Consider a polymer having N total mers constrained to lie in a plane and having the mers making 90 angles with each other, with the mers lying at 45 to the horizontal axis, as illustrated in Figure A3.1. Let the total x-projected length of the polymer equal L and the x-projected length of each mer equal a. If the number of mers pointed to the right exceeds that directed to the left by 2n then

Figure A3.1: Schematic two dimensional polymer illustrating horizontal component of end-to-end length L, as compared total length of polymer.

Thus, the number of mers pointed to the right is given by

while the number directed to the left is given by

It is now possible to set down an expression for the entropy of the polymer of x-projected length L as follows