The presentation of concepts of macromolecules (often called “polymers”) appeared in 1925 by the Nob — Organic Chemistry Chemistry Question

The presentation of concepts of macromolecules (often called “polymers”) appeared in 1925 by the Nobel Prize chemist, Dr. H. Staudinger (Germany). He opened a fascinating world of new organic materials presently utilized as plastics, fibers, rubbers, etc.
Macromolecules are roughly classified into two categories: vinyl and non-vinyl polymers. Unlike the former, which are usually prepared from corresponding vinyl monomers (= α-olefins) by the chain polymerization processes in the presence of initiators or catalysts, the latter are usually obtained by the step polymerizations of (combination of) bifunctional monomers, such as H₂N^-R^-COOH (to give polyamides), HO^-R^-COOH (polyesters), H₂N^-R^-NH₂ + HOOC^-R’-COOH (polyamides), HO^-R^-OH + HOOC^-R’-COOH (polyesters), etc. As easily understood from the last two instances of the step polymerization between the bifunctional monomers, the stoichiometric balance of component monomers is one of the most important factors in obtaining high molecular mass polymers.
When the elementary processes of step polymerization are reversible, such as esterification equilibria, it is also a matter of importance to shift the equilibria rightward. Here, we would like to discuss the relation between the equilibrium state and the length of polymers derived from the stoichiometric mixture of bifunctional monomers. Equation 1 is a typical example of an esterification reaction where the equilibrium constant K is relatively small, such as K = 4.20 at 78 oC (boiling temperature of ethanol).

K
CH₃COOH + HOCH₂CH₃ → CH₃CO^-OCH₂CH₃ + H₂O (1)
(acetic acid) (ethanol) (ester: ethyl acetate)

By replace of the monofunctional molecules in equation 1 with a dicarboxylic acid and a diol, the corresponding polycondensation reaction may produce linear chain polyesters. Although the polycondensation is composed of multi-step equilibria, the representation is often simplified as equation 2 supposing the same equilibrium constant in each step.

n HOOC^-R^1-COOH + n HO^-R^2-OH → HO^-[COR₁CO^-OR₂O]n^-H + (2n -1) H₂O (2)
(dicarboxylic acid) (diol) (polyester)

The length of polymer chain is very important in respect to material chemistry. The long chain polymers may provide enough mechanical strength to fabricate textiles and thin films. In turn, the shorter ones are useful as adhesives, coatings, detergents, etc. In order to discuss on the polymer length, it is easier to think about the degree of polymerization (abb. X) rather than the molecular weight of which calculation is dependent on the structures of R₁ and R₂. For instance in eq. 2, X is equal to 1 for the dicarboxylic acid or the diol, whereas it is 2n for the polyester (note that the structure in the brackets is already “dimer”). Because a polymer is a mixture of long, middle and short chain molecules, X is the averaged number. The HO^- and -H groups attached out of the brackets in eq. 2 are known as the end groups, and the -COR₁CO^-OR₂O^- group is known as the repeating unit of which the structure is already a dimeric conjunction as described. Therefore, the unit molecular mass, Mu, in the case of eq. 2 is defined as follows ;

Mu = molar mass of the repeating unit / 2 (3)

When the average molecular mass of a polymer is represented by M, the relationship among X, M and Mu is given as follows ;

X = (M - mass of end groups) / Mu ≈ M / Mu (4)

As understood from the calculation in 23.1 when the equilibrium constant of the designated reaction is relatively small, considerable amounts of starting materials remain unreacted even at the equilibrium state. The quantity of product can be determined by the analysis of the consumption of functional groups. Before discussion, we define “the degree (extent) of reaction“ p as follows ;

degree of reaction = p = 1 - (amount of unreacted functional groups / amount of initial functional groups) (≤ 1) (5)

For instance, in eq. 1, starting from each 1.00 mol of bifunctional monomers and reaching p = 0.80 after being reacted for a certain period, then 0.80 mol of the ester is obtained. In organic syntheses, p × 100 is equal to the yield (%). If one can achieve p = 0.80, it is generally satisfactorily high yield. However, p = 0.80 is not good enough in the step polymerization syntheses. As represented below, p = 0.80 means concomitant success 4 out of 5-times ―― with one failure, meanwhile. (●-● and o-o represent the dicarboxylic acid and diol residues, respectively.). X is ended with 5.0, in this case.

●-● – o-o – ●-● – o-o – ●-●…X…× or o-o – ●-● – o-o – ●-● – o-o…X …×
↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
OK OK OK OK fail OK OK OK OK fail

Consequently, p → 1 should be realized to prepare the polymers with large X. Dr. Wallace H. Carothers (USA) had studied the relationship between X and p, and presented eq. 6 in conclusion.

X = 1/(1– p) ［Carothers eq.］ (6)

Although even amateurs can easily prepare vinyl polymers, such as polystyrene, with M ≥ 10^6 (corresponding to X ≥ 10^4) by the chain polymerization of α-olefin monomers, exquisitely fabricated commercial polycondensation polymers, such as nylon^-6,6 or PET [=poly(ethylene terephthalate), or poly(oxyethyleneoxyterephthaloyl)], carry M of merely 1~8×10^4. Typically, M of ordinary PET is 4.000×10^4, corresponding to X = 416.3 (cf. Mu = 96.09), where the p value of the polycondensation between terephthalic acid and 1,2-ethanediol should exceed 0.9976 . It is understood that much effort is necessary for the production of step polymerization polymers with high M or X.

As estimated in 23.1, elaborative work is necessary to accomplish the reaction condition of p → 1 since K is relatively small in the case of esterification polycondensation. The by-product removal in accordance with the reaction progress is one of the schemes to realize p → 1. For easier consideration, let us simplify equation 2 into equation 7; starting from each (exactly) 1 mol of -COOH (of dicarboxylic acid) and -OH (of diol), p mol of ester linkage is formed at the equilibrium, whereas each (1 – p )mol of -COOH and -OH groups remain unreacted. To shift the equilibrium rightward, the quantity of water should be diminished from p mol to a negligibly small amount, nw mol.

K
-COOH of dicarboxylic acid + -OH of diol ⇌ -CO^-O^- of polyester + water (7)
Equilibrium: 1 – p 1 – p p p (→ nw)