Question

Find the mean-square radius of a polyethylene chain of molecular weight 2800 g/mol, if the C−C bond length is 0.154 nm.

Answer 1

For polyethylene, each repeat unit has two carbons and four hydrogens. Thus

mass =  2(AC) + 4(AH) =   (2)(12.01 g/mol) + (4)(1.008 g/mol) = 28.05 g/mol

DP= Mn / m = (2800 g/mol) / 28.05 g/mol = 99.82 = 100

which is the number of repeat units along an average chain. Since there are two carbon atoms per repeat unit, there are two C—C chain bonds per repeat unit, which means that the total number of chain bonds in the molecule, N, is just (2)(100) = 200 bonds

L = 25.07nm

It is now possible to calculate the average chain end-to-end distance, r,

mean square radius = 0.8009 * 0.8009 /6 = 0.1069