Molecular Chain (MIT, Princeton, Colorado)

Consider a one-dimensional chain consisting of N molecules which exist in two configurations, α, β, with corresponding energies  and lengths α and β. The chain is focus to a tensile force f.

a) Write down the partition function Z_N for the system.

b) Compute the average length (L) as a function f of and the temperature T.

c) Assume that  anda>b.  Evaluate the average length (L) in the absence of the tensile force f = 0 as a function of temperature.  What are the high-temperature and low-temperature limits and what is the characteristic temperature at which the changeover between the two limits takes place?

d) Estimate the linear response function

Produce a universal argument to show that X>0.