The simplest model of a polymer involves a sequence of bonds offixed length λ, where each bond can make any angle with theprevious bond. This is called the freely-jointed chain model. Herewill will study it in 3D. We start at the origin. Then we choose anangle θ randomly between 0 and 2π. We make a step of length λ at anangle of θ top the +x direction. We then repeat, making N steps intotal. We can measure the size of the polymer by finding the endto-end-vector R and squaring it. We then take the square root ofthis to get the root-mean-square size. We will set λ = 1 Note thatthis model is “off-lattice\" or continuum, we are not using anylattice.
You should: (1) Plot an example walk of say 100 steps.
(2) Generate walks between say 10 and 10^6 steps and make alog-log plot of the root mean square size versus total number ofsteps. You may need to average over several walks for each lengthto get good data.
