This preview shows page 1. Sign up to view the full content.
Unformatted text preview: to two dimensions, and the rods are connected by springs. If the angle between rod l and rod l + 1 is l then the energy of this joint is 2 l . (assume low temperatures such that /k B T 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 1 ,..., 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 1 ,..., 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 suciently long polymer such that Nk B T . ) 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 eective length a . What is a ?...
View Full
Document
 Spring '11
 ThomasVojta
 Physics, Work

Click to edit the document details