Knots in Fibers and Molecules

The phosphate fiber, DNA, has rekindled interest in the knotting of strings and ropes. During the time of sailing vessels much time and attention was devoted 

John W. Alexander was one of the first to develop polynomials capable of describing knots, but these polynomials can become very involved. If two knots have the same polynomial, they are the same even though the knots may at casual glance appear to be very different. More recently Jones developed entirely new polynomials that can be used to describe even more complicated knots based on links and crossings. Whether or not these types of treatment will have any bearing on understanding long-chain polyphosphate behavior is unknown, but there is little doubt that polyphosphate chains can become very twisted and knotted. Perhaps the simpler polynomials will be useful in future research as more is understood about why some of these systems cannot be crystallized. 

The problems encountered in attempting to crystallize some polyphosphate melts may well be a knotting of the strands of polyphosphate molecules. It has been adequately demonstrated that the physical behavior of strands of long-chain polyphosphates is highly dependent upon the ionic atmosphere surrounding these molecule-ions. 

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