( 5 points) Calculate how many % of the volume of the coil used to describe one single polyethylene (PE) chain is filled with that polymer chain and the percentage not occupied by that chain.
a. Radius of gyration (squareroot of the expected value of the radius of gyration to be scientifically accurate) V=20nm, measured at 140\deg C in 1,2,4 trichlorobenzene
b. Molar mass M (of that single chain) 100000(g)/(m)ol
c. Conditions are very close to \Theta -conditions
Hint: the percentage is relatively small
(2 points) What is the content of the remaining volume inside this sphere of the remaining coil?
(3 points) Assuming \Theta -conditions, what does this mean for the situation in bulk state (i.e. in a pure PE polymer melt at 140\deg C )