Philosophy (and Reality) of Persistence

In this course we consider three types of random chain structures,

1) Unfolded or denatured proteins
2) Random synthetic polymers
3) Ceramic fractal aggregates

Unfolded proteins and synthetic polymers display persistence while ceramic aggregates do not. 

Generally persistence is defined loosely as a rod-like substructure that can be though to be the building block of chain structure.  It could be thought that a ceramic aggregate would have the same claim to persistence as a polymer chain.  The reason a ceramic aggregate does not display persistence is that persistence is a statistical projection of all linear bond vectors in a polymer chain on a given bond vector.  For a synthetic polymer only the short-range chain subunits contribute to this projection since long-range projections occur at random directions.  Further, the end-to-end bonding scheme for polymers and fixed bond angles enhance the likelihood that at a short range there will be some type of persistence.  For a fractal aggregate persistence doesn't exist since there is no preferred direction except for that driven by excluded volume (coordination number z is infinite).  Protein chains also display persistence of subunit though the persistence subunits, helical coils and beta sheet secondary structures, are much larger than in synthetic polymers.