A synthetic elastomer chain is modelled as a freely jointed chain of bonds

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch The size and shape of a polymer chain

Problem

A synthetic elastomer chain is modelled as a freely jointed chain of n=3600n = 3600 bonds, each of length l=0.15 nml = 0.15\,\mathrm{nm}, with no correlation between the directions of successive bonds. ((a)) Calculate the root-mean-square end-to-end distance ⟨R2⟩1/2\langle R^2\rangle^{1/2}. ((b)) Calculate the most probable value of ∣R∣|\mathbf R| for the same chain, using the Gaussian chain distribution.

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