Polymer Molecular Weight Exercise Analysis

This exercise involves calculating the number average and weight average molecular weights, as well as the polydispersity index (PDI) for a sample of polystyrene composed of fractions with different molecular weights. The analysis includes determining the number of moles in each fraction, calculating the average molecular weights before and after adding a styrene oligomer, and evaluating the impact on the PDI.

• Polymer
• Molecular Weight
• Polystyrene
• Polydispersity Index
• Fraction Analysis

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1. Polymer Molecular Weight Exercise 1

2. Avarege molecular weights Equations for number average and weight average molecular weights as well as polydispersity index are defined as follows: = w n n M n i i = i M M M n = w PD i i 2 i wM nM nM n i w i i = = M w i i i where Mi ni wi molecular weight of molecules i number of molecules with molecular weight i mass of the molecules with molecular weight i

3. 2 A sample of polystyrene is composed of a series of fractions of different sized molecules. a) Calculate the number average and weight average molecular weights of this sample as well as the PDI. b) How would adding styrene oligomer change the average molecular weights? Added amount is 5wt.% of polymer mass and M=1000g/mol. Table 1. PS fractions. Fraction weight fraction Molecular weight [g/mol] A 0.130 11000 B 0.300 14000 C 0.400 17000 D 0.170 21000

4. 2a) Determine the number of moles in each fraction. Assume that the sample is 10 g in the beginning. Number of moles of the fraction is ni= wi/ Mi. fractio wi [g] 1.30 3.00 4.00 1.70 Mi ni n A B C D [g/mol] 11000 14000 17000 21000 [mmol] 0.118 0.214 0.235 0.0810 wi= 10.0 g ni= 0.648 mmol

5. 2a) Number average molecular weight: nM n w n 10.0 g i i i = = = = g 15400 M n mol 0.648 mmol i i Weight average molecular weight: (1.3 11000 3.0 14000 4.0 17000 1.7 21000) + + + wM g g i w i = = = g 16000 mol M w mol 10.0 g i Polydispersity index: M PD M g 16000 15400 = = = 1.04 w mol g mol n

6. 2b) When 5.0 wt-% of styrene oligomer (fraction E) is added, the total mass and number of moles increase as follow: fraction wi [g] 1.30 3.00 4.00 1.70 0.50 Mi ni [g/mol] 11000 14000 17000 21000 1000 [mmol] 0.118 0.214 0.235 0.0810 0.50 A B C D E wi= 10.5 g ni= 1.10 mmol

7. 2b) number average molecular weight nM n 10.5 1.10 g i i = = = g 9150 M n mol mmol i weight average molecular weight (1.3 11000 3.0 14000 4.0 17000 1.7 21000 0.5 1000) + + + + wM g g i w i = = = g 15300 mol M w mol 10.5 g i Polydispersity index g 15300 9150 M M = = 1,67 w mol g mol PD n