For a Gaussian polymer, the vector rnm = rn ? rm obeys t
Question and Solution
For a Gaussian polymer, the vector rnm = rn ? rm obeys the following Gaussian distribution (see eq. (3.29)) ?(rnm) = 2?|
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For a Gaussian polymer, the vector rnm = rn ? rm obeys the following Gaussian distribution (see eq. (3.29)) ?(rnm) = 2?|n ?3 m|b23/2 exp ?2|n3?r 2 nm m|b2 (8.127) Answer the following questions (a) Show that S(k) is given by S(k) = 1 N 0N dn 0N dm exp ?|n ? m6|k 2b2 (8.128) (b) Show that for large |k|, S(k) has the following asymptotic form S(k) = 12 k 2b2 (8.129) (c) Show that the pair correlation function g(r) for the polymer segments behaves as g(r) ? 1/r for small r.
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