Suppose that we treated the polymer as an "ideal chain." If one ?xes the ?rst monomer of the polymer chain, how many con?gurations would be accessible?

What is the con?gurational entropy for an ideal chain with n =4monomers?

Now suppose that we consider a SAW model for the same polymer with the ?rst monomer bonded to the wall.

A. Enumerate all con?gurations that are accessible to the polymer. How many such con?gurations are there and what is the probability of each? What is the entropy of the polymer?

B. Let Lx be the distance (transverse) from the wall of the last monomer. Determine the probability, px(Lx), that the polymer adopts a conformation with Lx =0, 1, 2, 3, 4, or 5. Calculate the ensemble average for Lx, i.e., 

C. Suppose that, by manipulating the experimental conditions as in, e.g., an AFM experiment, the macrostate now enforces Lx = 1. What is the entropy of the polymer? If one considers the con?gurations identi?ed in part 2(b)iiA, what is the probability for each of these con?gurations?

D. Suppose instead that, by manipulating the experimental conditions, the macrostate now enforces Lx = 2. What is the entropy of the polymer? If one considers the con?gurations identi?ed in part 2(b)iiA, what is the probability for each of these con?gurations?