 1,2-enchainment. Examination of molecular models reveals that runs of 1,2-enchained segments are considerably more restricted in their degrees of motional freedom than are runs of 1,4- enchained segments. The restriction arises partly from the absence of a "crankshaft" mode with 1,2-enchainment and partly from the steric interference of substituents on adjacent phenylene rings. 

A. Jones I don t feel the multiple internal rotations model is applicable for side chains any longer than or k carbons. As soon as it is longer than carbons, a crankshaft type of motion dominates Instead of multiple internal rotations. The viewpoint probably reflects some bias on my part. 

I. C. P. Smith, NRG - Ontario When you are testing those models, crankshafts, cut off and so on, there was a paucity of data on frequency dependence. Have you tried to fit the various models to say three magnetic fields ... 

On a lattice, so-called crankshaft moves are trivial implementations of concerted rotations [77]. They have been generalized to the off-lattice case [78] for a simplified protein model. For concerted rotation algorithms that allow conformational changes in the entire stretch, a discrete space of solutions arises when the number of constraints is exactly matched to the available degrees of freedom. The much-cited work by Go and Scheraga [79] formulates the loop-closure problem as a set of algebraic equations for six unknowns reducible... 

The motion responsible for the relaxation is a rotation about the two co-linear bonds 1 and 7 such that the carbon atoms between bonds 1 and 7 move in the manner of a crankshaft. The co-linearity of the two terminal bonds is achievable if there are four intervening carbon atoms on the assumption of tetrahedral valence angles and a rotational isomeric state model. Support is to be found for the crankshaft mechanism in the fact that the activation energy estimated for the model, 54 kJ/mol, is close to the experimental results, 50-63 kJ/mol, and in the fact that the predicted free volume of activation, about four times the molar volume of a CH2 unit, is also in good agreement with experimental estimates based on pressure studies. 

Fig. 16. Moves used to equilibrate coil configurations for the self-avoiding walk model of polymer chains on the simple cubic lattice (upper party end rotations, kinkjump motions and crankshaft rotations f 107]. From time to time these local moves alternate with a move (lower pan) where one attempts to replace an A-chain by a B-chain in an identical coil configuration, or vice versa. In the transition probability of this move, the chemical potential difference Ap as well as the energy change SjF enter. From Binder [2S8]...

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