Question

Problem 1. Consider a polymer molecule made up of N segments (monomers) of length l. We would like to build a 1D model to show how a single polymer molecule responds to forcef applied at its two ends. Many laboratories can now perform these experiments on single biopolymers such as DNA or proteins, or svnthetic polymers such as polyethyleneglycol (PEG. The polymer molecule reaches it length L (end-to-end distance) through a series of steps of length I taken in either positive or negative direction. Then each micro-state can be represented by a series of such steps, e.g. for L-3, two possible configurations are: When a molecule is stressed, each segment can align along or against applied force (since it is a 1D polymer, no other angles are allowed). Then the energy of a segment E - (force)(segment projection in the direction of force) can be represented by ε the force (i.e. having projected segment lengths -l or +l, respectively; ) fl and ε+-ザ1 for segments oriented anti-parallel or parallel with Find dependence of InW on the number of anti-parallel and parallel segments n_ and n+. Sketch (or plot using software of your choice) T versus U. Allow U to be both positive and a. b. Express Tfor the system of N segments having total energy U under applied force f. c. negative. Note that the overall length now has a direction (against or along applied force) and can be between -L and L. Comment on vour observations. d. Express U(T, N,jf) e. At fixed temperature, find the total polymer length L (defined as Las a function off.