A polymer resist being stretched or compressed by restorring force f. The sign convention of f is such that positive f leads to stretching or increasing R. This force appears in the expression for the free energy of anideal polymer. dG =-SdT - fdR Where R is the end to end distance. In this problem you will compute this force as a function of R and temp T
A) derive the relationship (df/dT)R=(dS/dR)T (they are partial derivatives -maxwell equations with the R and T constant
B) for an ideal polymer. S(R)=const-R^2 /(2Na^2)+2ln(R/a) use this equation to evaluate (dS/dR) T constant
C) using your results from parts a and b find f as a function of T and R. You will have to integrate (df/dT)Rt in temperature. From 0 to T. Assume that f(T=0)=0
D) which term in the nswer for part c resists compression? Which term resists stretching?
E) sketch a graph of f(R) at three different temperatures. Does it require more or less force to stretch the polymer as the temp increases?