Question

Polymer Chemistry:

Problem 2. Polystyrene chains dissolved in cyclohexane at 35°C (theta conditions) can be separated by ultrafiltration according to molecular weight. The ultrafiltration process employs pressure-driven flow of a solution through a porous membrane to separate solutes by their molecular size. Molecules larger than the pore size are retained upstream of the membrane while smaller molecules pass through. In this exercise, the root mean square end-end- distance will be considered to provide an appropriate measure of molecular size. The solution of interest contains polystyrene molecules of molecular weights 100,000 and 1,000,000 g/mol. The bond length of a polystyrene repeat unit is 3A, while the repeat unit molecular weight and characteristic ratio for this polymer are 104 g/mol and 10.8, respectively. What pore size might be selected to separate efficiently the two molecular weight polymers?

Answer 1

the the characteristic As ratio c is defined as care? e 2x e where C is the characters ti ratio of polymer, e is the length of the monomer whit X is the number of monomer unitin the chain on the degree of polymerization, re2 is the root mean square end-end distance so we have given two polyetyrene moleculs of molecular weights 1oo, ooo and 1000,000 g/mal Let us consider these polystyrene molecule as PA and PB so MpA = 100,000 g/mae mpo = 10000009 o me to calculate the degree of polymerization XpA and XPB XPA = MPA SE repeat unit molecular weight unit loo, ooo s 962 104 33

Similarly XPB = MPB 9 6 15 unit 104 Now rf² and SF2B can easily molecule Calculated for these polystyrene 2003 - Т2 eA ez xXPA so SF2A = cхe?XXPA - 10.8 (3) ² x 962 A02 c. as bond length of a polystyrene repeat unit is 3 A and characterstic ratio of polymes gimen 10-8 ) 8F2PA = 93506.4 A? similarly cxl 2x XPB 8f2 PB bro - 10.8 x (3)2 x 9615 A'? ta = 9 34 578 AO? for instance rfa PB = 34 578 AZ

rFPB U 934578 Ao - 966.74 A on 0.097 um so the pore size 0.097 um can not bass should be at so that larger through least molecules