Unformatted text preview: to two dimensions, and the rods are connected by springs. If the angle between rod l and rod l + 1 is Θ l then the energy of this joint is κ Θ 2 l . (assume low temperatures such that κ/k B T ² 1). Show that long enough polymers behave as a random walks. To this end: a) Write down the probability of having a particular set of angles Θ 1 ,..., Θ N at temperature T (use canonical ensemble, i.e., Boltzmann distribution) b) Put one end of the polymer at the origin. Find the coordinates ( x N ,y N ) of the other end as a function of the angles Θ 1 ,..., Θ N . (Hint: It helps to formulate the problem in the complex plane!) c) Find the thermal average h x 2 N + y 2 N i . (Assume a suﬃciently long polymer such that Nk B T ² κ. ) d) The result has the same form as expected for an ideal random walk, but the segment length a has to be replaced by by an eﬀective length ˜ a . What is ˜ a ?...
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 Spring '11
 ThomasVojta
 Physics, Chemistry, Work, Statistical Mechanics, Fundamental physics concepts, Condensed matter physics

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