A 3-kg batch of an experimental bearing material for a hip prosthesis was synthe

Question

A 3-kg batch of an experimental bearing material for a hip prosthesis was synthesized, consisting of an alternating copolymer of ethylene (mer = C_2H_4) and methyl methacrylate (mcr = C_5H_8O_2). Benzoyl peroxide [(C_6H_5CO)_2O_2] was used as the initiator. The yield strength of the material was measured to be 55 MPa and the failure strength was measured to be 78 MPa. (a) How many grams of benzoyl peroxide would be required to achieve the desired yield (3 kg) of the experimental copolymer if the average degree of polymerization is 800? Assume there are two benzoyl peroxide molecules per copolymer molecule. (b) Determine the average extended length of the copolymer.

Explanation / Answer

(a) Average degree of polymerization = 800. Therefore, each chain of the alternating copolymer has 400 ethylene units and 400 methyl methacrylate units. It is given that each copolymer molecule has two benzoyl peroxide molecules (should be moieties instead of molecules as benzoyl peroxide dissociates into two radicals one present in each terminal of the polymer chain).

The average molecular weight of the copolymer = (400 x M.wt. of ethylene) + (400 x M.wt. of methyl methacrylate) + Molecular weight of benzoyl peroxide = (400 x 28) + (400 x 100) + 242 = 51,442 g/mol

If 51,442 g of copolymer contains 242 g of benzoyl peroxide, 3000 g (3 kg) of the copolymer needs (3000x242)/51,442 = 14.11 g Benzoyl peroxide

(b) This is addition polymerization, wherein the C=C double bonds become C-C single bonds, forming new C-C single bonds with adjacent monomer molecules. So, the extended length of the copolymer chain can be calculated if we know the number of C-C single bonds present along the chain. For example, if an addition polymer forms from 8 units of ethylene alone, there will be (8x2) minus 1 i.e., 15 C-C single bonds along the chain. Thus in this question, there will be (800x2) minus 1 = 1599 C-C single bonds along the chain. A C-C single bond has a length of 154 pm. Therefore, the average extended chain length of the copolymer = 1599 x 154 pm = 246246 pm = 0.25 microns.

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