Question

what is the average end to end distance of a random coil polymer of 106 monomers (in units of segment length)?​

Answer 1

Since

a polymer chain isn't a regular object and because it's subject to dynamic structural equilibrium that involves stirring and further,

• because polymers display polydispersity in size, it's necessary to consider a statistical measure of chain size.
• For an arbitrary chain, the mean size is 0, = 0 since it's inversely likely to have positive and negative diversions from a chain path that leads back to the origin.
• also, the smallest order moment with a non-zero value reflecting the size of a polymer chain is the alternate order moment about the mean chain position or the compass of rotation.
• This is identical to the standard divagation of the mean for the chain length distribution.
• Where the totality is over all parts of a chain structure.
• An affiliated size is the compass of rotation, Rg, which is the moment of indolence for a structure.
• The moment of indolence is the distance from the centre of mass where all the mass could be placed to produce the same instigation on the gyration of a structure about the centre of mass. For an arbitrary direct chain structure( df = 2)

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