Polylactic acid (PLA) is an important biocompatible poly-mer. It is produced on a rather large scale — Organic Chemistry Chemistry Question
Polylactic Acid
Polylactic acid (PLA) is an important biocompatible poly-mer. It is produced on a rather large scale in The Netherlands. The building block is (+)-lactic acid which is obtained from sugar by fermentation. An attractive feature of PLA is its biodegrada-bility. PLA is used in medical applications, e.g. medical implants and controlled drug delivery. High-molecular weight PLA can be obtained from either lactic acid or its cyclic dilactone A.
It is assumed that during the polymerisation of lactic acid the reaction volume does not change and that the equilibrium constant K for the ester formation equals 4. The progress of polymerization is p. The average polymer chain length P = 1/(1 – p). The polymerization starts with U mol of lactic acid.
Give the equation for the formation of the tetramer of PLA starting from lactic acid.
Give the equation for the formation of the tetramer of PLA starting from cyclic dilactone A.
Calculate the maximal attainable average number of monomer units per chain when no water is removed.
Model Answer
The aim here is working with reactive groups.
[Ester][Water] / [-OH][-COOH] = (pU / (1-p)U) * (pU / (1-p)U) = p^2 / (1-p)^2 = K = 4
=> p / (1-p) = 2 ⇒ p = 2/3
P = 1 / (1-p) = 3
Calculate how much water has to be removed in the production of PLA from lactic acid to obtain an average number of monomer units per chain of 100, starting from 10 moles of lactic acid.
Model Answer
First the remaining amount of water at a chain length of 100 units is calculated:
[Ester][Water] / [-OH][-COOH] = (p^2 W) / ((1-p)^2 U) = 4
U = 10 and P = 100 ⇒ p = 0.99
(0.99^2 W) / (0.01^2 * 10) = 4 ⇒ W = 0.0040404 mol
Water formed: pU = 0.99 × 10 = 9.9 mol
Water removed: 9.9 – 0.0040404 = 9.896 mol = 178 g of H2O