Topological knot model

Upon the application of stress to the local topological knot, the polymer chain could either break (which is not thought too likely under our conditions of squeezing) or slide (as in the Doi-Edwards slip-link models. In addition, we propose as a possibility that the knot could stretch into a helical-like entity which could be followed by chain slippage. Hiis latter proposal could easily lead to an increase in the number of associative restraints. 

As a first step in constructing a topological model of the electromagnetic field, let us consider the set of electromagnetic knots defined by pairs of dual scalars (<)>, 0). If we try a theory based on these two scalars, the most natural election for the action integral is... 

As was shown in Section II, the magnetic and the electric helicities of any radiation electromagnetic field are equal. Moreover, in the case of the topological model, the helicities of the knots verily... 

Jean-Pierre Sauvage is a CNRS director of research and is located at the Universite Louis Pasteur in Strasbourg, France. His current research interests include the development of models of the photosynthetic reaction centre using transition metals and porphyrins [5], topology (synthetic catenanes and knots) [6], and molecular machines [7]. 

Chemical catenanes are modeled by topological links. A topological link is a finite union of mutually disjoint knots (including the unknot). A knot is therefore the special case of a link with only one component. Links are nontrivial if and only if they cannot be embedded in the plane without crossings. All the links referred to in this chapter are nontrivial, but the components are usually unknots. 

Theoretical understanding of DNA supercoiling. Quantitative explanation and prediction of a variety of DNA topological characteristics, most notably the data on the equilibrium knotting probability and on the equilibrium distribution of ccDNA over topoisomers, demonstrated a remarkable success of the DNA elastic-rod model. The model also proved to be extremely successful in theoretical treatment of the phenomenon of DNA super-coiling. 

To make this review self-contained and to provide a foundatitMi for further discussion, we have included the experimental methods and theoretical models of mechanical degradation for linear chains in the second and third sections, respectively. From the fourth to seventh sections, the mechanochemistry of cyclic polymers, graft polymers, star-shaped polymers (star-shaped polymers), dendrimers, and hyperbranched polymers is summarized. In the eighth section, we survey the mechanochemistry of supramolecular aggregates and knotted polymers, where the topology constraints are temporal. We hope our overview can serve as a guideline for the future work in the field of polymer mechanochemistry. 

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